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Sample records for algebraic turbulence model

  1. One-Equation Algebraic Model Of Turbulence

    NASA Technical Reports Server (NTRS)

    Baldwin, B. S.; Barth, T. J.

    1993-01-01

    One-equation model of turbulence based on standard equations of k-epsilon model of turbulence, where k is turbulent energy and e is rate of dissipation of k. Derivation of one-equation model motivated partly by inaccuracies of flows computed by some Navier-Stokes-equations-solving algorithms incorporating algebraic models of turbulence. Satisfies need to avoid having to determine algebraic length scales.

  2. On explicit algebraic stress models for complex turbulent flows

    NASA Technical Reports Server (NTRS)

    Gatski, T. B.; Speziale, C. G.

    1992-01-01

    Explicit algebraic stress models that are valid for three-dimensional turbulent flows in noninertial frames are systematically derived from a hierarchy of second-order closure models. This represents a generalization of the model derived by Pope who based his analysis on the Launder, Reece, and Rodi model restricted to two-dimensional turbulent flows in an inertial frame. The relationship between the new models and traditional algebraic stress models -- as well as anistropic eddy visosity models -- is theoretically established. The need for regularization is demonstrated in an effort to explain why traditional algebraic stress models have failed in complex flows. It is also shown that these explicit algebraic stress models can shed new light on what second-order closure models predict for the equilibrium states of homogeneous turbulent flows and can serve as a useful alternative in practical computations.

  3. An algebraic turbulence model for turbomachinery

    NASA Astrophysics Data System (ADS)

    Chima, Rodrick V.

    This paper presents a description and verification of RVC3D (rotor viscous code 3-D) which provides a Euler or Navier-Stokes analysis for steady three dimensional flows in turbomachinery. A motivation for this analysis is the calculation of turbine endwall heat transfer. Features of the turbulence model code include thin-layer formulation, Baldwin-Lomax or Cebeci-Smith turbulence models, node-centered finite difference formulation, and explicit four-stage Runge-Kutta time marching scheme. Results for flat plate, annular turbine cascade, turbine endwall heat transfer, and supersonic compressor blade test cases are presented.

  4. Algebraic turbulence modeling for unstructured and adaptive meshes

    NASA Technical Reports Server (NTRS)

    Mavriplis, Dimitri J.

    1990-01-01

    An algebraic turbulence model based on the Baldwin-Lomax model, has been implemented for use on unstructured grids. The implementation is based on the use of local background structured turbulence meshes. At each time-step, flow variables are interpolated from the unstructured mesh onto the background structured meshes, the turbulence model is executed on these meshes, and the resulting eddy viscosity values are interpolated back to the unstructured mesh. Modifications to the algebraic model were required to enable the treatment of more complicated flows, such as confluent boundary layers and wakes. The model is used in conjuction with an efficient unstructured multigrid finite-element Navier-Stokes solver in order to compute compressible turbulent flows on fully unstructured meshes. Solutions about single and multiple element airfoils are obtained and compared with experimental data.

  5. Algebraic Turbulence-Chemistry Interaction Model

    NASA Technical Reports Server (NTRS)

    Norris, Andrew T.

    2012-01-01

    The results of a series of Perfectly Stirred Reactor (PSR) and Partially Stirred Reactor (PaSR) simulations are compared to each other over a wide range of operating conditions. It is found that the PaSR results can be simulated by a PSR solution with just an adjusted chemical reaction rate. A simple expression has been developed that gives the required change in reaction rate for a PSR solution to simulate the PaSR results. This expression is the basis of a simple turbulence-chemistry interaction model. The interaction model that has been developed is intended for use with simple one-step global reaction mechanisms and for steady-state flow simulations. Due to the simplicity of the model there is very little additional computational cost in adding it to existing CFD codes.

  6. An algebraic turbulence model for three-dimensional viscous flows

    NASA Technical Reports Server (NTRS)

    Chima, R. V.; Giel, P. W.; Boyle, R. J.

    1993-01-01

    An algebraic turbulence model is proposed for use with three-dimensional Navier-Stokes analyses. It incorporates features of both the Baldwin-Lomax and Cebeci-Smith models. The Baldwin-Lomax model uses the maximum of a function f(y) to determine length and velocity scales. An analysis of the Baldwin-Lomax model shows that f(y) can have a spurious maximum close to the wall, causing numerical problems and non-physical results. The proposed model uses integral relations to determine delta(*) u(sub e) and delta used in the Cebeci-Smith mode. It eliminates a constant in the Baldwin-Lomax model and determines the two remaining constants by comparison to the Cebeci-Smith formulation. Pressure gradient effects, a new wake model, and the implementation of these features in a three-dimensional Navier-Stokes code are also described. Results are shown for a flat plate boundary layer, an annular turbine cascade, and endwall heat transfer in a linear turbine cascade. The heat transfer results agree well with experimental data which shows large variations in endwall Stanton number contours with Reynolds number.

  7. Computation of turbulent boundary layer flows with an algebraic stress turbulence model

    NASA Technical Reports Server (NTRS)

    Kim, Sang-Wook; Chen, Yen-Sen

    1986-01-01

    An algebraic stress turbulence model is presented, characterized by the following: (1) the eddy viscosity expression is derived from the Reynolds stress turbulence model; (2) the turbulent kinetic energy dissipation rate equation is improved by including a production range time scale; and (3) the diffusion coefficients for turbulence equations are adjusted so that the kinetic energy profile extends further into the free stream region found in most experimental data. The turbulent flow equations were solved using a finite element method. Examples include: fully developed channel flow, fully developed pipe flow, flat plate boundary layer flow, plane jet exhausting into a moving stream, circular jet exhausting into a moving stream, and wall jet flow. Computational results compare favorably with experimental data for most of the examples considered. Significantly improved results were obtained for the plane jet flow, the circular jet flow, and the wall jet flow; whereas the remainder are comparable to those obtained by finite difference methods using the standard kappa-epsilon turbulence model. The latter seems to be promising with further improvement of the expression for the eddy viscosity coefficient.

  8. Development of an algebraic turbulence model for analysis of propulsion flows

    NASA Technical Reports Server (NTRS)

    Georgiadis, N. J.; Drummond, J. E.; Leonard, B. P.

    1992-01-01

    A simple turbulence model that will be applicable to propulsion flows having both wall bounded and unbounded regions was developed and installed within the PARC Navier-Stokes code by linking two existing algebraic turbulence models. The first is the Modified Mixing Length (MML) model which is optimized for wall bounded flows. The second is the Thomas model, the standard algebraic turbulence model in PARC which has been used to calculate both bounded and unbounded turbulent flows but was optimized for the latter. This paper discusses both models and the method employed to link them into one model (referred to as the MMLT model). The PARC code with the MMLT model was applied to two dimensional turbulent flows over a flat plate and over a backward facing step to validate and optimize the model and to compare its predictions to those obtained with the three turbulence models already available in PARC.

  9. Performance of Renormalization Group Algebraic Turbulence Model on Boundary Layer Transition Simulation

    NASA Technical Reports Server (NTRS)

    Ahn, Kyung H.

    1994-01-01

    The RNG-based algebraic turbulence model, with a new method of solving the cubic equation and applying new length scales, is introduced. An analysis is made of the RNG length scale which was previously reported and the resulting eddy viscosity is compared with those from other algebraic turbulence models. Subsequently, a new length scale is introduced which actually uses the two previous RNG length scales in a systematic way to improve the model performance. The performance of the present RNG model is demonstrated by simulating the boundary layer flow over a flat plate and the flow over an airfoil.

  10. Algebraic turbulence models for the computation of two-dimensional high speed flows using unstructured grids

    NASA Technical Reports Server (NTRS)

    Rostand, Philippe

    1988-01-01

    The incorporation of algebraic turbulence models in a solver for the 2-D compressible Navier-Stokes equations using triangular grids is described. A practical way to use the Cebeci Smith model, and to modify it in separated regions is proposed. The ability of the model to predict high speed, perfect gas boundary layers is investigated from a numerical point of view.

  11. The addition of algebraic turbulence modeling to program LAURA

    NASA Technical Reports Server (NTRS)

    Cheatwood, F. Mcneil; Thompson, R. A.

    1993-01-01

    The Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA) is modified to allow the calculation of turbulent flows. This is accomplished using the Cebeci-Smith and Baldwin-Lomax eddy-viscosity models in conjunction with the thin-layer Navier-Stokes options of the program. Turbulent calculations can be performed for both perfect-gas and equilibrium flows. However, a requirement of the models is that the flow be attached. It is seen that for slender bodies, adequate resolution of the boundary-layer gradients may require more cells in the normal direction than a laminar solution, even when grid stretching is employed. Results for axisymmetric and three-dimensional flows are presented. Comparison with experimental data and other numerical results reveal generally good agreement, except in the regions of detached flow.

  12. Computation of turbulent rotating channel flow with an algebraic Reynolds stress model

    NASA Technical Reports Server (NTRS)

    Warfield, M. J.; Lakshminarayana, B.

    1986-01-01

    An Algebraic Reynolds Stress Model has been implemented to modify the Kolmogorov-Prandtl eddy viscosity relation to produce an anisotropic turbulence model. The eddy viscosity relation becomes a function of the local turbulent production to dissipation ratio and local turbulence/rotation parameters. The model is used to predict fully-developed rotating channel flow over a diverse range of rotation numbers. In addition, predictions are obtained for a developing channel flow with high rotation. The predictions are compared with the experimental data available. Good predictions are achieved for mean velocity and wall shear stress over most of the rotation speeds tested. There is some prediction breakdown at high rotation (rotation number greater than .10) where the effects of the rotation on turbulence become quite complex. At high rotation and low Reynolds number, the laminarization on the trailing side represents a complex effect of rotation which is difficult to predict with the described models.

  13. Elliptic-blending second-moment turbulence closure using an algebraic anisotropic dissipation rate tensor model

    NASA Astrophysics Data System (ADS)

    Shin, Jong-Keun; Seo, Jeong-Sik; Choi, Young-Don

    2009-06-01

    This study describes the amendment of an algebraic anisotropic dissipation rate model (ADRM) and its application to various turbulent flows to test the model's performance. Modeling anisotropies for the turbulence dissipation rate is considered by an analysis of the exact transport equation for the dissipation rate tensor. The second-moment closure, which is based on the explicit amended ADRM, is proposed and it is closely linked to the elliptic-blending model that is used for the prediction of Reynolds stresses. To develop and calibrate the present elliptic-blending second-moment closure that uses the amended ADRM, firstly, the distributions of both the mean velocity and Reynolds stress are solved for flows in a fully developed non-rotating channel and a straight square duct. And then, the fully developed turbulent flows in a rotating channel and a rotating straight square duct are predicted to test the ability of the explicit amended ADRM that is combined with the rotation effect. The prediction results are directly compared with the DNS and the large-eddy simulation (LES) to assess the performance of the new model predictions and to show their reasonable agreement with the DNS and LES data for all the flow fields that are analyzed for the present study. This paper is a modified version of the original article from the Proceedings of the 5th International Symposium on Turbulence and Shear Flow Phenomena held in Munich, Germany on 27-29 August 2007.

  14. Algebraic turbulence models for the computation of two-dimensional high-speed flows using unstructured grids

    NASA Technical Reports Server (NTRS)

    Rostand, Philippe

    1989-01-01

    The incorporation of algebraic turbulence models in a solver for the 2-D compressible Navier-Stokes equations using triangular grids is described. A practial way to use the Cebeci Smith model, and to modify it in separated regions is proposed. The ability of the model to predict high speed, perfect gas boundary layers is investigated from a numerical point of view.

  15. Study of Transitions in the Atmospheric Boundary Layer Using Explicit Algebraic Turbulence Models

    NASA Astrophysics Data System (ADS)

    Lazeroms, W. M. J.; Svensson, G.; Bazile, E.; Brethouwer, G.; Wallin, S.; Johansson, A. V.

    2016-08-01

    We test a recently developed engineering turbulence model, a so-called explicit algebraic Reynolds-stress (EARS) model, in the context of the atmospheric boundary layer. First of all, we consider a stable boundary layer used as the well-known first test case from the Global Energy and Water Cycle Experiment Atmospheric Boundary Layer Study (GABLS1). The model is shown to agree well with data from large-eddy simulations (LES), and this agreement is significantly better than for a standard operational scheme with a prognostic equation for turbulent kinetic energy. Furthermore, we apply the model to a case with a (idealized) diurnal cycle and make a qualitative comparison with a simpler first-order model. Some interesting features of the model are highlighted, pertaining to its stronger foundation on physical principles. In particular, the use of more prognostic equations in the model is shown to give a more realistic dynamical behaviour. This qualitative study is the first step towards a more detailed comparison, for which additional LES data are needed.

  16. A Comparison of Explicit Algebraic Turbulence Models and the Energy-Flux Budget (EFB) Closure in Gabls

    NASA Astrophysics Data System (ADS)

    Lazeroms, W. M.; Bazile, E.; Brethouwer, G.; Wallin, S.; Johansson, A. V.; Svensson, G.

    2014-12-01

    Turbulent flows with buoyancy effects occur in many situations, both in industry and in the atmosphere. It is challenging to correctly model such flows, especially in the case of stably stratified turbulence, where vertical motions are damped by buoyancy forces. For this purpose, we have derived a so-called explicit algebraic model for the Reynolds stresses and turbulent heat flux that gives accurate predictions in flows with buoyancy effects. Although inspired by turbulence models from engineering, the main aim of our work is to improve the parametrization of turbulence in the atmospheric boundary layer (ABL). Explicit algebraic turbulence models are a class of parametrizations that, on the one hand, are more advanced than standard eddy-diffusivity relations. On the other hand, they are signficantly easier to handle numerically than models that require the solution of the full flux-budget equations. To derive the algebraic model, we apply the assumption that transport terms of dimensionless fluxes can be neglected. Careful considerations of the algebra lead to a consistent formulation of the Reynolds stresses and turbulent heat flux, which is more general and robust than previous models of a similar kind. The model is shown to give good results compared to direct numerical simulations of engineering test cases, such as turbulent channel flow. Recent work has been aimed at testing the model in an atmospheric context. The first of these tests makes use of the GABLS1 case, in which a stable atmospheric boundary layer develops through a constant surface cooling rate. The model is able to give good predictions of this case compared to LES (see attached figure). Interestingly, the results are very close to the outcome of the recently developed Energy-Flux-Budget (EFB) closure by Zilitinkevich et al. (2013). A detailed discussion of the similarities and differences between these models will be given, which can give insight in the more general gap between engineering and

  17. Modifications of the law of the wall and algebraic turbulence modelling for separated boundary layers

    NASA Technical Reports Server (NTRS)

    Baldwin, B. S.; Maccormack, R. W.

    1976-01-01

    Various modifications of the conventional algebraic eddy viscosity turbulence model are investigated for application to separated flows. Friction velocity is defined in a way that avoids singular behavior at separation and reattachment but reverts to the conventional definition for flows with small pressure gradients. This leads to a modified law of the wall for separated flows. The effect on the calculated flow field of changes in the model that affect the eddy viscosity at various distances from the wall are determined by (1) switching from Prandtl's form to an inner layer formula due to Clauser at various distances from the wall, (2) varying the constant in the Van Driest damping factor, (3) using Clauser's inner layer formula all the way to the wall, and (4) applying a relaxation procedure in the evaluation of the constant in Clauser's inner layer formula. Numerical solutions of the compressible Navier-Stokes equations are used to determine the effects of the modifications. Experimental results from shock-induced separated flows at Mach numbers 2.93 and 8.45 are used for comparison. For these cases improved predictions of wall pressure distribution and positions of separation and reattachment are obtained from the relaxation version of the Clauser inner layer eddy viscosity formula.

  18. Algebraic Reynolds stress modeling of turbulence subject to rapid homogeneous and non-homogeneous compression or expansion

    NASA Astrophysics Data System (ADS)

    Grigoriev, I. A.; Wallin, S.; Brethouwer, G.; Grundestam, O.; Johansson, A. V.

    2016-02-01

    A recently developed explicit algebraic Reynolds stress model (EARSM) by Grigoriev et al. ["A realizable explicit algebraic Reynolds stress model for compressible turbulent flow with significant mean dilatation," Phys. Fluids 25(10), 105112 (2013)] and the related differential Reynolds stress model (DRSM) are used to investigate the influence of homogeneous shear and compression on the evolution of turbulence in the limit of rapid distortion theory (RDT). The DRSM predictions of the turbulence kinetic energy evolution are in reasonable agreement with RDT while the evolution of diagonal components of anisotropy correctly captures the essential features, which is not the case for standard compressible extensions of DRSMs. The EARSM is shown to give a realizable anisotropy tensor and a correct trend of the growth of turbulence kinetic energy K, which saturates at a power law growth versus compression ratio, as well as retaining a normalized strain in the RDT regime. In contrast, an eddy-viscosity model results in a rapid exponential growth of K and excludes both realizability and high magnitude of the strain rate. We illustrate the importance of using a proper algebraic treatment of EARSM in systems with high values of dilatation and vorticity but low shear. A homogeneously compressed and rotating gas cloud with cylindrical symmetry, related to astrophysical flows and swirling supercritical flows, was investigated too. We also outline the extension of DRSM and EARSM to include the effect of non-homogeneous density coupled with "local mean acceleration" which can be important for, e.g., stratified flows or flows with heat release. A fixed-point analysis of direct numerical simulation data of combustion in a wall-jet flow demonstrates that our model gives quantitatively correct predictions of both streamwise and cross-stream components of turbulent density flux as well as their influence on the anisotropies. In summary, we believe that our approach, based on a proper

  19. Turbulence Modeling: A NASA Perspective

    NASA Technical Reports Server (NTRS)

    Gatski, T. B.

    2001-01-01

    This paper presents turbulence modeling from NASA's perspective. The topics include: 1) Hierarchy of Solution Methods; 2) Turbulence Modeling Focus; 3) Linear Eddy Viscosity Models; and 4) Nonlinear Eddy Viscosity Algebraic Stress Models.

  20. A non-linear algebraic model for the turbulent scalar fluxes

    SciTech Connect

    Younis, B.A.; Speziale, C.G.; Clark, T.T.

    1995-09-01

    The need for a new approach to modelling the scalar fluxes stems from the lack of realism in the performance of the simple gradient-transport models and the inadequacy of many of the assumptions underlying the more complicated scalar-flux transport closures. The problems with the simple gradient-transport closures are well known. In models of this type, the scalar fluxes are related to the mean scalar field via a scalar turbulent diffusivity. The purpose of this paper is to report on a novel approach to the modelling of the turbulent scalar fluxes (u{sub i}{theta}) which arise as a consequence of time averaging the transport equation for a mean scalar ({Theta}). The focus of this paper will be on the case where {Theta} is a `passive` scalar; the extension of this approach to cases involving buoyancy and compressibility will be briefly discussed. Models of this type fail badly in complex and strongly-buoyant flows.

  1. Turbulence modeling

    NASA Technical Reports Server (NTRS)

    Bardina, Jorge E.

    1995-01-01

    The objective of this work is to develop, verify, and incorporate the baseline two-equation turbulence models which account for the effects of compressibility into the three-dimensional Reynolds averaged Navier-Stokes (RANS) code and to provide documented descriptions of the models and their numerical procedures so that they can be implemented into 3-D CFD codes for engineering applications.

  2. Turbulence modeling

    NASA Technical Reports Server (NTRS)

    Rubesin, Morris W.

    1987-01-01

    Recent developments at several levels of statistical turbulence modeling applicable to aerodynamics are briefly surveyed. Emphasis is on examples of model improvements for transonic, two-dimensional flows. Experience with the development of these improved models is cited to suggest methods of accelerating the modeling process necessary to keep abreast of the rapid movement of computational fluid dynamics into the computation of complex three-dimensional flows.

  3. A New Reynolds Stress Algebraic Equation Model

    NASA Technical Reports Server (NTRS)

    Shih, Tsan-Hsing; Zhu, Jiang; Lumley, John L.

    1994-01-01

    A general turbulent constitutive relation is directly applied to propose a new Reynolds stress algebraic equation model. In the development of this model, the constraints based on rapid distortion theory and realizability (i.e. the positivity of the normal Reynolds stresses and the Schwarz' inequality between turbulent velocity correlations) are imposed. Model coefficients are calibrated using well-studied basic flows such as homogeneous shear flow and the surface flow in the inertial sublayer. The performance of this model is then tested in complex turbulent flows including the separated flow over a backward-facing step and the flow in a confined jet. The calculation results are encouraging and point to the success of the present model in modeling turbulent flows with complex geometries.

  4. Turbulence Modeling Workshop

    NASA Technical Reports Server (NTRS)

    Rubinstein, R. (Editor); Rumsey, C. L. (Editor); Salas, M. D. (Editor); Thomas, J. L. (Editor); Bushnell, Dennis M. (Technical Monitor)

    2001-01-01

    Advances in turbulence modeling are needed in order to calculate high Reynolds number flows near the onset of separation and beyond. To this end, the participants in this workshop made the following recommendations. (1) A national/international database and standards for turbulence modeling assessment should be established. Existing experimental data sets should be reviewed and categorized. Advantage should be taken of other efforts already under-way, such as that of the European Research Community on Flow, Turbulence, and Combustion (ERCOFTAC) consortium. Carefully selected "unit" experiments will be needed, as well as advances in instrumentation, to fill the gaps in existing datasets. A high priority should be given to document existing turbulence model capabilities in a standard form, including numerical implementation issues such as grid quality and resolution. (2) NASA should support long-term research on Algebraic Stress Models and Reynolds Stress Models. The emphasis should be placed on improving the length-scale equation, since it is the least understood and is a key component of two-equation and higher models. Second priority should be given to the development of improved near-wall models. Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES) would provide valuable guidance in developing and validating new Reynolds-averaged Navier-Stokes (RANS) models. Although not the focus of this workshop, DNS, LES, and hybrid methods currently represent viable approaches for analysis on a limited basis. Therefore, although computer limitations require the use of RANS methods for realistic configurations at high Reynolds number in the foreseeable future, a balanced effort in turbulence modeling development, validation, and implementation should include these approaches as well.

  5. Workshop on Engineering Turbulence Modeling

    SciTech Connect

    Povinelli, L.A.; Liou, W.W.; Shabbir, A.; Shih, T.H.

    1992-03-01

    Discussed here is the future direction of various levels of engineering turbulence modeling related to computational fluid dynamics (CFD) computations for propulsion. For each level of computation, there are a few turbulence models which represent the state-of-the-art for that level. However, it is important to know their capabilities as well as their deficiencies in order to help engineers select and implement the appropriate models in their real world engineering calculations. This will also help turbulence modelers perceive the future directions for improving turbulence models. The focus is on one-point closure models (i.e., from algebraic models to higher order moment closure schemes and partial differential equation methods) which can be applied to CFD computations. However, other schemes helpful in developing one-point closure models, are also discussed.

  6. Workshop on Engineering Turbulence Modeling

    NASA Technical Reports Server (NTRS)

    Povinelli, Louis A. (Editor); Liou, W. W. (Editor); Shabbir, A. (Editor); Shih, T.-H. (Editor)

    1992-01-01

    Discussed here is the future direction of various levels of engineering turbulence modeling related to computational fluid dynamics (CFD) computations for propulsion. For each level of computation, there are a few turbulence models which represent the state-of-the-art for that level. However, it is important to know their capabilities as well as their deficiencies in order to help engineers select and implement the appropriate models in their real world engineering calculations. This will also help turbulence modelers perceive the future directions for improving turbulence models. The focus is on one-point closure models (i.e., from algebraic models to higher order moment closure schemes and partial differential equation methods) which can be applied to CFD computations. However, other schemes helpful in developing one-point closure models, are also discussed.

  7. Turbulence modeling for separated flow

    NASA Technical Reports Server (NTRS)

    Durbin, Paul A.

    1994-01-01

    Two projects are described in this report. The first involves assessing turbulence models in separated flow. The second addresses the anomalous behavior of certain turbulence models in stagnation point flow. The primary motivation for developing turbulent transport models is to provide tools for computing non-equilibrium, or complex, turbulent flows. Simple flows can be analyzed using data correlations or algebraic eddy viscosities, but in more complicated flows such as a massively separated boundary layer, a more elaborate level of modeling is required. It is widely believed that at least a two-equation transport model is required in such cases. The transport equations determine the evolution of suitable velocity and time-scales of the turbulence. The present study included assessment of second-moment closures in several separated flows, including sharp edge separation; smooth wall, pressure driven separation; and unsteady vortex shedding. Flows with mean swirl are of interest for their role in enhancing mixing both by turbulent and mean motion. The swirl can have a stabilizing effect on the turbulence. An axi-symmetric extension to the INS-2D computer program was written adding the capability of computing swirling flow. High swirl can produce vortex breakdown on the centerline of the jet and it occurs in various combustors.

  8. Prediction of Complex Aerodynamic Flows with Explicit Algebraic Stress Models

    NASA Technical Reports Server (NTRS)

    Abid, Ridha; Morrison, Joseph H.; Gatski, Thomas B.; Speziale, Charles G.

    1996-01-01

    An explicit algebraic stress equation, developed by Gatski and Speziale, is used in the framework of K-epsilon formulation to predict complex aerodynamic turbulent flows. The nonequilibrium effects are modeled through coefficients that depend nonlinearly on both rotational and irrotational strains. The proposed model was implemented in the ISAAC Navier-Stokes code. Comparisons with the experimental data are presented which clearly demonstrate that explicit algebraic stress models can predict the correct response to nonequilibrium flow.

  9. Survey of Turbulence Models for the Computation of Turbulent Jet Flow and Noise

    NASA Technical Reports Server (NTRS)

    Nallasamy, N.

    1999-01-01

    The report presents an overview of jet noise computation utilizing the computational fluid dynamic solution of the turbulent jet flow field. The jet flow solution obtained with an appropriate turbulence model provides the turbulence characteristics needed for the computation of jet mixing noise. A brief account of turbulence models that are relevant for the jet noise computation is presented. The jet flow solutions that have been directly used to calculate jet noise are first reviewed. Then, the turbulent jet flow studies that compute the turbulence characteristics that may be used for noise calculations are summarized. In particular, flow solutions obtained with the k-e model, algebraic Reynolds stress model, and Reynolds stress transport equation model are reviewed. Since, the small scale jet mixing noise predictions can be improved by utilizing anisotropic turbulence characteristics, turbulence models that can provide the Reynolds stress components must now be considered for jet flow computations. In this regard, algebraic stress models and Reynolds stress transport models are good candidates. Reynolds stress transport models involve more modeling and computational effort and time compared to algebraic stress models. Hence, it is recommended that an algebraic Reynolds stress model (ASM) be implemented in flow solvers to compute the Reynolds stress components.

  10. Assessment of an Explicit Algebraic Reynolds Stress Model

    NASA Technical Reports Server (NTRS)

    Carlson, Jan-Renee

    2005-01-01

    This study assesses an explicit algebraic Reynolds stress turbulence model in the in the three-dimensional Reynolds averaged Navier-Stokes (RANS) solver, ISAAC (Integrated Solution Algorithm for Arbitrary Con gurations). Additionally, it compares solutions for two select configurations between ISAAC and the RANS solver PAB3D. This study compares with either direct numerical simulation data, experimental data, or empirical models for several different geometries with compressible, separated, and high Reynolds number flows. In general, the turbulence model matched data or followed experimental trends well, and for the selected configurations, the computational results of ISAAC closely matched those of PAB3D using the same turbulence model.

  11. Modeling Compressed Turbulence

    SciTech Connect

    Israel, Daniel M.

    2012-07-13

    From ICE to ICF, the effect of mean compression or expansion is important for predicting the state of the turbulence. When developing combustion models, we would like to know the mix state of the reacting species. This involves density and concentration fluctuations. To date, research has focused on the effect of compression on the turbulent kinetic energy. The current work provides constraints to help development and calibration for models of species mixing effects in compressed turbulence. The Cambon, et al., re-scaling has been extended to buoyancy driven turbulence, including the fluctuating density, concentration, and temperature equations. The new scalings give us helpful constraints for developing and validating RANS turbulence models.

  12. Invariant turbulence models

    NASA Astrophysics Data System (ADS)

    Bihlo, Alexander; Dos Santos Cardoso-Bihlo, Elsa Maria; Nave, Jean-Christophe; Popovych, Roman

    2012-11-01

    Various subgrid-scale closure models break the invariance of the Euler or Navier-Stokes equations and thus violate the geometric structure of these equations. A method is shown which allows one to systematically derive invariant turbulence models starting from non-invariant turbulence models and thus to correct artificial symmetry-breaking. The method is illustrated by finding invariant hyperdiffusion schemes to be applied in the two-dimensional turbulence problem.

  13. A multiple-time-scale turbulence model based on variable partitioning of turbulent kinetic energy spectrum

    NASA Technical Reports Server (NTRS)

    Kim, S.-W.; Chen, C.-P.

    1987-01-01

    A multiple-time-scale turbulence model of a single point closure and a simplified split-spectrum method is presented. In the model, the effect of the ratio of the production rate to the dissipation rate on eddy viscosity is modeled by use of the multiple-time-scales and a variable partitioning of the turbulent kinetic energy spectrum. The concept of a variable partitioning of the turbulent kinetic energy spectrum and the rest of the model details are based on the previously reported algebraic stress turbulence model. Example problems considered include: a fully developed channel flow, a plane jet exhausting into a moving stream, a wall jet flow, and a weakly coupled wake-boundary layer interaction flow. The computational results compared favorably with those obtained by using the algebraic stress turbulence model as well as experimental data. The present turbulence model, as well as the algebraic stress turbulence model, yielded significantly improved computational results for the complex turbulent boundary layer flows, such as the wall jet flow and the wake boundary layer interaction flow, compared with available computational results obtained by using the standard kappa-epsilon turbulence model.

  14. A near-wall turbulence model and its application to fully developed turbulent channel and pipe flows

    NASA Technical Reports Server (NTRS)

    Kim, S.-W.

    1988-01-01

    A near wall turbulence model and its incorporation into a multiple-time-scale turbulence model are presented. In the method, the conservation of mass, momentum, and the turbulent kinetic energy equations are integrated up to the wall; and the energy transfer rate and the dissipation rate inside the near wall layer are obtained from algebraic equations. The algebraic equations for the energy transfer rate and the dissipation rate inside the near wall layer were obtained from a k-equation turbulence model and the near wall analysis. A fully developed turbulent channel flow and fully developed turbulent pipe flows were solved using a finite element method to test the predictive capability of the turbulence model. The computational results compared favorably with experimental data. It is also shown that the present turbulence model could resolve the over shoot phenomena of the turbulent kinetic energy and the dissipation rate in the region very close to the wall.

  15. Turbulence modeling for hypersonic flows

    NASA Technical Reports Server (NTRS)

    Marvin, J. G.; Coakley, T. J.

    1989-01-01

    Turbulence modeling for high speed compressible flows is described and discussed. Starting with the compressible Navier-Stokes equations, methods of statistical averaging are described by means of which the Reynolds-averaged Navier-Stokes equations are developed. Unknown averages in these equations are approximated using various closure concepts. Zero-, one-, and two-equation eddy viscosity models, algebraic stress models and Reynolds stress transport models are discussed. Computations of supersonic and hypersonic flows obtained using several of the models are discussed and compared with experimental results. Specific examples include attached boundary layer flows, shock wave boundary layer interactions and compressible shear layers. From these examples, conclusions regarding the status of modeling and recommendations for future studies are discussed.

  16. Linear stability analysis of swirling turbulent flows with turbulence models

    NASA Astrophysics Data System (ADS)

    Gupta, Vikrant; Juniper, Matthew

    2013-11-01

    In this paper, we consider the growth of large scale coherent structures in turbulent flows by performing linear stability analysis around a mean flow. Turbulent flows are characterized by fine-scale stochastic perturbations. The momentum transfer caused by these perturbations affects the development of larger structures. Therefore, in a linear stability analysis, it is important to include the perturbations' influence. One way to do this is to include a turbulence model in the stability analysis. This is done in the literature by using eddy viscosity models (EVMs), which are first order turbulence models. We extend this approach by using second order turbulence models, in this case explicit algebraic Reynolds stress models (EARSMs). EARSMs are more versatile than EVMs, in that they can be applied to a wider range of flows, and could also be more accurate. We verify our EARSM-based analysis by applying it to a channel flow and then comparing the results with those from an EVM-based analysis. We then apply the EARSM-based stability analysis to swirling pipe flows and Taylor-Couette flows, which demonstrates the main benefit of EARSM-based analysis. This project is supported by EPSRC and Rolls-Royce through a Dorothy Hodgkin Research Fellowship.

  17. Turbulent transport models for scramjet flowfields

    NASA Technical Reports Server (NTRS)

    Sindir, M. M.; Harsha, P. T.

    1984-01-01

    Turbulence modeling approaches were examined from the standpoint of their capability to predict the complex flowfield features observed in scramjet combustions. Thus, for example, the accuracy of each turbulence model, with respect to the prediction of recirculating flows, was examined. It was observed that for large diameter ratio axisymmetric sudden expansion flows, a choice of turbulence model was not critical because of the domination of their flowfields by pressure forces. For low diameter ratio axisymmetric sudden expansions and planar backward-facing steps flows, where turbulent shear stresses are of greater significance, the algebraic Reynolds stress approach, modified to increase its sensitivity to streamline curvature, was found to provide the best results. Results of the study also showed that strongly swirling flows provide a stringent test of turbulence model assumptions. Thus, although flows with very high swirl are not of great practical interest, they are useful for turbulence model development. Finally, it was also noted that numerical flowfields solution techniques have a strong interrelation with turbulence models, particularly with the turbulent transport models which involve source-dominated transport equations.

  18. Calculation of reattaching shear layers in divergent channel with a multiple-time-scale turbulence model

    NASA Technical Reports Server (NTRS)

    Kim, S.-W.

    1989-01-01

    Numerical calculations of turbulent reattaching shear layers in a divergent channel are presented. The turbulence is described by a multiple-time-scale turbulence model. The turbulent flow equations are solved by a control-volume based finite difference method. The computational results are compared with those obtained using k-epsilon turbulence models and algebraic Reynolds stress turbulence models. It is shown that the multiple-time-scale turbulence model yields significantly improved computational results than the other turbulence models in the region where the turbulence is in a strongly inequilibrium state.

  19. MODEL IDENTIFICATION AND COMPUTER ALGEBRA.

    PubMed

    Bollen, Kenneth A; Bauldry, Shawn

    2010-10-01

    Multiequation models that contain observed or latent variables are common in the social sciences. To determine whether unique parameter values exist for such models, one needs to assess model identification. In practice analysts rely on empirical checks that evaluate the singularity of the information matrix evaluated at sample estimates of parameters. The discrepancy between estimates and population values, the limitations of numerical assessments of ranks, and the difference between local and global identification make this practice less than perfect. In this paper we outline how to use computer algebra systems (CAS) to determine the local and global identification of multiequation models with or without latent variables. We demonstrate a symbolic CAS approach to local identification and develop a CAS approach to obtain explicit algebraic solutions for each of the model parameters. We illustrate the procedures with several examples, including a new proof of the identification of a model for handling missing data using auxiliary variables. We present an identification procedure for Structural Equation Models that makes use of CAS and that is a useful complement to current methods. PMID:21769158

  20. Characterization of Turbulent Flows for Turbulence Modeling

    NASA Astrophysics Data System (ADS)

    Reynolds, W. C.; Haire, S. L.

    1998-11-01

    A diagram for the characterization of turbulent flows using the invariants of the mean velocity gradient tensor is introduced. All mean flows, from irrotationally strained flows to shearing flows, to purely rotational flows, can be identified on this diagram. Different flow fields which occupy the same region on the diagram are said to be comprised of the same topological features. The current state of turbulence modeling can be identified on the diagram based on the type of mean flow fields which can be accurately computed. Regions on the diagram can be shown for which current capabilities in turbulence modeling fail to accurately resolve the turbulent structures. Relevant mean field topology is identified for future work in turbulence modeling. Using this analysis, we suggest a number of flows to be computed by DNS or LES and used as testing cases for new models.

  1. Assessment of turbulent models for scramjet flowfields

    NASA Technical Reports Server (NTRS)

    Sindir, M. M.; Harsha, P. T.

    1982-01-01

    The behavior of several turbulence models applied to the prediction of scramjet combustor flows is described. These models include the basic two equation model, the multiple dissipation length scale variant of the two equation model, and the algebraic stress model (ASM). Predictions were made of planar backward facing step flows and axisymmetric sudden expansion flows using each of these approaches. The formulation of each of these models are discussed, and the application of the different approaches to supersonic flows is described. A modified version of the ASM is found to provide the best prediction of the planar backward facing step flow in the region near the recirculation zone, while the basic ASM provides the best results downstream of the recirculation. Aspects of the interaction of numerica modeling and turbulences modeling as they affect the assessment of turbulence models are discussed.

  2. Modeling turbulent flame propagation

    SciTech Connect

    Ashurst, W.T.

    1994-08-01

    Laser diagnostics and flow simulation techniques axe now providing information that if available fifty years ago, would have allowed Damkoehler to show how turbulence generates flame area. In the absence of this information, many turbulent flame speed models have been created, most based on Kolmogorov concepts which ignore the turbulence vortical structure, Over the last twenty years, the vorticity structure in mixing layers and jets has been shown to determine the entrainment and mixing behavior and these effects need to be duplicated by combustion models. Turbulence simulations reveal the intense vorticity structure as filaments and simulations of passive flamelet propagation show how this vorticity Creates flame area and defines the shape of the expected chemical reaction surface. Understanding how volume expansion interacts with flow structure should improve experimental methods for determining turbulent flame speed. Since the last decade has given us such powerful new tools to create and see turbulent combustion microscopic behavior, it seems that a solution of turbulent combustion within the next decade would not be surprising in the hindsight of 2004.

  3. Modeling of turbulent chemical reaction

    NASA Technical Reports Server (NTRS)

    Chen, J.-Y.

    1995-01-01

    Viewgraphs are presented on modeling turbulent reacting flows, regimes of turbulent combustion, regimes of premixed and regimes of non-premixed turbulent combustion, chemical closure models, flamelet model, conditional moment closure (CMC), NO(x) emissions from turbulent H2 jet flames, probability density function (PDF), departures from chemical equilibrium, mixing models for PDF methods, comparison of predicted and measured H2O mass fractions in turbulent nonpremixed jet flames, experimental evidence of preferential diffusion in turbulent jet flames, and computation of turbulent reacting flows.

  4. An abbreviated Reynolds stress turbulence model for airfoil flows

    NASA Technical Reports Server (NTRS)

    Gaffney, R. L., Jr.; Hassan, H. A.; Salas, M. D.

    1990-01-01

    An abbreviated Reynolds stress turbulence model is presented for solving turbulent flow over airfoils. The model consists of two partial differential equations, one for the Reynolds shear stress and the other for the turbulent kinetic energy. The normal stresses and the dissipation rate of turbulent kinetic energy are computed from algebraic relationships having the correct asymptotic near wall behavior. This allows the model to be integrated all the way to the wall without the use of wall functions. Results for a flat plate at zero angle of attack, a NACA 0012 airfoil and a RAE 2822 airfoil are presented.

  5. Comparison of Turbulent Thermal Diffusivity and Scalar Variance Models

    NASA Technical Reports Server (NTRS)

    Yoder, Dennis A.

    2016-01-01

    In this study, several variable turbulent Prandtl number formulations are examined for boundary layers, pipe flow, and axisymmetric jets. The model formulations include simple algebraic relations between the thermal diffusivity and turbulent viscosity as well as more complex models that solve transport equations for the thermal variance and its dissipation rate. Results are compared with available data for wall heat transfer and profile measurements of mean temperature, the root-mean-square (RMS) fluctuating temperature, turbulent heat flux and turbulent Prandtl number. For wall-bounded problems, the algebraic models are found to best predict the rise in turbulent Prandtl number near the wall as well as the log-layer temperature profile, while the thermal variance models provide a good representation of the RMS temperature fluctuations. In jet flows, the algebraic models provide no benefit over a constant turbulent Prandtl number approach. Application of the thermal variance models finds that some significantly overpredict the temperature variance in the plume and most underpredict the thermal growth rate of the jet. The models yield very similar fluctuating temperature intensities in jets from straight pipes and smooth contraction nozzles, in contrast to data that indicate the latter should have noticeably higher values. For the particular low subsonic heated jet cases examined, changes in the turbulent Prandtl number had no effect on the centerline velocity decay.

  6. Teaching Modeling and Axiomatization with Boolean Algebra.

    ERIC Educational Resources Information Center

    De Villiers, Michael D.

    1987-01-01

    Presented is an alternative approach to the traditional teaching of Boolean algebra for secondary school mathematics. The main aim of the approach is to use Boolean algebra to teach pupils such mathematical processes as modeling and axiomatization. A course using the approach is described. (RH)

  7. Swirl flow turbulence modeling

    NASA Technical Reports Server (NTRS)

    Abujelala, M. T.; Jackson, T. W.; Lilley, D. G.

    1984-01-01

    Confined turbulent swirling flow data obtained from a single hot-wire using a six-orientation technique are analyzed numerically. The effects of swirl strength and the presence of a strong contraction nozzle further downstream on deduced parameters is also presented and discussed for the case of chamber-to-inlet diameter ratio D/d = 2. Three swirl strengths are considered with inlet swirl vane angles of 0, 45 and 70 deg. A strong contraction nozzle with an area ratio of 4 is located two chamber-diameters downstream of the inlet to the flowfield. It is found that both the swirl strength and the contraction have strong effects on the turbulence parameters. Generally, the most dramatic effect of increase of swirl strength is the considerable increase in values of all the parameters considered, (rx-viscosity, kinetic energy of turbulence, length scales, and degree of nonisotropy). The presence of a strong contraction nozzle tends to increase the turbulence parameter values in regions of acceleration and to reduce them in deceleration regions. Based on similarity of viscosity and length scale profiles, a C sub mu formulation is deduced which is shown to improve the predictive capability of the standard k-epsilon turbulence model in swirling recirculating flows.

  8. A multiple-time-scale turbulence model based on variable partitioning of the turbulent kinetic energy spectrum

    NASA Technical Reports Server (NTRS)

    Kim, S.-W.; Chen, C.-P.

    1989-01-01

    A multiple-time-scale turbulence model of a single point closure and a simplified split-spectrum method is presented. In the model, the effect of the ratio of the production rate to the dissipation rate on eddy viscosity is modeled by use of the multiple-time-scales and a variable partitioning of the turbulent kinetic energy spectrum. The concept of a variable partitioning of the turbulent kinetic energy spectrum and the rest of the model details are based on the previously reported algebraic stress turbulence model. Example problems considered include: a fully developed channel flow, a plane jet exhausting into a moving stream, a wall jet flow, and a weakly coupled wake-boundary layer interaction flow. The computational results compared favorably with those obtained by using the algebraic stress turbulence model as well as experimental data. The present turbulence model, as well as the algebraic stress turbulence model, yielded significantly improved computational results for the complex turbulent boundary layer flows, such as the wall jet flow and the wake boundary layer interaction flow, compared with available computational results obtained by using the standard kappa-epsilon turbulence model.

  9. The Use of DNS in Turbulence Modeling

    NASA Technical Reports Server (NTRS)

    Mansour, Nagi N.; Merriam, Marshal (Technical Monitor)

    1997-01-01

    The use of Direct numerical simulations (DNS) data in developing and testing turbulence models is reviewed. The data is used to test turbulence models at all levels: algebraic, one-equation, two-equation and full Reynolds stress models were tested. Particular examples on the development of models for the dissipation rate equation are presented. Homogeneous flows are used to test new scaling arguments for the various terms in the dissipation rate equation. The channel flow data is used to develop modifications to the equation model that take into account near-wall effects. DNS of compressible flows under mean compression are used in testing new compressible modifications to the two-equation models.

  10. Workshop on Computational Turbulence Modeling

    SciTech Connect

    Not Available

    1993-01-01

    This document contains presentations given at Workshop on Computational Turbulence Modeling held 15-16 Sep. 1993. The purpose of the meeting was to discuss the current status and future development of turbulence modeling in computational fluid dynamics for aerospace propulsion systems. Papers cover the following topics: turbulence modeling activities at the Center for Modeling of Turbulence and Transition (CMOTT); heat transfer and turbomachinery flow physics; aerothermochemistry and computational methods for space systems; computational fluid dynamics and the k-epsilon turbulence model; propulsion systems; and inlet, duct, and nozzle flow. Separate abstracts have been prepared for articles from this report.

  11. Workshop on Computational Turbulence Modeling

    NASA Technical Reports Server (NTRS)

    1993-01-01

    This document contains presentations given at Workshop on Computational Turbulence Modeling held 15-16 Sep. 1993. The purpose of the meeting was to discuss the current status and future development of turbulence modeling in computational fluid dynamics for aerospace propulsion systems. Papers cover the following topics: turbulence modeling activities at the Center for Modeling of Turbulence and Transition (CMOTT); heat transfer and turbomachinery flow physics; aerothermochemistry and computational methods for space systems; computational fluid dynamics and the k-epsilon turbulence model; propulsion systems; and inlet, duct, and nozzle flow.

  12. Turbulence modeling and experiments

    NASA Technical Reports Server (NTRS)

    Shabbir, Aamir

    1992-01-01

    The best way of verifying turbulence is to do a direct comparison between the various terms and their models. The success of this approach depends upon the availability of the data for the exact correlations (both experimental and DNS). The other approach involves numerically solving the differential equations and then comparing the results with the data. The results of such a computation will depend upon the accuracy of all the modeled terms and constants. Because of this it is sometimes difficult to find the cause of a poor performance by a model. However, such a calculation is still meaningful in other ways as it shows how a complete Reynolds stress model performs. Thirteen homogeneous flows are numerically computed using the second order closure models. We concentrate only on those models which use a linear (or quasi-linear) model for the rapid term. This, therefore, includes the Launder, Reece and Rodi (LRR) model; the isotropization of production (IP) model; and the Speziale, Sarkar, and Gatski (SSG) model. Which of the three models performs better is examined along with what are their weaknesses, if any. The other work reported deal with the experimental balances of the second moment equations for a buoyant plume. Despite the tremendous amount of activity toward the second order closure modeling of turbulence, very little experimental information is available about the budgets of the second moment equations. Part of the problem stems from our inability to measure the pressure correlations. However, if everything else appearing in these equations is known from the experiment, pressure correlations can be obtained as the closing terms. This is the closest we can come to in obtaining these terms from experiment, and despite the measurement errors which might be present in such balances, the resulting information will be extremely useful for the turbulence modelers. The purpose of this part of the work was to provide such balances of the Reynolds stress and heat

  13. Aircraft Dynamic Modeling in Turbulence

    NASA Technical Reports Server (NTRS)

    Morelli, Eugene A.; Cunninham, Kevin

    2012-01-01

    A method for accurately identifying aircraft dynamic models in turbulence was developed and demonstrated. The method uses orthogonal optimized multisine excitation inputs and an analytic method for enhancing signal-to-noise ratio for dynamic modeling in turbulence. A turbulence metric was developed to accurately characterize the turbulence level using flight measurements. The modeling technique was demonstrated in simulation, then applied to a subscale twin-engine jet transport aircraft in flight. Comparisons of modeling results obtained in turbulent air to results obtained in smooth air were used to demonstrate the effectiveness of the approach.

  14. Turbulence intermittency, vector multifractals and Lie cascades generated by stochastic Clifford algebra

    NASA Astrophysics Data System (ADS)

    Schertzer, Daniel; Tchiguirinskaia, Ioulia

    2014-05-01

    A complex key feature of turbulence is that the velocity is a vector field, whereas intermittency, another key feature, has been mostly understood, analysed and simulated in scalar frameworks. This gap has prevented many developments. Some years ago, the general framework of 'Lie cascades' was introduced (Schertzer and Lovejoy, 1993) to deal with both features by considering cascades generated by stochastic Lie algebra. However, the theoretical efforts were mostly concentrated on the decomposition of this algebra into its radical and a semi-simple algebra and faced too many degrees of freedom. In this communication, we show that the class of Clifford algebra is already wide enough, very convenient and physically meaningful to understand, analyse and simulate intermittent vector fields.

  15. Algebraic operator approach to gas kinetic models

    NASA Astrophysics Data System (ADS)

    Il'ichov, L. V.

    1997-02-01

    Some general properties of the linear Boltzmann kinetic equation are used to present it in the form ∂ tϕ = - †Âϕ with the operators Âand† possessing some nontrivial algebraic properties. When applied to the Keilson-Storer kinetic model, this method gives an example of quantum ( q-deformed) Lie algebra. This approach provides also a natural generalization of the “kangaroo model”.

  16. A turbulence model for nonequilibrium adverse pressure gradient flows

    NASA Technical Reports Server (NTRS)

    Horstman, C. C.

    1976-01-01

    This paper presents a method for calculating compressible adverse pressure gradient boundary layers by using an algebraic eddy viscosity turbulence model that has been modified for variable pressure gradient and turbulence memory effects. The pressure gradient corrections are based on previous incompressible data correlations. Several methods for including the effects of turbulence memory are evaluated. A new lag model, which gives good agreement with available experimental data, is developed. Finally, a correlation is developed for the lag length parameter employed in the model as a function of the known experimental flow variables.

  17. Prediction of High-Lift Flows using Turbulent Closure Models

    NASA Technical Reports Server (NTRS)

    Rumsey, Christopher L.; Gatski, Thomas B.; Ying, Susan X.; Bertelrud, Arild

    1997-01-01

    The flow over two different multi-element airfoil configurations is computed using linear eddy viscosity turbulence models and a nonlinear explicit algebraic stress model. A subset of recently-measured transition locations using hot film on a McDonnell Douglas configuration is presented, and the effect of transition location on the computed solutions is explored. Deficiencies in wake profile computations are found to be attributable in large part to poor boundary layer prediction on the generating element, and not necessarily inadequate turbulence modeling in the wake. Using measured transition locations for the main element improves the prediction of its boundary layer thickness, skin friction, and wake profile shape. However, using measured transition locations on the slat still yields poor slat wake predictions. The computation of the slat flow field represents a key roadblock to successful predictions of multi-element flows. In general, the nonlinear explicit algebraic stress turbulence model gives very similar results to the linear eddy viscosity models.

  18. Computational algebraic geometry of epidemic models

    NASA Astrophysics Data System (ADS)

    Rodríguez Vega, Martín.

    2014-06-01

    Computational Algebraic Geometry is applied to the analysis of various epidemic models for Schistosomiasis and Dengue, both, for the case without control measures and for the case where control measures are applied. The models were analyzed using the mathematical software Maple. Explicitly the analysis is performed using Groebner basis, Hilbert dimension and Hilbert polynomials. These computational tools are included automatically in Maple. Each of these models is represented by a system of ordinary differential equations, and for each model the basic reproductive number (R0) is calculated. The effects of the control measures are observed by the changes in the algebraic structure of R0, the changes in Groebner basis, the changes in Hilbert dimension, and the changes in Hilbert polynomials. It is hoped that the results obtained in this paper become of importance for designing control measures against the epidemic diseases described. For future researches it is proposed the use of algebraic epidemiology to analyze models for airborne and waterborne diseases.

  19. Numerical simulations and modeling of turbulent combustion

    NASA Astrophysics Data System (ADS)

    Cuenot, B.

    Turbulent combustion is the basic physical phenomenon responsible for efficient energy release by any internal combustion engine. However it is accompanied by other undesirable phenomena such as noise, pollutant species emission or damaging instabilities that may even lead to the system desctruction. It is then crucial to control this phenomenon, to understand all its mecanisms and to master it in industrial systems. For long time turbulent combustion has been explored only through theory and experiment. But the rapid increase of computers power during the last years has allowed an important development of numerical simulation, that has become today an essential tool for research and technical design. Direct numerical simulation has then allowed to rapidly progress in the knowledge of turbulent flame structures, leading to new modelisations for steady averaged simulations. Recently large eddy simulation has made a new step forward by refining the description of complex and unsteady flames. The main problem that arises when performing numerical simulation of turbulent combustion is linked to the description of the flame front. Being very thin, it can not however be reduced to a simple interface as it is the location of intense chemical transformation and of strong variations of thermodynamical quantities. Capturing the internal structure of a zone with a thickness of the order of 0.1 mm in a computation with a mesh step 10 times larger being impossible, it is necessary to model the turbulent flame. Models depend on the chemical structure of the flame, on the ambiant turbulence, on the combustion regime (flamelets, distributed combustion, etc.) and on the reactants injection mode (premixed or not). One finds then a large class of models, from the most simple algebraic model with a one-step chemical kinetics, to the most complex model involving probablity density functions, cross-correlations and multiple-step or fully complex chemical kinetics.

  20. Algebraic models of flexible manufacturing systems

    NASA Astrophysics Data System (ADS)

    Leskin, Aleksei Alekseevich

    Various aspects of the use of mathematical methods in the development of flexible manufacturing systems are examined. Attention is given to dynamical and structural models of flexible manufacturing systems developed by using methods of algebraic and differential geometry, topology, polynomial algebra, and extreme value problem theory. The principles of model integration are discussed, and approaches are proposed for solving problems related to the selection of flexible manufacturing equipment, real-time modeling of the manufacturing process, and optimization of local automation systems. The discussion is illustrated by examples.

  1. Solving stochastic epidemiological models using computer algebra

    NASA Astrophysics Data System (ADS)

    Hincapie, Doracelly; Ospina, Juan

    2011-06-01

    Mathematical modeling in Epidemiology is an important tool to understand the ways under which the diseases are transmitted and controlled. The mathematical modeling can be implemented via deterministic or stochastic models. Deterministic models are based on short systems of non-linear ordinary differential equations and the stochastic models are based on very large systems of linear differential equations. Deterministic models admit complete, rigorous and automatic analysis of stability both local and global from which is possible to derive the algebraic expressions for the basic reproductive number and the corresponding epidemic thresholds using computer algebra software. Stochastic models are more difficult to treat and the analysis of their properties requires complicated considerations in statistical mathematics. In this work we propose to use computer algebra software with the aim to solve epidemic stochastic models such as the SIR model and the carrier-borne model. Specifically we use Maple to solve these stochastic models in the case of small groups and we obtain results that do not appear in standard textbooks or in the books updated on stochastic models in epidemiology. From our results we derive expressions which coincide with those obtained in the classical texts using advanced procedures in mathematical statistics. Our algorithms can be extended for other stochastic models in epidemiology and this shows the power of computer algebra software not only for analysis of deterministic models but also for the analysis of stochastic models. We also perform numerical simulations with our algebraic results and we made estimations for the basic parameters as the basic reproductive rate and the stochastic threshold theorem. We claim that our algorithms and results are important tools to control the diseases in a globalized world.

  2. Multigrid solution of incompressible turbulent flows by using two-equation turbulence models

    SciTech Connect

    Zheng, X.; Liu, C.; Sung, C.H.

    1996-12-31

    Most of practical flows are turbulent. From the interest of engineering applications, simulation of realistic flows is usually done through solution of Reynolds-averaged Navier-Stokes equations and turbulence model equations. It has been widely accepted that turbulence modeling plays a very important role in numerical simulation of practical flow problem, particularly when the accuracy is of great concern. Among the most used turbulence models today, two-equation models appear to be favored for the reason that they are more general than algebraic models and affordable with current available computer resources. However, investigators using two-equation models seem to have been more concerned with the solution of N-S equations. Less attention is paid to the solution method for the turbulence model equations. In most cases, the turbulence model equations are loosely coupled with N-S equations, multigrid acceleration is only applied to the solution of N-S equations due to perhaps the fact the turbulence model equations are source-term dominant and very stiff in sublayer region.

  3. Shapes and stability of algebraic nuclear models

    NASA Technical Reports Server (NTRS)

    Lopez-Moreno, Enrique; Castanos, Octavio

    1995-01-01

    A generalization of the procedure to study shapes and stability of algebraic nuclear models introduced by Gilmore is presented. One calculates the expectation value of the Hamiltonian with respect to the coherent states of the algebraic structure of the system. Then equilibrium configurations of the resulting energy surface, which depends in general on state variables and a set of parameters, are classified through the Catastrophe theory. For one- and two-body interactions in the Hamiltonian of the interacting Boson model-1, the critical points are organized through the Cusp catastrophe. As an example, we apply this Separatrix to describe the energy surfaces associated to the Rutenium and Samarium isotopes.

  4. Workshop on Computational Turbulence Modeling

    NASA Technical Reports Server (NTRS)

    Shabbir, A. (Compiler); Shih, T.-H. (Compiler); Povinelli, L. A. (Compiler)

    1994-01-01

    The purpose of this meeting was to discuss the current status and future development of turbulence modeling in computational fluid dynamics for aerospace propulsion systems. Various turbulence models have been developed and applied to different turbulent flows over the past several decades and it is becoming more and more urgent to assess their performance in various complex situations. In order to help users in selecting and implementing appropriate models in their engineering calculations, it is important to identify the capabilities as well as the deficiencies of these models. This also benefits turbulence modelers by permitting them to further improve upon the existing models. This workshop was designed for exchanging ideas and enhancing collaboration between different groups in the Lewis community who are using turbulence models in propulsion related CFD. In this respect this workshop will help the Lewis goal of excelling in propulsion related research. This meeting had seven sessions for presentations and one panel discussion over a period of two days. Each presentation session was assigned to one or two branches (or groups) to present their turbulence related research work. Each group was asked to address at least the following points: current status of turbulence model applications and developments in the research; progress and existing problems; and requests about turbulence modeling. The panel discussion session was designed for organizing committee members to answer management and technical questions from the audience and to make concluding remarks.

  5. A process algebra model of QED

    NASA Astrophysics Data System (ADS)

    Sulis, William

    2016-03-01

    The process algebra approach to quantum mechanics posits a finite, discrete, determinate ontology of primitive events which are generated by processes (in the sense of Whitehead). In this ontology, primitive events serve as elements of an emergent space-time and of emergent fundamental particles and fields. Each process generates a set of primitive elements, using only local information, causally propagated as a discrete wave, forming a causal space termed a causal tapestry. Each causal tapestry forms a discrete and finite sampling of an emergent causal manifold (space-time) M and emergent wave function. Interactions between processes are described by a process algebra which possesses 8 commutative operations (sums and products) together with a non-commutative concatenation operator (transitions). The process algebra possesses a representation via nondeterministic combinatorial games. The process algebra connects to quantum mechanics through the set valued process and configuration space covering maps, which associate each causal tapestry with sets of wave functions over M. Probabilities emerge from interactions between processes. The process algebra model has been shown to reproduce many features of the theory of non-relativistic scalar particles to a high degree of accuracy, without paradox or divergences. This paper extends the approach to a semi-classical form of quantum electrodynamics.

  6. A Study of Grid Resolution, Transition and Turbulence Model Using the Transonic Simple Straked Delta Wing

    NASA Technical Reports Server (NTRS)

    Bartels, Robert E.

    2001-01-01

    Three-dimensional transonic flow over a delta wing is investigated using several turbulence models. The performance of linear eddy viscosity models and an explicit algebraic stress model is assessed at the start of vortex flow, and the results compared with experimental data. To assess the effect of transition location, computations that either fix transition aft of the leading edge or are fully turbulent are performed. These computations show that grid resolution, transition location and turbulence model significantly affect the 3D flowfield.

  7. A Realizable Reynolds Stress Algebraic Equation Model

    NASA Technical Reports Server (NTRS)

    Shih, Tsan-Hsing; Zhu, Jiang; Lumley, John L.

    1993-01-01

    The invariance theory in continuum mechanics is applied to analyze Reynolds stresses in high Reynolds number turbulent flows. The analysis leads to a turbulent constitutive relation that relates the Reynolds stresses to the mean velocity gradients in a more general form in which the classical isotropic eddy viscosity model is just the linear approximation of the general form. On the basis of realizability analysis, a set of model coefficients are obtained which are functions of the time scale ratios of the turbulence to the mean strain rate and the mean rotation rate. The coefficients will ensure the positivity of each component of the mean rotation rate. These coefficients will ensure the positivity of each component of the turbulent kinetic energy - realizability that most existing turbulence models fail to satisfy. Separated flows over backward-facing step configurations are taken as applications. The calculations are performed with a conservative finite-volume method. Grid-independent and numerical diffusion-free solutions are obtained by using differencing schemes of second-order accuracy on sufficiently fine grids. The calculated results are compared in detail with the experimental data for both mean and turbulent quantities. The comparison shows that the present proposal significantly improves the predictive capability of K-epsilon based two equation models. In addition, the proposed model is able to simulate rotational homogeneous shear flows with large rotation rates which all conventional eddy viscosity models fail to simulate.

  8. Advanced Turbulence Modeling Concepts

    NASA Technical Reports Server (NTRS)

    Shih, Tsan-Hsing

    2005-01-01

    The ZCET program developed at NASA Glenn Research Center is to study hydrogen/air injection concepts for aircraft gas turbine engines that meet conventional gas turbine performance levels and provide low levels of harmful NOx emissions. A CFD study for ZCET program has been successfully carried out. It uses the most recently enhanced National combustion code (NCC) to perform CFD simulations for two configurations of hydrogen fuel injectors (GRC- and Sandia-injector). The results can be used to assist experimental studies to provide quick mixing, low emission and high performance fuel injector designs. The work started with the configuration of the single-hole injector. The computational models were taken from the experimental designs. For example, the GRC single-hole injector consists of one air tube (0.78 inches long and 0.265 inches in diameter) and two hydrogen tubes (0.3 inches long and 0.0226 inches in diameter opposed at 180 degree). The hydrogen tubes are located 0.3 inches upstream from the exit of the air element (the inlet location for the combustor). To do the simulation, the single-hole injector is connected to a combustor model (8.16 inches long and 0.5 inches in diameter). The inlet conditions for air and hydrogen elements are defined according to actual experimental designs. Two crossing jets of hydrogen/air are simulated in detail in the injector. The cold flow, reacting flow, flame temperature, combustor pressure and possible flashback phenomena are studied. Two grid resolutions of the numerical model have been adopted. The first computational grid contains 0.52 million elements, the second one contains over 1.3 million elements. The CFD results have shown only about 5% difference between the two grid resolutions. Therefore, the CFD result obtained from the model of 1.3-million grid resolution can be considered as a grid independent numerical solution. Turbulence models built in NCC are consolidated and well tested. They can handle both coarse and

  9. Dynamic stall simulation including turbulence modeling

    SciTech Connect

    Allet, A.; Halle, S.; Paraschivoiu, I.

    1995-09-01

    The objective of this study is to investigate the two-dimensional unsteady flow around an airfoil undergoing a Darrieus motion in dynamic stall conditions. For this purpose, a numerical solver based on the solution of the Reynolds-averaged Navier-Stokes equations expressed in a streamfunction-vorticity formulation in a non-inertial frame of reference was developed. The governing equations are solved by the streamline upwind Petrov-Galerkin finite element method (FEM). Temporal discretization is achieved by second-order-accurate finite differences. The resulting global matrix system is linearized by the Newton method and solved by the generalized minimum residual method (GMRES) with an incomplete triangular factorization preconditioning (ILU). Turbulence effects are introduced in the solver by an eddy viscosity model. The investigation centers on an evaluation of the possibilities of several turbulence models, including the algebraic Cebeci-Smith model (CSM) and the nonequilibrium Johnson-King model (JKM). In an effort to predict dynamic stall features on rotating airfoils, first the authors present some testing results concerning the performance of both turbulence models for the flat plate case. Then, computed flow structure together with aerodynamic coefficients for a NACA 0015 airfoil in Darrieus motion under stall conditions are presented.

  10. Conceptual dynamical models for turbulence.

    PubMed

    Majda, Andrew J; Lee, Yoonsang

    2014-05-01

    Understanding the complexity of anisotropic turbulent processes in engineering and environmental fluid flows is a formidable challenge with practical significance because energy often flows intermittently from the smaller scales to impact the largest scales in these flows. Conceptual dynamical models for anisotropic turbulence are introduced and developed here which, despite their simplicity, capture key features of vastly more complicated turbulent systems. These conceptual models involve a large-scale mean flow and turbulent fluctuations on a variety of spatial scales with energy-conserving wave-mean-flow interactions as well as stochastic forcing of the fluctuations. Numerical experiments with a six-dimensional conceptual dynamical model confirm that these models capture key statistical features of vastly more complex anisotropic turbulent systems in a qualitative fashion. These features include chaotic statistical behavior of the mean flow with a sub-Gaussian probability distribution function (pdf) for its fluctuations whereas the turbulent fluctuations have decreasing energy and correlation times at smaller scales, with nearly Gaussian pdfs for the large-scale fluctuations and fat-tailed non-Gaussian pdfs for the smaller-scale fluctuations. This last feature is a manifestation of intermittency of the small-scale fluctuations where turbulent modes with small variance have relatively frequent extreme events which directly impact the mean flow. The dynamical models introduced here potentially provide a useful test bed for algorithms for prediction, uncertainty quantification, and data assimilation for anisotropic turbulent systems. PMID:24753605

  11. Conceptual dynamical models for turbulence

    PubMed Central

    Majda, Andrew J.; Lee, Yoonsang

    2014-01-01

    Understanding the complexity of anisotropic turbulent processes in engineering and environmental fluid flows is a formidable challenge with practical significance because energy often flows intermittently from the smaller scales to impact the largest scales in these flows. Conceptual dynamical models for anisotropic turbulence are introduced and developed here which, despite their simplicity, capture key features of vastly more complicated turbulent systems. These conceptual models involve a large-scale mean flow and turbulent fluctuations on a variety of spatial scales with energy-conserving wave–mean-flow interactions as well as stochastic forcing of the fluctuations. Numerical experiments with a six-dimensional conceptual dynamical model confirm that these models capture key statistical features of vastly more complex anisotropic turbulent systems in a qualitative fashion. These features include chaotic statistical behavior of the mean flow with a sub-Gaussian probability distribution function (pdf) for its fluctuations whereas the turbulent fluctuations have decreasing energy and correlation times at smaller scales, with nearly Gaussian pdfs for the large-scale fluctuations and fat-tailed non-Gaussian pdfs for the smaller-scale fluctuations. This last feature is a manifestation of intermittency of the small-scale fluctuations where turbulent modes with small variance have relatively frequent extreme events which directly impact the mean flow. The dynamical models introduced here potentially provide a useful test bed for algorithms for prediction, uncertainty quantification, and data assimilation for anisotropic turbulent systems. PMID:24753605

  12. Recent Turbulence Model Advances Applied to Multielement Airfoil Computations

    NASA Technical Reports Server (NTRS)

    Rumsey, Christopher L.; Gatski, Thomas B.

    2000-01-01

    A one-equation linear turbulence model and a two-equation nonlinear explicit algebraic stress model (EASM) are applied to the flow over a multielement airfoil. The effect of the K-epsilon and K-omega forms of the two-equation model are explored, and the K-epsilon form is shown to be deficient in the wall-bounded regions of adverse pressure gradient flows. A new K-omega form of EASM is introduced. Nonlinear terms present in EASM are shown to improve predictions of turbulent shear stress behind the trailing edge of the main element and near midflap. Curvature corrections are applied to both the one- and two-equation turbulence models and yield only relatively small local differences in the flap region, where the flow field undergoes the greatest curvature. Predictions of maximum lift are essentially unaffected by the turbulence model variations studied.

  13. An algebraic approach to the Hubbard model

    NASA Astrophysics Data System (ADS)

    de Leeuw, Marius; Regelskis, Vidas

    2016-02-01

    We study the algebraic structure of an integrable Hubbard-Shastry type lattice model associated with the centrally extended su (2 | 2) superalgebra. This superalgebra underlies Beisert's AdS/CFT worldsheet R-matrix and Shastry's R-matrix. The considered model specializes to the one-dimensional Hubbard model in a certain limit. We demonstrate that Yangian symmetries of the R-matrix specialize to the Yangian symmetry of the Hubbard model found by Korepin and Uglov. Moreover, we show that the Hubbard model Hamiltonian has an algebraic interpretation as the so-called secret symmetry. We also discuss Yangian symmetries of the A and B models introduced by Frolov and Quinn.

  14. Turbulence modeling for sharp-fin-induced shock wave/turbulent boundary-layer interactions

    NASA Technical Reports Server (NTRS)

    Horstman, C. C.

    1990-01-01

    Solutions of the Reynolds averaged Navier-Stokes equations are presented and compared with a family of experimental results for the 3-D interaction of a sharp fin induced shock wave with a turbulent boundary layer. Several algebraic and two equation eddy viscosity turbulence models are employed. The computed results are compared with experimental surface pressure, skin friction, and yaw angle data as well as the overall size of the interaction. Although the major feature of the flow fields are correctly predicted, several discrepancies are noted. Namely, the maximum skin friction values are significantly underpredicted for the strongest interaction cases. These and other deficiencies are discussed.

  15. Turbulence Modeling Verification and Validation

    NASA Technical Reports Server (NTRS)

    Rumsey, Christopher L.

    2014-01-01

    Computational fluid dynamics (CFD) software that solves the Reynolds-averaged Navier-Stokes (RANS) equations has been in routine use for more than a quarter of a century. It is currently employed not only for basic research in fluid dynamics, but also for the analysis and design processes in many industries worldwide, including aerospace, automotive, power generation, chemical manufacturing, polymer processing, and petroleum exploration. A key feature of RANS CFD is the turbulence model. Because the RANS equations are unclosed, a model is necessary to describe the effects of the turbulence on the mean flow, through the Reynolds stress terms. The turbulence model is one of the largest sources of uncertainty in RANS CFD, and most models are known to be flawed in one way or another. Alternative methods such as direct numerical simulations (DNS) and large eddy simulations (LES) rely less on modeling and hence include more physics than RANS. In DNS all turbulent scales are resolved, and in LES the large scales are resolved and the effects of the smallest turbulence scales are modeled. However, both DNS and LES are too expensive for most routine industrial usage on today's computers. Hybrid RANS-LES, which blends RANS near walls with LES away from walls, helps to moderate the cost while still retaining some of the scale-resolving capability of LES, but for some applications it can still be too expensive. Even considering its associated uncertainties, RANS turbulence modeling has proved to be very useful for a wide variety of applications. For example, in the aerospace field, many RANS models are considered to be reliable for computing attached flows. However, existing turbulence models are known to be inaccurate for many flows involving separation. Research has been ongoing for decades in an attempt to improve turbulence models for separated and other nonequilibrium flows. When developing or improving turbulence models, both verification and validation are important

  16. Separated transonic airfoil flow calculations with a nonequilibrium turbulence model

    NASA Technical Reports Server (NTRS)

    King, L. S.; Johnson, D. A.

    1985-01-01

    Navier-Stokes transonic airfoil calculations based on a recently developed nonequilibrium, turbulence closure model are presented for a supercritical airfoil section at transonic cruise conditions and for a conventional airfoil section at shock-induced stall conditions. Comparisons with experimental data are presented which show that this nonequilibrium closure model performs significantly better than the popular Baldwin-Lomax and Cebeci-Smith equilibrium algebraic models when there is boundary-layer separation that results from the inviscid-viscous interactions.

  17. More accurate predictions with transonic Navier-Stokes methods through improved turbulence modeling

    NASA Technical Reports Server (NTRS)

    Johnson, Dennis A.

    1989-01-01

    Significant improvements in predictive accuracies for off-design conditions are achievable through better turbulence modeling; and, without necessarily adding any significant complication to the numerics. One well established fact about turbulence is it is slow to respond to changes in the mean strain field. With the 'equilibrium' algebraic turbulence models no attempt is made to model this characteristic and as a consequence these turbulence models exaggerate the turbulent boundary layer's ability to produce turbulent Reynolds shear stresses in regions of adverse pressure gradient. As a consequence, too little momentum loss within the boundary layer is predicted in the region of the shock wave and along the aft part of the airfoil where the surface pressure undergoes further increases. Recently, a 'nonequilibrium' algebraic turbulence model was formulated which attempts to capture this important characteristic of turbulence. This 'nonequilibrium' algebraic model employs an ordinary differential equation to model the slow response of the turbulence to changes in local flow conditions. In its original form, there was some question as to whether this 'nonequilibrium' model performed as well as the 'equilibrium' models for weak interaction cases. However, this turbulence model has since been further improved wherein it now appears that this turbulence model performs at least as well as the 'equilibrium' models for weak interaction cases and for strong interaction cases represents a very significant improvement. The performance of this turbulence model relative to popular 'equilibrium' models is illustrated for three airfoil test cases of the 1987 AIAA Viscous Transonic Airfoil Workshop, Reno, Nevada. A form of this 'nonequilibrium' turbulence model is currently being applied to wing flows for which similar improvements in predictive accuracy are being realized.

  18. Turbulence modeling for compressible flows

    NASA Technical Reports Server (NTRS)

    Marvin, J. G.

    1977-01-01

    Material prepared for a course on Applications and Fundamentals of Turbulence given at the University of Tennessee Space Institute, January 10 and 11, 1977, is presented. A complete concept of turbulence modeling is described, and examples of progess for its use in computational aerodynimics are given. Modeling concepts, experiments, and computations using the concepts are reviewed in a manner that provides an up-to-date statement on the status of this problem for compressible flows.

  19. Advancements in engineering turbulence modeling

    NASA Technical Reports Server (NTRS)

    Shih, T.-H.

    1991-01-01

    Some new developments in two-equation models and second order closure models are presented. Two-equation models (k-epsilon models) have been widely used in computational fluid dynamics (CFD) for engineering problems. Most of low-Reynolds number two-equation models contain some wall-distance damping functions to account for the effect of wall on turbulence. However, this often causes the confusion and difficulties in computing flows with complex geometry and also needs an ad hoc treatment near the separation and reattachment points. A set of modified two-equation models is proposed to remove the aforementioned shortcomings. The calculations using various two-equation models are compared with direct numerical simulations of channel flow and flat boundary layers. Development of a second order closure model is also discussed with emphasis on the modeling of pressure related correlation terms and dissipation rates in the second moment equations. All the existing models poorly predict the normal stresses near the wall and fail to predict the 3-D effect of mean flow on the turbulence (e.g. decrease in the shear stress caused by the cross flow in the boundary layer). The newly developed second order near-wall turbulence model is described and is capable of capturing the near-wall behavior of turbulence as well as the effect of 3-D mean flow on the turbulence.

  20. Structure and modeling of turbulence

    SciTech Connect

    Novikov, E.A.

    1995-12-31

    The {open_quotes}vortex strings{close_quotes} scale l{sub s} {approximately} LRe{sup -3/10} (L-external scale, Re - Reynolds number) is suggested as a grid scale for the large-eddy simulation. Various aspects of the structure of turbulence and subgrid modeling are described in terms of conditional averaging, Markov processes with dependent increments and infinitely divisible distributions. The major request from the energy, naval, aerospace and environmental engineering communities to the theory of turbulence is to reduce the enormous number of degrees of freedom in turbulent flows to a level manageable by computer simulations. The vast majority of these degrees of freedom is in the small-scale motion. The study of the structure of turbulence provides a basis for subgrid-scale (SGS) models, which are necessary for the large-eddy simulations (LES).

  1. Turbulence modeling in aircraft icing

    NASA Technical Reports Server (NTRS)

    Potapczuk, Mark G.

    1993-01-01

    The Icing and Cryogenic Technology Branch develops computational tools which predict ice growth on aircraft surfaces and uses existing CFD technology to evaluate the aerodynamic changes associated with such accretions. Surface roughness, transition location, and laminar, transition, or turbulent convective heat transfer all influence the ice growth process on aircraft surfaces. Turbulence modeling is a critical element within the computational tools used for both ice shape prediction and for performance degradation evaluation.

  2. Modeling of Turbulent Swirling Flows

    NASA Technical Reports Server (NTRS)

    Shih, Tsan-Hsing; Zhu, Jiang; Liou, William; Chen, Kuo-Huey; Liu, Nan-Suey; Lumley, John L.

    1997-01-01

    Aircraft engine combustors generally involve turbulent swirling flows in order to enhance fuel-air mixing and flame stabilization. It has long been recognized that eddy viscosity turbulence models are unable to appropriately model swirling flows. Therefore, it has been suggested that, for the modeling of these flows, a second order closure scheme should be considered because of its ability in the modeling of rotational and curvature effects. However, this scheme will require solution of many complicated second moment transport equations (six Reynolds stresses plus other scalar fluxes and variances), which is a difficult task for any CFD implementations. Also, this scheme will require a large amount of computer resources for a general combustor swirling flow. This report is devoted to the development of a cubic Reynolds stress-strain model for turbulent swirling flows, and was inspired by the work of Launder's group at UMIST. Using this type of model, one only needs to solve two turbulence equations, one for the turbulent kinetic energy k and the other for the dissipation rate epsilon. The cubic model developed in this report is based on a general Reynolds stress-strain relationship. Two flows have been chosen for model evaluation. One is a fully developed rotating pipe flow, and the other is a more complex flow with swirl and recirculation.

  3. PDF turbulence modeling and DNS

    NASA Technical Reports Server (NTRS)

    Hsu, A. T.

    1992-01-01

    The problem of time discontinuity (or jump condition) in the coalescence/dispersion (C/D) mixing model is addressed in probability density function (pdf). A C/D mixing model continuous in time is introduced. With the continuous mixing model, the process of chemical reaction can be fully coupled with mixing. In the case of homogeneous turbulence decay, the new model predicts a pdf very close to a Gaussian distribution, with finite higher moments also close to that of a Gaussian distribution. Results from the continuous mixing model are compared with both experimental data and numerical results from conventional C/D models. The effect of Coriolis forces on compressible homogeneous turbulence is studied using direct numerical simulation (DNS). The numerical method used in this study is an eight order compact difference scheme. Contrary to the conclusions reached by previous DNS studies on incompressible isotropic turbulence, the present results show that the Coriolis force increases the dissipation rate of turbulent kinetic energy, and that anisotropy develops as the Coriolis force increases. The Taylor-Proudman theory does apply since the derivatives in the direction of the rotation axis vanishes rapidly. A closer analysis reveals that the dissipation rate of the incompressible component of the turbulent kinetic energy indeed decreases with a higher rotation rate, consistent with incompressible flow simulations (Bardina), while the dissipation rate of the compressible part increases; the net gain is positive. Inertial waves are observed in the simulation results.

  4. Predicting NonInertial Effects with Algebraic Stress Models which Account for Dissipation Rate Anisotropies

    NASA Technical Reports Server (NTRS)

    Jongen, T.; Machiels, L.; Gatski, T. B.

    1997-01-01

    Three types of turbulence models which account for rotational effects in noninertial frames of reference are evaluated for the case of incompressible, fully developed rotating turbulent channel flow. The different types of models are a Coriolis-modified eddy-viscosity model, a realizable algebraic stress model, and an algebraic stress model which accounts for dissipation rate anisotropies. A direct numerical simulation of a rotating channel flow is used for the turbulent model validation. This simulation differs from previous studies in that significantly higher rotation numbers are investigated. Flows at these higher rotation numbers are characterized by a relaminarization on the cyclonic or suction side of the channel, and a linear velocity profile on the anticyclonic or pressure side of the channel. The predictive performance of the three types of models are examined in detail, and formulation deficiencies are identified which cause poor predictive performance for some of the models. Criteria are identified which allow for accurate prediction of such flows by algebraic stress models and their corresponding Reynolds stress formulations.

  5. Some practical turbulence modeling options for Reynolds-averaged full Navier-Stokes calculations of three-dimensional flows

    NASA Technical Reports Server (NTRS)

    Bui, Trong T.

    1993-01-01

    New turbulence modeling options recently implemented for the 3-D version of Proteus, a Reynolds-averaged compressible Navier-Stokes code, are described. The implemented turbulence models include: the Baldwin-Lomax algebraic model, the Baldwin-Barth one-equation model, the Chien k-epsilon model, and the Launder-Sharma k-epsilon model. Features of this turbulence modeling package include: well documented and easy to use turbulence modeling options, uniform integration of turbulence models from different classes, automatic initialization of turbulence variables for calculations using one- or two-equation turbulence models, multiple solid boundaries treatment, and fully vectorized L-U solver for one- and two-equation models. Validation test cases include the incompressible and compressible flat plate turbulent boundary layers, turbulent developing S-duct flow, and glancing shock wave/turbulent boundary layer interaction. Good agreement is obtained between the computational results and experimental data. Sensitivity of the compressible turbulent solutions with the method of y(sup +) computation, the turbulent length scale correction, and some compressibility corrections are examined in detail. The test cases show that the highly optimized one-and two-equation turbulence models can be used in routine 3-D Navier-Stokes computations with no significant increase in CPU time as compared with the Baldwin-Lomax algebraic model.

  6. Computation of confined coflow jets with three turbulence models

    NASA Technical Reports Server (NTRS)

    Zhu, J.; Shih, T. H.

    1993-01-01

    A numerical study of confined jets in a cylindrical duct is carried out to examine the performance of two recently proposed turbulence models: an RNG-based K-epsilon model and a realizable Reynolds stress algebraic equation model. The former is of the same form as the standard K-epsilon model but has different model coefficients. The latter uses an explicit quadratic stress-strain relationship to model the turbulent stresses and is capable of ensuring the positivity of each turbulent normal stress. The flow considered involves recirculation with unfixed separation and reattachment points and severe adverse pressure gradients, thereby providing a valuable test of the predictive capability of the models for complex flows. Calculations are performed with a finite-volume procedure. Numerical credibility of the solutions is ensured by using second-order accurate differencing schemes and sufficiently fine grids. Calculations with the standard K-epsilon model are also made for comparison. Detailed comparisons with experiments show that the realizable Reynolds stress algebraic equation model consistently works better than does the standard K-epsilon model in capturing the essential flow features, while the RNG-based K-epsilon model does not seem to give improvements over the standard K-epsilon model under the flow conditions considered.

  7. Computation of confined coflow jets with three turbulence models

    NASA Astrophysics Data System (ADS)

    Zhu, J.; Shih, T. H.

    1993-07-01

    A numerical study of confined jets in a cylindrical duct is carried out to examine the performance of two recently proposed turbulence models: an RNG-based K-epsilon model and a realizable Reynolds stress algebraic equation model. The former is of the same form as the standard K-epsilon model but has different model coefficients. The latter uses an explicit quadratic stress-strain relationship to model the turbulent stresses and is capable of ensuring the positivity of each turbulent normal stress. The flow considered involves recirculation with unfixed separation and reattachment points and severe adverse pressure gradients, thereby providing a valuable test of the predictive capability of the models for complex flows. Calculations are performed with a finite-volume procedure. Numerical credibility of the solutions is ensured by using second-order accurate differencing schemes and sufficiently fine grids. Calculations with the standard K-epsilon model are also made for comparison. Detailed comparisons with experiments show that the realizable Reynolds stress algebraic equation model consistently works better than does the standard K-epsilon model in capturing the essential flow features, while the RNG-based K-epsilon model does not seem to give improvements over the standard K-epsilon model under the flow conditions considered.

  8. Multi-Matrix Models and Noncommutative Frobenius Algebras Obtained from Symmetric Groups and Brauer Algebras

    NASA Astrophysics Data System (ADS)

    Kimura, Yusuke

    2015-07-01

    It has been understood that correlation functions of multi-trace operators in SYM can be neatly computed using the group algebra of symmetric groups or walled Brauer algebras. On the other hand, such algebras have been known to construct 2D topological field theories (TFTs). After reviewing the construction of 2D TFTs based on symmetric groups, we construct 2D TFTs based on walled Brauer algebras. In the construction, the introduction of a dual basis manifests a similarity between the two theories. We next construct a class of 2D field theories whose physical operators have the same symmetry as multi-trace operators constructed from some matrices. Such field theories correspond to non-commutative Frobenius algebras. A matrix structure arises as a consequence of the noncommutativity. Correlation functions of the Gaussian complex multi-matrix models can be translated into correlation functions of the two-dimensional field theories.

  9. Turbulence Modeling for Unsteady Transonic Flows

    NASA Technical Reports Server (NTRS)

    Marvin, J. G.; Levy, L. L., Jr.; Seegmiller, H. L.

    1980-01-01

    Conditionally sampled, ensemble-averaged velocity measurements, made with a laser velocimeter, were taken in the flowfield over the rear half of an 18% thick circular arc airfoil at zero incidence tested at M = 0.76 and at a Reynolds number based on chord of 11 x 10(exp 6). Data for one cycle of periodic unsteady flow having a reduced frequency f of 0.49 are analyzed. A series of compression waves, which develop in the early stages of the cycle, strengthen and coalesce into a strong shock wave that moves toward the airfoil leading edge. A thick shear layer forms downstream of the shock wave. The kinetic energy and shear stresses increase dramatically, reach a maximum when dissipation and diffusion of the turbulence exceed production, and then decrease substantially. The response lime of the turbulence to the changes brought about by the shock-wave passage upstream depends on the shock-wave strength and position in the boundary layer. The cycle completes itself when the shock wave passes the midchord, weakens, and the shear layer collapses. Remarkably good comparisons are found with computations that employ the time-dependent Reynolds averaged form of the Navier-Stokes equations using an algebraic eddy viscosity model, developed for steady flows.

  10. Turbulence Modeling and Computation of Turbine Aerodynamics and Heat Transfer

    NASA Technical Reports Server (NTRS)

    Lakshminarayana, B.; Luo, J.

    1996-01-01

    The objective of the present research is to develop improved turbulence models for the computation of complex flows through turbomachinery passages, including the effects of streamline curvature, heat transfer and secondary flows. Advanced turbulence models are crucial for accurate prediction of rocket engine flows, due to existance of very large extra strain rates, such as strong streamline curvature. Numerical simulation of the turbulent flows in strongly curved ducts, including two 180-deg ducts, one 90-deg duct and a strongly concave curved turbulent boundary layer have been carried out with Reynolds stress models (RSM) and algebraic Reynolds stress models (ARSM). An improved near-wall pressure-strain correlation has been developed for capturing the anisotropy of turbulence in the concave region. A comparative study of two modes of transition in gas turbine, the by-pass transition and the separation-induced transition, has been carried out with several representative low-Reynolds number (LRN) k-epsilon models. Effects of blade surface pressure gradient, freestream turbulence and Reynolds number on the blade boundary layer development, and particularly the inception of transition are examined in detail. The present study indicates that the turbine blade transition, in the presence of high freestream turbulence, is predicted well with LRN k-epsilon models employed. The three-dimensional Navier-Stokes procedure developed by the present authors has been used to compute the three-dimensional viscous flow through the turbine nozzle passage of a single stage turbine. A low Reynolds number k-epsilon model and a zonal k-epsilon/ARSM (algebraic Reynolds stress model) are utilized for turbulence closure. An assessment of the performance of the turbulence models has been carried out. The two models are found to provide similar predictions for the mean flow parameters, although slight improvement in the prediction of some secondary flow quantities has been obtained by the

  11. Models for Turbulent Transport Processes.

    ERIC Educational Resources Information Center

    Hill, James C.

    1979-01-01

    Since the statistical theories of turbulence that have developed over the last twenty or thirty years are too abstract and unreliable to be of much use to chemical engineers, this paper introduces the techniques of single point models and suggests some areas of needed research. (BB)

  12. Transonic Turbulent Flow Predictions With Two-Equation Turbulence Models

    NASA Technical Reports Server (NTRS)

    Liou, William W.; Shih, Tsan-Hsing

    1996-01-01

    Solutions of the Favre-averaged Navier-Stokes equations for two well-documented transonic turbulent flows are compared in detail with existing experimental data. While the boundary layer in the first case remains attached, a region of extensive flow separation has been observed in the second case. Two recently developed k-epsilon, two-equation, eddy-viscosity models are used to model the turbulence field. These models satisfy the realizability constraints of the Reynolds stresses. Comparisons with the measurements are made for the wall pressure distribution, the mean streamwise velocity profiles, and turbulent quantities. Reasonably good agreement is obtained with the experimental data.

  13. Turbulence modeling for hypersonic flight

    NASA Technical Reports Server (NTRS)

    Bardina, Jorge E.

    1993-01-01

    The objective of the proposed work is to continue to develop, verify, and incorporate the baseline two-equation turbulence models, which account for the effects of compressibility at high speeds, into a three-dimensional Reynolds averaged Navier-Stokes (RANS) code. Additionally, we plan to provide documented descriptions of the models and their numerical procedures so that they can be implemented into the NASP CFD codes.

  14. Multifractal model for heliospheric turbulence

    NASA Astrophysics Data System (ADS)

    Szczepaniak, Anna

    Multifractal characteristics and models for astrophysical plasma at different regions of heliosphere are considered. We analyze the time series of the solar wind parameters measured in situby Helios 2 (0.3-1 AU), ACE (1 AU), and Voyager 2 (1-75 AU) spacecrafts [1]. We focus on the intermittent nature of the cascading eddies for solar wind turbulence. To look at intermittency we construct the multifractal measure describing energy transfer rate and we analyze its scaling properties [2,3]. This allows us to obtain generalized dimensions and multifractality spectra for different state of the solar wind depending on heliocentric distance and solar activity cycle. We also propose a generalization of the usual p-model [2] for the case when the turbulent cascade involves eddies of different sizes. Our model has two scaling parameters and a probability measure parameter allowing to decribe more intermittent data [4,5]. We compare the resulting generalized dimensions and singularity spectra for the solar wind with that for the generalized p-model. In this way we obtain a much better agreement with the solar wind data. Hence we hope that our model will be a useful tool to study complex nature of intermittent turbulence. [1] Burlaga, L. F.: Multifractal structure of the interplanetary magnetic field: Voyager 2 observations near 25 AU, 1987-1988, Geophys. Res. Lett. 18, 69-72, 1991. [2] Meneveau, C., and Sreenivasan, K. R.: Simple multifractal cascade model for fully developed turbulence, Phys. Rev. Lett. 59, 1424-1427, 1987. [3] Marsch, E., Tu, C.-Y., and Rosenbauer, H.: Multifractal scaling of the kinetic energy flux in solar wind turbulence, Ann. Geophys. 14, 259-269, 1996. [4] Macek, W. M. : Multifractality and intermittency in the solar wind, Nonlinear Proc. Geophys., 14, 695-700, 2007. [5] Macek, W. M., and Szczepaniak, A.: Generalized two-scale weighted Cantor set model for solar wind turbulence, Geophys. Res. Lett. 35, L02108, doi:10.1029/2007GL032263, 2008.

  15. A stochastic extension of the explicit algebraic subgrid-scale models

    SciTech Connect

    Rasam, A. Brethouwer, G.; Johansson, A. V.

    2014-05-15

    The explicit algebraic subgrid-scale (SGS) stress model (EASM) of Marstorp et al. [“Explicit algebraic subgrid stress models with application to rotating channel flow,” J. Fluid Mech. 639, 403–432 (2009)] and explicit algebraic SGS scalar flux model (EASFM) of Rasam et al. [“An explicit algebraic model for the subgrid-scale passive scalar flux,” J. Fluid Mech. 721, 541–577 (2013)] are extended with stochastic terms based on the Langevin equation formalism for the subgrid-scales by Marstorp et al. [“A stochastic subgrid model with application to turbulent flow and scalar mixing,” Phys. Fluids 19, 035107 (2007)]. The EASM and EASFM are nonlinear mixed and tensor eddy-diffusivity models, which improve large eddy simulation (LES) predictions of the mean flow, Reynolds stresses, and scalar fluxes of wall-bounded flows compared to isotropic eddy-viscosity and eddy-diffusivity SGS models, especially at coarse resolutions. The purpose of the stochastic extension of the explicit algebraic SGS models is to further improve the characteristics of the kinetic energy and scalar variance SGS dissipation, which are key quantities that govern the small-scale mixing and dispersion dynamics. LES of turbulent channel flow with passive scalar transport shows that the stochastic terms enhance SGS dissipation statistics such as length scale, variance, and probability density functions and introduce a significant amount of backscatter of energy from the subgrid to the resolved scales without causing numerical stability problems. The improvements in the SGS dissipation predictions in turn enhances the predicted resolved statistics such as the mean scalar, scalar fluxes, Reynolds stresses, and correlation lengths. Moreover, the nonalignment between the SGS stress and resolved strain-rate tensors predicted by the EASM with stochastic extension is in much closer agreement with direct numerical simulation data.

  16. A spatial operator algebra for manipulator modeling and control

    NASA Technical Reports Server (NTRS)

    Rodriguez, G.; Jain, A.; Kreutz-Delgado, K.

    1991-01-01

    A recently developed spatial operator algebra for manipulator modeling, control, and trajectory design is discussed. The elements of this algebra are linear operators whose domain and range spaces consist of forces, moments, velocities, and accelerations. The effect of these operators is equivalent to a spatial recursion along the span of a manipulator. Inversion of operators can be efficiently obtained via techniques of recursive filtering and smoothing. The operator algebra provides a high-level framework for describing the dynamic and kinematic behavior of a manipulator and for control and trajectory design algorithms. The interpretation of expressions within the algebraic framework leads to enhanced conceptual and physical understanding of manipulator dynamics and kinematics.

  17. Finite element solution of axial turbulent flow in a bare rod bundle using a one-equation turbulence model

    SciTech Connect

    Slagter, W.

    1982-11-01

    A new form of the one-equation turbulence model has been developed and verified by application to fully developed turbulent flow in smooth, bare rod bundles. The present model allows for the effect of anisotropic eddy viscosities on turbulent flow quantities. The finite element method has been used to predict local values of velocity and turbulent kinetic energy right up to the wall. A variational principle is applied to develop the finite element relationships. The resulting set of nonlinear algebraic equations for the nodal parameters is linearized by the successive-substitution scheme and solved by the frontal solution technique. The numerical results are shown to be in good agreement with available experimental data.

  18. Preparing Secondary Mathematics Teachers: A Focus on Modeling in Algebra

    ERIC Educational Resources Information Center

    Jung, Hyunyi; Mintos, Alexia; Newton, Jill

    2015-01-01

    This study addressed the opportunities to learn (OTL) modeling in algebra provided to secondary mathematics pre-service teachers (PSTs). To investigate these OTL, we interviewed five instructors of required mathematics and mathematics education courses that had the potential to include opportunities for PSTs to learn algebra at three universities.…

  19. Turbulence modelling of flow fields in thrust chambers

    NASA Technical Reports Server (NTRS)

    Chen, C. P.; Kim, Y. M.; Shang, H. M.

    1993-01-01

    Following the consensus of a workshop in Turbulence Modelling for Liquid Rocket Thrust Chambers, the current effort was undertaken to study the effects of second-order closure on the predictions of thermochemical flow fields. To reduce the instability and computational intensity of the full second-order Reynolds Stress Model, an Algebraic Stress Model (ASM) coupled with a two-layer near wall treatment was developed. Various test problems, including the compressible boundary layer with adiabatic and cooled walls, recirculating flows, swirling flows, and the entire SSME nozzle flow were studied to assess the performance of the current model. Detailed calculations for the SSME exit wall flow around the nozzle manifold were executed. As to the overall flow predictions, the ASM removes another assumption for appropriate comparison with experimental data to account for the non-isotropic turbulence effects.

  20. Turbulence modelling of flow fields in thrust chambers

    NASA Astrophysics Data System (ADS)

    Chen, C. P.; Kim, Y. M.; Shang, H. M.

    1993-02-01

    Following the consensus of a workshop in Turbulence Modelling for Liquid Rocket Thrust Chambers, the current effort was undertaken to study the effects of second-order closure on the predictions of thermochemical flow fields. To reduce the instability and computational intensity of the full second-order Reynolds Stress Model, an Algebraic Stress Model (ASM) coupled with a two-layer near wall treatment was developed. Various test problems, including the compressible boundary layer with adiabatic and cooled walls, recirculating flows, swirling flows, and the entire SSME nozzle flow were studied to assess the performance of the current model. Detailed calculations for the SSME exit wall flow around the nozzle manifold were executed. As to the overall flow predictions, the ASM removes another assumption for appropriate comparison with experimental data to account for the non-isotropic turbulence effects.

  1. Some practical turbulence modeling options for Reynolds-averaged full Navier-Stokes calculations of three-dimensional flows

    NASA Technical Reports Server (NTRS)

    Bui, Trong T.

    1993-01-01

    New turbulence modeling options recently implemented for the 3D version of Proteus, a Reynolds-averaged compressible Navier-Stokes code, are described. The implemented turbulence models include: the Baldwin-Lomax algebraic model, the Baldwin-Barth one-equation model, the Chien k-epsilon model, and the Launder-Sharma k-epsilon model. Features of this turbulence modeling package include: well documented and easy to use turbulence modeling options, uniform integration of turbulence models from different classes, automatic initialization of turbulence variables for calculations using one- or two-equation turbulence models, multiple solid boundaries treatment, and fully vectorized L-U solver for one- and two-equation models. Good agreements are obtained between the computational results and experimental data. Sensitivity of the compressible turbulent solutions with the method of y(+) computation, the turbulent length scale correction, and some compressibility corrections are examined in detail. Test cases show that the highly optimized one- and two-equation turbulence models can be used in routine 3D Navier-Stokes computations with no significant increase in CPU time as compared with the Baldwin-Lomax algebraic model.

  2. Study Of Compressibility Corrections To Turbulence Models

    NASA Technical Reports Server (NTRS)

    Viegas, J. R.; Rubesin, M. W.

    1993-01-01

    Effects on shear layers in simulated confined and unconfined flows studied. Report presents comparative study of some terms that correct for effects of compressibility in standard k-epsilon mathematical model of turbulence where k denotes turbulence kinetic energy and epsilon denotes rate of dissipation of turbulence kenetic energy. Involved simulation of flows by numerical solution of Reynolds-averaged Navier-Stokes equations.

  3. Center for modeling of turbulence and transition: Research briefs, 1993

    NASA Technical Reports Server (NTRS)

    Liou, William W. (Editor)

    1994-01-01

    This research brief contains the progress reports of the research staff of the Center for Modeling of Turbulence and Transition (CMOTT) from June 1992 to July 1993. It is also an annual report to the Institute for Computational Mechanics in Propulsion located at Ohio Aerospace Institute and NASA Lewis Research Center. The main objectives of the research activities at CMOTT are to develop, validate, and implement turbulence and transition models for flows of interest in propulsion systems. Currently, our research covers eddy viscosity one- and two-equation models, Reynolds-stress algebraic equation models, Reynolds-stress transport equation models, nonequilibrium multiple-scale models, bypass transition models, joint scalar probability density function models, and Renormalization Group Theory and Direct Interaction Approximation methods. Some numerical simulations (LES and DNS) have also been carried out to support the development of turbulence modeling. Last year was CMOTT's third year in operation. During this period, in addition to the above mentioned research, CMOTT has also hosted the following programs: an eighteen-hour short course on 'Turbulence--Fundamentals and Computational Modeling (Part I)' given by CMOTT at the NASA Lewis Research Center; a productive summer visitor research program that has generated many encouraging results; collaborative programs with industry customers to help improve their turbulent flow calculations for propulsion system designs; a biweekly CMOTT seminar series with speakers from within and without the NASA Lewis Research Center including foreign speakers. In addition, CMOTT members have been actively involved in the national and international turbulence research activities. The current CMOTT roster and organization are listed in Appendix A. Listed in Appendix B are the abstracts of the biweekly CMOTT seminar. Appendix C lists the papers contributed by CMOTT members.

  4. The applicability of turbulence models to aerodynamic and propulsion flowfields at McDonnell-Douglas Aerospace

    NASA Technical Reports Server (NTRS)

    Kral, Linda D.; Ladd, John A.; Mani, Mori

    1995-01-01

    The objective of this viewgraph presentation is to evaluate turbulence models for integrated aircraft components such as the forebody, wing, inlet, diffuser, nozzle, and afterbody. The one-equation models have replaced the algebraic models as the baseline turbulence models. The Spalart-Allmaras one-equation model consistently performs better than the Baldwin-Barth model, particularly in the log-layer and free shear layers. Also, the Sparlart-Allmaras model is not grid dependent like the Baldwin-Barth model. No general turbulence model exists for all engineering applications. The Spalart-Allmaras one-equation model and the Chien k-epsilon models are the preferred turbulence models. Although the two-equation models often better predict the flow field, they may take from two to five times the CPU time. Future directions are in further benchmarking the Menter blended k-w/k-epsilon and algorithmic improvements to reduce CPU time of the two-equation model.

  5. On the modeling of low-Reynolds-number turbulence

    NASA Technical Reports Server (NTRS)

    So, R. M. C.; Yoo, G. J.

    1986-01-01

    A full Reynolds-stress closure that is capable of describing the flow all the way to the wall was formulated for turbulent flow through circular pipe. Since viscosity does not appear explicitly in the pressure redistribution terms, conventional high-number models for these terms are found to be applicable. However, the models for turbulent diffusion and viscous dissipation have to be modified to account for viscous diffusion near a wall. Two redistribution and two diffusion models are investigated for their effects on the model calculations. Wall correction to pressure redistribution modeling is also examined. Diffusion effects on calculated turbulent properties are further investigated by simplifying the transport equations to algebraic equations for Reynolds stress. Two approximations are explored. These are the equilibrium and nonequilibrium turbulence assumptions. Finally, the two-equation closure is also used to calculate the flow in question and the results compared with all the other model calculations. Fully developed pipe flows at two moderate Reynolds numbers are used to validate these model calculations.

  6. Action Algebras and Model Algebras in Denotational Semantics

    NASA Astrophysics Data System (ADS)

    Guedes, Luiz Carlos Castro; Haeusler, Edward Hermann

    This article describes some results concerning the conceptual separation of model dependent and language inherent aspects in a denotational semantics of a programming language. Before going into the technical explanation, the authors wish to relate a story that illustrates how correctly and precisely posed questions can influence the direction of research. By means of his questions, Professor Mosses aided the PhD research of one of the authors of this article and taught the other, who at the time was a novice supervisor, the real meaning of careful PhD supervision. The student’s research had been partially developed towards the implementation of programming languages through denotational semantics specification, and the student had developed a prototype [12] that compared relatively well to some industrial compilers of the PASCAL language. During a visit to the BRICS lab in Aarhus, the student’s supervisor gave Professor Mosses a draft of an article describing the prototype and its implementation experiments. The next day, Professor Mosses asked the supervisor, “Why is the generated code so efficient when compared to that generated by an industrial compiler?” and “You claim that the efficiency is simply a consequence of the Object- Orientation mechanisms used by the prototype programming language (C++); this should be better investigated. Pay more attention to the class of programs that might have this good comparison profile.” As a result of these aptly chosen questions and comments, the student and supervisor made great strides in the subsequent research; the advice provided by Professor Mosses made them perceive that the code generated for certain semantic domains was efficient because it mapped to the “right aspect” of the language semantics. (Certain functional types, used to represent mappings such as Stores and Environments, were pushed to the level of the object language (as in gcc). This had the side-effect of generating

  7. Experience with turbulence interaction and turbulence-chemistry models at Fluent Inc.

    NASA Technical Reports Server (NTRS)

    Choudhury, D.; Kim, S. E.; Tselepidakis, D. P.; Missaghi, M.

    1995-01-01

    This viewgraph presentation discusses (1) turbulence modeling: challenges in turbulence modeling, desirable attributes of turbulence models, turbulence models in FLUENT, and examples using FLUENT; and (2) combustion modeling: turbulence-chemistry interaction and FLUENT equilibrium model. As of now, three turbulence models are provided: the conventional k-epsilon model, the renormalization group model, and the Reynolds-stress model. The renormalization group k-epsilon model has broadened the range of applicability of two-equation turbulence models. The Reynolds-stress model has proved useful for strongly anisotropic flows such as those encountered in cyclones, swirlers, and combustors. Issues remain, such as near-wall closure, with all classes of models.

  8. On the validation of a code and a turbulence model appropriate to circulation control airfoils

    NASA Technical Reports Server (NTRS)

    Viegas, J. R.; Rubesin, M. W.; Maccormack, R. W.

    1988-01-01

    A computer code for calculating flow about a circulation control airfoil within a wind tunnel test section has been developed. This code is being validated for eventual use as an aid to design such airfoils. The concept of code validation being used is explained. The initial stages of the process have been accomplished. The present code has been applied to a low-subsonic, 2-D flow about a circulation control airfoil for which extensive data exist. Two basic turbulence models and variants thereof have been successfully introduced into the algorithm, the Baldwin-Lomax algebraic and the Jones-Launder two-equation models of turbulence. The variants include adding a history of the jet development for the algebraic model and adding streamwise curvature effects for both models. Numerical difficulties and difficulties in the validation process are discussed. Turbulence model and code improvements to proceed with the validation process are also discussed.

  9. Fully-Explicit and Self-Consistent Algebraic Reynolds Stress Models

    NASA Technical Reports Server (NTRS)

    Girimaji, Sharath S.

    1995-01-01

    A fully-explicit, self-consistent algebraic expression for the Reynolds stress, which is the exact solution to the Reynolds stress transport equation in the 'weak equilibrium' limit for two-dimensional mean flows for all linear and some quasi-linear pressure-strain models, is derived. Current explicit algebraic Reynolds stress models derived by employing the 'weak equilibrium' assumption treat the production-to-dissipation (P/epsilon) ratio implicitly, resulting in an effective viscosity that can be singular away from the equilibrium limit. In the present paper, the set of simultaneous algebraic Reynolds stress equations are solved in the full non-linear form and the eddy viscosity is found to be non-singular. Preliminary tests indicate that the model performs adequately, even for three dimensional mean flow cases. Due to the explicit and non-singular nature of the effective viscosity, this model should mitigate many of the difficulties encountered in computing complex turbulent flows with the algebraic Reynolds stress models.

  10. New Atmospheric Turbulence Model for Shuttle Applications

    NASA Technical Reports Server (NTRS)

    Justus, C. G.; Campbell, C. W.; Doubleday, M. K.; Johnson, D. L.

    1990-01-01

    An updated NASA atmospheric turbulence model, from 0 to 200 km altitude, which was developed to be more realistic and less conservative when applied to space shuttle reentry engineering simulation studies involving control system fuel expenditures is presented. The prior model used extreme turbulence (3 sigma) for all altitudes, whereas in reality severe turbulence is patchy within quiescent atmospheric zones. The updated turublence model presented is designed to be more realistic. The prior turbulence statistics (sigma and L) were updated and were modeled accordingly.

  11. Research activities at the Center for Modeling of Turbulence and Transition

    NASA Technical Reports Server (NTRS)

    Shih, Tsan-Hsing

    1993-01-01

    The main research activities at the Center for Modeling of Turbulence and Transition (CMOTT) are described. The research objective of CMOTT is to improve and/or develop turbulence and transition models for propulsion systems. The flows of interest in propulsion systems can be both compressible and incompressible, three dimensional, bounded by complex wall geometries, chemically reacting, and involve 'bypass' transition. The most relevant turbulence and transition models for the above flows are one- and two-equation eddy viscosity models, Reynolds stress algebraic- and transport-equation models, pdf models, and multiple-scale models. All these models are classified as one-point closure schemes since only one-point (in time and space) turbulent correlations, such as second moments (Reynolds stresses and turbulent heat fluxes) and third moments, are involved. In computational fluid dynamics, all turbulent quantities are one-point correlations. Therefore, the study of one-point turbulent closure schemes is the focus of our turbulence research. However, other research, such as the renormalization group theory, the direct interaction approximation method, and numerical simulations are also pursued to support the development of turbulence modeling.

  12. Development of an algebraic stress/two-layer model for calculating thrust chamber flow fields

    NASA Technical Reports Server (NTRS)

    Chen, C. P.; Shang, H. M.; Huang, J.

    1993-01-01

    Following the consensus of a workshop in Turbulence Modeling for Liquid Rocket Thrust Chambers, the current effort was undertaken to study the effects of second-order closure on the predictions of thermochemical flow fields. To reduce the instability and computational intensity of the full second-order Reynolds Stress Model, an Algebraic Stress Model (ASM) coupled with a two-layer near wall treatment was developed. Various test problems, including the compressible boundary layer with adiabatic and cooled walls, recirculating flows, swirling flows and the entire SSME nozzle flow were studied to assess the performance of the current model. Detailed calculations for the SSME exit wall flow around the nozzle manifold were executed. As to the overall flow predictions, the ASM removes another assumption for appropriate comparison with experimental data, to account for the non-isotropic turbulence effects.

  13. Development of an algebraic stress/two-layer model for calculating thrust chamber flow fields

    NASA Astrophysics Data System (ADS)

    Chen, C. P.; Shang, H. M.; Huang, J.

    1993-07-01

    Following the consensus of a workshop in Turbulence Modeling for Liquid Rocket Thrust Chambers, the current effort was undertaken to study the effects of second-order closure on the predictions of thermochemical flow fields. To reduce the instability and computational intensity of the full second-order Reynolds Stress Model, an Algebraic Stress Model (ASM) coupled with a two-layer near wall treatment was developed. Various test problems, including the compressible boundary layer with adiabatic and cooled walls, recirculating flows, swirling flows and the entire SSME nozzle flow were studied to assess the performance of the current model. Detailed calculations for the SSME exit wall flow around the nozzle manifold were executed. As to the overall flow predictions, the ASM removes another assumption for appropriate comparison with experimental data, to account for the non-isotropic turbulence effects.

  14. Structure and scales in turbulence modeling

    NASA Astrophysics Data System (ADS)

    Reynolds, W. C.; Langer, C. A.; Kassinos, S. C.

    2002-07-01

    The enstrophy of the large-scale energy-containing turbulence is proposed as the second turbulence scale for use, in conjunction with the turbulence energy, in two-scale one-point engineering turbulence models. Its transport equation is developed in general and modeled for homogeneous turbulence in terms of the two scales and our new one-point structure tensors. The model produces the correct behavior of the scales for both two- and three-dimensional turbulence. Constants in the high Reynolds number model are evaluated only by reference to asymptotic analysis for decaying turbulence in stationary and rotating frames, and this model is then shown to provide an excellent prediction of homogeneous turbulent shear flow when used with the structure tensors for that flow. The low Reynolds number constant in the model is evaluated using the asymptotic decay rate for isotropic turbulence at zero Reynolds number, and numerical simulations of decay for intermediate Reynolds numbers are used to establish one remaining constant, the value of which does not affect high Reynolds number predictions.

  15. A multiple-time-scale turbulence model based on variable partitioning of turbulent kinetic energy spectrum

    NASA Technical Reports Server (NTRS)

    Kim, S.-W.; Chen, C.-P.

    1988-01-01

    The paper presents a multiple-time-scale turbulence model of a single point closure and a simplified split-spectrum method. Consideration is given to a class of turbulent boundary layer flows and of separated and/or swirling elliptic turbulent flows. For the separated and/or swirling turbulent flows, the present turbulence model yielded significantly improved computational results over those obtained with the standard k-epsilon turbulence model.

  16. Exploiting similarity in turbulent shear flows for turbulence modeling

    NASA Technical Reports Server (NTRS)

    Robinson, David F.; Harris, Julius E.; Hassan, H. A.

    1992-01-01

    It is well known that current k-epsilon models cannot predict the flow over a flat plate and its wake. In an effort to address this issue and other issues associated with turbulence closure, a new approach for turbulence modeling is proposed which exploits similarities in the flow field. Thus, if we consider the flow over a flat plate and its wake, then in addition to taking advantage of the log-law region, we can exploit the fact that the flow becomes self-similar in the far wake. This latter behavior makes it possible to cast the governing equations as a set of total differential equations. Solutions of this set and comparison with measured shear stress and velocity profiles yields the desired set of model constants. Such a set is, in general, different from other sets of model constants. The rational for such an approach is that if we can correctly model the flow over a flat plate and its far wake, then we can have a better chance of predicting the behavior in between. It is to be noted that the approach does not appeal, in any way, to the decay of homogeneous turbulence. This is because the asymptotic behavior of the flow under consideration is not representative of the decay of homogeneous turbulence.

  17. Single point modeling of rotating turbulent flows

    NASA Technical Reports Server (NTRS)

    Hadid, A. H.; Mansour, N. N.; Zeman, O.

    1994-01-01

    A model for the effects of rotation on turbulence is proposed and tested. These effects which influence mainly the rate of turbulence decay are modeled in a modified turbulent energy dissipation rate equation that has explicit dependence on the mean rotation rate. An appropriate definition of the rotation rate derived from critical point theory and based on the invariants of the deformation tensor is proposed. The modeled dissipation rate equation is numerically well behaved and can be used in conjunction with any level of turbulence closure. The model is applied to the two-equation kappa-epsilon turbulence model and is used to compute separated flows in a backward-facing step and an axisymmetric swirling coaxial jets into a sudden expansion. In general, the rotation modified dissipation rate model shows some improvements over the standard kappa-epsilon model.

  18. Single point modeling of rotating turbulent flows

    NASA Astrophysics Data System (ADS)

    Hadid, A. H.; Mansour, N. N.; Zeman, O.

    1994-12-01

    A model for the effects of rotation on turbulence is proposed and tested. These effects which influence mainly the rate of turbulence decay are modeled in a modified turbulent energy dissipation rate equation that has explicit dependence on the mean rotation rate. An appropriate definition of the rotation rate derived from critical point theory and based on the invariants of the deformation tensor is proposed. The modeled dissipation rate equation is numerically well behaved and can be used in conjunction with any level of turbulence closure. The model is applied to the two-equation kappa-epsilon turbulence model and is used to compute separated flows in a backward-facing step and an axisymmetric swirling coaxial jets into a sudden expansion. In general, the rotation modified dissipation rate model shows some improvements over the standard kappa-epsilon model.

  19. Application of Navier-Stokes code PAB3D with kappa-epsilon turbulence model to attached and separated flows

    NASA Technical Reports Server (NTRS)

    Abdol-Hamid, Khaled S.; Lakshmanan, B.; Carlson, John R.

    1995-01-01

    A three-dimensional Navier-Stokes solver was used to determine how accurately computations can predict local and average skin friction coefficients for attached and separated flows for simple experimental geometries. Algebraic and transport equation closures were used to model turbulence. To simulate anisotropic turbulence, the standard two-equation turbulence model was modified by adding nonlinear terms. The effects of both grid density and the turbulence model on the computed flow fields were also investigated and compared with available experimental data for subsonic and supersonic free-stream conditions.

  20. Approximate Model for Turbulent Stagnation Point Flow.

    SciTech Connect

    Dechant, Lawrence

    2016-01-01

    Here we derive an approximate turbulent self-similar model for a class of favorable pressure gradient wedge-like flows, focusing on the stagnation point limit. While the self-similar model provides a useful gross flow field estimate this approach must be combined with a near wall model is to determine skin friction and by Reynolds analogy the heat transfer coefficient. The combined approach is developed in detail for the stagnation point flow problem where turbulent skin friction and Nusselt number results are obtained. Comparison to the classical Van Driest (1958) result suggests overall reasonable agreement. Though the model is only valid near the stagnation region of cylinders and spheres it nonetheless provides a reasonable model for overall cylinder and sphere heat transfer. The enhancement effect of free stream turbulence upon the laminar flow is used to derive a similar expression which is valid for turbulent flow. Examination of free stream enhanced laminar flow suggests that the rather than enhancement of a laminar flow behavior free stream disturbance results in early transition to turbulent stagnation point behavior. Excellent agreement is shown between enhanced laminar flow and turbulent flow behavior for high levels, e.g. 5% of free stream turbulence. Finally the blunt body turbulent stagnation results are shown to provide realistic heat transfer results for turbulent jet impingement problems.

  1. Wave turbulence in one-dimensional models

    NASA Astrophysics Data System (ADS)

    Zakharov, V. E.; Guyenne, P.; Pushkarev, A. N.; Dias, F.

    2001-05-01

    A two-parameter nonlinear dispersive wave equation proposed by Majda, McLaughlin and Tabak is studied analytically and numerically as a model for the study of wave turbulence in one-dimensional systems. Our ultimate goal is to test the validity of weak turbulence theory. Although weak turbulence theory is independent on the sign of the nonlinearity of the model, the numerical results show a strong dependence on the sign of the nonlinearity. A possible explanation for this discrepancy is the strong influence of coherent structures - wave collapses and quasisolitons - in wave turbulence.

  2. Evaluation of three turbulence models for the prediction of steady and unsteady airloads

    NASA Technical Reports Server (NTRS)

    Wu, Jiunn-Chi; Sankar, L. N.; Huff, Dennis L.

    1989-01-01

    Two dimensional quasi-three dimensional Navier-Stokes solvers were used to predict the static and dynamic airload characteristics of airfoils. The following three turbulence models were used: the Baldwin-Lomax algebraic model, the Johnson-King ODE model for maximum turbulent shear stress, and a two equation k-e model with law-of-the-wall boundary conditions. It was found that in attached flow the three models have good agreement with experimental data. In unsteady separated flows, these models give only a fair correlation with experimental data.

  3. Evaluation of three turbulence models for the prediction of steady and unsteady airloads

    NASA Technical Reports Server (NTRS)

    Wu, Jiunn-Chi; Huff, Dennis L.; Sankar, L. N.

    1988-01-01

    Two dimensional quasi-three dimensional Navier-Stokes solvers were used to predict the static and dynamic airload characteristics of airfoils. The following three turbulence models were used: the Baldwin-Lomax algebraic model, the Johnson-King ODE model for maximum turbulent shear stress, and a two equation k-e model with law-of-the-wall boundary conditions. It was found that in attached flow the three models have good agreement with experimental data. In unsteady separated flows, these models give only a fair correlation with experimental data.

  4. Introduction to Drift Wave Turbulence Modeling

    SciTech Connect

    Garbet, X.

    2004-03-15

    This tutorial presents the techniques that are used to build a transport model from turbulence simulations. Achievements and limitations are reviewed. The main mechanisms leading to an improved confinement are also addressed. The results of turbulence modelling regarding this issue are assessed.

  5. Two-fluid models of turbulence

    NASA Technical Reports Server (NTRS)

    Spalding, D. B.

    1985-01-01

    The defects of turbulence models are summarized and the importance of so-called nongradient diffusion in turbulent fluxes is discussed. The mathematical theory of the flow of two interpenetrating continua is reviewed, and the mathematical formulation of the two fluid model is outlined. Results from plane wake, axisymmetric jet, and combustion studies are shown.

  6. Stochastic models for turbulent reacting flows

    SciTech Connect

    Kerstein, A.

    1993-12-01

    The goal of this program is to develop and apply stochastic models of various processes occurring within turbulent reacting flows in order to identify the fundamental mechanisms governing these flows, to support experimental studies of these flows, and to further the development of comprehensive turbulent reacting flow models.

  7. TURBULENCE MODELING APPLIED TO BUOYANT PLUMES

    EPA Science Inventory

    A viable computer model was developed that is based on second-order closure of the turbulent correlation equations for predicting the fate of nonchemically reacting contaminants released in the atmospheric boundary layer. The invariant turbulence model discussed in previous repor...

  8. A spatial operator algebra for manipulator modeling and control

    NASA Technical Reports Server (NTRS)

    Rodriguez, G.; Kreutz, K.; Milman, M.

    1988-01-01

    A powerful new spatial operator algebra for modeling, control, and trajectory design of manipulators is discussed along with its implementation in the Ada programming language. Applications of this algebra to robotics include an operator representation of the manipulator Jacobian matrix; the robot dynamical equations formulated in terms of the spatial algebra, showing the complete equivalence between the recursive Newton-Euler formulations to robot dynamics; the operator factorization and inversion of the manipulator mass matrix which immediately results in O(N) recursive forward dynamics algorithms; the joint accelerations of a manipulator due to a tip contact force; the recursive computation of the equivalent mass matrix as seen at the tip of a manipulator; and recursive forward dynamics of a closed chain system. Finally, additional applications and current research involving the use of the spatial operator algebra are discussed in general terms.

  9. Turbulence modeling of free shear layers for high-performance aircraft

    NASA Technical Reports Server (NTRS)

    Sondak, Douglas L.

    1993-01-01

    The High Performance Aircraft (HPA) Grand Challenge of the High Performance Computing and Communications (HPCC) program involves the computation of the flow over a high performance aircraft. A variety of free shear layers, including mixing layers over cavities, impinging jets, blown flaps, and exhaust plumes, may be encountered in such flowfields. Since these free shear layers are usually turbulent, appropriate turbulence models must be utilized in computations in order to accurately simulate these flow features. The HPCC program is relying heavily on parallel computers. A Navier-Stokes solver (POVERFLOW) utilizing the Baldwin-Lomax algebraic turbulence model was developed and tested on a 128-node Intel iPSC/860. Algebraic turbulence models run very fast, and give good results for many flowfields. For complex flowfields such as those mentioned above, however, they are often inadequate. It was therefore deemed that a two-equation turbulence model will be required for the HPA computations. The k-epsilon two-equation turbulence model was implemented on the Intel iPSC/860. Both the Chien low-Reynolds-number model and a generalized wall-function formulation were included.

  10. Development and application of a zonal k-epsilon turbulence model for complex 3-D flowfields

    NASA Astrophysics Data System (ADS)

    Ladd, J. A.; Kral, L. D.

    1992-07-01

    A compressible, low Reynolds number two-equation turbulence model is applied to complex engineering problems. An upwind, implicit, factored algorithm with an optional TVD operator is used to solve both the mean-flow equations and the k-epsilon equations for three-dimensional turbulenct flow. A zonal approach is used for solution of both the mean flow variables and the turbulence variables. The zonal method allows complex geometries to be broken down into smaller blocks which are then computed sequentially. Several low Reynolds number k-epsilon models are implemented and validated for a subsonic and supersonic flat plate boundary layer. Calculations using the k-epsilon turbulence model are also presented for an axisymmetric jet plume, a supersonic combusting shear layer, a multislot ejector nozzle, and an F/A-18 forebody at high angle of attack. Comparison of the two-equation turbulence model results is made with results using algebraic turbulence models as well as experimental measurements. The two-equation turbulence model predicts better many of the flowfield characteristics for these complex geometries when compared with the algebraic solutions.

  11. An algebraic cluster model based on the harmonic oscillator basis

    NASA Technical Reports Server (NTRS)

    Levai, Geza; Cseh, J.

    1995-01-01

    We discuss the semimicroscopic algebraic cluster model introduced recently, in which the internal structure of the nuclear clusters is described by the harmonic oscillator shell model, while their relative motion is accounted for by the Vibron model. The algebraic formulation of the model makes extensive use of techniques associated with harmonic oscillators and their symmetry group, SU(3). The model is applied to some cluster systems and is found to reproduce important characteristics of nuclei in the sd-shell region. An approximate SU(3) dynamical symmetry is also found to hold for the C-12 + C-12 system.

  12. Advanced in turbulence physics and modeling by direct numerical simulations

    NASA Technical Reports Server (NTRS)

    Reynolds, W. C.

    1987-01-01

    The advent of direct numerical simulations of turbulence has opened avenues for research on turbulence physics and turbulence modeling. Direct numerical simulation provides values for anything that the scientist or modeler would like to know about the flow. An overview of some recent advances in the physical understanding of turbulence and in turbulence modeling obtained through such simulations is presented.

  13. Center for Modeling of Turbulence and Transition (CMOTT). Research briefs: 1990

    NASA Technical Reports Server (NTRS)

    Povinelli, Louis A. (Compiler); Liou, Meng-Sing (Compiler); Shih, Tsan-Hsing (Compiler)

    1991-01-01

    Brief progress reports of the Center for Modeling of Turbulence and Transition (CMOTT) research staff from May 1990 to May 1991 are given. The objectives of the CMOTT are to develop, validate, and implement the models for turbulence and boundary layer transition in the practical engineering flows. The flows of interest are three dimensional, incompressible, and compressible flows with chemistry. The schemes being studied include the two-equation and algebraic Reynolds stress models, the full Reynolds stress (or second moment closure) models, the probability density function models, the Renormalization Group Theory (RNG) and Interaction Approximation (DIA), the Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS).

  14. Center for Modeling of Turbulence and Transition (CMOTT): Research Briefs, 1992

    NASA Technical Reports Server (NTRS)

    Liou, William W. (Editor)

    1992-01-01

    The progress is reported of the Center for Modeling of Turbulence and Transition (CMOTT). The main objective of the CMOTT is to develop, validate and implement the turbulence and transition models for practical engineering flows. The flows of interest are three-dimensional, incompressible and compressible flows with chemical reaction. The research covers two-equation (e.g., k-e) and algebraic Reynolds-stress models, second moment closure models, probability density function (pdf) models, Renormalization Group Theory (RNG), Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS).

  15. Turbulence Modeling for Shock Wave/Turbulent Boundary Layer Interactions

    NASA Technical Reports Server (NTRS)

    Lillard, Randolph P.

    2011-01-01

    Accurate aerodynamic computational predictions are essential for the safety of space vehicles, but these computations are of limited accuracy when large pressure gradients are present in the flow. The goal of the current project is to improve the state of compressible turbulence modeling for high speed flows with shock wave / turbulent boundary layer interactions (SWTBLI). Emphasis will be placed on models that can accurately predict the separated region caused by the SWTBLI. These flows are classified as nonequilibrium boundary layers because of the very large and variable adverse pressure gradients caused by the shock waves. The lag model was designed to model these nonequilibrium flows by incorporating history effects. Standard one- and two-equation models (Spalart Allmaras and SST) and the lag model will be run and compared to a new lag model. This new model, the Reynolds stress tensor lag model (lagRST), will be assessed against multiple wind tunnel tests and correlations. The basis of the lag and lagRST models are to preserve the accuracy of the standard turbulence models in equilibrium turbulence, when the Reynolds stresses are linearly related to the mean strain rates, but create a lag between mean strain rate effects and turbulence when nonequilibrium effects become important, such as in large pressure gradients. The affect this lag has on the results for SWBLI and massively separated flows will be determined. These computations will be done with a modified version of the OVERFLOW code. This code solves the RANS equations on overset grids. It was used for this study for its ability to input very complex geometries into the flow solver, such as the Space Shuttle in the full stack configuration. The model was successfully implemented within two versions of the OVERFLOW code. Results show a substantial improvement over the baseline models for transonic separated flows. The results are mixed for the SWBLI assessed. Separation predictions are not as good as the

  16. Reduced order modeling of wall turbulence

    NASA Astrophysics Data System (ADS)

    Moin, Parviz

    2015-11-01

    Modeling turbulent flow near a wall is a pacing item in computational fluid dynamics for aerospace applications and geophysical flows. Gradual progress has been made in statistical modeling of near wall turbulence using the Reynolds averaged equations of motion, an area of research where John Lumley has made numerous seminal contributions. More recently, Lumley and co-workers pioneered dynamical systems modeling of near wall turbulence, and demonstrated that the experimentally observed turbulence dynamics can be predicted using low dimensional dynamical systems. The discovery of minimal flow unit provides further evidence that the near wall turbulence is amenable to reduced order modeling. The underlying rationale for potential success in using low dimensional dynamical systems theory is based on the fact that the Reynolds number is low in close proximity to the wall. Presumably for the same reason, low dimensional models are expected to be successful in modeling of the laminar/turbulence transition region. This has been shown recently using dynamic mode decomposition. Furthermore, it is shown that the near wall flow structure and statistics in the late and non-linear transition region is strikingly similar to that in higher Reynolds number fully developed turbulence. In this presentation, I will argue that the accumulated evidence suggests that wall modeling for LES using low dimensional dynamical systems is a profitable avenue to pursue. The main challenge would be the numerical integration of such wall models in LES methodology.

  17. Nonlinear Reynolds stress model for turbulent shear flows

    NASA Technical Reports Server (NTRS)

    Barton, J. Michael; Rubinstein, R.; Kirtley, K. R.

    1991-01-01

    A nonlinear algebraic Reynolds stress model, derived using the renormalization group, is applied to equilibrium homogeneous shear flow and fully developed flow in a square duct. The model, which is quadratically nonlinear in the velocity gradients, successfully captures the large-scale inhomogeneity and anisotropy of the flows studied. The ratios of normal stresses, as well as the actual magnitudes of the stresses are correctly predicted for equilibrium homogeneous shear flow. Reynolds normal stress anisotropy and attendant turbulence driven secondary flow are predicted for a square duct. Profiles of mean velocity and normal stresses are in good agreement with measurements. Very close to walls, agreement with measurements diminishes. The model has the benefit of containing no arbitrary constants; all values are determined directly from the theory. It seems that near wall behavior is influenced by more than the large scale anisotropy accommodated in the current model. More accurate near wall calculations may well require a model for anisotropic dissipation.

  18. A new approach to turbulence modeling

    NASA Technical Reports Server (NTRS)

    Perot, B.; Moin, P.

    1996-01-01

    A new approach to Reynolds averaged turbulence modeling is proposed which has a computational cost comparable to two equation models but a predictive capability approaching that of Reynolds stress transport models. This approach isolates the crucial information contained within the Reynolds stress tensor, and solves transport equations only for a set of 'reduced' variables. In this work, Direct Numerical Simulation (DNS) data is used to analyze the nature of these newly proposed turbulence quantities and the source terms which appear in their respective transport equations. The physical relevance of these quantities is discussed and some initial modeling results for turbulent channel flow are presented.

  19. A critical evaluation of various turbulence models as applied to internal fluid flows

    NASA Technical Reports Server (NTRS)

    Nallasamy, M.

    1985-01-01

    Models employed in the computation of turbulent flows are described and their application to internal flows is evaluated by examining the predictions of various turbulence models in selected flow configurations. The main conclusions are: (1) the k-epsilon model is used in a majority of all the two-dimensional flow calculations reported in the literature; (2) modified forms of the k-epsilon model improve the performance for flows with streamline curvature and heat transfer; (3) for flows with swirl, the k-epsilon model performs rather poorly; the algebraic stress model performs better in this case; and (4) for flows with regions of secondary flow (noncircular duct flows), the algebraic stress model performs fairly well for fully developed flow, for developing flow, the algebraic stress model performance is not good; a Reynolds stress model should be used. False diffusion and inlet boundary conditions are discussed. Countergradient transport and its implications in turbulence modeling is mentioned. Two examples of recirculating flow predictions obtained using PHOENICS code are discussed. The vortex method, large eddy simulation (modeling of subgrid scale Reynolds stresses), and direct simulation, are considered. Some recommendations for improving the model performance are made. The need for detailed experimental data in flows with strong curvature is emphasized.

  20. Turbulence Model Evaluation on a High Pressure Turbine Stage 1 Vane

    NASA Astrophysics Data System (ADS)

    Osusky, Michal; Rostami, Sara; Shabbir, Aamir

    2015-11-01

    The accuracy of turbulence modeling depends heavily on the choice of turbulence model. Many turbulence models are only valid for a narrow range of flow regimes, and can produce numerically converged, but physically inaccurate results when applied outside the scope of their intended use. Additionally, the underlying modeling assumptions, such as the linear Boussinesq approximation, impacts the evolution of turbulence in the flow field. As part of the current work, we will study the impact of using various commonly used RANS turbulence models, such as k-omega, BSL, and SST, with and without transition modeling, on the flow field of realistic engine geometries. Additionally, advanced, non-linear turbulence models, such as the Explicit Algebraic Reynolds Stress Model (EARSM), will also be studied for their potential benefits in capturing additional physics in the simulation. Preliminary results show that the EARSM model has a significant impact on the location on laminar to turbulent transition, versus the SST model. All computational results will be compared against detailed experimental data.

  1. Inverse Modelling Problems in Linear Algebra Undergraduate Courses

    ERIC Educational Resources Information Center

    Martinez-Luaces, Victor E.

    2013-01-01

    This paper will offer an analysis from a theoretical point of view of mathematical modelling, applications and inverse problems of both causation and specification types. Inverse modelling problems give the opportunity to establish connections between theory and practice and to show this fact, a simple linear algebra example in two different…

  2. A Cognitive Model of Experts' Algebraic Solving Methods

    ERIC Educational Resources Information Center

    Cortes, Anibal

    2003-01-01

    We studied experts' solving methods and analyzed the nature of mathematical knowledge as well as their efficiency in algebraic calculations. We constructed a model of the experts cognitive functioning (notably teachers) in which the observed automatisms were modeled in terms of schemes and instruments. Mathematical justification of transformation…

  3. The Effects of the Content Enhancement Model in College Algebra

    ERIC Educational Resources Information Center

    VanCleave, Janet Milleret

    2010-01-01

    The purpose of this study was to investigate The Content Enhancement Model in the field of college algebra in a mid-western community college. The Content Enhancement Model is a teaching technique that teachers use to help students acquire the content information by helping them identify, organize, comprehend, and memorize material. This study…

  4. Optical linear algebra processors - Noise and error-source modeling

    NASA Technical Reports Server (NTRS)

    Casasent, D.; Ghosh, A.

    1985-01-01

    The modeling of system and component noise and error sources in optical linear algebra processors (OLAPs) are considered, with attention to the frequency-multiplexed OLAP. General expressions are obtained for the output produced as a function of various component errors and noise. A digital simulator for this model is discussed.

  5. Cognitive Load and Modelling of an Algebra Problem

    ERIC Educational Resources Information Center

    Chinnappan, Mohan

    2010-01-01

    In the present study, I examine a modelling strategy as employed by a teacher in the context of an algebra lesson. The actions of this teacher suggest that a modelling approach will have a greater impact on enriching student learning if we do not lose sight of the need to manage associated cognitive loads that could either aid or hinder the…

  6. Supersonic boundary-layer flow turbulence modeling

    NASA Technical Reports Server (NTRS)

    Wang, Chi-Rong

    1993-01-01

    Baldwin-Lomax and kappa-epsilon turbulence models were modified for use in Navier-Stokes numerical computations of Mach 2.9 supersonic turbulent boundary layer flows along compression ramps. The computational results of Reynolds shear stress profiles were compared with experimental data. The Baldwin-Lomax model was modified to account for the Reynolds shear stress amplification within the flow field. A hybrid kappa-epsilon model with viscous sublayer turbulence treatment was constructed to predict the Reynolds shear stress profiles within the entire flow field. These modified turbulence models were effective for the computations of the surface pressure and the skin friction factor variations along an 8 deg ramp surface. The hybrid kappa-epsilon model could improve the predictions of the Reynolds shear stress profile and the skin friction factor near the corner of a 16 deg ramp.

  7. Evaluation of turbulence models in the PARC code for transonic diffuser flows

    NASA Technical Reports Server (NTRS)

    Georgiadis, N. J.; Drummond, J. E.; Leonard, B. P.

    1994-01-01

    Flows through a transonic diffuser were investigated with the PARC code using five turbulence models to determine the effects of turbulence model selection on flow prediction. Three of the turbulence models were algebraic models: Thomas (the standard algebraic turbulence model in PARC), Baldwin-Lomax, and Modified Mixing Length-Thomas (MMLT). The other two models were the low Reynolds number k-epsilon models of Chien and Speziale. Three diffuser flows, referred to as the no-shock, weak-shock, and strong-shock cases, were calculated with each model to conduct the evaluation. Pressure distributions, velocity profiles, locations of shocks, and maximum Mach numbers in the duct were the flow quantities compared. Overall, the Chien k-epsilon model was the most accurate of the five models when considering results obtained for all three cases. However, the MMLT model provided solutions as accurate as the Chien model for the no-shock and the weak-shock cases, at a substantially lower computational cost (measured in CPU time required to obtain converged solutions). The strong shock flow, which included a region of shock-induced flow separation, was only predicted well by the two k-epsilon models.

  8. Signal modeling of turbulence-distorted imagery

    NASA Astrophysics Data System (ADS)

    Young, S. Susan; Driggers, Ronald G.; Krapels, Keith; Espinola, Richard L.; Reynolds, Joseph P.; Cha, Jae

    2009-05-01

    Understanding turbulence effects on wave propagation and imaging systems has been an active research area for more than 50 years. Conventional atmospheric optics methods use statistical models to analyze image degradation effects that are caused by turbulence. In this paper, we intend to understand atmospheric turbulence effects using a deterministic signal processing and imaging theory point of view and modeling. The model simulates the formed imagery by a lens by tracing the optical rays from the target through a band of turbulence. We examine the nature of the turbulence-degraded image, and identify its characteristics as the parameters of the band of turbulence, e.g., its width, angle, and index of refraction, are varied. Image degradation effects due to turbulence, such as image blurring and image dancing, are revealed by this signal modeling. We show that in fact these phenomena can be related not only to phase errors in the frequency domain of the image but also a 2D modulation effect in the image spectrum. Results with simulated and realistic data are provided.

  9. Turbulence modelling in CFD: Present status, future prospects

    NASA Technical Reports Server (NTRS)

    Launder, Brian E.

    1992-01-01

    Information is given in viewgraph form for turbulence modeling in computational fluid dynamics (CFD). The Eddy Viscosity Models (EVM), Algebraic Second Moment Closures (ASM), and Differential Second-Moment Closures (DSM) are considered. It is concluded that EVM's, ASM's, and DSM's will remain in use, though with a steady decline in importance of EVM's and ASM's in favor of DSM's. Improved versions of low-Re two-equation EVM's should lead to more reliable predictions of separated flows than are achievable at present. Further refinement of sub-models in second moment closures can be expected throughout this decade. There will be increasing attention given to interfacing SMC with higher order approaches such as LES, and an increased use of two-time-scale schemes providing distinct time scales for large and fairly small eddies.

  10. Comparison of Turbulence Models for Nozzle-Afterbody Flows with Propulsive Jets

    NASA Technical Reports Server (NTRS)

    Compton, William B., III

    1996-01-01

    A numerical investigation was conducted to assess the accuracy of two turbulence models when computing non-axisymmetric nozzle-afterbody flows with propulsive jets. Navier-Stokes solutions were obtained for a Convergent-divergent non-axisymmetric nozzle-afterbody and its associated jet exhaust plume at free-stream Mach numbers of 0.600 and 0.938 at an angle of attack of 0 deg. The Reynolds number based on model length was approximately 20 x 10(exp 6). Turbulent dissipation was modeled by the algebraic Baldwin-Lomax turbulence model with the Degani-Schiff modification and by the standard Jones-Launder kappa-epsilon turbulence model. At flow conditions without strong shocks and with little or no separation, both turbulence models predicted the pressures on the surfaces of the nozzle very well. When strong shocks and massive separation existed, both turbulence models were unable to predict the flow accurately. Mixing of the jet exhaust plume and the external flow was underpredicted. The differences in drag coefficients for the two turbulence models illustrate that substantial development is still required for computing very complex flows before nozzle performance can be predicted accurately for all external flow conditions.

  11. Closure models for turbulent reacting flows

    SciTech Connect

    Dutta, A.; Tarbell, J.M. . Dept. of Chemical Engineering)

    1989-12-01

    In this paper, a simple procedure based on fast and slow reaction asymptotics has been employed to drive first-order closure models for the nonlinear reaction terms in turbulent mass balances from mechanistic models of turbulent mixing and reaction. The coalescence-redispersion (CRD) model, the interaction by exchange with the mean (IEM) model, the three-environment (3E) model, and the four-environment (4E) model have been used to develop closure equations. The closure models have been tested extensively against experimental data for both single and multiple reactions. The closures based on slow asymptotics for the CRD, 3E and 4E models provide very good predictions of all of the experimental data, while other models available either in the literature or derived here are not adequate. The simple new closure equations developed in this paper may be useful in modeling systems involving turbulent mixing and complex chemical reactions.

  12. A spatial operator algebra for manipulator modeling and control

    NASA Technical Reports Server (NTRS)

    Rodriguez, G.; Kreutz, Kenneth; Jain, Abhinandan

    1989-01-01

    A recently developed spatial operator algebra, useful for modeling, control, and trajectory design of manipulators is discussed. The elements of this algebra are linear operators whose domain and range spaces consist of forces, moments, velocities, and accelerations. The effect of these operators is equivalent to a spatial recursion along the span of a manipulator. Inversion of operators can be efficiently obtained via techniques of recursive filtering and smoothing. The operator algebra provides a high level framework for describing the dynamic and kinematic behavior of a manipulator and control and trajectory design algorithms. The interpretation of expressions within the algebraic framework leads to enhanced conceptual and physical understanding of manipulator dynamics and kinematics. Furthermore, implementable recursive algorithms can be immediately derived from the abstract operator expressions by inspection. Thus, the transition from an abstract problem formulation and solution to the detailed mechanizaton of specific algorithms is greatly simplified. The analytical formulation of the operator algebra, as well as its implementation in the Ada programming language are discussed.

  13. Prediction of Transonic Vortex Flows Using Linear and Nonlinear Turbulent Eddy Viscosity Models

    NASA Technical Reports Server (NTRS)

    Bartels, Robert E.; Gatski, Thomas B.

    2000-01-01

    Three-dimensional transonic flow over a delta wing is investigated with a focus on the effect of transition and influence of turbulence stress anisotropies. The performance of linear eddy viscosity models and an explicit algebraic stress model is assessed at the start of vortex flow, and the results compared with experimental data. To assess the effect of transition location, computations that either fix transition or are fully turbulent are performed. To assess the effect of the turbulent stress anisotropy, comparisons are made between predictions from the algebraic stress model and the linear eddy viscosity models. Both transition location and turbulent stress anisotropy significantly affect the 3D flow field. The most significant effect is found to be the modeling of transition location. At a Mach number of 0.90, the computed solution changes character from steady to unsteady depending on transition onset. Accounting for the anisotropies in the turbulent stresses also considerably impacts the flow, most notably in the outboard region of flow separation.

  14. Algebraic approach to small-world network models

    NASA Astrophysics Data System (ADS)

    Rudolph-Lilith, Michelle; Muller, Lyle E.

    2014-01-01

    We introduce an analytic model for directed Watts-Strogatz small-world graphs and deduce an algebraic expression of its defining adjacency matrix. The latter is then used to calculate the small-world digraph's asymmetry index and clustering coefficient in an analytically exact fashion, valid nonasymptotically for all graph sizes. The proposed approach is general and can be applied to all algebraically well-defined graph-theoretical measures, thus allowing for an analytical investigation of finite-size small-world graphs.

  15. Turbulent motion of mass flows. Mathematical modeling

    NASA Astrophysics Data System (ADS)

    Eglit, Margarita; Yakubenko, Alexander; Yakubenko, Tatiana

    2016-04-01

    New mathematical models for unsteady turbulent mass flows, e.g., dense snow avalanches and landslides, are presented. Such models are important since most of large scale flows are turbulent. In addition to turbulence, the two other important points are taken into account: the entrainment of the underlying material by the flow and the nonlinear rheology of moving material. The majority of existing models are based on the depth-averaged equations and the turbulent character of the flow is accounted by inclusion of drag proportional to the velocity squared. In this paper full (not depth-averaged) equations are used. It is assumed that basal entrainment takes place if the bed friction equals the shear strength of the underlying layer (Issler D, M. Pastor Peréz. 2011). The turbulent characteristics of the flow are calculated using a three-parameter differential model (Lushchik et al., 1978). The rheological properties of moving material are modeled by one of the three types of equations: 1) Newtonian fluid with high viscosity, 2) power-law fluid and 3) Bingham fluid. Unsteady turbulent flows down long homogeneous slope are considered. The flow dynamical parameters and entrainment rate behavior in time as well as their dependence on properties of moving and underlying materials are studied numerically. REFERENCES M.E. Eglit and A.E. Yakubenko, 2014. Numerical modeling of slope flows entraining bottom material. Cold Reg. Sci. Technol., 108, 139-148 Margarita E. Eglit and Alexander E. Yakubenko, 2016. The effect of bed material entrainment and non-Newtonian rheology on dynamics of turbulent slope flows. Fluid Dynamics, 51(3) Issler D, M. Pastor Peréz. 2011. Interplay of entrainment and rheology in snow avalanches; a numerical study. Annals of Glaciology, 52(58), 143-147 Lushchik, V.G., Paveliev, A.A. , and Yakubenko, A.E., 1978. Three-parameter model of shear turbulence. Fluid Dynamics, 13, (3), 350-362

  16. Application of a Reynolds Stress turbulence model to a supersonic hydrogen-air diffusion flame

    NASA Technical Reports Server (NTRS)

    Chandrasekhar, R.; Tiwari, S. N.

    1991-01-01

    A second-order differential Reynolds Stress turbulence model has been applied to the Favre-averaged Navier-Stokes equations for the study of supersonic flows undergoing hydrogen-air chemical reactions. An assumed Beta Probability Density Function is applied to account for the chemical source terms in the conservation equations. An algebraic Reynolds Flux model is used for the fluctuating density-velocity as well as the species mass fraction-velocity correlations. The variances of temperature and species fluctuations are also modelled using an algebraic flux technique. A seven-species, seven-reaction finite rate chemistry mechanism is used to simulate the combustion processes. The resulting formulation is validated by comparison with experimental data on reacting supersonic axisymmetric jets. Results obtained for specific conditions indicate that the effect of chemical reaction on the turbulence is significant.

  17. Compressible turbulent flows: Modeling and similarity considerations

    NASA Technical Reports Server (NTRS)

    Zeman, Otto

    1991-01-01

    With the recent revitalization of high speed flow research, compressibility presents a new set of challenging problems to turbulence researchers. Questions arise as to what extent compressibility affects turbulence dynamics, structures, the Reynolds stress-mean velocity (constitutive) relation, and the accompanying processes of heat transfer and mixing. In astrophysical applications, compressible turbulence is believed to play an important role in intergalactic gas cloud dynamics and in accretion disk convection. Understanding and modeling of the compressibility effects in free shear flows, boundary layers, and boundary layer/shock interactions is discussed.

  18. Estimating Resolution Lengths of Hybrid Turbulence Models

    NASA Technical Reports Server (NTRS)

    Abdol-Hamid, Khaled S.; Girimaji, Sharath S.

    2006-01-01

    A two-stage procedure has been devised for estimating the spatial resolution achievable in the simulation of a given flow on a given computational grid by a computational fluid dynamics (CFD) code that incorporates a hybrid model of turbulence. The hybrid models to which this procedure is especially relevant are those of the Reynolds-averaged Navier-Stokes (RANS) and the partial-averaged Navier-Stokes (PANS) approaches. This procedure represents the first step toward adding variable-resolution turbulence-modeling capabilities to CFD codes as part of a continuing effort to increase the accuracy and robustness of CFD simulations of unsteady flows. Some background information is prerequisite to a meaningful summary of the procedure. Among experts in CFD, it is well known that combination of the Reynolds-averaged Navier-Stokes (RANS) approach and eddy-viscosity turbulence models offers limited capability for simulating unsteady and complex flows. The RANS approach includes an assumption that most of the energy in a given flow is modeled through turbulence-transport equations and is resolved in a computational grid used to simulate the flow. RANS also overpredicts eddy viscosity, thereby yielding excessive damping of unsteady motion. The eddy viscosity attains an unphysically large value because of unresolved scales, and suppresses most temporal and spatial fluctuations in the resolved flow field. One approach used to overcome this deficiency is to provide a mechanism for the RANS equations to resolve motion only on the largest scales and to use a hybrid model to represent effects at smaller scales. The RANS approach involves the use of a standard two-equation turbulence model in which the effect of turbulence is summarized by a viscosity that is a function of (1) the time-averaged kinetic- energy density (k) associated with the local fluctuating (turbulent) component of flow and (2) the time-averaged rate of dissipation of the turbulent-kinetic- energy density ( ). In

  19. Advanced Numerical Modeling of Turbulent Atmospheric Flows

    NASA Astrophysics Data System (ADS)

    Kühnlein, Christian; Dörnbrack, Andreas; Gerz, Thomas

    The present chapter introduces the method of computational simulation to predict and study turbulent atmospheric flows. This includes a description of the fundamental approach to computational simulation and the practical implementation using the technique of large-eddy simulation. In addition, selected contributions from IPA scientists to computational model development and various examples for applications are given. These examples include homogeneous turbulence, convective boundary layers, heated forest canopy, buoyant thermals, and large-scale flows with baroclinic wave instability.

  20. RAS one-equation turbulence model with non-singular eddy-viscosity coefficient

    NASA Astrophysics Data System (ADS)

    Rahman, M. M.; Agarwal, R. K.; Siikonen, T.

    2016-02-01

    A simplified consistency formulation for Pk/ε (production to dissipation ratio) is devised to obtain a non-singular Cμ (coefficient of eddy-viscosity) in the explicit algebraic Reynolds stress model of Gatski and Speziale. The coefficient Cμ depends non-linearly on both rotational/irrotational strains and is used in the framework of an improved RAS (Rahman-Agarwal-Siikonen) one-equation turbulence model to calculate a few well-documented turbulent flows, yielding predictions in good agreement with the direct numerical simulation and experimental data. The strain-dependent Cμ assists the RAS model in constructing the coefficients and functions such as to benefit complex flows with non-equilibrium turbulence. Comparisons with the Spalart-Allmaras one-equation model and the shear stress transport k-ω model demonstrate that Cμ improves the response of RAS model to non-equilibrium effects.

  1. Modeling scalar dissipation and scalar variance in large eddy simulation: Algebraic and transport equation closures

    NASA Astrophysics Data System (ADS)

    Knudsen, E.; Richardson, E. S.; Doran, E. M.; Pitsch, H.; Chen, J. H.

    2012-05-01

    Scalar dissipation rates and subfilter scalar variances are important modeling parameters in large eddy simulations (LES) of reacting flows. Currently available models capture the general behavior of these parameters, but these models do not always perform with the degree of accuracy that is needed for predictive LES. Here, two direct numerical simulations (DNS) are used to analyze LES dissipation rate and variance models, and to propose a new model for the dissipation rate that is based on a transport equation. The first DNS that is considered is a non-premixed auto-igniting C2H4 jet flame simulation originally performed by Yoo et al. [Proc. Combust. Inst. 33, 1619-1627 (2011)], 10.1016/j.proci.2010.06.147. A LES of this case is run using algebraic models for the dissipation rate and subfilter variance. It is shown that the algebraic models fail to adequately reproduce the DNS results. This motivates the introduction of a transport equation model for the LES dissipation rate. Closure of the equation is addressed by formulating a new adapted dynamic approach. This approach borrows dynamically computed information from LES quantities that, unlike the dissipation rate, do not reside on the smallest flow length scales. The adapted dynamic approach is analyzed by considering a second DNS of scalar mixing in homogeneous isotropic turbulence. Data from this second DNS are used to confirm that the adapted dynamic approach successfully closes the dissipation rate equation over a wide range of LES filter widths. The first reacting jet case is then returned to and used to test the LES transport equation models. The transport equation model for the dissipation rate is shown to be more accurate than its algebraic counterpoint, and the dissipation rate is eliminated as a source of error in the transported variance model.

  2. Generalization of Richardson-Gaudin models to rank-2 algebras

    SciTech Connect

    Errea, B; Lerma, S; Dukelsky, J; Dimitrova, S S; Pittel, S; Van Isacker, P; Gueorguiev, V G

    2006-07-20

    A generalization of Richardson-Gaudin models to the rank-2 SO(5) and SO(3,2) algebras is used to describe systems of two kinds of fermions or bosons interacting through a pairing force. They are applied to the proton-neutron neutron isovector pairing model and to the Interacting Boson Model 2, in the transition from vibration to gamma-soft nuclei, respectively. In both cases, the integrals of motion and their eigenvalues are obtained.

  3. Complex Geometry Creation and Turbulent Conjugate Heat Transfer Modeling

    SciTech Connect

    Bodey, Isaac T; Arimilli, Rao V; Freels, James D

    2011-01-01

    The multiphysics capabilities of COMSOL provide the necessary tools to simulate the turbulent thermal-fluid aspects of the High Flux Isotope Reactor (HFIR). Version 4.1, and later, of COMSOL provides three different turbulence models: the standard k-{var_epsilon} closure model, the low Reynolds number (LRN) k-{var_epsilon} model, and the Spalart-Allmaras model. The LRN meets the needs of the nominal HFIR thermal-hydraulic requirements for 2D and 3D simulations. COMSOL also has the capability to create complex geometries. The circular involute fuel plates used in the HFIR require the use of algebraic equations to generate an accurate geometrical representation in the simulation environment. The best-estimate simulation results show that the maximum fuel plate clad surface temperatures are lower than those predicted by the legacy thermal safety code used at HFIR by approximately 17 K. The best-estimate temperature distribution determined by COMSOL was then used to determine the necessary increase in the magnitude of the power density profile (PDP) to produce a similar clad surface temperature as compared to the legacy thermal safety code. It was determined and verified that a 19% power increase was sufficient to bring the two temperature profiles to relatively good agreement.

  4. Philosophies and fallacies in turbulence modeling

    NASA Astrophysics Data System (ADS)

    Spalart, Philippe R.

    2015-04-01

    We present a set of positions, likely to be controversial, on turbulence modeling for the Reynolds-Averaged Navier Stokes (RANS) equations. The paper has three themes. First is what we call the "fundamental paradox" of turbulence modeling, between the local character of the Partial Differential Equations strongly favored by CFD methods and the nonlocal physical nature of turbulence. Second, we oppose two philosophies. The "Systematic" philosophy attempts to model the exact transport equations for the Reynolds stresses or possibly higher moments term by term, gradually relegating the Closure Problem to higher moments and invoking the "Principle of Receding Influence" (although rarely formulating it). In contrast, the "Openly Empirical" philosophy produces models which satisfy strict constraints such as Galilean invariance, but lack an explicit connection with terms in the exact turbulence equations. The prime example is the eddy-viscosity assumption. Third, we explain a series of what we perceive as fallacies, many of them widely held and by senior observers, in turbulence knowledge, leading to turbulence models. We divide them into "hard" fallacies for which a short mathematical argument demonstrates that a particular statement is wrong or meaningless, and "soft" fallacies for which approximate physical arguments can be opposed, but we contend that a clear debate is overdue and wishful thinking has been involved. Some fallacies appear to be "intermediate." An example in the hard class is the supposed isotropy of the diagonal Reynolds stresses. Examples in the soft class are the need to match the decay rate of isotropic turbulence, and the value of realizability in a model. Our hope is to help the direct effort in this field away from simplistic and hopeless lines of work, and to foster debates.

  5. Nonlinear gyrofluid model of ITG turbulence

    SciTech Connect

    Dorland, W.; Hammett, G.w.; Hahm, T.S.; Beer, M.A. )

    1994-05-01

    Early results from nonlinear simulations and analysis based on a recently derived nonlinear gyrofluid model [W. Dorland and G. W. Hammett, Phys. Fluids B, 812 (1993)] of electrostatic ion-temperature-gradient driven turbulence are presented. Comparisons with gyrokinetic particle simulations reveal a few important simulation requirements (such as enforcing radial periodicity), and indicate that the gyrofluid description is probably adequate to describe three-dimensional, low-frequency drift-type turbulence. Results from a detailed weak-turbulence analysis of drift wave turbulence are presented which support this conclusion. The importance of keeping the proper adiabatic electron response is also discussed. In particular, perpendicular velocity shear is greatly enhanced when the magnetic shear is weak if the nonphysical radial transport of electrons is disallowed.

  6. Turbulence modeling for non-equilibrium flows

    NASA Technical Reports Server (NTRS)

    Durbin, Paul A.

    1993-01-01

    Two projects are reported. The first is the development and testing of an eddy viscosity transport model. This project also is a starting point for our work on developing computational tools for solving turbulence models in complex geometries. The second project is a stochastic analysis of the realizability of Reynolds stress transport models.

  7. Turbulent Convection: Old and New Models

    NASA Astrophysics Data System (ADS)

    Canuto, V. M.

    1996-08-01

    This paper contains (1) a physical argument to show that the one-eddy MLT model underestimates the convective flux Fc in the high-efficiency regime, while it overestimates Fc in the low-efficiency regime, and (2) a new derivation of the Fc(MLT) using a turbulence model in the one-eddy approximation. (3) We forsake the one-eddy approximation and adopt the Kolmogorov spectrum to represent the turbulent energy spectrum. The resulting Fc > Fc(MLT) in the high-efficiency regime, and Fc model. (4) By forsaking the Kolmogorov model and solving a two-point closure model, one obtains the CM model. The Fc(CM) satisfies (1). Fc(CM) corresponds to a "tilt" in efficiency space of Fc(MLT), an effect that cannot be achieved by changing α. We discuss the astrophysical tests of the CM model. (5) Concerning the laboratory turbulent convection, we show that the CM model provides a better fit than the MLT to recent high Rayleigh number (Ra) laboratory data on convection. (6) Concerning nonlocal convection, the most complete model available is the one-point closure model (Reynolds stress model), which entails five differential equations for the five second-order moments. We present the solution corresponding to the local, stationary case. The results are expressed analytically in terms of Ko (Kolmogorov constant), Pe (Peclet number), and S (convective efficiency). (7) We find that the superadiabatic temperature gradient is given by - ∂T/∂r - cp-1gr where the renormalized gr = g(1 + g-1p-1dpt/dz) and Pt is the turbulent pressure. This result, which follows naturally from the Reynolds stress approach, contrasts with previous empirical suggestions to include Pt. (8) We derive new expressions for the turbulence pressure using two different turbulence models and (9) we show that the often used Kolmogorov-Prandtl expression for the turbulent diffusivity is valid only in the high

  8. Highest weight representation for Sklyanin algebra sl(3)(u) with application to the Gaudin model

    SciTech Connect

    Burdik, C.; Navratil, O.

    2011-06-15

    We study the infinite-dimensional Sklyanin algebra sl(3)(u). Specifically we construct the highest weight representation for this algebra in an explicit form. Its application to the Gaudin model is mentioned.

  9. Boundary algebras and Kac modules for logarithmic minimal models

    NASA Astrophysics Data System (ADS)

    Morin-Duchesne, Alexi; Rasmussen, Jørgen; Ridout, David

    2015-10-01

    Virasoro Kac modules were originally introduced indirectly as representations whose characters arise in the continuum scaling limits of certain transfer matrices in logarithmic minimal models, described using Temperley-Lieb algebras. The lattice transfer operators include seams on the boundary that use Wenzl-Jones projectors. If the projectors are singular, the original prescription is to select a subspace of the Temperley-Lieb modules on which the action of the transfer operators is non-singular. However, this prescription does not, in general, yield representations of the Temperley-Lieb algebras and the Virasoro Kac modules have remained largely unidentified. Here, we introduce the appropriate algebraic framework for the lattice analysis as a quotient of the one-boundary Temperley-Lieb algebra. The corresponding standard modules are introduced and examined using invariant bilinear forms and their Gram determinants. The structures of the Virasoro Kac modules are inferred from these results and are found to be given by finitely generated submodules of Feigin-Fuchs modules. Additional evidence for this identification is obtained by comparing the formalism of lattice fusion with the fusion rules of the Virasoro Kac modules. These are obtained, at the character level, in complete generality by applying a Verlinde-like formula and, at the module level, in many explicit examples by applying the Nahm-Gaberdiel-Kausch fusion algorithm.

  10. Modification of the Two-equation Turbulence Model in NPARC to a Chien Low Reynolds Number K-epsilon Formulation

    NASA Technical Reports Server (NTRS)

    Georgiadis, Nicholas J.; Chitsomboon, Tawit; Zhu, Jiang

    1994-01-01

    This report documents the changes that were made to the two-equation k-epsilon turbulence model in the NPARC (National-PARC) code. The previous model based on the low Reynolds number model of Speziale, was replaced with the low Reynolds number k-epsilon model of Chien. The most significant difference was in the turbulent Prandtl numbers appearing in the diffusion terms of the k and epsilon transport equations. A new inflow boundary condition and stability enhancements were also implemented into the turbulence model within NPARC. The report provides the rationale for making the change to the Chien model, code modifications required, and comparisons of the performances of the new model with the previous k-epsilon model and algebraic models used most often in PARC/NPARC. The comparisons show that the Chien k-epsilon model installed here improves the capability of NPARC to calculate turbulent flows.

  11. Turbulence and modeling in transonic flow

    NASA Technical Reports Server (NTRS)

    Rubesin, Morris W.; Viegas, John R.

    1989-01-01

    A review is made of the performance of a variety of turbulence models in the evaluation of a particular well documented transonic flow. This is done to supplement a previous attempt to calibrate and verify transonic airfoil codes by including many more turbulence models than used in the earlier work and applying the calculations to an experiment that did not suffer from uncertainties in angle of attack and was free of wind tunnel interference. It is found from this work, as well as in the earlier study, that the Johnson-King turbulence model is superior for transonic flows over simple aerodynamic surfaces, including moderate separation. It is also shown that some field equation models with wall function boundary conditions can be competitive with it.

  12. Evaluation of Turbulence-Model Performance in Jet Flows

    NASA Technical Reports Server (NTRS)

    Woodruff, S. L.; Seiner, J. M.; Hussaini, M. Y.; Erlebacher, G.

    2001-01-01

    The importance of reducing jet noise in both commercial and military aircraft applications has made jet acoustics a significant area of research. A technique for jet noise prediction commonly employed in practice is the MGB approach, based on the Lighthill acoustic analogy. This technique requires as aerodynamic input mean flow quantities and turbulence quantities like the kinetic energy and the dissipation. The purpose of the present paper is to assess existing capabilities for predicting these aerodynamic inputs. Two modern Navier-Stokes flow solvers, coupled with several modern turbulence models, are evaluated by comparison with experiment for their ability to predict mean flow properties in a supersonic jet plume. Potential weaknesses are identified for further investigation. Another comparison with similar intent is discussed by Barber et al. The ultimate goal of this research is to develop a reliable flow solver applicable to the low-noise, propulsion-efficient, nozzle exhaust systems being developed in NASA focused programs. These programs address a broad range of complex nozzle geometries operating in high temperature, compressible, flows. Seiner et al. previously discussed the jet configuration examined here. This convergent-divergent nozzle with an exit diameter of 3.6 inches was designed for an exhaust Mach number of 2.0 and a total temperature of 1680 F. The acoustic and aerodynamic data reported by Seiner et al. covered a range of jet total temperatures from 104 F to 2200 F at the fully-expanded nozzle pressure ratio. The aerodynamic data included centerline mean velocity and total temperature profiles. Computations were performed independently with two computational fluid dynamics (CFD) codes, ISAAC and PAB3D. Turbulence models employed include the k-epsilon model, the Gatski-Speziale algebraic-stress model and the Girimaji model, with and without the Sarkar compressibility correction. Centerline values of mean velocity and mean temperature are

  13. Turbulence models for compressible boundary layers

    NASA Technical Reports Server (NTRS)

    Huang, P. G.; Bradshaw, P.; Coakley, T. J.

    1994-01-01

    It is shown that to satisfy the general accepted compressible law of the wall derived from the Van Driest transformation, turbulence modeling coefficients must actually be functions of density gradients. The transformed velocity profiles obtained by using standard turbulence model constants have too small a value of the effective von Karman constant kappa in the log-law region (inner layer). Thus, if the model is otherwise accurate, the wake component is overpredicted and the predicted skin friction is lower than the expected value.

  14. Shell model for buoyancy-driven turbulence.

    PubMed

    Kumar, Abhishek; Verma, Mahendra K

    2015-04-01

    In this paper we present a unified shell model for stably stratified and convective turbulence. Numerical simulation of this model for stably stratified flow shows Bolgiano-Obukhbov scaling in which the kinetic energy spectrum varies as k(-11/5). The shell model of convective turbulence yields Kolmogorov's spectrum. These results are consistent with the energy flux and energy feed due to buoyancy, and are in good agreement with direct numerical simulations of Kumar et al. [Phys. Rev. E 90, 023016 (2014)]. PMID:25974587

  15. Applications of algebraic image operators to model-based vision

    NASA Technical Reports Server (NTRS)

    Lerner, Bao-Ting; Morelli, Michael V.; Thomas, Hans J.

    1989-01-01

    A highly structured and compact algebraic representation of grey-level images is expanded. Addition and multiplication are defined for the set of all grey-level images, which can then be described as polynomials of two variables. Utilizing this new algebraic structure, an innovative, efficient edge-detection scheme is devised. A robust method for linear feature extraction is developed by combining the techniques of a Hough transform and a line follower with this new edge detection scheme. The major advantage of this feature extractor is its general, object-independent nature. Target attributes, such as line segment lengths, intersections, angles of intersection, and endpoints are derived by the feature extraction algorithm and employed during model matching. The feature extractor and model matcher are being incorporated into a distributed robot-control system.

  16. Simulation and Modeling of Homogeneous, Compressed Turbulence.

    NASA Astrophysics Data System (ADS)

    Wu, Chung-Teh

    Low Reynolds number homogeneous turbulence undergoing low Mach number isotropic and one-dimensional compression has been simulated by numerically solving the Navier-Stokes equations. The numerical simulations were carried out on a CYBER 205 computer using a 64 x 64 x 64 mesh. A spectral method was used for spatial differencing and the second -order Runge-Kutta method for time advancement. A variety of statistical information was extracted from the computed flow fields. These include three-dimensional energy and dissipation spectra, two-point velocity correlations, one -dimensional energy spectra, turbulent kinetic energy and its dissipation rate, integral length scales, Taylor microscales, and Kolmogorov length scale. It was found that the ratio of the turbulence time scale to the mean-flow time scale is an important parameter in these flows. When this ratio is large, the flow is immediately affected by the mean strain in a manner similar to that predicted by rapid distortion theory. When this ratio is small, the flow retains the character of decaying isotropic turbulence initially; only after the strain has been applied for a long period does the flow accumulate a significant reflection of the effect of mean strain. In these flows, the Kolmogorov length scale decreases rapidly with increasing total strain, due to the density increase that accompanies compression. Results from the simulated flow fields were used to test one-point-closure, two-equation turbulence models. The two-equation models perform well only when the compression rate is small compared to the eddy turn-over rate. A new one-point-closure, three-equation turbulence model which accounts for the effect of compression is proposed. The new model accurately calculates four types of flows (isotropic decay, isotropic compression, one-dimensional compression, and axisymmetric expansion flows) for a wide range of strain rates.

  17. Integrability in three dimensions: Algebraic Bethe ansatz for anyonic models

    NASA Astrophysics Data System (ADS)

    Khachatryan, Sh.; Ferraz, A.; Klümper, A.; Sedrakyan, A.

    2015-10-01

    We extend basic properties of two dimensional integrable models within the Algebraic Bethe Ansatz approach to 2 + 1 dimensions and formulate the sufficient conditions for the commutativity of transfer matrices of different spectral parameters, in analogy with Yang-Baxter or tetrahedron equations. The basic ingredient of our models is the R-matrix, which describes the scattering of a pair of particles over another pair of particles, the quark-anti-quark (meson) scattering on another quark-anti-quark state. We show that the Kitaev model belongs to this class of models and its R-matrix fulfills well-defined equations for integrability.

  18. Differential rotation and turbulent convection: A new Reynolds stress model and comparison with solar data

    NASA Technical Reports Server (NTRS)

    Canuto, V. M.; Minotti, F. O.; Schilling, O.

    1994-01-01

    In most hydrodynamic cases, the existence of a turbulent flow superimposed on a mean flow is caused by a shear instability in the latter. Boussinesq suggested the first model for the turbulent Reynolds stresses bar-(u(sub i)u(sub j)) in which the mean shear S(sub ij) is the cause (or source) of turbulence represented by the stress bar-(u(sub i)u(sub j)). In the case of solar differential rotation, exactly the reverse physical process occurs: turbulence (which must pre-exist) generates a mean flow which manifests itself in the form of differential rotation. Thus, the Boussinesq model is wholly inadequate because in the solar case, cause and effect are reversed. Since the Boussinesq model is inadequate, one needs an alternative model for the Reynolds stresses. We present a new dynamical model for the Reynolds stresses, convective fluxes, turbulent kinetic energy, and temperature fluctuations. The complete model requires the solution of 11 differential equations. We then introduce a set of simplifying assumptions which reduce the full dynamical model to a set of algebraic Reynolds stress models. We explicitly solve one of these models that entails only one differential equation. The overall agreement with the data is obtained with a model that is neither phenomenological nor one that requires a full numerical simulation, since it is algebraic in nature. The new model can play an important role in understanding the complex physics underlying the interplay between solar differential rotation and convection, as many physical processes can naturally be incorporated into the model.

  19. Transport enhancement and suppression in turbulent magnetic reconnection: A self-consistent turbulence model

    SciTech Connect

    Yokoi, N.; Higashimori, K.; Hoshino, M.

    2013-12-15

    Through the enhancement of transport, turbulence is expected to contribute to the fast reconnection. However, the effects of turbulence are not so straightforward. In addition to the enhancement of transport, turbulence under some environment shows effects that suppress the transport. In the presence of turbulent cross helicity, such dynamic balance between the transport enhancement and suppression occurs. As this result of dynamic balance, the region of effective enhanced magnetic diffusivity is confined to a narrow region, leading to the fast reconnection. In order to confirm this idea, a self-consistent turbulence model for the magnetic reconnection is proposed. With the aid of numerical simulations where turbulence effects are incorporated in a consistent manner through the turbulence model, the dynamic balance in the turbulence magnetic reconnection is confirmed.

  20. A spatial operator algebra for manipulator modeling and control

    NASA Technical Reports Server (NTRS)

    Rodriguez, G.; Kreutz, K.; Jain, A.

    1989-01-01

    A spatial operator algebra for modeling the control and trajectory design of manipulation is discussed, with emphasis on its analytical formulation and implementation in the Ada programming language. The elements of this algebra are linear operators whose domain and range spaces consist of forces, moments, velocities, and accelerations. The effect of these operators is equivalent to a spatial recursion along the span of the manipulator. Inversion is obtained using techniques of recursive filtering and smoothing. The operator alegbra provides a high-level framework for describing the dynamic and kinematic behavior of a manipulator and control and trajectory design algorithms. Implementable recursive algorithms can be immediately derived from the abstract operator expressions by inspection, thus greatly simplifying the transition from an abstract problem formulation and solution to the detailed mechanization of a specific algorithm.

  1. ODTLES : a model for 3D turbulent flow based on one-dimensional turbulence modeling concepts.

    SciTech Connect

    McDermott, Randy; Kerstein, Alan R.; Schmidt, Rodney Cannon

    2005-01-01

    This report describes an approach for extending the one-dimensional turbulence (ODT) model of Kerstein [6] to treat turbulent flow in three-dimensional (3D) domains. This model, here called ODTLES, can also be viewed as a new LES model. In ODTLES, 3D aspects of the flow are captured by embedding three, mutually orthogonal, one-dimensional ODT domain arrays within a coarser 3D mesh. The ODTLES model is obtained by developing a consistent approach for dynamically coupling the different ODT line sets to each other and to the large scale processes that are resolved on the 3D mesh. The model is implemented computationally and its performance is tested and evaluated by performing simulations of decaying isotropic turbulence, a standard turbulent flow benchmarking problem.

  2. Time dependent turbulence modeling and analytical theories of turbulence

    NASA Technical Reports Server (NTRS)

    Rubinstein, R.

    1993-01-01

    By simplifying the direct interaction approximation (DIA) for turbulent shear flow, time dependent formulas are derived for the Reynolds stresses which can be included in two equation models. The Green's function is treated phenomenologically, however, following Smith and Yakhot, we insist on the short and long time limits required by DIA. For small strain rates, perturbative evaluation of the correlation function yields a time dependent theory which includes normal stress effects in simple shear flows. From this standpoint, the phenomenological Launder-Reece-Rodi model is obtained by replacing the Green's function by its long time limit. Eddy damping corrections to short time behavior initiate too quickly in this model; in contrast, the present theory exhibits strong suppression of eddy damping at short times. A time dependent theory for large strain rates is proposed in which large scales are governed by rapid distortion theory while small scales are governed by Kolmogorov inertial range dynamics. At short times and large strain rates, the theory closely matches rapid distortion theory, but at long times it relaxes to an eddy damping model.

  3. Model experiment to study sonic boom propagation through turbulence. Part II. Effect of turbulence intensity and propagation distance through turbulence.

    PubMed

    Lipkens, B; Blackstock, D T

    1998-09-01

    A model experiment was reported to be successful in simulating the propagation of sonic booms through a turbulent atmosphere [B. Lipkens and D. T. Blackstock, J. Acoust. Soc. Am. 103, 148-158 (1998)]. In this study the effect on N wave characteristics of turbulence intensity and propagation distance through turbulence are investigated. The main parameters of interest are the rise time and the peak pressure. The effect of turbulence intensity and propagation distance is to flatten the rise time and peak pressure distributions. Rise time and peak pressure distributions always have positive skewness after propagation through turbulence. Average rise time grows with turbulence intensity and propagation distance. The scattering of rise time data is one-sided, i.e., rise times are almost always increased by turbulence. Average peak pressure decreases slowly with turbulence intensity and propagation distance. For the reported data a threefold increase in average rise time is observed and a maximum decrease of about 20% in average peak pressure. Rise times more than ten times that of the no turbulence value are observed. At most, the maximum peak pressure doubles after propagation through turbulence, and the minimum peak pressure values are about one-half the no-turbulence values. Rounded waveforms are always more common than peaked waveforms. PMID:9745733

  4. Continuous representation for shell models of turbulence

    NASA Astrophysics Data System (ADS)

    Mailybaev, Alexei A.

    2015-07-01

    In this work we construct and analyze continuous hydrodynamic models in one space dimension, which are induced by shell models of turbulence. After Fourier transformation, such continuous models split into an infinite number of uncoupled subsystems, which are all identical to the same shell model. The two shell models, which allow such a construction, are considered: the dyadic (Desnyansky-Novikov) model with the intershell ratio λ = 23/2 and the Sabra model of turbulence with λ = \\sqrt{2+\\sqrt{5}} ≈ 2.058 . The continuous models allow for understanding of various properties of shell model solutions and provide their interpretation in physical space. We show that the asymptotic solutions of the dyadic model with Kolmogorov scaling correspond to the shocks (discontinuities) for the induced continuous solutions in physical space, and the finite-time blowup together with its viscous regularization follow the scenario similar to the Burgers equation. For the Sabra model, we provide the physical space representation for blowup solutions and intermittent turbulent dynamics.

  5. Computation of turbulent flows using an extended k-epsilon turbulence closure model

    NASA Technical Reports Server (NTRS)

    Chen, Y.-S.; Kim, S.-W.

    1987-01-01

    An extended kappa-epsilon turbulence model is proposed and tested with successful results. An improved transport equation for the rate of dissipation of the turbulent kinetic energy, epsilon, is proposed. The proposed model gives more effective response to the energy production rate than does the standard kappa-epsilon turbulence model. An extra time scale of the production range is included in the dissipation rate equation. This enables the present model to perform equally well for several turbulent flows with different characteristics, e.g., plane and axisymmetric jets, turbulent boundary layer flow, turbulent flow over a backward-facing step, and a confined turbulent swirling flow. A second-order accurate finite difference boundary layer code and a nearly second-order accurate finite difference elliptic flow solver are used for the present numerical computations.

  6. Stochastic Modeling of Laminar-Turbulent Transition

    NASA Technical Reports Server (NTRS)

    Rubinstein, Robert; Choudhari, Meelan

    2002-01-01

    Stochastic versions of stability equations are developed in order to develop integrated models of transition and turbulence and to understand the effects of uncertain initial conditions on disturbance growth. Stochastic forms of the resonant triad equations, a high Reynolds number asymptotic theory, and the parabolized stability equations are developed.

  7. Turbulence Modeling: Progress and Future Outlook

    NASA Technical Reports Server (NTRS)

    Marvin, Joseph G.; Huang, George P.

    1996-01-01

    Progress in the development of the hierarchy of turbulence models for Reynolds-averaged Navier-Stokes codes used in aerodynamic applications is reviewed. Steady progress is demonstrated, but transfer of the modeling technology has not kept pace with the development and demands of the computational fluid dynamics (CFD) tools. An examination of the process of model development leads to recommendations for a mid-course correction involving close coordination between modelers, CFD developers, and application engineers. In instances where the old process is changed and cooperation enhanced, timely transfer is realized. A turbulence modeling information database is proposed to refine the process and open it to greater participation among modeling and CFD practitioners.

  8. Turbulence Modeling Validation, Testing, and Development

    NASA Technical Reports Server (NTRS)

    Bardina, J. E.; Huang, P. G.; Coakley, T. J.

    1997-01-01

    The primary objective of this work is to provide accurate numerical solutions for selected flow fields and to compare and evaluate the performance of selected turbulence models with experimental results. Four popular turbulence models have been tested and validated against experimental data often turbulent flows. The models are: (1) the two-equation k-epsilon model of Wilcox, (2) the two-equation k-epsilon model of Launder and Sharma, (3) the two-equation k-omega/k-epsilon SST model of Menter, and (4) the one-equation model of Spalart and Allmaras. The flows investigated are five free shear flows consisting of a mixing layer, a round jet, a plane jet, a plane wake, and a compressible mixing layer; and five boundary layer flows consisting of an incompressible flat plate, a Mach 5 adiabatic flat plate, a separated boundary layer, an axisymmetric shock-wave/boundary layer interaction, and an RAE 2822 transonic airfoil. The experimental data for these flows are well established and have been extensively used in model developments. The results are shown in the following four sections: Part A describes the equations of motion and boundary conditions; Part B describes the model equations, constants, parameters, boundary conditions, and numerical implementation; and Parts C and D describe the experimental data and the performance of the models in the free-shear flows and the boundary layer flows, respectively.

  9. Experiences with two-equation turbulence models

    NASA Technical Reports Server (NTRS)

    Singhal, Ashok K.; Lai, Yong G.; Avva, Ram K.

    1995-01-01

    This viewgraph presentation discusses the following: introduction to CFD Research Corporation; experiences with two-equation models - models used, numerical difficulties, validation and applications, and strengths and weaknesses; and answers to three questions posed by the workshop organizing committee - what are your customers telling you, what are you doing in-house, and how can NASA-CMOTT (Center for Modeling of Turbulence and Transition) help.

  10. Computation of unsteady turbulent boundary layers with flow reversal and evaluation of two separate turbulence models

    NASA Technical Reports Server (NTRS)

    Cebeci, T.; Carr, L. W.

    1981-01-01

    A procedure which solves the governing boundary layer equations within Keller's box method was developed for calculating unsteady laminar flows with flow reversal. This method is extended to turbulent boundary layers with flow reversal. Test cases are used to investigate the proposition that unsteady turbulent boundary layers also remain free of singularities. Turbulent flow calculations are performed. The governing equations for both models are solved. As in laminar flows, the unsteady turbulent boundary layers are free from singularities, but there is a clear indication of rapid thickening of the boundary layer with increasing flow reversal. Predictions of both turbulence models are the same for all practical purposes.

  11. Automorphism groups of composition algebras and quark models

    SciTech Connect

    Bjerregard, P.A.; Gonzalez, C.M.

    1996-12-01

    In this the authors study the automorphisms and derivations of real composition algebras with a view to its physical interpretations. They obtain canonical forms with a special stress in the four and eight dimensional cases. Also, using this description, they work with two mathematical models which describe some particles with certain observables in a surprising way. A first model, split g{sub 2}, describes two observables for three quarks, their antiquarks, and eight mesons combining the quarks involved. A second one, so(4,4) {circle_plus} so(2,2), describes all the observables for all quarks (u, d, s, c, b and t).

  12. A Modified Mixing Length Turbulence Model for Zero and Adverse Pressure Gradients. M.S. Thesis - Akron Univ., 1993

    NASA Technical Reports Server (NTRS)

    Conley, Julianne M.; Leonard, B. P.

    1994-01-01

    The modified mixing length (MML) turbulence model was installed in the Proteus Navier-Stokes code, then modified to make it applicable to a wider range of flows typical of aerospace propulsion applications. The modifications are based on experimental data for three flat-plate flows having zero, mild adverse, and strong adverse pressure gradients. Three transonic diffuser test cases were run with the new version of the model in order to evaluate its performance. All results are compared with experimental data and show improvements over calculations made using the Baldwin-Lomax turbulence model, the standard algebraic model in Proteus.

  13. A one-equation turbulence transport model for high Reynolds number wall-bounded flows

    NASA Technical Reports Server (NTRS)

    Baldwin, Barrett S.; Barth, Timothy J.

    1990-01-01

    A one-equation turbulence model that avoids the need for an algebraic length scale is derived from a simplified form of the standard k-epsilon model equations. After calibration based on well established properties of the flow over a flat plate, predictions of several other flows are compared with experiment. The preliminary results presented indicate that the model has predictive and numerical properties of sufficient interest to merit further investigation and refinement. The one-equation model is also analyzed numerically and robust solution methods are presented.

  14. A one-equation turbulence transport model for high Reynolds number wall-bounded flows

    NASA Technical Reports Server (NTRS)

    Baldwin, Barrett S.; Barth, Timothy J.

    1991-01-01

    A one-equation turbulence model that avoids the need for an algebraic length scale is derived from a simplified form of the standard-k-epsilon model equations. After calibration based on well established properties of the flow over a flat plate, predictions of several other flows are compared with experiment. The preliminary results presented indicate that the model has predictive and numerical properties of sufficient interest to merit further investigation and refinement. The one-equation model is also analyzed numerically and robust solution methods are presented.

  15. Modeling of Turbulent Free Shear Flows

    NASA Technical Reports Server (NTRS)

    Yoder, Dennis A.; DeBonis, James R.; Georgiadis, Nicolas J.

    2013-01-01

    The modeling of turbulent free shear flows is crucial to the simulation of many aerospace applications, yet often receives less attention than the modeling of wall boundary layers. Thus, while turbulence model development in general has proceeded very slowly in the past twenty years, progress for free shear flows has been even more so. This paper highlights some of the fundamental issues in modeling free shear flows for propulsion applications, presents a review of past modeling efforts, and identifies areas where further research is needed. Among the topics discussed are differences between planar and axisymmetric flows, development versus self-similar regions, the effect of compressibility and the evolution of compressibility corrections, the effect of temperature on jets, and the significance of turbulent Prandtl and Schmidt numbers for reacting shear flows. Large eddy simulation greatly reduces the amount of empiricism in the physical modeling, but is sensitive to a number of numerical issues. This paper includes an overview of the importance of numerical scheme, mesh resolution, boundary treatment, sub-grid modeling, and filtering in conducting a successful simulation.

  16. A RATIONALE FOR IMPLICIT TURBULENCE MODELING

    SciTech Connect

    L. G. MARGOLIN; W. J. RIDER

    2001-04-01

    We present a rationale for the success of nonoscillatory finite volume (NFV) difference schemes in modeling turbulent flows without need of subgrid scale models. Our exposition focuses on certain truncation terms that appear in the modified equation of one particular NFV scheme, MPDATA. We demonstrate that these truncation terms have physical justification, representing the modifications to the governing equations that arise when one considers the motion of finite volumes of fluid over finite intervals of time.

  17. Cascade modeling of single and two-phase turbulence

    NASA Astrophysics Data System (ADS)

    Bolotnov, Igor A.

    The analysis of turbulent two-phase flows requires closure models in order to perform reliable computational multiphase fluid dynamics (CFMD) analyses. A turbulence cascade model, which tracks the evolution of the turbulent kinetic energy between the various eddy sizes, has been developed for the analysis of the single and bubbly two-phase turbulence. Various flows are considered including the decay of isotropic grid-induced turbulence, uniform shear flow and turbulent channel flow. The model has been developed using a "building block" approach by moving from modeling of simpler turbulent flows (i.e., homogeneous, isotropic decay) to more involved turbulent flows (i.e., non-homogeneous channel flow). The spectral cascade-transport model's performance has been assessed against a number of experimental and direct numerical simulation (DNS) results.

  18. Simulations of turbulent mixing and reacting flows and their applications to turbulence modeling

    NASA Technical Reports Server (NTRS)

    Ferziger, J. H.; Cantwell, B. J.

    1986-01-01

    The method of full simulation is applied to reacting turbulent flows. Full simulation has proven of great value as a complement to experiments for the study of nonreacting turbulent flows. It provides insight into the physics of turbulent flows and their modeling. It is natural to try to extend these methods to the simulation of reacting turbulent flows. Because this is one of the first attempts at this type of simulation, a subsidiary goal of this work is to demonstrate the feasibility of using simulation to study turbulent reacting flows. In addition, it is shown that such simulations can be used to provide physical insight into the nature of turbulent combustion and to provide data that will help to construct models that can be used in engineering simulations of turbulent reacting flows.

  19. Modelling the pressure-strain correlation of turbulence - An invariant dynamical systems approach

    NASA Technical Reports Server (NTRS)

    Speziale, Charles G.; Sarkar, Sutanu; Gatski, Thomas B.

    1991-01-01

    The modeling of the pressure-strain correlation of turbulence is examined from a basic theoretical standpoint with a view toward developing improved second-order closure models. Invariance considerations along with elementary dynamical systems theory are used in the analysis of the standard hierarchy of closure models. In these commonly used models, the pressure-strain correlation is assumed to be a linear function of the mean velocity gradients with coefficients that depend algebraically on the anisotropy tensor. It is proven that for plane homogeneous turbulent flows the equilibrium structure of this hierarchy of models is encapsulated by a relatively simple model which is only quadratically nonlinear in the anisotropy tensor. This new quadratic model - the SSG model - is shown to outperform the Launder, Reece, and Rodi model (as well as more recent models that have a considerably more complex nonlinear structure) in a variety of homogeneous turbulent flows. Some deficiencies still remain for the description of rotating turbulent shear flows that are intrinsic to this general hierarchy of models and, hence, cannot be overcome by the mere introduction of more complex nonlinearities. It is thus argued that the recent trend of adding substantially more complex nonlinear terms containing the anisotropy tensor may be of questionable value in the modeling of the pressure-strain correlation. Possible alternative approaches are discussed briefly.

  20. Modeling the pressure-strain correlation of turbulence: An invariant dynamical systems approach

    NASA Technical Reports Server (NTRS)

    Speziale, Charles G.; Sarkar, Sutanu; Gatski, Thomas B.

    1990-01-01

    The modeling of the pressure-strain correlation of turbulence is examined from a basic theoretical standpoint with a view toward developing improved second-order closure models. Invariance considerations along with elementary dynamical systems theory are used in the analysis of the standard hierarchy of closure models. In these commonly used models, the pressure-strain correlation is assumed to be a linear function of the mean velocity gradients with coefficients that depend algebraically on the anisotropy tensor. It is proven that for plane homogeneous turbulent flows the equilibrium structure of this hierarchy of models is encapsulated by a relatively simple model which is only quadratically nonlinear in the anisotropy tensor. This new quadratic model - the SSG model - is shown to outperform the Launder, Reece, and Rodi model (as well as more recent models that have a considerably more complex nonlinear structure) in a variety of homogeneous turbulent flows. Some deficiencies still remain for the description of rotating turbulent shear flows that are intrinsic to this general hierarchy of models and, hence, cannot be overcome by the mere introduction of more complex nonlinearities. It is thus argued that the recent trend of adding substantially more complex nonlinear terms containing the anisotropy tensor may be of questionable value in the modeling of the pressure-strain correlation. Possible alternative approaches are discussed briefly.

  1. Applications Of Algebraic Image Operators To Model-Based Vision

    NASA Astrophysics Data System (ADS)

    Lerner, Bao-Ting; Morelli, Michael V.; Thomas, Hans J.

    1989-03-01

    This paper extends our previous research on a highly structured and compact algebraic representation of grey-level images. Addition and multiplication are defined for the set of all grey-level images, which can then be described as polynomials of two variables. Utilizing this new algebraic structure, we have devised an innovative, efficient edge detection scheme.We have developed a robust method for linear feature extraction by combining the techniques of a Hough transform and a line follower with this new edge detection scheme. The major advantage of this feature extractor is its general, object-independent nature. Target attributes, such as line segment lengths, intersections, angles of intersection, and endpoints are derived by the feature extraction algorithm and employed during model matching. The feature extractor and model matcher are being incorporated into a distributed robot control system. Model matching is accomplished using both top-down and bottom-up processing: a priori sensor and world model information are used to constrain the search of the image space for features, while extracted image information is used to update the model.

  2. Cascade Models of Turbulence and Mixing

    NASA Astrophysics Data System (ADS)

    Kadanoff, Leo P.

    1997-01-01

    This note describes two kinds of work on turbulence. First it describes a simplified model of turbulent energy-cascades called the GOY model. Second it mentions work on a model of mixing in fluids. In addition to a brief historical discussion, I include some mention of our own work carried on at the University of Chicago by Jane Wang, Detlef Lohse, Roberto Benzi, Norbert Schörghofer, Scott Wunsch, Tong Zhou and myself. Our own studies are in large measure the outgrowth of a paper by M. H. Jensen, G. Paladin, and A. Vulpiani [1]. I mention this connection with some sadness because I recall Paladin's recent death in a mountain accident.

  3. An investigation of turbulence modeling in transonic fans including a novel implementation of an implicit k-[var epsilon] turbulence model

    SciTech Connect

    Turner, M.G.; Jennions, I.K. )

    1993-04-01

    An explicit Navier-Stokes solver has been written with the option of using one of two types of turbulence model. One is the Baldwin-Lomax algebraic model and the other is an implicit k-[var epsilon] model which has been coupled with the explicit Navier-Stokes solver in a novel way. This type of coupling, which uses two different solution methods, is unique and combines the overall robustness of the implicit k-[var epsilon] solver with the simplicity of the explicit solver. The resulting code has been applied to the solution of the flow in a transonic fan rotor, which has been experimentally investigated by Wennerstrom. Five separate solutions, each identical except for the turbulence modeling details, have been obtained and compared with the experimental results. The five different turbulence models run were: the standard Baldwin-Lomax model both with and without wall functions, the Baldwin-Lomax model with modified constants and wall functions, a standard k-[var epsilon] model, and an extended k-[var epsilon] model, which accounts for multiple time scales by adding an extra term to the dissipation equation. In general, as the model includes more of the physics, the computed shock position becomes closer to the experimental results.

  4. A turbulence model for buoyant flows based on vorticity generation.

    SciTech Connect

    Domino, Stefan Paul; Nicolette, Vernon F.; O'Hern, Timothy John; Tieszen, Sheldon R.; Black, Amalia Rebecca

    2005-10-01

    A turbulence model for buoyant flows has been developed in the context of a k-{var_epsilon} turbulence modeling approach. A production term is added to the turbulent kinetic energy equation based on dimensional reasoning using an appropriate time scale for buoyancy-induced turbulence taken from the vorticity conservation equation. The resulting turbulence model is calibrated against far field helium-air spread rate data, and validated with near source, strongly buoyant helium plume data sets. This model is more numerically stable and gives better predictions over a much broader range of mesh densities than the standard k-{var_epsilon} model for these strongly buoyant flows.

  5. Numerical investigation of separated transonic turbulent flows with a multiple-time-scale turbulence model

    NASA Technical Reports Server (NTRS)

    Kim, S.-W.

    1990-01-01

    A numerical investigation of transonic turbulent flows separated by curvature and shock wave - boundary layer interaction is presented. The free stream Mach numbers considered are 0.4, 0.5, 0.6, 0.7, 0.8, 0.825, 0.85, 0.875, 0.90, and 0.925. In the numerical method, the conservation of mass equation is replaced by a pressure correction equation for compressible flows and thus incremental pressure is solved for instead of density. The turbulence is described by a multiple-time-scale turbulence model supplemented with a near-wall turbulence model. The present numerical results show that there exists a reversed flow region at all free stream Mach numbers considered whereas various k-epsilon turbulence models fail to predict such a reversed flow region at low free stream Mach numbers. The numerical results also show that the size of the reversed flow region grows extensively due to the shock wave - turbulent boundary layer interaction as the free stream Mach number is increased. These numerical results show that the turbulence model can resolve the turbulence field subjected to extra strains caused by the curvature and the shock wave - turbulent boundary layer interaction and that the numerical method yields a significantly accurate solution for the complex compressible turbulent flow.

  6. Comparative Study of Advanced Turbulence Models for Turbomachinery

    NASA Technical Reports Server (NTRS)

    Hadid, Ali H.; Sindir, Munir M.

    1996-01-01

    A computational study has been undertaken to study the performance of advanced phenomenological turbulence models coded in a modular form to describe incompressible turbulent flow behavior in two dimensional/axisymmetric and three dimensional complex geometry. The models include a variety of two equation models (single and multi-scale k-epsilon models with different near wall treatments) and second moment algebraic and full Reynolds stress closure models. These models were systematically assessed to evaluate their performance in complex flows with rotation, curvature and separation. The models are coded as self contained modules that can be interfaced with a number of flow solvers. These modules are stand alone satellite programs that come with their own formulation, finite-volume discretization scheme, solver and boundary condition implementation. They will take as input (from any generic Navier-Stokes solver) the velocity field, grid (structured H-type grid) and computational domain specification (boundary conditions), and will deliver, depending on the model used, turbulent viscosity, or the components of the Reynolds stress tensor. There are separate 2D/axisymmetric and/or 3D decks for each module considered. The modules are tested using Rocketdyn's proprietary code REACT. The code utilizes an efficient solution procedure to solve Navier-Stokes equations in a non-orthogonal body-fitted coordinate system. The differential equations are discretized over a finite-volume grid using a non-staggered variable arrangement and an efficient solution procedure based on the SIMPLE algorithm for the velocity-pressure coupling is used. The modules developed have been interfaced and tested using finite-volume, pressure-correction CFD solvers which are widely used in the CFD community. Other solvers can also be used to test these modules since they are independently structured with their own discretization scheme and solver methodology. Many of these modules have been

  7. Laminarization model for turbulent eddy transport in highly accelerated nozzle turbulent boundary layers

    NASA Technical Reports Server (NTRS)

    Schmidt, J. F.; Boldman, D. R.; Todd, C.

    1972-01-01

    A laminarization model which consists of a completely laminar sublayer region near the wall and a turbulent wake region is developed for the turbulent eddy transport in accelerated turbulent boundary layers. This laminarization model is used in a differential boundary layer calculation which was applied to nozzle flows. The resulting theoretical velocity profiles are in good agreement with the experimental nozzle data in the convergent region.

  8. Stochastic modeling of turbulent reacting flows

    NASA Technical Reports Server (NTRS)

    Fox, R. O.; Hill, J. C.; Gao, F.; Moser, R. D.; Rogers, M. M.

    1992-01-01

    Direct numerical simulations of a single-step irreversible chemical reaction with non-premixed reactants in forced isotropic turbulence at R(sub lambda) = 63, Da = 4.0, and Sc = 0.7 were made using 128 Fourier modes to obtain joint probability density functions (pdfs) and other statistical information to parameterize and test a Fokker-Planck turbulent mixing model. Preliminary results indicate that the modeled gradient stretching term for an inert scalar is independent of the initial conditions of the scalar field. The conditional pdf of scalar gradient magnitudes is found to be a function of the scalar until the reaction is largely completed. Alignment of concentration gradients with local strain rate and other features of the flow were also investigated.

  9. Evaluation of Turbulence Models for Unsteady Flows of an Oscillating Airfoil

    NASA Technical Reports Server (NTRS)

    Srinivasan, G. R.; Ekaterinaris, J. A.; McCroskey, W. J.

    1995-01-01

    Unsteady flowfields of a two-dimensional oscillating airfoil are calculated using an implicit, finite-difference, Navier Stokes numerical scheme. Five widely used turbulence models are used with the numerical scheme to assess the accuracy and suitability of the models for simulating the retreating blade stall of helicopter rotor in forward flight. Three unsteady flow conditions corresponding to an essentially attached flow, light-stall, and deep-stall cases of an oscillating NACA 0015 wing experiment were chosen as test cases for computations. Results of unsteady airloads hysteresis curves, harmonics of unsteady pressures, and instantaneous flowfield patterns are presented. Some effects of grid density, time-step size, and numerical dissipation on the unsteady solutions relevant to the evaluation of turbulence models are examined. Comparison of unsteady airloads with experimental data show that all models tested are deficient in some sense and no single model predicts airloads consistently and in agreement with experiment for the three flow regimes. The chief findings are that the simple algebraic model based on the renormalization group theory (RNG) offers some improvement over the Baldwin Lomax model in all flow regimes with nearly same computational cost. The one-equation models provide significant improvement over the algebraic and the half-equation models but have their own limitations. The Baldwin-Barth model overpredicts separation and underpredicts reattachment. In contrast, the Spalart-Allmaras model underpredicts separation and overpredicts reattachment.

  10. Simulation and modeling of homogeneous, compressed turbulence

    NASA Technical Reports Server (NTRS)

    Wu, C. T.; Ferziger, J. H.; Chapman, D. R.

    1985-01-01

    Low Reynolds number homogeneous turbulence undergoing low Mach number isotropic and one-dimensional compression was simulated by numerically solving the Navier-Stokes equations. The numerical simulations were performed on a CYBER 205 computer using a 64 x 64 x 64 mesh. A spectral method was used for spatial differencing and the second-order Runge-Kutta method for time advancement. A variety of statistical information was extracted from the computed flow fields. These include three-dimensional energy and dissipation spectra, two-point velocity correlations, one-dimensional energy spectra, turbulent kinetic energy and its dissipation rate, integral length scales, Taylor microscales, and Kolmogorov length scale. Results from the simulated flow fields were used to test one-point closure, two-equation models. A new one-point-closure, three-equation turbulence model which accounts for the effect of compression is proposed. The new model accurately calculates four types of flows (isotropic decay, isotropic compression, one-dimensional compression, and axisymmetric expansion flows) for a wide range of strain rates.

  11. Turbulence Modeling in Dust Forming Media

    NASA Astrophysics Data System (ADS)

    Helling, Ch.; Lüttke, M.; Sedlmayr, E.; Oeverman, M.; Klein, R.

    The process of dust formation is considered in a turbulent medium. The modeling for hydro- and thermodynamics follows the classical approach for an inviscid, compressible fluid and the dust formation process is described as a two step process, nucleation and growth, including element conservation. Our approach is to combine asymptotic techniques and multi-dimensional direct numerical simulations (DNS). The turbulence modeling will be performed by the simulation of regime-wise increased scales allowing for a detailed study of the corresponding behavior of the dust forming gas flow. Our investigations have been started in the microscopic scale regime (Kolmogoroff scale << lref << density scale height) where acoustic waves are continuously generated by turbulent motions caused by large-scale convection. We show that the local gas temperature can fall below a temperature threshold for efficient dust nucleation by the superposition of acoustic expansion waves. As the formed seed particles subsequently grow, radiation cooling is intensified causing new dust to form and a runaway effect sets in. An asymptotic model serves as an independent test of our DNS results and allows an investigation of the long term behavior of our dust forming system. Adopting the example of a brown dwarf atmosphere, intermittent dust distributions in space and time (clouds) are predicted by asymptotic calculations of stochastic acoustic interaction and have been studied further by 1D and 2D DNS.

  12. Simulation and modeling of homogeneous, compressed turbulence

    NASA Astrophysics Data System (ADS)

    Wu, C. T.; Ferziger, J. H.; Chapman, D. R.

    1985-05-01

    Low Reynolds number homogeneous turbulence undergoing low Mach number isotropic and one-dimensional compression was simulated by numerically solving the Navier-Stokes equations. The numerical simulations were performed on a CYBER 205 computer using a 64 x 64 x 64 mesh. A spectral method was used for spatial differencing and the second-order Runge-Kutta method for time advancement. A variety of statistical information was extracted from the computed flow fields. These include three-dimensional energy and dissipation spectra, two-point velocity correlations, one-dimensional energy spectra, turbulent kinetic energy and its dissipation rate, integral length scales, Taylor microscales, and Kolmogorov length scale. Results from the simulated flow fields were used to test one-point closure, two-equation models. A new one-point-closure, three-equation turbulence model which accounts for the effect of compression is proposed. The new model accurately calculates four types of flows (isotropic decay, isotropic compression, one-dimensional compression, and axisymmetric expansion flows) for a wide range of strain rates.

  13. A multiple-scale model for compressible turbulent flows

    NASA Technical Reports Server (NTRS)

    Liou, William W.; Shih, Tsan-Hsing

    1993-01-01

    A multiple-scale model for compressible turbulent flows is proposed. It is assumed that turbulent eddy shocklets are formed primarily by the 'collisions' of large energetic eddies. The extra straining of the large eddy, due to their interactions with shocklets, enhances the energy cascade to smaller eddies. Model transport equations are developed for the turbulent kinetic energies and the energy transfer rates of the different scale. The turbulent eddy viscosity is determined by the total turbulent kinetic energy and the rate of energy transfer from the large scale to the small scale, which is different from the energy dissipation rate. The model coefficients in the modeled turbulent transport equations depend on the ratio of the turbulent kinetic energy of the large scale to that of the small scale, which renders the model more adaptive to the characteristics of individual flow. The model is tested against compressible free shear layers. The results agree satisfactorily with measurements.

  14. A Frame Manipulation Algebra for ER Logical Stage Modelling

    NASA Astrophysics Data System (ADS)

    Furtado, Antonio L.; Casanova, Marco A.; Breitman, Karin K.; Barbosa, Simone D. J.

    The ER model is arguably today's most widely accepted basis for the conceptual specification of information systems. A further common practice is to use the Relational Model at an intermediate logical stage, in order to adequately prepare for physical implementation. Although the Relational Model still works well in contexts relying on standard databases, it imposes certain restrictions, not inherent in ER specifications, which make it less suitable in Web environments. This paper proposes frames as an alternative to move from ER specifications to logical stage modelling, and treats frames as an abstract data type equipped with a Frame Manipulation Algebra (FMA). It is argued that frames, with a long tradition in AI applications, are able to accommodate the irregularities of semi-structured data, and that frame-sets generalize relational tables, allowing to drop the strict homogeneity requirement. A prototype logic-programming tool has been developed to experiment with FMA. Examples are included to help describe the use of the operators.

  15. An Improved Model for the Turbulent PBL

    NASA Technical Reports Server (NTRS)

    Cheng, Y.; Canuto, V. M.; Howard, A. M.; Hansen, James E. (Technical Monitor)

    2001-01-01

    Second order turbulence models of the Mellor and Yamada type have been widely used to simulate the PBL. It is however known that these models have several deficiencies. For example, they all predict a critical Richardson number which is about four times smaller than the Large Eddy Simulation (LES) data, they are unable to match the surface data, and they predict a boundary layer height lower than expected. In the present model, we show that these difficulties are all overcome by a single new physical input: the use of the most complete expression for both the pressure-velocity and the pressure-temperature correlations presently available. Each of the new terms represents a physical process that, was not accounted for by previous models. The new model is presented in three different levels according to Mellor and Yamada's terminology, with new, ready-to-use expressions for the turbulent, moments. We show that the new model reproduces several experimental and LES data better than previous models. As far as the PBL is concerned, we show that the model reproduces both the Kansas data as analyzed by Businger et al. in the context of Monin-Obukhov similarity theory for smaller Richardson numbers, as well as the LES and laboratory data up to Richardson numbers of order unity. We also show that the model yields a higher PBL height than the previous models.

  16. Topological basis realization for BMW algebra and Heisenberg XXZ spin chain model

    NASA Astrophysics Data System (ADS)

    Liu, Bo; Xue, Kang; Wang, Gangcheng; Liu, Ying; Sun, Chunfang

    2015-04-01

    In this paper, we study three-dimensional (3D) reduced Birman-Murakami-Wenzl (BMW) algebra based on topological basis theory. Several examples of BMW algebra representations are reviewed. We also discuss a special solution of BMW algebra, which can be used to construct Heisenberg XXZ model. The theory of topological basis provides a useful method to solve quantum spin chain models. It is also shown that the ground state of XXZ spin chain is superposition state of topological basis.

  17. Higher order turbulence closure models

    NASA Technical Reports Server (NTRS)

    Amano, Ryoichi S.; Chai, John C.; Chen, Jau-Der

    1988-01-01

    Theoretical models are developed and numerical studies conducted on various types of flows including both elliptic and parabolic. The purpose of this study is to find better higher order closure models for the computations of complex flows. This report summarizes three new achievements: (1) completion of the Reynolds-stress closure by developing a new pressure-strain correlation; (2) development of a parabolic code to compute jets and wakes; and, (3) application to a flow through a 180 deg turnaround duct by adopting a boundary fitted coordinate system. In the above mentioned models near-wall models are developed for pressure-strain correlation and third-moment, and incorporated into the transport equations. This addition improved the results considerably and is recommended for future computations. A new parabolic code to solve shear flows without coordinate tranformations is developed and incorporated in this study. This code uses the structure of the finite volume method to solve the governing equations implicitly. The code was validated with the experimental results available in the literature.

  18. Implementation of Advanced Two Equation Turbulence Models in the USM3D Unstructured Flow Solver

    NASA Technical Reports Server (NTRS)

    Wang, Qun-Zhen; Massey, Steven J.; Abdol-Hamid, Khaled S.

    2000-01-01

    USM3D is a widely-used unstructured flow solver for simulating inviscid and viscous flows over complex geometries. The current version (version 5.0) of USM3D, however, does not have advanced turbulence models to accurately simulate complicated flow. We have implemented two modified versions of the original Jones and Launder k-epsilon "two-equation" turbulence model and the Girimaji algebraic Reynolds stress model in USM3D. Tests have been conducted for three flat plate boundary layer cases, a RAE2822 airfoil and an ONERA M6 wing. The results are compared with those from direct numerical simulation, empirical formulae, theoretical results, and the existing Spalart-Allmaras one-equation model.

  19. Solving Navier-Stokes Equations with Advanced Turbulence Models on Three-Dimensional Unstructured Grids

    NASA Technical Reports Server (NTRS)

    Wang, Qun-Zhen; Massey, Steven J.; Abdol-Hamid, Khaled S.; Frink, Neal T.

    1999-01-01

    USM3D is a widely-used unstructured flow solver for simulating inviscid and viscous flows over complex geometries. The current version (version 5.0) of USM3D, however, does not have advanced turbulence models to accurately simulate complicated flows. We have implemented two modified versions of the original Jones and Launder k-epsilon two-equation turbulence model and the Girimaji algebraic Reynolds stress model in USM3D. Tests have been conducted for two flat plate boundary layer cases, a RAE2822 airfoil and an ONERA M6 wing. The results are compared with those of empirical formulae, theoretical results and the existing Spalart-Allmaras one-equation model.

  20. A critique of some recent second-order turbulence closure models for compressible boundary layers

    NASA Technical Reports Server (NTRS)

    Rubesin, M. W.; Crisalli, A. J.; Horstman, C. C.; Acharya, M.; Lanfranco, M. J.

    1977-01-01

    Computations based on two recently developed second-order turbulence closure models are compared with a series of boundary-layer experiments and with predictions of these experiments using an algebraic mixing length model. One of the models employs an eddy viscosity, whereas the other evaluates components of the Reynolds stress tensor. For flat plates, the computations are compared with the van Driest skin-friction transformation to assess the handling of compressibility. For boundary layers in pressure gradients, four experiments at Mach 4 and one at Mach 6.7 are used as the bases for comparison. In general, both models represent mean velocities and skin friction reasonably well, but represent the turbulence shear stress less accurately.

  1. Modelling the effects of horizontal and vertical shear in stratified turbulent flows

    NASA Astrophysics Data System (ADS)

    Umlauf, Lars

    2005-05-01

    Direct numerical simulations (DNS) and model results from a number of one-point turbulence models are compared for homogeneous, stably stratified flows. Because of their wide spread use in numerical ocean modelling, only explicit algebraic second-moment models are investigated. Considered are two types of shear flows with either purely vertical or purely horizontal shear. The dissipation rate is evaluated from the observation that the shear-number becomes independent of stratification for low to moderate Richardson numbers as soon as the flow approaches self-similarity. For the cases with vertical shear, it is found that all statistical models essentially reproduced the DNS results, though with different accuracy. In contrast, only the most recent model was able to predict the salient features of horizontally sheared flows, i.e. a steady-state Richardson number that is about an order of magnitude larger and a vertical mixing efficiency that is about twice as large compared to the case with vertical shear. This model also reproduced other key parameters like the turbulent Froude number and the turbulent Prandtl number with good accuracy, but it failed to predict quantitatively the reduction of the shear anisotropy with increasing stratification. For strong stratification, none of the models was able to describe the rapid decrease of the mixing efficiency associated with the collapse and fossilisation of turbulence.

  2. Numerical comparison of strong Langmuir turbulence models

    NASA Technical Reports Server (NTRS)

    Shen, Mei-Mei; Nicholson, D. R.

    1987-01-01

    Two models of Langmuir turbulence, the nonlinear Schroedinger equation and the Zakharov equations, are solved numerically for an initial value problem in which the electric field evolves from an almost flat initial condition via the modulational instability and finally saturates into a set of solitons. The two models agree well with each other only when the initial dimensionless electric field has an amplitude less than unity. An analytic soliton gas model consisting of equal-amplitude, randomly spaced, zero-speed solitons is remarkably good at reproducing the time-averaged Fourier spectra in both cases.

  3. Subfilter Scale Combustion Modelling for Large Eddy Simulation of Turbulent Premixed Flames

    NASA Astrophysics Data System (ADS)

    Shahbazian, Nasim

    Large eddy simulation (LES) is a powerful computational tool for modelling turbulent combustion processes. However, for reactive flows, LES is still under significant development. In particular, for turbulent premixed flames, a considerable complication of LES is that the flame thickness is generally much smaller than the LES filter width such that the flame front and chemical reactions cannot be resolved on the grid. Accurate and robust subfilter-scale (SFS) models of the unresolved turbulence-chemistry interactions are therefore required and studies are needed to evaluate and improve them. In this thesis, a detailed comparison and evaluation of five different SFS models for turbulence- chemistry interactions in LES of premixed flames is presented. These approaches include both flamelet- and non-flamelet-based models, coupled with simple or tabulated chemistry. The mod- elling approaches considered herein are: algebraic- and transport-equation variants of the flame surface density (FSD) model, the presumed conditional moment (PCM) with flame prolongation of intrinsic low-dimensional manifold (FPI) tabulated chemistry, or PCM-FPI approach, evaluated with two different presumed probability density function (PDF) models; and conditional source-term estimation (CSE) approach. The predicted LES solutions are compared to the existing laboratory-scale experimental observation of Bunsen-type turbulent premixed methane-air flames, corresponding to lean and stoichiometric conditions lying from the upper limit of the flamelet regime to well within the thin reaction zones regime of the standard regimes diagram. Direct comparison of different SFS approaches allows investigation of stability and performance of the models, while the weaknesses and strengths of each approach are identified. Evaluation of algebraic and transported FSD models highlights the importance of non-equilibrium transport in turbulent premixed flames. The effect of the PDF type for the reaction progress

  4. Direct numerical simulations and modeling of a spatially-evolving turbulent wake

    NASA Technical Reports Server (NTRS)

    Cimbala, John M.

    1994-01-01

    Understanding of turbulent free shear flows (wakes, jets, and mixing layers) is important, not only for scientific interest, but also because of their appearance in numerous practical applications. Turbulent wakes, in particular, have recently received increased attention by researchers at NASA Langley. The turbulent wake generated by a two-dimensional airfoil has been selected as the test-case for detailed high-resolution particle image velocimetry (PIV) experiments. This same wake has also been chosen to enhance NASA's turbulence modeling efforts. Over the past year, the author has completed several wake computations, while visiting NASA through the 1993 and 1994 ASEE summer programs, and also while on sabbatical leave during the 1993-94 academic year. These calculations have included two-equation (K-omega and K-epsilon) models, algebraic stress models (ASM), full Reynolds stress closure models, and direct numerical simulations (DNS). Recently, there has been mutually beneficial collaboration of the experimental and computational efforts. In fact, these projects have been chosen for joint presentation at the NASA Turbulence Peer Review, scheduled for September 1994. DNS calculations are presently underway for a turbulent wake at Re(sub theta) = 1000 and at a Mach number of 0.20. (Theta is the momentum thickness, which remains constant in the wake of a two dimensional body.) These calculations utilize a compressible DNS code written by M. M. Rai of NASA Ames, and modified for the wake by J. Cimbala. The code employs fifth-order accurate upwind-biased finite differencing for the convective terms, fourth-order accurate central differencing for the viscous terms, and an iterative-implicit time-integration scheme. The computational domain for these calculations starts at x/theta = 10, and extends to x/theta = 610. Fully developed turbulent wake profiles, obtained from experimental data from several wake generators, are supplied at the computational inlet, along with

  5. Direct numerical simulations and modeling of a spatially-evolving turbulent wake

    NASA Astrophysics Data System (ADS)

    Cimbala, John M.

    1994-12-01

    Understanding of turbulent free shear flows (wakes, jets, and mixing layers) is important, not only for scientific interest, but also because of their appearance in numerous practical applications. Turbulent wakes, in particular, have recently received increased attention by researchers at NASA Langley. The turbulent wake generated by a two-dimensional airfoil has been selected as the test-case for detailed high-resolution particle image velocimetry (PIV) experiments. This same wake has also been chosen to enhance NASA's turbulence modeling efforts. Over the past year, the author has completed several wake computations, while visiting NASA through the 1993 and 1994 ASEE summer programs, and also while on sabbatical leave during the 1993-94 academic year. These calculations have included two-equation (K-omega and K-epsilon) models, algebraic stress models (ASM), full Reynolds stress closure models, and direct numerical simulations (DNS). Recently, there has been mutually beneficial collaboration of the experimental and computational efforts. In fact, these projects have been chosen for joint presentation at the NASA Turbulence Peer Review, scheduled for September 1994. DNS calculations are presently underway for a turbulent wake at Re(sub theta) = 1000 and at a Mach number of 0.20. (Theta is the momentum thickness, which remains constant in the wake of a two dimensional body.) These calculations utilize a compressible DNS code written by M. M. Rai of NASA Ames, and modified for the wake by J. Cimbala. The code employs fifth-order accurate upwind-biased finite differencing for the convective terms, fourth-order accurate central differencing for the viscous terms, and an iterative-implicit time-integration scheme. The computational domain for these calculations starts at x/theta = 10, and extends to x/theta = 610. Fully developed turbulent wake profiles, obtained from experimental data from several wake generators, are supplied at the computational inlet, along with

  6. An Algebraic Spline Model of Molecular Surfaces for Energetic Computations

    PubMed Central

    Zhao, Wenqi; Bajaj, Chandrajit; Xu, Guoliang

    2009-01-01

    In this paper, we describe a new method to generate a smooth algebraic spline (AS) approximation of the molecular surface (MS) based on an initial coarse triangulation derived from the atomic coordinate information of the biomolecule, resident in the PDB (Protein data bank). Our method first constructs a triangular prism scaffold covering the PDB structure, and then generates a piecewise polynomial F on the Bernstein-Bezier (BB) basis within the scaffold. An ASMS model of the molecular surface is extracted as the zero contours of F which is nearly C1 and has dual implicit and parametric representations. The dual representations allow us easily do the point sampling on the ASMS model and apply it to the accurate estimation of the integrals involved in the electrostatic solvation energy computations. Meanwhile comparing with the trivial piecewise linear surface model, fewer number of sampling points are needed for the ASMS, which effectively reduces the complexity of the energy estimation. PMID:21519111

  7. Parallel Computatinal Technology for Atmospheric Turbulence Modeling

    NASA Astrophysics Data System (ADS)

    Bian, Randy X.

    1997-08-01

    Desktop Atmospheric Turbulence Diffussion Modeling System (DATDMS) is used by analysts with varied backgrounds for performing air quality assessment and emergency response activities. This modeling system must be robust, well documented, have minimal and well controlled user inputs, and have clear outputs. Existing coarse-grained parallel computers can provide significant increases in computation speed in desktop atmospheric dispersion modeling without considerable increases in hardware cost. This increased speed will allow for significant improvements to be made in the scientific foundations of these applied models, in the form of more advanced diffusion schemes and better representation of the wind and turbulence fields. This is especially attractive for emergency response applications where speed and accuracy are of utmost importance. This presentation describes one particular application of coarse-grained parallel computer technology to a desktop complex terrain atmospheric dispersion modeling system. By comparing performance characteristics of the coarse-grained parallel version of the model with the single-processor version, we will demonstrate that applying coarse-grained parallel computer technology to desktop atmospheric dispersion modeling systems will allow us to address critical issues facing future requirements of this class of dispersion models.

  8. A Baroclinic Model of turbulent dusty flows

    SciTech Connect

    Kuhl, A.L.

    1992-04-01

    The problem considered here is the numerical simulation of the turbulent dusty flow induced by explosions over soil surfaces. Some of the unresolved issues are: (1) how much dust is scoured from such surfaces; (2) where does the dust go in the boundary layer; (3) what is the dusty boundary layer height versus time; (4) what are the dusty boundary layer profiles; (5) how much of the dust mass becomes entrained into the dust stem; and (6) where does the dust go in the buoyant cloud? The author proposes a Baroclinic Model for flows with large density variations that actually calculates the turbulent mixing and transport of dust on an adaptive grid. The model is based on the following idealizations: (1) a loose dust bed; (2) an instantaneous shock fluidization of the dust layer; (3) the dust and air are in local equilibrium (so air viscosity enforces the no-slip condition); (4) the dust-air mixture is treated as a continuum dense fluid with zero viscosity; and (5) the turbulent mixing is dominated by baroclinically-generated vorticity. These assumptions lead to an inviscid set of conservation laws for the mixture, which are solved by means of a high-order Godunov algorithm for gasdynamics. Adaptive Mesh Refinement (AMR) is used to capture the turbulent mixing processes on the grid. One of the unique characteristics of these flows is that mixing occurs because vorticity is produced by an inviscid, baroclinic mechanism. A number of examples are presented to illustrate these baroclinic effects including shock interactions with dense-gas layers and dust beds, and dusty wall jets of airblast precursors. The conclusion of these studies is that dusty boundary layers grow because of mass entrainment from the fluidized bed (and not because of viscous wall drag) as proven by the Mass Integral Equation.

  9. A Structural Model of Algebra Achievement: Computational Fluency and Spatial Visualisation as Mediators of the Effect of Working Memory on Algebra Achievement

    ERIC Educational Resources Information Center

    Tolar, Tammy Daun; Lederberg, Amy R.; Fletcher, Jack M.

    2009-01-01

    The goal of this study was to develop and evaluate a structural model of the relations among cognitive abilities and arithmetic skills and college students' algebra achievement. The model of algebra achievement was compared to a model of performance on the Scholastic Assessment in Mathematics (SAT-M) to determine whether the pattern of relations…

  10. Turbulence modeling for non-equilibrium flow

    NASA Technical Reports Server (NTRS)

    Durbin, P. A.

    1995-01-01

    The work performed during this year has involved further assessment and extension of the k-epsilon-v(exp 2) model, and initiation of work on scalar transport. The latter is introduced by the contribution of Y. Shabany to this volume. Flexible, computationally tractable models are needed for engineering CFD. As computational technology has progressed, the ability and need to use elaborate turbulence closure models has increased. The objective of our work is to explore and develop new analytical frameworks that might extend the applicability of the modeling techniques. In past years the development of a method for near-wall modeling was described. The method has been implemented into a CFD code and its viability has been demonstrated by various test cases. Further tests are reported herein. Non-equilibrium near-wall models are needed for some heat transfer applications. Scalar transport seems generally to be more sensitive to non-equilibrium effects than is momentum transport. For some applications turbulence anisotropy plays a role and an estimate of the full Reynolds stress tensor is needed. We have begun work on scalar transport per se, but in this brief I will only report on an extension of the k-epsilon-v(exp 2) model to predict the Reynolds stress tensor.

  11. Turbulence by Design: How to Initialize a Turbulence Model in the Case of the Rayleigh-Taylor Instability

    SciTech Connect

    Rollin, Bertrand; Andrews, Malcolm J.

    2012-07-17

    Importance of initial conditions for turbulence 'design' and prediction are that initial conditions could affect 'late-time' turbulent transport and mixing effectiveness. Hence, a challenge for prediction, but also an opportunity for turbulence 'design'. The objective is to provide a rational basis for setting up initial conditions in turbulence models. Conclusions are: (1) We constructed a modal model for multimode RT; (2) We use a two-fluid formulation for generating profiles of turbulence model variables in the self-similar regime; and (3) We defined an approach to remove any guess from initializing a turbulence model for Rayleigh-Taylor turbulent mixing.

  12. An application of a two-equation model of turbulence to three-dimensional chemically reacting flows

    NASA Technical Reports Server (NTRS)

    Lee, J.

    1994-01-01

    A numerical study of three dimensional chemically reacting and non-reacting flowfields is conducted using a two-equation model of turbulence. A generalized flow solver using an implicit Lower-Upper (LU) diagonal decomposition numerical technique and finite-rate chemistry has been coupled with a low-Reynolds number two-equation model of turbulence. This flow solver is then used to study chemically reacting turbulent supersonic flows inside combustors with synergetic fuel injectors. The reacting and non-reacting turbulent combustor solutions obtained are compared with zero-equation turbulence model solutions and with available experimental data. The hydrogen-air chemistry is modeled using a nine-species/eighteen reaction model. A low-Reynolds number k-epsilon model was used to model the effect of turbulence because, in general, the low-Reynolds number k-epsilon models are easier to implement numerically and are far more general than algebraic models. However, low-Reynolds number k-epsilon models require a much finer near-wall grid resolution than high-Reynolds number models to resolve accurately the near-wall physics. This is especially true in complex flowfields, where the stiff nature of the near-wall turbulence must be resolved. Therefore, the limitations imposed by the near-wall characteristics and compressible model corrections need to be evaluated further. The gradient-diffusion hypothesis is used to model the effects of turbulence on the mass diffusion process. The influence of this low-Reynolds number turbulence model on the reacting flowfield predictions was studied parametrically.

  13. Turbulence modeling for complex hypersonic flows

    NASA Technical Reports Server (NTRS)

    Huang, P. G.; Coakley, T. J.

    1993-01-01

    The paper presents results of calculations for a range of 2D turbulent hypersonic flows using two-equation models. The baseline models and the model corrections required for good hypersonic-flow predictions will be illustrated. Three experimental data sets were chosen for comparison. They are: (1) the hypersonic flare flows of Kussoy and Horstman, (2) a 2D hypersonic compression corner flow of Coleman and Stollery, and (3) the ogive-cylinder impinging shock-expansion flows of Kussoy and Horstman. Comparisons with the experimental data have shown that baseline models under-predict the extent of flow separation but over-predict the heat transfer rate near flow reattachment. Modifications to the models are described which remove the above-mentioned deficiencies. Although we have restricted the discussion only to the selected baseline models in this paper, the modifications proposed are universal and can in principle be transferred to any existing two-equation model formulation.

  14. A simplified Reynolds stress model for unsteady turbulent boundary layers

    NASA Technical Reports Server (NTRS)

    Fan, Sixin; Lakshminarayana, Budugur

    1993-01-01

    A simplified Reynolds stress model has been developed for the prediction of unsteady turbulent boundary layers. By assuming that the net transport of Reynolds stresses is locally proportional to the net transport of the turbulent kinetic energy, the time dependent full Reynolds stress model is reduced to a set of ordinary differential equations. These equations contain only time derivatives and can be readily integrated in a time dependent boundary layer or Navier-Stokes code. The turbulent kinetic energy and dissipation rate needed for the model are obtained by solving the k-epsilon equations. This simplified Reynolds stress turbulence model (SRSM) does not use the eddy viscosity assumption, which may not be valid for unsteady turbulent flows. The anisotropy of both the steady and the unsteady turbulent normal stresses can be captured by the SRSM model. Through proper damping of the shear stresses, the present model can be used in the near wall region of turbulent boundary layers. This model has been validated against data for steady and unsteady turbulent boundary layers, including periodic turbulent boundary layers subjected to a mean adverse pressure gradient. For the cases tested, the predicted unsteady velocity and turbulent stress components agree well with the experimental data. Comparison between the predictions from the SRSM model and a k-epsilon model is also presented.

  15. Model of non-stationary, inhomogeneous turbulence

    NASA Astrophysics Data System (ADS)

    Bragg, Andrew D.; Kurien, Susan; Clark, Timothy T.

    2016-07-01

    We compare results from a spectral model for non-stationary, inhomogeneous turbulence (Besnard et al. in Theor Comp Fluid Dyn 8:1-35, 1996) with direct numerical simulation (DNS) data of a shear-free mixing layer (SFML) (Tordella et al. in Phys Rev E 77:016309, 2008). The SFML is used as a test case in which the efficacy of the model closure for the physical-space transport of the fluid velocity field can be tested in a flow with inhomogeneity, without the additional complexity of mean-flow coupling. The model is able to capture certain features of the SFML quite well for intermediate to long times, including the evolution of the mixing-layer width and turbulent kinetic energy. At short-times, and for more sensitive statistics such as the generation of the velocity field anisotropy, the model is less accurate. We propose two possible causes for the discrepancies. The first is the local approximation to the pressure-transport and the second is the a priori spherical averaging used to reduce the dimensionality of the solution space of the model, from wavevector to wavenumber space. DNS data are then used to gauge the relative importance of both possible deficiencies in the model.

  16. Improved engineering models for turbulent wall flows

    NASA Astrophysics Data System (ADS)

    She, Zhen-Su; Chen, Xi; Zou, Hong-Yue; Hussain, Fazle

    2015-11-01

    We propose a new approach, called structural ensemble dynamics (SED), involving new concepts to describe the mean quantities in wall-bounded flows, and its application to improving the existing engineering turbulence models, as well as its physical interpretation. First, a revised k - ω model for pipe flows is obtained, which accurately predicts, for the first time, both mean velocity and (streamwise) kinetic energy for a wide range of the Reynolds number (Re), validated by Princeton experimental data. In particular, a multiplicative factor is introduced in the dissipation term to model an anomaly in the energy cascade in a meso-layer, predicting the outer peak of agreeing with data. Secondly, a new one-equation model is obtained for compressible turbulent boundary layers (CTBL), building on a multi-layer formula of the stress length function and a generalized temperature-velocity relation. The former refines the multi-layer description - viscous sublayer, buffer layer, logarithmic layer and a newly defined bulk zone - while the latter characterizes a parabolic relation between the mean velocity and temperature. DNS data show our predictions to have a 99% accuracy for several Mach numbers Ma = 2.25, 4.5, improving, up to 10%, a previous similar one-equation model (Baldwin & Lomax, 1978). Our results promise notable improvements in engineering models.

  17. On the modelling of non-reactive and reactive turbulent combustor flows

    NASA Technical Reports Server (NTRS)

    Nikjooy, Mohammad; So, Ronald M. C.

    1987-01-01

    A study of non-reactive and reactive axisymmetric combustor flows with and without swirl is presented. Closure of the Reynolds equations is achieved by three models: kappa-epsilon, algebraic stress and Reynolds stress closure. Performance of two locally nonequilibrium and one equilibrium algebraic stress models is analyzed assuming four pressure strain models. A comparison is also made of the performance of a high and a low Reynolds number model for combustor flow calculations using Reynolds stress closures. Effects of diffusion and pressure-strain models on these closures are also investigated. Two models for the scalar transport are presented. One employs the second-moment closure which solves the transport equations for the scalar fluxes, while the other solves the algebraic equations for the scalar fluxes. In addition, two cases of non-premixed and one case of premixed combustion are considered. Fast- and finite-rate chemistry models are applied to non-premixed combustion. Both show promise for application in gas turbine combustors. However, finite rate chemistry models need to be examined to establish a suitable coupling of the heat release effects on turbulence field and rate constants.

  18. Evaluation of laminar-turbulent transition and equilibrium near wall turbulence models

    SciTech Connect

    He, X.; Senocak, I.; Shyy, W.; Gangadharan, S.N.; Thakur, S.

    2000-02-11

    Accurate prediction of laminar-turbulent transition as well as fully turbulent flows is of much practical importance. In this study, both topics are investigated. The e{sup n} method is used to predict transition locations for flows with various angles of attack around on NACA 0012 airfoil. After the transition point the {kappa}-{epsilon} turbulence model is adopted. Computations for flow over a flat plate are done to understand the impact of grid distribution and the wall function treatment on the performance of the {kappa}-{epsilon} turbulence model. In attached and mildly separated flows, satisfactory predictions can be made with the pragmatic e{sup n} transition model and the {kappa}-{epsilon} turbulence model.

  19. A k-epsilon modeling of near wall turbulence

    NASA Technical Reports Server (NTRS)

    Yang, Z.; Shih, T. H.

    1991-01-01

    A k-epsilon model is proposed for turbulent bounded flows. In this model, the turbulent velocity scale and turbulent time scale are used to define the eddy viscosity. The time scale is shown to be bounded from below by the Kolmogorov time scale. The dissipation equation is reformulated using the time scale, removing the need to introduce the pseudo-dissipation. A damping function is chosen such that the shear stress satisfies the near wall asymptotic behavior. The model constants used are the same as the model constants in the commonly used high turbulent Reynolds number k-epsilon model. Fully developed turbulent channel flows and turbulent boundary layer flows over a flat plate at various Reynolds numbers are used to validate the model. The model predictions were found to be in good agreement with the direct numerical simulation data.

  20. Spectral models of strongly inhomogeneous turbulence

    NASA Astrophysics Data System (ADS)

    Bragg, Andrew; Kurien, Susan; Clark, Timothy

    2015-11-01

    We compare results from a spectral model for inhomogeneous turbulence (Besnard et al., Theor. Comp. Fluid. Dyn., vol. 8, pp 1-35, 1996) with DNS data of a shear-free mixing layer (SFML) (Tordella et al., Phys. Rev. E, vol. 77, 016309, 2008). The SFML is used as a test case in which the efficacy of the model closure for the physical-space energy transport can be tested in a flow with strong inhomogeneity, without the additional complexity of mean-flow coupling. The model is able to capture certain features of the SFML quite well for intermediate to long-times, including the evolution of the mixing-layer width and turbulent kinetic energy. At short-times, and for more sensitive statistics such as the generation of the velocity field anisotropy, the model does not work so well. It may be argued that the discrepancy arises due to the local approximation to the intrinsically non-local pressure transport in physical-space, the effect of which would be particularly strong at short-times when the inhomogeneity of the SFML is strongest. Motivated by these results, we briefly discuss a new model that captures the non-local transport effects, for arbitrarily strong inhomogeneities of the flow.

  1. Toward Better Modeling of Supercritical Turbulent Mixing

    NASA Technical Reports Server (NTRS)

    Selle, Laurent; Okongo'o, Nora; Bellan, Josette; Harstad, Kenneth

    2008-01-01

    study was done as part of an effort to develop computational models representing turbulent mixing under thermodynamic supercritical (here, high pressure) conditions. The question was whether the large-eddy simulation (LES) approach, developed previously for atmospheric-pressure compressible-perfect-gas and incompressible flows, can be extended to real-gas non-ideal (including supercritical) fluid mixtures. [In LES, the governing equations are approximated such that the flow field is spatially filtered and subgrid-scale (SGS) phenomena are represented by models.] The study included analyses of results from direct numerical simulation (DNS) of several such mixing layers based on the Navier-Stokes, total-energy, and conservation- of-chemical-species governing equations. Comparison of LES and DNS results revealed the need to augment the atmospheric- pressure LES equations with additional SGS momentum and energy terms. These new terms are the direct result of high-density-gradient-magnitude regions found in the DNS and observed experimentally under fully turbulent flow conditions. A model has been derived for the new term in the momentum equation and was found to perform well at small filter size but to deteriorate with increasing filter size. Several alternative models were derived for the new SGS term in the energy equation that would need further investigations to determine if they are too computationally intensive in LES.

  2. Phases and phase transitions in the algebraic microscopic shell model

    NASA Astrophysics Data System (ADS)

    Georgieva, A. I.; Drumev, K. P.

    2016-01-01

    We explore the dynamical symmetries of the shell model number conserving algebra, which define three types of pairing and quadrupole phases, with the aim to obtain the prevailing phase or phase transition for the real nuclear systems in a single shell. This is achieved by establishing a correspondence between each of the pairing bases with the Elliott's SU(3) basis that describes collective rotation of nuclear systems. This allows for a complete classification of the basis states of different number of particles in all the limiting cases. The probability distribution of the SU(3) basis states within theirs corresponding pairing states is also obtained. The relative strengths of dynamically symmetric quadrupole-quadrupole interaction in respect to the isoscalar, isovector and total pairing interactions define a control parameter, which estimates the importance of each term of the Hamiltonian in the correct reproduction of the experimental data for the considered nuclei.

  3. Finite-element numerical modeling of atmospheric turbulent boundary layer

    NASA Technical Reports Server (NTRS)

    Lee, H. N.; Kao, S. K.

    1979-01-01

    A dynamic turbulent boundary-layer model in the neutral atmosphere is constructed, using a dynamic turbulent equation of the eddy viscosity coefficient for momentum derived from the relationship among the turbulent dissipation rate, the turbulent kinetic energy and the eddy viscosity coefficient, with aid of the turbulent second-order closure scheme. A finite-element technique was used for the numerical integration. In preliminary results, the behavior of the neutral planetary boundary layer agrees well with the available data and with the existing elaborate turbulent models, using a finite-difference scheme. The proposed dynamic formulation of the eddy viscosity coefficient for momentum is particularly attractive and can provide a viable alternative approach to study atmospheric turbulence, diffusion and air pollution.

  4. Nonaxisymmetric anisotropy of solar wind turbulence as a direct test for models of magnetohydrodynamic turbulence.

    PubMed

    Turner, A J; Gogoberidze, G; Chapman, S C

    2012-02-24

    Single point spacecraft observations of the turbulent solar wind flow exhibit a characteristic nonaxisymmetric anisotropy that depends sensitively on the perpendicular power spectral exponent. We use this nonaxisymmetric anisotropy as a function of wave vector direction to test models of MHD turbulence. Using Ulysses magnetic field observations in the fast, quiet polar solar wind we find that the Goldreich-Sridhar model of MHD turbulence is not consistent with the observed anisotropy, whereas the observations are well reproduced by the "slab+2D" model. The Goldreich-Sridhar model alone cannot account for the observations unless an additional component is also present. PMID:22463536

  5. Numerical modeling of the interaction between an electric arc and a turbulent gas flow - A turbulence model

    NASA Astrophysics Data System (ADS)

    Artemov, V. I.; Sinkevich, O. A.

    1986-02-01

    A semiempirical turbulence model describing the interaction between an electric arc and a turbulent gas flow is proposed which is based on the closure of the balance equations of second-order moments. The model accounts for the effect of gas density and electrodynamic parameter fluctuations. Based on the model proposed here, an algorithm is developed for calculating turbulent plasma flows in channels with complex boundary conditions, such as injection and suction. The efficiency of the model is verified experimentally.

  6. Stellarator Turbulence: Subdominant Eigenmodes and Quasilinear Modeling

    NASA Astrophysics Data System (ADS)

    Pueschel, M. J.; Faber, B. J.; Citrin, J.; Hegna, C. C.; Terry, P. W.; Hatch, D. R.

    2016-02-01

    Owing to complex geometry, gyrokinetic simulations in stellarator geometry produce large numbers of subdominant unstable and stable, near-orthogonal eigenmodes. Here, results based on the full eigenmode spectrum in stellarator geometry are presented for the first time. In the nonlinear state of a low-magnetic-shear ion-temperature-gradient-driven case, a multitude of these modes are active and imprint the system. Turbulent frequency spectra are broadband as a consequence, in addition to a nonlinear, narrow signature at electron frequencies. It is shown that successful quasilinear, mixing-length transport modeling is possible in stellarators, where it is essential to account for all subdominant unstable modes.

  7. Low dimensional modeling of wall turbulence

    NASA Astrophysics Data System (ADS)

    Aubry, Nadine

    2015-11-01

    In this talk we will review the original low dimensional dynamical model of the wall region of a turbulent boundary layer [Aubry, Holmes, Lumley and Stone, Journal of Fluid Dynamics 192, 1988] and discuss its impact on the field of fluid dynamics. We will also invite a few researchers who would like to make brief comments on the influence Lumley had on their research paths. In collaboration with Philip Holmes, Program in Applied and Computational Mathematics and Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ.

  8. An Initial Investigation of the Effects of Turbulence Models on the Convergence of the RK/Implicit Scheme

    NASA Technical Reports Server (NTRS)

    Swanson, R. C.; Rossow, C.-C.

    2008-01-01

    A three-stage Runge-Kutta (RK) scheme with multigrid and an implicit preconditioner has been shown to be an effective solver for the fluid dynamic equations. This scheme has been applied to both the compressible and essentially incompressible Reynolds-averaged Navier-Stokes (RANS) equations using the algebraic turbulence model of Baldwin and Lomax (BL). In this paper we focus on the convergence of the RK/implicit scheme when the effects of turbulence are represented by either the Spalart-Allmaras model or the Wilcox k-! model, which are frequently used models in practical fluid dynamic applications. Convergence behavior of the scheme with these turbulence models and the BL model are directly compared. For this initial investigation we solve the flow equations and the partial differential equations of the turbulence models indirectly coupled. With this approach we examine the convergence behavior of each system. Both point and line symmetric Gauss-Seidel are considered for approximating the inverse of the implicit operator of the flow solver. To solve the turbulence equations we use a diagonally dominant alternating direction implicit (DDADI) scheme. Computational results are presented for three airfoil flow cases and comparisons are made with experimental data. We demonstrate that the two-dimensional RANS equations and transport-type equations for turbulence modeling can be efficiently solved with an indirectly coupled algorithm that uses the RK/implicit scheme for the flow equations.

  9. Turbulence modeling in non-inertial frames of reference

    NASA Technical Reports Server (NTRS)

    Speziale, Charles G.

    1988-01-01

    The effect of an arbitrary change of frame on the structure of turbulence models is examined from a fundamental theoretical standpoint. It is proven, as a rigorous consequence of the Navier-Stokes equations, that turbulence models must be form invariant under arbitrary translational accelerations of the reference frame and should only be affected by rotations through the intrinsic mean vorticity. A direct application of the invariance property along with the Taylor-Proudman Theorem, material frame-indifference in the limit of two-dimensional turbulence and Rapid Distortion Theory is shown to yield powerful constraints on the allowable form of turbulence models. Most of the commonly used turbulence models are demonstrated to be in serious violation of these constraints and consequently are inconsistent with the Navier-Stokes equations in non-inertial frames. Alternative models with improved non-inertial properties are developed and some simple applications to rotating turbulent flows are considered.

  10. Turbulence Modeling of Non-equilibrium Flows Using Turbulent Body Force Potentials

    NASA Astrophysics Data System (ADS)

    Wang, Hudong; Perot, Blair

    1998-11-01

    Results of a new turbulence model for non-equilibrium flow which is based on turbulent body force potentials are presented. Initial predictions of the model for basic turbulent flows produced promising results. This work concentrates on predicting more complex and realistic turbulent flows that are similar to the problems in design and manufacturing process. Three major cases are presented and the computational results are compared with existing experimental data and DNS data whenever possible. First, backwards-facing step flows at both high and low Reynolds numbers are investigated in order to evaluate the model's ability for correctly predicting separation and reattachment. Second, two adverse pressure gradient flows are analyzed, namely, the classic Samuel & Joubert flow and more severe case documented by Schubauer & Spangenberg. Finally, the performance of the model in predicting stagnation flows is evaluated by investigating planar and axisymmetric impinging jets. Comparisons show that model predictions match well with experimental data and DNS data. It is demonstrated that by introducing turbulent body force potentials this new non-equilibrium turbulence model is able to predict complex turbulent flows as well as Reynolds stress transport models with significant less computational cost and complexity.

  11. Wave turbulence in shallow water models.

    PubMed

    Clark di Leoni, P; Cobelli, P J; Mininni, P D

    2014-06-01

    We study wave turbulence in shallow water flows in numerical simulations using two different approximations: the shallow water model and the Boussinesq model with weak dispersion. The equations for both models were solved using periodic grids with up to 2048{2} points. In all simulations, the Froude number varies between 0.015 and 0.05, while the Reynolds number and level of dispersion are varied in a broader range to span different regimes. In all cases, most of the energy in the system remains in the waves, even after integrating the system for very long times. For shallow flows, nonlinear waves are nondispersive and the spectrum of potential energy is compatible with ∼k{-2} scaling. For deeper (Boussinesq) flows, the nonlinear dispersion relation as directly measured from the wave and frequency spectrum (calculated independently) shows signatures of dispersion, and the spectrum of potential energy is compatible with predictions of weak turbulence theory, ∼k{-4/3}. In this latter case, the nonlinear dispersion relation differs from the linear one and has two branches, which we explain with a simple qualitative argument. Finally, we study probability density functions of the surface height and find that in all cases the distributions are asymmetric. The probability density function can be approximated by a skewed normal distribution as well as by a Tayfun distribution. PMID:25019897

  12. Turbulence modeling for impinging jet flows

    NASA Technical Reports Server (NTRS)

    Childs, Robert E.; Rodman, Laura C.; Bradshaw, Peter; Bott, Donald M.; Shoemaker, William C.

    1992-01-01

    The objective of the present work is to improve the accuracy of the k-epsilon turbulence model for flows involving one or more jets impinging on a plate in a crossflow which generate a horseshoe vortex. The k-epsilon model is modified by adding source terms to the epsilon equation, which enables it to more accurately predict the shear stress in flows subject to streamline curvature and vortex stretching (or lateral divergence). Calculations with the modified model predict the ground vortex core to be about 15 percent upstream of its experimental location. This is a significant improvement over the standard model which yields higher errors for calculation of the vortex-core location.

  13. Re"modeling" College Algebra: An Active Learning Approach

    ERIC Educational Resources Information Center

    Pinzon, D.; Pinzon, K.; Stackpole, M.

    2016-01-01

    In this paper, we discuss active learning in College Algebra at Georgia Gwinnett College. This approach has been used in more than 20 sections of College Algebra taught by the authors in the past four semesters. Students work in small, structured groups on guided inquiry activities after watching 15-20 minutes of videos before class. We discuss a…

  14. Multigrid acceleration and turbulence models for computations of 3D turbulent jets in crossflow

    NASA Technical Reports Server (NTRS)

    Demuren, A. O.

    1992-01-01

    A multigrid method is presented for the calculation of three-dimensional turbulent jets in crossflow. Turbulence closure is achieved with either the standard k-epsilon model or a Reynolds stress model (RSM). Multigrid acceleration enables convergence rates which are far superior to that for a single grid method to be obtained with both turbulence models. With the k-epsilon model the rate approaches that for laminar flow, but with RSM it is somewhat slower. The increased stiffness of the system of equation in the latter may be responsible. Computed results with both turbulence models are compared to experimental data for a pair of opposed jets in crossflow. Both models yield reasonable agreement for the mean flow velocity, but RSM yields better predictions of the Reynolds stresses.

  15. Kolmogorov Behavior of Near-Wall Turbulence and Its Application in Turbulence Modeling

    NASA Technical Reports Server (NTRS)

    Shih, Tsan-Hsing; Lumley, John L.

    1992-01-01

    The near-wall behavior of turbulence is re-examined in a way different from that proposed by Hanjalic and Launder and followers. It is shown that at a certain distance from the wall, all energetic large eddies will reduce to Kolmogorov eddies (the smallest eddies in turbulence). All the important wall parameters, such as friction velocity, viscous length scale, and mean strain rate at the wall, are characterized by Kolmogorov microscales. According to this Kolmogorov behavior of near-wall turbulence, the turbulence quantities, such as turbulent kinetic energy, dissipation rate, etc. at the location where the large eddies become Kolmogorov eddies, can be estimated by using both direct numerical simulation (DNS) data and asymptotic analysis of near-wall turbulence. This information will provide useful boundary conditions for the turbulent transport equations. As an example, the concept is incorporated in the standard k-epsilon model which is then applied to channel and boundary flows. Using appropriate boundary conditions (based on Kolmogorov behavior of near-wall turbulence), there is no need for any wall-modification to the k-epsilon equations (including model constants). Results compare very well with the DNS and experimental data.

  16. Second-order closure models for supersonic turbulent flows

    NASA Technical Reports Server (NTRS)

    Speziale, Charles G.; Sarkar, Sutanu

    1991-01-01

    Recent work on the development of a second-order closure model for high-speed compressible flows is reviewed. This turbulent closure is based on the solution of modeled transport equations for the Favre-averaged Reynolds stress tensor and the solenoidal part of the turbulent dissipation rate. A new model for the compressible dissipation is used along with traditional gradient transport models for the Reynolds heat flux and mass flux terms. Consistent with simple asymptotic analyses, the deviatoric part of the remaining higher-order correlations in the Reynolds stress transport equations are modeled by a variable density extension of the newest incompressible models. The resulting second-order closure model is tested in a variety of compressible turbulent flows which include the decay of isotropic turbulence, homogeneous shear flow, the supersonic mixing layer, and the supersonic flat-plate turbulent boundary layer. Comparisons between the model predictions and the results of physical and numerical experiments are quite encouraging.

  17. Numerical modeling of pulsatile turbulent flow in stenotic vessels.

    PubMed

    Varghese, Sonu S; Frankel, Steven H

    2003-08-01

    Pulsatile turbulent flow in stenotic vessels has been numerically modeled using the Reynolds-averaged Navier-Stokes equation approach. The commercially available computational fluid dynamics code (CFD), FLUENT, has been used for these studies. Two different experiments were modeled involving pulsatile flow through axisymmetric stenoses. Four different turbulence models were employed to study their influence on the results. It was found that the low Reynolds number k-omega turbulence model was in much better agreement with previous experimental measurements than both the low and high Reynolds number versions of the RNG (renormalization-group theory) k-epsilon turbulence model and the standard k-epsilon model, with regard to predicting the mean flow distal to the stenosis including aspects of the vortex shedding process and the turbulent flow field. All models predicted a wall shear stress peak at the throat of the stenosis with minimum values observed distal to the stenosis where flow separation occurred. PMID:12968569

  18. Four-component numerical simulation model of radiative convective interactions in large-scale oxygen-hydrogen turbulent fire balls

    SciTech Connect

    Surzhikov, S.T.

    1996-12-31

    Two-dimensional radiative gas dynamics model for numerical simulation of oxygen-hydrogen fire ball which may be generated by an explosion of a launch vehicle with cryogenic (LO{sub 2}-LH{sub 2}) fuel components is presented. The following physical-chemical processes are taken into account in the numerical model: and effective chemical reaction between the gaseous components (O{sub 2}-H{sub 2}) of the propellant, turbulent mixing and diffusion of the components, and radiative heat transfer. The results of numerical investigations of the following problems are presented: The influence of radiative heat transfer on fire ball gas dynamics during the first 13 sec after explosion, the effect of the fuel gaseous components afterburning on fire ball gas dynamics, and the effect of turbulence on fire ball gas dynamics (in a framework of algebraic model of turbulent mixing).

  19. Improvement of the second- and third-moment modeling of turbulence: A study of Reynolds-stress closure model

    NASA Technical Reports Server (NTRS)

    Amano, R. S.; Goel, P.

    1986-01-01

    Four parts of the Reynolds-stress closure modeling are reported: (1) improvement of the k and epsilon equaitons; (2) development of the third-moment transport equation; (3) formulation of the diffusion coefficient of the momentum equation by using the algebraic-stress model of turbulence; and (4) the application of the Reynolds-stress model to a heat exchanger problem. It was demonstrated that the third-moment transport model improved the prediction of the triple-velocity products in the recirculating and reattaching flow regions in comparison with the existing algebraic models for the triple-velocity products. Optimum values for empirical coefficients are obtained for the prediction of the backward-facing step flows. A functional expression is derived for the coefficient of the momentum diffusion by employing the algebraic-stress model. The second-moment closure is applied to a heat transfer problem. The computations for the flow in a corrugated-wall channel show that the second-moment closure improves the prediction of the heat transfer rates by 30% over the k - epsilon model.

  20. Gyrofluid-Gyrokinetic Hybrid Turbulence Model

    NASA Astrophysics Data System (ADS)

    Dorland, William; Mandell, Noah

    2015-11-01

    Gyrofluid models of tokamak turbulence are efficient compared to gyrokinetic models, in three senses. First, it is typically easier to develop one's intuition from fluid equations than kinetic equations. Second, because gyrofluid equations are only three-dimensional (instead of 5D or 6D), simulations with gyrofluid models require less memory than kinetic simulations and can therefore more easily fit on highly-optimized computing hardware, such as graphics processors. The third advantage is a result of the first two: one can develop and test ideas quickly with gyrofluid models. The disadvantage of gyrofluid models is their potential lack of physics fidelity. In this poster, we present our attempt to take full advantage of gyrofluid models, without sacrificing physics fidelity. Our approach is encapsulated in the Gryf-X code, which is an implementation of hybrid gyrofluid/gyrokinetic equations. The key improvements that we have brought to bear are: an improved understanding of the cascade of free energy simultaneously in k⊥ and v⊥ an improved model of zonal flow physics; and an implementation of the equations on modern heterogeneous computing platforms, both as a standalone simulation tool and as a component of TRINITY (a transport modeling code for tokamaks).

  1. A weakened cascade model for turbulence in astrophysical plasmas

    SciTech Connect

    Howes, G. G.; TenBarge, J. M.; Dorland, W.

    2011-10-15

    A refined cascade model for kinetic turbulence in weakly collisional astrophysical plasmas is presented that includes both the transition between weak and strong turbulence and the effect of nonlocal interactions on the nonlinear transfer of energy. The model describes the transition between weak and strong MHD turbulence and the complementary transition from strong kinetic Alfven wave (KAW) turbulence to weak dissipating KAW turbulence, a new regime of weak turbulence in which the effects of shearing by large scale motions and kinetic dissipation play an important role. The inclusion of the effect of nonlocal motions on the nonlinear energy cascade rate in the dissipation range, specifically the shearing by large-scale motions, is proposed to explain the nearly power-law energy spectra observed in the dissipation range of both kinetic numerical simulations and solar wind observations.

  2. On specification of initial conditions in turbulence models

    SciTech Connect

    Rollin, Bertrand; Andrews, Malcolm J

    2010-12-01

    Recent research has shown that initial conditions have a significant influence on the evolution of a flow towards turbulence. This important finding offers a unique opportunity for turbulence control, but also raises the question of how to properly specify initial conditions in turbulence models. We study this problem in the context of the Rayleigh-Taylor instability. The Rayleigh-Taylor instability is an interfacial fluid instability that leads to turbulence and turbulent mixing. It occurs when a light fluid is accelerated in to a heavy fluid because of misalignment between density and pressure gradients. The Rayleigh-Taylor instability plays a key role in a wide variety of natural and man-made flows ranging from supernovae to the implosion phase of Inertial Confinement Fusion (ICF). Our approach consists of providing the turbulence models with a predicted profile of its key variables at the appropriate time in accordance to the initial conditions of the problem.

  3. Turbulence model development and application at Lockheed Fort Worth Company

    NASA Technical Reports Server (NTRS)

    Smith, Brian R.

    1995-01-01

    This viewgraph presentation demonstrates that computationally efficient k-l and k-kl turbulence models have been developed and implemented at Lockheed Fort Worth Company. Many years of experience have been gained applying two equation turbulence models to complex three-dimensional flows for design and analysis.

  4. Industry-Wide Workshop on Computational Turbulence Modeling

    NASA Technical Reports Server (NTRS)

    Shabbir, Aamir (Compiler)

    1995-01-01

    This publication contains the presentations made at the Industry-Wide Workshop on Computational Turbulence Modeling which took place on October 6-7, 1994. The purpose of the workshop was to initiate the transfer of technology developed at Lewis Research Center to industry and to discuss the current status and the future needs of turbulence models in industrial CFD.

  5. Turbulence modeling for high speed compressible flows

    NASA Technical Reports Server (NTRS)

    Chandra, Suresh

    1993-01-01

    The following grant objectives were delineated in the proposal to NASA: to offer course work in computational fluid dynamics (CFD) and related areas to enable mechanical engineering students at North Carolina A&T State University (N.C. A&TSU) to pursue M.S. studies in CFD, and to enable students and faculty to engage in research in high speed compressible flows. Since no CFD-related activity existed at N.C. A&TSU before the start of the NASA grant period, training of students in the CFD area and initiation of research in high speed compressible flows were proposed as the key aspects of the project. To that end, graduate level courses in CFD, boundary layer theory, and fluid dynamics were offered. This effort included initiating a CFD course for graduate students. Also, research work was performed on studying compressibility effects in high speed flows. Specifically, a modified compressible dissipation model, which included a fourth order turbulent Mach number term, was incorporated into the SPARK code and verified for the air-air mixing layer case. The results obtained for this case were compared with a wide variety of experimental data to discern the trends in the mixing layer growth rates with varying convective Mach numbers. Comparison of the predictions of the study with the results of several analytical models was also carried out. The details of the research study are described in the publication entitled 'Compressibility Effects in Modeling Turbulent High Speed Mixing Layers,' which is attached to this report.

  6. Turbulence modeling for high speed compressible flows

    NASA Astrophysics Data System (ADS)

    Chandra, Suresh

    1993-08-01

    The following grant objectives were delineated in the proposal to NASA: to offer course work in computational fluid dynamics (CFD) and related areas to enable mechanical engineering students at North Carolina A&T State University (N.C. A&TSU) to pursue M.S. studies in CFD, and to enable students and faculty to engage in research in high speed compressible flows. Since no CFD-related activity existed at N.C. A&TSU before the start of the NASA grant period, training of students in the CFD area and initiation of research in high speed compressible flows were proposed as the key aspects of the project. To that end, graduate level courses in CFD, boundary layer theory, and fluid dynamics were offered. This effort included initiating a CFD course for graduate students. Also, research work was performed on studying compressibility effects in high speed flows. Specifically, a modified compressible dissipation model, which included a fourth order turbulent Mach number term, was incorporated into the SPARK code and verified for the air-air mixing layer case. The results obtained for this case were compared with a wide variety of experimental data to discern the trends in the mixing layer growth rates with varying convective Mach numbers. Comparison of the predictions of the study with the results of several analytical models was also carried out. The details of the research study are described in the publication entitled 'Compressibility Effects in Modeling Turbulent High Speed Mixing Layers,' which is attached to this report.

  7. Analysis of DIRAC's behavior using model checking with process algebra

    NASA Astrophysics Data System (ADS)

    Remenska, Daniela; Templon, Jeff; Willemse, Tim; Bal, Henri; Verstoep, Kees; Fokkink, Wan; Charpentier, Philippe; Graciani Diaz, Ricardo; Lanciotti, Elisa; Roiser, Stefan; Ciba, Krzysztof

    2012-12-01

    DIRAC is the grid solution developed to support LHCb production activities as well as user data analysis. It consists of distributed services and agents delivering the workload to the grid resources. Services maintain database back-ends to store dynamic state information of entities such as jobs, queues, staging requests, etc. Agents use polling to check and possibly react to changes in the system state. Each agent's logic is relatively simple; the main complexity lies in their cooperation. Agents run concurrently, and collaborate using the databases as shared memory. The databases can be accessed directly by the agents if running locally or through a DIRAC service interface if necessary. This shared-memory model causes entities to occasionally get into inconsistent states. Tracing and fixing such problems becomes formidable due to the inherent parallelism present. We propose more rigorous methods to cope with this. Model checking is one such technique for analysis of an abstract model of a system. Unlike conventional testing, it allows full control over the parallel processes execution, and supports exhaustive state-space exploration. We used the mCRL2 language and toolset to model the behavior of two related DIRAC subsystems: the workload and storage management system. Based on process algebra, mCRL2 allows defining custom data types as well as functions over these. This makes it suitable for modeling the data manipulations made by DIRAC's agents. By visualizing the state space and replaying scenarios with the toolkit's simulator, we have detected race-conditions and deadlocks in these systems, which, in several cases, were confirmed to occur in the reality. Several properties of interest were formulated and verified with the tool. Our future direction is automating the translation from DIRAC to a formal model.

  8. Turbulence modeling of compound open-channel flows with and without vegetation on the floodplain using the Reynolds stress model

    NASA Astrophysics Data System (ADS)

    Kang, Hyeongsik; Choi, Sung-Uk

    2006-11-01

    A Reynolds stress model for the numerical simulation of compound open-channel flows with vegetation on the floodplain is described. The Reynolds stress model consists of various sub-models such as Speziale et al.'s model, Mellor and Herring's model, and Rotta's model for the pressure-strain correlation term, the turbulent diffusion term, and the dissipation term, respectively. For validation of the model, plain compound open-channel flows are simulated. The computed results were compared with measured data by [Tominaga A, Nezu I. Turbulent structure in compound open-channel flows. J Hydraul Eng, ASCE 1991;117(1):21-41] and the results show that the Reynolds stress model successfully simulates the mean flow and turbulence structure of plain compound channel flows. The model was then applied to compound open-channel flows with vegetated floodplains. Good agreement between the simulated results and data from an algebraic stress model by [Naot D, Nezu I, Nakagawa H. Hydrodynamic behavior of partly vegetated open channels. J Hydraul Eng, ASCE 1996;122(11):625-33] was found. However, it was shown that the RSM is capable of predicting the velocity dip and lateral shift in the maximum streamwise velocity, which were not observed in the data from algebraic stress modeling. Finally, a depth-averaged analysis of the streamwise momentum equation was performed to investigate the lateral momentum transfer in compound channel flows with vegetated floodplains. Compared with components by the secondary currents and Reynolds stress, the drag force due to the presence of vegetation appears to be a factor in reducing the bottom shear stress in both main channel and floodplain.

  9. Analysis of two-equation turbulence models for recirculating flows

    NASA Technical Reports Server (NTRS)

    Thangam, S.

    1991-01-01

    The two-equation kappa-epsilon model is used to analyze turbulent separated flow past a backward-facing step. It is shown that if the model constraints are modified to be consistent with the accepted energy decay rate for isotropic turbulence, the dominant features of the flow field, namely the size of the separation bubble and the streamwise component of the mean velocity, can be accurately predicted. In addition, except in the vicinity of the step, very good predictions for the turbulent shear stress, the wall pressure, and the wall shear stress are obtained. The model is also shown to provide good predictions for the turbulence intensity in the region downstream of the reattachment point. Estimated long time growth rates for the turbulent kinetic energy and dissipation rate of homogeneous shear flow are utilized to develop an optimal set of constants for the two equation kappa-epsilon model. The physical implications of the model performance are also discussed.

  10. Comparing turbulence models for flow through a rigid glottal model.

    PubMed

    Suh, Jungsoo; Frankel, Steven H

    2008-03-01

    Flow through a rigid model of the human vocal tract featuring a divergent glottis was numerically modeled using the Reynolds-averaged Navier-Stokes approach. A number of different turbulence models, available in a widely used commercial computational fluid dynamics code, were tested to determine their ability to capture various flow features recently observed in laboratory experiments and large eddy simulation studies. The study reveals that results from unsteady simulations employing the k-omega shear stress transport model were in much better agreement with previous measurements and predictions with regard to the ability to predict glottal jet skewing due to the Coanda effect and the intraglottal pressure distribution or related skin friction coefficient, than either steady or unsteady simulations using the Spalart-Allmaras model or any other two-equation turbulence model investigated in this study. PMID:18345812

  11. Modelling turbulent flame ignition and blowout

    NASA Technical Reports Server (NTRS)

    Radhakrishnan, K.; Heywood, J. B.

    1979-01-01

    A statistical mixing model incorporating an overall rate equation to describe the fuel oxidation process was developed for studies of ignition and blowout in a combustor primary zone. This zone is treated as a partially stirred reactor whose composition is described by a statistical ensemble of equal mass fluid elements. This ensemble experiences mixing interactions, which represent the turbulent mixing process, at time intervals governed by an empirically determined mixing frequency. Each mixing interaction is computed by ramdomly selecting two different elements which are then allowed to mix completely so that they reach a mean composition depending on their thermodynamic states prior to mixing. The two elements then separate, and the chemical kinetics proceed depending on their new composition and temperature.

  12. Turbulence modeling in supersonic combusting flows

    NASA Technical Reports Server (NTRS)

    Chitsomboon, Tawit

    1991-01-01

    To support the National Aerospace Plane project, the RPLUS3D CFD code has been developed at NASA Lewis. The code has the ability to solve three-dimensional flowfields with finite rate combustion of hydrogen and air. The combustion processes of the hydrogen-air system are simulated by an 18-reaction path, 8-species chemical kinetic mechanism. The code uses a Lower-Upper (LU) decomposition numerical algorithm as its basis, making it a very efficient and robust code. Except for the Jacobian matrix for the implicit chemistry source terms, there is no inversion of a matrix even though it uses a fully implicit numerical algorithm. A k-epsilon (two equation) turbulence model is incorporated into the RPLUS3D code.

  13. A critical comparison of two-equation turbulence models

    NASA Technical Reports Server (NTRS)

    Lang, N. J.; Shih, T. H.

    1991-01-01

    Several two-equation models were proposed and tested against benchmark flows by various researchers. For each study, different numerical methods or codes were used to obtain the results which were reported to be an improvement over other models. However, these comparisons may be overshadowed by the different numerical schemes used to obtain the results. With this in mind, several existing two-equation turbulence models, including k-epsilon, k-tau, k-omega, and q-omega models, are implemented into a common flow solver code for near wall turbulent flows. The quality of each model is based on several criteria, including robustness and accuracy of predicting the turbulent quantities.

  14. Modeling of Turbulence Effect on Liquid Jet Atomization

    NASA Technical Reports Server (NTRS)

    Trinh, H. P.

    2007-01-01

    Recent studies indicate that turbulence behaviors within a liquid jet have considerable effect on the atomization process. Such turbulent flow phenomena are encountered in most practical applications of common liquid spray devices. This research aims to model the effects of turbulence occurring inside a cylindrical liquid jet to its atomization process. The two widely used atomization models Kelvin-Helmholtz (KH) instability of Reitz and the Taylor analogy breakup (TAB) of O'Rourke and Amsden portraying primary liquid jet disintegration and secondary droplet breakup, respectively, are examined. Additional terms are formulated and appropriately implemented into these two models to account for the turbulence effect. Results for the flow conditions examined in this study indicate that the turbulence terms are significant in comparison with other terms in the models. In the primary breakup regime, the turbulent liquid jet tends to break up into large drops while its intact core is slightly shorter than those without turbulence. In contrast, the secondary droplet breakup with the inside liquid turbulence consideration produces smaller drops. Computational results indicate that the proposed models provide predictions that agree reasonably well with available measured data.

  15. A study of the second and third order closure models of turbulence for prediction of separated shear flows

    NASA Technical Reports Server (NTRS)

    Amano, R. S.

    1985-01-01

    The hybrid model of the Reynolds-stress turbulence closure is tested for the computation of the flows over a step and disk. Here it is attempted to improve the redistributive action of the turbulence energy among the Reynolds stresses. By evaluating the existing models for the pressure-strain correlation, better coefficients are obtained for the prediction of separating shear flows. Furthermore, the diffusion rate of the Reynolds stresses is reevaluated adopting several algebraic correlations for the triple-velocity products. The models of Cormack et al., Daly-Harlow, Hanjalic-Launder, and Shir were tested for the reattaching shear flows. It was generally observed that all these algebraic models give considerably low values of the triple-velocity products. This is attributed to the fact that none of the algebraic models can take the convective effect of the triple-velocity products into account in the separating shear flows, thus resulting in much lower diffusion rate than Reynolds stresses. In order to improve the evaluation of these quantities correction factors are introduced based on the comparison with some experimental data.

  16. Turbulence Model Comparisons and Reynolds Number Effects Over a High-Speed Aircraft at Transonic Speeds

    NASA Technical Reports Server (NTRS)

    Rivers, Melissa B.; Wahls, Richard A.

    1999-01-01

    This paper gives the results of a grid study, a turbulence model study, and a Reynolds number effect study for transonic flows over a high-speed aircraft using the thin-layer, upwind, Navier-Stokes CFL3D code. The four turbulence models evaluated are the algebraic Baldwin-Lomax model with the Degani-Schiff modifications, the one-equation Baldwin-Barth model, the one-equation Spalart-Allmaras model, and Menter's two-equation Shear-Stress-Transport (SST) model. The flow conditions, which correspond to tests performed in the NASA Langley National Transonic Facility (NTF), are a Mach number of 0.90 and a Reynolds number of 30 million based on chord for a range of angle-of-attacks (1 degree to 10 degrees). For the Reynolds number effect study, Reynolds numbers of 10 and 80 million based on chord were also evaluated. Computed forces and surface pressures compare reasonably well with the experimental data for all four of the turbulence models. The Baldwin-Lomax model with the Degani-Schiff modifications and the one-equation Baldwin-Barth model show the best agreement with experiment overall. The Reynolds number effects are evaluated using the Baldwin-Lomax with the Degani-Schiff modifications and the Baldwin-Barth turbulence models. Five angles-of-attack were evaluated for the Reynolds number effect study at three different Reynolds numbers. More work is needed to determine the ability of CFL3D to accurately predict Reynolds number effects.

  17. Modeling turbulent boundary layers in adverse pressure gradients

    NASA Technical Reports Server (NTRS)

    Belcher, Stephen E.

    1991-01-01

    Many of the turbulent layers encountered in practical flows develop in adverse pressure gradients; hence, the dynamics of the thickening and possible separation of the boundary layer has important implications for design practices. What are the key physical processes that govern how a turbulent boundary layer responds to an adverse pressure gradient, and how should these processes be modeled? Despite the ubiquity of such flows in engineering and nature, these equations remain largely unanswered. The turbulence closure models presently used to describe these flows commonly use 'wall functions' that have ad hoc corrections for the effects of pressure gradients. There is, therefore, a practical and theoretical need to examine the effects of adverse pressure gradients on wall bounded turbulent flows in order to develop models based on sound physical principle. The evolution of a turbulent boundary layer on a flat wall with an externally imposed pressure gradient is studied.

  18. Status of turbulence modeling for hypersonic propulsion flowpaths

    NASA Astrophysics Data System (ADS)

    Georgiadis, Nicholas J.; Yoder, Dennis A.; Vyas, Manan A.; Engblom, William A.

    2014-06-01

    This report provides an assessment of current turbulent flow calculation methods for hypersonic propulsion flowpaths, particularly the scramjet engine. Emphasis is placed on Reynolds-averaged Navier-Stokes (RANS) methods, but some discussion of newer methods such as large eddy simulation (LES) is also provided. The report is organized by considering technical issues throughout the scramjet-powered vehicle flowpath, including laminar-to-turbulent boundary layer transition, shock wave/turbulent boundary layer interactions, scalar transport modeling (specifically the significance of turbulent Prandtl and Schmidt numbers), and compressible mixing. Unit problems are primarily used to conduct the assessment. In the combustor, results from calculations of a direct connect supersonic combustion experiment are also used to address the effects of turbulence model selection and in particular settings for the turbulent Prandtl and Schmidt numbers. It is concluded that RANS turbulence modeling shortfalls are still a major limitation to the accuracy of hypersonic propulsion simulations, whether considering individual components or an overall system. Newer methods such as LES-based techniques may be promising, but are not yet at a maturity to be used routinely by the hypersonic propulsion community. The need for fundamental experiments to provide data for turbulence model development and validation is discussed.

  19. Turbulence modeling of gas-solid suspension flows

    NASA Technical Reports Server (NTRS)

    Chen, C. P.

    1988-01-01

    The purpose here is to discuss and review advances in two-phase turbulent modeling techniques and their applications in various gas-solid suspension flow situations. In addition to the turbulence closures, heat transfer effect, particle dispersion and wall effects are partially covered.

  20. Status of Turbulence Modeling for Hypersonic Propulsion Flowpaths

    NASA Technical Reports Server (NTRS)

    Georgiadis, Nicholas J.; Yoder, Dennis A.; Vyas, Manan A.; Engblom, William A.

    2012-01-01

    This report provides an assessment of current turbulent flow calculation methods for hypersonic propulsion flowpaths, particularly the scramjet engine. Emphasis is placed on Reynolds-averaged Navier-Stokes (RANS) methods, but some discussion of newer meth- ods such as Large Eddy Simulation (LES) is also provided. The report is organized by considering technical issues throughout the scramjet-powered vehicle flowpath including laminar-to-turbulent boundary layer transition, shock wave / turbulent boundary layer interactions, scalar transport modeling (specifically the significance of turbulent Prandtl and Schmidt numbers) and compressible mixing. Unit problems are primarily used to conduct the assessment. In the combustor, results from calculations of a direct connect supersonic combustion experiment are also used to address the effects of turbulence model selection and in particular settings for the turbulent Prandtl and Schmidt numbers. It is concluded that RANS turbulence modeling shortfalls are still a major limitation to the accuracy of hypersonic propulsion simulations, whether considering individual components or an overall system. Newer methods such as LES-based techniques may be promising, but are not yet at a maturity to be used routinely by the hypersonic propulsion community. The need for fundamental experiments to provide data for turbulence model development and validation is discussed.

  1. Analysis of an RNG based turbulence model for separated flows

    NASA Technical Reports Server (NTRS)

    Speziale, C. G.; Thangam, S.

    1992-01-01

    A two-equation turbulence model of the K-epsilon type was recently derived by using Renormalization Group (RNG) methods. It was later reported that this RNG based model yields substantially better predictions than the standard K-epsilon model for turbulent flow over a backward facing step - a standard test case used to benchmark the performance of turbulence models in separated flows. The improvements obtained from the RNG K-epsilon model were attributed to the better treatment of near wall turbulence effects. In contrast to these earlier claims, it is shown in this paper that the original version of the RNG K-epsilon model substantially underpredicts the reattachment point in the backstep problem. This is a deficiency that is traced to the modeling of the production of dissipation term. However, with the most recent improvements in the RNG K-epsilon model, excellent results for the backstep problem are now obtained.

  2. Clifford algebra-based spatio-temporal modelling and analysis for complex geo-simulation data

    NASA Astrophysics Data System (ADS)

    Luo, Wen; Yu, Zhaoyuan; Hu, Yong; Yuan, Linwang

    2013-10-01

    The spatio-temporal data simulating Ice-Land-Ocean interaction of Antarctic are used to demonstrate the Clifford algebra-based data model construction, spatio-temporal query and data analysis. The results suggest that Clifford algebra provides a powerful mathematical tool for the whole modelling and analysis chains for complex geo-simulation data. It can also help implement spatio-temporal analysis algorithms more clearly and simply.

  3. Recent Developments on the Turbulence Modeling Resource Website (Invited)

    NASA Technical Reports Server (NTRS)

    Rumssey, Christopher L.

    2015-01-01

    The NASA Langley Turbulence Model Resource (TMR) website has been active for over five years. Its main goal of providing a one-stop, easily accessible internet site for up-to-date information on Reynolds-averaged Navier-Stokes turbulence models remains unchanged. In particular, the site strives to provide an easy way for users to verify their own implementations of widely-used turbulence models, and to compare the results from different models for a variety of simple unit problems covering a range of flow physics. Some new features have been recently added to the website. This paper documents the site's features, including recent developments, future plans, and open questions.

  4. Multigrid acceleration and turbulence models for computations of 3D turbulent jets in crossflow

    NASA Technical Reports Server (NTRS)

    Demuren, A. O.

    1991-01-01

    A multigrid method is presented for the calculation of three-dimensional turbulent jets in crossflow. Turbulence closure is achieved with either the standard k-epsilon model or a Reynolds Stress Model (RSM). Multigrid acceleration enables convergence rates which are far superior to that for a single grid method. With the k-epsilon model the rate approaches that for laminar flow, but with RSM it is somewhat slower. The increased stiffness of the system of equations in the latter may be responsible. Computed results with both turbulence models are compared with experimental data for a pair of opposed jets in crossflow. Both models yield reasonable agreement with mean flow velocity but RSM yields better prediction of the Reynolds stresses.

  5. Turbulence modeling in three-dimensional stenosed arterial bifurcations.

    PubMed

    Banks, J; Bressloff, N W

    2007-02-01

    Under normal healthy conditions, blood flow in the carotid artery bifurcation is laminar. However, in the presence of a stenosis, the flow can become turbulent at the higher Reynolds numbers during systole. There is growing consensus that the transitional k-omega model is the best suited Reynolds averaged turbulence model for such flows. Further confirmation of this opinion is presented here by a comparison with the RNG k-epsilon model for the flow through a straight, nonbifurcating tube. Unlike similar validation studies elsewhere, no assumptions are made about the inlet profile since the full length of the experimental tube is simulated. Additionally, variations in the inflow turbulence quantities are shown to have no noticeable affect on downstream turbulence intensity, turbulent viscosity, or velocity in the k-epsilon model, whereas the velocity profiles in the transitional k-omega model show some differences due to large variations in the downstream turbulence quantities. Following this validation study, the transitional k-omega model is applied in a three-dimensional parametrically defined computer model of the carotid artery bifurcation in which the sinus bulb is manipulated to produce mild, moderate, and severe stenosis. The parametric geometry definition facilitates a powerful means for investigating the effect of local shape variation while keeping the global shape fixed. While turbulence levels are generally low in all cases considered, the mild stenosis model produces higher levels of turbulent viscosity and this is linked to relatively high values of turbulent kinetic energy and low values of the specific dissipation rate. The severe stenosis model displays stronger recirculation in the flow field with higher values of vorticity, helicity, and negative wall shear stress. The mild and moderate stenosis configurations produce similar lower levels of vorticity and helicity. PMID:17227097

  6. Review and assessment of turbulence models for hypersonic flows

    NASA Astrophysics Data System (ADS)

    Roy, Christopher J.; Blottner, Frederick G.

    2006-10-01

    Accurate aerodynamic prediction is critical for the design and optimization of hypersonic vehicles. Turbulence modeling remains a major source of uncertainty in the computational prediction of aerodynamic forces and heating for these systems. The first goal of this article is to update the previous comprehensive review of hypersonic shock/turbulent boundary-layer interaction experiments published in 1991 by Settles and Dodson (Hypersonic shock/boundary-layer interaction database. NASA CR 177577, 1991). In their review, Settles and Dodson developed a methodology for assessing experiments appropriate for turbulence model validation and critically surveyed the existing hypersonic experiments. We limit the scope of our current effort by considering only two-dimensional (2D)/axisymmetric flows in the hypersonic flow regime where calorically perfect gas models are appropriate. We extend the prior database of recommended hypersonic experiments (on four 2D and two 3D shock-interaction geometries) by adding three new geometries. The first two geometries, the flat plate/cylinder and the sharp cone, are canonical, zero-pressure gradient flows which are amenable to theory-based correlations, and these correlations are discussed in detail. The third geometry added is the 2D shock impinging on a turbulent flat plate boundary layer. The current 2D hypersonic database for shock-interaction flows thus consists of nine experiments on five different geometries. The second goal of this study is to review and assess the validation usage of various turbulence models on the existing experimental database. Here we limit the scope to one- and two-equation turbulence models where integration to the wall is used (i.e., we omit studies involving wall functions). A methodology for validating turbulence models is given, followed by an extensive evaluation of the turbulence models on the current hypersonic experimental database. A total of 18 one- and two-equation turbulence models are reviewed

  7. Ocean Turbulence I: One-Point Closure Model Momentum and Heat Vertical Diffusivities

    NASA Technical Reports Server (NTRS)

    Canuto, V. M.; Howard, A.; Cheng, Y.; Dubovikov, M. S.

    1999-01-01

    Since the early forties, one-point turbulence closure models have been the canonical tools used to describe turbulent flows in many fields. In geophysics, Mellor and Yamada applied such models using the 1980 state-of-the art. Since then, no improvements were introduced to alleviate two major difficulties: 1) closure of the pressure correlations, which affects the correct determination of the critical Richardson number Ri(sub cr) above which turbulent mixing is no longer possible and 2) the need to express the non-local third-order moments (TOM) in terms of lower order moments rather than via the down-gradient approximation as done thus far, since the latter seriously underestimates the TOMs. Since 1) and 2) are still being dealt with adjustable parameters which weaken the credibility of the models, alternative models, not based on turbulence modeling, have been suggested. The aim of this paper is to show that new information, partly derived from the newest 2-point closure model discussed, can be used to solve these shortcomings. The new one-point closure model, which in its simplest form is algebraic and thus simple to implement, is first shown to reproduce a variety of data. Then, it is used in a Ocean-General Circulation Model (O-GCM) where it reproduces well a large variety of ocean data. While phenomenological models are specifically tuned to ocean turbulence, the present model is not. It is first tested against laboratory data on stably stratified flows and then used in an O-GCM. It is more general, more predictive and more resilient, e.g., it can incorporate phenomena like wave-breaking at the surface, salinity diffusivity, non-locality, etc. One important feature that naturally comes out of the new model is that the predicted Richardson critical value Ri(sub cr) is Ri (sub cr approx. = 1) in agreement with both Large Eddy Simulations (LES) and empirical evidence while all previous models predicted Ri (sub cr approx. = 0.2) which led to a considerable

  8. Effects of Lewis number on turbulent scalar transport and its modelling in turbulent premixed flames

    SciTech Connect

    Chakraborty, Nilanjan; Cant, R.S.

    2009-07-15

    The behaviour of the turbulent scalar flux in premixed flames has been studied using Direct Numerical Simulation (DNS) with emphasis on the effects of Lewis number in the context of Reynolds-averaged closure modelling. A database was obtained from DNS of three-dimensional freely propagating statistically planar turbulent premixed flames with simplified chemistry and a range of global Lewis numbers from 0.34 to 1.2. Under the same initial conditions of turbulence, flames with low Lewis numbers are found to exhibit counter-gradient transport, whereas flames with higher Lewis numbers tend to exhibit gradient transport. The Reynolds-averaged transport equation for the turbulent scalar flux is analysed in detail and the performance of existing models for the unclosed terms is assessed with respect to corresponding quantities extracted from DNS data. Based on this assessment, existing models which are able to address the effects of non-unity Lewis number on turbulent scalar flux transport are identified, and new or modified models are suggested wherever necessary. In this way, a complete set of closure models for the scalar flux transport equation is prescribed for use in Reynolds-Averaged Navier-Stokes simulations. (author)

  9. A review of Reynolds stress models for turbulent shear flows

    NASA Technical Reports Server (NTRS)

    Speziale, Charles G.

    1995-01-01

    A detailed review of recent developments in Reynolds stress modeling for incompressible turbulent shear flows is provided. The mathematical foundations of both two-equation models and full second-order closures are explored in depth. It is shown how these models can be systematically derived for two-dimensional mean turbulent flows that are close to equilibrium. A variety of examples are provided to demonstrate how well properly calibrated versions of these models perform for such flows. However, substantial problems remain for the description of more complex turbulent flows where there are large departures from equilibrium. Recent efforts to extend Reynolds stress models to nonequilibrium turbulent flows are discussed briefly along with the major modeling issues relevant to practical naval hydrodynamics applications.

  10. On the subgrid-scale modeling of compressible turbulence

    NASA Technical Reports Server (NTRS)

    Speziale, C. G.; Erlebacher, G.; Zang, T. A.; Hussaini, M. Y.

    1987-01-01

    A subgrid-scale model recently derived for use in the large-eddy simulation of compressible turbulent flows is examined from a fundamental theoretical and computational standpoint. It is demonstrated that this model, which is applicable only to compressible turbulent flows in the limit of small density fluctuations, correlates somewhat poorly with the results of direct numerical simulations of compressible isotropic turbulence at low Mach numbers. An alternative model, based on Favre-filtered fields, is suggested which appears to reduce these limitations.

  11. The subgrid-scale modeling of compressible turbulence

    NASA Technical Reports Server (NTRS)

    Speziale, C. G.; Hussaini, M. Y.; Erlebacher, G.; Zang, T. A.

    1988-01-01

    A subgrid-scale model recently derived for use in the large-eddy simulation of compressible turbulent flows is examined from a fundamental theoretical and computational standpoint. It is demonstrated that this model, which is applicable only to compressible turbulent flows in the limit of small density fluctuations, correlates somewhat poorly with the results of direct numerical simulations of compressible isotropic turbulence at low Mach numbers. An alternative model, based on Favre-filtered fields, is suggested which appears to reduce these limitations.

  12. Implicit turbulence modeling for high reynolds number flows.

    SciTech Connect

    Margolin, L. G.; Smolarkiewicz, P. K.; Wyszogrodzki, A. A.

    2001-01-01

    We continue our investigation of the implicit turbulence modeling property of the nonoscillatory finite volume scheme MPDATA. We start by comparing MPDATA simulations of decaying turbulence in a triply periodic cube with analogous pseudospectral studies. In the regime of direct numerical simulation, MPDATA is shown to agree closely with the pseudospectral model. As viscosity is reduced, the two model results diverge. We study the MPDATA results in the inviscid limit, using a combination of mathematical analysis and computational experiment. We validate the inviscid MPDATA results as representing the turbulent flow in the limit of very high Reynolds number.

  13. Atmospheric turbulence parameters for modeling wind turbine dynamics

    NASA Technical Reports Server (NTRS)

    Holley, W. E.; Thresher, R. W.

    1982-01-01

    A model which can be used to predict the response of wind turbines to atmospheric turbulence is given. The model was developed using linearized aerodynamics for a three-bladed rotor and accounts for three turbulent velocity components as well as velocity gradients across the rotor disk. Typical response power spectral densities are shown. The system response depends critically on three wind and turbulence parameters, and models are presented to predict desired response statistics. An equation error method, which can be used to estimate the required parameters from field data, is also presented.

  14. Modeling Scramjet Flows with Variable Turbulent Prandtl and Schmidt Numbers

    NASA Technical Reports Server (NTRS)

    Xiao, X.; Hassan, H. A.; Baurle, R. A.

    2006-01-01

    A complete turbulence model, where the turbulent Prandtl and Schmidt numbers are calculated as part of the solution and where averages involving chemical source terms are modeled, is presented. The ability of avoiding the use of assumed or evolution Probability Distribution Functions (PDF's) results in a highly efficient algorithm for reacting flows. The predictions of the model are compared with two sets of experiments involving supersonic mixing and one involving supersonic combustion. The results demonstrate the need for consideration of turbulence/chemistry interactions in supersonic combustion. In general, good agreement with experiment is indicated.

  15. Stellar Turbulent Convection: A Self-consistent Model

    NASA Astrophysics Data System (ADS)

    Canuto, V. M.; Goldman, I.; Mazzitelli, I.

    1996-12-01

    We present a self-consistent model for stellar turbulent convection that is similar in spirit to the CM model (Canuto & Mazzitelli 1991) since it accounts for the full spectrum of the turbulent eddies rather than only one eddy, as done in the mixing length theory (MLT). The model differs from the CM model in the treatment of the rate of energy input nS(k) from the source that generates the turbulence. In the present model, nS(k) is controlled by both the source and the turbulence it ultimately generates, thus ensuring a self-consistent modeling of the turbulence. This improves the CM model in which nS(k) was taken to be equal to the growth rate of the linear unstable convective modes. However, since the formulation of a self-consistent treatment is far from simple, we were forced to use a representation of the nonlinear interactions less complete than the one in the CM model. The ensuing equations were solved numerically for a wide range of convective efficiencies. The results are the convective flux, the mean square turbulent velocity, the root mean squared turbulent pressure and the turbulent viscosity. We implemented the model in the ATON stellar structure code and computed the evolution of a solar model. The results are generally similar to those of the CM model and thus quite different from the MLT. The present model requires a smaller overshoot into the upper radiative zone than does the CM model, in accord with recent empirical estimates. Application to Population II stars and comparison with the very metal-poor globular cluster M68 yields an age in the range 11-12 Gyr. This is somewhat younger than the CM age, which in turn is younger than the corresponding MLT age, a result of possible cosmological interest

  16. Algebraic multigrid preconditioner for the cardiac bidomain model.

    PubMed

    Plank, Gernot; Liebmann, Manfred; Weber dos Santos, Rodrigo; Vigmond, Edward J; Haase, Gundolf

    2007-04-01

    The bidomain equations are considered to be one of the most complete descriptions of the electrical activity in cardiac tissue, but large scale simulations, as resulting from discretization of an entire heart, remain a computational challenge due to the elliptic portion of the problem, the part associated with solving the extracellular potential. In such cases, the use of iterative solvers and parallel computing environments are mandatory to make parameter studies feasible. The preconditioned conjugate gradient (PCG) method is a standard choice for this problem. Although robust, its efficiency greatly depends on the choice of preconditioner. On structured grids, it has been demonstrated that a geometric multigrid preconditioner performs significantly better than an incomplete LU (ILU) preconditioner. However, unstructured grids are often preferred to better represent organ boundaries and allow for coarser discretization in the bath far from cardiac surfaces. Under these circumstances, algebraic multigrid (AMG) methods are advantageous since they compute coarser levels directly from the system matrix itself, thus avoiding the complexity of explicitly generating coarser, geometric grids. In this paper, the performance of an AMG preconditioner (BoomerAMG) is compared with that of the standard ILU preconditioner and a direct solver. BoomerAMG is used in two different ways, as a preconditioner and as a standalone solver. Two 3-D simulation examples modeling the induction of arrhythmias in rabbit ventricles were used to measure performance in both sequential and parallel simulations. It is shown that the AMG preconditioner is very well suited for the solution of the bidomain equation, being clearly superior to ILU preconditioning in all regards, with speedups by factors in the range 5.9-7.7. PMID:17405366

  17. A dynamical model of plasma turbulence in the solar wind

    PubMed Central

    Howes, G. G.

    2015-01-01

    A dynamical approach, rather than the usual statistical approach, is taken to explore the physical mechanisms underlying the nonlinear transfer of energy, the damping of the turbulent fluctuations, and the development of coherent structures in kinetic plasma turbulence. It is argued that the linear and nonlinear dynamics of Alfvén waves are responsible, at a very fundamental level, for some of the key qualitative features of plasma turbulence that distinguish it from hydrodynamic turbulence, including the anisotropic cascade of energy and the development of current sheets at small scales. The first dynamical model of kinetic turbulence in the weakly collisional solar wind plasma that combines self-consistently the physics of Alfvén waves with the development of small-scale current sheets is presented and its physical implications are discussed. This model leads to a simplified perspective on the nature of turbulence in a weakly collisional plasma: the nonlinear interactions responsible for the turbulent cascade of energy and the formation of current sheets are essentially fluid in nature, while the collisionless damping of the turbulent fluctuations and the energy injection by kinetic instabilities are essentially kinetic in nature. PMID:25848075

  18. Two-equation turbulence modeling for 3-D hypersonic flows

    NASA Technical Reports Server (NTRS)

    Bardina, J. E.; Coakley, T. J.; Marvin, J. G.

    1992-01-01

    An investigation to verify, incorporate and develop two-equation turbulence models for three-dimensional high speed flows is presented. The current design effort of hypersonic vehicles has led to an intensive study of turbulence models for compressible hypersonic flows. This research complements an extensive review of experimental data and the current development of 2D turbulence models. The review of experimental data on 2D and 3D flows includes complex hypersonic flows with pressure profiles, skin friction, wall heat transfer, and turbulence statistics data. In a parallel effort, turbulence models for high speed flows have been tested against flat plate boundary layers, and are being tested against the 2D database. In the present paper, we present the results of 3D Navier-Stokes numerical simulations with an improved k-omega two-equation turbulence model against experimental data and empirical correlations of an adiabatic flat plate boundary layer, a cold wall flat plate boundary layer, and a 3D database flow, the interaction of an oblique shock wave and a thick turbulent boundary layer with a free stream Mach number = 8.18 and Reynolds number = 5 x 10 to the 6th.

  19. NATURALIST'S APPLICATION OF A PROMISING TURBULENCE MODEL

    EPA Science Inventory

    Turbulence has infinite applications to the biological sciences, affecting distributions, transport, feeding, mating, and other biological processes. The topic is like the universe for which five successive magnefications are required to finally focus on a topic that can be grasp...

  20. Excel Spreadsheets for Algebra: Improving Mental Modeling for Problem Solving

    ERIC Educational Resources Information Center

    Engerman, Jason; Rusek, Matthew; Clariana, Roy

    2014-01-01

    This experiment investigates the effectiveness of Excel spreadsheets in a high school algebra class. Students in the experiment group convincingly outperformed the control group on a post lesson assessment. The student responses, teacher observations involving Excel spreadsheet revealed that it operated as a mindtool, which formed the users'…

  1. A model for reaction rates in turbulent reacting flows

    NASA Technical Reports Server (NTRS)

    Chinitz, W.; Evans, J. S.

    1984-01-01

    To account for the turbulent temperature and species-concentration fluctuations, a model is presented on the effects of chemical reaction rates in computer analyses of turbulent reacting flows. The model results in two parameters which multiply the terms in the reaction-rate equations. For these two parameters, graphs are presented as functions of the mean values and intensity of the turbulent fluctuations of the temperature and species concentrations. These graphs will facilitate incorporation of the model into existing computer programs which describe turbulent reacting flows. When the model was used in a two-dimensional parabolic-flow computer code to predict the behavior of an experimental, supersonic hydrogen jet burning in air, some improvement in agreement with the experimental data was obtained in the far field in the region near the jet centerline. Recommendations are included for further improvement of the model and for additional comparisons with experimental data.

  2. From matrix models' topological expansion to topological string theories: counting surfaces with algebraic geometry

    NASA Astrophysics Data System (ADS)

    Orantin, N.

    2007-09-01

    The 2-matrix model has been introduced to study Ising model on random surfaces. Since then, the link between matrix models and combinatorics of discrete surfaces has strongly tightened. This manuscript aims to investigate these deep links and extend them beyond the matrix models, following my work's evolution. First, I take care to define properly the hermitian 2 matrix model which gives rise to generating functions of discrete surfaces equipped with a spin structure. Then, I show how to compute all the terms in the topological expansion of any observable by using algebraic geometry tools. They are obtained as differential forms on an algebraic curve associated to the model: the spectral curve. In a second part, I show how to define such differentials on any algebraic curve even if it does not come from a matrix model. I then study their numerous symmetry properties under deformations of the algebraic curve. In particular, I show that these objects coincide with the topological expansion of the observable of a matrix model if the algebraic curve is the spectral curve of this model. Finally, I show that fine tuning the parameters ensure that these objects can be promoted to modular invariants and satisfy the holomorphic anomaly equation of the Kodaira-Spencer theory. This gives a new hint that the Dijkgraaf-Vafa conjecture is correct.

  3. Computer modelling of turbulent recirculating flows in engineering applications

    NASA Astrophysics Data System (ADS)

    Khalil, E. E.; Assaf, H. M. W.

    A numerical computation procedure for solving the partial differential equations governing turbulent flows is presented, with an emphasis on swirling flows. The conservation equations for mass and momentum are defined, noting the inclusion of turbulence characteristics in Reynolds stress terms. A two-dimensional turbulence model is used, based on an eddy viscosity concept, with the Reynolds stress described in terms of the mean velocity gradient and the eddy viscosity. The model is used for the flow in a rotary air garbage classifier and the flow in a vortex tube. The flexibility of the technique is demonstrated through variations of the initial flow parameters.

  4. Second order closure modeling of turbulent buoyant wall plumes

    NASA Technical Reports Server (NTRS)

    Zhu, Gang; Lai, Ming-Chia; Shih, Tsan-Hsing

    1992-01-01

    Non-intrusive measurements of scalar and momentum transport in turbulent wall plumes, using a combined technique of laser Doppler anemometry and laser-induced fluorescence, has shown some interesting features not present in the free jet or plumes. First, buoyancy-generation of turbulence is shown to be important throughout the flow field. Combined with low-Reynolds-number turbulence and near-wall effect, this may raise the anisotropic turbulence structure beyond the prediction of eddy-viscosity models. Second, the transverse scalar fluxes do not correspond only to the mean scalar gradients, as would be expected from gradient-diffusion modeling. Third, higher-order velocity-scalar correlations which describe turbulent transport phenomena could not be predicted using simple turbulence models. A second-order closure simulation of turbulent adiabatic wall plumes, taking into account the recent progress in scalar transport, near-wall effect and buoyancy, is reported in the current study to compare with the non-intrusive measurements. In spite of the small velocity scale of the wall plumes, the results showed that low-Reynolds-number correction is not critically important to predict the adiabatic cases tested and cannot be applied beyond the maximum velocity location. The mean and turbulent velocity profiles are very closely predicted by the second-order closure models. but the scalar field is less satisfactory, with the scalar fluctuation level underpredicted. Strong intermittency of the low-Reynolds-number flow field is suspected of these discrepancies. The trends in second- and third-order velocity-scalar correlations, which describe turbulent transport phenomena, are also predicted in general, with the cross-streamwise correlations better than the streamwise one. Buoyancy terms modeling the pressure-correlation are shown to improve the prediction slightly. The effects of equilibrium time-scale ratio and boundary condition are also discussed.

  5. A new energy transfer model for turbulent free shear flow

    NASA Technical Reports Server (NTRS)

    Liou, William W.-W.

    1992-01-01

    A new model for the energy transfer mechanism in the large-scale turbulent kinetic energy equation is proposed. An estimate of the characteristic length scale of the energy containing large structures is obtained from the wavelength associated with the structures predicted by a weakly nonlinear analysis for turbulent free shear flows. With the inclusion of the proposed energy transfer model, the weakly nonlinear wave models for the turbulent large-scale structures are self-contained and are likely to be independent flow geometries. The model is tested against a plane mixing layer. Reasonably good agreement is achieved. Finally, it is shown by using the Liapunov function method, the balance between the production and the drainage of the kinetic energy of the turbulent large-scale structures is asymptotically stable as their amplitude saturates. The saturation of the wave amplitude provides an alternative indicator for flow self-similarity.

  6. A simple model of axisymmetric turbulent boundary layers along long thin circular cylinders

    NASA Astrophysics Data System (ADS)

    Jordan, Stephen A.

    2014-08-01

    Useful empirical and semi-empirical models of the turbulent boundary layer (TBL) and skin friction evolution along planar geometries are not applicable for axisymmetric thin cylinder flows. Their dissimilarity is readily detectable once the TBL thickness exceeds the cylinder radius (a). Although several recent empirically based axisymmetric models recognize this fact, their acceptable fidelity is either restrictive or deficient for general applicability. Herein, we correct this deficit by building a simple model for the specific canonical class of axisymmetric turbulent flows along long thin cylinders with a zero streamwise pressure gradient. Streamwise growth of the TBL thickness (δ/a), integral scales [displacement (δ*/a) and momentum thicknesses (θ/a)] and skin friction coefficient (Cf) can be estimated along the cylinder length via the respective axial mean velocity profile in wall units. This profile is given by Spalding's formula with algebraic expressions for the two input parameters (κ, κβ) that cover all turbulent Reynolds numbers. The necessary database for empirically tuning Spalding's parameters entails both experimental measurements and new numerical computations. Our present-day understanding of the axisymmetric TBL is replicated by the simple model where δ/a, δ*/a, and θ/a grow slower than the planar-type flow with Cf comparatively elevating once δ/a > O(1). These differences manifest themselves in the radial impact imposed by the thin cylinder transverse curvature. Interestingly, the axial-based Reynolds numbers Rea ≈ 7500 and a+ ≈ 350 at δ/a ≈ 21 mark earliest signs of a homogeneous streamwise state (constant Cf) near the cylinder wall. Owning a simple model of axisymmetric turbulent flows along thin cylinders eliminates expensive and timely experiments and/or computations. Its practicality targets both the Naval and oceanographic communities.

  7. Symmetric structure of field algebra of G-spin models determined by a normal subgroup

    SciTech Connect

    Xin, Qiaoling Jiang, Lining

    2014-09-15

    Let G be a finite group and H a normal subgroup. D(H; G) is the crossed product of C(H) and CG which is only a subalgebra of D(G), the double algebra of G. One can construct a C*-subalgebra F{sub H} of the field algebra F of G-spin models, so that F{sub H} is a D(H; G)-module algebra, whereas F is not. Then the observable algebra A{sub (H,G)} is obtained as the D(H; G)-invariant subalgebra of F{sub H}, and there exists a unique C*-representation of D(H; G) such that D(H; G) and A{sub (H,G)} are commutants with each other.

  8. A one-equation turbulence model for recirculating flows

    NASA Astrophysics Data System (ADS)

    Zhang, Yang; Bai, JunQiang; Xu, JingLei; Li, Yi

    2016-06-01

    A one-equation turbulence model which relies on the turbulent kinetic energy transport equation has been developed to predict the flow properties of the recirculating flows. The turbulent eddy-viscosity coefficient is computed from a recalibrated Bradshaw's assumption that the constant a 1 = 0.31 is recalibrated to a function based on a set of direct numerical simulation (DNS) data. The values of dissipation of turbulent kinetic energy consist of the near-wall part and isotropic part, and the isotropic part involves the von Karman length scale as the turbulent length scale. The performance of the new model is evaluated by the results from DNS for fully developed turbulence channel flow with a wide range of Reynolds numbers. However, the computed result of the recirculating flow at the separated bubble of NACA4412 demonstrates that an increase is needed on the turbulent dissipation, and this leads to an advanced tuning on the self-adjusted function. The improved model predicts better results in both the non-equilibrium and equilibrium flows, e.g. channel flows, backward-facing step flow and hump in a channel.

  9. Apparent Transition Behavior of Widely-Used Turbulence Models

    NASA Technical Reports Server (NTRS)

    Rumsey, Christopher L.

    2007-01-01

    The Spalart-Allmaras and the Menter SST k-omega turbulence models are shown to have the undesirable characteristic that, for fully turbulent computations, a transition region can occur whose extent varies with grid density. Extremely fine two-dimensional grids over the front portion of an airfoil are used to demonstrate the effect. As the grid density is increased, the laminar region near the nose becomes larger. In the Spalart-Allmaras model this behavior is due to convergence to a laminar-behavior fixed point that occurs in practice when freestream turbulence is below some threshold. It is the result of a feature purposefully added to the original model in conjunction with a special trip function. This degenerate fixed point can also cause non-uniqueness regarding where transition initiates on a given grid. Consistent fully turbulent results can easily be achieved by either using a higher freestream turbulence level or by making a simple change to one of the model constants. Two-equation k-omega models, including the SST model, exhibit strong sensitivity to numerical resolution near the area where turbulence initiates. Thus, inconsistent apparent transition behavior with grid refinement in this case does not appear to stem from the presence of a degenerate fixed point. Rather, it is a fundamental property of the k-omega model itself, and is not easily remedied.

  10. Apparent Transition Behavior of Widely-Used Turbulence Models

    NASA Technical Reports Server (NTRS)

    Rumsey, Christopher L.

    2006-01-01

    The Spalart-Allmaras and the Menter SST kappa-omega turbulence models are shown to have the undesirable characteristic that, for fully turbulent computations, a transition region can occur whose extent varies with grid density. Extremely fine two-dimensional grids over the front portion of an airfoil are used to demonstrate the effect. As the grid density is increased, the laminar region near the nose becomes larger. In the Spalart-Allmaras model this behavior is due to convergence to a laminar-behavior fixed point that occurs in practice when freestream turbulence is below some threshold. It is the result of a feature purposefully added to the original model in conjunction with a special trip function. This degenerate fixed point can also cause nonuniqueness regarding where transition initiates on a given grid. Consistent fully turbulent results can easily be achieved by either using a higher freestream turbulence level or by making a simple change to one of the model constants. Two-equation kappa-omega models, including the SST model, exhibit strong sensitivity to numerical resolution near the area where turbulence initiates. Thus, inconsistent apparent transition behavior with grid refinement in this case does not appear to stem from the presence of a degenerate fixed point. Rather, it is a fundamental property of the kappa-omega model itself, and is not easily remedied.

  11. A compressible Navier-Stokes code for turbulent flow modeling

    NASA Technical Reports Server (NTRS)

    Coakley, T. J.

    1984-01-01

    An implicit, finite volume code for solving two dimensional, compressible turbulent flows is described. Second order upwind differencing of the inviscid terms of the equations is used to enhance stability and accuracy. A diagonal form of the implicit algorithm is used to improve efficiency. Several zero and two equation turbulence models are incorporated to study their impact on overall flow modeling accuracy. Applications to external and internal flows are discussed.

  12. Improving model-based diagnosis through algebraic analysis: The Petri net challenge

    SciTech Connect

    Portinale, L.

    1996-12-31

    The present paper describes the empirical evaluation of a linear algebra approach to model-based diagnosis, in case the behavioral model of the device under examination is described through a Petri net model. In particular, we show that algebraic analysis based on P-invariants of the net model, can significantly improve the performance of a model-based diagnostic system, while keeping the integrity of a general framework defined from a formal logical theory. A system called INVADS is described and experimental results, performed on a car fault domain and involving the comparison of different implementations of P-invariant based diagnosis, are then discussed.

  13. Compressibility Considerations for kappa-omega Turbulence Models in Hypersonic Boundary Layer Applications

    NASA Technical Reports Server (NTRS)

    Rumsey, C. L.

    2009-01-01

    The ability of kappa-omega models to predict compressible turbulent skin friction in hypersonic boundary layers is investigated. Although uncorrected two-equation models can agree well with correlations for hot-wall cases, they tend to perform progressively worse - particularly for cold walls - as the Mach number is increased in the hypersonic regime. Simple algebraic models such as Baldwin-Lomax perform better compared to experiments and correlations in these circumstances. Many of the compressibility corrections described in the literature are summarized here. These include corrections that have only a small influence for kappa-omega models, or that apply only in specific circumstances. The most widely-used general corrections were designed for use with jet or mixing-layer free shear flows. A less well-known dilatation-dissipation correction intended for boundary layer flows is also tested, and is shown to agree reasonably well with the Baldwin-Lomax model at cold-wall conditions. It exhibits a less dramatic influence than the free shear type of correction. There is clearly a need for improved understanding and better overall physical modeling for turbulence models applied to hypersonic boundary layer flows.

  14. Effect of turbulence models on the submerged hydraulic jump simulation

    NASA Astrophysics Data System (ADS)

    Shekari, Y.; Javan, M.; Eghbalzadeh, A.

    2015-05-01

    This study presents a numerical investigation and prediction of the flow field in threedimensional submerged hydraulic jumps. The volume of fluid (VOF) method is used to simulate the free surface. The turbulent structure is simulated by using different turbulence models, such as the standard k-ɛ model, RNG k-ɛ model, realizable k-ɛ model, and Reynolds-stress model (RSM) closure schemes. The capabilities of the turbulence models are investigated with the standard wall functions and enhanced wall treatment methods. A comparison between the numerical and experimental results shows that the numerical model is adequate for predicting the flow pattern and free surface of submerged hydraulic jumps. The RNG k-ɛ turbulence model with the enhanced wall treatment method ensures the highest accuracy in the water surface simulation. Near the channel bed of a fully developed region, the RSM model with the enhanced wall treatment method shows better agreement with the experimental longitudinal velocity than the other turbulence models. The standard k-ɛ model predicts the longitudinal velocity more accurately than the RNG and realizable k-ɛ models.

  15. Predictive modeling of particle-laden, turbulent flows

    SciTech Connect

    Sinclair, J.L.

    1992-01-01

    The successful prediction of particle-laden, turbulent flows relies heavily on the representation of turbulence in the gas phase. Several types of turbulence models for single-phase gas flow have been developed which compare reasonably well with experimental data. In the present work, a low-Reynolds'' k-[epsilon], closure model is chosen to describe the Reynolds stresses associated with gas-phase turbulence. This closure scheme, which involves transport equations for the turbulent kinetic energy and its dissipation rate, is valid in the turbulent core as well as the viscous sublayer. Several versions of the low-Reynolds k-[epsilon] closure are documented in the literature. However, even those models which are similar in theory often differ considerably in their quantitative and qualitative predictions, making the selection of such a model a difficult task. The purpose of this progress report is to document our findings on the performance of ten different versions of the low-Reynolds k-[epsilon] model on predicting fully developed pipe flow. The predictions are compared with the experimental data of Schildknecht, et al. (1979). With the exception of the model put forth by Hoffman (1975), the predictions of all the closures show reasonable agreement for the mean velocity profile. However, important quantitative differences exist for the turbulent kinetic energy profile. In addition, the predicted eddy viscosity profile and the wall-region profile of the turbulent kinetic energy dissipation rate exhibit both quantitative and qualitative differences. An effort to extend the present comparisons to include experimental measurements of other researchers is recommended in order to further evaluate the performance of the models.

  16. A non-isotropic multiple-scale turbulence model

    NASA Technical Reports Server (NTRS)

    Chen, C. P.

    1990-01-01

    A newly developed non-isotropic multiple scale turbulence model (MS/ASM) is described for complex flow calculations. This model focuses on the direct modeling of Reynolds stresses and utilizes split-spectrum concepts for modeling multiple scale effects in turbulence. Validation studies on free shear flows, rotating flows and recirculating flows show that the current model perform significantly better than the single scale k-epsilon model. The present model is relatively inexpensive in terms of CPU time which makes it suitable for broad engineering flow applications.

  17. Modeling crowd turbulence by many-particle simulations

    NASA Astrophysics Data System (ADS)

    Yu, Wenjian; Johansson, Anders

    2007-10-01

    A recent study [D. Helbing, A. Johansson, and H. Z. Al-Abideen, Phys. Rev. E 75, 046109 (2007)] has revealed a “turbulent” state of pedestrian flows, which is characterized by sudden displacements and causes the falling and trampling of people. However, turbulent crowd motion is not reproduced well by current many-particle models due to their insufficient representation of the local interactions in areas of extreme densities. In this contribution, we extend the repulsive force term of the social force model to reproduce crowd turbulence. We perform numerical simulations of pedestrians moving through a bottleneck area with this model. The transitions from laminar to stop-and-go and turbulent flows are observed. The empirical features characterizing crowd turbulence, such as the structure function and the probability density function of velocity increments, are reproduced well; i.e., they are well compatible with an analysis of video data during the annual Muslim pilgrimage.

  18. Turbulence

    NASA Astrophysics Data System (ADS)

    Frisch, Uriel

    1996-01-01

    Written five centuries after the first studies of Leonardo da Vinci and half a century after A.N. Kolmogorov's first attempt to predict the properties of flow, this textbook presents a modern account of turbulence, one of the greatest challenges in physics. "Fully developed turbulence" is ubiquitous in both cosmic and natural environments, in engineering applications and in everyday life. Elementary presentations of dynamical systems ideas, probabilistic methods (including the theory of large deviations) and fractal geometry make this a self-contained textbook. This is the first book on turbulence to use modern ideas from chaos and symmetry breaking. The book will appeal to first-year graduate students in mathematics, physics, astrophysics, geosciences and engineering, as well as professional scientists and engineers.

  19. Efficiency of a statistical transport model for turbulent particle dispersion

    NASA Astrophysics Data System (ADS)

    Litchford, Ron J.; Jeng, San-Mou

    1992-05-01

    In developing its theory for turbulent dispersion transport, the Litchford and Jeng (1991) statistical transport model for turbulent particle dispersion took a generalized approach in which the perturbing influence of each turbulent eddy on consequent interactions was transported through all subsequent eddies. Nevertheless, examinations of this transport relation shows it to be able to decay rapidly: this implies that additional computational efficiency may be obtained via truncation of unneccessary transport terms. Attention is here given to the criterion for truncation, as well as to expected efficiency gains.

  20. Efficiency of a statistical transport model for turbulent particle dispersion

    SciTech Connect

    Litchford, R.J.; Jeng, San-Mou )

    1992-05-01

    In developing its theory for turbulent dispersion transport, the Litchford and Jeng (1991) statistical transport model for turbulent particle dispersion took a generalized approach in which the perturbing influence of each turbulent eddy on consequent interactions was transported through all subsequent eddies. Nevertheless, examinations of this transport relation shows it to be able to decay rapidly: this implies that additional computational efficiency may be obtained via truncation of unneccessary transport terms. Attention is here given to the criterion for truncation, as well as to expected efficiency gains. 2 refs.

  1. Efficiency of a statistical transport model for turbulent particle dispersion

    NASA Technical Reports Server (NTRS)

    Litchford, Ron J.; Jeng, San-Mou

    1992-01-01

    In developing its theory for turbulent dispersion transport, the Litchford and Jeng (1991) statistical transport model for turbulent particle dispersion took a generalized approach in which the perturbing influence of each turbulent eddy on consequent interactions was transported through all subsequent eddies. Nevertheless, examinations of this transport relation shows it to be able to decay rapidly: this implies that additional computational efficiency may be obtained via truncation of unneccessary transport terms. Attention is here given to the criterion for truncation, as well as to expected efficiency gains.

  2. The one dimensional collapse models of turbulent protostellar clouds

    NASA Astrophysics Data System (ADS)

    Zamozdra, S. N.

    The spherically-symmetric numerical modelling of the gravitational collapse of protostellar clouds is carried out, taking ambipolar diffusion and the pressure of Alfvenic turbulence into account. It is shown that the dependency of protostar formation time on ekg (the initial turbulent-to-gravitational energies ratio) is non-monotonic because it is determined by the complex interaction of large scale magnetosonic waves with the waves of turbulence amplification. Protostellar mass is almost independent on ekg while accretion rate variations with ekg can be of order of 10%.

  3. A study of hydrogen diffusion flames using PDF turbulence model

    NASA Technical Reports Server (NTRS)

    Hsu, Andrew T.

    1991-01-01

    The application of probability density function (pdf) turbulence models is addressed in this work. For the purpose of accurate prediction of turbulent combustion, an algorithm that combines a conventional CFD flow solver with the Monte Carlo simulation of the pdf evolution equation has been developed. The algorithm has been validated using experimental data for a heated turbulent plane jet. The study of H2-F2 diffusion flames has been carried out using this algorithm. Numerical results compared favorably with experimental data. The computuations show that the flame center shifts as the equivalence ratio changes, and that for the same equivalence ratio, similarity solutions for flames exist.

  4. A study of hydrogen diffusion flames using PDF turbulence model

    NASA Technical Reports Server (NTRS)

    Hsu, Andrew T.

    1991-01-01

    The application of probability density function (pdf) turbulence models is addressed. For the purpose of accurate prediction of turbulent combustion, an algorithm that combines a conventional computational fluid dynamic (CFD) flow solver with the Monte Carlo simulation of the pdf evolution equation was developed. The algorithm was validated using experimental data for a heated turbulent plane jet. The study of H2-F2 diffusion flames was carried out using this algorithm. Numerical results compared favorably with experimental data. The computations show that the flame center shifts as the equivalence ratio changes, and that for the same equivalence ratio, similarity solutions for flames exist.

  5. The study of PDF turbulence models in combustion

    NASA Technical Reports Server (NTRS)

    Hsu, Andrew T.

    1991-01-01

    The accurate prediction of turbulent combustion is still beyond reach for today's computation techniques. It is the consensus of the combustion profession that the predictions of chemically reacting flow were poor if conventional turbulence models were used. The main difficulty lies in the fact that the reaction rate is highly nonlinear, and the use of averaged temperature, pressure, and density produces excessively large errors. The probability density function (PDF) method is the only alternative at the present time that uses local instant values of the temperature, density, etc. in predicting chemical reaction rate, and thus it is the only viable approach for turbulent combustion calculations.

  6. An improved k-epsilon model for near wall turbulence

    NASA Technical Reports Server (NTRS)

    Shih, T. H.; Hsu, Andrew T.

    1991-01-01

    An improved k-epsilon model for low Reynolds number turbulence near a wall is presented. In the first part of this work, the near-wall asymptotic behavior of the eddy viscosity and the pressure transport term in the turbulent kinetic energy equation are analyzed. Based on these analyses, a modified eddy viscosity model with the correct near-wall behavior is suggested, and a model for the pressure transport term in the k-equation is proposed. In addition, a modeled dissipation rate equation is reformulated, and a boundary condition for the dissipation rate is suggested. In the second part of the work, one of the deficiencies of the existing k-epsilon models, namely, the wall distance dependency of the equations and the damping functions, is examined. An improved model that does not depend on any wall distance is introduced. Fully developed turbulent channel flows and turbulent boundary layers over a flat plate are studied as validations for the proposed new models. Numerical results obtained from the present and other previous k-epsilon models are compared with data from direct numerical simulation. The results show that the present k-epsilon model, with added robustness, performs as well as or better than other existing models in predicting the behavior of near-wall turbulence.

  7. Turbulence and transition modeling for high-speed flows

    NASA Technical Reports Server (NTRS)

    Wilcox, David C.

    1993-01-01

    Research conducted during the past three and a half years aimed at developing and testing a turbulence/transition model applicable to high-speed turbulent flows is summarized. The first two years of the project focused on fully turbulent flows, while emphasis shifted to boundary-layer development in the transition region during the final year and a half. A brief summary of research accomplished during the first three years is included and publications that describe research results in greater detail are cited. Research conducted during the final six months of the period of performance is summarized. The primary results of the last six months of the project are elimination of the k-omega model's sensitivity to the freestream value of omega and development of a method for triggering transition at a specified location, independent of the freestream turbulence level.

  8. SOLAR WIND MODELING WITH TURBULENCE TRANSPORT AND HEATING

    SciTech Connect

    Usmanov, Arcadi V.; Goldstein, Melvyn L.; Matthaeus, William H.; Breech, Benjamin A.

    2011-02-01

    We have developed an axisymmetric steady-state solar wind model that describes properties of the large-scale solar wind, interplanetary magnetic field, and turbulence throughout the heliosphere from 0.3 AU to 100 AU. The model is based on numerical solutions of large-scale Reynolds-averaged magnetohydrodynamic equations coupled with a set of small-scale transport equations for the turbulence energy, normalized cross helicity, and correlation scale. The combined set of time-dependent equations is solved in the frame of reference corotating with the Sun using a time-relaxation method. We use the model to study the self-consistent interaction between the large-scale solar wind and smaller-scale turbulence and the role of the turbulence in the large-scale structure and temperature distribution in the solar wind. To illuminate the roles of the turbulent cascade and the pickup protons in heating the solar wind depending on the heliocentric distance, we compare the model results with and without turbulence/pickup protons. The variations of plasma temperature in the outer heliosphere are compared with Ulysses and Voyager 2 observations.

  9. Particle dispersion in homogeneous turbulence using the one-dimensional turbulence model

    SciTech Connect

    Sun, Guangyuan; Lignell, David O.; Hewson, John C.; Gin, Craig R.

    2014-10-09

    Lagrangian particle dispersion is studied using the one-dimensional turbulence (ODT) model in homogeneous decaying turbulence configurations. The ODT model has been widely and successfully applied to a number of reacting and nonreacting flow configurations, but only limited application has been made to multiphase flows. We present a version of the particle implementation and interaction with the stochastic and instantaneous ODT eddy events. The model is characterized by comparison to experimental data of particle dispersion for a range of intrinsic particle time scales and body forces. Particle dispersion, velocity, and integral time scale results are presented. Moreover, the particle implementation introduces a single model parameter β p , and sensitivity to this parameter and behavior of the model are discussed. Good agreement is found with experimental data and the ODT model is able to capture the particle inertial and trajectory crossing effects. Our results serve as a validation case of the multiphase implementations of ODT for extensions to other flow configurations.

  10. Particle dispersion in homogeneous turbulence using the one-dimensional turbulence model

    SciTech Connect

    Sun, Guangyuan Lignell, David O.; Hewson, John C.; Gin, Craig R.

    2014-10-15

    Lagrangian particle dispersion is studied using the one-dimensional turbulence (ODT) model in homogeneous decaying turbulence configurations. The ODT model has been widely and successfully applied to a number of reacting and nonreacting flow configurations, but only limited application has been made to multiphase flows. Here, we present a version of the particle implementation and interaction with the stochastic and instantaneous ODT eddy events. The model is characterized by comparison to experimental data of particle dispersion for a range of intrinsic particle time scales and body forces. Particle dispersion, velocity, and integral time scale results are presented. The particle implementation introduces a single model parameter β{sub p}, and sensitivity to this parameter and behavior of the model are discussed. Good agreement is found with experimental data and the ODT model is able to capture the particle inertial and trajectory crossing effects. These results serve as a validation case of the multiphase implementations of ODT for extensions to other flow configurations.

  11. Application of dynamic global-coefficient subgrid-scale models to turbulent natural convection in an enclosed tall cavity

    NASA Astrophysics Data System (ADS)

    Lau, G. E.; Yeoh, G. H.; Timchenko, V.; Reizes, J. A.

    2012-09-01

    Large-eddy simulations examining natural convection in an enclosed cavity with the simultaneous presence of laminar, transitional, and turbulent flow regimes were conducted. The Rayleigh number based on height of the cavity is 4.6 × 1010. Different dynamic global-coefficient procedures to compute the Vreman [A. W. Vreman, "An eddy-viscosity subgrid-scale model for turbulent shear flow: Algebraic theory and applications," Phys. Fluids 16, 3670 (2004)] model coefficient were implemented for the subgrid-scale tensors in both the momentum and energy equations. Based on comparison with experimental and existing numerical data, it is shown that the dynamic model derived from the "global equilibrium" hypothesis gives favorable results in the mean flow and turbulence quantities. Nevertheless, because of higher subgrid-scale dissipation, transition to a turbulent flow is postponed when the Vreman model coefficient is either uniform or determined dynamically using the Germano identity approach. This suggests that much finer grid is desired when using these models in order to better capture the weak transitional boundary layer. Further, by exploring the instantaneous flow dynamics, it is demonstrated that characteristics of the coherent structures which resemble streaks in forced convection boundary layers are somewhat dissimilar in the different models.

  12. A Galilean Invariant Explicit Algebraic Reynolds Stress Model for Curved Flows

    NASA Technical Reports Server (NTRS)

    Girimaji, Sharath

    1996-01-01

    A Galilean invariant weak-equilbrium hypothesis that is sensitive to streamline curvature is proposed. The hypothesis leads to an algebraic Reynolds stress model for curved flows that is fully explicit and self-consistent. The model is tested in curved homogeneous shear flow: the agreement is excellent with Reynolds stress closure model and adequate with available experimental data.

  13. Designing Tasks for Math Modeling in College Algebra: A Critical Review

    ERIC Educational Resources Information Center

    Staats, Susan; Robertson, Douglas

    2014-01-01

    Over the last decade, the pedagogical approach known as mathematical modeling has received increased interest in college algebra classes in the United States. Math modeling assignments ask students to develop their own problem-solving tools to address non-routine, realistic scenarios. The open-ended quality of modeling activities creates dilemmas…

  14. History of wind shear turbulence models

    NASA Technical Reports Server (NTRS)

    Cusimano, Lou

    1987-01-01

    The Office of Flight Operations, Flight Technical Programs Div., at the FAA Headquarters, interfaces with industry, R&D communities and air carriers during the introduction of new types of equipment into operational services. A brief highlight of the need which FAA operations sees for new wind shear and turbulence data sets from the viewpoint of equipment certification and simulation is presented.

  15. Modelling atmospheric turbulence effects on ground-based telescope systems

    SciTech Connect

    Bradford, L.W.; Flatte, S.M.; Max, C.E.

    1993-09-30

    Questions still exist concerning the appropriate model for turbulence- induced phase fluctuations seen in ground-based telescopes. Bester et al. used a particular observable (slope of the Allan variance) with an infrared interferometer in an attempt to distinguish models. The authors have calculated that observable for Kolmogorov and {open_quotes}random walk{close_quotes} models with a variety of outer scales and altitude-dependent turbulence and wind velocity. The authors have found that clear distinction between models requires good data on the vertical distribution of wind and turbulence. Furthermore, measurements at time separations of order 60 s are necessary to distinguish the {open_quotes}random walk{close_quotes} model from the Kolmogorov model.

  16. AN ADA LINEAR ALGEBRA PACKAGE MODELED AFTER HAL/S

    NASA Technical Reports Server (NTRS)

    Klumpp, A. R.

    1994-01-01

    This package extends the Ada programming language to include linear algebra capabilities similar to those of the HAL/S programming language. The package is designed for avionics applications such as Space Station flight software. In addition to the HAL/S built-in functions, the package incorporates the quaternion functions used in the Shuttle and Galileo projects, and routines from LINPAK that solve systems of equations involving general square matrices. Language conventions in this package follow those of HAL/S to the maximum extent practical and minimize the effort required for writing new avionics software and translating existent software into Ada. Valid numeric types in this package include scalar, vector, matrix, and quaternion declarations. (Quaternions are fourcomponent vectors used in representing motion between two coordinate frames). Single precision and double precision floating point arithmetic is available in addition to the standard double precision integer manipulation. Infix operators are used instead of function calls to define dot products, cross products, quaternion products, and mixed scalar-vector, scalar-matrix, and vector-matrix products. The package contains two generic programs: one for floating point, and one for integer. The actual component type is passed as a formal parameter to the generic linear algebra package. The procedures for solving systems of linear equations defined by general matrices include GEFA, GECO, GESL, and GIDI. The HAL/S functions include ABVAL, UNIT, TRACE, DET, INVERSE, TRANSPOSE, GET, PUT, FETCH, PLACE, and IDENTITY. This package is written in Ada (Version 1.2) for batch execution and is machine independent. The linear algebra software depends on nothing outside the Ada language except for a call to a square root function for floating point scalars (such as SQRT in the DEC VAX MATHLIB library). This program was developed in 1989, and is a copyrighted work with all copyright vested in NASA.

  17. Strongly coupled fluid-particle flows in vertical channels. II. Turbulence modeling

    NASA Astrophysics Data System (ADS)

    Capecelatro, Jesse; Desjardins, Olivier; Fox, Rodney O.

    2016-03-01

    In Part I, simulations of strongly coupled fluid-particle flow in a vertical channel were performed with the purpose of understanding, in general, the fundamental physics of wall-bounded multiphase turbulence and, in particular, the roles of the spatially correlated and uncorrelated components of the particle velocity. The exact Reynolds-averaged (RA) equations for high-mass-loading suspensions were presented, and the unclosed terms that are retained in the context of fully developed channel flow were evaluated in an Eulerian-Lagrangian (EL) framework. Here, data from the EL simulations are used to validate a multiphase Reynolds-stress model (RSM) that predicts the wall-normal distribution of the two-phase, one-point turbulence statistics up to second order. It is shown that the anisotropy of the Reynolds stresses both near the wall and far away is a crucial component for predicting the distribution of the RA particle-phase volume fraction. Moreover, the decomposition of the phase-average (PA) particle-phase fluctuating energy into the spatially correlated and uncorrelated components is necessary to account for the boundary conditions at the wall. When these factors are properly accounted for in the RSM, the agreement with the EL turbulence statistics is satisfactory at first order (e.g., PA velocities) but less so at second order (e.g., PA turbulent kinetic energy). Finally, an algebraic stress model for the PA particle-phase pressure tensor and the Reynolds stresses is derived from the RSM using the weak-equilibrium assumption.

  18. Modeling of Turbulence Effects on Liquid Jet Atomization and Breakup

    NASA Technical Reports Server (NTRS)

    Trinh, Huu P.; Chen, C. P.

    2005-01-01

    Recent experimental investigations and physical modeling studies have indicated that turbulence behaviors within a liquid jet have considerable effects on the atomization process. This study aims to model the turbulence effect in the atomization process of a cylindrical liquid jet. Two widely used models, the Kelvin-Helmholtz (KH) instability of Reitz (blob model) and the Taylor-Analogy-Breakup (TAB) secondary droplet breakup by O Rourke et al, are further extended to include turbulence effects. In the primary breakup model, the level of the turbulence effect on the liquid breakup depends on the characteristic scales and the initial flow conditions. For the secondary breakup, an additional turbulence force acted on parent drops is modeled and integrated into the TAB governing equation. The drop size formed from this breakup regime is estimated based on the energy balance before and after the breakup occurrence. This paper describes theoretical development of the current models, called "T-blob" and "T-TAB", for primary and secondary breakup respectivety. Several assessment studies are also presented in this paper.

  19. Performance study for Francis-99 by using different turbulence models

    NASA Astrophysics Data System (ADS)

    Yaping, Zhao; Weili, Liao; Hui, Ruan; Xingqi, Luo

    2015-01-01

    The three-dimensional numerical investigation for turbine-99 at the best efficiency operation point, part load operation point and full load operation point was conducted by using the different turbulence models. By comparing the results of numerical simulation and experimental results, it was found that: there is a certain deviation between the numerical simulation results obtained by different turbulence models and experimental values, and the deviation increase with the reduction of output. Compared to other turbulence model, the result obtained by the standard k-e turbulent model has a relatively small difference with the experimental results. The main causes for the big difference between the numerical simulation and model test include two aspects: (1) the mesh generation and boundary conditions setting lead to differences between the research object and the actual model, (2) it is difficult to accurately simulate the unstable flow such as impact, flow separation and vortex in the turbine. Therefore, in the future actual flow pattern simulation, besides the reasonable choice of turbulence model, based on the actual flow characteristics, the boundary conditions and the simulation results will be amended to reduce the deviation between the numerical simulation and experimental results as much as possible.

  20. EPQ Models under Permissible Payment Delay: An Algebraic Approach

    NASA Astrophysics Data System (ADS)

    Huang, Yung-Fu; Hsu, Kuang-Hua

    The purpose of this research is to relax this assumption and establish the retailer`s inventory system as a cost minimization problem to determine the retailer`s optimal inventory cycle time. Then, an algebraic approach is provided and an easy-to-use theorem is derived to efficiently determine the optimal cycle time. From the final numerical examples, result implies that the retailer will order less quantity to take the benefits of the permissible delay in payments more frequently when the larger the differences between the unit selling price per item and the unit purchasing price per item.

  1. q-Deformation of symplectic dynamical symmetries in algebraic models of nuclear structure

    SciTech Connect

    Georgieva, A. I.; Sviratcheva, K. D.; Ivanov, M. I.; Draayer, J. P.

    2011-06-15

    With a view toward further nuclear structure applications of approaches based on quantum-deformed (or q-deformed) algebras, introduced to the authors by Yu.F. Smirnov, we construct a q analog of a boson realization of the symplectic noncompact sp(4, R) algebra together with a q analog of a fermion realization of the symplectic compact sp(4) algebra. The first study, on the q-deformed Sp(4,R) symmetry, is applied to the development of a q analog of the two-dimensional Interacting Boson Model with q-deformed SU(3) the underpinning dynamical symmetry group. An explicit realization in terms of q-tensor operators with respect to the standard su{sub q}(2) algebra is given. The group-subgroup structure of this framework yields the physical interpretation of the generators of the groups under consideration. The second symplectic algebra, the q-deformed sp(4), is applied to studying isovector pairing correlations in atomic nuclei. A specific q deformation of the sp(4) algebra is realized in terms of q deformed fermion creation and annihilation operators of the shell model. The generators of the algebra close on four distinct realizations of the u{sub q}(2) subalgebra. These reductions, which correspond to different types of pairing interactions, yield a complete classification of the basis states. An analysis of the role of the q deformation is based on a comparison of the results for energies of the lowest isovector-paired 0{sup +} states in the deformed and nondeformed cases.

  2. A local eddy viscosity model for turbulent shear flow

    NASA Technical Reports Server (NTRS)

    Ortwerth, P. J.; Rabe, D. C.; Mcerlean, D. P.

    1973-01-01

    In the model described, the eddy viscosity is assumed to be a fluid property dependent on the state of the fluid locally, namely the local density, turbulent kinetic energy, turbulence scale, and Mach number. An empirical law was found which related eddy viscosity to these properties satisfactorily for free jets. This law is used without modification for a set of test cases in free shear layers, free-jet decay, coaxial mixing, and wakes. The scale of turbulence is taken as a constant at any axial location equal to the width of the shear layer. By utilizing the boundary-layer order-of-magnitude analysis, a coupled set of fluid dynamic equations is formulated, which of necessity includes the equation for the production of turbulent kinetic energy.

  3. Atmospheric turbulence optical model (ATOM) based on fractal theory

    NASA Astrophysics Data System (ADS)

    Jaenisch, Holger M.; Handley, James W.; Scoggins, Jim; Carroll, Marvin P.

    1994-06-01

    An Atmospheric Turbulence Optical Model (ATOM) is presented that used cellular automata (CA) rules as the basis for modeling synthetic phase sheets. This method allows image fracture, scintillation and blur to be correctly models using the principle of convolution with a complex kernel derived from CA rules interaction. The model takes into account the changing distribution of turbules from micro-turbule domination at low altitudes to macro-domination at high altitudes. The wavelength of propagating images (such as a coherent laser beam) and the range are taken into account. The ATOM model is written in standard FORTRAN 77 and enables high-speed in-line calculation of atmospheric effects to be performed without resorting to computationally intensive solutions of Navier Stokes equations or Cn2 profiles.

  4. Center for Modeling of Turbulence and Transition: Research Briefs, 1995

    NASA Technical Reports Server (NTRS)

    1995-01-01

    This research brief contains the progress reports of the research staff of the Center for Modeling of Turbulence and Transition (CMOTT) from July 1993 to July 1995. It also constitutes a progress report to the Institute of Computational Mechanics in Propulsion located at the Ohio Aerospace Institute and the Lewis Research Center. CMOTT has been in existence for about four years. In the first three years, its main activities were to develop and validate turbulence and combustion models for propulsion systems, in an effort to remove the deficiencies of existing models. Three workshops on computational turbulence modeling were held at LeRC (1991, 1993, 1994). At present, CMOTT is integrating the CMOTT developed/improved models into CFD tools which can be used by the propulsion systems community. This activity has resulted in an increased collaboration with the Lewis CFD researchers.

  5. Modeling turbulence in flows with a strong rotational component

    SciTech Connect

    Burgess, D.E.; O`Rourke, P.J.

    1993-11-01

    We consider the effectiveness of various turbulence models in flows with a strong rotational component. To evaluate the models, we implement them into a one-dimensional test code and make comparisons with experimental data for swirling flow in a cylinder. The K - {epsilon} type turbulence models do poorly in predicting the experimental results. However, we find that the incorporation of a Reynolds stress evolution equation gives good agreement with the experimentally measured mean flow. Modeling the pressure-strain correlation tensor correctly is the key for obtaining good results. A combination of Launder`s basic model together with Yakhot`s dissipation rate equation {sup 3} works best in predicting both the mean flow and the turbulence intensity.

  6. Predictive modeling of particle-laden turbulent flows. Final report

    SciTech Connect

    Shaffer, F.; Bolio, E.J.; Hrenya, C.M.

    1993-12-31

    Earlier work of Sinclair and Jackson which treats the laminar flow of gas-solid suspensions is extended to model dilute turbulent flow. The random particle motion, often exceeding the turbulent fluctuations in the gas, is obtained using a model based on kinetic theory of granular materials. A two-equation low Reynolds number turbulence model is, modified to account for the presence of the dilute particle phase. Comparisons of the model predictions with available experimental data for the mean and fluctuating velocity profiles for both phases indicate that the resulting theory captures many of the flow features observed in the pneumatic transport of large particles. The model predictions did not manifest an extreme sensitivity to the degree of inelasticity in the particle-particle collisions for the range of solid loading ratios investigated.

  7. Validating the BHR RANS model for variable density turbulence

    SciTech Connect

    Israel, Daniel M; Gore, Robert A; Stalsberg - Zarling, Krista L

    2009-01-01

    The BHR RANS model is a turbulence model for multi-fluid flows in which density variation plays a strong role in the turbulence processes. In this paper they demonstrate the usefulness of BHR over a wide range of flows which include the effects of shear, buoyancy, and shocks. The results are in good agreement with experimental and DNS data across the entire set of validation cases, with no need to retune model coefficients between cases. The model has potential application to a number of aerospace related flow problems.

  8. The analysis and modeling of dilatational terms in compressible turbulence

    NASA Technical Reports Server (NTRS)

    Sarkar, S.; Erlebacher, G.; Hussaini, M. Y.; Kreiss, H. O.

    1989-01-01

    It is shown that the dilatational terms that need to be modeled in compressible turbulence include not only the pressure-dilatation term but also another term - the compressible dissipation. The nature of these dilatational terms in homogeneous turbulence is explored by asymptotic analysis of the compressible Navier-Stokes equations. A non-dimensional parameter which characterizes some compressible effects in moderate Mach number, homogeneous turbulence is identified. Direct numerical simulations (DNS) of isotropic, compressible turbulence are performed, and their results are found to be in agreement with the theoretical analysis. A model for the compressible dissipation is proposed; the model is based on the asymptotic analysis and the direct numerical simulations. This model is calibrated with reference to the DNS results regarding the influence of compressibility on the decay rate of isotropic turbulence. An application of the proposed model to the compressible mixing layer has shown that the model is able to predict the dramatically reduced growth rate of the compressible mixing layer.

  9. Turbulence model form uncertainty quantification in OpenFOAM

    NASA Astrophysics Data System (ADS)

    Hao, Zengrong; Zeoli, Stéphanie; Bricteux, Laurent; Gorlé, Catherine; CFD; UQ Team; Fluids-Machines Team

    2015-11-01

    Reynolds-averaged Navier-Stokes (RANS) simulations with a two-equation linear eddy-viscosity turbulence model remain a commonly used computational technique for engineering design and analysis of turbulent flows. The accuracy of the results is however limited by the inability of the turbulence model to correctly predict the complex flow features relevant to engineering applications. To enable supporting critical design decisions based on these imperfect model results it is essential to quantify the uncertainty related to the turbulence model form and define confidence levels for the results. The objective of this study is the implementation and validation of a previously developed approach for quantifying the uncertainty in RANS predictions of a turbulent flow in the open source code OpenFOAM. The methodology is based on two steps: 1. calculate a marker to determine where in the flow the model is plausibly inaccurate, and 2. perturb the modeled Reynolds stresses in the momentum equations. The perturbations are defined in terms of the decomposed Reynolds stress tensor, i.e., the tensor magnitude and the eigenvalues and eigenvectors of the normalized anisotropy tensor. Results for a square duct and the flow over a wavy wall will be presented for validation of the implementation.

  10. Compressible Turbulent Channel Flows: DNS Results and Modeling

    NASA Technical Reports Server (NTRS)

    Huang, P. G.; Coleman, G. N.; Bradshaw, P.; Rai, Man Mohan (Technical Monitor)

    1994-01-01

    The present paper addresses some topical issues in modeling compressible turbulent shear flows. The work is based on direct numerical simulation of two supersonic fully developed channel flows between very cold isothermal walls. Detailed decomposition and analysis of terms appearing in the momentum and energy equations are presented. The simulation results are used to provide insights into differences between conventional time-and Favre-averaging of the mean-flow and turbulent quantities. Study of the turbulence energy budget for the two cases shows that the compressibility effects due to turbulent density and pressure fluctuations are insignificant. In particular, the dilatational dissipation and the mean product of the pressure and dilatation fluctuations are very small, contrary to the results of simulations for sheared homogeneous compressible turbulence and to recent proposals for models for general compressible turbulent flows. This provides a possible explanation of why the Van Driest density-weighted transformation is so successful in correlating compressible boundary layer data. Finally, it is found that the DNS data do not support the strong Reynolds analogy. A more general representation of the analogy is analysed and shown to match the DNS data very well.

  11. One-dimensional turbulence modeling of a turbulent counterflow flame with comparison to DNS

    SciTech Connect

    Jozefik, Zoltan; Kerstein, Alan R.; Schmidt, Heiko; Lyra, Sgouria; Kolla, Hemanth; Chen, Jackie H.

    2015-06-01

    The one-dimensional turbulence (ODT) model is applied to a reactant-to-product counterflow configuration and results are compared with DNS data. The model employed herein solves conservation equations for momentum, energy, and species on a one dimensional (1D) domain corresponding to the line spanning the domain between nozzle orifice centers. The effects of turbulent mixing are modeled via a stochastic process, while the Kolmogorov and reactive length and time scales are explicitly resolved and a detailed chemical kinetic mechanism is used. Comparisons between model and DNS results for spatial mean and root-meansquare (RMS) velocity, temperature, and major and minor species profiles are shown. The ODT approach shows qualitatively and quantitatively reasonable agreement with the DNS data. Scatter plots and statistics conditioned on temperature are also compared for heat release rate and all species. ODT is able to capture the range of results depicted by DNS. However, conditional statistics show signs of underignition.

  12. Improved turbulence models based on large eddy simulation of homogeneous, incompressible turbulent flows

    NASA Technical Reports Server (NTRS)

    Bardino, J.; Ferziger, J. H.; Reynolds, W. C.

    1983-01-01

    The physical bases of large eddy simulation and subgrid modeling are studied. A subgrid scale similarity model is developed that can account for system rotation. Large eddy simulations of homogeneous shear flows with system rotation were carried out. Apparently contradictory experimental results were explained. The main effect of rotation is to increase the transverse length scales in the rotation direction, and thereby decrease the rates of dissipation. Experimental results are shown to be affected by conditions at the turbulence producing grid, which make the initial states a function of the rotation rate. A two equation model is proposed that accounts for effects of rotation and shows good agreement with experimental results. In addition, a Reynolds stress model is developed that represents the turbulence structure of homogeneous shear flows very well and can account also for the effects of system rotation.

  13. Radio Wave Scintillations and Models of Interstellar Turbulence

    NASA Astrophysics Data System (ADS)

    Spangler, Steven R.

    1998-05-01

    There are a number of well-established observational results from radio scintillations which have implications for the nature of interstellar turbulence. Among such results are evidence for anisotropy and a Kolmogorov spectrum for the density irregularities. It is probable the galactic magnetic field organizes these irregularities so that spatial gradients along the field are much less than those perpendicular to the field. Such a behavior for turbulence is predicted by theories of magnetohydrodynamic turbulence in which the amplitude is small. The turbulence is then described by a theory termed reduced magnetohydrodynamics. A limiting case of reduced magnetohydrodynamics is two dimensional magnetohydrodynamics, in which the direction of the large scale magnetic field z defines the ignorable coordinate. Two dimensional magnetohydrodynamics consists of a pair of coupled nonlinear partial differential equations for the velocity stream function psi and the z component of the magnetic vector potential A_z. A number of observed features of interstellar turbulence can be identified with solutions to the equations of two dimensional magnetohydrodynamics. Examples are the development of Kolmogorov-like spectra for the velocity and magnetic field from a wide class (although not totally general) initial conditions, a natural explanation for the formation of intermittancy in turbulence, and the rapid development of small scale, large spatial wavenumber fluctuations, in contrast to the eddy cascade of hydrodynamic turbulence. The equations of two dimensional magnetohydrodynamics may serve as a simple but tractable model of interstellar plasma turbulence that may complement and be superior to the traditional model of an ensemble of magnetohydrodynamic waves.

  14. Mathematical and Numerical Modeling of Turbulent Flows.

    PubMed

    Vedovoto, João M; Serfaty, Ricardo; Da Silveira Neto, Aristeu

    2015-01-01

    The present work is devoted to the development and implementation of a computational framework to perform numerical simulations of low Mach number turbulent flows over complex geometries. The algorithm under consideration is based on a classical predictor-corrector time integration scheme that employs a projection method for the momentum equations. The domain decomposition strategy is adopted for distributed computing, displaying very satisfactory levels of speed-up and efficiency. The Immersed Boundary Methodology is used to characterize the presence of a complex geometry. Such method demands two separate grids: An Eulerian, where the transport equations are solved with a Finite Volume, second order discretization and a Lagrangian domain, represented by a non-structured shell grid representing the immersed geometry. The in-house code developed was fully verified by the Method of Manufactured Solutions, in both Eulerian and Lagrangian domains. The capabilities of the resulting computational framework are illustrated on four distinct cases: a turbulent jet, the Poiseuille flow, as a matter of validation of the implemented Immersed Boundary methodology, the flow over a sphere covering a wide range of Reynolds numbers, and finally, with the intention of demonstrating the applicability of Large Eddy Simulations - LES - in an industrial problem, the turbulent flow inside an industrial fan. PMID:26131642

  15. The Model Method: Singapore Children's Tool for Representing and Solving Algebraic Word Problems

    ERIC Educational Resources Information Center

    Ng, Swee Fong; Lee, Kerry

    2009-01-01

    Solving arithmetic and algebraic word problems is a key component of the Singapore elementary mathematics curriculum. One heuristic taught, the model method, involves drawing a diagram to represent key information in the problem. We describe the model method and a three-phase theoretical framework supporting its use. We conducted 2 studies to…

  16. Large Eddy simulation of turbulence: A subgrid scale model including shear, vorticity, rotation, and buoyancy

    NASA Astrophysics Data System (ADS)

    Canuto, V. M.

    1994-06-01

    , which affects both geophysical and astrophysical turbulence (e.g., oceanic structure and convective overshooting in stars), has been singularly difficult to account for in turbulence modeling. For example, the widely used model of Deardorff has not been confirmed by recent LES results. As of today, there is no SGS model capable of incorporating buoyancy, rotation, shear, anistropy, and stable stratification (gravity waves). In this paper, we construct such a model which we call CM (complete model). We also present a hierarchy of simpler algebraic models (called AM) of varying complexity. Finally, we present a set of models which are simplified even further (called SM), the simplest of which is the Smagorinsky-Lilly model. The incorporation of these models into the presently available LES codes should begin with the SM, to be followed by the AM and finally by the CM.

  17. Optical Turbulence Characterization by WRF model above Ali, Tibet

    NASA Astrophysics Data System (ADS)

    Wang, Hongshuai; Yao, Yongqiang; Liu, Liyong; Qian, Xuan; Yin, Jia

    2015-04-01

    Atmospheric optical turbulence modeling and forecast for astronomy is a relatively recent discipline, but has played important roles in site survey, optimization of large telescope observing tables, and in the applications of adaptive optics technique. The numerical approach, by using of meteorological parameters and parameterization of optical turbulence, can provide all the optical turbulence parameters related, such as C2n profile, coherent length, wavefront coherent time, seeing, isoplanatic angle, and so on. This is particularly interesting for searching new sites without the long and expensive site testing campaigns with instruments. Earlier site survey results by the site survey team of National Astronomical Observatories of China imply that the south-west Tibet, Ali, is one of the world best IR and sub-mm site. For searching the best site in Ali area, numerical approach by Weather and Research Forecasting (WRF) model had been used to evaluate the climatology of the optical turbulence. The WRF model is configured over a domain 200km×200km with 1km horizontal resolution and 65 vertical levels from ground to the model top(10millibars) in 2010. The initial and boundary conditions for the model are provided by the 1° × 1° Global Final Analysis data from NCEP. The distribution and seasonal variation of optical turbulence parameters over this area are presented.

  18. Near-wall turbulence modeling for boundary layers with separation

    NASA Astrophysics Data System (ADS)

    Ko, S. H.

    1991-12-01

    As a turbulent boundary layer undergoes a strong adverse pressure gradient, the flow may separate from the wall, and the use of empirical wall functions is inappropriate. The turbulence transport equations as well as the momentum equations must be solved through the laminar sublayer to the wall. The laminar sublayer encompasses a region where viscous effects become increasingly important. For the past two decades, many proposals for near-wall turbulence models of the kappa-epsilon type have been presented for calculating near-wall flows. A thorough review and a systematic evaluation of these models was previously given. It was found that some of the models tested failed to reproduce even the simple flat-plate boundary layer flow. Overall, the authors concluded that the near-wall turbulence models needed further refinement if they were to be used with confidence to calculate near-wall flows. Recently, the use of a direct numerical simulation (DNS) data base has provided new insight and data for development and testing of near-wall turbulence models.

  19. Modelling Unsteady Wall Pressures Beneath Turbulent Boundary Layers

    NASA Technical Reports Server (NTRS)

    Ahn, B-K.; Graham, W. R.; Rizzi, S. A.

    2004-01-01

    As a structural entity of turbulence, hairpin vortices are believed to play a major role in developing and sustaining the turbulence process in the near wall region of turbulent boundary layers and may be regarded as the simplest conceptual model that can account for the essential features of the wall pressure fluctuations. In this work we focus on fully developed typical hairpin vortices and estimate the associated surface pressure distributions and their corresponding spectra. On the basis of the attached eddy model, we develop a representation of the overall surface pressure spectra in terms of the eddy size distribution. Instantaneous wavenumber spectra and spatial correlations are readily derivable from this representation. The model is validated by comparison of predicted wavenumber spectra and cross-correlations with existing emperical models and experimental data.

  20. Turbulence radiation interaction modeling in hydrocarbon pool fire simulations

    SciTech Connect

    BURNS,SHAWN P.

    1999-12-01

    The importance of turbulent fluctuations in temperature and species concentration in thermal radiation transport modeling for combustion applications is well accepted by the radiation transport and combustion communities. A number of experimental and theoretical studies over the last twenty years have shown that fluctuations in the temperature and species concentrations may increase the effective emittance of a turbulent flame by as much as 50% to 300% over the value that would be expected from the mean temperatures and concentrations. With the possibility of such a large effect on the principal mode of heat transfer from a fire, it is extremely important for fire modeling efforts that turbulence radiation interaction be well characterized and possible modeling approaches understood. Toward this end, this report seeks to accomplish three goals. First, the principal turbulence radiation interaction closure terms are defined. Second, an order of magnitude analysis is performed to understand the relative importance of the various closure terms. Finally, the state of the art in turbulence radiation interaction closure modeling is reviewed. Hydrocarbon pool fire applications are of particular interest in this report and this is the perspective from which this review proceeds. Experimental and theoretical analysis suggests that, for this type of heavily sooting flame, the turbulent radiation interaction effect is dominated by the nonlinear dependence of the Planck function on the temperature. Additional effects due to the correlation between turbulent fluctuations in the absorptivity and temperature may be small relative to the Planck function effect for heavily sooting flames. This observation is drawn from a number of experimental and theoretical discussions. Nevertheless, additional analysis and data is needed to validate this observation for heavily sooting buoyancy dominated plumes.

  1. A note on probabilistic models over strings: the linear algebra approach.

    PubMed

    Bouchard-Côté, Alexandre

    2013-12-01

    Probabilistic models over strings have played a key role in developing methods that take into consideration indels as phylogenetically informative events. There is an extensive literature on using automata and transducers on phylogenies to do inference on these probabilistic models, in which an important theoretical question is the complexity of computing the normalization of a class of string-valued graphical models. This question has been investigated using tools from combinatorics, dynamic programming, and graph theory, and has practical applications in Bayesian phylogenetics. In this work, we revisit this theoretical question from a different point of view, based on linear algebra. The main contribution is a set of results based on this linear algebra view that facilitate the analysis and design of inference algorithms on string-valued graphical models. As an illustration, we use this method to give a new elementary proof of a known result on the complexity of inference on the "TKF91" model, a well-known probabilistic model over strings. Compared to previous work, our proving method is easier to extend to other models, since it relies on a novel weak condition, triangular transducers, which is easy to establish in practice. The linear algebra view provides a concise way of describing transducer algorithms and their compositions, opens the possibility of transferring fast linear algebra libraries (for example, based on GPUs), as well as low rank matrix approximation methods, to string-valued inference problems. PMID:24135792

  2. Modeling of confined turbulent fluid-particle flows using Eulerian and Lagrangian schemes

    NASA Technical Reports Server (NTRS)

    Adeniji-Fashola, A.; Chen, C. P.

    1990-01-01

    Two important aspects of fluid-particulate interaction in dilute gas-particle turbulent flows (the turbulent particle dispersion and the turbulence modulation effects) are addressed, using the Eulerian and Lagrangian modeling approaches to describe the particulate phase. Gradient-diffusion approximations are employed in the Eulerian formulation, while a stochastic procedure is utilized to simulate turbulent dispersion in the Lagrangina formulation. The k-epsilon turbulence model is used to characterize the time and length scales of the continuous phase turbulence. Models proposed for both schemes are used to predict turbulent fully-developed gas-solid vertical pipe flow with reasonable accuracy.

  3. A minimal model of self-sustaining turbulence

    SciTech Connect

    Thomas, Vaughan L.; Gayme, Dennice F.; Farrell, Brian F.; Ioannou, Petros J.

    2015-10-15

    In this work, we examine the turbulence maintained in a Restricted Nonlinear (RNL) model of plane Couette flow. This model is a computationally efficient approximation of the second order statistical state dynamics obtained by partitioning the flow into a streamwise averaged mean flow and perturbations about that mean, a closure referred to herein as the RNL{sub ∞} model. The RNL model investigated here employs a single member of the infinite ensemble that comprises the covariance of the RNL{sub ∞} dynamics. The RNL system has previously been shown to support self-sustaining turbulence with a mean flow and structural features that are consistent with direct numerical simulations (DNS). Regardless of the number of streamwise Fourier components used in the simulation, the RNL system’s self-sustaining turbulent state is supported by a small number of streamwise varying modes. Remarkably, further truncation of the RNL system’s support to as few as one streamwise varying mode can suffice to sustain the turbulent state. The close correspondence between RNL simulations and DNS that has been previously demonstrated along with the results presented here suggest that the fundamental mechanisms underlying wall-turbulence can be analyzed using these highly simplified RNL systems.

  4. Turbulence transport modeling of the temporal outer heliosphere

    SciTech Connect

    Adhikari, L.; Zank, G. P.; Hu, Q.; Dosch, A.

    2014-09-20

    The solar wind can be regarded as a turbulent magnetofluid, evolving in an expanding solar wind and subject to turbulent driving by a variety of in situ sources. Furthermore, the solar wind and the drivers of turbulence are highly time-dependent and change with solar cycle. Turbulence transport models describing low-frequency magnetic and velocity fluctuations in the solar wind have so far neglected solar cycle effects. Here we consider the effects of solar cycle variability on a turbulence transport model developed by Zank et al. This model is appropriate for the solar wind beyond about 1 AU, and extensions have described the steady-state dependence of the magnetic energy density fluctuations, correlation length, and solar wind temperature throughout the outer heliosphere. We find that the temporal solar wind introduces a periodic variability, particularly beyond ∼10 AU, in the magnetic energy density fluctuations, correlation length, and solar wind temperature. The variability is insufficient to account for the full observed variability in these quantities, but we find that the time-dependent solutions trace the steady-state solutions quite well, suggesting that the steady-state models are reasonable first approximations.

  5. The lagRST Model: A Turbulence Model for Non-Equilibrium Flows

    NASA Technical Reports Server (NTRS)

    Lillard, Randolph P.; Oliver, A. Brandon; Olsen, Michael E.; Blaisdell, Gregory A.; Lyrintzis, Anastasios S.

    2011-01-01

    This study presents a new class of turbulence model designed for wall bounded, high Reynolds number flows with separation. The model addresses deficiencies seen in the modeling of nonequilibrium turbulent flows. These flows generally have variable adverse pressure gradients which cause the turbulent quantities to react at a finite rate to changes in the mean flow quantities. This "lag" in the response of the turbulent quantities can t be modeled by most standard turbulence models, which are designed to model equilibrium turbulent boundary layers. The model presented uses a standard 2-equation model as the baseline for turbulent equilibrium calculations, but adds transport equations to account directly for non-equilibrium effects in the Reynolds Stress Tensor (RST) that are seen in large pressure gradients involving shock waves and separation. Comparisons are made to several standard turbulence modeling validation cases, including an incompressible boundary layer (both neutral and adverse pressure gradients), an incompressible mixing layer and a transonic bump flow. In addition, a hypersonic Shock Wave Turbulent Boundary Layer Interaction with separation is assessed along with a transonic capsule flow. Results show a substantial improvement over the baseline models for transonic separated flows. The results are mixed for the SWTBLI flows assessed. Separation predictions are not as good as the baseline models, but the over prediction of the peak heat flux downstream of the reattachment shock that plagues many models is reduced.

  6. Constructing and Modeling Algebraic Statements in the Multiplicative Domain: Investigating Fourth-Grade Student and Teacher Learning

    ERIC Educational Resources Information Center

    Grandau, Laura

    2013-01-01

    This study of fourth-grade students and teachers explores mathematics teaching and learning that focuses on discovering and modeling algebraic relationships. The study has two parts: an investigation of how students learn to construct algebraic statements and models for comparisons and measurement situations in the multiplicative domain, and an…

  7. Time-domain inflow boundary condition for turbulence-airfoil interaction noise prediction using synthetic turbulence modeling

    NASA Astrophysics Data System (ADS)

    Kim, Daehwan; Heo, Seung; Cheong, Cheolung

    2015-03-01

    The present paper deals with development of the synthetic turbulence inflow boundary condition (STIBC) to predict inflow broadband noise generated by interaction between turbulence and an airfoil/a cascade of airfoils in the time-domain. The STIBC is derived by combining inflow boundary conditions that have been successfully applied in external and internal computational aeroacoustics (CAA) simulations with a synthetic turbulence model. The random particle mesh (RPM) method based on a digital filter is used as the synthetic turbulence model. Gaussian and Liepmann spectra are used to define the filters for turbulence energy spectra. The linearized Euler equations are used as governing equations to evaluate the suitability of the STIBC in time-domain CAA simulations. First, the velocity correlations and energy spectra of the synthesized turbulent velocities are compared with analytic ones. The comparison results reveal that the STIBC can reproduce a turbulent velocity field satisfying the required statistical characteristics of turbulence. Particularly, the Liepmann filter representing a non-Gaussian filter is shown to be effectively described by superposing the Gaussian filters. Each Gaussian filter has a different turbulent kinetic energy and integral length scale. Second, two inflow noise problems are numerically solved using the STIBC: the turbulence-airfoil interaction and the turbulence-a cascade of airfoils interaction problems. The power spectrum of noise due to an isolated flat plate airfoil interacting with incident turbulence is predicted, and its result is successfully validated against Amiet's analytic model (Amiet, 1975) [4]. The prediction results of the upstream and downstream acoustic power spectra from a cascade of flat plates are then compared with Cheong's analytic model (Cheong et al., 2006) [30]. These comparisons are also in excellent agreement. On the basis of these illustrative computation results, the STIBC is expected to be applied to

  8. Fractional Order Modeling of Atmospheric Turbulence - A More Accurate Modeling Methodology for Aero Vehicles

    NASA Technical Reports Server (NTRS)

    Kopasakis, George

    2014-01-01

    The presentation covers a recently developed methodology to model atmospheric turbulence as disturbances for aero vehicle gust loads and for controls development like flutter and inlet shock position. The approach models atmospheric turbulence in their natural fractional order form, which provides for more accuracy compared to traditional methods like the Dryden model, especially for high speed vehicle. The presentation provides a historical background on atmospheric turbulence modeling and the approaches utilized for air vehicles. This is followed by the motivation and the methodology utilized to develop the atmospheric turbulence fractional order modeling approach. Some examples covering the application of this method are also provided, followed by concluding remarks.

  9. Turbulence Model Selection for Low Reynolds Number Flows

    PubMed Central

    2016-01-01

    One of the major flow phenomena associated with low Reynolds number flow is the formation of separation bubbles on an airfoil’s surface. NACA4415 airfoil is commonly used in wind turbines and UAV applications. The stall characteristics are gradual compared to thin airfoils. The primary criterion set for this work is the capture of laminar separation bubble. Flow is simulated for a Reynolds number of 120,000. The numerical analysis carried out shows the advantages and disadvantages of a few turbulence models. The turbulence models tested were: one equation Spallart Allmars (S-A), two equation SST K-ω, three equation Intermittency (γ) SST, k-kl-ω and finally, the four equation transition γ-Reθ SST. However, the variation in flow physics differs between these turbulence models. Procedure to establish the accuracy of the simulation, in accord with previous experimental results, has been discussed in detail. PMID:27104354

  10. Turbulence Model Selection for Low Reynolds Number Flows.

    PubMed

    Aftab, S M A; Mohd Rafie, A S; Razak, N A; Ahmad, K A

    2016-01-01

    One of the major flow phenomena associated with low Reynolds number flow is the formation of separation bubbles on an airfoil's surface. NACA4415 airfoil is commonly used in wind turbines and UAV applications. The stall characteristics are gradual compared to thin airfoils. The primary criterion set for this work is the capture of laminar separation bubble. Flow is simulated for a Reynolds number of 120,000. The numerical analysis carried out shows the advantages and disadvantages of a few turbulence models. The turbulence models tested were: one equation Spallart Allmars (S-A), two equation SST K-ω, three equation Intermittency (γ) SST, k-kl-ω and finally, the four equation transition γ-Reθ SST. However, the variation in flow physics differs between these turbulence models. Procedure to establish the accuracy of the simulation, in accord with previous experimental results, has been discussed in detail. PMID:27104354

  11. Temperature-Corrected Model of Turbulence in Hot Jet Flows

    NASA Technical Reports Server (NTRS)

    Abdol-Hamid, Khaled S.; Pao, S. Paul; Massey, Steven J.; Elmiligui, Alaa

    2007-01-01

    An improved correction has been developed to increase the accuracy with which certain formulations of computational fluid dynamics predict mixing in shear layers of hot jet flows. The CFD formulations in question are those derived from the Reynolds-averaged Navier-Stokes equations closed by means of a two-equation model of turbulence, known as the k-epsilon model, wherein effects of turbulence are summarized by means of an eddy viscosity. The need for a correction arises because it is well known among specialists in CFD that two-equation turbulence models, which were developed and calibrated for room-temperature, low Mach-number, plane-mixing-layer flows, underpredict mixing in shear layers of hot jet flows. The present correction represents an attempt to account for increased mixing that takes place in jet flows characterized by high gradients of total temperature. This correction also incorporates a commonly accepted, previously developed correction for the effect of compressibility on mixing.

  12. A rational approach to the use of Prandtl's mixing length model in free turbulent shear flow calculations

    NASA Technical Reports Server (NTRS)

    Rudy, D. H.; Bushnell, D. M.

    1973-01-01

    Prandtl's basic mixing length model was used to compute 22 test cases on free turbulent shear flows. The calculations employed appropriate algebraic length scale equations and single values of mixing length constant for planar and axisymmetric flows, respectively. Good agreement with data was obtained except for flows, such as supersonic free shear layers, where large sustained sensitivity changes occur. The inability to predict the more gradual mixing in these flows is tentatively ascribed to the presence of a significant turbulence-induced transverse static pressure gradient which is neglected in conventional solution procedures. Some type of an equation for length scale development was found to be necessary for successful computation of highly nonsimilar flow regions such as jet or wake development from thick wall flows.

  13. Hyperbolic Kac-Moody algebras and chaos in Kaluza-Klein models

    NASA Astrophysics Data System (ADS)

    Damour, T.; Henneaux, M.; Julia, B.; Nicolai, H.

    2001-06-01

    Some time ago, it was found that the never-ending oscillatory chaotic behaviour discovered by Belinskii, Khalatnikov and Lifshitz (BKL) for the generic solution of the vacuum Einstein equations in the vicinity of a spacelike (``cosmological'') singularity disappears in spacetime dimensions /D≡d+1>10. Recently, a study of the generalization of the BKL chaotic behaviour to the superstring effective Lagrangians has revealed that this chaos is rooted in the structure of the fundamental Weyl chamber of some underlying hyperbolic Kac-Moody algebra. In this Letter we show that the same connection applies to pure gravity in any spacetime dimension />=4, where the relevant algebras are AEd. In this way the disappearance of chaos in pure gravity models in /D>=11 dimensions becomes linked to the fact that the Kac-Moody algebras AEd are no longer hyperbolic for /d>=10.

  14. The Lag Model, a Turbulence Model for Wall Bounded Flows Including Separation

    NASA Technical Reports Server (NTRS)

    Olsen, Michael E.; Coakley, Thomas J.; Kwak, Dochan (Technical Monitor)

    2001-01-01

    A new class of turbulence model is described for wall bounded, high Reynolds number flows. A specific turbulence model is demonstrated, with results for favorable and adverse pressure gradient flowfields. Separation predictions are as good or better than either Spalart Almaras or SST models, do not require specification of wall distance, and have similar or reduced computational effort compared with these models.

  15. Reynolds-Averaged Turbulence Model Assessment for a Highly Back-Pressured Isolator Flowfield

    NASA Technical Reports Server (NTRS)

    Baurle, Robert A.; Middleton, Troy F.; Wilson, L. G.

    2012-01-01

    The use of computational fluid dynamics in scramjet engine component development is widespread in the existing literature. Unfortunately, the quantification of model-form uncertainties is rarely addressed with anything other than sensitivity studies, requiring that the computational results be intimately tied to and calibrated against existing test data. This practice must be replaced with a formal uncertainty quantification process for computational fluid dynamics to play an expanded role in the system design, development, and flight certification process. Due to ground test facility limitations, this expanded role is believed to be a requirement by some in the test and evaluation community if scramjet engines are to be given serious consideration as a viable propulsion device. An effort has been initiated at the NASA Langley Research Center to validate several turbulence closure models used for Reynolds-averaged simulations of scramjet isolator flows. The turbulence models considered were the Menter BSL, Menter SST, Wilcox 1998, Wilcox 2006, and the Gatski-Speziale explicit algebraic Reynolds stress models. The simulations were carried out using the VULCAN computational fluid dynamics package developed at the NASA Langley Research Center. A procedure to quantify the numerical errors was developed to account for discretization errors in the validation process. This procedure utilized the grid convergence index defined by Roache as a bounding estimate for the numerical error. The validation data was collected from a mechanically back-pressured constant area (1 2 inch) isolator model with an isolator entrance Mach number of 2.5. As expected, the model-form uncertainty was substantial for the shock-dominated, massively separated flowfield within the isolator as evidenced by a 6 duct height variation in shock train length depending on the turbulence model employed. Generally speaking, the turbulence models that did not include an explicit stress limiter more closely

  16. A new turbulence-based model for sand transport

    NASA Astrophysics Data System (ADS)

    Mayaud, Jerome; Wiggs, Giles; Bailey, Richard

    2016-04-01

    Knowledge of the changing rate of sediment flux in space and time is essential for quantifying surface erosion and deposition in desert landscapes. While many aeolian studies have relied on time-averaged parameters such as wind velocity (U) and wind shear velocity (u*) to determine sediment flux, there is increasing evidence that high-frequency turbulence is an important driving force behind the entrainment and transport of sand. However, turbulence has yet to be incorporated into a functional sand transport model that can be used for predictive purposes. In this study we present a new transport model (the 'turbulence model') that accounts for high-frequency variations in the horizontal (u) and vertical (w) components of wind flow. The turbulence model is fitted to wind velocity and sediment transport data from a field experiment undertaken in Namibia's Skeleton Coast National Park, and its performance at three temporal resolutions (10 Hz, 1 Hz, 1 min) is compared to two existing models that rely on time-averaged wind velocity data (Radok, 1977; Dong et al., 2003). The validity of the three models is analysed under a variety of saltation conditions, using a 2-hour (1 Hz measurement resolution) dataset from the Skeleton Coast and a 5-hour (1 min measurement resolution) dataset from the southwestern Kalahari Desert. The turbulence model is shown to outperform the Radok and Dong models when predicting total saltation count over the three experimental periods. For all temporal resolutions presented in this study (10 Hz-10 min), the turbulence model predicted total saltation count to within at least 0.34%, whereas the Radok and Dong models over- or underestimated total count by up to 5.50% and 20.53% respectively. The strong performance of the turbulence model can be attributed to a lag in mass flux response built into its formulation, which can be adapted depending on the temporal resolution of investigation. This accounts for the inherent lag within the physical

  17. On the limiters of two-equation turbulence models

    NASA Astrophysics Data System (ADS)

    Park, Chang Hwan; Park, Seung O.

    2005-01-01

    When two-equation turbulence models are used, unrealistically large values of turbulence variables can appear due to the infringement of a realizability condition or to numerical error. To cure this in practical calculations, various limiters on the source terms are often employed. In the present work, a mathematically correct bound for eddy viscosity is obtained from the realizability condition itself. From this, realizability bounds for several terms of model equations are given. The effects of various bounds including the present one, are investigated on the predictions of fundamental flows including simple shear flows, supersonic compression ramp flow and supersonic base flow. It is shown that the limiter affects the prediction very significantly.

  18. Modeling of Turbulence Generated Noise in Jets

    NASA Technical Reports Server (NTRS)

    Khavaran, Abbas; Bridges, James

    2004-01-01

    A numerically calculated Green's function is used to predict jet noise spectrum and its far-field directivity. A linearized form of Lilley's equation governs the non-causal Green s function of interest, with the non-linear terms on the right hand side identified as the source. In this paper, contributions from the so-called self- and shear-noise source terms will be discussed. A Reynolds-averaged Navier-Stokes solution yields the required mean flow as well as time- and length scales of a noise-generating turbulent eddy. A non-compact source, with exponential temporal and spatial functions, is used to describe the turbulence velocity correlation tensors. It is shown that while an exact non-causal Green's function accurately predicts the observed shift in the location of the spectrum peak with angle as well as the angularity of sound at moderate Mach numbers, at high subsonic and supersonic acoustic Mach numbers the polar directivity of radiated sound is not entirely captured by this Green's function. Results presented for Mach 0.5 and 0.9 isothermal jets, as well as a Mach 0.8 hot jet conclude that near the peak radiation angle a different source/Green's function convolution integral may be required in order to capture the peak observed directivity of jet noise.

  19. CSOS models descending from chiral Potts models: degeneracy of the eigenspace and loop algebra

    NASA Astrophysics Data System (ADS)

    Au-Yang, Helen; Perk, Jacques H. H.

    2016-04-01

    Monodromy matrices of the {{\\boldsymbol{τ }}}2\\phantom{^{\\prime }} model are known to satisfy a Yang-Baxter equation with a six-vertex R-matrix as the intertwiner. The commutation relations of the elements of the monodromy matrices are completely determined by this R-matrix. We show the reason why in the superintegrable case the eigenspace is degenerate, but not in the general case. We then show that the eigenspaces of special CSOS models descending from the chiral Potts model are also degenerate. The existence of an L({{sl}}2) quantum loop algebra (or subalgebra) in these models is established by showing that the Serre relations hold for the generators. The highest weight polynomial (or the Drinfeld polynomial) of the representation is obtained by using the method of Baxter for the superintegrable case. As a byproduct, the eigenvalues of all such CSOS models are given explicitly.

  20. The Application of Boolean Algebra in Modelling of Leakage Condition of a Car Hydraulic Braking System

    NASA Astrophysics Data System (ADS)

    Idzikowski, A.; Salamon, S.

    2013-06-01

    A general characteristics of a car hydraulic braking system (CHBS) is presented in this publication. A graphical model of properties-component objects is developed for the above-mentioned system. Moreover, four mathematical models in terms of logic, the set theory and the Boolean algebra of Boolean functions are developed. The examination is ended with a general model of the CHBS for n - Boolean variables and the construction and mathematical-technical interpretation of this model is presented.

  1. Existence of standard models of conic fibrations over non-algebraically-closed fields

    SciTech Connect

    Avilov, A A

    2014-12-31

    We prove an analogue of Sarkisov's theorem on the existence of a standard model of a conic fibration over an algebraically closed field of characteristic different from two for three-dimensional conic fibrations over an arbitrary field of characteristic zero with an action of a finite group. Bibliography: 16 titles.

  2. The algebraic Bethe ansatz for scalar products in SU(3)-invariant integrable models

    NASA Astrophysics Data System (ADS)

    Belliard, S.; Pakuliak, S.; Ragoucy, E.; Slavnov, N. A.

    2012-10-01

    We study SU(3)-invariant integrable models solvable by a nested algebraic Bethe ansatz. We obtain a determinant representation for the particular case of scalar products of Bethe vectors. This representation can be used for the calculation of form factors and correlation functions of the XXX SU(3)-invariant Heisenberg chain.

  3. Mathematical Modelling in Engineering: An Alternative Way to Teach Linear Algebra

    ERIC Educational Resources Information Center

    Domínguez-García, S.; García-Planas, M. I.; Taberna, J.

    2016-01-01

    Technological advances require that basic science courses for engineering, including Linear Algebra, emphasize the development of mathematical strengths associated with modelling and interpretation of results, which are not limited only to calculus abilities. Based on this consideration, we have proposed a project-based learning, giving a dynamic…

  4. Optimal thermalization in a shell model of homogeneous turbulence

    NASA Astrophysics Data System (ADS)

    Thalabard, Simon; Turkington, Bruce

    2016-04-01

    We investigate the turbulence-induced dissipation of the large scales in a statistically homogeneous flow using an ‘optimal closure,’ which one of us (BT) has recently exposed in the context of Hamiltonian dynamics. This statistical closure employs a Gaussian model for the turbulent scales, with corresponding vanishing third cumulant, and yet it captures an intrinsic damping. The key to this apparent paradox lies in a clear distinction between true ensemble averages and their proxies, most easily grasped when one works directly with the Liouville equation rather than the cumulant hierarchy. We focus on a simple problem for which the optimal closure can be fully and exactly worked out: the relaxation arbitrarily far-from-equilibrium of a single energy shell towards Gibbs equilibrium in an inviscid shell model of 3D turbulence. The predictions of the optimal closure are validated against DNS and contrasted with those derived from EDQNM closure.

  5. Modeling of Turbulent Flow in Electromagnetically Levitated Metal Droplets

    NASA Technical Reports Server (NTRS)

    Berry, S.; Hyers, R. W.; Abedian, B.; Racz, L. M.; Rose, M. Franklin (Technical Monitor)

    2001-01-01

    This article details an effort to improve the understanding and prediction of turbulent flow inside a droplet of molten metal levitated in an electromagnetic field. It is shown that the flow field in a test case, a nickel droplet levitated under microgravity conditions, is in the transitional regime between laminar and turbulent flow. Past research efforts have used laminar, enhanced viscosity, and k-epsilon turbulence models to describe the flow. The method highlighted in our study is the renormalization group (RNG) algorithm. We show that an accurate description of the turbulent eddy viscosity is critical in order to obtain realistic velocity fields, and that the turbulent eddy viscosity cannot be uniform in levitated droplets. The RNG method does not impose isotropic length or time scales on the flow field, thus allowing such nonuniform features to be captured. A number of other materials processing applications exhibit similarly complex flow characteristics, such as highly recirculating, transitional, and free surface flows, for which this modeling approach may prove useful.

  6. Gup-Based and Snyder Noncommutative Algebras, Relativistic Particle Models, Deformed Symmetries and Interaction: a Unified Approach

    NASA Astrophysics Data System (ADS)

    Pramanik, Souvik; Ghosh, Subir

    2013-10-01

    We have developed a unified scheme for studying noncommutative algebras based on generalized uncertainty principle (GUP) and Snyder form in a relativistically covariant point particle Lagrangian (or symplectic) framework. Even though the GUP-based algebra and Snyder algebra are very distinct, the more involved latter algebra emerges from an approximation of the Lagrangian model of the former algebra. Deformed Poincaré generators for the systems that keep space-time symmetries of the relativistic particle models have been studied thoroughly. From a purely constrained dynamical analysis perspective the models studied here are very rich and provide insights on how to consistently construct approximate models from the exact ones when nonlinear constraints are present in the system. We also study dynamics of the GUP particle in presence of external electromagnetic field.

  7. Gup-Based and Snyder Noncommutative Algebras, Relativistic Particle Models, Deformed Symmetries and Interaction: a Unified Approach

    NASA Astrophysics Data System (ADS)

    Pramanik, Souvik; Ghosh, Subir

    2013-08-01

    We have developed a unified scheme for studying noncommutative algebras based on generalized uncertainty principle (GUP) and Snyder form in a relativistically covariant point particle Lagrangian (or symplectic) framework. Even though the GUP-based algebra and Snyder algebra are very distinct, the more involved latter algebra emerges from an approximation of the Lagrangian model of the former algebra. Deformed Poincaré generators for the systems that keep space-time symmetries of the relativistic particle models have been studied thoroughly. From a purely constrained dynamical analysis perspective the models studied here are very rich and provide insights on how to consistently construct approximate models from the exact ones when nonlinear constraints are present in the system. We also study dynamics of the GUP particle in presence of external electromagnetic field.

  8. Modified anisotropic turbulence refractive-index fluctuations spectral model and its application in moderate-to-strong anisotropic turbulence.

    PubMed

    Cui, Linyan; Xue, Bindang; Zhou, Fugen

    2016-04-01

    In this study, the modified anisotropic turbulence refractive-index fluctuations spectral model is derived based on the extended Rytov approximation theory for the theoretical investigations of optical plane and spherical waves propagating through moderate-to-strong anisotropic non-Kolmogorov turbulence. The anisotropic factor which parameterizes the asymmetry of turbulence cells or eddies in the horizontal and vertical directions is introduced. The general spectral power law in the range of 3-4 is also considered compared with the conventional classic value of 11/3 for Kolmogorov turbulence. Based on the modified anisotropic turbulence refractive-index fluctuations spectrum, the analytic expressions of the irradiance scintillation index are also derived for optical plane and spherical waves propagating through moderate-to-strong anisotropic non-Kolmogorov turbulence. They are applicable in a wide range of turbulence strengths and can reduce correctly to the previously published results in the special cases of weak anisotropic turbulence and moderate-to-strong isotropic turbulence. Calculations are performed to analyze the derived models. PMID:27140754

  9. Turbulent flow in a 180 deg bend: Modeling and computations

    NASA Technical Reports Server (NTRS)

    Kaul, Upender K.

    1989-01-01

    A low Reynolds number k-epsilon turbulence model was presented which yields accurate predictions of the kinetic energy near the wall. The model is validated with the experimental channel flow data of Kreplin and Eckelmann. The predictions are also compared with earlier results from direct simulation of turbulent channel flow. The model is especially useful for internal flows where the inflow boundary condition of epsilon is not easily prescribed. The model partly derives from some observations based on earlier direct simulation results of near-wall turbulence. The low Reynolds number turbulence model together with an existing curvature correction appropriate to spinning cylinder flows was used to simulate the flow in a U-bend with the same radius of curvature as the Space Shuttle Main Engine (SSME) Turn-Around Duct (TAD). The present computations indicate a space varying curvature correction parameter as opposed to a constant parameter as used in the spinning cylinder flows. Comparison with limited available experimental data is made. The comparison is favorable, but detailed experimental data is needed to further improve the curvature model.

  10. Computation of flows in a turn-around duct and a turbine cascade using advanced turbulence models

    NASA Technical Reports Server (NTRS)

    Lakshminarayana, B.; Luo, J.

    1993-01-01

    Numerical investigation has been carried out to evaluate the capability of the Algebraic Reynolds Stress Model (ARSM) and the Nonlinear Stress Model (NLSM) to predict strongly curved turbulent flow in a turn-around duct (TAD). The ARSM includes the near-wall damping term of pressure-strain correlation phi(sub ij,w), which enables accurate prediction of individual Reynolds stress components in wall flows. The TAD mean flow quantities are reasonably well predicted by various turbulence models. The ARSM yields better predictions for both the mean flow and the turbulence quantities than the NLSM and the k-epsilon (k = turbulent kinetic energy, epsilon = dissipation rate of k) model. The NLSM also shows slight improvement over the k-epsilon model. However, all the models fail to capture the recovery of the flow from strong curvature effects. The formulation for phi(sub ij,w) appears to be incorrect near the concave surface. The hybrid k-epsilon/ARSM, Chien's k-epsilon model, and Coakley's q-omega (q = the square root of k, omega = epsilon/k) model have also been employed to compute the aerodynamics and heat transfer of a transonic turbine cascade. The surface pressure distributions and the wake profiles are predicted well by all the models. The k-epsilon model and the k-epsilon/ARSM model provide better predictions of heat transfer than the q-omega model. The k-epsilon/ARSM solutions show significant differences in the predicted skin friction coefficients, heat transfer rates and the cascade performance parameters, as compared to the k-epsilon model. The k-epsilon/ARSM model appears to capture, qualitatively, the anisotropy associated with by-pass transition.

  11. Validation of two-equation turbulence models for propulsion flowfields

    NASA Technical Reports Server (NTRS)

    Deshpande, Manish; Venkateswaran, S.; Merkle, Charles L.

    1994-01-01

    The objective of the study is to assess the capability of two-equation turbulence models for simulating propulsion-related flowfields. The standard kappa-epsilon model with Chien's low Reynolds number formulation for near-wall effects is used as the baseline turbulence model. Several experimental test cases, representative of rocket combustor internal flowfields, are used to catalog the performance of the baseline model. Specific flowfields considered here include recirculating flow behind a backstep, mixing between coaxial jets and planar shear layers. Since turbulence solutions are notoriously dependent on grid and numerical methodology, the effects of grid refinement and artificial dissipation on numerical accuracy are studied. In the latter instance, computational results obtained with several central-differenced and upwind-based formulations are compared. Based on these results, improved turbulence modes such as enhanced kappa-epsilon models as well as other two-equation formulations (e.g., kappa-omega) are being studied. In addition, validation of swirling and reacting flowfields are also currently underway.

  12. Modeling complex chemical effects in turbulent nonpremixed combustion

    NASA Technical Reports Server (NTRS)

    Smith, Nigel S. A.

    1995-01-01

    Virtually all of the energy derived from the consumption of combustibles occurs in systems which utilize turbulent fluid motion. Since combustion is largely related to the mixing of fluids and mixing processes are orders of magnitude more rapid when enhanced by turbulent motion, efficiency criteria dictate that chemically powered devices necessarily involve fluid turbulence. Where combustion occurs concurrently with mixing at an interface between two reactive fluid bodies, this mode of combustion is called nonpremixed combustion. This is distinct from premixed combustion where flame-fronts propagate into a homogeneous mixture of reactants. These two modes are limiting cases in the range of temporal lag between mixing of reactants and the onset of reaction. Nonpremixed combustion occurs where this lag tends to zero, while premixed combustion occurs where this lag tends to infinity. Many combustion processes are hybrids of these two extremes with finite non-zero lag times. Turbulent nonpremixed combustion is important from a practical standpoint because it occurs in gas fired boilers, furnaces, waste incinerators, diesel engines, gas turbine combustors, and afterburners etc. To a large extent, past development of these practical systems involved an empirical methodology. Presently, efficiency standards and emission regulations are being further tightened (Correa 1993), and empiricism has had to give way to more fundamental research in order to understand and effectively model practical combustion processes (Pope 1991). A key element in effective modeling of turbulent combustion is making use of a sufficiently detailed chemical kinetic mechanism. The prediction of pollutant emission such as oxides of nitrogen (NO(x)) and sulphur (SO(x)) unburned hydrocarbons, and particulates demands the use of detailed chemical mechanisms. It is essential that practical models for turbulent nonpremixed combustion are capable of handling large numbers of 'stiff' chemical species

  13. A spray-suppression model for turbulent combustion

    SciTech Connect

    DESJARDIN,PAUL E.; TIESZEN,SHELDON R.; GRITZO,LOUIS A.

    2000-02-14

    A spray-suppression model that captures the effects of liquid suppressant on a turbulent combusting flow is developed and applied to a turbulent diffusion flame with water spray suppression. The spray submodel is based on a stochastic separated flow approach that accounts for the transport and evaporation of liquid droplets. Flame extinguishment is accounted for by using a perfectly stirred reactor (PSR) submodel of turbulent combustion. PSR pre-calculations of flame extinction times are determined using CHEMKIN and are compared to local turbulent time scales of the flow to determine if local flame extinguishment has occurred. The PSR flame extinguishment and spray submodels are incorporated into Sandia's flow fire simulation code, VULCAN, and cases are run for the water spray suppression studies of McCaffrey for turbulent hydrogen-air jet diffusion flames. Predictions of flame temperature decrease and suppression efficiency are compared to experimental data as a function of water mass loading using three assumed values of drop sizes. The results show that the suppression efficiency is highly dependent on the initial droplet size for a given mass loading. A predicted optimal suppression efficiency was observed for the smallest class of droplets while the larger drops show increasing suppression efficiency with increasing mass loading for the range of mass loadings considered. Qualitative agreement to the experiment of suppression efficiency is encouraging, however quantitative agreement is limited due to the uncertainties in the boundary conditions of the experimental data for the water spray.

  14. MODELING MAGNETOROTATIONAL TURBULENCE IN PROTOPLANETARY DISKS WITH DEAD ZONES

    SciTech Connect

    Okuzumi, Satoshi; Hirose, Shigenobu

    2011-12-01

    Turbulence driven by magnetorotational instability (MRI) crucially affects the evolution of solid bodies in protoplanetary disks. On the other hand, small dust particles stabilize MRI by capturing ionized gas particles needed for the coupling of the gas and magnetic fields. To provide an empirical basis for modeling the coevolution of dust and MRI, we perform three-dimensional, ohmic-resistive MHD simulations of a vertically stratified shearing box with an MRI-inactive 'dead zone' of various sizes and with a net vertical magnetic flux of various strengths. We find that the vertical structure of turbulence is well characterized by the vertical magnetic flux and three critical heights derived from the linear analysis of MRI in a stratified disk. In particular, the turbulent structure depends on the resistivity profile only through the critical heights and is insensitive to the details of the resistivity profile. We discover scaling relations between the amplitudes of various turbulent quantities (velocity dispersion, density fluctuation, vertical diffusion coefficient, and outflow mass flux) and vertically integrated accretion stresses. We also obtain empirical formulae for the integrated accretion stresses as a function of the vertical magnetic flux and the critical heights. These empirical relations allow us to predict the vertical turbulent structure of a protoplanetary disk for a given strength of the magnetic flux and a given resistivity profile.

  15. Teaching Algebra without Algebra

    ERIC Educational Resources Information Center

    Kalman, Richard S.

    2008-01-01

    Algebra is, among other things, a shorthand way to express quantitative reasoning. This article illustrates ways for the classroom teacher to convert algebraic solutions to verbal problems into conversational solutions that can be understood by students in the lower grades. Three reasonably typical verbal problems that either appeared as or…

  16. Turbulence modeling in aerodynamic shear flows - Status and problems

    NASA Technical Reports Server (NTRS)

    Bushnell, D. M.

    1991-01-01

    This paper briefly summarizes the status and problems of turbulence modeling for aerodynamical applications. For complex flows the 'approach of choice' is (increasingly) full second-order (Reynolds stress equation) closure. These closures have not yet developed to anywhere near their full potential, significant further research is required especially regarding length-scale equations, representation of pressure-strain correlations, and wall region treatments. Recent developments in computer capability, algorithms, numerical simulations, theory and quantitative flow visualization should assist in and hasten this research. Several problem areas such as shock interaction and discrete dynamic instabilities of turbulent flows may require mega-to-large eddy simulation or theoretical adjuncts.

  17. Two-dimensional magnetohydrodynamic turbulence - Cylindrical, non-dissipative model

    NASA Technical Reports Server (NTRS)

    Montgomery, D.; Vahala, G.

    1979-01-01

    Incompressible magnetohydrodynamic turbulence is treated in the presence of cylindrical boundaries which are perfectly conducting and rigidly smooth. The model treated is non-dissipative and two-dimensional, the variation of all quantities in the axial direction being ignored. Equilibrium Gibbs ensemble predictions are explored assuming the constraint of constant axial current (appropriate to tokamak operation). No small-amplitude approximations are made. The expectation value of the turbulent kinetic energy is found to approach zero for the state of maximum mean-square vector potential to energy ratio. These are the only states for which large velocity fluctuations are not expected.

  18. Large Eddy Simulations and Turbulence Modeling for Film Cooling

    NASA Technical Reports Server (NTRS)

    Acharya, Sumanta

    1999-01-01

    The objective of the research is to perform Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES) for film cooling process, and to evaluate and improve advanced forms of the two equation turbulence models for turbine blade surface flow analysis. The DNS/LES were used to resolve the large eddies within the flow field near the coolant jet location. The work involved code development and applications of the codes developed to the film cooling problems. Five different codes were developed and utilized to perform this research. This report presented a summary of the development of the codes and their applications to analyze the turbulence properties at locations near coolant injection holes.

  19. Implementation of algebraic stress models in a general 3-D Navier-Stokes method (PAB3D)

    NASA Technical Reports Server (NTRS)

    Abdol-Hamid, Khaled S.

    1995-01-01

    A three-dimensional multiblock Navier-Stokes code, PAB3D, which was developed for propulsion integration and general aerodynamic analysis, has been used extensively by NASA Langley and other organizations to perform both internal (exhaust) and external flow analysis of complex aircraft configurations. This code was designed to solve the simplified Reynolds Averaged Navier-Stokes equations. A two-equation k-epsilon turbulence model has been used with considerable success, especially for attached flows. Accurate predicting of transonic shock wave location and pressure recovery in separated flow regions has been more difficult. Two algebraic Reynolds stress models (ASM) have been recently implemented in the code that greatly improved the code's ability to predict these difficult flow conditions. Good agreement with Direct Numerical Simulation (DNS) for a subsonic flat plate was achieved with ASM's developed by Shih, Zhu, and Lumley and Gatski and Speziale. Good predictions were also achieved at subsonic and transonic Mach numbers for shock location and trailing edge boattail pressure recovery on a single-engine afterbody/nozzle model.

  20. Effects of turbulence on a kinetic auroral arc model

    NASA Technical Reports Server (NTRS)

    Cornwall, J. M.; Chiu, Y. T.

    1981-01-01

    A plasma kinetic model of an inverted-V auroral arc structure which includes the effects of electrostatic turbulence is proposed. In the absence of turbulence, a parallel potential drop is supported by magnetic mirror forces and charge quasi neutrality, with energetic auroral ions penetrating to low altitudes; relative to the electrons, the ions' pitch angle distribution is skewed toward smaller pitch angles. The electrons energized by the potential drop form a current which excites electrostatic turbulence. In equilibrium the plasma is marginally stable. The conventional anomalous resistivity contribution to the potential drop is very small. Anomalous resistivity processes are far too dissipative to be powered by auroral particles. It is concluded that under certain circumstances equilibrium may be impossible and relaxation oscillations set in.

  1. Description of a Website Resource for Turbulence Modeling Verification and Validation

    NASA Technical Reports Server (NTRS)

    Rumsey, Christopher L.; Smith, Brian R.; Huang, George P.

    2010-01-01

    The activities of the Turbulence Model Benchmarking Working Group - which is a subcommittee of the American Institute of Aeronautics and Astronautics (AIAA) Fluid Dynamics Technical Committee - are described. The group s main purpose is to establish a web-based repository for Reynolds-averaged Navier-Stokes turbulence model documentation, including verification and validation cases. This turbulence modeling resource has been established based on feedback from a survey on what is needed to achieve consistency and repeatability in turbulence model implementation and usage, and to document and disseminate information on new turbulence models or improvements to existing models. The various components of the website are described in detail: description of turbulence models, turbulence model readiness rating system, verification cases, validation cases, validation databases, and turbulence manufactured solutions. An outline of future plans of the working group is also provided.

  2. Performance of Smagorinsky and dynamic models in near surface turbulence

    NASA Astrophysics Data System (ADS)

    Brasseur, James G.; Juneja, Anurag

    1997-11-01

    In LES of high-Reynolds-number wall bounded turbulence such as the atmospheric boundary layer (ABL), a viscous sublayer either does not exist or is within the first grid cell, and some integral scale motions are necessarily under-resolved at the first few grid locations. Here the subgrid terms dominate the evolution of resolved velocity and the SGS model performance becomes crucial. To develop improved closures for surface layer turbulence (under-resolved and anisotropic), we explore (a) why current SGS closures fail and (b) what needs to be fixed. We evaluate the performance of the Smagorinsky and dynamic models using DNS data from shear- and buoyancy-driven turbulence as a function of filter cutoff location. We find that the underlying assumption of good alignment between the subgrid stress and resolved strain-rate tensors is not correct in general. More importantly, the Smagorinsky model incorrectly predicts a strong preference in the direction of the SGS stress divergence vector, a spurious prediction that is directly related to the anisotropic structure of the resolved turbulence field. This, and its under-estimation of the SGS pressure gradient, are likely sources of the errors observed in LES of the ABL. Whereas the dynamic formulations do a better job predicting some SGS dynamics, the model fails when the filter cutoff is near an integral scale, and predicts unreasonable fluctuation levels-- although performance is sensitive to type of averaging. *supported by ARO grant DAAL03-92-0117.

  3. Stably stratified shear turbulence: A new model for the energy dissipation length scale

    NASA Technical Reports Server (NTRS)

    Cheng, Y.; Canuto, V. M.

    1994-01-01

    A model is presented to compute the turbulent kinetic energy dissipation length scale l(sub epsilon) in a stably stratified shear flow. The expression for l(sub epsilon) is derived from solving the spectral balance equation for the turbulent kinetic energy. The buoyancy spectrum entering such equation is constructed using a Lagrangian timescale with modifications due to stratification. The final result for l(sub epsilon) is given in algebraic form as a function of the Froude number Fr and the flux Richardson number R(sub f), l(sub epsilon) = l(sub epsilon)(Fr, R(sub f). The model predicts that for R(sub f) less than R(sub fc), l(sub epsilon) decreases with stratification. An attractive feature of the present model is that it encompasses, as special cases, some seemingly different models for l(sub epsilon) that have been proposed in the past by Deardorff, Hunt et al., Weinstock, and Canuto and Minotti. An alternative form for the dissipation rate epsilon is also discussed that may be useful when one uses a prognostic equation for the heat flux. The present model is applicable to subgrid-scale models, which are needed in large eddy simulations (LES), as well as to ensemble average models. The model is applied to predict the variation of l(sub epsilon) with height z in the planetary boundary layer. The resulting l(sub epsilon) versus z profile reproduces very closely the nonmonotonic profile of l(sub epsilon) exhibited by many LES calculations, beginning with the one by Deardorff in 1974.

  4. A turbulent inflow model based on velocity modulation

    NASA Astrophysics Data System (ADS)

    Huyer, Stephen A.; Beal, David

    2007-11-01

    This article presents a novel turbulent inflow model based on modulation of the velocity field for use with time-domain propulsor calculations. Given an experimental mean and rms turbulent inflow, a model can be constructed by modulating the velocity field over a range of frequencies. Assuming the turbulence is homogeneous, the inflow can be constructed as a Fourier series where the frequencies can also be modulated to smooth the broadband output. To demonstrate the effectiveness of the model, experimental inflow velocity data were acquired for an upstream stator, downstream rotor configuration mounted on an undersea vehicle afterbody. Two main sources of turbulence originated from the vorticity shed from the stator wakes and the boundary layer vorticity produced on the hull body. Three-dimensional, unsteady velocity data were acquired using hot-wire anemometry and reduced to provide mean and rms velocity values. Time-series data were processed to provide velocity power spectra used to calibrate the model. Simulations were performed using a modified version of the propulsor unsteady flow code capable of computing fully turbulent inflows. This solver models the propulsor blade as a vortex lattice and sheds the vorticity into the wake to solve the unsteady potential flow. The no-flux boundary conditions are satisfied at the lattice control points and the resulting unsteady circulation is a function of the instantaneous inflow velocity field over the blade. Vorticity is shed into the wake to account for the full time history of the inflow velocity field. To demonstrate the full effectiveness of the model, computed surface pressure data were exported to a code to compute the far-field radiated noise (both tonal and broadband). Simulated data were compared with experimentally obtained noise data with favorable results. Applications of this methodology in the incompressible flow domain include broadband analysis of propulsor-radiated noise on undersea vehicles and

  5. Computation of turbulent high speed mixing layers using a two-equation turbulence model

    NASA Technical Reports Server (NTRS)

    Narayan, J. R.; Sekar, B.

    1991-01-01

    A two-equation turbulence model was extended to be applicable for compressible flows. A compressibility correction based on modelling the dilational terms in the Reynolds stress equations were included in the model. The model is used in conjunction with the SPARK code for the computation of high speed mixing layers. The observed trend of decreasing growth rate with increasing convective Mach number in compressible mixing layers is well predicted by the model. The predictions agree well with the experimental data and the results from a compressible Reynolds stress model. The present model appears to be well suited for the study of compressible free shear flows. Preliminary results obtained for the reacting mixing layers are included.

  6. Particle dispersion in homogeneous turbulence using the one-dimensional turbulence model

    DOE PAGESBeta

    Sun, Guangyuan; Lignell, David O.; Hewson, John C.; Gin, Craig R.

    2014-10-09

    Lagrangian particle dispersion is studied using the one-dimensional turbulence (ODT) model in homogeneous decaying turbulence configurations. The ODT model has been widely and successfully applied to a number of reacting and nonreacting flow configurations, but only limited application has been made to multiphase flows. We present a version of the particle implementation and interaction with the stochastic and instantaneous ODT eddy events. The model is characterized by comparison to experimental data of particle dispersion for a range of intrinsic particle time scales and body forces. Particle dispersion, velocity, and integral time scale results are presented. Moreover, the particle implementation introducesmore » a single model parameter β p , and sensitivity to this parameter and behavior of the model are discussed. Good agreement is found with experimental data and the ODT model is able to capture the particle inertial and trajectory crossing effects. Our results serve as a validation case of the multiphase implementations of ODT for extensions to other flow configurations.« less

  7. Group-kinetic theory and modeling of atmospheric turbulence

    NASA Technical Reports Server (NTRS)

    Tchen, C. M.

    1989-01-01

    A group kinetic method is developed for analyzing eddy transport properties and relaxation to equilibrium. The purpose is to derive the spectral structure of turbulence in incompressible and compressible media. Of particular interest are: direct and inverse cascade, boundary layer turbulence, Rossby wave turbulence, two phase turbulence; compressible turbulence, and soliton turbulence. Soliton turbulence can be found in large scale turbulence, turbulence connected with surface gravity waves and nonlinear propagation of acoustical and optical waves. By letting the pressure gradient represent the elementary interaction among fluid elements and by raising the Navier-Stokes equation to higher dimensionality, the master equation was obtained for the description of the microdynamical state of turbulence.

  8. Modeling of Fine-Particle Formation in Turbulent Flames

    NASA Astrophysics Data System (ADS)

    Raman, Venkat; Fox, Rodney O.

    2016-01-01

    The generation of nanostructured particles in high-temperature flames is important both for the control of emissions from combustion devices and for the synthesis of high-value chemicals for a variety of applications. The physiochemical processes that lead to the production of fine particles in turbulent flames are highly sensitive to the flow physics and, in particular, the history of thermochemical compositions and turbulent features they encounter. Consequently, it is possible to change the characteristic size, structure, composition, and yield of the fine particles by altering the flow configuration. This review describes the complex multiscale interactions among turbulent fluid flow, gas-phase chemical reactions, and solid-phase particle evolution. The focus is on modeling the generation of soot particles, an unwanted pollutant from automobile and aircraft engines, as well as metal oxides, a class of high-value chemicals sought for specialized applications, including emissions control. Issues arising due to the numerical methods used to approximate the particle number density function, the modeling of turbulence-chemistry interactions, and model validation are also discussed.

  9. New DNS and modeling results for turbulent pipe flow

    NASA Astrophysics Data System (ADS)

    Johansson, Arne; El Khoury, George; Grundestam, Olof; Schlatter, Philipp; Brethouwer, Geert; Linne Flow Centre Team

    2013-11-01

    The near-wall region of turbulent pipe and channel flows (as well as zero-pressure gradient boundary layers) have been shown to exhibit a very high degree of similarity in terms of all statistical moments and many other features, while even the mean velocity profile in the two cases exhibits significant differences between in the outer region. The wake part of the profile, i.e. the deviation from the log-law, in the outer region is of substantially larger amplitude in pipe flow as compared to channel flow (although weaker than in boundary layer flow). This intriguing feature has been well known but has no simple explanation. Model predictions typically give identical results for the two flows. We have analyzed a new set of DNS for pipe and channel flows (el Khoury et al. 2013, Flow, Turbulence and Combustion) for friction Reynolds numbers up to 1000 and made comparing calculations with differential Reynolds stress models (DRSM). We have strong indications that the key factor behind the difference in mean velocity in the outer region can be coupled to differences in the turbulent diffusion in this region. This is also supported by DRSM results, where interesting differences are seen depending on the sophistication of modeling the turbulent diffusion coefficient.

  10. A Lagrangian model of Copepod dynamics in turbulent flows

    NASA Astrophysics Data System (ADS)

    Ardeshiri, Hamidreza; Benkeddad, Ibtissem; Schmitt, Francois G.; Souissi, Sami; Toschi, Federico; Calzavarini, Enrico

    2016-04-01

    Planktonic copepods are small crustaceans that have the ability to swim by quick powerful jumps. Such an aptness is used to escape from high shear regions, which may be caused either by flow perturbations, produced by a large predator such as fish larave, or by the inherent highly turbulent dynamics of the ocean. Through a combined experimental and numerical study, we investigate the impact of jumping behaviour on the small-scale patchiness of copepods in a turbulent environment. Recorded velocity tracks of copepods displaying escape response jumps in still water are used to define and tune a Lagrangian Copepod (LC) model. The model is further employed to simulate the behaviour of thousands of copepods in a fully developed hydrodynamic turbulent flow obtained by direct numerical simulation of the Navier-Stokes equations. First, we show that the LC velocity statistics is in qualitative agreement with available experimental observations of copepods in turbulence. Second, we quantify the clustering of LC, via the fractal dimension D2. We show that D2 can be as low as 2.3, corresponding to local sheetlike aggregates, and that it critically depends on the shear-rate sensitivity of the proposed LC model. We further investigate the effect of jump intensity, jump orientation and geometrical aspect ratio of the copepods on the small-scale spatial distribution. Possible ecological implications of the observed clustering on encounter rates and mating success are discussed.

  11. Modelling of the pressure-velocity correlation in turbulence diffusion

    NASA Astrophysics Data System (ADS)

    Fu, Song

    1993-05-01

    In the context of second-moment closure, the mechanism of turbulence diffusion consists of mainly two parts: a triple velocity correlation and a pressure-velocity correlation. The first correlation is measurable and can be analyzed theoretically through its transport equation. The second correlation cannot, however, be obtained directly from experiments and knowledge about it is comparatively limited. Most current computations of turbulent flows adopt diffusion models which neglect the effect of the pressure-velocity correlation in the diffusion process. The importance of this correlation effect is elucidated; the neglect of this effect constitutes some of the major defects in the application of the second-moment closures. Through the relation between the two correlations, established by Lumley (1978), we propose a new type of turbulence diffusion model which takes into account the pressure effect. Application of this new model in the computation of the turbulence shearless mixing layer and plane- and round-jet flows shows that the spreading rates of these flows can be captured satisfactorily.

  12. On the modeling of wave-enhanced turbulence nearshore

    NASA Astrophysics Data System (ADS)

    Moghimi, Saeed; Thomson, Jim; Özkan-Haller, Tuba; Umlauf, Lars; Zippel, Seth

    2016-07-01

    A high resolution k-ω two-equation turbulence closure model, including surface wave forcing was employed to fully resolve turbulence dissipation rate profiles close to the ocean surface. Model results were compared with observations from Surface Wave Instrument Floats with Tracking (SWIFTs) in the nearshore region at New River Inlet, North Carolina USA, in June 2012. A sensitivity analysis for different physical parameters and wave and turbulence formulations was performed. The flux of turbulent kinetic energy (TKE) prescribed by wave dissipation from a numerical wave model was compared with the conventional prescription using the wind friction velocity. A surface roughness length of 0.6 times the significant wave height was proposed, and the flux of TKE was applied at a distance below the mean sea surface that is half of this roughness length. The wave enhanced layer had a total depth that is almost three times the significant wave height. In this layer the non-dimensionalized Terray scaling with power of - 1.8 (instead of - 2) was applicable.

  13. The study of PDF turbulence models in combustion

    NASA Technical Reports Server (NTRS)

    Hsu, Andrew T.

    1991-01-01

    In combustion computations, it is known that the predictions of chemical reaction rates are poor if conventional turbulence models are used. The probability density function (pdf) method seems to be the only alternative that uses local instantaneous values of the temperature, density, etc., in predicting chemical reaction rates, and thus is the only viable approach for more accurate turbulent combustion calculations. The fact that the pdf equation has a very large dimensionality renders finite difference schemes extremely demanding on computer memories and thus impractical. A logical alternative is the Monte Carlo scheme. Since CFD has a certain maturity as well as acceptance, it seems that the use of a combined CFD and Monte Carlo scheme is more beneficial. Therefore, a scheme is chosen that uses a conventional CFD flow solver in calculating the flow field properties such as velocity, pressure, etc., while the chemical reaction part is solved using a Monte Carlo scheme. The discharge of a heated turbulent plane jet into quiescent air was studied. Experimental data for this problem shows that when the temperature difference between the jet and the surrounding air is small, buoyancy effect can be neglected and the temperature can be treated as a passive scalar. The fact that jet flows have a self-similar solution lends convenience in the modeling study. Futhermore, the existence of experimental data for turbulent shear stress and temperature variance make the case ideal for the testing of pdf models wherein these values can be directly evaluated.

  14. Potential capabilities of Reynolds stress turbulence model in the COMMIX-RSM code

    NASA Technical Reports Server (NTRS)

    Chang, F. C.; Bottoni, M.

    1994-01-01

    A Reynolds stress turbulence model has been implemented in the COMMIX code, together with transport equations describing turbulent heat fluxes, variance of temperature fluctuations, and dissipation of turbulence kinetic energy. The model has been verified partially by simulating homogeneous turbulent shear flow, and stable and unstable stratified shear flows with strong buoyancy-suppressing or enhancing turbulence. This article outlines the model, explains the verifications performed thus far, and discusses potential applications of the COMMIX-RSM code in several domains, including, but not limited to, analysis of thermal striping in engineering systems, simulation of turbulence in combustors, and predictions of bubbly and particulate flows.

  15. Interplay between the pairing and quadrupole interactions in the algebraic realization of the microscopic shell model

    NASA Astrophysics Data System (ADS)

    Drumev, Kalin; Georgieva, Ana

    2015-04-01

    We explore the algebraic realization of the Pairing-Plus-Quadrupole Model/PQM/ in the framework of the Elliott‘s SU(3) Model with the aim to obtain the complementary and competing features of the two interactions through the relation between the pairing and the SU(3) bases. First, we establish a correspondence between the SO(8) pairing basis and the Elliott's SU(3) basis. It is derived from their complementarity to the same LST coupling chain of the shell-model number-conserving algebra. The probability distribution of the SU(3) basis states within the SO(8) pairing states is also obtained and allows the investigation of the interplay between the pairing and quadrupole interactions in the Hamiltonian of the PQM, containing both of them as limiting cases. The description of some realistic N∼Z nuclear systems is investigated in a SU(3)-symmetry-adapted basis within a model space of one and two oscillator shells.

  16. Development of a recursion RNG-based turbulence model

    NASA Technical Reports Server (NTRS)

    Zhou, YE; Vahala, George; Thangam, S.

    1993-01-01

    Reynolds stress closure models based on the recursion renormalization group theory are developed for the prediction of turbulent separated flows. The proposed model uses a finite wavenumber truncation scheme to account for the spectral distribution of energy. In particular, the model incorporates effects of both local and nonlocal interactions. The nonlocal interactions are shown to yield a contribution identical to that from the epsilon-renormalization group (RNG), while the local interactions introduce higher order dispersive effects. A formal analysis of the model is presented and its ability to accurately predict separated flows is analyzed from a combined theoretical and computational stand point. Turbulent flow past a backward facing step is chosen as a test case and the results obtained based on detailed computations demonstrate that the proposed recursion -RNG model with finite cut-off wavenumber can yield very good predictions for the backstep problem.

  17. Particle-Turbulence Interaction Model for Aluminum Combustion

    NASA Astrophysics Data System (ADS)

    Sinha, Neeraj; Calhoon, William; Tomes, Jeremy

    2011-06-01

    Particle-turbulence interactions will have a substantial impact on the performance of thermobaric explosives that rely on the particle combustion for secondary heat release. Modeling these interactions from a fundamental perspective is very difficult and intractable for large-scale problems of practical interest. Alternatively, these interactions may be modeled from a macroscopic perspective that seeks to account for the probability distribution function (PDF) of variables within the modeled laminar burning rate for the particulates. Such a formulation would account for the first order effect of turbulent fluctuations on the burning rate within a computationally affordable model. This paper will describe the development of such a model for aluminum particle combustion in both the diffusion and kinetic burning regimes. This formulation is based on an assumed PDF method that may be parameterized into a database that may be deployed within a flow solver. As a result, the formulation is computational efficient and affordable for large-scale simulations.

  18. Studies of turbulent round jets through experimentation, simulation, and modeling

    NASA Astrophysics Data System (ADS)

    Keedy, Ryan

    This thesis studies the physics of the turbulent round jet. In particular, it focuses on three different problems that have the turbulent round jet as their base flow. The first part of this thesis examines a compressible turbulent round jet at its sonic condition. We investigate the shearing effect such a jet has when impinging on a solid surface that is perpendicular to the flow direction. We report on experiments to evaluate the jet's ability to remove different types of explosive particles from a glass surface. Theoretical analysis revealed trends and enabled modeling to improve the predictability of particle removal for various jet conditions. The second part of thesis aims at developing a non-intrusive measurement technique for free-shear turbulent flows in nature. Most turbulent jet investigations in the literature, both in the laboratory and in the field, required specialized intrusive instrumentation and/or complex optical setups. There are many situations in naturally-occurring flows where the environment may prove too hostile or remote for existing instrumentation. We have developed a methodology for analyzing video of the exterior of a naturally-occurring flow and calculating the flow velocity. We found that the presence of viscosity gradients affects the velocity analysis. While these effects produce consistent, predictable changes, we became interested in the mechanism by which the viscosity gradients affect the mixing and development of the turbulent round jet. We conducted a stability analysis of the axisymmetric jet when a viscosity gradient is present. Finally, the third problem addressed in this thesis is the growth of liquid droplets by condensation in a turbulent round jet. A vapor-saturated turbulent jet issues into a cold, dry environment. The resulting mixing produces highly inhomogeneous regions of supersaturation, where droplets grow and evaporate. Non-linear interactions between the droplet growth rate and the supersaturation field make

  19. Turbulence Model Comparisons for a High-Speed Aircraft

    NASA Technical Reports Server (NTRS)

    Rivers, Melissa B.; Wahls, Richard A.

    1999-01-01

    Four turbulence models are described and evaluated for transonic flows over the High-Speed Research/industry baseline configuration known as Reference H by using the thin-layer, upwind, Navier-Stokes solver known as CFL3D. The turbulence models studied are the equilibrium model of Baldwin-Lomax (B-L) with the Degani-Schiff (D-S) modifications, the one-equation Baldwin-Barth (B-B) model, the one-equation Spalart-Allmaras (S-A) model, and Menter's two-equation Shear Stress Transport (SST) model. The flow conditions, which correspond to tests performed in the National Transonic Facility (NTF) at Langley Research Center, are a Mach number of 0.90 and a Reynolds number of 30 x 10 (exp. 6) based on mean aerodynamic chord for angles of attack of 1 deg., 5 deg., and 10 deg. The effects of grid topology and the representation of the actual wind tunnel model geometry are also investigated. Computed forces and surface pressures compare reasonably well with the experimental data for all four turbulence models.

  20. Turbulence Models for Accurate Aerothermal Prediction in Hypersonic Flows

    NASA Astrophysics Data System (ADS)

    Zhang, Xiang-Hong; Wu, Yi-Zao; Wang, Jiang-Feng

    Accurate description of the aerodynamic and aerothermal environment is crucial to the integrated design and optimization for high performance hypersonic vehicles. In the simulation of aerothermal environment, the effect of viscosity is crucial. The turbulence modeling remains a major source of uncertainty in the computational prediction of aerodynamic forces and heating. In this paper, three turbulent models were studied: the one-equation eddy viscosity transport model of Spalart-Allmaras, the Wilcox k-ω model and the Menter SST model. For the k-ω model and SST model, the compressibility correction, press dilatation and low Reynolds number correction were considered. The influence of these corrections for flow properties were discussed by comparing with the results without corrections. In this paper the emphasis is on the assessment and evaluation of the turbulence models in prediction of heat transfer as applied to a range of hypersonic flows with comparison to experimental data. This will enable establishing factor of safety for the design of thermal protection systems of hypersonic vehicle.

  1. Turbulence regulation by stochastic zonal flows in dynamical models

    SciTech Connect

    Kim, Eun-jin

    2005-09-15

    A theory of turbulence reduction by zonal flows is presented in the interchange turbulence model. Zonal flows with a finite correlation time {tau}{sub ZF} are shown to lead to a significant reduction in particle transport and turbulence amplitude, with the scalings {upsilon}{sub x}{proportional_to}{tau}{sub D}{omega}{sub eff}{sup -1}{proportional_to}{omega}{sub eff}{sup -3/2}, n{sup 2}{proportional_to}{tau}{sub D}{proportional_to}{omega}{sub eff}{sup -1/2}, and {upsilon}{sub x}{sup 2}{proportional_to}{tau}{sub D}{omega}{sub eff}{sup -2}{proportional_to}{omega}{sub eff}{sup -5/2}. Here, {omega}{sub eff}={tau}{sub ZF}{omega}{sub rms}{sup 2}, {tau}{sub D}=({tau}{sub {eta}}/{omega}{sub eff}){sup 1/2}, and {tau}{sub {eta}} are the effective shearing rate, effective decorrelation time, and diffusive turbulent scattering time, respectively. Compared to the transport of passive scalar fields [E. Kim and P. H. Diamond, Phys. Plasmas, 11, L77 (2004)], the reduction is much more severe due to the suppression of turbulent velocity. However, the overall transport and turbulence amplitude are still larger compared with the case of coherent shearing because shearing by random zonal flows with a finite correlation time is less efficient, with a longer decorrelation time {tau}{sub D} than ({tau}{sub {eta}}/{omega}{sup 2}){sup 1/3} in the case of coherent shearing.

  2. Measurement of terms and parameters in turbulent models

    NASA Technical Reports Server (NTRS)

    Sandborn, Virgil A.

    1989-01-01

    Experimental measurements of the mean and turbulent velocity field in a water flow, turn-around-duct is documented. The small radius of curvature duct experiments were made over a range of Reynolds numbers (based on a duct height of 10 cm) from 70,000 to 500,000. For this particular channel, the flow is dominated by the inertia forces. Use of the local bulk velocity to non-dimensionalize the local velocity was found to limit Reynolds number effects to the regions very close to the wall. Only secondary effects on the flow field were observed when the inlet or exit boundary conditions were altered. The flow over the central two-thirds of the channel was two-dimensional. Mean tangetial and radial velocities, streamlines, pressure distributions, surface shear stress; tangential, radial and lateral turbulent velocities and the Reynolds turbulent shear values are tabulated in other reports. It is evident from the experimental study that a complex numerical modeling technique must be developed to predict the flow in the turn-around-duct. The model must be able to predict relaminarization along the inner-convex-wall. It must also allow for the major increase in turbulence produced by the outer-concave-wall.

  3. Turbulence and dissipation in a computational model of Luzon Strait

    NASA Astrophysics Data System (ADS)

    Jalali, Masoud; Sarkar, Sutanu

    2014-11-01

    Generation sites for topographic internal gravity waves can also be sites of intense turbulence. Bottom-intensified flow at critical slopes leads to convective instability and turbulent overturns [Gayen & Sarkar (2011)]. A steep ridge with small excursion number, Ex , but large super criticality can lead to nonlinear features according to observations [Klymak et al. (2008)] and numerical simulations [Legg & Klymak (2008)]. The present work uses high resolution 3-D LES to simulate flow over a model with multiscale topography patterned after a cross-section of Luzon Strait, a double-ridge generation site which was the subject of the recent IWISE experiment. A 1:100 scaling of topography was employed and environmental parameters were chosen to match the slope criticality and Fr number in the field. Several turbulent zones were identified including breaking lee waves, critical slope boundary layer, downslope jets, internal wave beams, and vortical valley flows. The multiscale model topography has subridges where a local Ex may be defined. Wave breaking and turbulence at these subridges can be understood if the local value of Ex is employed when using the Ex -based regimes identified by Jalali et al. (2014) in their DNS of oscillating flow over a single triangular obstacle.

  4. A Model for Jet-Surface Interaction Noise Using Physically Realizable Upstream Turbulence Conditions

    NASA Technical Reports Server (NTRS)

    Afsar, Mohammed Z.; Leib, Stewart J.; Bozak, Richard F.

    2016-01-01

    This paper is a continuation of previous work in which a generalized Rapid Distortion Theory (RDT) formulation was used to model low-frequency trailing-edge noise. The research was motivated by proposed next-generation aircraft configurations where the exhaust system is tightly integrated with the airframe. Data from recent experiments at NASA on the interaction between high-Reynolds-number subsonic jet flows and an external flat plate showed that the power spectral density (PSD) of the far-field pressure underwent considerable amplification at low frequencies. For example, at the 90deg observation angle, the low-frequency noise could be as much as 10 dB greater than the jet noise itself. In this paper, we present predictions of the noise generated by the interaction of a rectangular jet with the trailing edge of a semi-infinite flat plate. The calculations are based on a formula for the acoustic spectrum of this noise source derived from an exact formal solution of the linearized Euler equations involving (in this case) one arbitrary convected scalar quantity and a Rayleigh equation Green's function. A low-frequency asymptotic approximation for the Green's function based on a two-dimensional mean flow is used in the calculations along with a physically realizable upstream turbulence spectrum, which includes a finite decorrelation region. Numerical predictions of the sound field, based on three-dimensional RANS solutions to determine the mean flow, turbulent kinetic energy and turbulence length and time scales, for a range of subsonic acoustic Mach number jets and nozzle aspect ratios are compared with experimental data. Comparisons of the RANS results with flow data are also presented for selected cases. We find that a finite decorrelation region in the turbulence spectrum increases the low-frequency algebraic decay (the low frequency "roll-off") of the acoustic spectrum with angular frequency thereby producing much closer agreement with noise data for Strouhal

  5. Magnetic reversals in a modified shell model for magnetohydrodynamics turbulence.

    PubMed

    Nigro, Giuseppina; Carbone, Vincenzo

    2010-07-01

    The aim of the paper is the study of dynamo action using a simple nonlinear model in the framework of magnetohydrodynamic turbulence. The nonlinear behavior of the system is described by using a shell model for velocity field and magnetic field fluctuations, modified for the magnetic field at the largest scale by a term describing a supercritical pitchfork bifurcation. Turbulent fluctuations generate a dynamical situation where the large-scale magnetic field jumps between two states which represent the opposite polarities of the magnetic field. Despite its simplicity, the model has the capability to describe a long time series of reversals from which we infer results about the statistics of persistence times and scaling laws of cancellations between opposite polarities for different magnetic diffusivity coefficients. These properties of the model are compared with real paleomagnetic data, thus revealing the origin of long-range correlations in the process. PMID:20866731

  6. Magnetic reversals in a modified shell model for magnetohydrodynamics turbulence

    NASA Astrophysics Data System (ADS)

    Nigro, Giuseppina; Carbone, Vincenzo

    2010-07-01

    The aim of the paper is the study of dynamo action using a simple nonlinear model in the framework of magnetohydrodynamic turbulence. The nonlinear behavior of the system is described by using a shell model for velocity field and magnetic field fluctuations, modified for the magnetic field at the largest scale by a term describing a supercritical pitchfork bifurcation. Turbulent fluctuations generate a dynamical situation where the large-scale magnetic field jumps between two states which represent the opposite polarities of the magnetic field. Despite its simplicity, the model has the capability to describe a long time series of reversals from which we infer results about the statistics of persistence times and scaling laws of cancellations between opposite polarities for different magnetic diffusivity coefficients. These properties of the model are compared with real paleomagnetic data, thus revealing the origin of long-range correlations in the process.

  7. The remarkable ability of turbulence model equations to describe transition

    NASA Technical Reports Server (NTRS)

    Wilcox, David C.

    1992-01-01

    This paper demonstrates how well the k-omega turbulence model describes the nonlinear growth of flow instabilities from laminar flow into the turbulent flow regime. Viscous modifications are proposed for the k-omega model that yield close agreement with measurements and with Direct Numerical Simulation results for channel and pipe flow. These modifications permit prediction of subtle sublayer details such as maximum dissipation at the surface, k approximately y(exp 2) as y approaches 0, and the sharp peak value of k near the surface. With two transition specific closure coefficients, the model equations accurately predict transition for an incompressible flat-plate boundary layer. The analysis also shows why the k-epsilon model is so difficult to use for predicting transition.

  8. Flamelet Model Application for Non-Premixed Turbulent Combustion

    NASA Technical Reports Server (NTRS)

    Secundov, A.; Bezgin, L.; Buriko, Yu.; Guskov, O.; Kopchenov, V.; Laskin, I.; Lomkov, K.; Tshepin, S.; Volkov, D.; Zaitsev, S.

    1996-01-01

    The current Final Report contains results of the study which was performed in Scientific Research Center 'ECOLEN' (Moscow, Russia). The study concerns the development and verification of non-expensive approach for modeling of supersonic turbulent diffusion flames based on flamelet consideration of the chemistry/turbulence interaction (FL approach). Research work included: development of the approach and CFD tests of the flamelet model for supersonic jet flames; development of the simplified procedure for solution of the flamelet equations based on partial equilibrium chemistry assumption; study of the flame ignition/extinction predictions provided by flamelet model. The performed investigation demonstrated that FL approach allowed to describe satisfactory main features of supersonic H 2/air jet flames. Model demonstrated also high capabilities for reduction of the computational expenses in CFD modeling of the supersonic flames taking into account detailed oxidation chemistry. However, some disadvantages and restrictions of the existing version of approach were found in this study. They were: (1) inaccuracy in predictions of the passive scalar statistics by our turbulence model for one of the considered test cases; and (2) applicability of the available version of the flamelet model to flames without large ignition delay distance only. Based on the results of the performed investigation, we formulated and submitted to the National Aeronautics and Space Administration our Project Proposal for the next step research directed toward further improvement of the FL approach.

  9. One-dimensional turbulence modeling of a turbulent counterflow flame with comparison to DNS

    DOE PAGESBeta

    Jozefik, Zoltan; Kerstein, Alan R.; Schmidt, Heiko; Lyra, Sgouria; Kolla, Hemanth; Chen, Jackie H.

    2015-06-01

    The one-dimensional turbulence (ODT) model is applied to a reactant-to-product counterflow configuration and results are compared with DNS data. The model employed herein solves conservation equations for momentum, energy, and species on a one dimensional (1D) domain corresponding to the line spanning the domain between nozzle orifice centers. The effects of turbulent mixing are modeled via a stochastic process, while the Kolmogorov and reactive length and time scales are explicitly resolved and a detailed chemical kinetic mechanism is used. Comparisons between model and DNS results for spatial mean and root-meansquare (RMS) velocity, temperature, and major and minor species profiles aremore » shown. The ODT approach shows qualitatively and quantitatively reasonable agreement with the DNS data. Scatter plots and statistics conditioned on temperature are also compared for heat release rate and all species. ODT is able to capture the range of results depicted by DNS. However, conditional statistics show signs of underignition.« less

  10. Modeling Compressibility Effects in High-Speed Turbulent Flows

    NASA Technical Reports Server (NTRS)

    Sarkar, S.

    2004-01-01

    Man has strived to make objects fly faster, first from subsonic to supersonic and then to hypersonic speeds. Spacecraft and high-speed missiles routinely fly at hypersonic Mach numbers, M greater than 5. In defense applications, aircraft reach hypersonic speeds at high altitude and so may civilian aircraft in the future. Hypersonic flight, while presenting opportunities, has formidable challenges that have spurred vigorous research and development, mainly by NASA and the Air Force in the USA. Although NASP, the premier hypersonic concept of the eighties and early nineties, did not lead to flight demonstration, much basic research and technology development was possible. There is renewed interest in supersonic and hypersonic flight with the HyTech program of the Air Force and the Hyper-X program at NASA being examples of current thrusts in the field. At high-subsonic to supersonic speeds, fluid compressibility becomes increasingly important in the turbulent boundary layers and shear layers associated with the flow around aerospace vehicles. Changes in thermodynamic variables: density, temperature and pressure, interact strongly with the underlying vortical, turbulent flow. The ensuing changes to the flow may be qualitative such as shocks which have no incompressible counterpart, or quantitative such as the reduction of skin friction with Mach number, large heat transfer rates due to viscous heating, and the dramatic reduction of fuel/oxidant mixing at high convective Mach number. The peculiarities of compressible turbulence, so-called compressibility effects, have been reviewed by Fernholz and Finley. Predictions of aerodynamic performance in high-speed applications require accurate computational modeling of these "compressibility effects" on turbulence. During the course of the project we have made fundamental advances in modeling the pressure-strain correlation and developed a code to evaluate alternate turbulence models in the compressible shear layer.

  11. Turbulence modeling for Francis turbine water passages simulation

    NASA Astrophysics Data System (ADS)

    Maruzewski, P.; Hayashi, H.; Munch, C.; Yamaishi, K.; Hashii, T.; Mombelli, H. P.; Sugow, Y.; Avellan, F.

    2010-08-01

    The applications of Computational Fluid Dynamics, CFD, to hydraulic machines life require the ability to handle turbulent flows and to take into account the effects of turbulence on the mean flow. Nowadays, Direct Numerical Simulation, DNS, is still not a good candidate for hydraulic machines simulations due to an expensive computational time consuming. Large Eddy Simulation, LES, even, is of the same category of DNS, could be an alternative whereby only the small scale turbulent fluctuations are modeled and the larger scale fluctuations are computed directly. Nevertheless, the Reynolds-Averaged Navier-Stokes, RANS, model have become the widespread standard base for numerous hydraulic machine design procedures. However, for many applications involving wall-bounded flows and attached boundary layers, various hybrid combinations of LES and RANS are being considered, such as Detached Eddy Simulation, DES, whereby the RANS approximation is kept in the regions where the boundary layers are attached to the solid walls. Furthermore, the accuracy of CFD simulations is highly dependent on the grid quality, in terms of grid uniformity in complex configurations. Moreover any successful structured and unstructured CFD codes have to offer a wide range to the variety of classic RANS model to hybrid complex model. The aim of this study is to compare the behavior of turbulent simulations for both structured and unstructured grids topology with two different CFD codes which used the same Francis turbine. Hence, the study is intended to outline the encountered discrepancy for predicting the wake of turbine blades by using either the standard k-epsilon model, or the standard k-epsilon model or the SST shear stress model in a steady CFD simulation. Finally, comparisons are made with experimental data from the EPFL Laboratory for Hydraulic Machines reduced scale model measurements.

  12. Modification of the MML turbulence model for adverse pressure gradient flows. M.S. Thesis - Akron Univ., 1993

    NASA Technical Reports Server (NTRS)

    Conley, Julianne M.

    1994-01-01

    Computational fluid dynamics is being used increasingly to predict flows for aerospace propulsion applications, yet there is still a need for an easy to use, computationally inexpensive turbulence model capable of accurately predicting a wide range of turbulent flows. The Baldwin-Lomax model is the most widely used algebraic model, even though it has known difficulties calculating flows with strong adverse pressure gradients and large regions of separation. The modified mixing length model (MML) was developed specifically to handle the separation which occurs on airfoils and has given significantly better results than the Baldwin-Lomax model. The success of these calculations warrants further evaluation and development of MML. The objective of this work was to evaluate the performance of MML for zero and adverse pressure gradient flows, and modify it as needed. The Proteus Navier-Stokes code was used for this study and all results were compared with experimental data and with calculations made using the Baldwin-Lomax algebraic model, which is currently available in Proteus. The MML model was first evaluated for zero pressure gradient flow over a flat plate, then modified to produce the proper boundary layer growth. Additional modifications, based on experimental data for three adverse pressure gradient flows, were also implemented. The adapted model, called MMLPG (modified mixing length model for pressure gradient flows), was then evaluated for a typical propulsion flow problem, flow through a transonic diffuser. Three cases were examined: flow with no shock, a weak shock and a strong shock. The results of these calculations indicate that the objectives of this study have been met. Overall, MMLPG is capable of accurately predicting the adverse pressure gradient flows examined in this study, giving generally better agreement with experimental data than the Baldwin-Lomax model.

  13. Entanglement in a model for Hawking radiation: An application of quadratic algebras

    SciTech Connect

    Bambah, Bindu A.; Mukku, C.; Shreecharan, T.; Siva Prasad, K.

    2013-03-15

    Quadratic polynomially deformed su(1,1) and su(2) algebras are utilized in model Hamiltonians to show how the gravitational system consisting of a black hole, infalling radiation and outgoing (Hawking) radiation can be solved exactly. The models allow us to study the long-time behaviour of the black hole and its outgoing modes. In particular, we calculate the bipartite entanglement entropies of subsystems consisting of (a) infalling plus outgoing modes and (b) black hole modes plus the infalling modes, using the Janus-faced nature of the model. The long-time behaviour also gives us glimpses of modifications in the character of Hawking radiation. Finally, we study the phenomenon of superradiance in our model in analogy with atomic Dicke superradiance. - Highlights: Black-Right-Pointing-Pointer We examine a toy model for Hawking radiation with quantized black hole modes. Black-Right-Pointing-Pointer We use quadratic polynomially deformed su(1,1) algebras to study its entanglement properties. Black-Right-Pointing-Pointer We study the 'Dicke Superradiance' in black hole radiation using quadratically deformed su(2) algebras. Black-Right-Pointing-Pointer We study the modification of the thermal character of Hawking radiation due to quantized black hole modes.

  14. Atmospheric Turbulence Modeling for Aero Vehicles: Fractional Order Fits

    NASA Technical Reports Server (NTRS)

    Kopasakis, George

    2015-01-01

    Atmospheric turbulence models are necessary for the design of both inlet/engine and flight controls, as well as for studying coupling between the propulsion and the vehicle structural dynamics for supersonic vehicles. Models based on the Kolmogorov spectrum have been previously utilized to model atmospheric turbulence. In this paper, a more accurate model is developed in its representative fractional order form, typical of atmospheric disturbances. This is accomplished by first scaling the Kolmogorov spectral to convert them into finite energy von Karman forms and then by deriving an explicit fractional circuit-filter type analog for this model. This circuit model is utilized to develop a generalized formulation in frequency domain to approximate the fractional order with the products of first order transfer functions, which enables accurate time domain simulations. The objective of this work is as follows. Given the parameters describing the conditions of atmospheric disturbances, and utilizing the derived formulations, directly compute the transfer function poles and zeros describing these disturbances for acoustic velocity, temperature, pressure, and density. Time domain simulations of representative atmospheric turbulence can then be developed by utilizing these computed transfer functions together with the disturbance frequencies of interest.

  15. Atmospheric Turbulence Modeling for Aero Vehicles: Fractional Order Fits

    NASA Technical Reports Server (NTRS)

    Kopasakis, George

    2010-01-01

    Atmospheric turbulence models are necessary for the design of both inlet/engine and flight controls, as well as for studying coupling between the propulsion and the vehicle structural dynamics for supersonic vehicles. Models based on the Kolmogorov spectrum have been previously utilized to model atmospheric turbulence. In this paper, a more accurate model is developed in its representative fractional order form, typical of atmospheric disturbances. This is accomplished by first scaling the Kolmogorov spectral to convert them into finite energy von Karman forms and then by deriving an explicit fractional circuit-filter type analog for this model. This circuit model is utilized to develop a generalized formulation in frequency domain to approximate the fractional order with the products of first order transfer functions, which enables accurate time domain simulations. The objective of this work is as follows. Given the parameters describing the conditions of atmospheric disturbances, and utilizing the derived formulations, directly compute the transfer function poles and zeros describing these disturbances for acoustic velocity, temperature, pressure, and density. Time domain simulations of representative atmospheric turbulence can then be developed by utilizing these computed transfer functions together with the disturbance frequencies of interest.

  16. A comprehensive comparison of turbulence models in the far wake

    NASA Technical Reports Server (NTRS)

    Cimbala, John M.

    1993-01-01

    In the present study, the far wake was examined numerically using an implicit, upwind, finite-volume, compressible Navier-Stokes code. The numerical grid started at 500 equivalent circular cylinder diameters in the wave, and extended to 4000 equivalent diameters. By concentrating only on the far wake, the numerical difficulties and fine mesh requirements near the wake-generating body were eliminated. At the time of this writing, results for the K-epsilon and K-omega turbulence models at low Mach number have been completed and show excellent agreement with previous incompressible results and far-wake similarity solutions. The code is presently being used to compare the performance of various other turbulence models, including Reynolds stress models and the new anisotropic two-equation turbulence models being developed at NASA Langley. By increasing our physical understanding of the deficiencies and limits of these models, it is hoped that improvements to the universality of the models can be made. Future plans include examination of two-dimensional momentumless wakes as well.

  17. Development of one-equation transition/turbulence models

    SciTech Connect

    Edwards, J.R.; Roy, C.J.; Blottner, F.G.; Hassan, H.A.

    2000-01-14

    This paper reports on the development of a unified one-equation model for the prediction of transitional and turbulent flows. An eddy viscosity--transport equation for nonturbulent fluctuation growth based on that proposed by Warren and Hassan is combined with the Spalart-Allmaras one-equation model for turbulent fluctuation growth. Blending of the two equations is accomplished through a multidimensional intermittency function based on the work of Dhawan and Narasimha. The model predicts both the onset and extent of transition. Low-speed test cases include transitional flow over a flat plate, a single element airfoil, and a multi-element airfoil in landing configuration. High-speed test cases include transitional Mach 3.5 flow over a 5{degree} cone and Mach 6 flow over a flared-cone configuration. Results are compared with experimental data, and the grid-dependence of selected predictions is analyzed.

  18. Turbulent Chemical Interaction Models in NCC: Comparison

    NASA Technical Reports Server (NTRS)

    Norris, Andrew T.; Liu, Nan-Suey

    2006-01-01

    The performance of a scalar PDF hydrogen-air combustion model in predicting a complex reacting flow is evaluated. In addition the results are compared to those obtained by running the same case with the so-called laminar chemistry model and also a new model based on the concept of mapping partially stirred reactor data onto perfectly stirred reactor data. The results show that the scalar PDF model produces significantly different results from the other two models, and at a significantly higher computational cost.

  19. Progress in the development of PDF turbulence models for combustion

    NASA Technical Reports Server (NTRS)

    Hsu, Andrew T.

    1991-01-01

    A combined Monte Carlo-computational fluid dynamic (CFD) algorithm was developed recently at Lewis Research Center (LeRC) for turbulent reacting flows. In this algorithm, conventional CFD schemes are employed to obtain the velocity field and other velocity related turbulent quantities, and a Monte Carlo scheme is used to solve the evolution equation for the probability density function (pdf) of species mass fraction and temperature. In combustion computations, the predictions of chemical reaction rates (the source terms in the species conservation equation) are poor if conventional turbulence modles are used. The main difficulty lies in the fact that the reaction rate is highly nonlinear, and the use of averaged temperature produces excessively large errors. Moment closure models for the source terms have attained only limited success. The probability density function (pdf) method seems to be the only alternative at the present time that uses local instantaneous values of the temperature, density, etc., in predicting chemical reaction rates, and thus may be the only viable approach for more accurate turbulent combustion calculations. Assumed pdf's are useful in simple problems; however, for more general combustion problems, the solution of an evolution equation for the pdf is necessary.

  20. Intelligently deciphering unintelligible designs: algorithmic algebraic model checking in systems biology

    PubMed Central

    Mishra, Bud

    2009-01-01

    Systems biology, as a subject, has captured the imagination of both biologists and systems scientists alike. But what is it? This review provides one researcher's somewhat idiosyncratic view of the subject, but also aims to persuade young scientists to examine the possible evolution of this subject in a rich historical context. In particular, one may wish to read this review to envision a subject built out of a consilience of many interesting concepts from systems sciences, logic and model theory, and algebra, culminating in novel tools, techniques and theories that can reveal deep principles in biology—seen beyond mere observations. A particular focus in this review is on approaches embedded in an embryonic program, dubbed ‘algorithmic algebraic model checking’, and its powers and limitations. PMID:19364723

  1. Constraint algebra of general relativity from a formal continuum limit of canonical tensor model

    NASA Astrophysics Data System (ADS)

    Sasakura, Naoki; Sato, Yuki

    2015-10-01

    Canonical tensor model (CTM for short below) is a rank-three tensor model formulated as a totally constrained system in the canonical formalism. In the classical case, the constraints form a first-class constraint Poisson algebra with structures similar to that of the ADM formalism of general relativity, qualifying CTM as a possible discrete formalism for quantum gravity. In this paper, we show that, in a formal continuum limit, the constraint Poisson algebra of CTM with no cosmological constant exactly reproduces that of the ADM formalism. To this end, we obtain the expression of the metric tensor field in general relativity in terms of one of the dynamical rank-three tensors in CTM, and determine the correspondence between the constraints of CTM and those of the ADM formalism. On the other hand, the cosmological constant term of CTM seems to induce non-local dynamics, and is inconsistent with an assumption about locality of the continuum limit.

  2. Comparative study of turbulence models in predicting hypersonic inlet flows

    NASA Technical Reports Server (NTRS)

    Kapoor, Kamlesh; Anderson, Bernhard H.; Shaw, Robert J.

    1992-01-01

    A numerical study was conducted to analyze the performance of different turbulence models when applied to the hypersonic NASA P8 inlet. Computational results from the PARC2D code, which solves the full two-dimensional Reynolds-averaged Navier-Stokes equation, were compared with experimental data. The zero-equation models considered for the study were the Baldwin-Lomax model, the Thomas model, and a combination of the Baldwin-Lomax and Thomas models; the two-equation models considered were the Chien model, the Speziale model (both low Reynolds number), and the Launder and Spalding model (high Reynolds number). The Thomas model performed best among the zero-equation models, and predicted good pressure distributions. The Chien and Speziale models compared very well with the experimental data, and performed better than the Thomas model near the walls.

  3. Comparative study of turbulence models in predicting hypersonic inlet flows

    NASA Technical Reports Server (NTRS)

    Kapoor, Kamlesh; Anderson, Bernhard H.; Shaw, Robert J.

    1992-01-01

    A numerical study was conducted to analyze the performance of different turbulence models when applied to the hypersonic NASA P8 inlet. Computational results from the PARC2D code, which solves the full two-dimensional Reynolds-averaged Navier-Stokes equation, were compared with experimental data. The zero-equation models considered for the study were the Baldwin-Lomax model, the Thomas model, and a combination of the Baldwin-Lomax and Thomas models; the two-equation models considered were the Chien model, the Speziale model (both low Reynolds number), and the Launder and Spalding model (high Reynolds number). The Thomas model performed best among the zero-equation models, and predicted good pressure distributions. The Chien and Speziale models compared wery well with the experimental data, and performed better than the Thomas model near the walls.

  4. Anisotropic Turbulence Modeling for Accurate Rod Bundle Simulations

    SciTech Connect

    Baglietto, Emilio

    2006-07-01

    An improved anisotropic eddy viscosity model has been developed for accurate predictions of the thermal hydraulic performances of nuclear reactor fuel assemblies. The proposed model adopts a non-linear formulation of the stress-strain relationship in order to include the reproduction of the anisotropic phenomena, and in combination with an optimized low-Reynolds-number formulation based on Direct Numerical Simulation (DNS) to produce correct damping of the turbulent viscosity in the near wall region. This work underlines the importance of accurate anisotropic modeling to faithfully reproduce the scale of the turbulence driven secondary flows inside the bundle subchannels, by comparison with various isothermal and heated experimental cases. The very low scale secondary motion is responsible for the increased turbulence transport which produces a noticeable homogenization of the velocity distribution and consequently of the circumferential cladding temperature distribution, which is of main interest in bundle design. Various fully developed bare bundles test cases are shown for different geometrical and flow conditions, where the proposed model shows clearly improved predictions, in close agreement with experimental findings, for regular as well as distorted geometries. Finally the applicability of the model for practical bundle calculations is evaluated through its application in the high-Reynolds form on coarse grids, with excellent results. (author)

  5. Construction of linear models: A framework based on commutative Jordan algebras

    NASA Astrophysics Data System (ADS)

    Covas, R.; Carvalho, F.

    2016-06-01

    We show how to obtain the necessary structures for statistical analysis of the folllowing orthogonal models Y˜(1 μ +∑i Xiβi ,∑j σj2Mj+σ2I ) . These structures rely on the existence of Jordan algebras, in the sequence of [24], [8], [12], [9], [5] and [10].

  6. Development and application of a non-Gaussian atmospheric turbulence model for use in flight simulators

    NASA Technical Reports Server (NTRS)

    Reeves, P. M.; Campbell, G. S.; Ganzer, V. M.; Joppa, R. G.

    1974-01-01

    A method is described for generating time histories which model the frequency content and certain non-Gaussian probability characteristics of atmospheric turbulence including the large gusts and patchy nature of turbulence. Methods for time histories using either analog or digital computation are described. A STOL airplane was programmed into a 6-degree-of-freedom flight simulator, and turbulence time histories from several atmospheric turbulence models were introduced. The pilots' reactions are described.

  7. Comment paper: Workshop on Engineering Turbulence Modeling

    NASA Technical Reports Server (NTRS)

    Spalart, P. R.

    1992-01-01

    The speaker for this paper describes and evaluates a k-epsilon model for calculating Samuel-Joubert flow. He proceeds to present both Boeing's and his positions on the state-of-the-art in this area and future goals. Finally, presented is a one equation mathematical model for calculating Samuel-Joubert flow. All results are presented in viewgraph format.

  8. Comment paper: Workshop on Engineering Turbulence Modeling

    NASA Astrophysics Data System (ADS)

    Spalart, P. R.

    1992-03-01

    The speaker for this paper describes and evaluates a k-epsilon model for calculating Samuel-Joubert flow. He proceeds to present both Boeing's and his positions on the state-of-the-art in this area and future goals. Finally, presented is a one equation mathematical model for calculating Samuel-Joubert flow. All results are presented in viewgraph format.

  9. Characterizing the Severe Turbulence Environments Associated With Commercial Aviation Accidents: A Real-Time Turbulence Model (RTTM) Designed for the Operational Prediction of Hazardous Aviation Turbulence Environments

    NASA Technical Reports Server (NTRS)

    Kaplan, Michael L.; Lux, Kevin M.; Cetola, Jeffrey D.; Huffman, Allan W.; Riordan, Allen J.; Slusser, Sarah W.; Lin, Yuh-Lang; Charney, Joseph J.; Waight, Kenneth T.

    2004-01-01

    Real-time prediction of environments predisposed to producing moderate-severe aviation turbulence is studied. We describe the numerical model and its postprocessing system designed for said prediction of environments predisposed to severe aviation turbulence as well as presenting numerous examples of its utility. The numerical model is MASS version 5.13, which is integrated over three different grid matrices in real time on a university work station in support of NASA Langley Research Center s B-757 turbulence research flight missions. The postprocessing system includes several turbulence-related products, including four turbulence forecasting indices, winds, streamlines, turbulence kinetic energy, and Richardson numbers. Additionally, there are convective products including precipitation, cloud height, cloud mass fluxes, lifted index, and K-index. Furthermore, soundings, sounding parameters, and Froude number plots are also provided. The horizontal cross-section plot products are provided from 16 000 to 46 000 ft in 2000-ft intervals. Products are available every 3 hours at the 60- and 30-km grid interval and every 1.5 hours at the 15-km grid interval. The model is initialized from the NWS ETA analyses and integrated two times a day.

  10. Small Scale Response and Modeling of Periodically Forced Turbulence

    NASA Technical Reports Server (NTRS)

    Bos, Wouter; Clark, Timothy T.; Rubinstein, Robert

    2007-01-01

    The response of the small scales of isotropic turbulence to periodic large scale forcing is studied using two-point closures. The frequency response of the turbulent kinetic energy and dissipation rate, and the phase shifts between production, energy and dissipation are determined as functions of Reynolds number. It is observed that the amplitude and phase of the dissipation exhibit nontrivial frequency and Reynolds number dependence that reveals a filtering effect of the energy cascade. Perturbation analysis is applied to understand this behavior which is shown to depend on distant interactions between widely separated scales of motion. Finally, the extent to which finite dimensional models (standard two-equation models and various generalizations) can reproduce the observed behavior is discussed.

  11. Closure of the algebra of constraints for a nonprojectable Horava model

    SciTech Connect

    Bellorin, Jorge; Restuccia, Alvaro

    2011-02-15

    We perform the Hamiltonian analysis for a nonprojectable Horava model whose potential is composed of R and R{sup 2} terms. We show that Dirac's algorithm for the preservation of the constraints can be done in a closed way, hence the algebra of constraints for this model is consistent. The model has an extra, odd, scalar mode whose decoupling limit can be seen in a linear-order perturbative analysis on weakly varying backgrounds. Although our results for this model point in favor of the consistency of the Horava theory, the validity of the full nonprojectable theory still remains unanswered.

  12. New mixing-length model for turbulent high-speed flows

    NASA Technical Reports Server (NTRS)

    Situ, M.; Schetz, J. A.

    1989-01-01

    A modification of Prandtl's mixing-length model is presented which takes into account the effects of compressibility on turbulence for high speed flows. A parameter is introduced into the turbulent transport formula which acts like an effective turbulent Schmidt number for mixtures of gases or a turbulent Prandtl number for a homogeneous gas. Results presented for such cases as high Mach number turbulent boundary layer flows over a flat surface, tangential slot injection problems, and shock/turbulent shear-layer and boundary-layer interactions agree well with experimental data.

  13. Atmospheric Turbulence Modeling for Aerospace Vehicles: Fractional Order Fit

    NASA Technical Reports Server (NTRS)

    Kopasakis, George (Inventor)

    2015-01-01

    An improved model for simulating atmospheric disturbances is disclosed. A scale Kolmogorov spectral may be scaled to convert the Kolmogorov spectral into a finite energy von Karman spectral and a fractional order pole-zero transfer function (TF) may be derived from the von Karman spectral. Fractional order atmospheric turbulence may be approximated with an integer order pole-zero TF fit, and the approximation may be stored in memory.

  14. The lag RST turbulence model applied to vortical flows

    NASA Astrophysics Data System (ADS)

    Churchfield, Matthew John

    The subject of this work is the application of Olsen and Coakley's Reynolds stress relaxation turbulence model, which they call the lag Reynold stress transport (RST) model, to wingtip vortex flows. The lag RST model is meant for general non-equilibrium turbulent flows, and has not been applied to vortical flows before this work. Such a model relaxes the Reynolds stresses toward their equilibrium value, determined by the Boussinesq approximation, at a rate depending on a model constant, alpha0, multiplied by the specific dissipation rate of the turbulence, o. The alpha 0 constant can be adjusted to vary the rate at which the Reynolds stress tensor relaxes toward its equilibrium value. It performs this relaxation by solving for the equilibrium Reynolds stresses using Wilcox's k-o model, but then uses a relaxation equation to solve for the actual Reynolds stress tensor. The lag RST turbulence model allows the principal axes of the Reynolds stress tensor to be misaligned with those of the mean strain rate tensor, something linear eddy viscosity models cannot do, but something that occurs in actual vortical flows. The lag RST model is used with the Reynolds-averaged Navier-Stokes (RANS) equations to compute a one-dimensional, time-varying, line vortex with axial flow, called the q-vortex. Direct numerical simulation (DNS) data is available for comparison. Also, a modified version of the OVERFLOW code is used to solve the RANS and lag RST model equations in a three-dimensional wingtip vortex flow, for which there is experimental data. This work shows that computations performed with the lag RST model have a mean flow in much better agreement with the DNS or experimental data than those performed with the k-o model, the lag RST model's base. In fact, the lag RST model performs equally or better in this these flows than the well performing Spalart-Allmaras model with a correction for streamline curvature and rotation. As the lag parameter alpha0 is decreased, the amount

  15. A deformation of quantum affine algebra in squashed Wess-Zumino-Novikov-Witten models

    SciTech Connect

    Kawaguchi, Io; Yoshida, Kentaroh

    2014-06-01

    We proceed to study infinite-dimensional symmetries in two-dimensional squashed Wess-Zumino-Novikov-Witten models at the classical level. The target space is given by squashed S³ and the isometry is SU(2){sub L}×U(1){sub R}. It is known that SU(2){sub L} is enhanced to a couple of Yangians. We reveal here that an infinite-dimensional extension of U(1){sub R} is a deformation of quantum affine algebra, where a new deformation parameter is provided with the coefficient of the Wess-Zumino term. Then we consider the relation between the deformed quantum affine algebra and the pair of Yangians from the viewpoint of the left-right duality of monodromy matrices. The integrable structure is also discussed by computing the r/s-matrices that satisfy the extended classical Yang-Baxter equation. Finally, two degenerate limits are discussed.

  16. Development of a One-Equation Transition/Turbulence Model

    SciTech Connect

    EDWARDS,JACK R.; ROY,CHRISTOPHER J.; BLOTTNER,FREDERICK G.; HASSAN,HASSAN A.

    2000-09-26

    This paper reports on the development of a unified one-equation model for the prediction of transitional and turbulent flows. An eddy viscosity - transport equation for non-turbulent fluctuation growth based on that proposed by Warren and Hassan (Journal of Aircraft, Vol. 35, No. 5) is combined with the Spalart-Allmaras one-equation model for turbulent fluctuation growth. Blending of the two equations is accomplished through a multidimensional intermittence function based on the work of Dhawan and Narasimha (Journal of Fluid Mechanics, Vol. 3, No. 4). The model predicts both the onset and extent of transition. Low-speed test cases include transitional flow over a flat plate, a single element airfoil, and a multi-element airfoil in landing configuration. High-speed test cases include transitional Mach 3.5 flow over a 5{degree} cone and Mach 6 flow over a flared-cone configuration. Results are compared with experimental data, and the spatial accuracy of selected predictions is analyzed.

  17. Stellar turbulent convection - A new model and applications

    NASA Technical Reports Server (NTRS)

    Canuto, V. M.; Mazzitelli, I.

    1991-01-01

    Improvements of the mixing-length theory (MLT) of turbulent convection in stellar atmospheres are developed theoretically. It is pointed out that inaccuracies are introduced into MLT by the approximating assumptions of a single large eddy (rather than many eddies of different sizes) and of incompressibility. In the proposed new model, the full spectrum of turbulent eddies is determined using more recent turbulence models (e.g., the eddy-damped quasi-normal Markovian model of Orszag, 1977), and a new formula for the convective flux is obtained which gives values up to 10 times greater than those of the MLT at high convective efficiencies. The problem of compressibility is addressed by adding one of two new expressions (one with no free parameters) for the mixing length. Numerical results from simulations of a solar-type star and a 0.8-solar-mass globular-cluster star are presented in tables and graphs and discussed in detail; the agreement with observations is found to be better than with the MLT.

  18. Realtime capable first principle based modelling of tokamak turbulent transport

    NASA Astrophysics Data System (ADS)

    Citrin, Jonathan; Breton, Sarah; Felici, Federico; Imbeaux, Frederic; Redondo, Juan; Aniel, Thierry; Artaud, Jean-Francois; Baiocchi, Benedetta; Bourdelle, Clarisse; Camenen, Yann; Garcia, Jeronimo

    2015-11-01

    Transport in the tokamak core is dominated by turbulence driven by plasma microinstabilities. When calculating turbulent fluxes, maintaining both a first-principle-based model and computational tractability is a strong constraint. We present a pathway to circumvent this constraint by emulating quasilinear gyrokinetic transport code output through a nonlinear regression using multilayer perceptron neural networks. This recovers the original code output, while accelerating the computing time by five orders of magnitude, allowing realtime applications. A proof-of-principle is presented based on the QuaLiKiz quasilinear transport model, using a training set of five input dimensions, relevant for ITG turbulence. The model is implemented in the RAPTOR real-time capable tokamak simulator, and simulates a 300s ITER discharge in 10s. Progress in generalizing the emulation to include 12 input dimensions is presented. This opens up new possibilities for interpretation of present-day experiments, scenario preparation and open-loop optimization, realtime controller design, realtime discharge supervision, and closed-loop trajectory optimization.

  19. Effect of Turbulence Modeling on an Excited Jet

    NASA Technical Reports Server (NTRS)

    Brown, Clifford A.; Hixon, Ray

    2010-01-01

    The flow dynamics in a high-speed jet are dominated by unsteady turbulent flow structures in the plume. Jet excitation seeks to control these flow structures through the natural instabilities present in the initial shear layer of the jet. Understanding and optimizing the excitation input, for jet noise reduction or plume mixing enhancement, requires many trials that may be done experimentally or computationally at a significant cost savings. Numerical simulations, which model various parts of the unsteady dynamics to reduce the computational expense of the simulation, must adequately capture the unsteady flow dynamics in the excited jet for the results are to be used. Four CFD methods are considered for use in an excited jet problem, including two turbulence models with an Unsteady Reynolds Averaged Navier-Stokes (URANS) solver, one Large Eddy Simulation (LES) solver, and one URANS/LES hybrid method. Each method is used to simulate a simplified excited jet and the results are evaluated based on the flow data, computation time, and numerical stability. The knowledge gained about the effect of turbulence modeling and CFD methods from these basic simulations will guide and assist future three-dimensional (3-D) simulations that will be used to understand and optimize a realistic excited jet for a particular application.

  20. Towards CFD modeling of turbulent pipeline material transportation

    NASA Astrophysics Data System (ADS)

    Shahirpour, Amir; Herzog, Nicoleta; Egbers, Cristoph

    2013-04-01

    Safe and financially efficient pipeline transportation of carbon dioxide is a critical issue in the developing field of the CCS Technology. In this part of the process, carbon dioxide is transported via pipes with diameter of 1.5 m and entry pressure of 150 bar, with Reynolds number of 107 and viscosity of 8×10(-5) Pa.s as dense fluid [1]. Presence of large and small scale structures in the pipeline, high Reynolds numbers at which CO2 should be transferred, and 3 dimensional turbulence caused by local geometrical modifications, increase the importance of simulation of turbulent material transport through the individual components of the CO2 chain process. In this study, incompressible turbulent channel flow and pipe flow have been modeled using OpenFoam, an open source CFD software. In the first step, simulation of a turbulent channel flow has been considered using LES for shear Reynolds number of 395. A simple geometry has been chosen with cyclic fluid inlet and outlet boundary conditions to simulate a fully developed flow. The mesh is gradually refined towards the wall to provide values close enough to the wall for the wall coordinate (y+). Grid resolution study has been conducted for One-Equation model. The accuracy of the results is analyzed with respect to the grid smoothness in order to reach an optimized resolution for carrying out the next simulations. Furthermore, three LES models, One-Equation, Smagorinsky and Dynamic Smagorinsky are applied for the grid resolution of (60 × 100 × 80) in (x, y, z) directions. The results are then validated with reference to the DNS carried out by Moser et al.[2] for the similar geometry using logarithmic velocity profile (U+) and Reynolds stress tensor components. In the second step the similar flow is modeled using Reynolds averaged method. Several RANS models, like K-epsilon and Launder-Reece-Rodi are applied and validated against DNS and LES results in a similar fashion. In the most recent step, it has been intended

  1. Gyrofluid turbulence models with kinetic effects

    SciTech Connect

    Dorland, W.; Hammett, G.W.

    1992-12-01

    Nonlinear gyrofluid equations are derived by taking moments of the nonlinear, electrostatic gyrokinetic equation. The principal model presented includes evolution equations for the guiding center n, u[parallel], T[parallel], and T[perpendicular] along with an equation expressing the quasineutrality constraint. Additional evolution equations for higher moments are derived which may be used if greater accuracy is desired. The moment hierarchy is closed with a Landau-damping model which is equivalent to a multi-pole approximation to the plasma dispersion function, extended to include finite Larmor radius effects. In particular, new dissipative, nonlinear terms are found which model the perpendicular phase-mixing of the distribution function along contours of constant electrostatic potential. These FLR phase-mixing'' terms introduce a hyperviscosity-like damping [proportional to] k[sub [perpendicular

  2. A shell model for turbulent dynamos

    NASA Astrophysics Data System (ADS)

    Nigro, G.; Perrone, D.; Veltri, P.

    2011-06-01

    A self-consistent nonlinear dynamo model is presented. The nonlinear behavior of the plasma at small scale is described by using a MHD shell model for fields fluctuations; this allow us to study the dynamo problem in a large parameter regime which characterizes the dynamo phenomenon in many natural systems and which is beyond the power of supercomputers at today. The model is able to reproduce dynamical situations in which the system can undergo transactions to different dynamo regimes. In one of these the large-scale magnetic field jumps between two states reproducing the magnetic polarity reversals. From the analysis of long time series of reversals we infer results about the statistics of persistence times, revealing the presence of hidden long-time correlations in the chaotic dynamo process.

  3. Teaching Algebra and Geometry Concepts by Modeling Telescope Optics

    ERIC Educational Resources Information Center

    Siegel, Lauren M.; Dickinson, Gail; Hooper, Eric J.; Daniels, Mark

    2008-01-01

    This article describes preparation and delivery of high school mathematics lessons that integrate mathematics and astronomy through The Geometer's Sketchpad models, traditional proof, and inquiry-based activities. The lessons were created by a University of Texas UTeach preservice teacher as part of a project-based field experience in which high…

  4. Numerical model of sonic boom in 3D kinematic turbulence

    NASA Astrophysics Data System (ADS)

    Coulouvrat, François; Luquet, David; Marchiano, Régis

    2015-10-01

    stratified wind superimposed to a 3D random turbulent realization. Propagation is performed either in the case of a shadow zone or of an atmospheric waveguide. To model the turbulent ABL, the mean flow and the fluctuations are handled separately. The wind fluctuations are generated using the Random Fluctuations Generation method assuming a von Kármán spectrum and a homogeneous and isotropic turbulence. The mean stratified wind is modeled based on the Monin-Obhukov Similarity Theory (MOST). To illustrate the method, the typical case of a sunny day with a strong wind has been chosen. Statistics are obtained on several parameters. It shows the importance of turbulence, which leads to an increase of the mean maximum peak pressure in the shadow zone and to its decrease in the waveguide. Moreover, the formation of random caustics that can lead to an increase of the noise perceived locally is outlined.

  5. One-dimensional hydrodynamic model generating a turbulent cascade

    NASA Astrophysics Data System (ADS)

    Matsumoto, Takeshi; Sakajo, Takashi

    2016-05-01

    As a minimal mathematical model generating cascade analogous to that of the Navier-Stokes turbulence in the inertial range, we propose a one-dimensional partial-differential-equation model that conserves the integral of the squared vorticity analog (enstrophy) in the inviscid case. With a large-scale random forcing and small viscosity, we find numerically that the model exhibits the enstrophy cascade, the broad energy spectrum with a sizable correction to the dimensional-analysis prediction, peculiar intermittency, and self-similarity in the dynamical system structure.

  6. Energy transfers in shell models for magnetohydrodynamics turbulence.

    PubMed

    Lessinnes, Thomas; Carati, Daniele; Verma, Mahendra K

    2009-06-01

    A systematic procedure to derive shell models for magnetohydrodynamic turbulence is proposed. It takes into account the conservation of ideal quadratic invariants such as the total energy, the cross helicity, and the magnetic helicity, as well as the conservation of the magnetic energy by the advection term in the induction equation. This approach also leads to simple expressions for the energy exchanges as well as to unambiguous definitions for the energy fluxes. When applied to the existing shell models with nonlinear interactions limited to the nearest-neighbor shells, this procedure reproduces well-known models but suggests a reinterpretation of the energy fluxes. PMID:19658594

  7. Modeling the dissipation rate in rotating turbulent flows

    NASA Technical Reports Server (NTRS)

    Speziale, Charles G.; Raj, Rishi; Gatski, Thomas B.

    1990-01-01

    A variety of modifications to the modeled dissipation rate transport equation that have been proposed during the past two decades to account for rotational strains are examined. The models are subjected to two crucial test cases: the decay of isotropic turbulence in a rotating frame and homogeneous shear flow in a rotating frame. It is demonstrated that these modifications do not yield substantially improved predictions for these two test cases and in many instances give rise to unphysical behavior. An alternative proposal, based on the use of the tensor dissipation rate, is made for the development of improved models.

  8. Modeling of turbulent separated flows for aerodynamic applications

    NASA Technical Reports Server (NTRS)

    Marvin, J. G.

    1983-01-01

    Steady, high speed, compressible separated flows modeled through numerical simulations resulting from solutions of the mass-averaged Navier-Stokes equations are reviewed. Emphasis is placed on benchmark flows that represent simplified (but realistic) aerodynamic phenomena. These include impinging shock waves, compression corners, glancing shock waves, trailing edge regions, and supersonic high angle of attack flows. A critical assessment of modeling capabilities is provided by comparing the numerical simulations with experiment. The importance of combining experiment, numerical algorithm, grid, and turbulence model to effectively develop this potentially powerful simulation technique is stressed.

  9. Influence of atmospheric turbulence on OAM-based FSO system with use of realistic link model

    NASA Astrophysics Data System (ADS)

    Li, Ming; Yu, Zhongyuan; Cvijetic, Milorad

    2016-04-01

    We study the influence of atmospheric turbulence on OAM-based free-space optical (FSO) communication by using the Pump turbulence spectrum model which accurately characterizes the realistic FSO link. A comprehensive comparison is made between the Pump and Kolmogorov spectrum models with respect to the turbulence impact. The calculated results show that obtained turbulence-induced crosstalk is lower, which means that a higher channel capacity is projected when the realistic Pump spectrum is used instead of the Kolmogorov spectrum. We believe that our results prove that performance of practical OAM-based FSO is better than one predicted by using the original Kolmogorov turbulence model.

  10. The Dissipation Rate Transport Equation and Subgrid-Scale Models in Rotating Turbulence

    NASA Technical Reports Server (NTRS)

    Rubinstein, Robert; Ye, Zhou

    1997-01-01

    The dissipation rate transport equation remains the most uncertain part of turbulence modeling. The difficulties arc increased when external agencies like rotation prevent straightforward dimensional analysis from determining the correct form of the modelled equation. In this work, the dissipation rate transport equation and subgrid scale models for rotating turbulence are derived from an analytical statistical theory of rotating turbulence. In the strong rotation limit, the theory predicts a turbulent steady state in which the inertial range energy spectrum scales as k(sup -2) and the turbulent time scale is the inverse rotation rate. This scaling has been derived previously by heuristic arguments.

  11. Gyrofluid turbulence models with kinetic effects

    SciTech Connect

    Dorland, W.; Hammett, G.W.

    1992-12-01

    Nonlinear gyrofluid equations are derived by taking moments of the nonlinear, electrostatic gyrokinetic equation. The principal model presented includes evolution equations for the guiding center n, u{parallel}, T{parallel}, and T{perpendicular} along with an equation expressing the quasineutrality constraint. Additional evolution equations for higher moments are derived which may be used if greater accuracy is desired. The moment hierarchy is closed with a Landau-damping model which is equivalent to a multi-pole approximation to the plasma dispersion function, extended to include finite Larmor radius effects. In particular, new dissipative, nonlinear terms are found which model the perpendicular phase-mixing of the distribution function along contours of constant electrostatic potential. These ``FLR phase-mixing`` terms introduce a hyperviscosity-like damping {proportional_to} k{sub {perpendicular}}{sup 2}{vert_bar}{Phi}{sub {rvec k}}{rvec k} {times}{rvec k}{prime}{vert_bar} which should provide a physics-based damping mechanism at high k{perpendicular}{rho} which is potentially as important as the usual polarization drift nonlinearity. The moments are taken in guiding center space to pick up the correct nonlinear FLR terms and the gyroaveraging of the shear. The equations are solved with a nonlinear, three dimensional initial value code. Linear results are presented, showing excellent agreement with linear gyrokinetic theory.

  12. One-dimensional wave bottom boundary layer model comparison: specific eddy viscosity and turbulence closure models

    USGS Publications Warehouse

    Puleo, J.A.; Mouraenko, O.; Hanes, D.M.

    2004-01-01

    Six one-dimensional-vertical wave bottom boundary layer models are analyzed based on different methods for estimating the turbulent eddy viscosity: Laminar, linear, parabolic, k—one equation turbulence closure, k−ε—two equation turbulence closure, and k−ω—two equation turbulence closure. Resultant velocity profiles, bed shear stresses, and turbulent kinetic energy are compared to laboratory data of oscillatory flow over smooth and rough beds. Bed shear stress estimates for the smooth bed case were most closely predicted by the k−ω model. Normalized errors between model predictions and measurements of velocity profiles over the entire computational domain collected at 15° intervals for one-half a wave cycle show that overall the linear model was most accurate. The least accurate were the laminar and k−ε models. Normalized errors between model predictions and turbulence kinetic energy profiles showed that the k−ω model was most accurate. Based on these findings, when the smallest overall velocity profile prediction error is required, the processing requirements and error analysis suggest that the linear eddy viscosity model is adequate. However, if accurate estimates of bed shear stress and TKE are required then, of the models tested, the k−ω model should be used.

  13. Current Trends in Modeling Research for Turbulent Aerodynamic Flows

    NASA Technical Reports Server (NTRS)

    Gatski, Thomas B.; Rumsey, Christopher L.; Manceau, Remi

    2007-01-01

    The engineering tools of choice for the computation of practical engineering flows have begun to migrate from those based on the traditional Reynolds-averaged Navier-Stokes approach to methodologies capable, in theory if not in practice, of accurately predicting some instantaneous scales of motion in the flow. The migration has largely been driven by both the success of Reynolds-averaged methods over a wide variety of flows as well as the inherent limitations of the method itself. Practitioners, emboldened by their ability to predict a wide-variety of statistically steady, equilibrium turbulent flows, have now turned their attention to flow control and non-equilibrium flows, that is, separation control. This review gives some current priorities in traditional Reynolds-averaged modeling research as well as some methodologies being applied to a new class of turbulent flow control problems.

  14. Three-fluid, Three-dimensional Magnetohydrodynamic Solar Wind Model with Eddy Viscosity and Turbulent Resistivity

    NASA Astrophysics Data System (ADS)

    Usmanov, Arcadi V.; Goldstein, Melvyn L.; Matthaeus, William H.

    2014-06-01

    We have developed a three-fluid, three-dimensional magnetohydrodynamic solar wind model that incorporates turbulence transport, eddy viscosity, turbulent resistivity, and turbulent heating. The solar wind plasma is described as a system of co-moving solar wind protons, electrons, and interstellar pickup protons, with separate energy equations for each species. Numerical steady-state solutions of Reynolds-averaged solar wind equations coupled with turbulence transport equations for turbulence energy, cross helicity, and correlation length are obtained by the time relaxation method in the corotating with the Sun frame of reference in the region from 0.3 to 100 AU (but still inside the termination shock). The model equations include the effects of electron heat conduction, Coulomb collisions, photoionization of interstellar hydrogen atoms and their charge exchange with the solar wind protons, turbulence energy generation by pickup protons, and turbulent heating of solar wind protons and electrons. The turbulence transport model is based on the Reynolds decomposition and turbulence phenomenologies that describe the conversion of fluctuation energy into heat due to a turbulent cascade. In addition to using separate energy equations for the solar wind protons and electrons, a significant improvement over our previous work is that the turbulence model now uses an eddy viscosity approximation for the Reynolds stress tensor and the mean turbulent electric field. The approximation allows the turbulence model to account for driving of turbulence by large-scale velocity gradients. Using either a dipole approximation for the solar magnetic field or synoptic solar magnetograms from the Wilcox Solar Observatory for assigning boundary conditions at the coronal base, we apply the model to study the global structure of the solar wind and its three-dimensional properties, including embedded turbulence, heating, and acceleration throughout the heliosphere. The model results are

  15. Three-fluid, three-dimensional magnetohydrodynamic solar wind model with eddy viscosity and turbulent resistivity

    SciTech Connect

    Usmanov, Arcadi V.; Matthaeus, William H.; Goldstein, Melvyn L.

    2014-06-10

    We have developed a three-fluid, three-dimensional magnetohydrodynamic solar wind model that incorporates turbulence transport, eddy viscosity, turbulent resistivity, and turbulent heating. The solar wind plasma is described as a system of co-moving solar wind protons, electrons, and interstellar pickup protons, with separate energy equations for each species. Numerical steady-state solutions of Reynolds-averaged solar wind equations coupled with turbulence transport equations for turbulence energy, cross helicity, and correlation length are obtained by the time relaxation method in the corotating with the Sun frame of reference in the region from 0.3 to 100 AU (but still inside the termination shock). The model equations include the effects of electron heat conduction, Coulomb collisions, photoionization of interstellar hydrogen atoms and their charge exchange with the solar wind protons, turbulence energy generation by pickup protons, and turbulent heating of solar wind protons and electrons. The turbulence transport model is based on the Reynolds decomposition and turbulence phenomenologies that describe the conversion of fluctuation energy into heat due to a turbulent cascade. In addition to using separate energy equations for the solar wind protons and electrons, a significant improvement over our previous work is that the turbulence model now uses an eddy viscosity approximation for the Reynolds stress tensor and the mean turbulent electric field. The approximation allows the turbulence model to account for driving of turbulence by large-scale velocity gradients. Using either a dipole approximation for the solar magnetic field or synoptic solar magnetograms from the Wilcox Solar Observatory for assigning boundary conditions at the coronal base, we apply the model to study the global structure of the solar wind and its three-dimensional properties, including embedded turbulence, heating, and acceleration throughout the heliosphere. The model results are

  16. Development and application of an atmospheric turbulence model for use in flight simulators in flight simulators

    NASA Technical Reports Server (NTRS)

    Jacobson, I. D.; Joshi, D. S.

    1976-01-01

    The influence of simulated turbulence on aircraft handling qualities was investigated. Pilot opinion of the handling qualities of a light general aviation aircraft were evaluated in a motion-base simulator using a simulated turbulence environment. A realistic representation of turbulence disturbances is described in terms of rms intensity and scale length and their random variations with time. The time histories generated by the proposed turbulence models showed characteristics which appear to be more similar to real turbulence than the frequently-used Gaussian turbulence model. In addition, the proposed turbulence models can flexibly accommodate changes in atmospheric conditions and be easily implemented in flight simulator studies. Six turbulence time histories, including the conventional Gaussian model, were used in an IFR-tracking task. The realism of each of the turbulence models and the handling qualities of the simulated airplane were evaluated. Analysis of pilot opinions shows that at approximately the same rms intensities of turbulence, the handling quality ratings transit from the satisfactory level, for the simple Gaussian model, to an unacceptable level for more realistic and compositely structured turbulence models.

  17. Algebraic approach to the projected deformed oscillator model

    NASA Astrophysics Data System (ADS)

    Asherova, R. M.; Smirnov, Yu. F.; Tolstoy, V. N.; Shustov, A. P.

    1981-03-01

    A new method of calculation in terms of the projected deformed oscillator model is proposed. The method involves expansion of its wave functions in terms of the wave functions of an isotropic oscillator potential. Only overlap integrals between projected wave functions and reduced probabilities B(E2) of E2 transitions are examined. B(E2) values are expressed as a series containing the corresponding values of the Elliott SU(3) scheme. The convergence of these expansions is shown to be fairly good. The expectation values of operators ( QQ) and ( QQQ), which characterize the effective internal non-sphericity and non-axiality of the nucleus, are also calculated and discussed.

  18. PDF Modeling of Turbulent Lean Premixed Combustion

    SciTech Connect

    Yilmaz, S.L.; •Givi, P.; Strakey, P.A.

    2007-10-01

    The joint velocity-scalar-frequency probability density function (PDF) methodology is employed for prediction of a bluff-body stabilized lean premixed methane-air flame. A reduced mechanism with CO and NO chemistry is used to describe fuel oxidation. The predicted mean and rms values of the velocity, temperature and concentrations of major and minor species are compared with laboratory measurements. This technical effort was performed in support of the National Energy Technology Laboratory’s on-going research in “Assessment of Turbo-Chemistry Models for Gas Turbine Combustion Emissions” under the RDS contract DE-AC26-04NT41817.

  19. Modeling anisotropic MHD turbulence in simulations of liquid metal flows

    NASA Astrophysics Data System (ADS)

    Widlund, O.

    2001-06-01

    The dynamical properties of the MHD turbulence model proposed by Widlund etal. are examined for the case of homogeneous decaying turbulence. The model is a Reynolds stress closure, extended with a transport equation for a dimensional anisotropy variable, α, which carries information about length scale anisotropy. The analysis suggests that the model term originally proposed for the nonlinear energy transfer in the α equation should be modified. A unique set of model coefficients could be determined, which makes the model consistent with theory and experiments for interaction parameters N ranging from zero to infinity. The model coincides with the standard K-eps model when there is no magnetic field. In the linear regime of large N, it produces the K˜ t^{-1/2} energy decay predicted by linear theory. When nonlinear effects are important, the model predicts K˜ t^{-1.7} and L_∥ ˜ t^{0.65}, in agreement with the classical experiments by Alemany etal. Figs 5, Refs 11.

  20. Effective Inflow Conditions for Turbulence Models in Aerodynamic Calculations

    NASA Technical Reports Server (NTRS)

    Spalart, Philippe R.; Rumsey, Christopher L.

    2007-01-01

    The selection of inflow values at boundaries far upstream of an aircraft is considered, for one- and two-equation turbulence models. Inflow values are distinguished from the ambient values near the aircraft, which may be much smaller. Ambient values should be selected first, and inflow values that will lead to them after the decay second; this is not always possible, especially for the time scale. The two-equation decay during the approach to the aircraft is shown; often, the time scale has been set too short for this decay to be calculated accurately on typical grids. A simple remedy for both issues is to impose floor values for the turbulence variables, outside the viscous sublayer, and it is argued that overriding the equations in this manner is physically justified. Selecting laminar ambient values is easy, if the boundary layers are to be tripped, but a more common practice is to seek ambient values that will cause immediate transition in boundary layers. This opens up a wide range of values, and selection criteria are discussed. The turbulent Reynolds number, or ratio of eddy viscosity to laminar viscosity has a huge dynamic range that makes it unwieldy; it has been widely mis-used, particularly by codes that set upper limits on it. The value of turbulent kinetic energy in a wind tunnel or the atmosphere is also of dubious value as an input to the model. Concretely, the ambient eddy viscosity must be small enough to preserve potential cores in small geometry features, such as flap gaps. The ambient frequency scale should also be small enough, compared with shear rates in the boundary layer. Specific values are recommended and demonstrated for airfoil flows

  1. Extensions of algebraic image operators: An approach to model-based vision

    NASA Technical Reports Server (NTRS)

    Lerner, Bao-Ting; Morelli, Michael V.

    1990-01-01

    Researchers extend their previous research on a highly structured and compact algebraic representation of grey-level images which can be viewed as fuzzy sets. Addition and multiplication are defined for the set of all grey-level images, which can then be described as polynomials of two variables. Utilizing this new algebraic structure, researchers devised an innovative, efficient edge detection scheme. An accurate method for deriving gradient component information from this edge detector is presented. Based upon this new edge detection system researchers developed a robust method for linear feature extraction by combining the techniques of a Hough transform and a line follower. The major advantage of this feature extractor is its general, object-independent nature. Target attributes, such as line segment lengths, intersections, angles of intersection, and endpoints are derived by the feature extraction algorithm and employed during model matching. The algebraic operators are global operations which are easily reconfigured to operate on any size or shape region. This provides a natural platform from which to pursue dynamic scene analysis. A method for optimizing the linear feature extractor which capitalizes on the spatially reconfiguration nature of the edge detector/gradient component operator is discussed.

  2. A Study of Two-Equation Turbulence Models on the Elliptic Streamline Flow

    NASA Technical Reports Server (NTRS)

    Blaisdell, Gregory A.; Qin, Jim H.; Shariff, Karim; Rai, Man Mohan (Technical Monitor)

    1995-01-01

    Several two-equation turbulence models are compared to data from direct numerical simulations (DNS) of the homogeneous elliptic streamline flow, which combines rotation and strain. The models considered include standard two-equation models and models with corrections for rotational effects. Most of the rotational corrections modify the dissipation rate equation to account for the reduced dissipation rate in rotating turbulent flows, however, the DNS data shows that the production term in the turbulent kinetic energy equation is not modeled correctly by these models. Nonlinear relations for the Reynolds stresses are considered as a means of modifying the production term. Implications for the modeling of turbulent vortices will be discussed.

  3. Three-dimensional Fast Flux Test Facility plenum model turbulent flow prediction and data comparison

    SciTech Connect

    Eyler, L.L.; Sawdye, R.W.

    1981-01-01

    Two- and three-dimensional numerical simulations of turbulent flow in a scaled Fast Flux Test Facility (FFTF) upper plenum model were performed using the TEMPEST hydrothermal code. A standard k-element of model was used to describe turbulence through an effective viscosity. Comparisons with previously reported mean velocity and turbulence field data measured in the plenum model and two-dimensional numerical simulations using the TEACH code were made. Predicted horizontal and vertical mean velocities and turbulent kinetic energy are shown to be in good agreement with available experimental data when inlet conditions of the dissipation of turbulent kinetic energy are appropriately prescribed. The three-dimensional quarter-symmetry simulation predicts the turbulent kinetic energy field significantly better than the two-dimensional centerplane simulations. These results lead to conclusions concerning deficiencies in the experimental data and the turbulence model.

  4. Microburst Simulation via Vortex-Ring and Turbulent Jet Models.

    NASA Astrophysics Data System (ADS)

    Wan, Tung

    Microbursts, suggested as primary causes of many aircraft fatal crashes, are the subject of this research. A microburst, or low-level intense wind shear, is generated by a thunderstorm or a small rain cloud, and presents hazardous conditions for aircraft during take-off and landing maneuvers. Recently released data show that a microburst resembles a transient vortex ring. Three microburst models have been constructed in this study. First, the turbulent jet model encompasses a free jet at high altitude and a wall jet near the ground surface. Second, the vortex ring model is a combination of a primary and an image vortex ring, with an inviscid -viscous interaction at the central axial and surface regions. An unsteady version of this model is also provided by solving the trajectory equation with the Direct Formal Integration (DFI) method or with the Runge-Kutta method. Third and finally, the complete unsteady microburst model equations (conservation of mass, momentum, and energy), or what has been referred to as the Navier-Stokes model formulation, are solved by the successive over relaxation method. Results show that the microburst can be simulated accurately by impulsive turbulent jet at high altitude and a transient vortex ring in mid-air and near the ground surface. In addition to improved understanding of the physical nature of microbursts, the models presented here can also be used for flight simulation and the pilot training purposes.

  5. Modeling extinction and reignition in turbulent flames

    SciTech Connect

    Kronenburg, A.; Kostka, M.

    2005-12-01

    The conditional moment closure method (CMC) has been extended to improve reactive species predictions in flames with significant local extinction and reignition. Simple first-order closure of the conditionally averaged reaction rate term does not give satisfactory results due to large fluctuations around the conditional mean and an alternative closure is suggested here. The new closure is based on a precomputed parameterized reference field that maps reactive species mass fractions as functions of mixture fraction and sensible enthalpy. During the computations, the reference field is continuously adjusted to ensure consistency with the CMC solution and doubly conditioned chemical source terms that are functions of time, space, mixture fraction, and sensible enthalpy can thus be obtained. Integration over sensible enthalpy space yields the improved singly conditioned chemical source term that can be used for the solution of the CMC equations. Full closure can be achieved by assuming a {beta}-PDF for the probability distribution in sensible enthalpy space and an additional conditional variance equation needs to be solved. The overall agreement between the measured and the computed variance is satisfactory and the extended CMC model is applied to Sandia Flames D, E, and F. Excellent predictions of temperature, major species, intermediates, and NO are obtained in Flames D and E while temperature predictions can be significantly improved in Sandia Flame F.

  6. Modelling of Landau-Darrieus and thermo-diffusive instability effects for CFD simulations of laminar and turbulent premixed combustion

    NASA Astrophysics Data System (ADS)

    Keppeler, Roman; Pfitzner, Michael

    2015-01-01

    An algebraic model is derived that accounts for the effects of non-resolved Landau-Darrieus and thermo-diffusive instabilities on the propagation speed of fully premixed laminar and turbulent flame fronts in the Large Eddy Simulation (LES) context provided that the laminar flame speed appears as a model parameter in the LES combustion model. The model is derived assuming fractal characteristics of flames which exhibit cellular structures due to instabilities. The smallest and largest unstable wavelengths are computed employing a dispersion relation for nominally planar flames. Values for the fractal dimension characterising the flame structures are taken from the literature. A phenomenological model accounts for the stabilising effect of strain. Based on experimental data, a correlation for a critical strain rate, which indicates the onset of instabilities, is formulated. To validate the new model which accounts for instabilities on the effective speed of laminar flame propagation, laminar expanding spherical methane-air flames at p = 5 bar and p = 10 bar are simulated in the LES context. Values for the fractal dimension, as proposed in the literature, are varied. The predicted flame propagation speed is in very good agreement with experimental data when applying a fractal dimension of about D = 2.06. The critical strain turns out to be a suitable parameter to indicate the onset of instabilities and to quantify the influence of instabilities. Simulations applying a second model proposed by Bradley and valid for spherically expanding flames show similar results. LES of turbulent Bunsen flames at 1, 5 and 10 bar, which are characterised by u‧/s0L < 1, are performed to evaluate the derived instability model for turbulent flames. The simulated flames (from the Kobayashi database) have already been experimentally investigated in the context of Landau-Darrieus and thermo-diffusive instabilities. In agreement with conclusions from these investigations, for the

  7. Uncertainty Quantification and Validation for RANS Turbulence Models

    NASA Astrophysics Data System (ADS)

    Oliver, Todd; Moser, Robert

    2011-11-01

    Uncertainty quantification and validation procedures for RANS turbulence models are developed and applied. The procedures used here rely on a Bayesian view of probability. In particular, the uncertainty quantification methodology requires stochastic model development, model calibration, and model comparison, all of which are pursued using tools from Bayesian statistics. Model validation is also pursued in a probabilistic framework. The ideas and processes are demonstrated on a channel flow example. Specifically, a set of RANS models--including Baldwin-Lomax, Spalart-Allmaras, k- ɛ, k- ω, and v2- f--and uncertainty representations are analyzed using DNS data for fully-developed channel flow. Predictions of various quantities of interest and the validity (or invalidity) of the various models for making those predictions will be examined. This work is supported by the Department of Energy [National Nuclear Security Administration] under Award Number [DE-FC52-08NA28615].

  8. Algebraic Construction of the Eigenstates for the Second Conserved Operator of the Quantum Calogero Model

    NASA Astrophysics Data System (ADS)

    Ujino, Hideaki; Wadati, Miki

    1996-03-01

    An algebraic construction of the eigenstates for the quantum Calogero modelis investigated. Extending the method of Lapointe and Vinet, weconstruct the eigenstates for the second conservedoperator of the quantum Calogero model.All the eigenstates can be factorizedinto symmetric polynomials which we call “Hi-Jack symmetric polynomials”and the ground state wave function.The conjectured formula for the eigenvalue of the second conserved operatoris confirmed.The Hi-Jack polynomials are strong candidates for the orthogonalbasis of the quantum Calogero model.

  9. Modeling Turbulent Combustion for Variable Prandtl and Schmidt Number

    NASA Technical Reports Server (NTRS)

    Hassan, H. A.

    2004-01-01

    This report consists of two abstracts submitted for possible presentation at the AIAA Aerospace Science Meeting to be held in January 2005. Since the submittal of these abstracts we are continuing refinement of the model coefficients derived for the case of a variable Turbulent Prandtl number. The test cases being investigated are a Mach 9.2 flow over a degree ramp and a Mach 8.2 3-D calculation of crossing shocks. We have developed an axisymmetric code for treating axisymmetric flows. In addition the variable Schmidt number formulation was incorporated in the code and we are in the process of determining the model constants.

  10. Turbulent Impurity Transport Modeling for C-Mod

    NASA Astrophysics Data System (ADS)

    Fu, Xiangrong; Horton, Wendell; Rowan, William; Bespamyatnov, Igor; Benkadda, Sadruddin; Fiore, Catherine

    2012-03-01

    Turbulent particle transport is investigated by analyzing boron impurity transport experiments in the Alcator C-Mod transport experiments with a quasilinear theory. Eigenvalue problems for sets of reduced fluid equations for the multi-component plasmas are solved to get the fluctuating field vector composed of the electric potential φ, the main ion density δni, the impurity density δnz and the ion temperature fluctuation δTi(for ITG). For Alcator C-Mod parameters, we investigate three drift waves models (1) the usual drift waves driven by density gradients, (2)impurity drift waves supported by the impurity density gradients and (3)turbulence driven by ITG mode. With turbulent spectrum obtained from simulations or nonlinear theories, we calculate particle transport coefficients and compare with the experiment and the neoclassical theory. This procedure results in a fast code that could run in real-time on the transport time scale to give the particle fluxes as a function of the state of the plasma. The code may be extended to include multiple modes for a more complete description of plasmas. Examples for the particle fluxes are given for C-Mod in the H modes and newly discovered I modes. Recent experiments reported on LHD are briefly discussed.

  11. Modeling the Effects of Turbulence in Rotating Detonation Engines

    NASA Astrophysics Data System (ADS)

    Towery, Colin; Smith, Katherine; Hamlington, Peter; van Schoor, Marthinus; TESLa Team; Midé Team

    2014-03-01

    Propulsion systems based on detonation waves, such as rotating and pulsed detonation engines, have the potential to substantially improve the efficiency and power density of gas turbine engines. Numerous technical challenges remain to be solved in such systems, however, including obtaining more efficient injection and mixing of air and fuels, more reliable detonation initiation, and better understanding of the flow in the ejection nozzle. These challenges can be addressed using numerical simulations. Such simulations are enormously challenging, however, since accurate descriptions of highly unsteady turbulent flow fields are required in the presence of combustion, shock waves, fluid-structure interactions, and other complex physical processes. In this study, we performed high-fidelity three dimensional simulations of a rotating detonation engine and examined turbulent flow effects on the operation, performance, and efficiency of the engine. Along with experimental data, these simulations were used to test the accuracy of commonly-used Reynolds averaged and subgrid-scale turbulence models when applied to detonation engines. The authors gratefully acknowledge the support of the Defense Advanced Research Projects Agency (DARPA).

  12. Dynamic and Thermal Turbulent Time Scale Modelling for Homogeneous Shear Flows

    NASA Technical Reports Server (NTRS)

    Schwab, John R.; Lakshminarayana, Budugur

    1994-01-01

    A new turbulence model, based upon dynamic and thermal turbulent time scale transport equations, is developed and applied to homogeneous shear flows with constant velocity and temperature gradients. The new model comprises transport equations for k, the turbulent kinetic energy; tau, the dynamic time scale; k(sub theta), the fluctuating temperature variance; and tau(sub theta), the thermal time scale. It offers conceptually parallel modeling of the dynamic and thermal turbulence at the two equation level, and eliminates the customary prescription of an empirical turbulent Prandtl number, Pr(sub t), thus permitting a more generalized prediction capability for turbulent heat transfer in complex flows and geometries. The new model also incorporates constitutive relations, based upon invariant theory, that allow the effects of nonequilibrium to modify the primary coefficients for the turbulent shear stress and heat flux. Predictions of the new model, along with those from two other similar models, are compared with experimental data for decaying homogeneous dynamic and thermal turbulence, homogeneous turbulence with constant temperature gradient, and homogeneous turbulence with constant temperature gradient and constant velocity gradient. The new model offers improvement in agreement with the data for most cases considered in this work, although it was no better than the other models for several cases where all the models performed poorly.

  13. A Two-length Scale Turbulence Model for Single-phase Multi-fluid Mixing

    SciTech Connect

    Schwarzkopf, J. D.; Livescu, D.; Baltzer, J. R.; Gore, R. A.; Ristorcelli, J. R.

    2015-09-08

    A two-length scale, second moment turbulence model (Reynolds averaged Navier-Stokes, RANS) is proposed to capture a wide variety of single-phase flows, spanning from incompressible flows with single fluids and mixtures of different density fluids (variable density flows) to flows over shock waves. The two-length scale model was developed to address an inconsistency present in the single-length scale models, e.g. the inability to match both variable density homogeneous Rayleigh-Taylor turbulence and Rayleigh-Taylor induced turbulence, as well as the inability to match both homogeneous shear and free shear flows. The two-length scale model focuses on separating the decay and transport length scales, as the two physical processes are generally different in inhomogeneous turbulence. This allows reasonable comparisons with statistics and spreading rates over such a wide range of turbulent flows using a common set of model coefficients. The specific canonical flows considered for calibrating the model include homogeneous shear, single-phase incompressible shear driven turbulence, variable density homogeneous Rayleigh-Taylor turbulence, Rayleigh-Taylor induced turbulence, and shocked isotropic turbulence. The second moment model shows to compare reasonably well with direct numerical simulations (DNS), experiments, and theory in most cases. The model was then applied to variable density shear layer and shock tube data and shows to be in reasonable agreement with DNS and experiments. Additionally, the importance of using DNS to calibrate and assess RANS type turbulence models is highlighted.

  14. Boundary-layer turbulence modeling and vorticity dynamics: I. A kangaroo-process mixing model of boundary-layer turbulence

    NASA Astrophysics Data System (ADS)

    Dekker, H.; de Leeuw, G.; van den Brink, A. Maassen

    A nonlocal turbulence transport theory is presented by means of a novel analysis of the Reynolds stress, inter alia involving the construct of a sample path space and a stochastic hypothesis. An analytical sampling rate model (satisfying exchange) and a nonlinear scaling relation (mapping the path space onto the boundary layer) lead to an integro-differential equation for the mixing of scalar densities, which represents fully-developed boundary-layer turbulence as a nondiffusive (Kubo-Anderson or kangaroo) type stochastic process. The underlying near-wall behavior (i.e. for y +→0) of fluctuating velocities fully agrees with recent direct numerical simulations. The model involves a scaling exponent ɛ, with ɛ→∞ in the diffusion limit. For the (partly analytical) solution for the mean velocity profile, excellent agreement with the experimental data yields ɛ≈0.58. The significance of ɛ as a turbulence Cantor set dimension (in the logarithmic profile region, i.e. for y +→∞) is discussed.

  15. Modeling atmospheric turbulence effects on ground-based telescope systems

    SciTech Connect

    Flatte, S.M.; Bradford, L.W.; Max, C.E.

    1994-12-31

    Bester et al. report measurements of atmospheric fluctuations made with the Infrared Spatial Interferometer, which indicated behavior not in accord with the standard Kolmogorov model with only a single constant wind velocity. The numerical simulations use relatively complex models of the atmosphere to investigate both Kolmogorov and non-Kolmogorov models. The authors find that the measurements of Bester et al. for light passing through the upper atmosphere are within the limits of behavior for Kolmogorov models, but often only if the outer scale of turbulent fluctuations is between 15 to 100 meters. The possibility that the measured behavior might be non-Kolmogorov is not excluded. They also examine measurements made along short paths in the surface boundary layer, where some measurements of Bester et al. showed variations in the atmospheric fluctuations with seeing conditions which appeared to be non-Kolmogorov. These variations can perhaps be explained by standard models, but require that seeing improve with increasing wind speed in the surface layer. They discuss some other measurements which lend some support to that idea. However, they cannot exclude non-Kolmogorov behavior. They find that meteorological data is needed concurrent with astronomical observations, to help constrain the models. The size of the outer scale, the wind velocity profile and the turbulence spectrum are important to the ultimate capabilities of interferometers and other systems with adaptive optics.

  16. Near-wall modelling of compressible turbulent flows

    NASA Technical Reports Server (NTRS)

    So, Ronald M. C.

    1990-01-01

    Work was carried out to formulate near-wall models for the equations governing the transport of the temperature-variance and its dissipation rate. With these equations properly modeled, a foundation is laid for their extension together with the heat-flux equations to compressible flows. This extension is carried out in a manner similar to that used to extend the incompressible near-wall Reynolds-stress models to compressible flows. The methodology used to accomplish the extension of the near-wall Reynolds-stress models is examined and the actual extension of the models for the Reynolds-stress equations and the near-wall dissipation-rate equation to compressible flows is given. Then the formulation of the near-wall models for the equations governing the transport of the temperature variance and its dissipation rate is discussed. Finally, a sample calculation of a flat plate compressible turbulent boundary-layer flow with adiabatic wall boundary condition and a free-stream Mach number of 2.5 using a two-equation near-wall closure is presented. The results show that the near-wall two-equation closure formulated for compressible flows is quite valid and the calculated properties are in good agreement with measurements. Furthermore, the near-wall behavior of the turbulence statistics and structure parameters is consistent with that found in incompressible flows.

  17. On the coalescence-dispersion modeling of turbulent molecular mixing

    NASA Technical Reports Server (NTRS)

    Givi, Peyman; Kosaly, George

    1987-01-01

    The general coalescence-dispersion (C/D) closure provides phenomenological modeling of turbulent molecular mixing. The models of Curl and Dopazo and O'Brien appear as two limiting C/D models that bracket the range of results one can obtain by various models. This finding is used to investigate the sensitivtiy of the results to the choice of the model. Inert scalar mixing is found to be less model-sensitive than mixing accompanied by chemical reaction. Infinitely fast chemistry approximation is used to relate the C/D approach to Toor's earlier results. Pure mixing and infinite rate chemistry calculations are compared to study further a recent result of Hsieh and O'Brien who found that higher concentration moments are not sensitive to chemistry.

  18. NASA Trapezoidal Wing Computations Including Transition and Advanced Turbulence Modeling

    NASA Technical Reports Server (NTRS)

    Rumsey, C. L.; Lee-Rausch, E. M.

    2012-01-01

    Flow about the NASA Trapezoidal Wing is computed with several turbulence models by using grids from the first High Lift Prediction Workshop in an effort to advance understanding of computational fluid dynamics modeling for this type of flowfield. Transition is accounted for in many of the computations. In particular, a recently-developed 4-equation transition model is utilized and works well overall. Accounting for transition tends to increase lift and decrease moment, which improves the agreement with experiment. Upper surface flap separation is reduced, and agreement with experimental surface pressures and velocity profiles is improved. The predicted shape of wakes from upstream elements is strongly influenced by grid resolution in regions above the main and flap elements. Turbulence model enhancements to account for rotation and curvature have the general effect of increasing lift and improving the resolution of the wing tip vortex as it convects downstream. However, none of the models improve the prediction of surface pressures near the wing tip, where more grid resolution is needed.

  19. Anomalous spectral laws in differential models of turbulence

    NASA Astrophysics Data System (ADS)

    Thalabard, Simon; Nazarenko, Sergey; Galtier, Sébastien; Medvedev, Sergey

    2015-07-01

    Differential models for hydrodynamic, passive-scalar and wave turbulence given by nonlinear first- and second-order evolution equations for the energy spectrum in the k-space were analysed. Both types of models predict formation an anomalous transient power-law spectra. The second-order models were analysed in terms of self-similar solutions of the second kind, and a phenomenological formula for the anomalous spectrum exponent was constructed using numerics for a broad range of parameters covering all known physical examples. The first-order models were examined analytically, including finding an analytical prediction for the anomalous exponent of the transient spectrum and description of formation of the Kolmogorov-type spectrum as a reflection wave from the dissipative scale back into the inertial range. The latter behaviour was linked to pre-shock/shock singularities similar to the ones arising in the Burgers equation. Existence of the transient anomalous scaling and the reflection-wave scenario are argued to be a robust feature common to the finite-capacity turbulence systems. The anomalous exponent is independent of the initial conditions but varies for for different models of the same physical system.

  20. A ``true'' Unsteady RANS model of turbulence with inherent forcing

    NASA Astrophysics Data System (ADS)

    Jakirlic, Suad; Maduta, Robert; Darmstadt University of Technology Team

    2012-11-01

    Usually, a turbulence model designed and calibrated in the steady RANS (Reynolds-Averaged Navier-Stokes) framework has been straightforwardly applied to an unsteady calculation. It ended up in a steady velocity field in the case of confined wall-bounded flows; a somewhat better outcome is to be expected in globally unstable flows, such as bluff body configurations. However, only a weakly unsteady mean flow can be returned with the level of unsteadiness being by far lower compared to a referent database. Presently, an instability-sensitive, eddy-resolving model based on a differential, near-wall Reynolds stress model of turbulence is formulated and applied to several attached and separated wall-bounded configurations - channel and duct flows, external and internal flows separated from sharp-edged and continuous curved surfaces. In all cases considered the fluctuating velocity field was obtained started from the steady RANS results. The model proposed does not comprise any parameter depending explicitly on the grid spacing. An additional term in the corresponding length-scale determining equation providing a selective assessment of its production, modelled in terms of the von Karman length scale (comprising the second derivative of the velocity field) in line with the SAS (Scale-Adaptive Simulation) proposal (Menter and Egorov, 2010), represents here the key parameter.