Comparison of PDF and Moment Closure Methods in the Modeling of Turbulent Reacting Flows
NASA Technical Reports Server (NTRS)
Norris, Andrew T.; Hsu, Andrew T.
1994-01-01
In modeling turbulent reactive flows, Probability Density Function (PDF) methods have an advantage over the more traditional moment closure schemes in that the PDF formulation treats the chemical reaction source terms exactly, while moment closure methods are required to model the mean reaction rate. The common model used is the laminar chemistry approximation, where the effects of turbulence on the reaction are assumed negligible. For flows with low turbulence levels and fast chemistry, the difference between the two methods can be expected to be small. However for flows with finite rate chemistry and high turbulence levels, significant errors can be expected in the moment closure method. In this paper, the ability of the PDF method and the moment closure scheme to accurately model a turbulent reacting flow is tested. To accomplish this, both schemes were used to model a CO/H2/N2- air piloted diffusion flame near extinction. Identical thermochemistry, turbulence models, initial conditions and boundary conditions are employed to ensure a consistent comparison can be made. The results of the two methods are compared to experimental data as well as to each other. The comparison reveals that the PDF method provides good agreement with the experimental data, while the moment closure scheme incorrectly shows a broad, laminar-like flame structure.
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.
Shima, N. . College of Engineering)
1993-03-01
The purpose of this two-part paper is to assess the performance of a second-moment closure applicable up to a wall. In the present part, the turbulence model is applied to the boundary layers with periodic pressure gradient, with wall transpiration and with free-stream turbulence. The predictions are shown to be in good agreement with experiments and a direct simulation. In particular, a tendency towards relaminarization and a subsequent retransition in the oscillating boundary layer are faithfully reproduced, and the effect of the length scale of free-stream turbulence is correctly captured.
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.
NASA Technical Reports Server (NTRS)
Amano, R. S.; Goel, P.
1986-01-01
A numerical study of computations in backward-facing steps with flow separation and reattachment, using the Reynolds stress closure is presented. The highlight of this study is the improvement of the Reynold-stress model (RSM) by modifying the diffusive transport of the Reynolds stresses through the formulation, solution and subsequent incorporation of the transport equations of the third moments, bar-u(i)u(j)u(k), into the turbulence model. The diffusive transport of the Reynolds stresses, represented by the gradients of the third moments, attains greater significance in recirculating flows. The third moments evaluated by the development and solution of the complete transport equations are superior to those obtained by existing algebraic correlations. A low-Reynolds number model for the transport equations of the third moments is developed and considerable improvement in the near-wall profiles of the third moments is observed. The values of the empirical constants utilized in the development of the model are recommended. The Reynolds-stress closure is consolidated by incorporating the equations of k and e, containing the modified diffusion coefficients, and the transport equations of the third moments into the Reynolds stress equations. Computational results obtained by the original k-e model, the original RSM and the consolidated and modified RSM are compared with experimental data. Overall improvement in the predictions is seen by consolidation of the RMS and a marked improvement in the profiles of bar-u(i)u(j)u(k) is obtained around the reattachment region.
Second-moment closures and length scales for weakly stratified turbulent shear flows
NASA Astrophysics Data System (ADS)
Baumert, Helmut; Peters, Hartmut
2000-03-01
For the special hydrodynamic situation of unbounded homogeneous shear layers, turbulence closure models of Mellor-Yamada type (MY) and k-ɛ type are put into a single canonical form. For this situation we show that conventional versions of MY and various k-ɛ versions lack a proper steady state, and are unable to simulate the most basic properties of stratified shear flows exemplified in, for example, the Rohr et al. [1988] experiments: exponential growth at sufficiently low gradient Richardson number (Rg), exponential decay at sufficiently large Rg, and a steady state in between. Proper choice of one special model parameter readily solves the problems. In the fairly general case of structural equilibrium (state of exponential evolution) in weakly to moderately stratified turbulence (Rg ≲ 0.25), the ratio between the Thorpe scale (or Ellison scale) and the Ozmidov scale varies like the gradient Richardson number (Rg) to the power 3/4, and the ratio of the Thorpe scale to the buoyancy scale varies like Rg1/2. Length scales predicted by our current model are consistent with laboratory measurements of Rohr et al. [1988], with large-eddy numerical simulations of Schumann and Gerz [1995], and with microstructure measurements from the 1987 Tropic Heat Experiment in the equatorial Pacific by Peters et al. [1995].
Autonomic closure for turbulence simulations
NASA Astrophysics Data System (ADS)
King, Ryan N.; Hamlington, Peter E.; Dahm, Werner J. A.
2016-03-01
A new approach to turbulence closure is presented that eliminates the need to specify a predefined turbulence model and instead provides for fully adaptive, self-optimizing, autonomic closures. The closure is autonomic in the sense that the simulation itself determines the optimal local, instantaneous relation between any unclosed term and resolved quantities through the solution of a nonlinear, nonparametric system identification problem. This nonparametric approach allows the autonomic closure to freely adapt to varying nonlinear, nonlocal, nonequilibrium, and other turbulence characteristics in the flow. Even a simple implementation of the autonomic closure for large eddy simulations provides remarkably more accurate results in a priori tests than do dynamic versions of traditional prescribed closures.
Autonomic closure for turbulence simulations.
King, Ryan N; Hamlington, Peter E; Dahm, Werner J A
2016-03-01
A new approach to turbulence closure is presented that eliminates the need to specify a predefined turbulence model and instead provides for fully adaptive, self-optimizing, autonomic closures. The closure is autonomic in the sense that the simulation itself determines the optimal local, instantaneous relation between any unclosed term and resolved quantities through the solution of a nonlinear, nonparametric system identification problem. This nonparametric approach allows the autonomic closure to freely adapt to varying nonlinear, nonlocal, nonequilibrium, and other turbulence characteristics in the flow. Even a simple implementation of the autonomic closure for large eddy simulations provides remarkably more accurate results in a priori tests than do dynamic versions of traditional prescribed closures. PMID:27078285
A Quadratic Closure for Compressible Turbulence
Futterman, J A
2008-09-16
We have investigated a one-point closure model for compressible turbulence based on third- and higher order cumulant discard for systems undergoing rapid deformation, such as might occur downstream of a shock or other discontinuity. In so doing, we find the lowest order contributions of turbulence to the mean flow, which lead to criteria for Adaptive Mesh Refinement. Rapid distortion theory (RDT) as originally applied by Herring closes the turbulence hierarchy of moment equations by discarding third order and higher cumulants. This is similar to the fourth-order cumulant discard hypothesis of Millionshchikov, except that the Millionshchikov hypothesis was taken to apply to incompressible homogeneous isotropic turbulence generally, whereas RDT is applied only to fluids undergoing a distortion that is 'rapid' in the sense that the interaction of the mean flow with the turbulence overwhelms the interaction of the turbulence with itself. It is also similar to Gaussian closure, in which both second and fourth-order cumulants are retained. Motivated by RDT, we develop a quadratic one-point closure for rapidly distorting compressible turbulence, without regard to homogeneity or isotropy, and make contact with two equation turbulence models, especially the K-{var_epsilon} and K-L models, and with linear instability growth. In the end, we arrive at criteria for Adaptive Mesh Refinement in Finite Volume simulations.
NASA Technical Reports Server (NTRS)
Demuren, A. O.
1990-01-01
A multigrid method is presented for calculating turbulent jets in crossflow. Fairly rapid convergence is obtained with the k-epsilon turbulence model, but computations with a full Reynolds stress turbulence model (RSM) are not yet very efficient. Grid dependency tests show that there are slight differences between results obtained on the two finest grid levels. Computations using the RSM are significantly different from those with k-epsilon model and compare better to experimental data. Some work is still required to improve the efficiency of the computations with the RSM.
Moment closure and the stochastic logistic model.
Nåsell, Ingemar
2003-03-01
The quasi-stationary distribution of the stochastic logistic model is studied in the parameter region where its body is approximately normal. Improved asymptotic approximations of its first three cumulants are derived. It is shown that the same results can be derived with the aid of the moment closure method. This indicates that the moment closure method leads to expressions for the cumulants that are asymptotic approximations of the cumulants of the quasi-stationary distribution. PMID:12615498
Second Moment Closure Near the Two-component Limit
NASA Technical Reports Server (NTRS)
Rubinstein, Robert; Girimaji, Sharath S.
2006-01-01
The purpose of this paper is to explore some wider implications of the two-component limit for both single point turbulence models and spectral closure theories. Although the two-component limit arises most naturally in inhomogeneous problems like wall-bounded turbulence, the analysis will be restricted to homogeneous turbulence. But since homogeneous turbulence is the crucial case for realizability, the conclusions will nevertheless be applicable to modeling. Th essential point of our argument is that whereas the evolution of the stochastic velocity field is Markovian because it is governed by the Navier-Stokes equations, the exact stress evolution equation is not Markovian because it is unclosed. This property of moment evolution has been stressed by Kraichnan (1959). We will show that modeling stress evolution at the two-component limit with a closure that is Markovian in the stresses alone leads to basic inconsistencies in single-point modeling and, perhaps surprisingly, in spectral modes as well.
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.
Closure models for turbulent reacting flows
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.
Moment Closures on Two-Dimensional Cartesian Grids
2015-07-31
Some moment methods for kinetic equations are complicated and take time to develop. Over the course of a couple years, this software was developed to test different closures on standard test problems in the literature. With this software, researchers in the field of moment closures will be able to rapidly test new methods.
Formulation and closure of compressible turbulence equations in the light of kinetic theory
NASA Technical Reports Server (NTRS)
Tsuge, S.; Sagara, K.
1976-01-01
Fluid-dynamic moment equations, based on a kinetic hierarchy system, are derived governing the interaction between turbulent and thermal fluctuations. The kinetic theory is shown to reduce the inherent complexity of the conventional formalism of compressible turbulence theory and to minimize arbitrariness in formulating the closure condition.
Mapping Closure Approximation to Conditional Dissipation Rate for Turbulent Scalar Mixing
NASA Technical Reports Server (NTRS)
He, Gouwei; Rubinstein, R.
2000-01-01
A novel mapping closure approximation (MCA) technique is developed to construct a model for the conditional dissipation rate (CDR) of a scalar in homogeneous turbulence. It is shown that the CDR model from amplitude mapping closure is incorrect in asymptotic behavior for unsymmetric binary mixing. The correct asymptotic behavior can be described by the CDR model formulated by the MCA technique. The MCA approach is outlined for constructing successive approximation to probability density function (PDF) and conditional moment.
Quantum hydrodynamic model by moment closure of Wigner equation
NASA Astrophysics Data System (ADS)
Cai, Zhenning; Fan, Yuwei; Li, Ruo; Lu, Tiao; Wang, Yanli
2012-10-01
In this paper, we derive the quantum hydrodynamics models based on the moment closure of the Wigner equation. The moment expansion adopted is of the Grad type first proposed by Grad ["On the kinetic theory of rarefied gases," Commun. Pure Appl. Math. 2(4), 331-407 (1949), 10.1002/cpa.3160020403]. The Grad's moment method was originally developed for the Boltzmann equation. Recently, a regularization method for the Grad's moment system of the Boltzmann equation was proposed by Cai et al. [Commun. Pure Appl. Math. "Globally hyperbolic regularization of Grad's moment system" (in press)] to achieve the global hyperbolicity so that the local well-posedness of the moment system is attained. With the moment expansion of the Wigner function, the drift term in the Wigner equation has exactly the same moment representation as in the Boltzmann equation, thus the regularization applies. The moment expansion of the nonlocal Wigner potential term in the Wigner equation turns out to be a linear source term, which can only induce very mild growth of the solution. As a result, the local well-posedness of the regularized moment system for the Wigner equation remains as for the Boltzmann equation.
Multivariate moment closure techniques for stochastic kinetic models
Lakatos, Eszter Ale, Angelique; Kirk, Paul D. W.; Stumpf, Michael P. H.
2015-09-07
Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs.
Multivariate moment closure techniques for stochastic kinetic models
NASA Astrophysics Data System (ADS)
Lakatos, Eszter; Ale, Angelique; Kirk, Paul D. W.; Stumpf, Michael P. H.
2015-09-01
Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs.
Multivariate moment closure techniques for stochastic kinetic models.
Lakatos, Eszter; Ale, Angelique; Kirk, Paul D W; Stumpf, Michael P H
2015-09-01
Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs. PMID:26342359
Myong, R. S.; Nagdewe, S. P.
2011-05-20
The Grad's closure for the high-order moment equation is revisited and, by extending his theory, a physically motivated closure is developed for the one-dimensional velocity shear gas flow. The closure is based on the physical argument of the relative importance of various terms appearing in the moment equation. Also, the closure is derived such that the resulting theory may be inclusive of the well established linear theory (Navier-Stokes-Fourier) as limiting case near local thermal equilibrium.
Sreedhara, S.; Huh, Kang Y.
2005-12-01
The performance of second-order conditional moment closure (CMC) depends on models to evaluate conditional variances and covariances of temperature and species mass fractions. In this paper the closure schemes based on the steady laminar flamelet model (SLFM) are validated against direct numerical simulation (DNS) involving extinction and ignition. Scaling is performed to reproduce proper absolute magnitudes, irrespective of the origin of mismatch between local flamelet structures and scalar dissipation rates. DNS based on the pseudospectral method is carried out to study hydrogen-air combustion with a detailed kinetic mechanism, in homogeneous, isotropic, and decaying turbulent media. Lewis numbers are set equal to unity to avoid complication of differential diffusion. The SLFM-based closures for correlations among fluctuations of reaction rate, scalar dissipation rate, and species mass fractions show good comparison with DNS. The variance parameter in lognormal PDF and the constants in the dissipation term have been estimated from DNS results. Comparison is made for the resulting conditional profiles from DNS, first-order CMC, and second-order CMC with correction to the most critical reaction step according to sensitivity analysis. Overall good agreement ensures validity of the SLFM-based closures for modeling conditional variances and covariances in second-order CMC.
Entropy production moment closures and effective transport coefficients
NASA Astrophysics Data System (ADS)
Christen, Thomas; Kassubek, Frank
2014-09-01
If transport of a given (classical, fermionic, or bosonic) particle species in media is described by a Boltzmann transport equation (BTE), it is often expedient to solve this BTE in the framework of a moment expansion of the particle distribution function, while an exact solution or simulation of the problem with real material properties and complex geometries is unpractical or even unfeasible. Whereas for local thermal equilibrium (LTE) the well-known hydrodynamic equations for the densities of the conserved quantities are derived from the BTE, for non-LTE it is not obvious how to define moments and to close the truncated hierarchy of partial differential equations for these moments. This paper reviews a closure based on entropy production rate minimization, which is applicable to incoherent transport of independent particles in non-LTE interacting with an LTE-medium. The BTE is then linear, includes emission-absorption and elastic scattering processes, and is equivalent to radiative transfer equations. In a large range from diffusive (opaque media) to ballistic (transparent media) transport behaviour, the closure provides useful mean transport coefficients that are exact in the LTE limit, in contrast to the often used maximum entropy moment closure. After an introduction into the underlying theory for massive and wave-like particles, two illustrative examples are discussed. First, the two-moment approximation of radiative heat transfer is reviewed and effective absorption coefficients and the Eddington factor are calculated for a real absorption spectrum. Secondly, the approach is applied to semi-classical electric transport in mesoscopic systems and is shown to provide the correct conductance of a quasi-one-dimensional ballistic conductor with elastic scattering.
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.
A PDF closure model for compressible turbulent chemically reacting flows
NASA Technical Reports Server (NTRS)
Kollmann, W.
1992-01-01
The objective of the proposed research project was the analysis of single point closures based on probability density function (pdf) and characteristic functions and the development of a prediction method for the joint velocity-scalar pdf in turbulent reacting flows. Turbulent flows of boundary layer type and stagnation point flows with and without chemical reactions were be calculated as principal applications. Pdf methods for compressible reacting flows were developed and tested in comparison with available experimental data. The research work carried in this project was concentrated on the closure of pdf equations for incompressible and compressible turbulent flows with and without chemical reactions.
Nonlinear closures for scale separation in supersonic magnetohydrodynamic turbulence
NASA Astrophysics Data System (ADS)
Grete, Philipp; Vlaykov, Dimitar G.; Schmidt, Wolfram; Schleicher, Dominik R. G.; Federrath, Christoph
2015-02-01
Turbulence in compressible plasma plays a key role in many areas of astrophysics and engineering. The extreme plasma parameters in these environments, e.g. high Reynolds numbers, supersonic and super-Alfvenic flows, however, make direct numerical simulations computationally intractable even for the simplest treatment—magnetohydrodynamics (MHD). To overcome this problem one can use subgrid-scale (SGS) closures—models for the influence of unresolved, subgrid-scales on the resolved ones. In this work we propose and validate a set of constant coefficient closures for the resolved, compressible, ideal MHD equations. The SGS energies are modeled by Smagorinsky-like equilibrium closures. The turbulent stresses and the electromotive force (EMF) are described by expressions that are nonlinear in terms of large scale velocity and magnetic field gradients. To verify the closures we conduct a priori tests over 137 simulation snapshots from two different codes with varying ratios of thermal to magnetic pressure ({{β }p}=0.25,1,2.5,5,25) and sonic Mach numbers ({{M}s}=2,2.5,4). Furthermore, we make a comparison to traditional, phenomenological eddy-viscosity and α -β -γ closures. We find only mediocre performance of the kinetic eddy-viscosity and α -β -γ closures, and that the magnetic eddy-viscosity closure is poorly correlated with the simulation data. Moreover, three of five coefficients of the traditional closures exhibit a significant spread in values. In contrast, our new closures demonstrate consistently high correlations and constant coefficient values over time and over the wide range of parameters tested. Important aspects in compressible MHD turbulence such as the bi-directional energy cascade, turbulent magnetic pressure and proper alignment of the EMF are well described by our new closures.
Validity conditions for moment closure approximations in stochastic chemical kinetics
Schnoerr, David; Sanguinetti, Guido; Grima, Ramon
2014-08-28
Approximations based on moment-closure (MA) are commonly used to obtain estimates of the mean molecule numbers and of the variance of fluctuations in the number of molecules of chemical systems. The advantage of this approach is that it can be far less computationally expensive than exact stochastic simulations of the chemical master equation. Here, we numerically study the conditions under which the MA equations yield results reflecting the true stochastic dynamics of the system. We show that for bistable and oscillatory chemical systems with deterministic initial conditions, the solution of the MA equations can be interpreted as a valid approximation to the true moments of the chemical master equation, only when the steady-state mean molecule numbers obtained from the chemical master equation fall within a certain finite range. The same validity criterion for monostable systems implies that the steady-state mean molecule numbers obtained from the chemical master equation must be above a certain threshold. For mean molecule numbers outside of this range of validity, the MA equations lead to either qualitatively wrong oscillatory dynamics or to unphysical predictions such as negative variances in the molecule numbers or multiple steady-state moments of the stationary distribution as the initial conditions are varied. Our results clarify the range of validity of the MA approach and show that pitfalls in the interpretation of the results can only be overcome through the systematic comparison of the solutions of the MA equations of a certain order with those of higher orders.
The closure problem for turbulence in meteorology and oceanography
NASA Technical Reports Server (NTRS)
Pierson, W. J., Jr.
1985-01-01
The dependent variables used for computer based meteorological predictions and in plans for oceanographic predictions are wave number and frequency filtered values that retain only scales resolvable by the model. Scales unresolvable by the grid in use become 'turbulence'. Whether or not properly processed data are used for initial values is important, especially for sparce data. Fickian diffusion with a constant eddy diffusion is used as a closure for many of the present models. A physically realistic closure based on more modern turbulence concepts, especially one with a reverse cascade at the right times and places, could help improve predictions.
Modeling near wall effects in second moment closures by elliptic relaxation
NASA Technical Reports Server (NTRS)
Laurence, D.; Durbin, P.
1994-01-01
The elliptic relaxation model of Durbin (1993) for modeling near-wall turbulence using second moment closures (SMC) is compared to DNS data for a channel flow at Re(sub t) = 395. The agreement for second order statistics and even the terms in their balance equation is quite satisfactory, confirming that very little viscous effects (via Kolmogoroff scales) need to be added to the high Reynolds versions of SMC for near-wall-turbulence. The essential near-wall feature is thus the kinematic blocking effect that a solid wall exerts on the turbulence through the fluctuating pressure, which is best modeled by an elliptic operator. Above the transition layer, the effect of the original elliptic operator decays rapidly, and it is suggested that the log-layer is better reproduced by adding a non-homogeneous reduction of the return to isotropy, the gradient of the turbulent length scale being used as a measure of the inhomogeneity of the log-layer. The elliptic operator was quite easily applied to the non-linear Craft & Launder pressure-strain model yielding an improved distinction between the spanwise and wall normal stresses, although at higher Reynolds number (Re) and away from the wall, the streamwise component is severely underpredicted, as well as the transition in the mean velocity from the log to the wake profiles. In this area a significant change of behavior was observed in the DNS pressure-strain term, entirely ignored in the models.
Validating a turbulence closure against estuarine microstructure measurements
NASA Astrophysics Data System (ADS)
Peters, Hartmut; Baumert, Helmut Z.
A simple k- ɛ turbulence closure is introduced which has no stability functions but instead a Richardson number-dependent turbulent Prandtl number. Its free parameters are determined in a comparison with microstructure observations from a stratified and sheared tidal estuary and laboratory measurements. The closure is able to simulate observed turbulent dissipation rates ( ɛ) and turbulent length scales ( lth) in regions of strong mean shear and small gradient Richardson number ( Rg) to within factors of 2-3. It fails in regions of small shear and large Rg, presumably because of the dominance of internal wave-driven mixing. Additional simulations with a k- ɛ closure with stability functions taken from Canuto et al. [Canuto, V.M., Howard, A., Cheng, Y., Dubovikov, M.S., 2001. Ocean turbulence I: one-point closure model. Momentum and heat vertical diffusivities. J. Phys. Oceanogr. 31, 1413-1426] and with the closure of Baumert and Peters [Baumert, H., Peters, H., 2004. Turbulence closure, steady state, and collapse into waves. J. Phys. Oceanogr. 34, 505-512] show poor performance. Establishing a valid 1:1 comparison of simulated and observed ɛ and lth requires nudging the model velocity and density toward observed values because free model integrations quickly diverge from the observations. Steady state gradient Richardson numbers are constrained to a range of 0.18-0.25, while flux Richardson numbers are constrained to the range of 0.1-0.22. The closure output is rather insensitive to such parameter variations. The simulations are sensitive, however, to the treatment of the observed velocity and density used to nudge the model. Good closure performance requires averaging the measured tidal flow over about an hour, a time scale for which conventional numerical models of estuarine circulations should be able to match observed shears. In the closure simulations the TKE balance stays close to a production-dissipation balance. The time rate of change and vertical
Contribution to the second-moment modeling of sublayer turbulent transport
NASA Astrophysics Data System (ADS)
Launder, B. E.; Tselepidakis, D. P.
The paper examines the question of developing a full second-moment closure within the viscosity affected sublayer near a wall. The effects of different processes are considered in turn. For the influential pressure-strain process, new forms are adopted that have emerged from research at UMIST on free shear flows. Results indicate the importance of the strongly nonisotropic nature of the dissipation process and the role of pressure-driven transport of both Reynolds stress and the turbulence energy dissipation rate. The question of whether the turbulence Reynolds number must be retained as a parameter in the pressure-containing correlations remains unresolved though, if it does, its influence will be less important than in earlier closure proposals.
Fairweather, M.; Woolley, R.M.
2007-07-15
Presented are results obtained from the application of a first- and higher-order conditional moment closure (CMC) approach to the modeling of three methane diffusion flames at differing levels of local extinction. In addition to the analysis of higher-order chemistry applications, the results obtained from an elliptic formulation of the CMC equation are considered next to parabolic results presented in previous work. All predictions are based upon second-moment turbulence and scalar-flux closures, and the chemistry applied to represent mean production rates of species is a 16-step reduced mechanism. A second-order chemistry is implemented on the basis of a two-step kinetic representation of methane combustion, used to correct first-order rates. In general, predictions obtained using the second-order model improve significantly upon first-order results for both major and minor species under fuel-rich conditions. The simplified chemistry employed does not however fully capture the effects of local extinction, and suggestions are made regarding the further developments required to permit the accurate prediction of highly strained flames using CMC methods. (author)
Turbulent fluid motion IV-averages, Reynolds decomposition, and the closure problem
NASA Technical Reports Server (NTRS)
Deissler, Robert G.
1992-01-01
Ensemble, time, and space averages as applied to turbulent quantities are discussed, and pertinent properties of the averages are obtained. Those properties, together with Reynolds decomposition, are used to derive the averaged equations of motion and the one- and two-point moment or correlation equations. The terms in the various equations are interpreted. The closure problem of the averaged equations is discussed, and possible closure schemes are considered. Those schemes usually require an input of supplemental information unless the averaged equations are closed by calculating their terms by a numerical solution of the original unaveraged equations. The law of the wall for velocities and temperatures, the velocity- and temperature-defect laws, and the logarithmic laws for velocities and temperatures are derived. Various notions of randomness and their relation to turbulence are considered in light of ergodic theory.
Compressibility Corrections to Closure Approximations for Turbulent Flow Simulations
Cloutman, L D
2003-02-01
We summarize some modifications to the usual closure approximations for statistical models of turbulence that are necessary for use with compressible fluids at all Mach numbers. We concentrate here on the gradient-flu approximation for the turbulent heat flux, on the buoyancy production of turbulence kinetic energy, and on a modification of the Smagorinsky model to include buoyancy. In all cases, there are pressure gradient terms that do not appear in the incompressible models and are usually omitted in compressible-flow models. Omission of these terms allows unphysical rates of entropy change.
Moment Closure Approximations of the Boltzmann Equation Based on \\varphi -Divergences
NASA Astrophysics Data System (ADS)
Abdelmalik, M. R. A.; van Brummelen, E. H.
2016-07-01
This paper is concerned with approximations of the Boltzmann equation based on the method of moments. We propose a generalization of the setting of the moment-closure problem from relative entropy to \\varphi -divergences and a corresponding closure procedure based on minimization of \\varphi -divergences. The proposed description encapsulates as special cases Grad's classical closure based on expansion in Hermite polynomials and Levermore's entropy-based closure. We establish that the generalization to divergence-based closures enables the construction of extended thermodynamic theories that avoid essential limitations of the standard moment-closure formulations such as inadmissibility of the approximate phase-space distribution, potential loss of hyperbolicity and singularity of flux functions at local equilibrium. The divergence-based closure leads to a hierarchy of tractable symmetric hyperbolic systems that retain the fundamental structural properties of the Boltzmann equation.
New results on the realizability of Reynolds stress turbulence closures
NASA Technical Reports Server (NTRS)
Speziale, Charles G.; Abid, Ridha; Durbin, Paul A.
1993-01-01
The realizability of Reynolds stress models in homogeneous turbulence is critically assessed from a theoretical standpoint. It is proven that a well known second-order closure formulated by Shih and Lumley using the strong realizability constraints of Schumann is, in fact, not a realizable model. The problem arises from the failure to properly satisfy the necessary positive second time derivative constraint when a principal Reynolds stress vanishes - a fatal flaw that becomes apparent when the non-analytic terms in their model are made single-valued as required on physical grounds. It is furthermore shown that the centrifugal acceleration generated by rotations of the principal axes of the Reynolds stress tensor can make the second derivative singular at the most extreme limits of realizable turbulence. This previously overlooked effect appears to make it impossible to identically satisfy the strong form of realizability in any version of the present generation of second-order closures. On the other hand, models properly formulated to satisfy the weak form of realizability - wherein states of one or two component turbulence are not accessible in finite time are found to be realizable. However, unlike the simpler and more commonly used second order closures, these models can be ill-behaved near the extreme limits of realizable turbulence due to the way that higher-degree nonlinearities are often unnecessarily introduced to satisfy realizability. Illustrative computations of homogeneous shear flows are presented to demonstrate these points which can have important implications for turbulence modeling.
On the relation between the conditional moment closure and unsteady flamelets
NASA Astrophysics Data System (ADS)
Klimenko, A. Y.
2001-09-01
We consider the relation between the conditional moment closure (CMC) and the unsteady flamelet model (FM). The CMC equations were originally constructed as global equations, while FM was derived asymptotically for a thin reaction zone. The recent tendency is to use FM-type equations as global equations. We investigate the possible consequences and suggest a new version of FM: coordinate-invariant FM (CIFM). Unlike FM, CIFM complies with conditional properties of the exact transport equations which are used effectively in CMC. We analyse the assumptions needed to obtain another global version of FM: representative interactive flamelets (RIF), from original FM and demonstrate that, in homogeneous turbulence, one of these assumptions is equivalent to the main CMC hypothesis.
Visibility moments and power spectrum of turbulence velocity
NASA Astrophysics Data System (ADS)
Dutta, Prasun
2016-02-01
Here we introduce moments of visibility function and discuss how those can be used to estimate the power spectrum of the turbulent velocity of external spiral galaxies. We perform numerical simulation to confirm the credibility of this method and found that for galaxies with lower inclination angles it works fine. The estimator outlined here is unbiased and has the potential to recover the turbulent velocity spectrum completely from radio interferometric observations.
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.
Inertial-particle accelerations in turbulence: a Lagrangian closure
NASA Astrophysics Data System (ADS)
Vajedi, S.; Gustavsson, K.; Mehlig, B.; Biferale, L.
2016-07-01
The distribution of particle accelerations in turbulence is intermittent, with non-Gaussian tails that are quite different for light and heavy particles. In this article we analyse a closure scheme for the acceleration fluctuations of light and heavy inertial particles in turbulence, formulated in terms of Lagrangian correlation functions of fluid tracers. We compute the variance and the flatness of inertial particle accelerations and we discuss their dependency on the Stokes number. The closure incorporates effects induced by the Lagrangian correlations along the trajectories of fluid tracers, and its predictions agree well with results of direct numerical simulations of inertial particles in turbulence, provided that the effects induced by the inertial preferential sampling of heavy/light particles outside/inside vortices are negligible. In particular, the scheme predicts the correct functional behaviour of the acceleration variance, as a function of Stokes, as well as the presence of a minimum/maximum for the flatness of the acceleration of heavy/light particles, in good qualitative agreement with numerical data. We also show that the closure works well when applied to the Lagrangian evolution of particles using a stochastic surrogate for the underlying Eulerian velocity field. Our results support the conclusion that there exist important contributions to the statistics of the acceleration of inertial particles independent of the preferential sampling. For heavy particles we observe deviations between the predictions of the closure scheme and direct numerical simulations, at Stokes numbers of order unity. For light particles the deviation occurs for larger Stokes numbers.
Assessment of Higher-Order RANS Closures in a Decelerated Planar Wall-Bounded Turbulent Flow
NASA Technical Reports Server (NTRS)
Jeyapaul, Elbert; Coleman, Gary N.; Rumsey, Christopher L.
2014-01-01
A reference DNS database is presented, which includes third- and fourth-order moment budgets for unstrained and strained planar channel flow. Existing RANS closure models for third- and fourth-order terms are surveyed, and new model ideas are introduced. The various models are then compared with the DNS data term by term using a priori testing of the higher-order budgets of turbulence transport, velocity-pressure-gradient, and dissipation for both the unstrained and strained databases. Generally, the models for the velocity-pressure-gradient terms are most in need of improvement.
Derivation of the conditional moment closure equations for spray combustion
Mortensen, Mikael; Bilger, Robert W.
2009-01-15
In this work we derive the fundamental equations for conditional moment closure (CMC) modelling of individual phases set in a two-phase flow. The derivation is based on the instantaneous transport equations for the single phase that involve a level set/indicator function technique for accounting for interfaces. Special emphasis is put on spray combustion with the CMC equations formulated for the gas phase. The CMC equations are to be viewed as an adjunct to existing methods for the modelling of the dynamics of sprays: they provide a refinement of the modelling of chemical reactions in the gas phase. The resulting CMC equations differ significantly from those already in use in the literature. They contain, of course, unclosed terms that need to be modelled. Investigation of the unclosed terms associated with evaporation at the droplet surface is well beyond the capabilities of laboratory measurement or direct numerical simulation. It is proposed that modelling of these terms be based on the well-established 'laws' of similarity between heat and mass transfer: an example is detailed for one example of the general modelling of the spray dynamics. Other unclosed terms are important throughout the gas phase. Models used for these terms in single-phase flows are reviewed and it is proposed that any modifications needed for these models be investigated by DNS of suitable model problems having good resolution of the flow and mixing in the inter-droplet space. It is proposed that a spray analogue of the scalar mixing layer that has been widely studied in single-phase flows be used as the model problem for such DNS studies and also for LES and RANS modelling. (author)
Some Results Relevant to Statistical Closures for Compressible Turbulence
NASA Technical Reports Server (NTRS)
Ristorcelli, J. R.
1998-01-01
For weakly compressible turbulent fluctuations there exists a small parameter, the square of the fluctuating Mach number, that allows an investigation using a perturbative treatment. The consequences of such a perturbative analysis in three different subject areas are described: 1) initial conditions in direct numerical simulations, 2) an explanation for the oscillations seen in the compressible pressure in the direct numerical simulations of homogeneous shear, and 3) for turbulence closures accounting for the compressibility of velocity fluctuations. Initial conditions consistent with small turbulent Mach number asymptotics are constructed. The importance of consistent initial conditions in the direct numerical simulation of compressible turbulence is dramatically illustrated: spurious oscillations associated with inconsistent initial conditions are avoided, and the fluctuating dilatational field is some two orders of magnitude smaller for a compressible isotropic turbulence. For the isotropic decay it is shown that the choice of initial conditions can change the scaling law for the compressible dissipation. A two-time expansion of the Navier-Stokes equations is used to distinguish compressible acoustic and compressible advective modes. A simple conceptual model for weakly compressible turbulence - a forced linear oscillator is described. It is shown that the evolution equations for the compressible portions of turbulence can be understood as a forced wave equation with refraction. Acoustic modes of the flow can be amplified by refraction and are able to manifest themselves in large fluctuations of the compressible pressure.
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
Moment closures based on minimizing the residual of the PN angular expansion in radiation transport
NASA Astrophysics Data System (ADS)
Zheng, Weixiong; McClarren, Ryan G.
2016-06-01
In this work we present two new closures for the spherical harmonics (PN) method in slab geometry transport problems. Our approach begins with an analysis of the squared-residual of the transport equation where we show that the standard truncation and diffusive closures do not minimize the residual of the PN expansion. Based on this analysis we derive two models, a moment-limited diffusive (ML DN) closure and a transient PN (TPN) closure that attempt to address shortcomings of common closures. The form of these closures is similar to flux-limiters for diffusion with the addition of a time-derivative in the definition of the closure. Numerical results on a pulsed plane source problem, the Gordian knot of slab-geometry transport problems, indicate that our new closure outperforms existing linear closures. Additionally, on a deep penetration problem we demonstrate that the TPN closure does not suffer from the artificial shocks that can arise in the MN entropy-based closure. Finally, results for Reed's problem demonstrate that the TPN solution is as accurate as the PN+3 solution. We further extend the TPN closure to 2D Cartesian geometry. The line source test problem demonstrates the model effectively damps oscillations and negative densities.
Vector Third Moment of Turbulent MHD Fluctuations: Theory and Interpretation
NASA Astrophysics Data System (ADS)
Forman, M. A.; MacBride, B. T.; Smith, C. W.
2006-12-01
We call attention to the fact that a certain vector third moment of turbulent MHD fluctuations, even if they are anisotropic, obeys an exact scaling relation in the inertial range. Politano and Pouquet (1998, PP) proved it from the MHD equations specifically. It is a direct analog of the long-known von Karman-Howarth-Monin (KHM) vector relation in anisotropic hydrodynamic turbulence, which follows from the Navier-Stokes equations (see Frisch, 1995). The relevant quantities in MHD are the plus and minus Elsasser vectors and their fluctuations over vector spatial differences. These are used in the mixed vector third moment S+/-(r). The mixed moment is essential, because in the MHD equations for the Elsasser variables, the z + and z- are mixed in the non-linear term. The PP relation is div (S+/-(r))= -4*(epsilon +/-) where (epsilon +/-) is the turbulent energy dissipation rate in the +/- cascade, in Joules/(kg-sec). Of the many possible vector and tensor third moments of MHD vector fluctuations, S+/-(r) is the only one known to have an exact (although vector differential) scaling valid in anisotropic MHD in the inertial range. The PP scaling of a distinctly non-zero third moment indicates that an inertial range cascade is present. The PP scaling does NOT simply result from a dimensional argument, but is derived directly from the MHD equations. A power-law power spectrum alone does not necessarily imply an inertial cascade is present. Furthermore, only the scaling of S+/-(r) gives the epsilon +/- directly. Earlier methods of determining epsilon +/-, based on the amplitude of the power spectrum, make assumptions about isotropy, Alfvenicity and scaling that are not exact. Thus, the observation of a finite S+/-(r) and its scaling with vector r, are fundamental to MHD turbulence in the solar wind, or in any magnetized plasma. We are engaged in evaluating S+/-(r )and its anisotropic scaling in the solar wind, beginning with ACE field and plasma data. For this, we are using
NASA Technical Reports Server (NTRS)
Ristorcelli, J. R.
1993-01-01
The turbulent mass flux, or equivalently the fluctuating Favre velocity mean, appears in the first and second moment equations of compressible kappa-epsilon and Reynolds stress closures. Mathematically it is the difference between the unweighted and density-weighted averages of the velocity field and is therefore a measure of the effects of compressibility through variations in density. It appears to be fundamental to an inhomogeneous compressible turbulence, in which it characterizes the effects of the mean density gradients, in the same way the anisotropy tensor characterizes the effects of the mean velocity gradients. An evolution equation for the turbulent mass flux is derived. A truncation of this equation produces an algebraic expression for the mass flux. The mass flux is found to be proportional to the mean density gradients with a tensor eddy-viscosity that depends on both the mean deformation and the Reynolds stresses. The model is tested in a wall bounded DNS at Mach 4.5 with notable results.
Exact and approximate moment closures for non-Markovian network epidemics.
Pellis, Lorenzo; House, Thomas; Keeling, Matt J
2015-10-01
Moment-closure techniques are commonly used to generate low-dimensional deterministic models to approximate the average dynamics of stochastic systems on networks. The quality of such closures is usually difficult to asses and furthermore the relationship between model assumptions and closure accuracy are often difficult, if not impossible, to quantify. Here we carefully examine some commonly used moment closures, in particular a new one based on the concept of maximum entropy, for approximating the spread of epidemics on networks by reconstructing the probability distributions over triplets based on those over pairs. We consider various models (SI, SIR, SEIR and Reed-Frost-type) under Markovian and non-Markovian assumption characterising the latent and infectious periods. We initially study with care two special networks, namely the open triplet and closed triangle, for which we can obtain analytical results. We then explore numerically the exactness of moment closures for a wide range of larger motifs, thus gaining understanding of the factors that introduce errors in the approximations, in particular the presence of a random duration of the infectious period and the presence of overlapping triangles in a network. We also derive a simpler and more intuitive proof than previously available concerning the known result that pair-based moment closure is exact for the Markovian SIR model on tree-like networks under pure initial conditions. We also extend such a result to all infectious models, Markovian and non-Markovian, in which susceptibles escape infection independently from each infected neighbour and for which infectives cannot regain susceptible status, provided the network is tree-like and initial conditions are pure. This works represent a valuable step in enriching intuition and deepening understanding of the assumptions behind moment closure approximations and for putting them on a more rigorous mathematical footing. PMID:25975999
A 3-D multiband closure for radiation and neutron transfer moment models
Ripoll, J.-F. Wray, A.A.
2008-02-01
We derive a 3D multi-band moment model and its associated closure for radiation and neutron transfer. The new closure is analytical and nonlinear but very simple. Its derivation is based on the maximum entropy closure and assumes a Wien shape for the intensity when used in the Eddington tensor. In the multi-band approach, the opacity is re-arranged (binned) according to the opacity value. The multi-band model propagates identically all photons/neutrons having the same opacity. This has been found to be a good approximation on average since the transport is mostly determined by the opacities and less by the frequencies. This same concept is used to derive the closure. We prove on two complex test atmospheres (the solar atmosphere and an artificial atmosphere) that the closure we have derived has good accuracy. All approximations made in deriving the model have been carefully numerically checked and quantified.
NASA Astrophysics Data System (ADS)
Wright, Y. M.; Bolla, M.; Boulouchos, K.; Borghesi, G.; Mastorakos, E.
2015-01-01
Energy conversion devices of practical interest such as engines or combustors operate in highly turbulent flow regimes. Due to the nature of the hydrocarbon fuels employed, the oxidation chemistry involves a broad range of time-scales some of which cannot be decoupled from the flow. Among the approaches utilised to tackle the modelling of turbulent combustion, Conditional Moment Closure (CMC), belonging to the computationally efficient class of presumed PDF methods, has shown great potential. For single-phase flows it has been demonstrated on non-premixed turbulent lifted and opposed jets, lifted flames and auto-igniting jets. Here we seek to review recent advances in both modelling and application of CMC for auto-ignition of fuel sprays. The experiments chosen for code validation and model improvement include generic spray test rigs with dimensions of passenger car as well as large two-stroke marine engines. Data for a broad range of operating conditions of a heavy-duty truck engine is additionally employed to assess the predictive capability of the model with respect to NOx emissions. An outlook on future enhancements including e.g. LES-CMC formulation also for two-phase flows as well as developments in the field of soot emissions are summarised briefly.
Complete hierarchies of SIR models on arbitrary networks with exact and approximate moment closure.
Sharkey, Kieran J; Wilkinson, Robert R
2015-06-01
We first generalise ideas discussed by Kiss et al. (2015) to prove a theorem for generating exact closures (here expressing joint probabilities in terms of their constituent marginal probabilities) for susceptible-infectious-removed (SIR) dynamics on arbitrary graphs (networks). For Poisson transmission and removal processes, this enables us to obtain a systematic reduction in the number of differential equations needed for an exact 'moment closure' representation of the underlying stochastic model. We define 'transmission blocks' as a possible extension of the block concept in graph theory and show that the order at which the exact moment closure representation is curtailed is the size of the largest transmission block. More generally, approximate closures of the hierarchy of moment equations for these dynamics are typically defined for the first and second order yielding mean-field and pairwise models respectively. It is frequently implied that, in principle, closed models can be written down at arbitrary order if only we had the time and patience to do this. However, for epidemic dynamics on networks, these higher-order models have not been defined explicitly. Here we unambiguously define hierarchies of approximate closed models that can utilise subsystem states of any order, and show how well-known models are special cases of these hierarchies. PMID:25829147
Comparison of different moment-closure approximations for stochastic chemical kinetics.
Schnoerr, David; Sanguinetti, Guido; Grima, Ramon
2015-11-14
In recent years, moment-closure approximations (MAs) of the chemical master equation have become a popular method for the study of stochastic effects in chemical reaction systems. Several different MA methods have been proposed and applied in the literature, but it remains unclear how they perform with respect to each other. In this paper, we study the normal, Poisson, log-normal, and central-moment-neglect MAs by applying them to understand the stochastic properties of chemical systems whose deterministic rate equations show the properties of bistability, ultrasensitivity, and oscillatory behaviour. Our results suggest that the normal MA is favourable over the other studied MAs. In particular, we found that (i) the size of the region of parameter space where a closure gives physically meaningful results, e.g., positive mean and variance, is considerably larger for the normal closure than for the other three closures, (ii) the accuracy of the predictions of the four closures (relative to simulations using the stochastic simulation algorithm) is comparable in those regions of parameter space where all closures give physically meaningful results, and (iii) the Poisson and log-normal MAs are not uniquely defined for systems involving conservation laws in molecule numbers. We also describe the new software package MOCA which enables the automated numerical analysis of various MA methods in a graphical user interface and which was used to perform the comparative analysis presented in this paper. MOCA allows the user to develop novel closure methods and can treat polynomial, non-polynomial, as well as time-dependent propensity functions, thus being applicable to virtually any chemical reaction system. PMID:26567686
Comparison of different moment-closure approximations for stochastic chemical kinetics
NASA Astrophysics Data System (ADS)
Schnoerr, David; Sanguinetti, Guido; Grima, Ramon
2015-11-01
In recent years, moment-closure approximations (MAs) of the chemical master equation have become a popular method for the study of stochastic effects in chemical reaction systems. Several different MA methods have been proposed and applied in the literature, but it remains unclear how they perform with respect to each other. In this paper, we study the normal, Poisson, log-normal, and central-moment-neglect MAs by applying them to understand the stochastic properties of chemical systems whose deterministic rate equations show the properties of bistability, ultrasensitivity, and oscillatory behaviour. Our results suggest that the normal MA is favourable over the other studied MAs. In particular, we found that (i) the size of the region of parameter space where a closure gives physically meaningful results, e.g., positive mean and variance, is considerably larger for the normal closure than for the other three closures, (ii) the accuracy of the predictions of the four closures (relative to simulations using the stochastic simulation algorithm) is comparable in those regions of parameter space where all closures give physically meaningful results, and (iii) the Poisson and log-normal MAs are not uniquely defined for systems involving conservation laws in molecule numbers. We also describe the new software package MOCA which enables the automated numerical analysis of various MA methods in a graphical user interface and which was used to perform the comparative analysis presented in this paper. MOCA allows the user to develop novel closure methods and can treat polynomial, non-polynomial, as well as time-dependent propensity functions, thus being applicable to virtually any chemical reaction system.
Comparison of different moment-closure approximations for stochastic chemical kinetics
Schnoerr, David; Sanguinetti, Guido; Grima, Ramon
2015-11-14
In recent years, moment-closure approximations (MAs) of the chemical master equation have become a popular method for the study of stochastic effects in chemical reaction systems. Several different MA methods have been proposed and applied in the literature, but it remains unclear how they perform with respect to each other. In this paper, we study the normal, Poisson, log-normal, and central-moment-neglect MAs by applying them to understand the stochastic properties of chemical systems whose deterministic rate equations show the properties of bistability, ultrasensitivity, and oscillatory behaviour. Our results suggest that the normal MA is favourable over the other studied MAs. In particular, we found that (i) the size of the region of parameter space where a closure gives physically meaningful results, e.g., positive mean and variance, is considerably larger for the normal closure than for the other three closures, (ii) the accuracy of the predictions of the four closures (relative to simulations using the stochastic simulation algorithm) is comparable in those regions of parameter space where all closures give physically meaningful results, and (iii) the Poisson and log-normal MAs are not uniquely defined for systems involving conservation laws in molecule numbers. We also describe the new software package MOCA which enables the automated numerical analysis of various MA methods in a graphical user interface and which was used to perform the comparative analysis presented in this paper. MOCA allows the user to develop novel closure methods and can treat polynomial, non-polynomial, as well as time-dependent propensity functions, thus being applicable to virtually any chemical reaction system.
A k-{\\varepsilon} turbulence closure model of an isothermal dry granular dense matter
NASA Astrophysics Data System (ADS)
Fang, Chung
2016-07-01
The turbulent flow characteristics of an isothermal dry granular dense matter with incompressible grains are investigated by the proposed first-order k-{\\varepsilon} turbulence closure model. Reynolds-filter process is applied to obtain the balance equations of the mean fields with two kinematic equations describing the time evolutions of the turbulent kinetic energy and dissipation. The first and second laws of thermodynamics are used to derive the equilibrium closure relations satisfying turbulence realizability conditions, with the dynamic responses postulated by a quasi-linear theory. The established closure model is applied to analyses of a gravity-driven stationary flow down an inclined moving plane. While the mean velocity decreases monotonically from its value on the moving plane toward the free surface, the mean porosity increases exponentially; the turbulent kinetic energy and dissipation evolve, respectively, from their minimum and maximum values on the plane toward their maximum and minimum values on the free surface. The evaluated mean velocity and porosity correspond to the experimental outcomes, while the turbulent dissipation distribution demonstrates a similarity to that of Newtonian fluids in turbulent shear flows. When compared to the zero-order model, the turbulent eddy evolution tends to enhance the transfer of the turbulent kinetic energy and plane shearing across the flow layer, resulting in more intensive turbulent fluctuation in the upper part of the flow. Solid boundary as energy source and sink of the turbulent kinetic energy becomes more apparent in the established first-order model.
A k-{\\varepsilon} turbulence closure model of an isothermal dry granular dense matter
NASA Astrophysics Data System (ADS)
Fang, Chung
2015-07-01
The turbulent flow characteristics of an isothermal dry granular dense matter with incompressible grains are investigated by the proposed first-order k-{\\varepsilon} turbulence closure model. Reynolds-filter process is applied to obtain the balance equations of the mean fields with two kinematic equations describing the time evolutions of the turbulent kinetic energy and dissipation. The first and second laws of thermodynamics are used to derive the equilibrium closure relations satisfying turbulence realizability conditions, with the dynamic responses postulated by a quasi-linear theory. The established closure model is applied to analyses of a gravity-driven stationary flow down an inclined moving plane. While the mean velocity decreases monotonically from its value on the moving plane toward the free surface, the mean porosity increases exponentially; the turbulent kinetic energy and dissipation evolve, respectively, from their minimum and maximum values on the plane toward their maximum and minimum values on the free surface. The evaluated mean velocity and porosity correspond to the experimental outcomes, while the turbulent dissipation distribution demonstrates a similarity to that of Newtonian fluids in turbulent shear flows. When compared to the zero-order model, the turbulent eddy evolution tends to enhance the transfer of the turbulent kinetic energy and plane shearing across the flow layer, resulting in more intensive turbulent fluctuation in the upper part of the flow. Solid boundary as energy source and sink of the turbulent kinetic energy becomes more apparent in the established first-order model.
NASA Technical Reports Server (NTRS)
Shih, Tsan-Hsing; Lumley, John L.
1991-01-01
Recently, several second order closure models have been proposed for closing the second moment equations, in which the velocity-pressure gradient (and scalar-pressure gradient) tensor and the dissipation rate tensor are two of the most important terms. In the literature, these correlation tensors are usually decomposed into a so called rapid term and a return-to-isotropy term. Models of these terms have been used in global flow calculations together with other modeled terms. However, their individual behavior in different flows have not been fully examined because they are un-measurable in the laboratory. Recently, the development of direct numerical simulation (DNS) of turbulence has given us the opportunity to do this kind of study. With the direct numerical simulation, we may use the solution to exactly calculate the values of these correlation terms and then directly compare them with the values from their modeled formulations (models). Here, we make direct comparisons of five representative rapid models and eight return-to-isotropy models using the DNS data of forty five homogeneous flows which were done by Rogers et al. (1986) and Lee et al. (1985). The purpose of these direct comparisons is to explore the performance of these models in different flows and identify the ones which give the best performance. The modeling procedure, model constraints, and the various evaluated models are described. The detailed results of the direct comparisons are discussed, and a few concluding remarks on turbulence models are given.
NASA Astrophysics Data System (ADS)
Kadantsev, Evgeny; Fortelius, Carl; Druzhinin, Oleg; Mortikov, Evgeny; Glazunov, Andrey; Zilitinkevich, Sergej
2016-04-01
We examine and validate the EFB turbulence closure model (Zilitinkevich et al., 2013), which is based on the budget equations for basic second moments, namely, two energies: turbulent kinetic energy EK and turbulent potential energy EP, and vertical turbulent fluxes of momentum and potential temperature, τi (i = 1, 2) and Fz. Instead of traditional postulation of down-gradient turbulent transport, the EFB closure determines the eddy viscosity and eddy conductivity from the steady-state version of the budget equations for τi and Fz. Furthermore, the EFB closure involves new prognostic equation for turbulent dissipation time scale tT, and extends the theory to non-steady turbulence regimes accounting for non-gradient and non-local turbulent transports (when the traditional concepts of eddy viscosity and eddy conductivity become generally inconsistent). Our special interest is in asymptotic behavior of the EFB closure in strongly stable stratification. For this purpose, we consider plane Couette flow, namely, the flow between two infinite parallel plates, one of which is moving relative to another. We use a set of Direct Numerical Simulation (DNS) experiments at the highest possible Reynolds numbers for different bulk Richardson numbers (Druzhinin et al., 2015). To demonstrate potential improvements in Numerical Weather Prediction models, we test the new closure model in various idealized cases, varying stratification from the neutral and conventionally neutral to stable (GABLS1) running a test RANS model and HARMONIE/AROME model in single-column mode. Results are compared with DNS and LES (Large Eddy Simulation) runs and different numerical weather prediction models.
Using field inversion to quantify functional errors in turbulence closures
NASA Astrophysics Data System (ADS)
Singh, Anand Pratap; Duraisamy, Karthik
2016-04-01
A data-informed approach is presented with the objective of quantifying errors and uncertainties in the functional forms of turbulence closure models. The approach creates modeling information from higher-fidelity simulations and experimental data. Specifically, a Bayesian formalism is adopted to infer discrepancies in the source terms of transport equations. A key enabling idea is the transformation of the functional inversion procedure (which is inherently infinite-dimensional) into a finite-dimensional problem in which the distribution of the unknown function is estimated at discrete mesh locations in the computational domain. This allows for the use of an efficient adjoint-driven inversion procedure. The output of the inversion is a full-field of discrepancy that provides hitherto inaccessible modeling information. The utility of the approach is demonstrated by applying it to a number of problems including channel flow, shock-boundary layer interactions, and flows with curvature and separation. In all these cases, the posterior model correlates well with the data. Furthermore, it is shown that even if limited data (such as surface pressures) are used, the accuracy of the inferred solution is improved over the entire computational domain. The results suggest that, by directly addressing the connection between physical data and model discrepancies, the field inversion approach materially enhances the value of computational and experimental data for model improvement. The resulting information can be used by the modeler as a guiding tool to design more accurate model forms, or serve as input to machine learning algorithms to directly replace deficient modeling terms.
Optimization and large scale computation of an entropy-based moment closure
Hauck, Cory D.; Hill, Judith C.; Garrett, C. Kristopher
2015-09-10
We present computational advances and results in the implementation of an entropy-based moment closure, M_{N}, in the context of linear kinetic equations, with an emphasis on heterogeneous and large-scale computing platforms. Entropy-based closures are known in several cases to yield more accurate results than closures based on standard spectral approximations, such as P_{N}, but the computational cost is generally much higher and often prohibitive. Several optimizations are introduced to improve the performance of entropy-based algorithms over previous implementations. These optimizations include the use of GPU acceleration and the exploitation of the mathematical properties of spherical harmonics, which are used as test functions in the moment formulation. To test the emerging high-performance computing paradigm of communication bound simulations, we present timing results at the largest computational scales currently available. Lastly, these results show, in particular, load balancing issues in scaling the M_{N} algorithm that do not appear for the P_{N} algorithm. We also observe that in weak scaling tests, the ratio in time to solution of M_{N} to P_{N} decreases.
Optimization and large scale computation of an entropy-based moment closure
Hauck, Cory D.; Hill, Judith C.; Garrett, C. Kristopher
2015-09-10
We present computational advances and results in the implementation of an entropy-based moment closure, MN, in the context of linear kinetic equations, with an emphasis on heterogeneous and large-scale computing platforms. Entropy-based closures are known in several cases to yield more accurate results than closures based on standard spectral approximations, such as PN, but the computational cost is generally much higher and often prohibitive. Several optimizations are introduced to improve the performance of entropy-based algorithms over previous implementations. These optimizations include the use of GPU acceleration and the exploitation of the mathematical properties of spherical harmonics, which are used asmore » test functions in the moment formulation. To test the emerging high-performance computing paradigm of communication bound simulations, we present timing results at the largest computational scales currently available. Lastly, these results show, in particular, load balancing issues in scaling the MN algorithm that do not appear for the PN algorithm. We also observe that in weak scaling tests, the ratio in time to solution of MN to PN decreases.« less
Optimization and large scale computation of an entropy-based moment closure
NASA Astrophysics Data System (ADS)
Kristopher Garrett, C.; Hauck, Cory; Hill, Judith
2015-12-01
We present computational advances and results in the implementation of an entropy-based moment closure, MN, in the context of linear kinetic equations, with an emphasis on heterogeneous and large-scale computing platforms. Entropy-based closures are known in several cases to yield more accurate results than closures based on standard spectral approximations, such as PN, but the computational cost is generally much higher and often prohibitive. Several optimizations are introduced to improve the performance of entropy-based algorithms over previous implementations. These optimizations include the use of GPU acceleration and the exploitation of the mathematical properties of spherical harmonics, which are used as test functions in the moment formulation. To test the emerging high-performance computing paradigm of communication bound simulations, we present timing results at the largest computational scales currently available. These results show, in particular, load balancing issues in scaling the MN algorithm that do not appear for the PN algorithm. We also observe that in weak scaling tests, the ratio in time to solution of MN to PN decreases.
NASA Astrophysics Data System (ADS)
Podesta, J. J.
It is known that Kolmogorov's four-fifths law for statistically homogeneous and isotropic turbulence can be generalized to anisotropic turbulence. This fundamental result for homogeneous anisotropic turbulence says that in the inertial range the divergence of the vector third-order moment |v(r) is constant and is equal to -4, where is the dissipation rate of the turbulence. This law can be extended to incompressible magnetohydrodyamic (MHD) turbulence where statistical isotropy is often not valid due, for example, to the presence of a large-scale magnetic field. Laws for anisotropic incompressible MHD turbulence were first derived by Politano and Pouquet. In this paper, the laws for vector third-order moments in homogeneous non-isotropic incompressible MHD turbulence are derived by a technique due to Frisch that clarifies the relationship between the energy flux in Fourier space and the vector third-order moments in physical space. This derivation is different from the original derivation of Politano and Pouquet which is based on the Kn-Howarth equation, and provides some new physical insights. Separate laws are derived for the cascades of energy, cross-helicity and magnetic-helicity, the three ideal invariants of incompressible MHD for flows in three dimensions. These laws are of fundamental importance in the theory of MHD turbulence where non-isotropic turbulence is much more prevalent than isotropic turbulence.
Simulations of Nocturnal Drainage Flows by a q2l Turbulence Closure Model.
NASA Astrophysics Data System (ADS)
Yamada, T.
1983-01-01
Nocturnal drainage flows observed over a nearly two-dimensional ridge called Rattlesnake Hills near Richland, Washington are simulated by using a simplified turbulence closure model in which only turbulence kinetic energy and turbulence length scale equations are solved prognostically. The present model is slightly simpler than a level 2.5 model which has been extensively used in previous simulations of various atmospheric boundary layer phenomena. Wind and temperature profiles computed by the present model are generally in excellent agreement with observations made by towers erected on the slope of Rattlesnake Hills. Strong coupling between the mean and turbulence variables is also demonstrated.
Simulations of nocturnal drainage flows by a q/sup 2/l turbulence closure model
Yamada, T.
1983-01-01
Nocturnal drainage flows observed over a nearly two-dimensional ridge called Rattlesnake Hills near Richland, Washington are simulated by using a simplified turbulence closure model in which only turbulence kinetic energy and turbulence length scale equations are solved prognostically. The present model is slightly simpler than a level 2.5 model which has been extensively used in previous simulations of various atmospheric boundary layer phenomena. Wind and temperature profiles computed by the present model are generally in excellent agreement with observations made by towers erected on the slope of Rattlesnake Hills. Strong coupling between the mean and turbulence variables is also demonstrated.
Measurements of turbulence moments in boundary layers over transversely grooved surfaces
NASA Technical Reports Server (NTRS)
Bandyopadhyay, P. R.; Watson, R. D.
1987-01-01
Wind tunnel measurements of second, third, and fourth order turbulence moments in turbulent boundary layers over d-types and k-types of grooved and smooth surfaces are discussed. The near-wall turbulence structure is found to vary with the spanwise aspect ratio. For decreasing height, the third moment of the normal velocity fluctuations is shown to become negative over crop canopies and model plant canopies, although not in smooth, two-dimensional, sandgrain or gravel roughness. The instantaneous motions related to the flux of shear stress near the wall in smooth and transversely grooved surfaces are shown to be opposite in sign to those in three-dimensional roughness.
Uncertainty Quantification of Turbulence Model Closure Coefficients for Transonic Wall-Bounded Flows
NASA Technical Reports Server (NTRS)
Schaefer, John; West, Thomas; Hosder, Serhat; Rumsey, Christopher; Carlson, Jan-Renee; Kleb, William
2015-01-01
The goal of this work was to quantify the uncertainty and sensitivity of commonly used turbulence models in Reynolds-Averaged Navier-Stokes codes due to uncertainty in the values of closure coefficients for transonic, wall-bounded flows and to rank the contribution of each coefficient to uncertainty in various output flow quantities of interest. Specifically, uncertainty quantification of turbulence model closure coefficients was performed for transonic flow over an axisymmetric bump at zero degrees angle of attack and the RAE 2822 transonic airfoil at a lift coefficient of 0.744. Three turbulence models were considered: the Spalart-Allmaras Model, Wilcox (2006) k-w Model, and the Menter Shear-Stress Trans- port Model. The FUN3D code developed by NASA Langley Research Center was used as the flow solver. The uncertainty quantification analysis employed stochastic expansions based on non-intrusive polynomial chaos as an efficient means of uncertainty propagation. Several integrated and point-quantities are considered as uncertain outputs for both CFD problems. All closure coefficients were treated as epistemic uncertain variables represented with intervals. Sobol indices were used to rank the relative contributions of each closure coefficient to the total uncertainty in the output quantities of interest. This study identified a number of closure coefficients for each turbulence model for which more information will reduce the amount of uncertainty in the output significantly for transonic, wall-bounded flows.
A numerical study of a separating and reattaching flow by using Reynolds-stress turbulence closure
NASA Technical Reports Server (NTRS)
Amano, R. S.; Goel, P.
1984-01-01
The numerical study of the Reynolds-stress turbulence closure for separating, reattaching, recirculating and redeveloping flow is summarized. The calculations were made for two different closure models of pressure-strain correlation. The results were compared with the experimental data. Furthermore, these results were compared with the computations made by using the one layer and three layer treatment of k-epsilon turbulence model which were developed. Generally the computations by the Reynolds-stress model show better results than those by the k-epsilon model, in particular, some improvement was noticed in the redeveloping region of the separating and reattaching flow in a pipe with sudden expansion.
Analytical methods for the development of Reynolds stress closures in turbulence
NASA Technical Reports Server (NTRS)
Speziale, Charles G.
1990-01-01
Analytical methods for the development of Reynolds stress models in turbulence are reviewed in detail. Zero, one and two equation models are discussed along with second-order closures. A strong case is made for the superior predictive capabilities of second-order closure models in comparison to the simpler models. The central points are illustrated by examples from both homogeneous and inhomogeneous turbulence. A discussion of the author's views concerning the progress made in Reynolds stress modeling is also provided along with a brief history of the subject.
A second-order closure prediction of premixed turbulent combustion in jets
NASA Astrophysics Data System (ADS)
Davé, N.; Kollmann, W.
1987-02-01
In this paper, a numerical prediction is reported involving second-order closure of a turbulent flow of a vertically burning, lean mixture of premixed combustible gases discharging from a pipe and developing into a turbulent combusting roundjet. Classical closures are used where available. Expressions for the chemical reaction rate term and other unclosed terms related to variable density flow in the Favre-averaged turbulent transport equations are based on the Bray-Moss-Libby aerothermochemistry for premixed turbulent combustion, extended to variable enthalpy systems. Mixing of hot burned and cool ambient gases and the attendant buoyancy effects are found to be significant physical phenomena in the behavior of such lean premixed combusting jets. Results of the simulation are compared with experimental data of Yoshida [Proceedings of the Eighteenth International Symposium on Combustion (The Combustion Institute, Pittsburgh, 1981), p. 931] with which reasonable numerical agreement is obtained. Reasons for discrepancies and possible lines for future research are discussed.
Fluid simulation of tokamak ion temperature gradient turbulence with zonal flow closure model
NASA Astrophysics Data System (ADS)
Yamagishi, Osamu; Sugama, Hideo
2016-03-01
Nonlinear fluid simulation of turbulence driven by ion temperature gradient modes in the tokamak fluxtube configuration is performed by combining two different closure models. One model is a gyrofluid model by Beer and Hammett [Phys. Plasmas 3, 4046 (1996)], and the other is a closure model to reproduce the kinetic zonal flow response [Sugama et al., Phys. Plasmas 14, 022502 (2007)]. By including the zonal flow closure, generation of zonal flows, significant reduction in energy transport, reproduction of the gyrokinetic transport level, and nonlinear upshift on the critical value of gradient scale length are observed.
Second-order closure PBL model with new third-order moments: Comparison with LES data
NASA Technical Reports Server (NTRS)
Canuto, V. M.; Minotti, F.; Ronchi, C.; Ypma, R. M.; Zeman, O.
1994-01-01
This paper contains two parts. In the first part, a new set of diagnostic equations is derived for the third-order moments for a buoyancy-driven flow, by exact inversion of the prognostic equations for the third-order moment equations in the stationary case. The third-order moments exhibit a universal structure: they all are a linear combination of the derivatives of all the second-order moments, bar-w(exp 2), bar-w theta, bar-theta(exp 2), and bar-q(exp 2). Each term of the sum contains a turbulent diffusivity D(sub t), which also exhibits a universal structure of the form D(sub t) = a nu(sub t) + b bar-w theta. Since the sign of the convective flux changes depending on stable or unstable stratification, D(sub t) varies according to the type of stratification. Here nu(sub t) approximately equal to wl (l is a mixing length and w is an rms velocity) represents the 'mechanical' part, while the 'buoyancy' part is represented by the convective flux bar-w theta. The quantities a and b are functions of the variable N(sub tau)(exp 2), where N(exp 2) = g alpha derivative of Theta with respect to z and tau is the turbulence time scale. The new expressions for the third-order moments generalize those of Zeman and Lumley, which were subsequently adopted by Sun and Ogura, Chen and Cotton, and Finger and Schmidt in their treatments of the convective boundary layer. In the second part, the new expressions for the third-order moments are used to solve the ensemble average equations describing a purely convective boundary laye r heated from below at a constant rate. The computed second- and third-order moments are then compared with the corresponding Large Eddy Simulation (LES) results, most of which are obtained by running a new LES code, and part of which are taken from published results. The ensemble average results compare favorably with the LES data.
Hamiltonian fluid closures of the Vlasov-Ampère equations: From water-bags to N moment models
Perin, M.; Chandre, C.; Tassi, E.; Morrison, P. J.
2015-09-15
Moment closures of the Vlasov-Ampère system, whereby higher moments are represented as functions of lower moments with the constraint that the resulting fluid system remains Hamiltonian, are investigated by using water-bag theory. The link between the water-bag formalism and fluid models that involve density, fluid velocity, pressure and higher moments is established by introducing suitable thermodynamic variables. The cases of one, two, and three water-bags are treated and their Hamiltonian structures are provided. In each case, we give the associated fluid closures and we discuss their Casimir invariants. We show how the method can be extended to an arbitrary number of fields, i.e., an arbitrary number of water-bags and associated moments. The thermodynamic interpretation of the resulting models is discussed. Finally, a general procedure to derive Hamiltonian N-field fluid models is proposed.
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.
Triantafyllidis, A.; Mastorakos, E.; Eggels, R.L.G.M.
2009-12-15
Large Eddy Simulations (LES) of forced ignition of a bluff-body stabilised non-premixed methane flame using the Conditional Moment Closure (CMC) turbulent combustion model have been performed. The aim is to investigate the feasibility of the use of CMC/LES for ignition problems and to examine which, if any, of the characteristics already observed in related experiments could be predicted. A three-dimensional formulation of the CMC equation was used with simple and detailed chemical mechanisms, and sparks with different parameters (location, size) were used. It was found that the correct pattern of flame expansion and overall flame appearance were predicted with reasonable accuracy with both mechanisms, but the detailed mechanism resulted in expansion rates closer to the experiment. Moreover, the distribution of OH was predicted qualitatively accurately, with patches of high and low concentration in the recirculation zone during the ignition transient, consistent with experimental data. The location of the spark relative to the recirculation zone was found to determine the pattern of the flame propagation and the total time for the flame stabilisation. The size was also an important parameter, since it was found that the flame extinguishes when the spark is very small, in agreement with expectations from experiment. The stabilisation mechanism of the flame was dominated by the convection and sub-grid scale diffusion of hot combustion products from the recirculation zone to the cold gases that enter the burner, as revealed by analysis of the CMC equation. (author)
NASA Astrophysics Data System (ADS)
Cheng, A.; Xu, K.
2013-12-01
This presentation describes the implementation and testing of an advanced third-order turbulence closure, an intermediately-prognostic higher-order turbulence closure (IPHOC), into the Community Atmosphere Model version 5 (CAM5). The third-order turbulence closure introduces a joint double-Gaussian distribution of liquid water potential temperature, total water mixing ratio, and vertical velocity to represent the subgrid scale variations including skewed turbulence circulations. The distribution is inferred from the first-, second-, and third-order moments of the variables given above and is used to diagnose cloud fraction and grid-mean liquid water mixing ratio, as well as the buoyancy term and fourth-order terms in the equations describing the evolution of the second- and third-order moments. In addition, a diagnostic planetary boundary layer (PBL) height approach has been incorporated in IPHOC in order to resolve the strong inversion above PBL for the coarse general circulation model (GCM) vertical grid-spacing. The IPHOC replaces PBL, shallow convection, and cloud macrophysics parameterizations in CAM5. The coupling of CAM5 with IPHOC (CAM5-IP) represents a more unified treatment of boundary layer and shallow convective processes. Results from global climate simulations are presented and suggest that CAM5-IP can provide a better treatment of boundary layer clouds and processes when compared to CAM5. The global annual mean low cloud fraction and precipitation are compared among CAM5, CAM5-IP, and a multi-scale modeling framework model with IPHOC (MMF-IP). The low cloud amounts near the west coast of the subtropical continents are well produced in CAM5-IP and are more abundant than in other two models. The global mean liquid water path is the closest to the SSM/I observation. The cloud structures from CAM5-IP, represented by the cloud fraction and cloud water content at 15°S transect, compare well with the CloudSat/CALIPSO observations. The shallow cumulus
Technology Transfer Automated Retrieval System (TEKTRAN)
The lack of energy closure has been a longstanding issue with Eddy Covariance (EC). Multiple mechanisms have been proposed to explain the discrepancies in energy balance including diurnal energy storage changes, advection of energy, and larger scale turbulent processes that cannot be resolved by fi...
Three-dimensional structures and turbulence closure of the wake developing in a wall shear layer
NASA Technical Reports Server (NTRS)
Hah, C.
1981-01-01
The turbulent wake interacting with the rotating wall shear layer is investigated analytically and numerically. The turbulent wakes of the rotating blades in a compressor which are interacting with the rotating hub-wall boundary layer are analyzed. A modified version of the closure model of the pressure-strain correlation term in the Reynolds stress transport equation is developed to predict the effect of rotation, which is appreciable for the present flow because the thick hub-wall boundary layer is interacting with the rotor wake. It is noted that the Poisson type equation for the pressure-strain correlation has an extra rotation term when the entire flow field is rotating. This extra rotation term is modeled to accommodate the effect of rotation. In addition, the standard correction for the wall effect is incorporated for the utilized Reynolds stress closure model. The rotation-modified Reynolds stress closure model is used to predict the present flow, and the predictions are compared with the experimental data. The experimental data reveal that the characteristics of the three-dimensional turbulent wake interacting with the wall shear layer are considerably altered by the effects of the wall and the rotation. These features are predicted with good accuracy by the turbulence closure model developed.
Navier-Stokes computation of compressible turbulent flows with a second order closure, part 1
NASA Technical Reports Server (NTRS)
Haminh, Hieu; Kollmann, Wolfgang; Vandromme, Dany
1990-01-01
A second order closure turbulence model for compressible flows is developed and implemented in a 2D Reynolds-averaged Navier-Stokes solver. From the beginning where a kappa-epsilon turbulence model was implemented in the bidiagonal implicit method of MACCORMACK (referred to as the MAC3 code) to the final stage of implementing a full second order closure in the efficient line Gauss-Seidel algorithm, numerous work was done, individually and collectively. Besides the collaboration itself, the final product of this work is a second order closure derived from the Launder, Reece, and Rodi model to account for near wall effects, which has been called FRAME model, which stands for FRench-AMerican-Effort. During the reporting period, two different problems were worked out. The first was to provide Ames researchers with a reliable compressible boundary layer code including a wide collection of turbulence models for quick testing of new terms, both in two equations and in second order closure (LRR and FRAME). The second topic was to complete the implementation of the FRAME model in the MAC5 code. The work related to these two different contributions is reported. dilatation in presence of stron shocks. This work, which has been conducted during a work at the Center for Turbulence Research with Zeman aimed also to cros-check earlier assumptions by Rubesin and Vandromme.
About the coupling of turbulence closure models with averaged Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Vandromme, D.; Ha Minh, H.
1986-01-01
The MacCormack implicit predictor-corrector model (1981) for numerical solution of the coupled Navier-Stokes equations for turbulent flows is extended to nonconservative multiequation turbulence models, as well as the inclusion of second-order Reynolds stress turbulence closure. A scalar effective pressure turbulent contribution to the pressure field is defined to approximate the effects of the Reynolds stress in strongly sheared flows. The Jacobian matrices of the transport equations are diagonalized to reduce the required computer memory and run time. Techniques are defined for including turbulence in the diagonalization. Application of the method is demonstrated with solutions generated for transonic nozzle flow and for the interaction between a supersonic flat plate boundary layer and a 12 deg compression-expansion ramp.
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.
Performance of four turbulence closure models implemented using a generic length scale method
Warner, J.C.; Sherwood, C.R.; Arango, H.G.; Signell, R.P.
2005-01-01
A two-equation turbulence model (one equation for turbulence kinetic energy and a second for a generic turbulence length-scale quantity) proposed by Umlauf and Burchard [J. Marine Research 61 (2003) 235] is implemented in a three-dimensional oceanographic model (Regional Oceanographic Modeling System; ROMS v2.0). These two equations, along with several stability functions, can represent many popular turbulence closures, including the k-kl (Mellor-Yamada Level 2.5), k-??, and k-?? schemes. The implementation adds flexibility to the model by providing an unprecedented range of turbulence closure selections in a single 3D oceanographic model and allows comparison and evaluation of turbulence models in an otherwise identical numerical environment. This also allows evaluation of the effect of turbulence models on other processes such as suspended-sediment distribution or ecological processes. Performance of the turbulence models and sediment-transport schemes is investigated with three test cases for (1) steady barotropic flow in a rectangular channel, (2) wind-induced surface mixed-layer deepening in a stratified fluid, and (3) oscillatory stratified pressure-gradient driven flow (estuarine circulation) in a rectangular channel. Results from k-??, k-??, and gen (a new closure proposed by Umlauf and Burchard [J. Marine Research 61 (2003) 235]) are very similar for these cases, but the k-kl closure results depend on a wall-proximity function that must be chosen to suit the flow. Greater variations appear in simulations of suspended-sediment concentrations than in salinity simulations because the transport of suspended-sediment amplifies minor variations in the methods. The amplification is caused by the added physics of a vertical settling rate, bottom stress dependent resuspension, and diffusive transport of sediment in regions of well mixed salt and temperature. Despite the amplified sensitivity of sediment to turbulence models in the estuary test case, the four
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.
NASA Astrophysics Data System (ADS)
Anderson, R. G.; Wang, D.
2012-12-01
Eddy Covariance (EC) is widely used for direct, non-invasive observations of land-atmosphere energy and mass fluxes. However, EC observations of available energy fluxes are usually less than fluxes inferred from radiometer and soil heat flux observations; thus introducing additional uncertainty in using and interpreting EC flux measurements. We compare EC observations from two towers established over sugarcane (Saccharum officinarum L.) in Hawai'i, USA under similar cultivation, temperature, sunlight, and precipitation, but drastically different wind conditions due to orographic effects. At a daily scale, we find that energy closure for both towers occurs on days when the entire 24 hours has sufficient turbulence. At our windier site, this turbulence condition occurs over 60% of the time, which contributes to substantially better daily energy closure (~98%) than at the calmer site (~75%). At our windy site, we then invert the daily energy closure for continuously windy days to calculate canopy energy storage. At full canopy, peak daily canopy energy storage fluxes (200-400 Wm-2) are approximately an order of magnitude larger than soil heat flux (20-40 Wm-2). As a fraction of net radiation, canopy energy storage appears to vary seasonally and shows substantially greater variability than soil heat flux. The results illustrate the importance of sustained turbulence for accurate, direct measurement of land-atmosphere fluxes. As increasing number of EC towers are established in complex terrain, these results indicate the need for preliminary wind studies to optimize tower placement where orography enhances, rather than suppresses, turbulence.
Analytical methods for the development of Reynolds-stress closures in turbulence
NASA Technical Reports Server (NTRS)
Speziale, Charles G.
1991-01-01
The derivation of Reynolds-stress models for viscous incompressible turbulent flow on the basis of the Navier-Stokes and continuity equations is explored in an analytical review. The formulation of the basic equations is outlined, and particular attention is given to zero-equation and one-equation models based on eddy viscosity, two-equation (k-l, k-epsilon, and k-omega) models, and second-order closure models. The superior performance of the second-order models is demonstrated by numerical results for (1) the return to isotropy from anisotropic homogeneous turbulence, (2) homogeneous turbulent shear flow in a rotating frame, (3) and fully developed inhomogeneous turbulent channel flow in a rotating frame. The inherent limitations of the Reynolds-stress approach and areas for further improvement are discussed.
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.
A compressible Navier-Stokes solver with two-equation and Reynolds stress turbulence closure models
NASA Technical Reports Server (NTRS)
Morrison, Joseph H.
1992-01-01
This report outlines the development of a general purpose aerodynamic solver for compressible turbulent flows. Turbulent closure is achieved using either two equation or Reynolds stress transportation equations. The applicable equation set consists of Favre-averaged conservation equations for the mass, momentum and total energy, and transport equations for the turbulent stresses and turbulent dissipation rate. In order to develop a scheme with good shock capturing capabilities, good accuracy and general geometric capabilities, a multi-block cell centered finite volume approach is used. Viscous fluxes are discretized using a finite volume representation of a central difference operator and the source terms are treated as an integral over the control volume. The methodology is validated by testing the algorithm on both two and three dimensional flows. Both the two equation and Reynolds stress models are used on a two dimensional 10 degree compression ramp at Mach 3, and the two equation model is used on the three dimensional flow over a cone at angle of attack at Mach 3.5. With the development of this algorithm, it is now possible to compute complex, compressible high speed flow fields using both two equation and Reynolds stress turbulent closure models, with the capability of eventually evaluating their predictive performance.
Two-Point Turbulence Closure Applied to Variable Resolution Modeling
NASA Technical Reports Server (NTRS)
Girimaji, Sharath S.; Rubinstein, Robert
2011-01-01
Variable resolution methods have become frontline CFD tools, but in order to take full advantage of this promising new technology, more formal theoretical development is desirable. Two general classes of variable resolution methods can be identified: hybrid or zonal methods in which RANS and LES models are solved in different flow regions, and bridging or seamless models which interpolate smoothly between RANS and LES. This paper considers the formulation of bridging methods using methods of two-point closure theory. The fundamental problem is to derive a subgrid two-equation model. We compare and reconcile two different approaches to this goal: the Partially Integrated Transport Model, and the Partially Averaged Navier-Stokes method.
On the consistency of Reynolds stress turbulence closures with hydrodynamic stability theory
NASA Technical Reports Server (NTRS)
Speziale, Charles G.; Abid, Ridha; Blaisdell, Gregory A.
1995-01-01
The consistency of second-order closure models with results from hydrodynamic stability theory is analyzed for the simplified case of homogeneous turbulence. In a recent study, Speziale, Gatski, and MacGiolla Mhuiris showed that second-order closures are capable of yielding results that are consistent with hydrodynamic stability theory for the case of homogeneous shear flow in a rotating frame. It is demonstrated in this paper that this success is due to the fact that the stability boundaries for rotating homogeneous shear flow are not dependent on the details of the spatial structure of the disturbances. For those instances where they are -- such as in the case of elliptical flows where the instability mechanism is more subtle -- the results are not so favorable. The origins and extent of this modeling problem are examined in detail along with a possible resolution based on rapid distortion theory (RDT) and its implications for turbulence modeling.
Quadrature Moments Method for the Simulation of Turbulent Reactive Flows
NASA Technical Reports Server (NTRS)
Raman, Venkatramanan; Pitsch, Heinz; Fox, Rodney O.
2003-01-01
A sub-filter model for reactive flows, namely the DQMOM model, was formulated for Large Eddy Simulation (LES) using the filtered mass density function. Transport equations required to determine the location and size of the delta-peaks were then formulated for a 2-peak decomposition of the FDF. The DQMOM scheme was implemented in an existing structured-grid LES solver. Simulations of scalar shear layer using an experimental configuration showed that the first and second moments of both reactive and inert scalars are in good agreement with a conventional Lagrangian scheme that evolves the same FDF. Comparisons with LES simulations performed using laminar chemistry assumption for the reactive scalar show that the new method provides vast improvements at minimal computational cost. Currently, the DQMOM model is being implemented for use with the progress variable/mixture fraction model of Pierce. Comparisons with experimental results and LES simulations using a single-environment for the progress-variable are planned. Future studies will aim at understanding the effect of increase in environments on predictions.
NASA Astrophysics Data System (ADS)
Jamaly, Seyed Mohammad; Hasan Saidi, Mohammad; Ghafourian, Akbar
2007-11-01
In this study, due to the weaknesses of the models with Lagrangian approaches, an attempt has been made to model the spray flow with Eulerian approach. In this regard, the quadrature-based moment closure model for the spray equation, the so-called DQMOM, is applied. This method overcomes the shortcoming of other Eulerian methods while it is in good agreement with the Lagrangian methods. After that, the model has been developed to be able to deal with the evaporating droplets. Moreover, the feasibility of applying non-linear external forces, such as drag forces, and evaporation laws for the droplets are considered and implemented. The required order for the equations in this method has been studied thoroughly as well. Finally, the solution procedure for accurate computations of multi dimension problems is presented. In general, the proposed modified DQMOM method can consider and solve all kinds of spray flows with any desirable dimension for the problem. Here, assuming one-way coupling situation with the gas-phase in an axial engine, the spray phase equations are solved by the proposed method to account for evaporating droplets. Results are compared with the methods with Lagrangian approach and the computational costs and accuracies of the methods are compared as well.
NASA Astrophysics Data System (ADS)
Ochrymiuk, Tomasz
2016-06-01
Numerical simulations were performed to predict the film cooling effectiveness on the fiat plate with a three- dimensional discrete-hole film cooling arrangement. The effects of basic geometrical characteristics of the holes, i.e. diameter D, length L and pitch S/D were studied. Different turbulent heat transfer models based on constant and variable turbulent Prandtl number approaches were considered. The variability of the turbulent Prandtl number Pr t in the energy equation was assumed using an algebraic relation proposed by Kays and Crawford, or employing the Abe, Kondoh and Nagano eddy heat diffusivity closure with two differential transport equations for the temperature variance k θ and its destruction rate ɛ θ . The obtained numerical results were directly compared with the data that came from an experiment based on Transient Liquid Crystal methodology. All implemented models for turbulent heat transfer performed sufficiently well for the considered case. It was confirmed, however, that the two- equation closure can give a detailed look into film cooling problems without using any time-consuming and inherently unsteady models.
Wang, Minghuai; Larson, Vincent E.; Ghan, Steven J.; Ovchinnikov, Mikhail; Schanen, D.; Xiao, Heng; Liu, Xiaohong; Rasch, Philip J.; Guo, Zhun
2015-06-01
In this study, a higher-order turbulence closure scheme, called Cloud Layers Unified by Binormals (CLUBB), is implemented into a Multi-scale Modeling Framework (MMF) model to improve low cloud simulations. The performance of CLUBB in MMF simulations with two different microphysics configurations (one-moment cloud microphysics without aerosol treatment and two-moment cloud microphysics coupled with aerosol treatment) is evaluated against observations and further compared with results from the Community Atmosphere Model, Version 5 (CAM5) with conventional cloud parameterizations. CLUBB is found to improve low cloud simulations in the MMF, and the improvement is particularly evident in the stratocumulus-to-cumulus transition regions. Compared to the single-moment cloud microphysics, CLUBB with two-moment microphysics produces clouds that are closer to the coast, and agrees better with observations. In the stratocumulus-to cumulus transition regions, CLUBB with two-moment cloud microphysics produces shortwave cloud forcing in better agreement with observations, while CLUBB with single moment cloud microphysics overestimates shortwave cloud forcing. CLUBB is further found to produce quantitatively similar improvements in the MMF and CAM5, with slightly better performance in the MMF simulations (e.g., MMF with CLUBB generally produces low clouds that are closer to the coast than CAM5 with CLUBB). Improved low cloud simulations in MMF make it an even more attractive tool for studying aerosol-cloud-precipitation interactions.
a Second-Order Closure Prediction of Premixed Turbulent Combustion in Jets
NASA Astrophysics Data System (ADS)
Dave, Nikhil
1985-12-01
This thesis is a report on work carried out and results obtained in the prediction of a turbulent flow of premixed combustible gases discharging from a pipe and developing into a turbulent, combusting roundjet. The expressions for the chemical reaction rate term and other unclosed terms in the Favre averaged turbulent transport equations at the level of second-order closure are based on the Bray-Moss-Libby aerothermochemistry for premixed turbulent combustion, extended to variable enthalpy systems as in Bray, Champion, Dave, Libby (referenced herein). The numerical technique used is a parabolic solver developed by Kollmann from the GENMIX program due to Patankar and Spalding. Various test cases such as constant density and variable density jets are calculated using the program and the results are compared herein with experimentally observed values. Results for premixed turbulent combusting jets are compared with experimental data of Yoshida and of Shepherd and Moss. Buoyancy is found to play an important role in the behavior of these primixed combusting jets. Reasonable numerical agreement is obtained with the results of Yoshida, and good qualitative agreement is obtained with the data of Shepherd and Moss. Reasons for the discrepancies and limitations of the numerical simulation are discussed.
Inhomogeneous closure and statistical mechanics for Rossby wave turbulence over topography
NASA Astrophysics Data System (ADS)
Frederiksen, Jorgen S.; O'Kane, Terence J.
2005-09-01
The quasi-diagonal direct interaction approximation (QDIA) closure theory is formulated for the interaction of mean fields, Rossby waves and inhomogeneous turbulence over topography on a generalized beta-plane. An additional small term, corresponding to the solid-body rotation vorticity on the sphere, is included in the barotropic equation and it is shown that this results in a one-to-one correspondence between the dynamical equations, Rossby wave dispersion relations, nonlinear stability criteria and canonical equilibrium theory on the generalized beta-plane and on the sphere. The dynamics, kinetic energy spectra, mean field structures and mean streamfunction tendencies contributed by transient eddies are compared with the ensemble-averaged results from direct numerical simulations (DNS) at moderate resolution. A series of numerical experiments is performed to examine the generation of Rossby waves when eastward large-scale flows impinge on a conical mountain in the presence of moderate to strong two-dimensional turbulence. The ensemble predictability of northern hemisphere flows in 10-day forecasts is also examined on a generalized beta-plane. In all cases, the QDIA closure is found to be in very good agreement with the statistics of DNS except in situations of strong turbulence and weak mean fields where ensemble-averaged DNS fails to predict mean field amplitudes correctly owing to sampling problems even with as many as 1800 ensemble members.
Development of an enstrophy-based two-equation turbulence closure model
NASA Astrophysics Data System (ADS)
Robinson, David Franklin
The development of a new two-equation turbulence closure model based on the exact turbulent kinetic energy, k and the variance of vorticity, or enstrophy, zeta is presented. The primary motivation was to develop a model, applicable to complex three-dimensional flowfields, that employs one set of model constants and does not use damping functions or geometrical factors. Development begins by considering a number of two-dimensional and axisymmetric flowfields in order to determine the appropriate closure coefficients. First, similarity solutions of a variety of both planar and axisymmetric free shear flows are considered. Next, a variety of wall bounded flows are examined beginning with a boundary layer solution of a flat plate and proceeding to the Navier-Stokes solutions for a variety of two-dimensional airfoils. The airfoils considered range from a low speed stalled airfoil to a transonic airfoil with shock induced separation. Final model validation was performed by considering a supersonic three-dimensional Cylinder-Offset flare. In general, good agreement with experiment is indicated. Moreover, the k-zeta model performed, in most cases, as well as or better than the other models. The above objective has been achieved. The current model is shown to accurately predict growth rates as well as similarity profiles of velocity, turbulent kinetic energy, and shear stress for a variety of both planar and axisymmetric free shear flows. Moreover, the model predicts skin-friction, pressure distribution, and shock position with good accuracy for a variety of wall bounded flows, including flows with large adverse pressure gradients and shock induced separation. Also, the current model solves both the free shear and wall bounded flows using only one set of closure coefficients and boundary conditions. Furthermore, the current model is free of wall damping functions and geometrical factors in both the governing equations and in the definition of eddy viscosity. This makes the
A second-order closure analysis of turbulent diffusion flames. [combustion physics
NASA Technical Reports Server (NTRS)
Varma, A. K.; Fishburne, E. S.; Beddini, R. A.
1977-01-01
A complete second-order closure computer program for the investigation of compressible, turbulent, reacting shear layers was developed. The equations for the means and the second order correlations were derived from the time-averaged Navier-Stokes equations and contain third order and higher order correlations, which have to be modeled in terms of the lower-order correlations to close the system of equations. In addition to fluid mechanical turbulence models and parameters used in previous studies of a variety of incompressible and compressible shear flows, a number of additional scalar correlations were modeled for chemically reacting flows, and a typical eddy model developed for the joint probability density function for all the scalars. The program which is capable of handling multi-species, multistep chemical reactions, was used to calculate nonreacting and reacting flows in a hydrogen-air diffusion flame.
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.
Power and Nonpower Laws of Passive Scalar Moments Convected by Isotropic Turbulence
NASA Astrophysics Data System (ADS)
Gotoh, Toshiyuki; Watanabe, Takeshi
2015-09-01
The scaling behavior of the moments of two passive scalars that are excited by two different methods and simultaneously convected by the same isotropic steady turbulence at Rλ=805 and Sc=0.72 is studied by using direct numerical simulation with N =40963 grid points. The passive scalar θ is excited by a random source that is Gaussian and white in time, and the passive scalar q is excited by the mean uniform scalar gradient. In the inertial convective range, the n th-order moments of the scalar increment δ θ (r ) do not obey a simple power law, but have the local scaling exponents ξnθ+βnlog (r /r*) with βn>0 . In contrast, the local scaling exponents of q have well-developed plateaus and saturate with increasing order. The power law of passive scalar moments is not trivial. The universality of passive scalars is found not in the moments, but in the normalized moments.
Power and nonpower laws of passive scalar moments convected by isotropic turbulence.
Gotoh, Toshiyuki; Watanabe, Takeshi
2015-09-11
The scaling behavior of the moments of two passive scalars that are excited by two different methods and simultaneously convected by the same isotropic steady turbulence at R_{λ}=805 and Sc=0.72 is studied by using direct numerical simulation with N=4096^{3} grid points. The passive scalar θ is excited by a random source that is Gaussian and white in time, and the passive scalar q is excited by the mean uniform scalar gradient. In the inertial convective range, the nth-order moments of the scalar increment δθ(r) do not obey a simple power law, but have the local scaling exponents ξ_{n}^{θ}+β_{n}log(r/r_{*}) with β_{n}>0. In contrast, the local scaling exponents of q have well-developed plateaus and saturate with increasing order. The power law of passive scalar moments is not trivial. The universality of passive scalars is found not in the moments, but in the normalized moments. PMID:26406833
Zhou, Ye; Schilling, Oleg; Ghosh, Sanjoy
2002-08-01
The spectral eddy and backscatter viscosity and the spectral eddy and backscatter resistivity for incompressible, three-dimensional, isotropic, nonhelical magnetohydrodynamic (MHD) turbulence are constructed using the eddy-damped quasinormal Markovian statistical closure model developed by Pouquet, Frisch, and Léorat [J. Fluid Mech. 77, 321 (1976)] in terms of primitive variables. The approach used is an extension of the methodology developed by Leslie and Quarini [J. Fluid Mech. 91, 65 (1979)] for fluid turbulence to MHD turbulence. The eddy and backscatter viscosities and the eddy and backscatter resistivities are calculated numerically for assumed kinetic and magnetic energy spectra, E(v)(k) and E(B)(k), with a production subrange and a k(-5/3) inertial subrange for the two cases r(A)=1 and r(A)=1 / 2, where r(A)=E(v)(k)/E(B)(k) is the Alfvén ratio. It is shown that the effects of the unresolved subgrid scales on the resolved-scale velocity and magnetic field consist of an eddy damping and backscatter. The eddy viscosity and resistivity, and the backscatter viscosity and resistivity (the correlation function of the stochastic velocity and magnetic backscatter force) are shown to have a dependence on k/k(c), where k(c) is the cutoff wave number, which is very similar to the dependence calculated in the pure (i.e., nonmagnetic) Navier-Stokes turbulence case. The eddy viscosity and resistivity, and the backscatter viscosity and resistivity numerically calculated here can be used to develop improved subgrid-scale parametrizations for spectral large-eddy simulations of homogenous MHD turbulence. PMID:12241287
NASA Astrophysics Data System (ADS)
Hong, Liu; Yang, Zaibao; Zhu, Yi; Yong, Wen-An
2015-12-01
In this article, we propose a novel approach to construct macroscopic balance equations and constitutive equations describing various irreversible phenomena. It is based on the general principles of non-equilibrium thermodynamics and consists of four basic steps: picking suitable state variables, choosing a strictly concave entropy function, properly separating entropy fluxes and production rates, and determining a dissipation matrix. Our approach takes advantage of both extended irreversible thermodynamics and GENERIC formalisms and shows a direct correspondence with Levermore's moment-closure hierarchies for the Boltzmann equation. As a direct application, a new ten-moment model beyond the classical hierarchies is constructed and is shown to recover the Euler equations in the equilibrium state. These interesting results may put various macroscopic modeling approaches, starting from the general principles of non-equilibrium thermodynamics, on a solid microscopic foundation based on the Boltzmann equation.
NASA Astrophysics Data System (ADS)
Tassi, Emanuele
2014-07-01
We address the problem of the existence of the Hamiltonian structure for an electrostatic drift-kinetic model and for the related fluid models describing the evolution of the first two moments of the distribution function with respect to the parallel velocity. The drift-kinetic model, which accounts for background density and temperature gradients as well as polarization effects, is shown to possess a noncanonical Hamiltonian structure. The corresponding Poisson bracket is expressed in terms of the fluid moments and it is found that the set of functionals of the zero order moment forms a sub-algebra, thus automatically leading to a class of one-moment Hamiltonian fluid models. In particular, in the limit of weak spatial variations of the background quantities, the Charney-Hasegawa-Mima equation, with its Hamiltonian structure, is recovered. For the set of functionals of the first two moments, which, unlike the case of the Vlasov equation, turns out not to form a sub-algebra, we look for closures that lead to a closed Poisson bracket restricted to this set of functionals. The constraint of the Jacobi identity turns out to select the adiabatic equation of state for an ideal gas with one-degree-of-freedom molecules, as the only admissible closure in this sense. When the so called δf ordering is applied to the model, on the other hand, a Poisson bracket is obtained if the second order moment is a linear combination of the first two moments of the total distribution function. By means of this procedure, three-dimensional Hamiltonian fluid models that couple a generalized Charney-Hasegawa-Mima equation with an evolution equation for the parallel velocity are derived. Among these, a model adopted by Meiss and Horton [Phys. Fluids 26, 990 (1983)] to describe drift waves coupled to ion-acoustic waves, is obtained and its Hamiltonian structure is provided explicitly. Contribution to the Topical Issue "Theory and Applications of the Vlasov Equation", edited by Francesco
NASA Technical Reports Server (NTRS)
Johnson, D. A.; King, L. S.
1984-01-01
A new turbulence closure model designed specifically to treat two-dimensional, turbulent boundary layers with strong adverse pressure gradients and attendant separation, is presented. The influence of history effects are modeled by using an ordinary differential equation (ODE) derived from the turbulence kinetic-energy equation, to describe the streamwise development of the maximum Reynolds shear stress in conjunction with an assumed eddy-viscosity distribution which has as its velocity scale the maximum Reynolds shear stress. In the outer part of the boundary layer, the eddy viscosity is treated as a free parameter which is adjusted in order to satisfy the ODE for the maximum shear stress. Because of this, the model s not simply an eddy-viscosity model, but contains features of a Reynolds-stress model. Comparisons with experiments are presented which clearly show the proposed model to be superior to the Cebeci-Smith model in treating strongly retarded and separated flows. In contrast to two-equation, eddy-viscosity models, it requires only slightly more computational effort than simple models like the Cebeci-Smith model.
Raghib, Michael; Hill, Nicholas A; Dieckmann, Ulf
2011-05-01
The prevalence of structure in biological populations challenges fundamental assumptions at the heart of continuum models of population dynamics based only on mean densities (local or global). Individual-based models (IBMs) were introduced during the last decade in an attempt to overcome this limitation by following explicitly each individual in the population. Although the IBM approach has been quite useful, the capability to follow each individual usually comes at the expense of analytical tract ability, which limits the generality of the statements that can be made. For the specific case of spatial structure in populations of sessile (and identical) organisms, space-time point processes with local regulation seem to cover the middle ground between analytical tract ability and a higher degree of biological realism. This approach has shown that simplified representations of fecundity, local dispersal and density-dependent mortality weighted by the local competitive environment are sufficient to generate spatial patterns that mimic field observations. Continuum approximations of these stochastic processes try to distill their fundamental properties, and they keep track of not only mean densities, but also higher order spatial correlations. However, due to the non-linearities involved they result in infinite hierarchies of moment equations. This leads to the problem of finding a 'moment closure'; that is, an appropriate order of (lower order) truncation, together with a method of expressing the highest order density not explicitly modelled in the truncated hierarchy in terms of the lower order densities. We use the principle of constrained maximum entropy to derive a closure relationship for truncation at second order using normalisation and the product densities of first and second orders as constraints, and apply it to one such hierarchy. The resulting 'maxent' closure is similar to the Kirkwood superposition approximation, or 'power-3' closure, but it is
Fast Maximum Entropy Moment Closure Approach to Solving the Boltzmann Equation
NASA Astrophysics Data System (ADS)
Summy, Dustin; Pullin, Dale
2015-11-01
We describe a method for a moment-based solution of the Boltzmann Equation (BE). This is applicable to an arbitrary set of velocity moments whose transport is governed by partial-differential equations (PDEs) derived from the BE. The equations are unclosed, containing both higher-order moments and molecular-collision terms. These are evaluated using a maximum-entropy reconstruction of the velocity distribution function f (c , x , t) , from the known moments, within a finite-box domain of single-particle velocity (c) space. Use of a finite-domain alleviates known problems (Junk and Unterreiter, Continuum Mech. Thermodyn., 2002) concerning existence and uniqueness of the reconstruction. Unclosed moments are evaluated with quadrature while collision terms are calculated using any desired method. This allows integration of the moment PDEs in time. The high computational cost of the general method is greatly reduced by careful choice of the velocity moments, allowing the necessary integrals to be reduced from three- to one-dimensional in the case of strictly 1D flows. A method to extend this enhancement to fully 3D flows is discussed. Comparison with relaxation and shock-wave problems using the DSMC method will be presented. Partially supported by NSF grant DMS-1418903.
Third-Moment Studies of Cascade Dynamics in Solar Wind Turbulence (Invited)
NASA Astrophysics Data System (ADS)
Smith, C. W.; Stawarz, J. E.; Vasquez, B. J.; Forman, M. A.; MacBride, B. T.
2010-12-01
Kolmogorov [1941] and Yaglom [1949] showed that the incompressible hydrodynamic equations governing fluid turbulence could be manipulated to yield a rigorous third-order structure function expression for the energy cascade at inertial range scales. In that derivation the structure function scales linearly with separation distance and the proportionality constant is a factor of the energy cascade rate. For decades it has been argued that the most commonly studied spatial scales for magnetic and velocity fluctuations in the solar wind form an inertial range in an MHD analogy to hydrodynamic turbulence. Politano and Pouquet [1998a,b] and Podesta [2008] derived third-moment expressions for the inertial range cascade in MHD in direct analogy with the earlier hydrodynamic results. We have been exploring the use of these expressions for both isotropic and anisotropic solar wind turbulence [MacBride 2005, 2008; Stawarz 2009, 2010; Smith 2009, 2010; Forman 2010a,b] and find (1) the measured third moments do scale linearly with separation and (2) the resulting estimate for the energy cascade rate accurately account for the energy cascade budget required for turbulence to heat the solar wind. In addition, the anisotropic formalism shows preferential cascade perpendicular to the mean magnetic field. Recent results show the unexpected backward transfer of energy associated with the dominant outward-propagating component when the cross-helicity < δ V \\cdot δ B > is large. The latter behavior is thought to exist over only a limited range of heliocentric distances forming a transient turbulent dynamic near 1 AU. We will include some important comments about the need to monitor convergence and error analyses when using solar wind data. Kolmogorov, 1941, Dokl. Akad. Nauk SSSR, 32, 16. Forman, et al., 2010a, Physical Review Letters, 104, 189001. Forman, et al., 2010b, Solar Wind 12, 176. MacBride, et al., 2005, Solar Wind 11, 613. MacBride, et al., 2008, The Astrophysical Journal
NASA Astrophysics Data System (ADS)
Łobocki, Lech
2014-03-01
Derivation of surface-layer flux-gradient relationships from a local-equilibrium, turbulence-closure model for a forced flow over inclined terrain is presented. Results are shown as a generalization of Monin-Obukhov universal functions respesenting non-dimensional wind and temperature gradients.
NASA Astrophysics Data System (ADS)
Xu, Yonggen; Li, Yude; Dan, Youquan; Du, Quan; Wang, Shijian
2016-07-01
The Wigner distribution function (WDF) has been used to study the propagation properties of partially coherent Laguerre Gaussian (PCLG) beams through atmospheric turbulence. Based on the extended Huygens-Fresnel principle, an analytical formula of the propagation matrixes in terms of the second-order moments of the WDF for PCLG Beams in the receiving plane is derived. And then the analytical formulae for the curvature radii of PCLG Beams propagating in turbulence are given by the second-order moments of the WDF. The numerical results indicate that the curvature radius of PCLG Beams changes more rapidly in turbulence than that in the free space. The influence of the transverse coherence width and the beam waist width on the curvature radius of PCLG Beams is obvious, while the laser wavelength and the inner scale of turbulence have a slight effect. The study results may be useful for remote sensing and free space optical communications.
NASA Astrophysics Data System (ADS)
Grete, Philipp; Vlaykov, Dimitar G.; Schmidt, Wolfram; Schleicher, Dominik R. G.
2016-06-01
Even though compressible plasma turbulence is encountered in many astrophysical phenomena, its effect is often not well understood. Furthermore, direct numerical simulations are typically not able to reach the extreme parameters of these processes. For this reason, large-eddy simulations (LES), which only simulate large and intermediate scales directly, are employed. The smallest, unresolved scales and the interactions between small and large scales are introduced by means of a subgrid-scale (SGS) model. We propose and verify a new set of nonlinear SGS closures for future application as an SGS model in LES of compressible magnetohydrodynamics. We use 15 simulations (without explicit SGS model) of forced, isotropic, homogeneous turbulence with varying sonic Mach number Ms=0.2 -20 as reference data for the most extensive a priori tests performed so far in literature. In these tests, we explicitly filter the reference data and compare the performance of the new closures against the most widely tested closures. These include eddy-viscosity and scale-similarity type closures with different normalizations. Performance indicators are correlations with the turbulent energy and cross-helicity flux, the average SGS dissipation, the topological structure and the ability to reproduce the correct magnitude and the direction of the SGS vectors. We find that only the new nonlinear closures exhibit consistently high correlations (median value > 0.8) with the data over the entire parameter space and outperform the other closures in all tests. Moreover, we show that these results are independent of resolution and chosen filter scale. Additionally, the new closures are effectively coefficient-free with a deviation of less than 20%.
NASA Technical Reports Server (NTRS)
Canuto, V. M.; Dubovikov, M. S.; Howard, A.; Cheng, Y.
1999-01-01
In papers 1 and 2 we have presented the results of the most updated 1-point closure model for the turbulent vertical diffusivities of momentum, heat and salt, K(sub m,h,s). In this paper, we derive the analytic expressions for K(sub m,h,s) using a new 2-point closure model that has recently been developed and successfully tested against some approx. 80 turbulence statistics for different flows. The new model has no free parameters. The expressions for K(sub m, h. s) are analytical functions of two stability parameters: the Turner number R(sub rho) (salinity gradient/temperature gradient) and the Richardson number R(sub i) (temperature gradient/shear). The turbulent kinetic energy K and its rate of dissipation may be taken local or non-local (K-epsilon model). Contrary to all previous models that to describe turbulent mixing below the mixed layer (ML) have adopted three adjustable "background diffusivities" for momentum. heat and salt, we propose a model that avoids such adjustable diffusivities. We assume that below the ML, K(sub m,h,s) have the same functional dependence on R(sub i) and R(sub rho) derived from the turbulence model. However, in order to compute R(sub i) below the ML, we use data of vertical shear due to wave-breaking measured by Gargett et al. (1981). The procedure frees the model from adjustable background diffusivities and indeed we use the same model throughout the entire vertical extent of the ocean. Using the new K(sub m,h, s), we run an O-GCM and present a variety of results that we compare with Levitus and the KPP model. Since the traditional 1-point (used in papers 1 and 2) and the new 2-point closure models used here represent different modeling philosophies and procedures, testing them in an O-GCM is indispensable. The basic motivation is to show that the new 2-point closure model gives results that are overall superior to the 1-point closure in spite of the fact that the latter rely on several adjustable parameters while the new 2-point
Applying an economical scale-aware PDF-based turbulence closure model in NOAA NCEP GCMs.
NASA Astrophysics Data System (ADS)
Krueger, S. K.; Belochitski, A.; Moorthi, S.; Bogenschutz, P.; Pincus, R.
2015-12-01
A novel unified representation of sub-grid scale (SGS) turbulence, cloudiness, and shallow convection is being implemented into the NOAA NCEP Global Forecasting System (GFS) general circulation model. The approach, known as Simplified High Order Closure (SHOC), is based on predicting a joint PDF of SGS thermodynamic variables and vertical velocity and using it to diagnose turbulent diffusion coefficients, SGS fluxes, condensation and cloudiness. Unlike other similar methods, only one new prognostic variable, turbulent kinetic energy (TKE), needs to be intoduced, making the technique computationally efficient.SHOC code was adopted for a global model environment from its origins in a cloud resolving model, and incorporated into NCEP GFS. SHOC was first tested in a non-interactive mode, a configuration where SHOC receives inputs from the host model, but its outputs are not returned to the GFS. In this configuration: a) SGS TKE values produced by GFS SHOC are consistent with those produced by SHOC in a CRM, b) SGS TKE in GFS SHOC exhibits a well defined diurnal cycle, c) there's enhanced boundary layer turbulence in the subtropical stratocumulus and tropical transition-to-cumulus areas d) buoyancy flux diagnosed from the assumed PDF is consistent with independently calculated Brunt-Vaisala frequency in identifying stable and unstable regions.Next, SHOC was coupled to GFS, namely turbulent diffusion coefficients computed by SHOC are now used in place of those currently produced by the GFS boundary layer and shallow convection schemes (Han and Pan, 2011), as well as condensation and cloud fraction diagnosed from the SGS PDF replace those calculated in the current large-scale cloudines scheme (Zhao and Carr, 1997). Ongoing activities consist of debugging the fully coupled GFS/SHOC.Future work will consist of evaluating model performance and tuning the physics if necessary, by performing medium-range NWP forecasts with prescribed initial conditions, and AMIP-type climate
Smith, W.S.; Kao, C.Y.J.
1996-01-01
A high-resolution one-dimensional version of a second-order turbulence closure radiative-convective model, developed at Los Alamos National Laboratory, is used to simulate the interactions among turbulence, radiation, and bulk cloud parameters in stratiform clouds observed during the Arctic Stratus Experiment conducted during June 1980 over the Beaufort Sea. The fidelity of the model to the underlying physics is assessed by comparing the modeled evolution of the cloud-capped boundary layer against data reported for two particular days of observations. Over the period encompassed by these observations, the boundary layer evolved from a well-mixed cloud-capped boundary layer overlying a stable cloudy surface layer to a shallower well-mixed boundary layer with a single upper cloud deck and a clear, diminished, stable surface layer. The model was able to reproduce the observed profiles of the liquid water content, cloud-base height, radiative heating rates, and the mean and turbulence variables over the period of observation fairly well. The formation and eventual dissipation of the surface cloud feature over the period of the simulation was found to be caused by the formation of a stable surface layer as the modeled air mass moved over the relatively cold Beaufort Sea region. Condensation occurred as heat in the surface layer was transported downward toward the sea surface. Eventual dissipation of the surface cloud layer resulted from the transport of moisture in the surface layer downward toward the sea surface. The results show that the subsidence was the major influence on the evolution of the cloud-top height but was not a major factor for dissipation of either cloud layer during the simulation. 17 refs., 9 figs.
Analysis of Highly-Resolved Simulations of 2-D Humps Toward Improvement of Second-Moment Closures
NASA Technical Reports Server (NTRS)
Jeyapaul, Elbert; Rumsey Christopher
2013-01-01
Fully resolved simulation data of flow separation over 2-D humps has been used to analyze the modeling terms in second-moment closures of the Reynolds-averaged Navier- Stokes equations. Existing models for the pressure-strain and dissipation terms have been analyzed using a priori calculations. All pressure-strain models are incorrect in the high-strain region near separation, although a better match is observed downstream, well into the separated-flow region. Near-wall inhomogeneity causes pressure-strain models to predict incorrect signs for the normal components close to the wall. In a posteriori computations, full Reynolds stress and explicit algebraic Reynolds stress models predict the separation point with varying degrees of success. However, as with one- and two-equation models, the separation bubble size is invariably over-predicted.
Quadrature Method of Moments for the Simulation of Turbulent Reacting Flows
NASA Astrophysics Data System (ADS)
Raman, Venkatramanan; Pitsch, Heinz; Fox, Rodney
2003-11-01
Computational schemes for turbulent reacting flow systems typically solve the species transport equations using a grid-based Eulerian technique. Such schemes inherently do not contain information about the sub-grid scalar PDF required for the computation of the non-linear reaction source terms and sub-grid scalar dissipation. Though a transport equation for the scalar PDF can be formulated, the high-dimensional equation has to be solved using a computationally expensive particle-based Lagrangian scheme. To overcome this difficulty, the Direct Quadrature Method of Moments (DQMOM) is used to approximate the joint composition PDF by a set of delta functions. The delta-functions are characterized by their location and size, both of which are obtained by solving Eulerian transport equations. Using a N-peak description, N species-moments can be forced to be accurate. The Direct QMOM model is extended to LES schemes and comparisons are made with transported-PDF simulations for both reacting and non-reacting mixing layer setup. Re-formulation of the DQMOM equation leads to conditional multi-environment method that can be used for describing combustion systems that exhibit extinction.
NASA Astrophysics Data System (ADS)
Soulard, Olivier; Griffond, Jérôme; Gréa, Benoît-Joseph
2016-06-01
The purpose of this paper is to highlight the existence of simple algebraic expressions linking the second order moments of velocity and concentration in Rayleigh-Taylor turbulence, in the Boussinesq limit. Focusing on the concentration variance, these relations allow to underline the influence of mixing on the remaining second order correlations, as well as on the growth rate of the mixing zone.
NASA Technical Reports Server (NTRS)
Cheng, Anning; Xu, Kuan-Man
2006-01-01
The abilities of cloud-resolving models (CRMs) with the double-Gaussian based and the single-Gaussian based third-order closures (TOCs) to simulate the shallow cumuli and their transition to deep convective clouds are compared in this study. The single-Gaussian based TOC is fully prognostic (FP), while the double-Gaussian based TOC is partially prognostic (PP). The latter only predicts three important third-order moments while the former predicts all the thirdorder moments. A shallow cumulus case is simulated by single-column versions of the FP and PP TOC models. The PP TOC improves the simulation of shallow cumulus greatly over the FP TOC by producing more realistic cloud structures. Large differences between the FP and PP TOC simulations appear in the cloud layer of the second- and third-order moments, which are related mainly to the underestimate of the cloud height in the FP TOC simulation. Sensitivity experiments and analysis of probability density functions (PDFs) used in the TOCs show that both the turbulence-scale condensation and higher-order moments are important to realistic simulations of the boundary-layer shallow cumuli. A shallow to deep convective cloud transition case is also simulated by the 2-D versions of the FP and PP TOC models. Both CRMs can capture the transition from the shallow cumuli to deep convective clouds. The PP simulations produce more and deeper shallow cumuli than the FP simulations, but the FP simulations produce larger and wider convective clouds than the PP simulations. The temporal evolutions of cloud and precipitation are closely related to the turbulent transport, the cold pool and the cloud-scale circulation. The large amount of turbulent mixing associated with the shallow cumuli slows down the increase of the convective available potential energy and inhibits the early transition to deep convective clouds in the PP simulation. When the deep convective clouds fully develop and the precipitation is produced, the cold pools
NASA Technical Reports Server (NTRS)
Lichtenstein, J. H.
1978-01-01
An analytical method of computing the averaging effect of wing-span size on the loading of a wing induced by random turbulence was adapted for use on a digital electronic computer. The turbulence input was assumed to have a Dryden power spectral density. The computations were made for lift, rolling moment, and bending moment for two span load distributions, rectangular and elliptic. Data are presented to show the wing-span averaging effect for wing-span ratios encompassing current airplane sizes. The rectangular wing-span loading showed a slightly greater averaging effect than did the elliptic loading. In the frequency range most bothersome to airplane passengers, the wing-span averaging effect can reduce the normal lift load, and thus the acceleration, by about 7 percent for a typical medium-sized transport. Some calculations were made to evaluate the effect of using a Von Karman turbulence representation. These results showed that using the Von Karman representation generally resulted in a span averaging effect about 3 percent larger.
NASA Astrophysics Data System (ADS)
Thayer-Calder, K.; Larson, V. E.; Gettelman, A.; Craig, C.; Goldhaber, S.; Schanen, D.
2013-12-01
Global climate models (GCMs) have long had trouble representing climate variability that is highly dependent on convective variability. Convective clouds operate on scales far too small to actually simulate on a large GCM grid. To rectify these issues, GCM development is moving in several directions simultaneously. While much work is focusing on improved convective parameterizations, some modelers are increasing resolution to the point where deep convective clouds can be resolved on the grid scale. Others are using a super-parameterized approach, where small-scale models are embedded within the large-scale grid. Our study utilizes a new approach to modeling convective variability that attempts to model coupled convective and microphysics processes more explicitly than traditional parameterizations. Using the new Community Atmosphere Model (CAM) subcolumn framework, we create several instances of local cloudy or clear air profiles within the large-scale GCM grid. Each sub-column is instantiated through Latin-Hypercube sampling of double-gaussian PDFs predicted by a higher-order closure cloud parameterization known as CLUBB (Cloud Layers Unified By Binormals). The CAM microphysics code then runs with each instance, and the resulting heat and moisture tendencies are averaged and returned to the GCM in the same way as traditional parameterizations. Here, we present results from single-column simulations of CAM using this sub-column approach to coupling the moist turbulence parameterization to the microphysics scheme.
NASA Astrophysics Data System (ADS)
Ilıcak, Mehmet; Özgökmen, Tamay M.; Peters, Hartmut; Baumert, Helmut Z.; Iskandarani, Mohamed
Mixing of overflows released from polar and marginal seas is a key process shaping the structure of the meridional overturning circulation. Ocean general circulation models have difficulty in resolving the overflows, and therefore they must rely on parameterizations. In this study, the performance of a set of turbulence closures in reproducing mixing of an overflow is quantified. We simulate the Red Sea overflow by employing standard k- ɛ, k- ω and Mellor-Yamada schemes with various stability functions, as well as a modified k- ɛ model that relies on the prescription of the turbulent Prandtl number rather than on stability functions. The simpler KPP mixing scheme and experiments without turbulent fluxes serve as useful references. To our knowledge, this is the first time that the performance of two-equation turbulence models has been examined so closely using data from an overflow. It is found that without turbulence closures, the hydrodynamic model has difficulty in reproducing the correct three-dimensional pathway of the Red Sea overflow, consisting of a distinct bifurcation into two diverging channels. All turbulence models capture the vertical structure of this overflow consisting of an interfacial layer, characterized by the density gradient, and a well-mixed bottom layer. Mean eddy diffusivity values from most closures are comparable those from observations. But we find that KPP leads to eddy diffusivity values that are too small while those from Mellor-Yamada with Galperin [Galperin, B., Kantha, L.H., Hassid, S., Rosati, A., 1988. A quasi-equilibrium turbulent energy model for geophysical flows. J. Atmos. Sci. 45, 55-62] stability functions are too large. Such high diffusivities lead to excessive mixing in the bottom layer of the overflow, ultimately resulting in a salinity deficit of approximately 1 psu in the product water mass. Salinity deviations between the models and observations are quantified using both data taken along the channels and two
Frasca, Mattia; Sharkey, Kieran J
2016-06-21
Understanding the dynamics of spread of infectious diseases between individuals is essential for forecasting the evolution of an epidemic outbreak or for defining intervention policies. The problem is addressed by many approaches including stochastic and deterministic models formulated at diverse scales (individuals, populations) and different levels of detail. Here we consider discrete-time SIR (susceptible-infectious-removed) dynamics propagated on contact networks. We derive a novel set of 'discrete-time moment equations' for the probability of the system states at the level of individual nodes and pairs of nodes. These equations form a set which we close by introducing appropriate approximations of the joint probabilities appearing in them. For the example case of SIR processes, we formulate two types of model, one assuming statistical independence at the level of individuals and one at the level of pairs. From the pair-based model we then derive a model at the level of the population which captures the behavior of epidemics on homogeneous random networks. With respect to their continuous-time counterparts, the models include a larger number of possible transitions from one state to another and joint probabilities with a larger number of individuals. The approach is validated through numerical simulation over different network topologies. PMID:27038669
NASA Technical Reports Server (NTRS)
Xu, Kuan-Man
2015-01-01
Low-level clouds cover nearly half of the Earth and play a critical role in regulating the energy and hydrological cycle. Despite the fact that a great effort has been put to advance the modeling and observational capability in recent years, low-level clouds remains one of the largest uncertainties in the projection of future climate change. Low-level cloud feedbacks dominate the uncertainty in the total cloud feedback in climate sensitivity and projection studies. These clouds are notoriously difficult to simulate in climate models due to its complicated interactions with aerosols, cloud microphysics, boundary-layer turbulence and cloud dynamics. The biases in both low cloud coverage/water content and cloud radiative effects (CREs) remain large. A simultaneous reduction in both cloud and CRE biases remains elusive. This presentation first reviews the effort of implementing the higher-order turbulence closure (HOC) approach to representing subgrid-scale turbulence and low-level cloud processes in climate models. There are two HOCs that have been implemented in climate models. They differ in how many three-order moments are used. The CLUBB are implemented in both CAM5 and GDFL models, which are compared with IPHOC that is implemented in CAM5 by our group. IPHOC uses three third-order moments while CLUBB only uses one third-order moment while both use a joint double-Gaussian distribution to represent the subgrid-scale variability. Despite that HOC is more physically consistent and produces more realistic low-cloud geographic distributions and transitions between cumulus and stratocumulus regimes, GCMs with traditional cloud parameterizations outperform in CREs because tuning of this type of models is more extensively performed than those with HOCs. We perform several tuning experiments with CAM5 implemented with IPHOC in an attempt to produce the nearly balanced global radiative budgets without deteriorating the low-cloud simulation. One of the issues in CAM5-IPHOC
NASA Technical Reports Server (NTRS)
Helfand, H. M.; Labraga, J. C.
1988-01-01
The suitability of applying the Mellor and Yamada (1974, 1982) Level 2.5 second-order turbulence closure model to general circulation models is investigated by examining not only the scheme's simulation of fully (or nearly fully) developed turbulence, but also its simulation of rapidly growing or strongly decaying turbulence. The behavior of the model is presented over its entire domain of definition, with special consideration given to the pathologies of the model. The model is then modified for the case of growing turbulence to rectify some of its physical shortcomings for that case, and to remove the pathologies that prohibit its use in a general circulation model. The performance of the modified Level 2.5 model is compared to the performance of various other modified versions through the numerical simulation for a growing convective PBL. The results show that the modified Level 2.5 model is a viable candidate for the prediction of turbulence and the simulation of the PBL in general circulation models.
NASA Technical Reports Server (NTRS)
Canuto, V. M.; Howard, A.; Cheng, Y.; Dubovikov, M. S.
1999-01-01
We develop and test a 1-point closure turbulence model with the following features: 1) we include the salinity field and derive the expression for the vertical turbulent diffusivities of momentum K(sub m) , heat K(sub h) and salt K(sub s) as a function of two stability parameters: the Richardson number R(sub i) (stratification vs. shear) and the Turner number R(sub rho) (salinity gradient vs. temperature gradient). 2) to describe turbulent mixing below the mixed layer (ML), all previous models have adopted three adjustable "background diffusivities" for momentum, heat and salt. We propose a model that avoids such adjustable diffusivities. We assume that below the ML, the three diffusivities have the same functional dependence on R( sub i) and R(sub rho) as derived from the turbulence model. However, in order to compute R(sub i) below the ML, we use data of vertical shear due to wave-breaking.measured by Gargett et al. The procedure frees the model from adjustable background diffusivities and indeed we employ the same model throughout the entire vertical extent of the ocean. 3) in the local model, the turbulent diffusivities K(sub m,h,s) are given as analytical functions of R(sub i) and R(sub rho). 5) the model is used in an O-GCM and several results are presented to exhibit the effect of double diffusion processes. 6) the code is available upon request.
Closure theories with non-Gaussian restarts for truncated two-dimensional turbulence
NASA Astrophysics Data System (ADS)
Frederiksen, J. S.; Davies, A. G.; Bell, R. C.
1994-09-01
NonMarkovian closure theories, with and without non-Gaussian restarts, are compared with ensemble averaged direct numerical simulations (DNS) for severely truncated two-dimensional Navier-Stokes flows. Both the closures and DNS are formulated for discrete spectra relevant to flows on the doubly periodic domain allowing unambiguous comparisons between the closure and DNS results. We examine the performance of the direct interaction approximation (DIA), self-consistent field theory (SCFT) and local energy-transfer theory (LET) closures and are particularly interested in the reliability of cumulant update versions of these closures (CUDIA, CUSCFT, and CULET). In the latter, the potentially long time-history integrals are periodically truncated and the closures are restarted using a three-point cumulant as the new non-Gaussian initial conditions, thus yielding computationally much more efficient closures. In 80-day integrations, the DIA replicates the DNS results most faithfully in inviscid, viscous decay and forced dissipative experiments. With an update time of T=10 days, the CUDIA is particularly promising performing nearly as well but with some extra oscillations at intermediate times. The SCFT and particularly LET, have spurious oscillations in inviscid and viscous decay experiments; this is also the case, but to a greater degree, for the CUSCFT and CULET closures.
Workshop on Engineering Turbulence Modeling
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.
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.
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
Applications of direct numerical simulation of turbulence in second order closures
NASA Technical Reports Server (NTRS)
Shih, Tsan-Hsing; Lumley, John L.
1995-01-01
This paper discusses two methods of developing models for the rapid pressure-strain correlation term in the Reynolds stress transport equation using direct numerical simulation (DNS) data. One is a perturbation about isotropic turbulence, the other is a perturbation about two-component turbulence -- an extremely anisotropic turbulence. A model based on the latter method is proposed and is found to be very promising when compared with DNS data and other models.
NASA Technical Reports Server (NTRS)
Bennett, Floyd V.; Yntema, Robert T.
1959-01-01
Several approximate procedures for calculating the bending-moment response of flexible airplanes to continuous isotropic turbulence are presented and evaluated. The modal methods (the mode-displacement and force-summation methods) and a matrix method (segmented-wing method) are considered. These approximate procedures are applied to a simplified airplane for which an exact solution to the equation of motion can be obtained. The simplified airplane consists of a uniform beam with a concentrated fuselage mass at the center. Airplane motions are limited to vertical rigid-body translation and symmetrical wing bending deflections. Output power spectra of wing bending moments based on the exact transfer-function solutions are used as a basis for the evaluation of the approximate methods. It is shown that the force-summation and the matrix methods give satisfactory accuracy and that the mode-displacement method gives unsatisfactory accuracy.
NASA Astrophysics Data System (ADS)
Alldredge, Graham; Schneider, Florian
2015-08-01
We implement a high-order numerical scheme for the entropy-based moment closure, the so-called MN model, for linear kinetic equations in slab geometry. A discontinuous Galerkin (DG) scheme in space along with a strong-stability preserving Runge-Kutta time integrator is a natural choice to achieve a third-order scheme, but so far, the challenge for such a scheme in this context is the implementation of a linear scaling limiter when the numerical solution leaves the set of realizable moments (that is, those moments associated with a positive underlying distribution). The difficulty for such a limiter lies in the computation of the intersection of a ray with the set of realizable moments. We avoid this computation by using quadrature to generate a convex polytope which approximates this set. The half-space representation of this polytope is used to compute an approximation of the required intersection straightforwardly, and with this limiter in hand, the rest of the DG scheme is constructed using standard techniques. We consider the resulting numerical scheme on a new manufactured solution and standard benchmark problems for both traditional MN models and the so-called mixed-moment models. The manufactured solution allows us to observe the expected convergence rates and explore the effects of the regularization in the optimization.
Modeling flows over gravel beds by a drag force method and a modified S-A turbulence closure
NASA Astrophysics Data System (ADS)
Zeng, C.; Li, C. W.
2012-09-01
A double-averaged Navier-Stokes equations (DANS) model has been developed for depth-limited open channel flows over gravels. Three test cases are used to validate the model: an open-channel flow over a densely packed gravel bed with small-scale uniform roughness (D/d50 ˜ 13, d50 = median diameter of roughness elements, D = water depth), open-channel flows over large-scale sparsely distributed roughness elements (D/Δ ˜ 2.3-8.7, Δ = roughness height) and steep slope gravel-bed river flows with D/d50 ˜ 7-25. Various methods of treatment of the gravel-induced resistance effect have been investigated. The results show that the wall function approach (WFA) is successful in simulating flows over small gravels but is not appropriate for large gravels since the vertical profile of the longitudinal velocity does not follow the logarithmic-linear relationship. The drag force method (DFM) performs better but the non-logarithmic velocity distribution generated by sparsely distributed gravels cannot be simulated accurately. Noting that the turbulence length scale within the gravel layer is governed by the gravel size, the DANS model incorporating the DFM and a modified Spalart-Allmaras (S-A) turbulence closure is proposed. The turbulence length scale parameter in the S-A model is modified to address the change in the turbulence structure within the gravel layer. The computed velocity profiles agree well with the corresponding measured profiles in all cases. Particularly, the model reproduces the S-shape velocity profile for sparsely distributed large size roughness elements. The modeling methodology is robust and can be easily integrated into the existing numerical models.
Osman, K T; Wan, M; Matthaeus, W H; Weygand, J M; Dasso, S
2011-10-14
The first direct determination of the inertial range energy cascade rate, using an anisotropic form of Yaglom's law for magnetohydrodynamic turbulence, is obtained in the solar wind with multispacecraft measurements. The two-point mixed third-order structure functions of Elsässer fluctuations are integrated over a sphere in magnetic field-aligned coordinates, and the result is consistent with a linear scaling. Therefore, volume integrated heating and cascade rates are obtained that, unlike previous studies, make only limited assumptions about the underlying spectral geometry of solar wind turbulence. These results confirm the turbulent nature of magnetic and velocity field fluctuations in the low frequency limit, and could supply the energy necessary to account for the nonadiabatic heating of the solar wind. PMID:22107393
Boschung, Jonas
2015-10-01
Following an approach by Siggia, we present coefficients C(n) relating the moments of the dissipation of kinetic energy 〈ɛ〉 and the longitudinal velocity gradient 〈∂u(1)/∂x(1)〉 under the assumption of isotropy and continuity. Particularly, we find that the moment 〈ɛ(n)〉 of order n is completely determined by 〈(∂u(1)/∂x(1))(2n)〉 and an order- (and viscosity-) dependent coefficient for all n under the assumption of (local) isotropy. This implies that all theories which specify 〈ɛ(n)〉 also implicitly determine 〈(∂u(1)/∂x(1))(2n)〉 and vice versa. As a corollary to the direct connection between the moments of the dissipation and the longitudinal velocity gradient, the even standardized moments of order 2n of ∂u(1)/∂x(1) (flatness, hyperflatness, and so on) are directly related to the ratio of the moments 〈ɛ(n)〉/〈ɛ〉(n). We compare the theoretical values of the coefficients C(n) up to n=6 with homogeneous isotropic DNS data ranging from Re(λ)=88 to Re(λ)=529. PMID:26565338
NASA Technical Reports Server (NTRS)
Cheng, Anning; Xu, Kuan-Man
2015-01-01
Five-year simulation experiments with a multi-scale modeling Framework (MMF) with a advanced intermediately prognostic higher-order turbulence closure (IPHOC) in its cloud resolving model (CRM) component, also known as SPCAM-IPHOC (super parameterized Community Atmospheric Model), are performed to understand the fast tropical (30S-30N) cloud response to an instantaneous doubling of CO2 concentration with SST held fixed at present-day values. SPCAM-IPHOC has substantially improved the low-level representation compared with SPCAM. It is expected that the cloud responses to greenhouse warming in SPCAM-IPHOC is more realistic. The change of rising motion, surface precipitation, cloud cover, and shortwave and longwave cloud radiative forcing in SPCAM-IPHOC from the greenhouse warming will be presented in the presentation.
A hybrid Reynolds averaged/PDF closure model for supersonic turbulent combustion
NASA Technical Reports Server (NTRS)
Frankel, Steven H.; Hassan, H. A.; Drummond, J. Philip
1990-01-01
A hybrid Reynolds averaged/assumed pdf approach has been developed and applied to the study of turbulent combustion in a supersonic mixing layer. This approach is used to address the 'laminar-like' treatment of the thermochemical terms that appear in the conservation equations. Calculations were carried out for two experiments involving H2-air supersonic turbulent mixing. Two different forms of the pdf were implemented. In general, the results show modest improvement from previous calculations. Moreover, the results appear to be somewhat independent of the form of the assumed pdf.
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.
Third-moment descriptions of the interplanetary turbulent cascade, intermittency and back transfer
Coburn, Jesse T.; Forman, Miriam A.; Smith, Charles W.; Vasquez, Bernard J.; Stawarz, Julia E.
2015-01-01
We review some aspects of solar wind turbulence with an emphasis on the ability of the turbulence to account for the observed heating of the solar wind. Particular attention is paid to the use of structure functions in computing energy cascade rates and their general agreement with the measured thermal proton heating. We then examine the use of 1 h data samples that are comparable in length to the correlation length for the fluctuations to obtain insights into local inertial range dynamics and find evidence for intermittency in the computed energy cascade rates. When the magnetic energy dominates the kinetic energy, there is evidence of anti-correlation in the cascade of energy associated with the outward- and inward-propagating components that we can only partially explain. PMID:25848079
Third-moment descriptions of the interplanetary turbulent cascade, intermittency and back transfer.
Coburn, Jesse T; Forman, Miriam A; Smith, Charles W; Vasquez, Bernard J; Stawarz, Julia E
2015-05-13
We review some aspects of solar wind turbulence with an emphasis on the ability of the turbulence to account for the observed heating of the solar wind. Particular attention is paid to the use of structure functions in computing energy cascade rates and their general agreement with the measured thermal proton heating. We then examine the use of 1 h data samples that are comparable in length to the correlation length for the fluctuations to obtain insights into local inertial range dynamics and find evidence for intermittency in the computed energy cascade rates. When the magnetic energy dominates the kinetic energy, there is evidence of anti-correlation in the cascade of energy associated with the outward- and inward-propagating components that we can only partially explain. PMID:25848079
NASA Technical Reports Server (NTRS)
Xu, Kuan-Man; Cheng, Anning
2007-01-01
The effects of subgrid-scale condensation and transport become more important as the grid spacings increase from those typically used in large-eddy simulation (LES) to those typically used in cloud-resolving models (CRMs). Incorporation of these effects can be achieved by a joint probability density function approach that utilizes higher-order moments of thermodynamic and dynamic variables. This study examines how well shallow cumulus and stratocumulus clouds are simulated by two versions of a CRM that is implemented with low-order and third-order turbulence closures (LOC and TOC) when a typical CRM horizontal resolution is used and what roles the subgrid-scale and resolved-scale processes play as the horizontal grid spacing of the CRM becomes finer. Cumulus clouds were mostly produced through subgrid-scale transport processes while stratocumulus clouds were produced through both subgrid-scale and resolved-scale processes in the TOC version of the CRM when a typical CRM grid spacing is used. The LOC version of the CRM relied upon resolved-scale circulations to produce both cumulus and stratocumulus clouds, due to small subgrid-scale transports. The mean profiles of thermodynamic variables, cloud fraction and liquid water content exhibit significant differences between the two versions of the CRM, with the TOC results agreeing better with the LES than the LOC results. The characteristics, temporal evolution and mean profiles of shallow cumulus and stratocumulus clouds are weakly dependent upon the horizontal grid spacing used in the TOC CRM. However, the ratio of the subgrid-scale to resolved-scale fluxes becomes smaller as the horizontal grid spacing decreases. The subcloud-layer fluxes are mostly due to the resolved scales when a grid spacing less than or equal to 1 km is used. The overall results of the TOC simulations suggest that a 1-km grid spacing is a good choice for CRM simulation of shallow cumulus and stratocumulus.
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.
Forced Alfvén-wave turbulence and subgrid-scale closure
NASA Astrophysics Data System (ADS)
Zhou, Ye; Vahala, George
1989-02-01
The renormalization-group method is applied to the problem of forced turbulence in the simplified Alfvén model of Chen and Mahajan. The effects of small unresolvable subgrid modes on the large-scale turbulence leads to a renormalized response function ɛ. In certain limits, the resulting recursion relation for the response function can be converted into a differential equation that can be solved analytically. For Gaussian forcing terms satisfying a power-law wavenumber correlation k-y but white-noise frequency spectrum, it is found that the response function exhibits second-harmonic generation of waves at frequency ω = 2ΛvA for all exponents y ≥ 0, where Λ is the wavenumber separating the subgrid and supergrid modes.
Turbulent Transport in Fusion Plasmas, Effects of Toroidicity and Fluid Closure
Weiland, Jan
2009-11-10
Basic aspects of turbulent transport in toroidal magnetized plasmas are discussed. In particular Kadomtsev's mixing length estimate is found to work well for the Cyclone base case at the experimental gradient. Generalizations to include non-Markovian effects and off diagonal fluxes are given. The importance of toroidal effects is stressed These enter particularly strongly in convective or off diagonal fluxes. This feature applies also to momentum ttransport.
NASA Technical Reports Server (NTRS)
Eisfeld, Bernhard; Rumsey, Chris; Togiti, Vamshi
2015-01-01
The implementation of the SSG/LRR-omega differential Reynolds stress model into the NASA flow solvers CFL3D and FUN3D and the DLR flow solver TAU is verified by studying the grid convergence of the solution of three different test cases from the Turbulence Modeling Resource Website. The model's predictive capabilities are assessed based on four basic and four extended validation cases also provided on this website, involving attached and separated boundary layer flows, effects of streamline curvature and secondary flow. Simulation results are compared against experimental data and predictions by the eddy-viscosity models of Spalart-Allmaras (SA) and Menter's Shear Stress Transport (SST).
A numerical method for prediction of compressible turbulent flows with closure models
NASA Technical Reports Server (NTRS)
Huang, P. G.
1990-01-01
A new computer code to solve the time averaged Navier-Stokes equations is developed. Many of the state-of-the-art numerical techniques and algorithms have been tested and implemented in the program in order to achieve a better numerical accuracy and code efficiency. Various turbulence models are tested for a wide range of flows. The initial focus has been on two-equation eddy-viscosity models, which are the most advanced available in current compressible flow codes. The long term goal will be to test Reynolds-Stress models and to explore their performance in the high Mach number range. Although testing and improvement of turbulence models for supersonic and hypersonic flows is the primary objective of this research, part of the effort has been devoted to analyzing the vortex breakdown phenomena using new computer programs. Some preliminary results on the breakdown of a vortex flow in a tube are reported. Present calculations are restricted to two dimensional flow geometry.
Renormalization Group Theory Technique and Subgrid Scale Closure for Fluid and Plasma Turbulence.
NASA Astrophysics Data System (ADS)
Zhou, Ye.
Renormalization group theory is applied to incompressible three-dimension Navier-Stokes turbulence so as to eliminate unresolvable small scales. The renormalized Navier-Stokes equation includes a triple nonlinearity with the eddy viscosity exhibiting a mild cusp behavior, in qualitative agreement with the test-field model results of Kraichnan. For the cusp behavior to arise, not only is the triple nonlinearity necessary but the effects of pressure must be incorporated in the triple term. Renormalization group theory is also applied to a model Alfven wave turbulence equation. In particular, the effect of small unresolvable subgrid scales on the large scales is computed. It is found that the removal of the subgrid scales leads to a renormalized response function. (i) This response function can be calculated analytically via the difference renormalization group technique. Strong absorption can occur around the Alfven frequency for sharply peaked subgrid frequency spectra. (ii) With the epsilon - expansion renormalization group approach, the Lorenzian wavenumber spectrum of Chen and Mahajan can be recovered for finite epsilon , but the nonlinear coupling constant still remains small, fully justifying the neglect of higher order nonlinearities introduced by the renormalization group procedure.
Mean velocity and moments of turbulent velocity fluctuations in the wake of a model ship propulsor
NASA Astrophysics Data System (ADS)
Pêgo, J. P.; Lienhart, H.; Durst, F.
2007-08-01
; Schneekluth and Bertram in Ship design for efficiency and economy, 1998), the co-rotating propellers model showed a much stronger swirl in the wake of the propulsor. The anisotropy of turbulence was analyzed using the anisotropy tensor introduced by Lumley and Newman (J Fluid Mech 82(1):161-178, 1977). The invariants of the anisotropy tensor of the wake flow were computed and were plotted in the Lumley-Newman-diagram. These measurements revealed that the anisotropy tensor in the wake of ship propellers is located near to the borders of the invariant map, showing a large degree of anisotropy. They will be presented and will be discussed with respect to applications of turbulence models to predict swirling flows.
NASA Technical Reports Server (NTRS)
1977-01-01
Basic differential equations governing compressible turbulent boundary layer flow are reviewed, including conservation of mass and energy, momentum equations derived from Navier-Stokes equations, and equations of state. Closure procedures were broken down into: (1) simple or zeroth-order methods, (2) first-order or mean field closure methods, and (3) second-order or mean turbulence field methods.
Closure Models for Turbulent Particle-laden Flows from Particle-resolved Direct Numerical Simulation
NASA Astrophysics Data System (ADS)
Subramaniam, Shankar; Tenneti, Sudheer; Mehrabadi, Mohammad; Garg, Rahul
2012-11-01
Gas-phase velocity fluctuations in fixed particle beds and freely evolving suspensions are quantified using a particle-resolved direct numerical simulation (PR-DNS). The flow regime corresponds to gas-solid systems typically encountered in fluidized bed risers, with high solid to gas density ratio and particle diameter being greater than the dissipative length scales. The kinetic energy associated with gas-phase velocity fluctuations in homogeneous monodisperse fixed beds is characterized as a function of solid volume fraction φ and the Reynolds number based on the mean slip velocity Re. A simple scaling analysis is used to explain the dependence of k on ɛ and Re. The steady value of k results from the balance between the source of k due to interphase transfer of kinetic energy, and the dissipation rate (ɛ) of k in the gas-phase. It is found that the dissipation rate of k in gas-solid flows can be modeled using a length scale that is analogous to the Taylor microscale used in single-phase turbulence. Using the PR-DNS data for k and ɛ we also infer an eddy viscosity for gas-solid flow. For the parameter values considered here, the level of gas-phase velocity fluctuations in freely evolving suspensions differs by only 10% from the value for the corresponding fixed beds. Funded in part by the US Department of Energy's National Energy Technology Laboratory Grant DE-FC26-07NT43098 (Advanced Research) and the National Science Foundation's grant CBET 1134500.
NASA Astrophysics Data System (ADS)
Yang, X. I. A.; Meneveau, C.; Marusic, I.; Biferale, L.
2016-08-01
In wall-bounded turbulence, the moment generating functions (MGFs) of the streamwise velocity fluctuations
Domingo, Pascale; Vervisch, Luc; Payet, Sandra; Hauguel, Raphaeel
2005-12-01
Two complementary simulations of premixed turbulent flames are discussed. Low Reynolds number two-dimensional direct numerical simulation of a premixed turbulent V flame is first performed, to further analyze the behavior of various flame quantities and to study key ingredients of premixed turbulent combustion modeling. Flame surface density, subgrid-scale variance of progress variables, and unresolved turbulent fluxes are analyzed. These simulations include fully detailed chemistry from a flame-generated tabulation (FPI) and the analysis focuses on the dynamics of the thin flame front. Then, a novel subgrid scale closure for large eddy simulation of premixed turbulent combustion (FSD-PDF) is proposed. It combines the flame surface density (FSD) approach with a presumed probability density function (PDF) of the progress variable that is used in FPI chemistry tabulation. The FSD is useful for introducing in the presumed PDF the influence of the spatially filtered thin reaction zone evolving within the subgrid. This is achieved via the exact relation between the PDF and the FSD. This relation involves the conditional filtered average of the magnitude of the gradient of the progress variable. In the modeling, this conditional filtered mean is approximated from the filtered gradient of the progress variable of the FPI laminar flame. Balance equations providing mean and variance of the progress variable together with the measure of the filtered gradient are used to presume the PDF. A three-dimensional larger Reynolds number flow configuration (ORACLES experiment) is then computed with FSD-PDF and the results are compared with measurements.
NASA Technical Reports Server (NTRS)
1996-01-01
Topics considered include: New approach to turbulence modeling; Second moment closure analysis of the backstep flow database; Prediction of the backflow and recovery regions in the backward facing step at various Reynolds numbers; Turbulent flame propagation in partially premixed flames; Ensemble averaged dynamic modeling. Also included a study of the turbulence structures of wall-bounded shear flows; Simulation and modeling of the elliptic streamline flow.
NASA Technical Reports Server (NTRS)
Xu, Kuan-Man; Cheng, Anning
2010-01-01
This study presents preliminary results from a multiscale modeling framework (MMF) with an advanced third-order turbulence closure in its cloud-resolving model (CRM) component. In the original MMF, the Community Atmosphere Model (CAM3.5) is used as the host general circulation model (GCM), and the System for Atmospheric Modeling with a first-order turbulence closure is used as the CRM for representing cloud processes in each grid box of the GCM. The results of annual and seasonal means and diurnal variability are compared between the modified and original MMFs and the CAM3.5. The global distributions of low-level cloud amounts and precipitation and the amounts of low-level clouds in the subtropics and middle-level clouds in mid-latitude storm track regions in the modified MMF show substantial improvement relative to the original MMF when both are compared to observations. Some improvements can also be seen in the diurnal variability of precipitation.
NASA Technical Reports Server (NTRS)
Wang, Shouping; Wang, Qing
1994-01-01
This study focuses on the effects of drizzle in a one-dimensional third-order turbulence closure model of the nocturnal stratus-topped marine boundary layer. When the simulated drizzle rate is relatively small (maximum approximately equal to 0.6 mm/day), steady-state solutions are obtained. The boundary layer stabilizes essentially because drizzle causes evaporative cooling of the subcloud layer. This stabilization considerably reduces the buoyancy flux and turbulence kinetic energy below the stratus cloud. Thus, drizzle tends to decouple the cloud from the subcloud layer in the model, as suggested by many observational studies. In addition, the evaporation of drizzle in the subcloud layer creates small scattered clouds, which are likely to represent cumulus clouds, below the solid stratus cloud in the model. The sensitivity experiments show that these scattered clouds help maintain a coupled boundary layer. When the drizzle rate is relatively large (maximum approximately equal to 0.9 mm/day), the response of the model becomes transient with bursts in turbulent fluxes. This phenomenon is related to the formation of the scattered cloud layer below the solid stratus cloud. It appears that the model is inadequate to represent the heat and moisture transport by strong updrafts covering a small fractional area in cumulus convection.
Ihme, Matthias; Pitsch, Heinz
2008-10-15
Previously conducted studies of the flamelet/progress variable model for the prediction of nonpremixed turbulent combustion processes identified two areas for model improvements: the modeling of the presumed probability density function (PDF) for the reaction progress parameter and the consideration of unsteady effects [Ihme et al., Proc. Combust. Inst. 30 (2005) 793]. These effects are of particular importance during local flame extinction and subsequent reignition. Here, the models for the presumed PDFs for conserved and reactive scalars are re-examined and a statistically most likely distribution (SMLD) is employed and tested in a priori studies using direct numerical simulation (DNS) data and experimental results from the Sandia flame series. In the first part of the paper, the SMLD model is employed for a reactive scalar distribution. Modeling aspects of the a priori PDF, accounting for the bias in composition space, are discussed. The convergence of the SMLD with increasing number of enforced moments is demonstrated. It is concluded that information about more than two moments is beneficial to accurately represent the reactive scalar distribution in turbulent flames with strong extinction and reignition. In addition to the reactive scalar analysis, the potential of the SMLD for the representation of conserved scalar distributions is also analyzed. In the a priori study using DNS data it is found that the conventionally employed beta distribution provides a better representation for the scalar distribution. This is attributed to the fact that the beta-PDF implicitly enforces higher moment information that is in excellent agreement with the DNS data. However, the SMLD outperforms the beta distribution in free shear flow applications, which are typically characterized by strongly skewed scalar distributions, in the case where higher moment information can be enforced. (author)
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.
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.
NASA Technical Reports Server (NTRS)
Demuren, A. O.; Sarkar, S.
1993-01-01
The roles of pressure-strain and turbulent diffusion models in the numerical calculation of turbulent plane channel flows with second-moment closure models are investigated. Three turbulent diffusion and five pressure-strain models are utilized in the computations. The main characteristics of the mean flow and the turbulent fields are compared against experimental data. All the features of the mean flow are correctly predicted by all but one of the Reynolds stress closure models. The Reynolds stress anisotropies in the log layer are predicted to varying degrees of accuracy (good to fair) by the models. None of the models could predict correctly the extent of relaxation towards isotropy in the wake region near the center of the channel. Results from the directional numerical simulation are used to further clarify this behavior of the models.
Systematic study of Reynolds stress closure models in the computations of plane channel flows
NASA Technical Reports Server (NTRS)
Demuren, A. O.; Sarkar, S.
1992-01-01
The roles of pressure-strain and turbulent diffusion models in the numerical calculation of turbulent plane channel flows with second-moment closure models are investigated. Three turbulent diffusion and five pressure-strain models are utilized in the computations. The main characteristics of the mean flow and the turbulent fields are compared against experimental data. All the features of the mean flow are correctly predicted by all but one of the Reynolds stress closure models. The Reynolds stress anisotropies in the log layer are predicted to varying degrees of accuracy (good to fair) by the models. None of the models could predict correctly the extent of relaxation towards isotropy in the wake region near the center of the channel. Results from the directional numerical simulation are used to further clarify this behavior of the models.
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.
NASA Astrophysics Data System (ADS)
Behrendt, A.; Wulfmeyer, V.; Hammann, E.; Muppa, S. K.; Pal, S.
2015-05-01
The rotational Raman lidar (RRL) of the University of Hohenheim (UHOH) measures atmospheric temperature profiles with high resolution (10 s, 109 m). The data contain low-noise errors even in daytime due to the use of strong UV laser light (355 nm, 10 W, 50 Hz) and a very efficient interference-filter-based polychromator. In this paper, the first profiling of the second- to fourth-order moments of turbulent temperature fluctuations is presented. Furthermore, skewness profiles and kurtosis profiles in the convective planetary boundary layer (CBL) including the interfacial layer (IL) are discussed. The results demonstrate that the UHOH RRL resolves the vertical structure of these moments. The data set which is used for this case study was collected in western Germany (50°53'50.56'' N, 6°27'50.39'' E; 110 m a.s.l.) on 24 April 2013 during the Intensive Observations Period (IOP) 6 of the HD(CP)2 (High-Definition Clouds and Precipitation for advancing Climate Prediction) Observational Prototype Experiment (HOPE). We used the data between 11:00 and 12:00 UTC corresponding to 1 h around local noon (the highest position of the Sun was at 11:33 UTC). First, we investigated profiles of the total noise error of the temperature measurements and compared them with estimates of the temperature measurement uncertainty due to shot noise derived with Poisson statistics. The comparison confirms that the major contribution to the total statistical uncertainty of the temperature measurements originates from shot noise. The total statistical uncertainty of a 20 min temperature measurement is lower than 0.1 K up to 1050 m a.g.l. (above ground level) at noontime; even for single 10 s temperature profiles, it is smaller than 1 K up to 1020 m a.g.l. Autocovariance and spectral analyses of the atmospheric temperature fluctuations confirm that a temporal resolution of 10 s was sufficient to resolve the turbulence down to the inertial subrange. This is also indicated by the integral scale of
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.
Deriving statistical closure from dynamical optimization
NASA Astrophysics Data System (ADS)
Turkington, Bruce
2015-11-01
Turbulence theorists have traditionally deduced statistical models by generating a hierarchy of moment equations and invoking some closure rules to truncate the hierarchy. In this talk a conceptually different approach to model reduction and statistical closure will be presented, and its implications for coarse-graining fluid turbulence will be indicated. The author has developed this method in the context of nonequilibrium statistical descriptions of Hamiltonian systems with many degrees of freedom. With respect to a chosen parametric statistical model, the lack-of-fit of model paths to the full dynamics is minimized in a time-integrated, mean-squared sense. This optimal closure method is applied to coarse-grain spectrally-truncated inviscid dynamics, including the Burgers-Hopf equation and incompressible two-dimensional flow, using the means and/or variances of low modes as resolved variables. The derived reduced dynamics for these test cases contain (1) scale-dependent dissipation which is not a local eddy viscosity, (2) modified nonlinear interactions between resolved modes, and (3) coupling between the mean and variance of each resolved mode. These predictions are validated against direct numerical simulations of ensembles for the fully resolved dynamics.
NASA Astrophysics Data System (ADS)
Behrendt, A.; Wulfmeyer, V.; Hammann, E.; Muppa, S. K.; Pal, S.
2014-11-01
The rotational Raman lidar of the University of Hohenheim (UHOH) measures atmospheric temperature profiles during daytime with high resolution (10 s, 109 m). The data contain low noise errors even in daytime due to the use of strong UV laser light (355 nm, 10 W, 50 Hz) and a very efficient interference-filter-based polychromator. In this paper, we present the first profiling of the second- to forth-order moments of turbulent temperature fluctuations as well as of skewness and kurtosis in the convective boundary layer (CBL) including the interfacial layer (IL). The results demonstrate that the UHOH RRL resolves the vertical structure of these moments. The data set which is used for this case study was collected in western Germany (50°53'50.56'' N, 6°27'50.39'' E, 110 m a.s.l.) within one hour around local noon on 24 April 2013 during the Intensive Observations Period (IOP) 6 of the HD(CP)2 Observational Prototype Experiment (HOPE), which is embedded in the German project HD(CP)2 (High-Definition Clouds and Precipitation for advancing Climate Prediction). First, we investigated profiles of the noise variance and compared it with estimates of the statistical temperature measurement uncertainty Δ T based on Poisson statistics. The agreement confirms that photon count numbers obtained from extrapolated analog signal intensities provide a lower estimate of the statistical errors. The total statistical uncertainty of a 20 min temperature measurement is lower than 0.1 K up to 1050 m a.g.l. at noontime; even for single 10 s temperature profiles, it is smaller than 1 K up to 1000 m a.g.l.. Then we confirmed by autocovariance and spectral analyses of the atmospheric temperature fluctuations that a temporal resolution of 10 s was sufficient to resolve the turbulence down to the inertial subrange. This is also indicated by the profile of the integral scale of the temperature fluctuations, which was in the range of 40 to 120 s in the CBL. Analyzing then profiles of the second
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.
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
Problems in simulating the stratocumulus-topped boundary layer with a third-order closure model
NASA Technical Reports Server (NTRS)
Moeng, C.-H.; Randall, D. A.
1984-01-01
The Andre et al. (1976, 1978) third-order closure model, in which the time rate of change terms, the relaxation and rapid effects for pressure-related terms, and the clipping approximation are used along with the quasi-normal closure, is invoked in the study of turbulence in a cloudy layer that is radiatively cooled from above. A spurious oscillation whose greatest amplitude lies near the inversion is shown by analysis to arise from the mean gradient and buoyancy terms of the triple-moment equations. An attempt is made to damp the oscillation through the introduction of diffusion terms into the triple-moment equations. The results obtained are noted to be sensitive to the ad hoc eddy coefficient applied in the third-moment equations.
The URAPS closure for the normalized Reynolds stress
NASA Astrophysics Data System (ADS)
Koppula, Karuna S.; Muthu, Satish; Bénard, André; Petty, Charles A.
2013-07-01
The Reynolds-averaged Navier-Stokes (RANS)-equation for constant property Newtonian fluids is an exact, albeit unclosed, first-order moment equation for the mean velocity field. The RANS-equation and the Reynolds-averaged continuity equation together with a model for the Reynolds stress provide a set of closed equations that govern the behavior of the mean velocity and mean pressure fields. In this turbulent mixing and beyond (TMB) paper, the key ideas related to a recently developed universal closure for the normalized Reynolds (NR)-stress are reviewed. The new approach relates the NR-stress to four characteristic time scales: a turbulent time scale, a viscous time scale, a time scale related to the mean field velocity gradient and a time scale associated with a rigid body frame-of-reference. The theory stems from an analysis of the Navier-Stokes equation and is formulated as a universal non-negative mapping of the NR-stress into itself. Consequently, all solutions of the NR-stress equation are non-negative dyadic-valued linear operators regardless of the class of benchmark flows used to determine closure parameters. The new closure model predicts that the Coriolis acceleration causes an anisotropic re-distribution of turbulent kinetic energy among the three components of the fluctuating velocity in rotating homogeneous decay.
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.
Methods of separation of variables in turbulence theory
NASA Technical Reports Server (NTRS)
Tsuge, S.
1978-01-01
Two schemes of closing turbulent moment equations are proposed both of which make double correlation equations separated into single-point equations. The first is based on neglected triple correlation, leading to an equation differing from small perturbed gasdynamic equations where the separation constant appears as the frequency. Grid-produced turbulence is described in this light as time-independent, cylindrically-isotropic turbulence. Application to wall turbulence guided by a new asymptotic method for the Orr-Sommerfeld equation reveals a neutrally stable mode of essentially three dimensional nature. The second closure scheme is based on an assumption of identity of the separated variables through which triple and quadruple correlations are formed. The resulting equation adds, to its equivalent of the first scheme, an integral of nonlinear convolution in the frequency describing a role due to triple correlation of direct energy-cascading.
On recontamination and directional-bias problems in Monte Carlo simulation of PDF turbulence models
NASA Technical Reports Server (NTRS)
Hsu, Andrew T.
1991-01-01
Turbulent combustion can not be simulated adequately by conventional moment closure turbulence models. The difficulty lies in the fact that the reaction rate is in general an exponential function of the temperature, and the higher order correlations in the conventional moment closure models of the chemical source term can not be neglected, making the applications of such models impractical. The probability density function (pdf) method offers an attractive alternative: in a pdf model, the chemical source terms are closed and do not require additional models. A grid dependent Monte Carlo scheme was studied, since it is a logical alternative, wherein the number of computer operations increases only linearly with the increase of number of independent variables, as compared to the exponential increase in a conventional finite difference scheme. A new algorithm was devised that satisfies a restriction in the case of pure diffusion or uniform flow problems. Although for nonuniform flows absolute conservation seems impossible, the present scheme has reduced the error considerably.
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.
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.
NASA Technical Reports Server (NTRS)
Bingham, G. J.; Noonan, K. W.
1974-01-01
An investigation was conducted in a low-turbulence pressure tunnel to determine the two-dimensional lift and pitching-moment characteristics of an NACA 6716 and an NACA 4416 airfoil with 35-percent-chord single-slotted flaps. Both models were tested with flaps deflected from 0 deg to 45 deg, at angles of attack from minus 6 deg to several degrees past stall, at Reynolds numbers from 3.0 million to 13.8 million, and primarily at a Mach number of 0.23. Tests were also made to determine the effect of several slot entry shapes on performance.
Some Basic Laws of Isotropic Turbulent Flow
NASA Technical Reports Server (NTRS)
Loitsianskii, L. G.
1945-01-01
An Investigation is made of the diffusion of artificially produced turbulence behind screens or other turbulence producers. The method is based on the author's concept of disturbance moment as a certain theoretically well-founded measure of turbulent disturbances.
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
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).
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).
Turbulent flow computation in a circular U-Bend
NASA Astrophysics Data System (ADS)
Miloud, Abdelkrim; Aounallah, Mohammed; Belkadi, Mustapha; Adjlout, Lahouari; Imine, Omar; Imine, Bachir
2014-03-01
Turbulent flows through a circular 180° curved bend with a curvature ratio of 3.375, defined as the the bend mean radius to pipe diameter is investigated numerically for a Reynolds number of 4.45×104. The computation is performed for a U-Bend with full long pipes at the entrance and at the exit. The commercial ANSYS FLUENT is used to solve the steady Reynolds-Averaged Navier-Stokes (RANS) equations. The performances of standard k-ɛ and the second moment closure RSM models are evaluated by comparing their numerical results against experimental data and testing their capabilities to capture the formation and extend this turbulence driven vortex. It is found that the secondary flows occur in the cross-stream half-plane of such configurations and primarily induced by high anisotropy of the cross-stream turbulent normal stresses near the outer bend.
Statistical turbulence theory and turbulence phenomenology
NASA Technical Reports Server (NTRS)
Herring, J. R.
1973-01-01
The application of deductive turbulence theory for validity determination of turbulence phenomenology at the level of second-order, single-point moments is considered. Particular emphasis is placed on the phenomenological formula relating the dissipation to the turbulence energy and the Rotta-type formula for the return to isotropy. Methods which deal directly with most or all the scales of motion explicitly are reviewed briefly. The statistical theory of turbulence is presented as an expansion about randomness. Two concepts are involved: (1) a modeling of the turbulence as nearly multipoint Gaussian, and (2) a simultaneous introduction of a generalized eddy viscosity operator.
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.
PDF methods for turbulent reactive flows
NASA Technical Reports Server (NTRS)
Hsu, Andrew T.
1995-01-01
Viewgraphs are presented on computation of turbulent combustion, governing equations, closure problem, PDF modeling of turbulent reactive flows, validation cases, current projects, and collaboration with industry and technology transfer.
ERIC Educational Resources Information Center
Williams, Kate
2012-01-01
The informatics moment is the moment when a person seeks help in using some digital technology that is new to him or her. This article examines the informatics moment in people's everyday lives as they sought help at a branch public library. Four types of literacy were involved: basic literacy (reading and writing), computer literacy (use of a…
Conditional statistics in a turbulent premixed flame derived from direct numerical simulation
NASA Technical Reports Server (NTRS)
Mantel, Thierry; Bilger, Robert W.
1994-01-01
The objective of this paper is to briefly introduce conditional moment closure (CMC) methods for premixed systems and to derive the transport equation for the conditional species mass fraction conditioned on the progress variable based on the enthalpy. Our statistical analysis will be based on the 3-D DNS database of Trouve and Poinsot available at the Center for Turbulence Research. The initial conditions and characteristics (turbulence, thermo-diffusive properties) as well as the numerical method utilized in the DNS of Trouve and Poinsot are presented, and some details concerning our statistical analysis are also given. From the analysis of DNS results, the effects of the position in the flame brush, of the Damkoehler and Lewis numbers on the conditional mean scalar dissipation, and conditional mean velocity are presented and discussed. Information concerning unconditional turbulent fluxes are also presented. The anomaly found in previous studies of counter-gradient diffusion for the turbulent flux of the progress variable is investigated.
Characteristics of 3D turbulent jets in crossflow
NASA Technical Reports Server (NTRS)
Demuren, A. O.
1991-01-01
Three dimensional turbulent jets in crossflow at low to medium jet-to-crossflow velocity ratios are computed with a finite volume numerical procedure which utilizes a second-moment closure model to approximate the Reynolds stresses. A multigrid method is used to accelerate the convergence rate of the procedure. Comparison of the computations to measured data show good qualitative agreement. All trends are correctly predicted, though there is some uncertainty on the height of penetration of the jet. The evolution of the vorticity field is used to explore the jet-crossflow interaction.
Inhomogeneous turbulence in magnetic reconnection
NASA Astrophysics Data System (ADS)
Yokoi, Nobumitsu
2016-07-01
Turbulence is expected to play an essential role in enhancing magnetic reconnection. Turbulence associated with magnetic reconnection is highly inhomogeneous: it is generated by inhomogeneities of the field configuration such as the velocity shear, temperature gradient, density stratification, magnetic shear, etc. This self-generated turbulence affects the reconnection through the turbulent transport. In this reconnection--turbulence interaction, localization of turbulent transport due to dynamic balance between several turbulence effects plays an essential role. For investigating inhomogeneous turbulence in a strongly nonlinear regime, closure or turbulence modeling approaches provide a powerful tool. A turbulence modeling approach for the magnetic reconnection is introduced. In the model, the mean-field equations with turbulence effects incorporated are solved simultaneously with the equations of turbulent statistical quantities that represent spatiotemporal properties of turbulence under the effect of large-scale field inhomogeneities. Numerical simulations of this Reynolds-averaged turbulence model showed that self-generated turbulence enhances magnetic reconnection. It was pointed out that reconnection states may be divided into three category depending on the turbulence level: (i) laminar reconnection; (ii) turbulent reconnection, and (iii) turbulent diffusion. Recent developments in this direction are also briefly introduced, which includes the magnetic Prandtl number dependence, spectral evolution, and guide-field effects. Also relationship of this fully nonlinear turbulence approach with other important approaches such as plasmoid instability reconnection will be discussed.
NASA Technical Reports Server (NTRS)
Ristorcelli, J. R.
1995-01-01
The mathematical consequences of a few simple scaling assumptions about the effects of compressibility are explored using a simple singular perturbation idea and the methods of statistical fluid mechanics. Representations for the pressure-dilation and dilatational dissipation covariances appearing in single-point moment closures for compressible turbulence are obtained. While the results are expressed in the context of a second-order statistical closure they provide some interesting and very clear physical metaphors for the effects of compressibility that have not been seen using more traditional linear stability methods. In the limit of homogeneous turbulence with quasi-normal large-scales the expressions derived are - in the low turbulent Mach number limit - asymptotically exact. The expressions obtained are functions of the rate of change of the turbulence energy, its correlation length scale, and the relative time scale of the cascade rate. The expressions for the dilatational covariances contain constants which have a precise and definite physical significance; they are related to various integrals of the longitudinal velocity correlation. The pressure-dilation covariance is found to be a nonequilibrium phenomena related to the time rate of change of the internal energy and the kinetic energy of the turbulence. Also of interest is the fact that the representation for the dilatational dissipation in turbulence, with or without shear, features a dependence on the Reynolds number. This article is a documentation of an analytical investigation of the implications of a pseudo-sound theory for the effects of compressibility.
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.
Group-kinetic theory of turbulence
NASA Technical Reports Server (NTRS)
Tchen, C. M.
1986-01-01
The two phases are governed by two coupled systems of Navier-Stokes equations. The couplings are nonlinear. These equations describe the microdynamical state of turbulence, and are transformed into a master equation. By scaling, a kinetic hierarchy is generated in the form of groups, representing the spectral evolution, the diffusivity and the relaxation. The loss of memory in formulating the relaxation yields the closure. The network of sub-distributions that participates in the relaxation is simulated by a self-consistent porous medium, so that the average effect on the diffusivity is to make it approach equilibrium. The kinetic equation of turbulence is derived. The method of moments reverts it to the continuum. The equation of spectral evolution is obtained and the transport properties are calculated. In inertia turbulence, the Kolmogoroff law for weak coupling and the spectrum for the strong coupling are found. As the fluid analog, the nonlinear Schrodinger equation has a driving force in the form of emission of solitons by velocity fluctuations, and is used to describe the microdynamical state of turbulence. In order for the emission together with the modulation to participate in the transport processes, the non-homogeneous Schrodinger equation is transformed into a homogeneous master equation. By group-scaling, the master equation is decomposed into a system of transport equations, replacing the Bogoliubov system of equations of many-particle distributions. It is in the relaxation that the memory is lost when the ensemble of higher-order distributions is simulated by an effective porous medium. The closure is thus found. The kinetic equation is derived and transformed into the equation of spectral flow.
Tieszen, Sheldon Robert; Domino, Stefan Paul; Black, Amalia Rebecca
2005-06-01
A validation study has been conducted for a turbulence model used to close the temporally filtered Navier Stokes (TFNS) equations. A turbulence model was purposely built to support fire simulations under the Accelerated Strategic Computing (ASC) program. The model was developed so that fire transients could be simulated and it has been implemented in SIERRA/Fuego. The model is validated using helium plume data acquired for the Weapon System Certification Campaign (C6) program in the Fire Laboratory for Model Accreditation and Experiments (FLAME). The helium plume experiments were chosen as the first validation problem for SIERRA/Fuego because they embody the first pair-wise coupling of scalar and momentum fields found in fire plumes. The validation study includes solution verification through grid and time step refinement studies. A formal statistical comparison is used to assess the model uncertainty. The metric uses the centerline vertical velocity of the plume. The results indicate that the simple model is within the 95% confidence interval of the data for elevations greater than 0.4 meters and is never more than twice the confidence interval from the data. The model clearly captures the dominant puffing mode in the fire but under resolves the vorticity field. Grid dependency of the model is noted.
On the prediction of turbulent secondary flows
NASA Technical Reports Server (NTRS)
Speziale, C. G.; So, R. M. C.; Younis, B. A.
1992-01-01
The prediction of turbulent secondary flows, with Reynolds stress models, in circular pipes and non-circular ducts is reviewed. Turbulence-driven secondary flows in straight non-circular ducts are considered along with turbulent secondary flows in pipes and ducts that arise from curvature or a system rotation. The physical mechanisms that generate these different kinds of secondary flows are outlined and the level of turbulence closure required to properly compute each type is discussed in detail. Illustrative computations of a variety of different secondary flows obtained from two-equation turbulence models and second-order closures are provided to amplify these points.
ERIC Educational Resources Information Center
Groffman, Sidney
An experimental test of visual closure based on an information-theory concept of perception was devised to test the ability to discriminate visual stimuli with reduced cues. The test is to be administered in a timed individual situation in which the subject is presented with sets of incomplete drawings of simple objects that he is required to name…
Randall, David A.; Cheng, Anning; Ghan, Steve; Khairoutdinov, Marat; Larson, Vince; Moeng, Chin-Hoh
2015-07-27
The intermediately-prognostic higher-order turbulence closure (IPHOC) introduces a joint double-Gaussian distribution of liquid water potential temperature (θ_{l} ), total water mixing ratio (q_{t }), and vertical velocity (w ) to represent any skewed turbulence circulations .The distribution is inferred from the first-, second-, and third-order moments of the variables given above, and is used to diagnose cloud fraction and grid-mean liquid water mixing ratio, as well as the buoyancy and fourth-order terms in the equations describing the evolution of the second- and third-order moments. Only three third-order moments (those of θ_{l} , q_{t }, and w ) are predicted in the IPHOC.
Computing aerodynamic sound using advanced statistical turbulence theories
NASA Technical Reports Server (NTRS)
Hecht, A. M.; Teske, M. E.; Bilanin, A. J.
1981-01-01
It is noted that the calculation of turbulence-generated aerodynamic sound requires knowledge of the spatial and temporal variation of Q sub ij (xi sub k, tau), the two-point, two-time turbulent velocity correlations. A technique is presented to obtain an approximate form of these correlations based on closure of the Reynolds stress equations by modeling of higher order terms. The governing equations for Q sub ij are first developed for a general flow. The case of homogeneous, stationary turbulence in a unidirectional constant shear mean flow is then assumed. The required closure form for Q sub ij is selected which is capable of qualitatively reproducing experimentally observed behavior. This form contains separation time dependent scale factors as parameters and depends explicitly on spatial separation. The approximate forms of Q sub ij are used in the differential equations and integral moments are taken over the spatial domain. The velocity correlations are used in the Lighthill theory of aerodynamic sound by assuming normal joint probability.
Dynamics and structure of turbulent premixed flames
NASA Technical Reports Server (NTRS)
Bilger, R. W.; Swaminathan, N.; Ruetsch, G. R.; Smith, N. S. A.
1995-01-01
In earlier work (Mantel & Bilger, 1994) the structure of the turbulent premixed flame was investigated using statistics based on conditional averaging with the reaction progress variable as the conditioning variable. The DNS data base of Trouve and Poinsot (1994) was used in this investigation. Attention was focused on the conditional dissipation and conditional axial velocity in the flame with a view to modeling these quantities for use in the conditional moment closure (CMC) approach to analysis of kinetics in premixed flames (Bilger, 1993). Two remarkable findings were made: there was almost no acceleration of the axial velocity in the flame front itself; and the conditional scalar dissipation remained as high, or higher, than that found in laminar premixed flames. The first finding was surprising since in laminar flames all the fluid acceleration occurs through the flame front, and this could be expected also for turbulent premixed flames at the flamelet limit. The finding gave hope of inventing a new approach to the dynamics of turbulent premixed flames through use of rapid distortion theory or an unsteady Bernoulli equation. This could lead to a new second order closure for turbulent premixed flames. The second finding was contrary to our measurements with laser diagnostics in lean hydrocarbon flames where it is found that conditional scalar dissipation drops dramatically below that for laminar flamelets when the turbulence intensity becomes high. Such behavior was not explainable with a one-step kinetic model, even at non-unity Lewis number. It could be due to depletion of H2 from the reaction zone by preferential diffusion. The capacity of the flame to generate radicals is critically dependent on the levels of H2 present (Bilger, et al., 1991). It seemed that a DNS computation with a multistep reduced mechanism would be worthwhile if a way could be found to make this feasible. Truly innovative approaches to complex problems often come only when there is the
Vowell, Kennison L.
1987-01-01
A closure for an inclined duct having an open upper end and defining downwardly extending passageway. The closure includes a cap for sealing engagement with the open upper end of the duct. Associated with the cap are an array of vertically aligned plug members, each of which has a cross-sectional area substantially conforming to the cross-sectional area of the passageway at least adjacent the upper end of the passageway. The plug members are interconnected in a manner to provide for free movement only in the plane in which the duct is inclined. The uppermost plug member is attached to the cap means and the cap means is in turn connected to a hoist means which is located directly over the open end of the duct.
Scaling laws for homogeneous turbulent shear flows in a rotating frame
NASA Technical Reports Server (NTRS)
Speziale, Charles G.; Mhuiris, Nessan Macgiolla
1988-01-01
The scaling properties of plane homogeneous turbulent shear flows in a rotating frame are examined mathematically by a direct analysis of the Navier-Stokes equations. It is proved that two such shear flows are dynamically similar if and only if their initial dimensionless energy spectrum E star (k star, 0), initial dimensionless shear rate SK sub 0/epsilon sub 0, initial Reynolds number K squared sub 0/nu epsilon sub 0, and the ration of the rotation rate to the shear rate omega/S are identical. Consequently, if universal equilibrium states exist, at high Reynolds numbers, they will only depend on the single parameter omega/S. The commonly assumed dependence of such equilibrium states on omega/S through the Richardson number Ri=-2(omega/S)(1-2 omega/S) is proven to be inconsistent with the full Navier-Stokes equations and to constitute no more than a weak approximation. To be more specific, Richardson number similarity is shown to only rigorously apply to certain low-order truncations of the Navier-Stokes equations (i.e., to certain second-order closure models) wherein closure is achieved at the second-moment level by assuming that the higher-order moments are a small perturbation of their isotropic states. The physical dependence of rotating turbulent shear flows on omega/S is discussed in detail along with the implications for turbulence modeling.
Nonlocal Closures for Plasma Fluid Simulations
NASA Astrophysics Data System (ADS)
Held, Eric
2003-10-01
Theoretical tools applied to lab and astrophysical plasmas tend toward two extremes: kinetic models rife with physics but operating for short times and fluid models employing simplified closure relations but operating for long times. Until computers are fast enough to calculate kinetic physics over resistive times, efforts to extend plasma fluid models to handle a wider range of physics are critical. In this work, we generalize the program of fluid closure to capture kinetic effects in nonlocal, integral forms for higher-order fluid moments. These closures embody collisional, particle-trapping and Landau physics by integrating the fluid drives and closure moments along characteristics of the distribution function, F. The inversion of an operator that includes these physical effects begins with an expansion in eigenfunctions of the collision operator. Next, the characteristics of F are identified by diagonalizing the resultant system of hyperbolic equations. Integrating and taking the closure moments of F results in coupled Volterra equations involving the fluid drives and closures. It is shown that the collisional and nearly collisionless limits of these integral equations match onto previous expressions. In addition to significantly advancing the realism of previous fluid closures, integration along comparatively few ( ˜ 100)characteristics represents a significant reduction in work compared to kinetic treatments that follow millions of particles. These characteristics uncover the essential velocity-space dependence of F and hence render this closure scheme suitable for simulation of long time scale behavior. As a specific example, we conclude this talk by discussing the incorporation of these closures in plasma fluid simulations of neoclassical tearing modes in ITER-relevant discharges.
LES, DNS and RANS for the analysis of high-speed turbulent reacting flows
NASA Technical Reports Server (NTRS)
Adumitroaie, V.; Colucci, P. J.; Taulbee, D. B.; Givi, P.
1995-01-01
The purpose of this research is to continue our efforts in advancing the state of knowledge in large eddy simulation (LES), direct numerical simulation (DNS), and Reynolds averaged Navier Stokes (RANS) methods for the computational analysis of high-speed reacting turbulent flows. In the second phase of this work, covering the period 1 Aug. 1994 - 31 Jul. 1995, we have focused our efforts on two programs: (1) developments of explicit algebraic moment closures for statistical descriptions of compressible reacting flows and (2) development of Monte Carlo numerical methods for LES of chemically reacting flows.
Electron parallel closures for arbitrary collisionality
Ji, Jeong-Young Held, Eric D.
2014-12-15
Electron parallel closures for heat flow, viscosity, and friction force are expressed as kernel-weighted integrals of thermodynamic drives, the temperature gradient, relative electron-ion flow velocity, and flow-velocity gradient. Simple, fitted kernel functions are obtained for arbitrary collisionality from the 6400 moment solution and the asymptotic behavior in the collisionless limit. The fitted kernels circumvent having to solve higher order moment equations in order to close the electron fluid equations. For this reason, the electron parallel closures provide a useful and general tool for theoretical and computational models of astrophysical and laboratory plasmas.
NASA Astrophysics Data System (ADS)
Krueger, S. K.; Lesage, A. T.; Bogenschutz, P.
2014-12-01
We are using a cloud-resolving model, SAM (System for Atmospheric Modeling) to examine the sensitivity of our simulations of an evolving mixed-phase cloud-topped boundary layer during a cold-air outbreak over the North Atlantic Ocean to the representations of the SGS turbulence and cloudiness and of the microphysics. Our version of SAM includes SHOC (Simplified Higher-Order Closure, Bogenschutz and Krueger 2013) which combines several existing components: A prognostic SGS turbulence kinetic energy (TKE) equation, an assumed double-Gaussian PDF following Golaz et al. (2002), the diagnostic second-moment closure of Redelsperger and Sommeria (1986), the diagnostic closure for the third moment of vertical velocity by Canuto et al. (2001), and a turbulence length scale related to the SGS TKE (Teixeira and Cheinet 2004) and to eddy length scales. Cold-air outbreaks typically produce an evolving cloud-topped boundary layer whose structure is influenced by strong surface fluxes of sensible and latent heat, mixed-phase microphysics, cloud-top radiative cooling, and cloud-top entrainment. By systematically varying the horizontal resolution from 1 to 100 km and comparing the results to a benchmark large-eddy simulation of the case, we will assess the ability of SHOC to represent this type of boundary layer. The image shows the cloud water path from a large-eddy simulation of the CONSTRAIN case. The domain size is 64 km by 64 km. Such simulations are used as benchmarks for coarse-grid simulations that use SHOC.
BOOK REVIEW: Statistical Mechanics of Turbulent Flows
NASA Astrophysics Data System (ADS)
Cambon, C.
2004-10-01
This is a handbook for a computational approach to reacting flows, including background material on statistical mechanics. In this sense, the title is somewhat misleading with respect to other books dedicated to the statistical theory of turbulence (e.g. Monin and Yaglom). In the present book, emphasis is placed on modelling (engineering closures) for computational fluid dynamics. The probabilistic (pdf) approach is applied to the local scalar field, motivated first by the nonlinearity of chemical source terms which appear in the transport equations of reacting species. The probabilistic and stochastic approaches are also used for the velocity field and particle position; nevertheless they are essentially limited to Lagrangian models for a local vector, with only single-point statistics, as for the scalar. Accordingly, conventional techniques, such as single-point closures for RANS (Reynolds-averaged Navier-Stokes) and subgrid-scale models for LES (large-eddy simulations), are described and in some cases reformulated using underlying Langevin models and filtered pdfs. Even if the theoretical approach to turbulence is not discussed in general, the essentials of probabilistic and stochastic-processes methods are described, with a useful reminder concerning statistics at the molecular level. The book comprises 7 chapters. Chapter 1 briefly states the goals and contents, with a very clear synoptic scheme on page 2. Chapter 2 presents definitions and examples of pdfs and related statistical moments. Chapter 3 deals with stochastic processes, pdf transport equations, from Kramer-Moyal to Fokker-Planck (for Markov processes), and moments equations. Stochastic differential equations are introduced and their relationship to pdfs described. This chapter ends with a discussion of stochastic modelling. The equations of fluid mechanics and thermodynamics are addressed in chapter 4. Classical conservation equations (mass, velocity, internal energy) are derived from their
Direct numerical simulation of soot formation and transport in turbulent nonpremixed ethylene flames
NASA Astrophysics Data System (ADS)
Lignell, David Owen
Combustion is central to society and accounts for the majority of the world's energy production. Soot formation, transport, and emission from turbulent flames are an important process in nonpremixed combustion. Soot is a major air pollutant with adverse health effects; its emission reduces combustion efficiencies associated with unburned fuel; and soot interacts strongly with the composition and temperature fields of flames, contributing to the bulk of radiative heat transfer. Simulation of combustion is an important and emerging discipline that compliments theoretical and experimental investigations and can provide fundamental insight into turbulent combustion environments and aid in engineering design of practical equipment. Simulations of practical combustion environments cannot fully resolve all flow and chemical phenomena due to the wide range of timescales and lengthscales present and must rely on models to capture the effects of unresolved turbulent transport and turbulence-chemistry interactions. Very little is know about soot formation in turbulent flames due to the difficulty of experimental measurements and the computational cost of simulation. Direct numerical simulation (DNS) resolves all relevant flow and chemical structures in turbulent flames, requiring no turbulence closure models. DNS of soot formation with realistic combustion chemistry and soot formation is presented in this dissertation. A series of increasingly complex flow configurations is investigated including one-dimensional relaxing diffusion flames, two-dimensional mixing layers and decaying turbulence simulations, and a three-dimensional temporally evolving jet flame. A reduced ethylene mechanism consisting of 19 transported species is coupled to a four-step soot model using the method of moments. The DNS are used to quantify soot formation and transport in turbulent flames. The proximity of soot to a flame is important, as this impacts the soot reaction and radiation rates
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.
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.
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.
Parallel Simulation of Unsteady Turbulent Flames
NASA Technical Reports Server (NTRS)
Menon, Suresh
1996-01-01
Time-accurate simulation of turbulent flames in high Reynolds number flows is a challenging task since both fluid dynamics and combustion must be modeled accurately. To numerically simulate this phenomenon, very large computer resources (both time and memory) are required. Although current vector supercomputers are capable of providing adequate resources for simulations of this nature, the high cost and their limited availability, makes practical use of such machines less than satisfactory. At the same time, the explicit time integration algorithms used in unsteady flow simulations often possess a very high degree of parallelism, making them very amenable to efficient implementation on large-scale parallel computers. Under these circumstances, distributed memory parallel computers offer an excellent near-term solution for greatly increased computational speed and memory, at a cost that may render the unsteady simulations of the type discussed above more feasible and affordable.This paper discusses the study of unsteady turbulent flames using a simulation algorithm that is capable of retaining high parallel efficiency on distributed memory parallel architectures. Numerical studies are carried out using large-eddy simulation (LES). In LES, the scales larger than the grid are computed using a time- and space-accurate scheme, while the unresolved small scales are modeled using eddy viscosity based subgrid models. This is acceptable for the moment/energy closure since the small scales primarily provide a dissipative mechanism for the energy transferred from the large scales. However, for combustion to occur, the species must first undergo mixing at the small scales and then come into molecular contact. Therefore, global models cannot be used. Recently, a new model for turbulent combustion was developed, in which the combustion is modeled, within the subgrid (small-scales) using a methodology that simulates the mixing and the molecular transport and the chemical kinetics
Advances in turbulence studies. [Magnetohydrodynamic flows
Branover, H.; Unger, Y.
1993-01-01
Important contemporary trends in both experimental and theoretical turbulence research are reported. Particular attention is given to vortex reconnection, cascade, and mixing in turbulent flows; intermittent turbulence from closures; tearing instabilities in 2D MHD turbulence; axisymmetric hydromagnetic dynamo; bifurcations in MHD flow generated by electric current discharge; renormalization group analysis of MHD turbulence with low magnetic Reynolds number; Solution for turbulent primary azimuthal velocity in liquid-metal flows in sliding electric contacts; analogies between geophysical and hydromagnetic flows; turbulent electrically-induced vortical flows; dissipation length scale dynamics; two-phase grid turbulence; abridged octave wavenumber ring models for 2D turbulence; rag theory of magnetic fluctuations in turbulent flow; and instabilities of the nonuniform flows of a low-temperature plasma in MHD channels.
Linzell, S.M.; Dorcy, D.J.
1958-08-26
A quick opening type of stuffing box employing two banks of rotatable shoes, each of which has a caraming action that forces a neoprene sealing surface against a pipe or rod where it passes through a wall is presented. A ring having a handle or wrench attached is placed eccentric to and between the two banks of shoes. Head bolts from the shoes fit into slots in this ring, which are so arranged that when the ring is rotated a quarter turn in one direction the shoes are thrust inwardly to cramp the neopnrene about the pipe, malting a tight seal. Moving the ring in the reverse direction moves the shoes outwardly and frees the pipe which then may be readily removed from the stuffing box. This device has particular application as a closure for the end of a coolant tube of a neutronic reactor.
Autonomic Closure for Large Eddy Simulation
NASA Astrophysics Data System (ADS)
King, Ryan; Hamlington, Peter; Dahm, Werner J. A.
2015-11-01
A new autonomic subgrid-scale closure has been developed for large eddy simulation (LES). The approach poses a supervised learning problem that captures nonlinear, nonlocal, and nonequilibrium turbulence effects without specifying a predefined turbulence model. By solving a regularized optimization problem on test filter scale quantities, the autonomic approach identifies a nonparametric function that represents the best local relation between subgrid stresses and resolved state variables. The optimized function is then applied at the grid scale to determine unknown LES subgrid stresses by invoking scale similarity in the inertial range. A priori tests of the autonomic approach on homogeneous isotropic turbulence show that the new approach is amenable to powerful optimization and machine learning methods and is successful for a wide range of filter scales in the inertial range. In these a priori tests, the autonomic closure substantially improves upon the dynamic Smagorinsky model in capturing the instantaneous, statistical, and energy transfer properties of the subgrid stress field.
Near-wall turbine closure for curved flows
NASA Technical Reports Server (NTRS)
So, R. M. C.; Lai, Y. G.; Hwang, B. C.
1991-01-01
At present, turbulence closures for curved flows only account for curvature effects in the fully turbulent region where the Reynolds number is large. The justification is that, near a wall, viscous effects dominate and curvature effects are only of secondary importance. Recent direct simulation data show that this assumption is not valid, even for simple two-dimensional fully developed turbulent curved channel flows. This paper presents an approach to develop a near-wall turbulence closure for wall-bounded curved flows. The curved channel direct simulation data is used as a guide to held develop such a closure. The proposed closure has the unique property of approaching conventional high-Reynolds-number Reynolds-stress closures far away from the wall. Hence, curvature effects in both the near-wall and the fully turbulent parts of the flow are accounted for properly. Validations of the closure are carried out with a set of low-Reynolds-number simulation data and with experimental measurements at high Reynolds number. Good agreement is obtained in both cases; in particular, the anisotropic behavior of the normal stresses and the shear stress behavior near the convex and concave walls.
LES, DNS and RANS for the analysis of high-speed turbulent reacting flows
NASA Technical Reports Server (NTRS)
Givi, Peyman; Taulbee, Dale B.; Adumitroaie, Virgil; Sabini, George J.; Shieh, Geoffrey S.
1994-01-01
The purpose of this research is to continue our efforts in advancing the state of knowledge in large eddy simulation (LES), direct numerical simulation (DNS), and Reynolds averaged Navier Stokes (RANS) methods for the computational analysis of high-speed reacting turbulent flows. In the second phase of this work, covering the period 1 Sep. 1993 - 1 Sep. 1994, we have focused our efforts on two research problems: (1) developments of 'algebraic' moment closures for statistical descriptions of nonpremixed reacting systems, and (2) assessments of the Dirichlet frequency in presumed scalar probability density function (PDF) methods in stochastic description of turbulent reacting flows. This report provides a complete description of our efforts during this past year as supported by the NASA Langley Research Center under Grant NAG1-1122.
NASA Astrophysics Data System (ADS)
Sundaram, Brruntha; Klimenko, Alexander Yuri; Cleary, Matthew John; Ge, Yipeng
2016-07-01
This work presents a direct and transparent interpretation of two concepts for modelling turbulent combustion: generalised Multiple Mapping Conditioning (MMC) and sparse-Lagrangian Large Eddy Simulation (LES). The MMC approach is presented as a hybrid between the Probability Density Function (PDF) method and approaches based on conditioning (e.g. Conditional Moment Closure, flamelet, etc.). The sparse-Lagrangian approach, which allows for a dramatic reduction of computational cost, is viewed as an alternative interpretation of the Filtered Density Function (FDF) methods. This work presents simulations of several turbulent diffusion flame cases and discusses the universality of the localness parameter between these cases and the universality of sparse-Lagrangian FDF methods with MMC.
Kinetic Electron Closures for Electromagnetic Simulation of Drift and Shear-Alfven Waves (II)
Cohen, B I; Dimits, A M; Nevins, W M; Chen, Y; Parker, S
2001-10-11
An electromagnetic hybrid scheme (fluid electrons and gyrokinetic ions) is elaborated in example calculations and extended to toroidal geometry. The scheme includes a kinetic electron closure valid for {beta}{sub e} > m{sub e}/m{sub i} ({beta}{sub e} is the ratio of the plasma electron pressure to the magnetic field energy density). The new scheme incorporates partially linearized ({delta}f) drift-kinetic electrons whose pressure and number density moments are used to close the fluid momentum equation for the electron fluid (Ohm's law). The test cases used are small-amplitude kinetic shear-Alfven waves with electron Landau damping, the ion-temperature-gradient instability, and the collisionless drift instability (universal mode) in an unsheared slab as a function of the plasma {beta}{sub e}. Attention is given to resolution and convergence issues in simulations of turbulent steady states.
Angular distribution of turbulence in wave space
NASA Technical Reports Server (NTRS)
Coleman, G.; Ferziger, J. H.; Bertoglio, J. P.
1987-01-01
An alternative to the one-point closure model for turbulence, the large eddy simulation (LES), together with its more exact relative, direct numerical simulation (DNS) are discussed. These methods are beginning to serve as partial substitutes for turbulence experiments. The eddy damped quasi-normal Markovian (EDQNM) theory is reviewed. Angular distribution of the converted data was examined in relationship to EDQNM.
TURBULENCE MODELING APPLIED TO BUOYANT PLUMES
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...
Lacunarity and intermittency in fluid turbulence
NASA Technical Reports Server (NTRS)
Smith, L. A.; Fournier, J.-D.; Spiegel, E. A.
1986-01-01
It is shown that oscillations in the high-order moments of turbulent velocity fields are inherent to the fractal character of intermittent turbulence and are a feature of the lacunarity of fractal sets. Oscillations in simple Cantor sets are described, and a single parameter to measure lacunarity is identified. The connection between oscillations in fractals and in the turbulent velocity correlations is discussed using the phenomenological beta model of intermittent turbulence (Frisch et al., 1978).
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.
NASA Astrophysics Data System (ADS)
Tse, K. L.; Mahalov, A.; Nicolaenko, B.; Joseph, B.
2004-09-01
Shear-convective turbulence is studied using a high resolution 3D direct numerical simulation (DNS). Flow configuration consisting of a modeled jet capping a thermally unstable layer is simulated and the results are compared with the reference situation where only the convective layer is present. Quasi-equilibrium turbulent datasets, in which the turbulent energy budgets are nearly balanced, are obtained. A ‘mechanical’ barrier is identified near the jet centerline in the shear-convective case. Intense and elongated vorticity regions are created in a narrow layer above the barrier in a way similar to the shear-sheltering effect. Vertical profiles of turbulence statistics and budgets are presented. We have unambiguously identified layers of counter-gradient momentum and heat fluxes which occur near regions of penetrative convection. Using quasi-equilibrium DNS datasets, we evaluate the performance of some popular second-order closure models of turbulence. The models satisfactorily predict the triple moments and dissipation, except in the counter-gradient region. The models, however, fail to predict the pressure correlation terms.
Merci, Bart; Roekaerts, Dirk; Naud, Bertrand; Pope, Stephen B.
2006-07-15
Numerical simulation results are presented for turbulent jet diffusion flames with various levels of turbulence-chemistry interaction, stabilized behind a bluff body (Sydney Flames HM1-3). Interaction between turbulence and combustion is modeled with the transported joint-scalar PDF approach. The mass density function transport equation is solved in a Lagrangian manner. A second-moment-closure turbulence model is applied to obtain accurate mean flow and turbulent mixing fields. The behavior of two micromixing models is discussed: the Euclidean minimum spanning tree model and the modified Curl coalescence dispersion model. The impact of the micromixing model choice on the results in physical space is small, although some influence becomes visible as the amount of local extinction increases. Scatter plots and profiles of conditional means and variances of thermochemical quantities, conditioned on the mixture fraction, are discussed both within and downstream of the recirculation region. A distinction is made between local extinction and incomplete combustion, based on the CO species mass fraction. The differences in qualitative behavior between the micromixing models are explained and quantitative comparison to experimental data is made. (author)
Numerical Simulation of High-Speed Turbulent Reacting Flows
NASA Technical Reports Server (NTRS)
Givi, P.; Taulbee, D. B.; Madnia, C. K.; Jaberi, F. A.; Colucci, P. J.; Gicquel, L. Y. M.; Adumitroaie, V.; James, S.
1999-01-01
The objectives of this research are: (1) to develop and implement a new methodology for large eddy simulation of (LES) of high-speed reacting turbulent flows. (2) To develop algebraic turbulence closures for statistical description of chemically reacting turbulent flows.
Calculation methods for compressible turbulent boundary layers, 1976
NASA Technical Reports Server (NTRS)
Bushnell, D. M.; Cary, A. M., Jr.; Harris, J. E.
1977-01-01
Equations and closure methods for compressible turbulent boundary layers are discussed. Flow phenomena peculiar to calculation of these boundary layers were considered, along with calculations of three dimensional compressible turbulent boundary layers. Procedures for ascertaining nonsimilar two and three dimensional compressible turbulent boundary layers were appended, including finite difference, finite element, and mass-weighted residual methods.
Calculation methods for compressible turbulent boundary layers
NASA Technical Reports Server (NTRS)
Bushnell, D. M.; Cary, A. M., Jr.; Harris, J. E.
1976-01-01
Calculation procedures for non-reacting compressible two- and three-dimensional turbulent boundary layers were reviewed. Integral, transformation and correlation methods, as well as finite difference solutions of the complete boundary layer equations summarized. Alternative numerical solution procedures were examined, and both mean field and mean turbulence field closure models were considered. Physics and related calculation problems peculiar to compressible turbulent boundary layers are described. A catalog of available solution procedures of the finite difference, finite element, and method of weighted residuals genre is included. Influence of compressibility, low Reynolds number, wall blowing, and pressure gradient upon mean field closure constants are reported.
Boltzmann kinetic equation for filtered fluid turbulence.
Girimaji, Sharath S
2007-07-20
We develop a kinetic Boltzmann equation for describing filtered fluid turbulence applicable for continuum and noncontinuum effects. The effect of unresolved turbulent motion on the resolved distribution function is elucidated and closure modeling issues of kinetic Boltzmann and Navier-Stokes descriptions are reconciled. This could pave the way for unifying turbulence modeling at kinetic and continuum levels and the development of numerical methods that are valid over a wide range of flow physics. PMID:17678288
Multilevel turbulence simulations
Tziperman, E.
1994-12-31
The authors propose a novel method for the simulation of turbulent flows, that is motivated by and based on the Multigrid (MG) formalism. The method, called Multilevel Turbulence Simulations (MTS), is potentially more efficient and more accurate than LES. In many physical problems one is interested in the effects of the small scales on the larger ones, or in a typical realization of the flow, and not in the detailed time history of each small scale feature. MTS takes advantage of the fact that the detailed simulation of small scales is not needed at all times, in order to make the calculation significantly more efficient, while accurately accounting for the effects of the small scales on the larger scale of interest. In MTS, models of several resolutions are used to represent the turbulent flow. The model equations in each coarse level incorporate a closure term roughly corresponding to the tau correction in the MG formalism that accounts for the effects of the unresolvable scales on that grid. The finer resolution grids are used only a small portion of the simulation time in order to evaluate the closure terms for the coarser grids, while the coarse resolution grids are then used to accurately and efficiently calculate the evolution of the larger scales. The methods efficiency relative to direct simulations is of the order of the ratio of required integration time to the smallest eddies turnover time, potentially resulting in orders of magnitude improvement for a large class of turbulence problems.
Stirring turbulence with turbulence
NASA Astrophysics Data System (ADS)
Cekli, Hakki Ergun; Joosten, René; van de Water, Willem
2015-12-01
We stir wind-tunnel turbulence with an active grid that consists of rods with attached vanes. The time-varying angle of these rods is controlled by random numbers. We study the response of turbulence on the statistical properties of these random numbers. The random numbers are generated by the Gledzer-Ohkitani-Yamada shell model, which is a simple dynamical model of turbulence that produces a velocity field displaying inertial-range scaling behavior. The range of scales can be adjusted by selection of shells. We find that the largest energy input and the smallest anisotropy are reached when the time scale of the random numbers matches that of the largest eddies of the wind-tunnel turbulence. A large mismatch of these times creates a highly intermittent random flow with interesting but quite anomalous statistics.
40 CFR 264.113 - Closure; time allowed for closure.
Code of Federal Regulations, 2011 CFR
2011-07-01
... 40 Protection of Environment 26 2011-07-01 2011-07-01 false Closure; time allowed for closure. 264... (CONTINUED) STANDARDS FOR OWNERS AND OPERATORS OF HAZARDOUS WASTE TREATMENT, STORAGE, AND DISPOSAL FACILITIES Closure and Post-Closure § 264.113 Closure; time allowed for closure. (a) Within 90 days after...
40 CFR 265.113 - Closure; time allowed for closure.
Code of Federal Regulations, 2011 CFR
2011-07-01
... 40 Protection of Environment 26 2011-07-01 2011-07-01 false Closure; time allowed for closure. 265... (CONTINUED) INTERIM STATUS STANDARDS FOR OWNERS AND OPERATORS OF HAZARDOUS WASTE TREATMENT, STORAGE, AND DISPOSAL FACILITIES Closure and Post-Closure § 265.113 Closure; time allowed for closure. (a) Within...
Mechanics of fatigue crack closure
NASA Technical Reports Server (NTRS)
Newman, J. C., Jr. (Editor); Elber, Wolf (Editor)
1988-01-01
Papers are presented on plasticity induced crack closure, crack closure in fatigue crack growth, the dependence of crack closure on fatigue loading variables, and a procedure for standardizing crack closure levels. Also considered are a statistical approach to crack closure determination, the crack closure behavior of surface cracks under pure bending, closure measurements on short fatigue cracks, and crack closure under plane strain conditions. Other topics include fatigue crack closure behavior at high stress ratios, the use of acoustic waves for the characterization of closed fatigue cracks, and the influence of fatigue crack wake length and state of stress on crack closure.
A closure scheme for chemical master equations
Smadbeck, Patrick; Kaznessis, Yiannis N.
2013-01-01
Probability reigns in biology, with random molecular events dictating the fate of individual organisms, and propelling populations of species through evolution. In principle, the master probability equation provides the most complete model of probabilistic behavior in biomolecular networks. In practice, master equations describing complex reaction networks have remained unsolved for over 70 years. This practical challenge is a reason why master equations, for all their potential, have not inspired biological discovery. Herein, we present a closure scheme that solves the master probability equation of networks of chemical or biochemical reactions. We cast the master equation in terms of ordinary differential equations that describe the time evolution of probability distribution moments. We postulate that a finite number of moments capture all of the necessary information, and compute the probability distribution and higher-order moments by maximizing the information entropy of the system. An accurate order closure is selected, and the dynamic evolution of molecular populations is simulated. Comparison with kinetic Monte Carlo simulations, which merely sample the probability distribution, demonstrates this closure scheme is accurate for several small reaction networks. The importance of this result notwithstanding, a most striking finding is that the steady state of stochastic reaction networks can now be readily computed in a single-step calculation, without the need to simulate the evolution of the probability distribution in time. PMID:23940327
Evolution equations for the joint probability of several compositions in turbulent combustion
Bakosi, Jozsef
2010-01-01
One-point statistical simulations of turbulent combustion require models to represent the molecular mixing of species mass fractions, which then determine the reaction rates. For multi-species mixing the Dirichlet distribution has been used to characterize the assumed joint probability density function (PDF) of several scalars, parametrized by solving modeled evolution equations for their means and the sum of their variances. The PDF is then used to represent the mixing state and to obtain the chemical reactions source terms in moment closures or large eddy simulation. We extend the Dirichlet PDF approach to transported PDF methods by developing its governing stochastic differential equation (SDE). The transport equation, as opposed to parametrizing the assumed PDF, enables (1) the direct numerical computation of the joint PDF (and therefore the mixing model to directly account for the flow dynamics (e.g. reaction) on the shape of the evolving PDF), and (2) the individual specification of the mixing timescales of each species. From the SDE, systems of equations are derived that govern the first two moments, based on which constraints are established that provide consistency conditions for material mixing. A SDE whose solution is the generalized Dirichlet PDF is also developed and some of its properties from the viewpoint of material mixing are investigated. The generalized Dirichlet distribution has the following advantages over the standard Dirichlet distribution due to its more general covariance structure: (1) its ability to represent differential diffusion (i.e. skewness) without affecting the scalar means, and (2) it can represent both negatively and positively correlated scalars. The resulting development is a useful representation of the joint PDF of inert or reactive scalars in turbulent flows: (1) In moment closures, the mixing physics can be consistently represented by one underlying modeling principle, the Dirichlet or the generalized Dirichlet PDF, and
Computation of turbulent channel flow using Large-Eddy Interaction Model
NASA Technical Reports Server (NTRS)
Hong, S. K.; Payne, F. R.
1987-01-01
The objective of the paper is to investigate the nature and values of closure parameters appearing in the proposed Large-Eddy Interaction Model for prediction of turbulent flow field. Effects of two closure parameters on predicted Reynolds stresses and other turbulence structural quantities are examined for channel flows at two Reynolds numbers.
Moment-to-Moment Emotions during Reading
ERIC Educational Resources Information Center
Graesser, Arthur C.; D'Mello, Sidney
2012-01-01
Moment-to-moment emotions are affective states that dynamically change during reading and potentially influence comprehension. Researchers have recently identified these emotions and the emotion trajectories in reading, tutoring, and problem solving. The primary learning-centered emotions are boredom, frustration, confusion, flow (engagement),…
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.
Partial moment entropy approximation to radiative heat transfer
Frank, Martin . E-mail: frank@mathematik.uni-kl.de; Dubroca, Bruno . E-mail: Bruno.Dubroca@math.u-bordeaux.fr; Klar, Axel . E-mail: klar@mathematik.uni-kl.de
2006-10-10
We extend the half moment entropy closure for the radiative heat transfer equations presented in Dubroca and Klar [B. Dubroca, A. Klar, Half moment closure for radiative transfer equations, J. Comput. Phys. 180 (2002) 584-596] and Turpault et al. [R. Turpault, M. Frank, B. Dubroca, A. Klar, Multigroup half space moment approximations to the radiative heat transfer equations, J. Comput. Phys. 198 (2004) 363-371] to multi-D. To that end, we consider a partial moment system with general partitions of the unit sphere closed by an entropy minimization principle. We give physical and mathematical reasons for this choice of model and study its properties. Several numerical examples in different physical regimes are presented.
Bumblebee Flight in Heavy Turbulence
NASA Astrophysics Data System (ADS)
Engels, T.; Kolomenskiy, D.; Schneider, K.; Lehmann, F.-O.; Sesterhenn, J.
2016-01-01
High-resolution numerical simulations of a tethered model bumblebee in forward flight are performed superimposing homogeneous isotropic turbulent fluctuations to the uniform inflow. Despite tremendous variation in turbulence intensity, between 17% and 99% with respect to the mean flow, we do not find significant changes in cycle-averaged aerodynamic forces, moments, or flight power when averaged over realizations, compared to laminar inflow conditions. The variance of aerodynamic measures, however, significantly increases with increasing turbulence intensity, which may explain flight instabilities observed in freely flying bees.
Energy transfer in compressible turbulence
NASA Technical Reports Server (NTRS)
Bataille, Francoise; Zhou, YE; Bertoglio, Jean-Pierre
1995-01-01
This letter investigates the compressible energy transfer process. We extend a methodology developed originally for incompressible turbulence and use databases from numerical simulations of a weak compressible turbulence based on Eddy-Damped-Quasi-Normal-Markovian (EDQNM) closure. In order to analyze the compressible mode directly, the well known Helmholtz decomposition is used. While the compressible component has very little influence on the solenoidal part, we found that almost all of the compressible turbulence energy is received from its solenoidal counterpart. We focus on the most fundamental building block of the energy transfer process, the triadic interactions. This analysis leads us to conclude that, at low turbulent Mach number, the compressible energy transfer process is dominated by a local radiative transfer (absorption) in both inertial and energy containing ranges.
NASA Astrophysics Data System (ADS)
Fox, Rodney O.; Vie, Aymeric; Laurent, Frederique; Chalons, Christophe; Massot, Marc
2012-11-01
Numerous applications involve a disperse phase carried by a gaseous flow. To simulate such flows, one can resort to a number density function (NDF) governed a kinetic equation. Traditionally, Lagrangian Monte-Carlo methods are used to solve for the NDF, but are expensive as the number of numerical particles needed must be large to control statistical errors. Moreover, such methods are not well adapted to high-performance computing because of the intrinsic inhomogeneity of the NDF. To overcome these issues, Eulerian methods can be used to solve for the moments of the NDF resulting in an unclosed Eulerian system of hyperbolic conservation laws. To obtain closure, in this work a multivariate bi-Gaussian quadrature is used, which can account for particle trajectory crossing (PTC) over a large range of Stokes numbers. This closure uses up to four quadrature points in 2-D velocity phase space to capture large-scale PTC, and an anisotropic Gaussian distribution around each quadrature point to model small-scale PTC. Simulations of 2-D particle-laden isotropic turbulence at different Stokes numbers are employed to validate the Eulerian models against results from the Lagrangian approach. Good agreement is found for the number density fields over the entire range of Stokes numbers tested. Research carried out at the Center for Turbulence Research 2012 Summer Program.
A Stochastic Model for the Relative Motion of High Stokes Number Particles in Isotropic Turbulence
NASA Astrophysics Data System (ADS)
Dhariwal, Rohit; Rani, Sarma; Koch, Donald
2014-11-01
In the current study, a novel analytical closure for the diffusion current in the PDF equation is presented that is applicable to high-inertia particle pairs with Stokes numbers Str >> 1 . Here Str is a Stokes number based on the time-scale τr of eddies whose size scales with pair separation r. Using this closure, Langevin equations were solved to evolve particle-pair relative velocities and separations in stationary isotropic turbulence. The Langevin equation approach enables the simulation of the full PDF of pair relative motion, instead of only the first few moments of the PDF as is the case in a moments-based approach. Accordingly, PDFs Ω (U | r) and Ω (Ur | r) are computed for various separations r, where the former is the PDF of relative velocity U and the latter is the PDF of the radial component of relative velocity Ur, both conditioned upon the separation r. Consistent with the DNS study of Sundaram & Collins, the Langevin simulations capture the transition of Ω (U | r) from being Gaussian at integral-scale separations to an exponential PDF at Kolmogorov-scale separations. The radial distribution functions (RDFs) computed from these simulations also show reasonable quantitative agreement with those from the DNS of Fevrier et al.
Transcatheter closure of ruptured sinus of valsalva to left ventricle
Manuel, Devi A; Lahiri, Anandaroop; George, Oommen K
2016-01-01
We report a rare case of ruptured right sinus of valsalva into the left ventricle (LV). Transthoracic echocardiography showed a marked turbulent flow from the right aortic sinus to the LV. We describe a novel technique of closure of this defect with duct occluder, involving the formation of an arterio-arterial loop, without resorting to the usual arteriovenous loop. PMID:27011698
Transcatheter closure of ruptured sinus of valsalva to left ventricle.
Manuel, Devi A; Lahiri, Anandaroop; George, Oommen K
2016-01-01
We report a rare case of ruptured right sinus of valsalva into the left ventricle (LV). Transthoracic echocardiography showed a marked turbulent flow from the right aortic sinus to the LV. We describe a novel technique of closure of this defect with duct occluder, involving the formation of an arterio-arterial loop, without resorting to the usual arteriovenous loop. PMID:27011698
Turbulence transport with nonlocal interactions
Linn, R.R.; Clark, T.T.; Harlow, F.H.; Turner, L.
1998-03-01
This preliminary report describes a variety of issues in turbulence transport analysis with particular emphasis on closure procedures that are nonlocal in wave-number and/or physical space. Anomalous behavior of the transport equations for large scale parts of the turbulence spectrum are resolved by including the physical space nonlocal interactions. Direct and reverse cascade processes in wave-number space are given a much richer potential for realistic description by the nonlocal formulations. The discussion also describes issues, many still not resolved, regarding new classes of self-similar form functions.
Theory of strong turbulence by renormalization
NASA Technical Reports Server (NTRS)
Tchen, C. M.
1981-01-01
The hydrodynamical equations of turbulent motions are inhomogeneous and nonlinear in their inertia and force terms and will generate a hierarchy. A kinetic method was developed to transform the hydrodynamic equations into a master equation governing the velocity distribution, as a function of the time, the position and the velocity as an independent variable. The master equation presents the advantage of being homogeneous and having fewer nonlinear terms and is therefore simpler for the investigation of closure. After the closure by means of a cascade scaling procedure, the kinetic equation is derived and possesses a memory which represents the nonMarkovian character of turbulence. The kinetic equation is transformed back to the hydrodynamical form to yield an energy balance in the cascade form. Normal and anomalous transports are analyzed. The theory is described for incompressible, compressible and plasma turbulence. Applications of the method to problems relating to sound generation and the propagation of light in a nonfrozen turbulence are considered.
Probability density function of a passive scalar in turbulent shear flows
Kollmann, W.; Janicka, J.
1982-10-01
The transport equation for the probability density function of a scalar in turbulent shear flow is analyzed and the closure based on the gradient flux model for the turbulent flux and an integral model for the scalar dissipation term is put forward. The probability density function equation is complemented by a two-equation turbulence model. Application to several shear flows proves the capability of the closure model to determine the probability density function of passive scalars.
Solvents level dipole moments.
Liang, Wenkel; Li, Xiaosong; Dalton, Larry R; Robinson, Bruce H; Eichinger, Bruce E
2011-11-01
The dipole moments of highly polar molecules measured in solution are usually smaller than the molecular dipole moments that are calculated with reaction field methods, whereas vacuum values are routinely calculated in good agreement with available vapor phase data. Whether from Onsager's theory (or variations thereof) or from quantum mechanical methods, the calculated molecular dipoles in solution are found to be larger than those measured. The reason, of course, is that experiments measure the net dipole moment of solute together with the polarized (perturbed) solvent "cloud" surrounding it. Here we show that the reaction field charges that are generated in the quantum mechanical self-consistent reaction field (SCRF) method give a good estimate of the net dipole moment of the solute molecule together with the moment arising from the reaction field charges. This net dipole is a better description of experimental data than the vacuum dipole moment and certainly better than the bare dipole moment of the polarized solute molecule. PMID:21923185
Stochastic superparameterization in quasigeostrophic turbulence
Grooms, Ian; Majda, Andrew J.
2014-08-15
In this article we expand and develop the authors' recent proposed methodology for efficient stochastic superparameterization algorithms for geophysical turbulence. Geophysical turbulence is characterized by significant intermittent cascades of energy from the unresolved to the resolved scales resulting in complex patterns of waves, jets, and vortices. Conventional superparameterization simulates large scale dynamics on a coarse grid in a physical domain, and couples these dynamics to high-resolution simulations on periodic domains embedded in the coarse grid. Stochastic superparameterization replaces the nonlinear, deterministic eddy equations on periodic embedded domains by quasilinear stochastic approximations on formally infinite embedded domains. The result is a seamless algorithm which never uses a small scale grid and is far cheaper than conventional SP, but with significant success in difficult test problems. Various design choices in the algorithm are investigated in detail here, including decoupling the timescale of evolution on the embedded domains from the length of the time step used on the coarse grid, and sensitivity to certain assumed properties of the eddies (e.g. the shape of the assumed eddy energy spectrum). We present four closures based on stochastic superparameterization which elucidate the properties of the underlying framework: a ‘null hypothesis’ stochastic closure that uncouples the eddies from the mean, a stochastic closure with nonlinearly coupled eddies and mean, a nonlinear deterministic closure, and a stochastic closure based on energy conservation. The different algorithms are compared and contrasted on a stringent test suite for quasigeostrophic turbulence involving two-layer dynamics on a β-plane forced by an imposed background shear. The success of the algorithms developed here suggests that they may be fruitfully applied to more realistic situations. They are expected to be particularly useful in providing accurate and
Course 4: Statistical Turbulence Modelling for the Computation of Physically Complex Flows
NASA Astrophysics Data System (ADS)
Leschziner, M. A.
Contents 1 Approaches to characterising turbulence 2 Some basic statistical properties of turbulence and associated implications 3 Review of "simple" modelling approaches 3.1 The eddy-viscosity concept 3.2 Model categories 3.3 Model applicability 4 Second-moment equations and implied stress-strain interactions 4.1 Near-wall shear 4.2 Streamline curvature 4.3 Separation and recirculating flow 4.4 Rotation 4.5 Irrotational strain 4.6 Heat transfer and stratification 5 Second moment closure 6 Non-linear eddy-viscosity models 7 Application examples 7.1 Overview 7.2 Asymmetric diffuser 7.3 Aerospatiale aerofoil 7.4 Cascade blade 7.5 Axisymmetric impinging jet 7.6 Prolate spheroid 7.7 Round-to-rectangular transition duct 7.8 Wing/flat-plate junction 7.9 Fin-plate junction 7.10 Jet-afterbody combination 8 Concluding remarks
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.
Realizable Closure Model for the Reynolds Stress in Rotating Frames
NASA Astrophysics Data System (ADS)
Petty, Charles; Benard, Andre
2015-11-01
The Reynolds-averaged Navier-Stokes equation for constant property Newtonian fluids is unclosed due to the explicit appearance of the normalized Reynolds stress and the turbulent kinetic energy. A non-negative algebraic mapping of the normalized Reynolds stress into itself provides a practical closure for a wide class of flows. Unlike eddy viscosity closure models, the theory predict the redistribution of the turbulent kinetic energy among the three components of the fluctuating velocity field for statistically stationary spanwise rotating channel flows as well as the Coriolis re-distribution of turbulent kinetic energy among the three components of the fluctuating velocity field in rotating homogeneous decay. The results partially support the conjecture that the index-of-refraction of the troposphere is anisotropic at all scales.
A B-B-G-K-Y framework for fluid turbulence
NASA Technical Reports Server (NTRS)
Montgomery, D.
1975-01-01
A kinetic theory for fluid turbulence is developed from the Liouville equation and the associated BBGKY hierarchy. Real and imaginary parts of Fourier coefficients of fluid variables play the roles of particles. Closure is achieved by the assumption of negligible five-coefficient correlation functions and probability distributions of Fourier coefficients are the basic variables of the theory. An additional approximation leads to a closed-moment description similar to the so-called eddy-damped Markovian approximation. A kinetic equation is derived for which conservation laws and an H-theorem can be rigorously established, the H-theorem implying relaxation of the absolute equilibrium of Kraichnan. The equation can be cast in the Fokker-Planck form, and relaxation times estimated from its friction and diffusion coefficients. An undetermined parameter in the theory is the free decay time for triplet correlations. Some attention is given to the inclusion of viscous damping and external driving forces.
NASA Astrophysics Data System (ADS)
Lecoustre, Vivien; Arias, Paul; Roy, Somesh; Wang, Wei; Luo, Zhaoyu; Haworth, Dan; Im, Hong; Lu, Tianfeng; Ma, Kwan-Liu; Sankaran, Ramanan; Trouve, Arnaud
2011-11-01
Direct numerical simulations of 2D temporally-evolving luminous turbulent ethylene-air jet diffusion flames are performed using a high-order compressible Navier-Stokes solver. The simulations use a reduced mechanism derived from a detailed ethylene-air chemical kinetic mechanism that includes the reaction pathways for the formation of polycyclic aromatic hydrocarbons. The gas-phase chemistry is coupled with a detailed soot particle model based on the method of moments with interpolative closure that accounts for soot nucleation, coagulation, surface growth through HACA mechanism, and oxidation. Radiative heat transfer of CO2, H2O, and soot is treated by solving the radiative transfer equation using the discrete transfer method. This work presents preliminary results of radiation effects on soot dynamics at the tip of a jet diffusion flame with a particular focus on soot formation/oxidation.
NASA Technical Reports Server (NTRS)
Bilanin, A. J.; Teske, M. E.; Hirsh, J. E.
1978-01-01
Enhanced dispersion of two-dimensional trailed vortex pairs within simplified neutral atmospheric backgrounds is studied numerically for three conditions: when the pair is imbedded in a constant turbulent bath (constant dissipation); when the pair is subjected to a mean cross-wind shear; and when the pair is near the ground. Turbulent transport is modeled using second-order closure turbulent transport theory. The turbulent background fields are constructed using a superequilibrium approximation. The computed results allow several general conclusions to be drawn with regard to the reduction in circulation of the vortex pair and the rolling moment induced on a following aircraft: (1) the rate of decay of a vortex pair increases with increasing background dissipation rate; (2) cross-wind shear disperses the vortex whose vorticity is opposite to the background; and (3) the proximity of a ground plane reduces the hazard of the pair by scrubbing. The phenomenon of vortex bounce is explained in terms of secondary vorticity produced at the ground plane. Qualitative comparisons are made with available experimental data, and inferences of these results upon the persistence of aircraft trailing vortices are discussed.
Recent developments in the theory and simulation of turbulent mixing.
Cheng, B.; George, E.; Glimm, James; Jin, H.; Li, X.; Sharp, D. H.; Xu, Z.; Zhang, Y.
2004-01-01
We report on recent developments of the authors and coworkers on theory and simulation of turbulent mixing. Our main theoretical results are new and improved closures for averaged equations. We have simulations consistent with experiment for RT mixing and a quantitative explanation of the failure of many simulation codes to do this. New front tracking algorithms will enable improved simulations of the complex microphyics of mixing. We report on two new developments for the closure of averaged equations. We continue our study of the complete first order closure of the multiphase equations, in that each phase has complete and independent thermodynamic parameters. We extend the incompressible closure to an arbitrary number n of fluids. We specify the interfacial velocities as a function of the phase mean velocities in a new closure relation. For n = 2 compressible fluids, a new closure satisfies energy conservation and for smooth flows, conservation of phase entropy. An analysis of the entropy of averaging supports this closure.
PDF approach for turbulent scalar field: Some recent developments
NASA Technical Reports Server (NTRS)
Gao, Feng
1993-01-01
The probability density function (PDF) method has been proven a very useful approach in turbulence research. It has been particularly effective in simulating turbulent reacting flows and in studying some detailed statistical properties generated by a turbulent field There are, however, some important questions that have yet to be answered in PDF studies. Our efforts in the past year have been focused on two areas. First, a simple mixing model suitable for Monte Carlo simulations has been developed based on the mapping closure. Secondly, the mechanism of turbulent transport has been analyzed in order to understand the recently observed abnormal PDF's of turbulent temperature fields generated by linear heat sources.
Studying Turbulence Using Numerical Simulation Databases. Proceedings of the 1987 Summer Program
NASA Technical Reports Server (NTRS)
Moin, Parviz (Editor); Reynolds, William C. (Editor); Kim, John (Editor)
1987-01-01
The focus was on the use of databases obtained from direct numerical simulations of turbulent flows, for study of turbulence physics and modeling. Topics addressed included: stochastic decomposition/chaos/bifurcation; two-point closure (or k-space) modeling; scalar transport/reacting flows; Reynolds stress modeling; and structure of turbulent boundary layers.
Closure modeling using field inversion and machine learning
NASA Astrophysics Data System (ADS)
Duraisamy, Karthik
2015-11-01
The recent acceleration in computational power and measurement resolution has made possible the availability of extreme scale simulations and data sets. In this work, a modeling paradigm that seeks to comprehensively harness large scale data is introduced, with the aim of improving closure models. Full-field inversion (in contrast to parameter estimation) is used to obtain corrective, spatially distributed functional terms, offering a route to directly address model-form errors. Once the inference has been performed over a number of problems that are representative of the deficient physics in the closure model, machine learning techniques are used to reconstruct the model corrections in terms of variables that appear in the closure model. These machine-learned functional forms are then used to augment the closure model in predictive computations. The approach is demonstrated to be able to successfully reconstruct functional corrections and yield predictions with quantified uncertainties in a range of turbulent flows.
Numerical Simulation of High-Speed Turbulent Reacting Flows
NASA Technical Reports Server (NTRS)
Givi, P.; Taulbee, D. B.; Madnia, C. K.; Jaberi, F. A.; Colucci, P. J.; Gicquel, L. Y. M.; Adumitroaie, V.; James, S.
1999-01-01
The objectives of this research are: (1) to develop and implement a new methodology for large eddy simulation of (LES) of high-speed reacting turbulent flows. (2) To develop algebraic turbulence closures for statistical description of chemically reacting turbulent flows. We have just completed the third year of Phase III of this research. This is the Final Report of our activities on this research sponsored by the NASA LaRC.
A CLASS OF PHYSICALLY MOTIVATED CLOSURES FOR RADIATION HYDRODYNAMICS
Chan, Chi-kwan
2011-02-01
Radiative transfer and radiation hydrodynamics use the relativistic Boltzmann equation to describe the kinetics of photons. It is difficult to solve the six-dimensional time-dependent transfer equation unless the problem is highly symmetric or in equilibrium. When the radiation field is smooth, it is natural to take angular moments of the transfer equation to reduce the degrees of freedom. However, low order moment equations contain terms that depend on higher order moments. To close the system of moment equations, approximations are made to truncate this hierarchy. Popular closures used in astrophysics include flux-limited diffusion and the M{sub 1} closure, which are rather ad hoc and do not necessarily capture the correct physics. In this paper, we propose a new class of closures for radiative transfer and radiation hydrodynamics. We start from a different perspective and highlight the consistency of a fully relativistic formalism. We present a generic framework to approximate radiative transfer based on relativistic Grad's moment method. We then derive a 14-field method that minimizes unphysical photon self-interaction.
NASA Technical Reports Server (NTRS)
White, III, Dorsey E. (Inventor); Updike, deceased, Benjamin T. (Inventor); Allred, Johnny W. (Inventor)
1989-01-01
A quick actuating closure for a pressure vessel 80 in which a wedge ring 30 with a conical outer surface 31 is moved forward to force shear blocks 40, with conical inner surfaces 41, radially outward to lock an end closure plug 70 within an opening 81 in the pressure vessel 80. A seal ring 60 and a preload ramp 50 sit between the shear blocks 40 and the end closure plug 70 to provide a backup sealing capability. Conical surfaces 44 and 55 of the preload ramp 50 and the shear blocks 40 interact to force the seal ring 60 into shoulders 73 and 85 in the end closure plug 70 and opening 81 to form a tight seal. The end closure plug 70 is unlocked by moving the wedge ring 30 rearward, which causes T-bars 32 of the wedge ring 30 riding within T -slots 42 of the shear blocks 40 to force them radially inward. The end closure plug 70 is then removed, allowing access to the interior of the pressure vessel 80.
Michael Ramsey-Musolf; Wick Haxton; Ching-Pang Liu
2002-03-29
Nuclear anapole moments are parity-odd, time-reversal-even E1 moments of the electromagnetic current operator. Although the existence of this moment was recognized theoretically soon after the discovery of parity nonconservation (PNC), its experimental isolation was achieved only recently, when a new level of precision was reached in a measurement of the hyperfine dependence of atomic PNC in 133Cs. An important anapole moment bound in 205Tl also exists. In this paper, we present the details of the first calculation of these anapole moments in the framework commonly used in other studies of hadronic PNC, a meson exchange potential that includes long-range pion exchange and enough degrees of freedom to describe the five independent S-P amplitudes induced by short-range interactions. The resulting contributions of pi-, rho-, and omega-exchange to the single-nucleon anapole moment, to parity admixtures in the nuclear ground state, and to PNC exchange currents are evaluated, using configuration-mixed shell-model wave functions. The experimental anapole moment constraints on the PNC meson-nucleon coupling constants are derived and compared with those from other tests of the hadronic weak interaction. While the bounds obtained from the anapole moment results are consistent with the broad ''reasonable ranges'' defined by theory, they are not in good agreement with the constraints from the other experiments. We explore possible explanations for the discrepancy and comment on the potential importance of new experiments.
ERIC Educational Resources Information Center
Zichittella, Jack
1998-01-01
Discusses Henri Cartier-Bresson's notion of the "aesthetic of the decisive moment" and its role in photographic composition. Argues that recording spontaneous moments from real life can produce significant and complex photographs. Suggests that instilling this technique in photography students frees them to experiment without fear of failure. (DSK)
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.
Valentine, Christine
2007-01-01
The "moment of death," once a dominant concept in preparing for a "good death", has been eclipsed by a focus on the wider concept of the "dying trajectory". However, findings from interviews with 25 bereaved individuals suggest that dying loved ones' final moments may still be experienced as highly significant in their own right. In some accounts the dying individual's final moments did not feature or made little impression, either because the survivor was not present, or there was no obviously definable moment, or because other, usually medical factors, such as whether to resuscitate the person, took precedence. However, in six cases such moments were constructed as profound, special, and memorable occasions. These constructions are explored in relation to achieving a good death, the dying trajectory as a whole, and making sense of the bereavement experience. Their implications for sociological theories of identity and embodiment are also considered. PMID:18214069
NASA Astrophysics Data System (ADS)
Bogenschutz, Peter A.
Over the past few years a new type of general circulation model (GCM) has emerged that is known as the multiscale modeling framework (MMF). The Colorado State University (CSU) MMF represents a coupling between the Community Atmosphere Model (CAM) GCM and the System of Atmospheric Modeling (SAM) cloud resolving model (CRM). Within this MMF the embedded CRM replaces the traditionally used parameterized moist physics in CAM to represent subgrid-scale (SGS) convection. However, due to substantial increases of computational burden associated with the MMF, the embedded CRM is typically run with a horizontal grid size of 4 km. With a horizontal grid size of 4 km, a low-order closure CRM cannot adequately represent shallow convective processes, such as trade-wind cumulus or stratocumulus. A computationally inexpensive parameterization of turbulence and clouds is presented in this dissertation. An extensive a priori test is performed to determine which functional form of an assumed PDF is best suited for coarse-grid CRMs for both deep shallow and deep convection. The diagnostic approach to determine the input moments needed for the assumed PDFs uses the subgrid-scale (SGS) turbulent kinetic energy (TKE) as the basis for the parameterization. The term known as the turbulent length scale (L) is examined, as it is needed to parameterize the dissipation of turbulence and therefore is needed to better balance the budgets of SGS TKE. A new formulation of this term is added to the model code which appears to be able to partition resolved and SGS TKE fairly accurately. Results from "offline" tests of the simple diagnostic closure within SAM shows that the cloud and turbulence properties of shallow convection can be adequately represented when compared to large eddy simulation (LES) benchmark simulations. Results are greatly improved when compared to the standard version of SAM. The preliminary test of the scheme within the embedded CRM of the MMF shows promising results with the
Maximum-entropy closures for kinetic theories of neuronal network dynamics.
Rangan, Aaditya V; Cai, David
2006-05-01
We analyze (1 + 1)D kinetic equations for neuronal network dynamics, which are derived via an intuitive closure from a Boltzmann-like equation governing the evolution of a one-particle (i.e., one-neuron) probability density function. We demonstrate that this intuitive closure is a generalization of moment closures based on the maximum-entropy principle. By invoking maximum-entropy closures, we show how to systematically extend this kinetic theory to obtain higher-order, kinetic equations and to include coupled networks of both excitatory and inhibitory neurons. PMID:16712338
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.
Simulation of Turbulence Using the Stabilization Principle
NASA Astrophysics Data System (ADS)
Meyers, Ronald E.; Deacon, Keith S.
2000-11-01
The Stabilization Principle developed by Zak and Meyers for solving Navier-Stokes turbulence [ 1,2 ] has been used to simulate turbulent flow over a flat plate and a cylinder. The Stabilization Principle acts on the instantaneous Reynolds stress like a closure by allowing turbulent fluctuations to grow to the level of neutral instability. Experimental stability measurements suppport this approach. Theory and visualization of results will be presented. Computed results appear to provide very realistic space and time simulations of turbulence. [1] M.Zak, J.P. Zbilut, R.E. Meyers, "From Instability to Intelligence: Complexity and Predictability in Nonlinear Dynamics", Springer-Verlag, Lecture Notes in Physics, June 1997. [2] R.E. Meyers, M.Zak, "Representation of Turbulence and Chaos Using the Stabilization Principle", ZAMM, 76, 1996.
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.
Turbulence kinetic energy equation for dilute suspensions
NASA Technical Reports Server (NTRS)
Abou-Arab, T. W.; Roco, M. C.
1989-01-01
A multiphase turbulence closure model is presented which employs one transport equation, namely the turbulence kinetic energy equation. The proposed form of this equation is different from the earlier formulations in some aspects. The power spectrum of the carrier fluid is divided into two regions, which interact in different ways and at different rates with the suspended particles as a function of the particle-eddy size ratio and density ratio. The length scale is described algebraically. A mass/time averaging procedure for the momentum and kinetic energy equations is adopted. The resulting turbulence correlations are modeled under less retrictive assumptions comparative to previous work. The closures for the momentum and kinetic energy equations are given. Comparisons of the predictions with experimental results on liquid-solid jet and gas-solid pipe flow show satisfactory agreement.
Moment inference from tomograms
Day-Lewis, F. D.; Chen, Y.; Singha, K.
2007-01-01
Time-lapse geophysical tomography can provide valuable qualitative insights into hydrologic transport phenomena associated with aquifer dynamics, tracer experiments, and engineered remediation. Increasingly, tomograms are used to infer the spatial and/or temporal moments of solute plumes; these moments provide quantitative information about transport processes (e.g., advection, dispersion, and rate-limited mass transfer) and controlling parameters (e.g., permeability, dispersivity, and rate coefficients). The reliability of moments calculated from tomograms is, however, poorly understood because classic approaches to image appraisal (e.g., the model resolution matrix) are not directly applicable to moment inference. Here, we present a semi-analytical approach to construct a moment resolution matrix based on (1) the classic model resolution matrix and (2) image reconstruction from orthogonal moments. Numerical results for radar and electrical-resistivity imaging of solute plumes demonstrate that moment values calculated from tomograms depend strongly on plume location within the tomogram, survey geometry, regularization criteria, and measurement error. Copyright 2007 by the American Geophysical Union.
Horton, W.; Hu, G.
1998-07-01
The origin of plasma turbulence from currents and spatial gradients in plasmas is described and shown to lead to the dominant transport mechanism in many plasma regimes. A wide variety of turbulent transport mechanism exists in plasmas. In this survey the authors summarize some of the universally observed plasma transport rates.
Chang, D. . Dept. of Physics and Astronomy Fermi National Accelerator Lab., Batavia, IL ); Senjanovic, G. . Dept. of Theoretical Physics)
1990-01-01
We review attempts to achieve a large neutrino magnetic moment ({mu}{sub {nu}} {le} 10{sup {minus}11}{mu}{sub B}), while keeping neutrino light or massless. The application to the solar neutrino puzzle is discussed. 24 refs.
NASA Technical Reports Server (NTRS)
Bock, G.
1946-01-01
When flying in a turn or pulling out of a dive, the airscrew exerts a gyroscopic moment on the aircraft, In the case of airscrews with three or more blades, arranged symmetrically, the value of the gyroscopic moment is J(sub x) omega(sub x) omega(sub y), where J(sub x) denotes the axial moment of inertia about the axis of rotation of the airscrew, omega(sub x) the angular upeed of the airscrew about its axis, and omega (sub Y) the rotary speed of the whole aircraft about an axis parallel to the plane of the airscrew (e.g., when pulling up, the transverse axis of the aircraft). The gyroscopic moment then tends to rotate the aircraft about an axis perpendicular to those of the two angular speeds and, in the came of airscrews with three or more blades, is constant during a revolution of the airscrew. With two-bladed airscrews, on the contrary, although the calculate gyroscopic moment represents the mean value in time, it fluctuates about this value with a frequency equal to twice the revolutions per minute. In addition, pulsating moments likewise occur about the other two axes. This fact is known from the theory of the asymmetrical gyro; the calculations that have been carried out for the determination of the various gyroscopic moments, however, mostly require an exact knowledge of the gyro theory. The problem will therefore be approached in another manner based on quite elementary considerations. The considerations are of importance, not only in connection with the gyroscopic moments exerted by the two-bladed airscrew on the aircraft, but also with the stressing of the blades of airscrews with an arbitrary number of blades.
Bradburne, John; Patton, Tisha C.
2001-02-25
When Fluor Fernald took over the management of the Fernald Environmental Management Project in 1992, the estimated closure date of the site was more than 25 years into the future. Fluor Fernald, in conjunction with DOE-Fernald, introduced the Accelerated Cleanup Plan, which was designed to substantially shorten that schedule and save taxpayers more than $3 billion. The management of Fluor Fernald believes there are three fundamental concerns that must be addressed by any contractor hoping to achieve closure of a site within the DOE complex. They are relationship management, resource management and contract management. Relationship management refers to the interaction between the site and local residents, regulators, union leadership, the workforce at large, the media, and any other interested stakeholder groups. Resource management is of course related to the effective administration of the site knowledge base and the skills of the workforce, the attraction and retention of qualified a nd competent technical personnel, and the best recognition and use of appropriate new technologies. Perhaps most importantly, resource management must also include a plan for survival in a flat-funding environment. Lastly, creative and disciplined contract management will be essential to effecting the closure of any DOE site. Fluor Fernald, together with DOE-Fernald, is breaking new ground in the closure arena, and ''business as usual'' has become a thing of the past. How Fluor Fernald has managed its work at the site over the last eight years, and how it will manage the new site closure contract in the future, will be an integral part of achieving successful closure at Fernald.
6. Launch closure, close up of closure motor, view towards ...
6. Launch closure, close up of closure motor, view towards north - Ellsworth Air Force Base, Delta Flight, Launch Facility, On County Road T512, south of Exit 116 off I-90, Interior, Jackson County, SD
Entropy production rate as a constraint for collisionless fluid closures
Fleurence, E.; Sarazin, Y.; Garbet, X.; Dif-Pradalier, G.; Ghendrih, Ph.; Grandgirard, V.; Ottaviani, M.
2006-11-30
A novel method is proposed to construct collisionless fluid closures accounting for some kinetic properties. The first dropped fluid moment is assumed to be a linear function of the lower order ones. Optimizing the agreement between the fluid and kinetic entropy production rates is used to constrain the coefficients of the linear development. This procedure is applied to a reduced version of the interchange instability. The closure, involving the absolute value of the wave vector, is non-local in real space. In this case, the linear instability thresholds are the same, and the linear growth rates exhibit similar characteristics. Such a method is applicable to other models and classes of instabilities.
40 CFR 264.310 - Closure and post-closure care.
Code of Federal Regulations, 2014 CFR
2014-07-01
... 40 Protection of Environment 26 2014-07-01 2014-07-01 false Closure and post-closure care. 264.310... Landfills § 264.310 Closure and post-closure care. (a) At final closure of the landfill or upon closure of...) After final closure, the owner or operator must comply with all post-closure requirements contained...
40 CFR 264.258 - Closure and post-closure care.
Code of Federal Regulations, 2013 CFR
2013-07-01
... 40 Protection of Environment 27 2013-07-01 2013-07-01 false Closure and post-closure care. 264.258... Waste Piles § 264.258 Closure and post-closure care. (a) At closure, the owner or operator must remove... facility and perform post-closure care in accordance with the closure and post-closure care...
Caldwell, T.B.
1997-04-18
A reducing grout has been developed for closing high level waste tanks at the Savannah River Site in Aiken, South Carolina. The grout has a low redox potential, which minimizes the mobility of Sr{sup 90}, the radionuclide with the highest dose potential after closure. The grout also has a high pH which reduces the solubility of the plutonium isotopes. The grout has a high compressive strength and low permeability, which enhances its ability to limit the migration of contaminants after closure. The grout was designed and tested by Construction Technology Laboratories, Inc. Placement methods were developed by the Savannah River Site personnel.
Reynolds stress closure modeling in wall-bounded flows
NASA Technical Reports Server (NTRS)
Durbin, Paul A.
1993-01-01
This report describes two projects. Firstly, a Reynolds stress closure for near-wall turbulence is described. It was motivated by the simpler k-epsilon-(v-bar(exp 2)) model described in last year's annual research brief. Direct Numerical Simulation of three-dimensional channel flow shows a curious decrease of the turbulent kinetic energy. The second topic of this report is a model which reproduces this effect. That model is described and used to discuss the relevance of the three dimensional channel flow simulation to swept wing boundary layers.
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.
Mattingly, J.T.
1963-02-12
This invention provides a simple pressure-actuated closure whereby windowless observation ports are opened to the atmosphere at preselected altitudes. The closure comprises a disk which seals a windowless observation port in rocket hull. An evacuated instrument compartment is affixed to the rocket hull adjacent the inner surface of the disk, while the outer disk surface is exposed to the atmosphere through which the rocket is traveling. The pressure differential between the evacuated instrument compartment and the relatively high pressure external atmosphere forces the disk against the edge of the observation port, thereby effecting a tight seai. The instrument compartment is evacuated to a pressure equal to the atmospheric pressure existing at the altitude at which it is desiretl that the closure should open. When the rocket reaches this preselected altitude, the inwardly directed atmospheric force on the disk is just equaled by the residual air pressure force within the instrument compartment. Consequently, the closure disk falls away and uncovers the open observation port. The separation of the disk from the rocket hull actuates a switch which energizes the mechanism of a detecting instrument disposed within the instrument compartment. (AE C)
Evaluation of Two Energy Balance Closure Parametrizations
NASA Astrophysics Data System (ADS)
Eder, Fabian; De Roo, Frederik; Kohnert, Katrin; Desjardins, Raymond L.; Schmid, Hans Peter; Mauder, Matthias
2014-05-01
A general lack of energy balance closure indicates that tower-based eddy-covariance (EC) measurements underestimate turbulent heat fluxes, which calls for robust correction schemes. Two parametrization approaches that can be found in the literature were tested using data from the Canadian Twin Otter research aircraft and from tower-based measurements of the German Terrestrial Environmental Observatories (TERENO) programme. Our analysis shows that the approach of Huang et al. (Boundary-Layer Meteorol 127:273-292, 2008), based on large-eddy simulation, is not applicable to typical near-surface flux measurements because it was developed for heights above the surface layer and over homogeneous terrain. The biggest shortcoming of this parametrization is that the grid resolution of the model was too coarse so that the surface layer, where EC measurements are usually made, is not properly resolved. The empirical approach of Panin and Bernhofer (Izvestiya Atmos Oceanic Phys 44:701-716, 2008) considers landscape-level roughness heterogeneities that induce secondary circulations and at least gives a qualitative estimate of the energy balance closure. However, it does not consider any feature of landscape-scale heterogeneity other than surface roughness, such as surface temperature, surface moisture or topography. The failures of both approaches might indicate that the influence of mesoscale structures is not a sufficient explanation for the energy balance closure problem. However, our analysis of different wind-direction sectors shows that the upwind landscape-scale heterogeneity indeed influences the energy balance closure determined from tower flux data. We also analyzed the aircraft measurements with respect to the partitioning of the "missing energy" between sensible and latent heat fluxes and we could confirm the assumption of scalar similarity only for Bowen ratios 1.
Turbulent Damping without Eddy Viscosity
NASA Astrophysics Data System (ADS)
Thalabard, Simon
2015-11-01
The intrinsic Non-Gaussianity of turbulence may explain why the standard Quasi-Normal cumulant discard closures can fail dramatically, an example being the development of negative energy spectra in Millionshtchikov's 1941 Quasi-Normal (QN) theory. While Orszag's 1977 EDQNM provides an ingenious patch to the issue, the reason why QN fails so badly is not so clear. Is it because of the Gaussian Ansatz itself? Or rather its inconsistent use? The purpose of the talk is to argue in favor of the latter option, using the lights of a new ``optimal closure'' recently exposed by [Turkington,2013], which allows Gaussians to be used consistently with an intrinsic damping. The key to this apparent paradox lies in a clear distinction between the ensemble averages and their proxies, most easily grasped provided one uses the Liouville equation rather than the cumulant hierarchy as a starting point. Schematically said, closure is achieved by minimizing a lack-of-fit residual, that retains the intrinsic features of the dynamics. For the sake of clarity, I will discuss the optimal closure on a problem where it can be entirely implemented and compared to DNS: the relaxation of an arbitrarily far from equilibrium energy shell towards the Gibbs equilibrium for truncated Euler dynamics.
ERIC Educational Resources Information Center
Hanratty, Thomas J.
1980-01-01
This paper gives an account of research on the structure of turbulence close to a solid boundary. Included is a method to study the flow close to the wall of a pipe without interferring with it. (Author/JN)
NASA Astrophysics Data System (ADS)
Nazarenko, Sergey
2015-07-01
Wave turbulence is the statistical mechanics of random waves with a broadband spectrum interacting via non-linearity. To understand its difference from non-random well-tuned coherent waves, one could compare the sound of thunder to a piece of classical music. Wave turbulence is surprisingly common and important in a great variety of physical settings, starting with the most familiar ocean waves to waves at quantum scales or to much longer waves in astrophysics. We will provide a basic overview of the wave turbulence ideas, approaches and main results emphasising the physics of the phenomena and using qualitative descriptions avoiding, whenever possible, involved mathematical derivations. In particular, dimensional analysis will be used for obtaining the key scaling solutions in wave turbulence - Kolmogorov-Zakharov (KZ) spectra.
Reynold stress closure in jet flows using wave models
NASA Technical Reports Server (NTRS)
Morris, P. J.
1988-01-01
Research program efforts have continued to concentrate on the development of the numerical methods that will form the computational part of the turbulence closure scheme. Studies have continued on the wave model for the two dimensional shear layer. This configuration is being used as a test case for the closure schemes. Several numerical schemes for the solution of the non-separable Rayleigh equation were developed. This solution is required for the closure scheme in more complex geometries. The most efficient method found is a Hybrid scheme that combines both pseudospectral and finite difference techniques. In addition, conformal transformation techniques were developed to transform the arbitrary geometry of the jet to a simple computational domain. The study of the shock structure in arbitrary geometry jets and multiple jets. These developments are described briefly.
NASA Astrophysics Data System (ADS)
Coclite, A.; Pascazio, G.; De Palma, P.; Cutrone, L.
2016-07-01
Flamelet-Progress-Variable (FPV) combustion models allow the evaluation of all thermochemical quantities in a reacting flow by computing only the mixture fraction Z and a progress variable C. When using such a method to predict turbulent combustion in conjunction with a turbulence model, a probability density function (PDF) is required to evaluate statistical averages (e. g., Favre averages) of chemical quantities. The choice of the PDF is a compromise between computational costs and accuracy level. The aim of this paper is to investigate the influence of the PDF choice and its modeling aspects to predict turbulent combustion. Three different models are considered: the standard one, based on the choice of a β-distribution for Z and a Dirac-distribution for C; a model employing a β-distribution for both Z and C; and the third model obtained using a β-distribution for Z and the statistically most likely distribution (SMLD) for C. The standard model, although widely used, does not take into account the interaction between turbulence and chemical kinetics as well as the dependence of the progress variable not only on its mean but also on its variance. The SMLD approach establishes a systematic framework to incorporate informations from an arbitrary number of moments, thus providing an improvement over conventionally employed presumed PDF closure models. The rational behind the choice of the three PDFs is described in some details and the prediction capability of the corresponding models is tested vs. well-known test cases, namely, the Sandia flames, and H2-air supersonic combustion.
Comments on the present state of second-order closure models for incompressible flows
NASA Technical Reports Server (NTRS)
Speziale, Charles G.
1992-01-01
Second-order closure models account for history and nonlocal effects of the mean velocity gradients on the Reynolds stress tensor. Turbulent flows involving body forces or curvature, Reynolds stress relaxational effects, and counter-gradient transport are usually better described. The topics are presented in viewgraph form and include: (1) the Reynolds stress transport equation; (2) issues in second-order closure modeling; and (3) near wall models.
Transport Coefficients in Rotating Weakly Compressible Turbulence
NASA Technical Reports Server (NTRS)
Rubinstein, Robert; Zhou, Ye; Erlebacher, Gordon
1998-01-01
Analytical studies of compressible turbulence have found that compressible velocity fluctuations create both effective fluid transport properties and an effective equation of state. This paper investigates the effects of rotation on compressible turbulence. It is shown that rotation modifies the transport properties of compressible turbulence by replacing the turbulence time scale by a rotational time scale, much as rotation modifies the transport properties of incompressible turbulence. But thermal equilibrium properties are modified in a more complex manner. Two regimes are possible: one dominated by incompressible fluctuations, in which the sound speed is modified as it is in non-rotating turbulence, and a rotation dominated regime in which the sound speed enhancement is rotation dependent. The dimensionless parameter which discriminates between regimes is identified. In general, rotation is found to suppress the effects of compressibility. A novel feature of the present analysis is the use of a non-Kolmogorov steady state as the reference state of turbulence. introduction of such steady states expands the power and utility of analytical turbulence closures to a wider range of problems.
Universal Realizable Anisotropic Prestress (URAPS) Closure for the Reynolds Stress
NASA Astrophysics Data System (ADS)
Petty, Charles; Koppula, Karuna; Benard, Andre; MSU Collaboration
2013-11-01
The Reynolds-averaged Navier-Stokes (RANS-) equation for constant property Newtonian fluids is unclosed due to the explicit appearance of the normalized Reynolds (NR-) stress and the turbulent kinetic energy. Clearly, any solution to an NS-closure model must be a non-negative operator. This longstanding problem has recently been addressed by developing a non-negative algebraic mapping of the NR-stress into itself. Consequently, all solutions of the URAPS NR-stress equation are non-negative dyadic-valued linear operators regardless of the class of benchmark flows used to determine closure parameters. Most significantly, unlike the class of Boussinesq closures for the NR-stress, the new theory predicts the redistribution of the turbulent kinetic energy among the three components of the fluctuating velocity field for statistically stationary spanwise rotating channel flows. Furthermore, the URAPS theory also predicts that the Coriolis acceleration causes an anisotropic re-distribution of turbulent kinetic energy among the three components of the fluctuating velocity field in rotating homogeneous decay.
Temporal Moments in Hydrogeophysics
NASA Astrophysics Data System (ADS)
Pollock, D.; Cirpka, O. A.
2007-12-01
Electrical Resistivity Tomography (ERT) has been tested as monitoring tool for salt-tracer experiments by various authors. So far, the analysis of such experiments has been done by a two-step procedure [Kemna et al., 2002; Vanderborght et al., 2005; Singha and Gorelick, 2005]. In the first step, classical geophysical inversion methods have been used to infer the distribution of electrical conductivity, which is transferred to an estimated concentration distribution of the tracer. Subsequently, the inferred concentration images were analyzed to estimate hydraulic quantities such as the velocity distribution. This approach has two disadvantages: The concentration distribution is reconstructed with a high spatial resolution, but the estimate is uncertain, and the estimation uncertainty is spatially correlated. These correlated uncertainties should be accounted for in the estimation of hydraulic conductivity from concentration values. The latter, unfortunately, is not practical because the reconstructed data sets are very large. The geophysical inversion is not enforced to be in agreement with basic hydromechanical constraints. E.g., Singha and Gorelick [2005] observed an apparent loss of solute mass when using ERT as monitoring tool. We propose considering the temporal moments of potential-difference time series. These temporal moments depend on temporal moments of concentration, which have already been used in the inference of hydraulic- conductivity distributions (Cirpka and Kitanidis, 2000). In our contribution, we present the complete set of equations leading from hydraulic conductivity via hydraulic heads, velocities, temporal moments of concentrations to temporal moments of potential differences for given flow and transport boundary conditions and electrode configurations. We also present how the sensitivity of temporal moments of potential differences on the hydraulic conductivity field can be computed without the need of storing intermediate sensitivities
Numerical Simulation of a Convective Turbulence Encounter
NASA Technical Reports Server (NTRS)
Proctor, Fred H.; Hamilton, David W.; Bowles, Roland L.
2002-01-01
A numerical simulation of a convective turbulence event is investigated and compared with observational data. The numerical results show severe turbulence of similar scale and intensity to that encountered during the test flight. This turbulence is associated with buoyant plumes that penetrate the upper-level thunderstorm outflow. The simulated radar reflectivity compares well with that obtained from the aircraft's onboard radar. Resolved scales of motion as small as 50 m are needed in order to accurately diagnose aircraft normal load accelerations. Given this requirement, realistic turbulence fields may be created by merging subgrid-scales of turbulence to a convective-cloud simulation. A hazard algorithm for use with model data sets is demonstrated. The algorithm diagnoses the RMS normal loads from second moments of the vertical velocity field and is independent of aircraft motion.
Geometric invariance of compressible turbulent boundary layers
NASA Astrophysics Data System (ADS)
Bi, Wei-Tao; Wu, Bin; She, Zhen-Su; Hussain, Fazle
2015-11-01
A symmetry based approach is applied to analyze the mean velocity and temperature fields of compressible, flat plate turbulent boundary layers (CTBL). A Reynolds stress length scale and a turbulent heat flux length scale are identified to possess the same defect scaling law in the CTBL bulk, which is solely owing to the constraint of the wall to the geometry of the wall-attached eddies, but invariant to compressibility and wall heat transfer. This invariance is called the geometric invariance of CTBL eddies and is likely the origin of the Mach number invariance of Morkovin's hypothesis, as well as the similarity of energy and momentum transports. A closure for the turbulent transport by using the invariant lengths is attainted to predict the mean velocity and temperature profiles in the CTBL bulk- superior to the van Driest transformation and the Reynolds analogy based relations for its sound physics and higher accuracy. Additionally, our approach offers a new understanding of turbulent Prandtl number.
Non-isothermal dispersed phase of particles in turbulent flow
NASA Astrophysics Data System (ADS)
Pandya, R. V. R.; Mashayek, F.
2003-01-01
In this paper we consider, for modelling and simulation, a non-isothermal turbulent flow laden with non-evaporating spherical particles which exchange heat with the surrounding fluid and do not collide with each other during the course of their journey under the influence of the stochastic fluid drag force. In the modelling part of this study, a closed kinetic or probability density function (p.d.f.) equation is derived which describes the distribution of position x, velocity v, and temperature [theta] of the particles in the flow domain at time t. The p.d.f. equation represents the transport of the ensemble-average (denoted by [left angle bracket] [right angle bracket]) phase-space density [left angle bracket]W(x, v, [theta], t)[right angle bracket]. The process of ensemble averaging generates unknown terms, namely the phase-space diffusion current j = [beta]v[left angle bracket]u[prime prime or minute]W[right angle bracket] and the phase-space heat current h = [beta][theta][left angle bracket]t[prime prime or minute]W[right angle bracket], which pose closure problems in the kinetic equation. Here, u[prime prime or minute] and t[prime prime or minute] are the fluctuating parts of the velocity and temperature, respectively, of the fluid in the vicinity of the particle, and [beta]v and [beta][theta] are inverse of the time constants for the particle velocity and temperature, respectively. The closure problems are first solved for the case of homogeneous turbulence with uniform mean velocity and temperature for the fluid phase by using Kraichnan’s Lagrangian history direct interaction (LHDI) approximation method and then the method is generalized to the case of inhomogeneous flows. Another method, which is due to Van Kampen, is used to solve the closure problems, resulting in a closed kinetic equation identical to the equation obtained by the LHDI method. Then, the closed equation is shown to be compatible with the transformation constraint
Numerical study of a separating and reattaching flow by using Reynolds-stress tubulence closure
NASA Technical Reports Server (NTRS)
Amano, R. S.; Goel, P.
1983-01-01
The numerical study of the Reynolds-stress turbulence closure for separating, reattaching, recirculating and redeveloping flow is summarized. The calculations were made for two different closure models of pressure - strain correlation. The results were compared with the experimental data. Furthermore, these results were compared with the computations made by using the one layer and three layer treatment of k-epsilon turbulence model which were developed. Generally the computations by the Reynolds-stress model show better results than those by the k-epsilon model, in particular, some improvement was noticed in the redeveloping region of the separating and reattaching flow in a pipe with sudden expansion.
Efficient Moment Matrix Generation for Arbitrary Chemical Networks
Smadbeck, P.; Kaznessis, Y. N.
2012-01-01
As stochastic simulations become increasingly common in biological research, tools for analysis of such systems are in demand. The deterministic analogue to stochastic models, a set of probability moment equations equivalent to the Chemical Master Equation (CME), offers the possibility of a priori analysis of systems without the need for computationally costly Monte Carlo simulations. Despite the drawbacks of the method, in particular non-linearity in even the simplest of cases, the use of moment equations combined with moment-closure techniques has been used effectively in many fields. The techniques currently available to generate moment equations rely upon analytical expressions that are not efficient upon scaling. Additionally, the resulting moment-dependent matrix is lower diagonal and demands massive memory allocation in extreme cases. Here it is demonstrated that by utilizing factorial moments and the probability generating function (the Z-transform of the probability distribution) a recursive algorithm is produced. The resulting method is scalable and particularly efficient when high-order moments are required. The matrix produced is banded and often demands substantially less memory resources. PMID:23175571
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.
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.
Numerical experiments in homogeneous turbulence
NASA Technical Reports Server (NTRS)
Rogallo, R. S.
1981-01-01
The direct simulation methods developed by Orszag and Patternson (1972) for isotropic turbulence were extended to homogeneous turbulence in an incompressible fluid subjected to uniform deformation or rotation. The results of simulations for irrotational strain (plane and axisymmetric), shear, rotation, and relaxation toward isotropy following axisymmetric strain are compared with linear theory and experimental data. Emphasis is placed on the shear flow because of its importance and because of the availability of accurate and detailed experimental data. The computed results are used to assess the accuracy of two popular models used in the closure of the Reynolds-stress equations. Data from a variety of the computed fields and the details of the numerical methods used in the simulation are also presented.
ERIC Educational Resources Information Center
Terr, Lenore C.; McDermott, John F.; Benson, Ronald M.; Blos, Peter, Jr.; Deeney, John M.; Rogers, Rita R.; Zrull, Joel P.
2005-01-01
In the summer of 2004, a number of psychotherapists with old ties to the University of Michigan or UCLA decided to write 500-word vignettes that attempted to capture a turning point in one of their child patient's psychotherapies. What did the child and adolescent psychiatrist do to elicit such a moment? Upon receiving seven vignettes, one of us…
ERIC Educational Resources Information Center
Child & Youth Services, 2004
2004-01-01
This chapter presents additional stories and interpretations by John Korsmo, Molly Weingrod, Joseph Stanley, Quinn Wilder, Amy Evans, Rick Flowers, Arcelia Martinez, and Pam Ramsey. The stories and interpretations are presented as teachable moments that are examples of how people are learning to understand youthwork and, as such, are open to…
ERIC Educational Resources Information Center
Higgins, Chris
2014-01-01
In "The Humanist Moment," Chris Higgins sets out to recover a tenable, living humanism, rejecting both the version vilified by the anti-humanists and the one sentimentalized by the reactionary nostalgists. Rescuing humanism from such polemics is only the first step, as we find at least nine rival, contemporary definitions of humanism.…
ERIC Educational Resources Information Center
Goodrow, Mary Ellen
2000-01-01
Details how an unplanned activity involving spinning wool presented a teachable moment for children in a family child care setting. Notes how activities related to farming, spinning wool, and using wool cloth resulted from following the children's lead. Concludes that everyday activities provide opportunities to listen to children, learn about…
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.
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.
NASA Technical Reports Server (NTRS)
Tchen, C. M.
1986-01-01
Theoretical and numerical works in atmospheric turbulence have used the Navier-Stokes fluid equations exclusively for describing large-scale motions. Controversy over the existence of an average temperature gradient for the very large eddies in the atmosphere suggested that a new theoretical basis for describing large-scale turbulence was necessary. A new soliton formalism as a fluid analogue that generalizes the Schrodinger equation and the Zakharov equations has been developed. This formalism, processing all the nonlinearities including those from modulation provided by the density fluctuations and from convection due to the emission of finite sound waves by velocity fluctuations, treats large-scale turbulence as coalescing and colliding solitons. The new soliton system describes large-scale instabilities more explicitly than the Navier-Stokes system because it has a nonlinearity of the gradient type, while the Navier-Stokes has a nonlinearity of the non-gradient type. The forced Schrodinger equation for strong fluctuations describes the micro-hydrodynamical state of soliton turbulence and is valid for large-scale turbulence in fluids and plasmas where internal waves can interact with velocity fluctuations.
Airway closure in microgravity.
Dutrieue, Brigitte; Verbanck, Sylvia; Darquenne, Chantal; Prisk, G Kim
2005-08-25
Recent single breath washout (SBW) studies in microgravity and on the ground have suggested an important effect of airway closure on gas mixing in the human lung, reflected particularly in the phase III slope of vital capacity SBW and bolus tests. In order to explore this effect, we designed a SBW in which subjects inspired 2-l from residual volume (RV) starting with a 150 ml bolus of He and SF6. In an attempt to vary the pattern of airways closure configuration before the test, the experiments were conducted in 1G and in microgravity during parabolic flight allowing the pre-test expiration to RV to be either in microgravity or at 1.8 G, with the actual test gas inhalation performed entirely in microgravity. Contrary to our expectations, the measured phase III slope and phase IV height and volume obtained from seven subjects in microgravity were essentially identical irrespective of the gravity level during the pre-test expiration to RV. The results suggest that airway closure configuration at RV before the test inspiration has no apparent impact on phases III and IV generation. PMID:15979418
Hexokinase mediates stomatal closure.
Kelly, Gilor; Moshelion, Menachem; David-Schwartz, Rakefet; Halperin, Ofer; Wallach, Rony; Attia, Ziv; Belausov, Eduard; Granot, David
2013-09-01
Stomata, composed of two guard cells, are the gates whose controlled movement allows the plant to balance the demand for CO2 for photosynthesis with the loss of water through transpiration. Increased guard-cell osmolarity leads to the opening of the stomata and decreased osmolarity causes the stomata to close. The role of sugars in the regulation of stomata is not yet clear. In this study, we examined the role of hexokinase (HXK), a sugar-phosphorylating enzyme involved in sugar-sensing, in guard cells and its effect on stomatal aperture. We show here that increased expression of HXK in guard cells accelerates stomatal closure. We further show that this closure is induced by sugar and is mediated by abscisic acid. These findings support the existence of a feedback-inhibition mechanism that is mediated by a product of photosynthesis, namely sucrose. When the rate of sucrose production exceeds the rate at which sucrose is loaded into the phloem, the surplus sucrose is carried toward the stomata by the transpiration stream and stimulates stomatal closure via HXK, thereby preventing the loss of precious water. PMID:23738737
Separated shear-layer instability reproduction by a Reynolds stress model of turbulence
NASA Astrophysics Data System (ADS)
Jakirlic, Suad; Maduta, Robert
2013-11-01
A boundary layer separating from a solid wall transforms into a `separated shear layer' exhibiting a broader frequency range. Such a highly-unsteady shear layer separating the mean stream from the flow reversal is dominated by the organized, large-scale coherent structures, influencing to a large extent the overall flow behavior. Unlike in the case of a flat-plate boundary layer separating at a fixed point characterizing a backward-facing step geometry, which can be reasonably well captured by a statistical model of turbulence, the separation process pertinent to continuous curved surfaces as well as some fence- or rib-shaped configurations is beyond the reach of any RANS (Reynolds-Averaged Navier Stokes) model independent of the modeling level. The latter issue motivated the present work, dealing with an appropriate extension of a near-wall Second-Moment Closure (SMC) model towards an instability-sensitive formulation. The production term in the corresponding scale-supplying equation is selectively enhanced through introduction of the ratio of the first to the second derivative of the velocity field, the latter representing the integral part of the von Karman length scale, enabling appropriate capturing of the fluctuating turbulence and accordingly the reproduction of the separated shear-layer instability. The analysis is performed by simulating the flow separated from a fence, an axisymmetric hill and a cylinder configuration.
On recontamination and directional-bias problems in Monte Carlo simulation of PDF turbulence models
NASA Astrophysics Data System (ADS)
Hsu, Andrew T.
1992-02-01
Turbulent combustion can not be simulated adequately by conventional moment closure turbulent models. The probability density function (PDF) method offers an attractive alternative: in a PDF model, the chemical source terms are closed and do not require additional models. Because the number of computational operations grows only linearly in the Monte Carlo scheme, it is chosen over finite differencing schemes. A grid dependent Monte Carlo scheme following J.Y. Chen and W. Kollmann has been studied in the present work. It was found that in order to conserve the mass fractions absolutely, one needs to add further restrictions to the scheme, namely alpha(sub j) + gamma(sub j) = alpha(sub j - 1) + gamma(sub j + 1). A new algorithm was devised that satisfied this restriction in the case of pure diffusion or uniform flow problems. Using examples, it is shown that absolute conservation can be achieved. Although for non-uniform flows absolute conservation seems impossible, the present scheme has reduced the error considerably.
Large eddy simulation and direct numerical simulation of high speed turbulent reacting flows
NASA Technical Reports Server (NTRS)
Adumitroaie, V.; Frankel, S. H.; Madnia, C. K.; Givi, P.
1993-01-01
The objective of this research is to make use of Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) for the computational analyses of high speed reacting flows. Our efforts in the first phase of this research conducted within the past three years have been directed in several issues pertaining to intricate physics of turbulent reacting flows. In our previous 5 semi-annual reports submitted to NASA LaRC, as well as several technical papers in archival journals, the results of our investigations have been fully described. In this progress report which is different in format as compared to our previous documents, we focus only on the issue of LES. The reason for doing so is that LES is the primary issue of interest to our Technical Monitor and that our other findings were needed to support the activities conducted under this prime issue. The outcomes of our related investigations, nevertheless, are included in the appendices accompanying this report. The relevance of the materials in these appendices are, therefore, discussed only briefly within the body of the report. Here, results are presented of a priori and a posterior analyses for validity assessments of assumed Probability Density Function (PDF) methods as potential subgrid scale (SGS) closures for LES of turbulent reacting flows. Simple non-premixed reacting systems involving an isothermal reaction of the type A + B yields Products under both chemical equilibrium and non-equilibrium conditions are considered. A priori analyses are conducted of a homogeneous box flow, and a spatially developing planar mixing layer to investigate the performance of the Pearson Family of PDF's as SGS models. A posteriori analyses are conducted of the mixing layer using a hybrid one-equation Smagorinsky/PDF SGS closure. The Smagorinsky closure augmented by the solution of the subgrid turbulent kinetic energy (TKE) equation is employed to account for hydrodynamic fluctuations, and the PDF is employed for modeling the
A transport equation for reaction rate in turbulent flows
NASA Astrophysics Data System (ADS)
Sabelnikov, V. A.; Lipatnikov, A. N.; Chakraborty, N.; Nishiki, S.; Hasegawa, T.
2016-08-01
New transport equations for chemical reaction rate and its mean value in turbulent flows have been derived and analyzed. Local perturbations of the reaction zone by turbulent eddies are shown to play a pivotal role even for weakly turbulent flows. The mean-reaction-rate transport equation is shown to involve two unclosed dominant terms and a joint closure relation for the sum of these two terms is developed. Obtained analytical results and, in particular, the closure relation are supported by processing two widely recognized sets of data obtained from earlier direct numerical simulations of statistically planar 1D premixed flames associated with both weak large-scale and intense small-scale turbulence.
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.
NASA Astrophysics Data System (ADS)
Firl, G. J.; Randall, D. A.
2013-12-01
The so-called "assumed probability density function (PDF)" approach to subgrid-scale (SGS) parameterization has shown to be a promising method for more accurately representing boundary layer cloudiness under a wide range of conditions. A new parameterization has been developed, named the Two-and-a-Half ORder closure (THOR), that combines this approach with a higher-order turbulence closure. THOR predicts the time evolution of the turbulence kinetic energy components, the variance of ice-liquid water potential temperature (θil) and total non-precipitating water mixing ratio (qt) and the covariance between the two, and the vertical fluxes of horizontal momentum, θil, and qt. Ten corresponding third-order moments in addition to the skewnesses of θil and qt are calculated using diagnostic functions assuming negligible time tendencies. The statistical moments are used to define a trivariate double Gaussian PDF among vertical velocity, θil, and qt. The first three statistical moments of each variable are used to estimate the two Gaussian plume means, variances, and weights. Unlike previous similar models, plume variances are not assumed to be equal or zero. Instead, they are parameterized using the idea that the less dominant Gaussian plume (typically representing the updraft-containing portion of a grid cell) has greater variance than the dominant plume (typically representing the "environmental" or slowly subsiding portion of a grid cell). Correlations among the three variables are calculated using the appropriate covariance moments, and both plume correlations are assumed to be equal. The diagnosed PDF in each grid cell is used to calculate SGS condensation, SGS fluxes of cloud water species, SGS buoyancy terms, and to inform other physical parameterizations about SGS variability. SGS condensation is extended from previous similar models to include condensation over both liquid and ice substrates, dependent on the grid cell temperature. Implementations have been
Adams, Allan; Chesler, Paul M; Liu, Hong
2014-04-18
We construct turbulent black holes in asymptotically AdS4 spacetime by numerically solving Einstein's equations. Using the AdS/CFT correspondence we find that both the dual holographic fluid and bulk geometry display signatures of an inverse cascade with the bulk geometry being well approximated by the fluid-gravity gradient expansion. We argue that statistically steady-state black holes dual to d dimensional turbulent flows have horizons whose area growth has a fractal-like structure with fractal dimension D=d+4/3. PMID:24785028
Turbulence in Compressible Flows
NASA Technical Reports Server (NTRS)
1997-01-01
Lecture notes for the AGARD Fluid Dynamics Panel (FDP) Special Course on 'Turbulence in Compressible Flows' have been assembled in this report. The following topics were covered: Compressible Turbulent Boundary Layers, Compressible Turbulent Free Shear Layers, Turbulent Combustion, DNS/LES and RANS Simulations of Compressible Turbulent Flows, and Case Studies of Applications of Turbulence Models in Aerospace.
Bumblebees meet fully developed turbulence: high resolution numerical simulations
NASA Astrophysics Data System (ADS)
Engels, Thomas; Kolomenskiy, Dmitry; Schneider, Kai; Sesterhenn, Joern; Lehmann, Fritz-Olaf
2015-11-01
Numerical experiments of a tethered bumblebee in a wind tunnel with turbulent inflow of different intensity are performed at realistic Reynolds numbers on massively parallel computers. Ensemble averaging of different flow realizations shows that the mean forces (lift and drag, or horizontal and vertical), the moments (roll, pitch and yaw), and power, are robust and are not modified significantly by the turbulent inflow. Phase averaging of the vorticity field illustrates that in all cases the leading edge vortex is indeed persistent (in the average sense) as it is the case for laminar inflow, which explains the above findings. However, as expected, the corresponding standard deviations do increase with the turbulence intensity. In particular the roll moment shows the strongest increase of standard deviation. Considering that the moment of inertia of the bumblebee is the smallest around this axis yields a possible explanation for the experimentally observed flight instability around the roll axis under turbulent flow conditions.
Kinematics of velocity and vorticity correlations in turbulent flow
NASA Technical Reports Server (NTRS)
Bernard, P. S.
1983-01-01
The kinematic problem of calculating second-order velocity moments from given values of the vorticity covariance is examined. Integral representation formulas for second-order velocity moments in terms of the two-point vorticity correlation tensor are derived. The special relationships existing between velocity moments in isotropic turbulence are expressed in terms of the integral formulas yielding several kinematic constraints on the two-point vorticity correlation tensor in isotropic turbulence. Numerical evaluation of these constraints suggests that a Gaussian curve may be the only form of the longitudinal velocity correlation coefficient which is consistent with the requirement of isotropy. It is shown that if this is the case, then a family of exact solutions to the decay of isotropic turbulence may be obtained which contains Batchelor's final period solution as a special case. In addition, the computed results suggest a method of approximating the integral representation formulas in general turbulent shear flows.
Predictive modeling of particle-laden, turbulent flows
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.
Closure and ratio correlation analysis of lunar chemical and grain size data
NASA Technical Reports Server (NTRS)
Butler, J. C.
1976-01-01
Major element and major element plus trace element analyses were selected from the lunar data base for Apollo 11, 12 and 15 basalt and regolith samples. Summary statistics for each of the six data sets were compiled, and the effects of closure on the Pearson product moment correlation coefficient were investigated using the Chayes and Kruskal approximation procedure. In general, there are two types of closure effects evident in these data sets: negative correlations of intermediate size which are solely the result of closure, and correlations of small absolute value which depart significantly from their expected closure correlations which are of intermediate size. It is shown that a positive closure correlation will arise only when the product of the coefficients of variation is very small (less than 0.01 for most data sets) and, in general, trace elements in the lunar data sets exhibit relatively large coefficients of variation.
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.
Talbot, L.; Cheng, R.K.
1993-12-01
Turbulent combustion is the dominant process in heat and power generating systems. Its most significant aspect is to enhance the burning rate and volumetric power density. Turbulent mixing, however, also influences the chemical rates and has a direct effect on the formation of pollutants, flame ignition and extinction. Therefore, research and development of modern combustion systems for power generation, waste incineration and material synthesis must rely on a fundamental understanding of the physical effect of turbulence on combustion to develop theoretical models that can be used as design tools. The overall objective of this program is to investigate, primarily experimentally, the interaction and coupling between turbulence and combustion. These processes are complex and are characterized by scalar and velocity fluctuations with time and length scales spanning several orders of magnitude. They are also influenced by the so-called {open_quotes}field{close_quotes} effects associated with the characteristics of the flow and burner geometries. The authors` approach is to gain a fundamental understanding by investigating idealized laboratory flames. Laboratory flames are amenable to detailed interrogation by laser diagnostics and their flow geometries are chosen to simplify numerical modeling and simulations and to facilitate comparison between experiments and theory.
Nevada Test Site closure program
Shenk, D.P.
1994-08-01
This report is a summary of the history, design and development, procurement, fabrication, installation and operation of the closures used as containment devices on underground nuclear tests at the Nevada Test Site. It also addresses the closure program mothball and start-up procedures. The Closure Program Document Index and equipment inventories, included as appendices, serve as location directories for future document reference and equipment use.
Analytical and phenomenological studies of rotating turbulence
NASA Technical Reports Server (NTRS)
Mahalov, Alex; Zhou, YE
1995-01-01
A framework, which combines mathematical analysis, closure theory, and phenomenological treatment, is developed to study the spectral transfer process and reduction of dimensionality in turbulent flows that are subject to rotation. First, we outline a mathematical procedure that is particularly appropriate for problems with two disparate time scales. The approach which is based on the Green's method leads to the Poincare velocity variables and the Poincare transformation when applied to rotating turbulence. The effects of the rotation are now reflected in the modifications to the convolution of a nonlinear term. The Poincare transformed equations are used to obtain a time-dependent analog of the Taylor-Proudman theorem valid in the asymptotic limit when the non-dimensional parameter mu is identical to Omega(t) approaches infinity (Omega is the rotation rate and t is the time). The 'split' of the energy transfer in both direct and inverse directions is established. Secondly, we apply the Eddy-Damped-Quasinormal-Markovian (EDQNM) closure to the Poincare transformed Euler/Navier-Stokes equations. This closure leads to expressions for the spectral energy transfer. In particular, an unique triple velocity decorrelation time is derived with an explicit dependence on the rotation rate. This provides an important input for applying the phenomenological treatment of Zhou. In order to characterize the relative strength of rotation, another non-dimensional number, a spectral Rossby number, which is defined as the ratio of rotation and turbulence time scales, is introduced. Finally, the energy spectrum and the spectral eddy viscosity are deduced.
System for closure of a physical anomaly
Bearinger, Jane P; Maitland, Duncan J; Schumann, Daniel L; Wilson, Thomas S
2014-11-11
Systems for closure of a physical anomaly. Closure is accomplished by a closure body with an exterior surface. The exterior surface contacts the opening of the anomaly and closes the anomaly. The closure body has a primary shape for closing the anomaly and a secondary shape for being positioned in the physical anomaly. The closure body preferably comprises a shape memory polymer.
Diagnostic Statistics for the Assessment and Characterization of Complex Turbulent Flows
NASA Technical Reports Server (NTRS)
Ristorcelli, J. R.
1995-01-01
A simple parameterization scheme for a complex turbulent flow using nondimensional parameters coming from the Reynolds stress equations is given. Definitions and brief descriptions of the physical significance of several nondimensional parameters that are used to characterize turbulence from the viewpoint of single-point turbulence closures are given. These nondimensional parameters reflect measures of (1) the spectral band width of the turbulence; (2) deviations from the ideal Kolmogorov behavior; (3) the relative magnitude, orientation, and temporal duration of the deformation to which the turbulence is subjected; (4) one and two-point measures of the large and small scale anisotropy of the turbulence; and (5) inhomogeneity. This is an attempt to create a more systematic methodology for the diagnosis and classification of turbulent flows as well as in the development, validation, and application of turbulence model strategies. The parameters serve also to indicate the adequacy of various assumptions made in single-point turbulence models and in suggesting the appropriate turbulence strategy for a particular complex flow. The compilation will be of interest to experimentalists and to those involved in either computing turbulent flows or whose interests lies in verifying the adequacy of the phenomenological beliefs used in turbulence closures.
Can we characterize turbulence in premixed flames?
Lipatnikov, A.N.
2009-06-15
Modeling of premixed turbulent combustion involves averaging reaction rates in turbulent flows. The focus of most approaches to resolving this problem has been placed on determining the dependence of the mean rate w of product creation on the laminar flame speed S{sub L}, the rms turbulence velocity u', etc. The goal of the present work is to draw attention to another issue: May the input quantity u{sup '} for a model of w= w(u'/S{sub L},..) be considered to be known? The point is that heat release substantially affects turbulence and, hence, turbulence characteristics in premixed flames should be modeled. However, standard moment methods for numerically simulating turbulent flows do not allow us to evaluate the true turbulence characteristics in a flame. For instance, the Reynolds stresses in premixed flames are affected not only by turbulence itself, but also by velocity jump across flamelets. A common way to resolving this problem consists of considering the Reynolds stresses conditioned on unburned (or burned) mixture to be the true turbulence characteristics. In the present paper, this widely accepted but never proved hypothesis is put into question, first, by considering simple model constant-density problems (flame motion in an oscillating one-dimensional laminar flow; flame stabilized in a periodic shear, one-dimensional, laminar flow; turbulent mixing). In all the cases, the magnitude of velocity fluctuations, calculated using the conditioned Reynolds stresses, is affected by the intermittency of reactants and products and, hence, is not the true rms velocity. Second, the above claim is further supported by comparing balance equations for the mean and conditioned Reynolds stresses. The conditioned Reynolds stresses do not characterize the true turbulence in flames, because conditional averaging cuts off flow regions characterized by either high or low velocities. (author)
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.
FINAL CLOSURE PLAN SURFACE IMPOUNDMENTS CLOSURE, SITE 300
Lane, J E; Scott, J E; Mathews, S E
2004-09-29
Lawrence Livermore National Laboratory of the University of California (LLNL) operates two Class II surface impoundments that store wastewater that is discharged from a number of buildings located on the Site 300 Facility (Site 300). The wastewater is the by-product of explosives processing. Reduction in the volume of water discharged from these buildings over the past several years has significantly reduced the wastewater storage needs. In addition, the impoundments were constructed in 1984, and the high-density polyethylene (HDPE) geomembrane liners are nearing the end of their service life. The purpose of this project is to clean close the surface impoundments and provide new wastewater storage using portable, above ground storage tanks at six locations. The tanks will be installed prior to closure of the impoundments and will include heaters for allowing evaporation during relatively cool weather. Golder Associates (Golder) has prepared this Final Closure Plan (Closure Plan) on behalf of LLNL to address construction associated with the clean closure of the impoundments. This Closure Plan complies with State Water Resources Control Board (SWRCB) Section 21400 of the California Code of Regulations Title 27 (27 CCR {section}21400). As required by these regulations and guidance, this Plan provides the following information: (1) A site characterization, including the site location, history, current operations, and geology and hydrogeology; (2) The regulatory requirements relevant to clean closure of the impoundments; (3) The closure procedures; and, (4) The procedures for validation and documentation of clean closure.
Fracture mechanics analyses of partial crack closure in shell structures
NASA Astrophysics Data System (ADS)
Zhao, Jun
2007-12-01
This thesis presents the theoretical and finite element analyses of crack-face closure behavior in shells and its effect on the stress intensity factor under a bending load condition. Various shell geometries, such as spherical shell, cylindrical shell containing an axial crack, cylindrical shell containing a circumferential crack and shell with double curvatures, are all studied. In addition, the influence of material orthotropy on the crack closure effect in shells is also considered. The theoretical formulation is developed based on the shallow shell theory of Delale and Erdogan, incorporating the effect of crack-face closure at the compressive edges. The line-contact assumption, simulating the crack-face closure at the compressive edges, is employed so that the contact force at the closure edges is introduced, which can be translated to the mid-plane of the shell, accompanied by an additional distributed bending moment. The unknown contact force is computed by solving a mixed-boundary value problem iteratively, that is, along the crack length, either the normal displacement of the crack face at the compressive edges is equal to zero or the contact pressure is equal to zero. It is found that due to the curvature effects crack closure may not always occur on the entire length of the crack, depending on the direction of the bending load and the geometry of the shell. The crack-face closure influences significantly the magnitude of the stress intensity factors; it increases the membrane component but decreases the bending component. The maximum stress intensity factor is reduced by the crack-face closure. The significant influence of geometry and material orthotropy on rack closure behavior in shells is also predicted based on the analytical solutions. Three-dimensional FEA is performed to validate the theoretical solutions. It demonstrates that the crack face closure occurs actually over an area, not on a line, but the theoretical solutions of the stress intensity
Moment tensors of ten witwatersrand mine tremors
McGarr, A.
1992-01-01
Ground motions, recorded both underground and on the surface in two of the South African Gold mining districts, were inverted to determine complete moment tensors for 10 mining-induced tremors in the magnitude range 1.9 to 3.3. The resulting moment tensors fall into two separate categories. Seven of the events involve substantial coseismic volumetric reduction-??V together with normal faulting entailing shear deformation ??AD, where the summation is over fault planes of area A and average slip D. For these events the ratio-??V/??AD ranges from 0.58 to 0.92, with an average value of 0.71. For the remaining three events ??V is not significantly different from zero; these events are largely double-couple sources involving normal faulting. Surprisingly, the two types of source mechanism appear to be very distinct in that there is not a continuous distribution of the source mix from ??V=0 to-??V?????AD. Presumably, the coseismic closure indicates substantial interaction between a mine stope and adjacent shear failure in the surrounding rock, under the influence of an ambient stress for which the maximum principal stress is oriented vertically. ?? 1992 Birkha??user Verlag.
Turbulent reacting flow computations including turbulence-chemistry interactions
NASA Technical Reports Server (NTRS)
Narayan, J. R.; Girimaji, S. S.
1992-01-01
A two-equation (k-epsilon) turbulence model has been extended to be applicable for compressible reacting flows. A compressibility correction model based on modeling the dilatational terms in the Reynolds stress equations has been used. A turbulence-chemistry interaction model is outlined. In this model, the effects of temperature and species mass concentrations fluctuations on the species mass production rates are decoupled. The effect of temperature fluctuations is modeled via a moment model, and the effect of concentration fluctuations is included using an assumed beta-pdf model. Preliminary results obtained using this model are presented. A two-dimensional reacting mixing layer has been used as a test case. Computations are carried out using the Navier-Stokes solver SPARK using a finite rate chemistry model for hydrogen-air combustion.
40 CFR 265.310 - Closure and post-closure care.
Code of Federal Regulations, 2014 CFR
2014-07-01
... 40 Protection of Environment 26 2014-07-01 2014-07-01 false Closure and post-closure care. 265.310... DISPOSAL FACILITIES Landfills § 265.310 Closure and post-closure care. (a) At final closure of the landfill... subsoils present. (b) After final closure, the owner or operator must comply with all...
40 CFR 264.228 - Closure and post-closure care.
Code of Federal Regulations, 2014 CFR
2014-07-01
... 40 Protection of Environment 26 2014-07-01 2014-07-01 false Closure and post-closure care. 264.228... Surface Impoundments § 264.228 Closure and post-closure care. (a) At closure, the owner or operator must... materials are left in place at final closure, the owner or operator must comply with all...
40 CFR 265.228 - Closure and post-closure care.
Code of Federal Regulations, 2014 CFR
2014-07-01
... 40 Protection of Environment 26 2014-07-01 2014-07-01 false Closure and post-closure care. 265.228... DISPOSAL FACILITIES Surface Impoundments § 265.228 Closure and post-closure care. (a) At closure, the owner... impoundment and provide post-closure care for a landfill under subpart G and § 265.310, including...
40 CFR 264.228 - Closure and post-closure care.
Code of Federal Regulations, 2013 CFR
2013-07-01
... 40 Protection of Environment 27 2013-07-01 2013-07-01 false Closure and post-closure care. 264.228... Surface Impoundments § 264.228 Closure and post-closure care. (a) At closure, the owner or operator must... materials are left in place at final closure, the owner or operator must comply with all...
40 CFR 265.197 - Closure and post-closure care.
Code of Federal Regulations, 2013 CFR
2013-07-01
... 40 Protection of Environment 27 2013-07-01 2013-07-01 false Closure and post-closure care. 265.197... DISPOSAL FACILITIES Tank Systems § 265.197 Closure and post-closure care. (a) At closure of a tank system..., then the owner or operator must close the tank system and perform post-closure care in accordance...
40 CFR 264.1102 - Closure and post-closure care.
Code of Federal Regulations, 2013 CFR
2013-07-01
... 40 Protection of Environment 27 2013-07-01 2013-07-01 false Closure and post-closure care. 264... FACILITIES Containment Buildings § 264.1102 Closure and post-closure care. (a) At closure of a containment... or decontaminated, he must close the facility and perform post-closure care in accordance with...
40 CFR 265.258 - Closure and post-closure care.
Code of Federal Regulations, 2013 CFR
2013-07-01
... 40 Protection of Environment 27 2013-07-01 2013-07-01 false Closure and post-closure care. 265.258... DISPOSAL FACILITIES Waste Piles § 265.258 Closure and post-closure care. (a) At closure, the owner or... or decontaminated, he must close the facility and perform post-closure care in accordance with...
40 CFR 264.197 - Closure and post-closure care.
Code of Federal Regulations, 2013 CFR
2013-07-01
... 40 Protection of Environment 27 2013-07-01 2013-07-01 false Closure and post-closure care. 264.197... Tank Systems § 264.197 Closure and post-closure care. (a) At closure of a tank system, the owner or..., then the owner or operator must close the tank system and perform post-closure care in accordance...
40 CFR 265.228 - Closure and post-closure care.
Code of Federal Regulations, 2013 CFR
2013-07-01
... 40 Protection of Environment 27 2013-07-01 2013-07-01 false Closure and post-closure care. 265.228... DISPOSAL FACILITIES Surface Impoundments § 265.228 Closure and post-closure care. (a) At closure, the owner... impoundment and provide post-closure care for a landfill under subpart G and § 265.310, including...
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.
Method for computing three-dimensional turbulent flows
Bernard, P.S.; Berger, B.S.
1982-06-01
The MVC (mean vorticity and covariance) turbulence closure is derived for three-dimensional turbulent flows. The derivation utilizes Lagrangian time expansion techniques applied to the unclosed terms of the mean vorticity and covariance equations. The closed mean vorticity equation is applied to the numerical solution of fully developed three-dimensional channel flow. Anisotropies in the wall region are modelled by pairs of counterrotating streamwise vortices. The numerical results are in close agreement with experimental data. Analysis of the contributions of the terms in the mean vorticity equation gives insight into the dynamics of the turbulent boundary. 41 references, 7 figures.
Effects of Lewis number on turbulent scalar transport and its modelling in turbulent premixed flames
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)
27 CFR 26.136 - Affixing closures.
Code of Federal Regulations, 2010 CFR
2010-04-01
... OF THE TREASURY LIQUORS LIQUORS AND ARTICLES FROM PUERTO RICO AND THE VIRGIN ISLANDS Closures for Distilled Spirits From Puerto Rico § 26.136 Affixing closures. Closures or other devices shall be...
27 CFR 19.523 - Affixing closures.
Code of Federal Regulations, 2011 CFR
2011-04-01
... OF THE TREASURY LIQUORS DISTILLED SPIRITS PLANTS Liquor Bottle, Label, and Closure Requirements Closure Requirements § 19.523 Affixing closures. Each bottle or other container of spirits having...
27 CFR 19.523 - Affixing closures.
Code of Federal Regulations, 2013 CFR
2013-04-01
... OF THE TREASURY ALCOHOL DISTILLED SPIRITS PLANTS Liquor Bottle, Label, and Closure Requirements Closure Requirements § 19.523 Affixing closures. Each bottle or other container of spirits having...
27 CFR 19.523 - Affixing closures.
Code of Federal Regulations, 2014 CFR
2014-04-01
... OF THE TREASURY ALCOHOL DISTILLED SPIRITS PLANTS Liquor Bottle, Label, and Closure Requirements Closure Requirements § 19.523 Affixing closures. Each bottle or other container of spirits having...
27 CFR 19.523 - Affixing closures.
Code of Federal Regulations, 2012 CFR
2012-04-01
... OF THE TREASURY LIQUORS DISTILLED SPIRITS PLANTS Liquor Bottle, Label, and Closure Requirements Closure Requirements § 19.523 Affixing closures. Each bottle or other container of spirits having...
NASA Astrophysics Data System (ADS)
Kühnen, Jakob; Hof, Björn
2015-11-01
We show that a simple modification of the velocity profile in a pipe can lead to a complete collapse of turbulence and the flow fully relaminarises. The annihilation of turbulence is achieved by a steady manipulation of the streamwise velocity component alone, greatly reducing control efforts. Several different control techniques are presented: one with a local modification of the flow profile by means of a stationary obstacle, one employing a nozzle injecting fluid through a small gap at the pipe wall and one with a moving wall, where a part of the pipe is shifted in the streamwise direction. All control techniques act on the flow such that the streamwise velocity profile becomes more flat and turbulence gradually grows faint and disappears. In a smooth straight pipe the flow remains laminar downstream of the control. Hence a reduction in skin friction by a factor of 8 and more can be accomplished. Stereoscopic PIV-measurements and movies of the development of the flow during relaminarisation are presented.
Closedure - Mine Closure Technologies Resource
NASA Astrophysics Data System (ADS)
Kauppila, Päivi; Kauppila, Tommi; Pasanen, Antti; Backnäs, Soile; Liisa Räisänen, Marja; Turunen, Kaisa; Karlsson, Teemu; Solismaa, Lauri; Hentinen, Kimmo
2015-04-01
Closure of mining operations is an essential part of the development of eco-efficient mining and the Green Mining concept in Finland to reduce the environmental footprint of mining. Closedure is a 2-year joint research project between Geological Survey of Finland and Technical Research Centre of Finland that aims at developing accessible tools and resources for planning, executing and monitoring mine closure. The main outcome of the Closedure project is an updatable wiki technology-based internet platform (http://mineclosure.gtk.fi) in which comprehensive guidance on the mine closure is provided and main methods and technologies related to mine closure are evaluated. Closedure also provides new data on the key issues of mine closure, such as performance of passive water treatment in Finland, applicability of test methods for evaluating cover structures for mining wastes, prediction of water effluents from mine wastes, and isotopic and geophysical methods to recognize contaminant transport paths in crystalline bedrock.
Turbulent Flow Between Rotating Cylinders
NASA Technical Reports Server (NTRS)
Shih-I, Pai
1943-01-01
The turbulent air flow between rotating cylinders was investigated. The distributions of mean speed and of turbulence were measured in the gap between a rotating inner and a stationary outer cylinder. The measurements led to the conclusion that the turbulent flow in the gap cannot be considered two dimensional, but that a particular type of secondary motion takes place. It is shown that the experimentally found velocity distribution can be fully understood under the assumption that this secondary motion consists of three-dimensional ring-shape vortices. The vortices occur only in pairs, and their number and size depend on the speed of the rotating cylinder; the number was found to decrease with increasing speed. The secondary motion has an essential part in the transmission of the moment of momentum. In regions where the secondary motion is negligible, the momentum transfer follows the laws known for homologous turbulence. Ring-shape vortices are known to occur in the laminar flow between rotating cylinders, but it was hitherto unknown that they exist even at speeds that are several hundred times the critical limit.
Turbulence sensitivity study in the IBI region
NASA Astrophysics Data System (ADS)
Reffray, G.; Chanut, J.; Cailleau, S.; Levier, B.
2009-04-01
In the framework of building a high resolution operational system covering the IBI area (Iberian Biscay Irish), a turbulence sensitivity study is carried out to improve the results of the NEMO model. This is particularly important on the shelf where the mixing is very strong and mainly induced by the intense tidal currents. The investigated work is to test some parameterizations more sophisticated (for ex: stability functions from Canuto (2001) or surface boundary conditions including wave effects from Mellor and Blumberg 2003) and to note if the biases with the observations are reduced as expected. To make this numerical study easier, the Generic Length Scale model (Umlauf and Burchard, 2003) has been implemented. The choice of the dissipation rate as turbulent scale has been done because this closure is well documented and contrary to the Mellor-Yamada turbulent scale, this equation does not need any wall function to provide results physically relevant.
The pdf approach to turbulent flow
NASA Technical Reports Server (NTRS)
Kollmann, W.
1990-01-01
This paper provides a detailed discussion of the theory and application of probability density function (pdf) methods, which provide a complete statistical description of turbulent flow fields at a single point or a finite number of points. The basic laws governing the flow of Newtonian fluids are set up in the Eulerian and the Lagrangian frame, and the exact and linear equations for the characteristic functionals in those frames are discussed. Pdf equations in both frames are derived as Fourier transforms of the equations of the characteristic functions. Possible formulations for the nonclosed terms in the pdf equation are discussed, their properties are assessed, and closure modes for the molecular-transport and the fluctuating pressure-gradient terms are reviewed. The application of pdf methods to turbulent combustion flows, supersonic flows, and the interaction of turbulence with shock waves is discussed.
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
Assisted closure of fasciotomy wounds
Fowler, J. R.; Kleiner, M. T.; Das, R.; Gaughan, J. P.; Rehman, S.
2012-01-01
Introduction Negative pressure wound therapy (NPWT) and vessel loop assisted closure are two common methods used to assist with the closure of fasciotomy wounds. This retrospective review compares these two methods using a primary outcome measurement of skin graft requirement. Methods A retrospective search was performed to identify patients who underwent fasciotomy at our institution. Patient demographics, location of the fasciotomy, type of assisted closure, injury characteristics, need for skin graft, length of stay and evidence of infection within 90 days were recorded. Results A total of 56 patients met the inclusion criteria. Of these, 49 underwent vessel loop closure and seven underwent NPWT assisted closure. Patients who underwent NPWT assisted closure were at higher risk for requiring skin grafting than patients who underwent vessel loop closure, with an odds ratio of 5.9 (95% confidence interval 1.11 to 31.24). There was no difference in the rate of infection or length of stay between the two groups. Demographic factors such as age, gender, fracture mechanism, location of fasciotomy and presence of open fracture were not predictive of the need for skin grafting. Conclusion This retrospective descriptive case series demonstrates an increased risk of skin grafting in patients who underwent fasciotomy and were treated with NPWT assisted wound closure. In our series, vessel loop closure was protective against the need for skin grafting. Due to the small sample size in the NPWT group, caution should be taken when generalising these results. Further research is needed to determine if NPWT assisted closure of fasciotomy wounds truly leads to an increased requirement for skin grafting, or if the vascular injury is the main risk factor. PMID:23610668
Noce, T.E.; Holzer, T.L.
2003-01-01
The long-term stability of deep holes 1.75 inches. (4.4 cm) in diameter by 98.4 feet (30 m) created by cone penetration testing (CPT) was monitored at a site in California underlain by Holocene and Pleistocene age alluvial fan deposits. Portions of the holes remained open both below and above the 28.6-foot (8.7 m)-deep water table for approximately three years, when the experiment was terminated. Hole closure appears to be a very slow process that may take decades in the stiff soils studied here. Other experience suggests holes in softer soils may also remain open. Thus, despite their small diameter, CPT holes may remain open for years and provide paths for rapid migration of contaminants. The observations confirm the need to grout holes created by CPT soundings as well as other direct-push techniques in areas where protection of shallow ground water is important.
Alyami, Mohammad S.; Lundberg, Peter W.; Cotte, Eddy G.; Glehen, Olivier J.
2016-01-01
Iatrogenic ileostomies are routinely placed during colorectal surgery for the diversion of intestinal contents to permit healing of the distal anastomosis prior to elective reversal. We present an interesting case of spontaneous closure of a diverting ileostomy without any adverse effects to the patient. A 65-year-old woman, positive for hereditary non-polyposis colorectal cancer type-I, with locally invasive cancer of the distal colon underwent en-bloc total colectomy, hysterectomy, and bilateral salpingoophorectomy with creation of a proximal loop ileostomy. The ostomy temporarily closed without reoperation at 10 weeks, after spontaneously reopening, it definitively closed, again without surgical intervention at 18 weeks following the original surgery. This rare phenomenon has occurred following variable colorectal pathology and is poorly understood, particularly in patients with aggressive disease and adjunct perioperative interventions. PMID:27279518
Construction of momentum theorem using cross moments
NASA Astrophysics Data System (ADS)
Hahm, T. S.; Wang, Lu; Diamond, P. H.
2009-11-01
Charney-Drazin theorem has been extended to Hasegawa Wakatani system for zonal flow problem in magnetic fusion [P.H. Diamond, et al., Plasma Phys. Control. Fusion 50, 124018 (2008)]. For this model, the guiding center density is the potential vorticity and zonal flow is influenced by the particle flux. In this work we construct momentum theorems in terms of a hierarchy of cross moments
Conservational PDF Equations of Turbulence
NASA Technical Reports Server (NTRS)
Shih, Tsan-Hsing; Liu, Nan-Suey
2010-01-01
Recently we have revisited the traditional probability density function (PDF) equations for the velocity and species in turbulent incompressible flows. They are all unclosed due to the appearance of various conditional means which are modeled empirically. However, we have observed that it is possible to establish a closed velocity PDF equation and a closed joint velocity and species PDF equation through conditions derived from the integral form of the Navier-Stokes equations. Although, in theory, the resulted PDF equations are neither general nor unique, they nevertheless lead to the exact transport equations for the first moment as well as all higher order moments. We refer these PDF equations as the conservational PDF equations. This observation is worth further exploration for its validity and CFD application
Maximum wave velocity in the moments system of a relativistic gas
NASA Astrophysics Data System (ADS)
Boillat, Guy; Ruggeri, Tommaso
We consider the system of moments associated with the relativistic Boltzmann-Chernikov equation. Using the particular symmetric form obtained by the closure procedure of Extended Thermodynamics we deduce a lower bound for the maximum velocity of wave propagation in terms of the number of moments for a non-degenerate gas. When the number of moments increases this velocity tends to the speed of light. We also give the lower bound estimate in the limit cases of ultrarelativistic fluids and in the non relativistic approximation.
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.
Statistical moments of soliton field in shallow water
NASA Astrophysics Data System (ADS)
Shurgalina, Ekaterina; Pelinovsky, Efim
2013-04-01
The ensemble of solitons plays an important role in the long-term dynamics of a wave field which can be interpreted as soliton turbulence. Dynamics of a soliton field in shallow water in the framework of Korteweg - de Vries equation is studied. The statistical ensemble is generated from the isolated solitons with random phases and amplitudes. Main interest is paid to the first four statistical moments (mean, variance, skewness and kurtosis) playing an important role in the turbulence theory. They are computed analytically for initial random soliton field presenting the linear superposition of the solitary pulses. It is demonstrated that the random soliton field is not Gaussian. Then the time evolution of the statistical moments is studied numerically. It is confirmed that first two moments being the invariants of the Korteweg - de Vries equation remain to be constant. The skewness and kurtosis vary in time in each realization but tends to the constants in the average. The averaged magnitude of these moments is decreased to compare with initial values with increase of the soliton density. This effect is related with features of the two-soliton interaction described in (E.N.Pelinovsky et al., Physics Letters A (2012) http://dx.doi.org/10.1016/j.physleta.2012.11.037). As a result, the nonlinear soliton interaction leads to tendency of normalization of the random process. This study was supported by the Federal Targeted Program "Research and educational personnel of innovation Russia" for 2009-2013 and Dynasty Foundation.
Rapid Distortion Theory in astrophysical turbulence
NASA Astrophysics Data System (ADS)
Safonov, Sergey; Petrosyan, Arakel
2016-04-01
In this report, we study statistical properties of astrophysical turbulent plasma flows using Rapid Distortion Theory (RDT). The core assumption is that the turbulence responds to the external distortion so fast, that inertial and viscous forces result in a negligible change in velocity distribution. Thus it is assumed that the response to the external effect takes place in the time interval much smaller than turbulence decay time. This allows to linearize equations and to derive equations for second moments of turbulence. We apply RDT to incompressible turbulent MHD flows distorted with external magnetic field and linear velocity shear in cases of rotating and non-rotating plasma. It is shown that even with a strong nonlinearity many properties of turbulence can be qualitatively studied using a linear theory. A closed system of linear equations for velocity and magnetic field fluctuations is derived. Development of initially isotropic turbulence and transition to anisotropy are studied. Equations for fluid, current and cross helicity are derived. Differences in cases of rotating and non-rotating flows are discussed. Changes introduced by considering Hall effect are discussed.
Plasma sheet turbulence observed by Cluster II
NASA Technical Reports Server (NTRS)
Weygand, James M.; Kivelson, M. G.; Khurana, K. K.; Schwarzl, H. K.; Thompson, S. M.; McPherron, R. L.; Balogh, A.; Kistler, L. M.; Goldstein, M. L.; Borovsky, J.
2005-01-01
Cluster fluxgate magnetometer (FGM) and ion spectrometer (CIS) data are employed to analyze magnetic field fluctuations within the plasma sheet during passages through the magnetotail region in the summers of 2001 and 2002 and, in particular, to look for characteristics of magnetohydrodynamic (MHD) turbulence. Power spectral indices determined from power spectral density functions are on average larger than Kolmogorov's theoretical value for fluid turbulence as well as Kraichnan's theoretical value for MHD plasma turbulence. Probability distribution functions of the magnetic fluctuations show a scaling law over a large range of temporal scales with non-Gaussian distributions at small dissipative scales and inertial scales and more Gaussian distribution at large driving scales. Furthermore, a multifractal analysis of the magnetic field components shows scaling behavior in the inertial range of the fluctuations from about 20 s to 13 min for moments through the fifth order. Both the scaling behavior of the probability distribution functions and the multifractal structure function suggest that intermittent turbulence is present within the plasma sheet. The unique multispacecraft aspect and fortuitous spacecraft spacing allow us to examine the turbulent eddy scale sizes. Dynamic autocorrelation and cross correlation analysis of the magnetic field components allow us to determine that eddy scale sizes fit within the plasma sheet. These results suggest that magnetic field turbulence is occurring within the plasma sheet resulting in turbulent energy dissipation.
Large-eddy simulations of mean and turbulence dynamics in unsteady Ekman boundary layers
NASA Astrophysics Data System (ADS)
Momen, Mostafa; Bou-Zeid, Elie
2015-11-01
Unsteady geostrophic forcing in the atmosphere or ocean not only influences the mean wind, but also affects the turbulent statistics. In order to see when turbulence is in quasi-equilibrium with the mean, one needs to understand how the turbulence decays or develops, and how do the turbulent production, transport and dissipation respond to changes in the imposed forcing. This helps us understand the underlying dynamics of the unsteady boundary layers and develop better turbulence closures for weather/climate models and engineering applications. The present study focuses on the unsteady Ekman boundary layer where pressure gradient, Coriolis, and friction forces interact but are not necessarily in equilibrium. Several cases are simulated using LES to examine how the turbulence and resolved TKE budget terms are modulated by the variability of the mean pressure gradient. We also examine the influence of the forcing variability time-scale on the turbulence equilibrium and TKE budget. It is shown that when the forcing time-scale is in the order of the turbulence characteristic time-scale, the turbulence is no longer in quasi-equilibrium due to highly nonlinear mean-turbulence interactions and hence the conventional log-law and turbulence closures are no longer valid. NSF-PDM under AGS-10266362. Simulations performed at NCAR, and Della server at Princeton University. Cooperative Institute for Climate Science, NOAA-Princeton University under NA08OAR4320752.
Wang, Liang Germaschewski, K.; Hakim, Ammar H.; Bhattacharjee, A.
2015-01-15
We introduce an extensible multi-fluid moment model in the context of collisionless magnetic reconnection. This model evolves full Maxwell equations and simultaneously moments of the Vlasov-Maxwell equation for each species in the plasma. Effects like electron inertia and pressure gradient are self-consistently embedded in the resulting multi-fluid moment equations, without the need to explicitly solving a generalized Ohm's law. Two limits of the multi-fluid moment model are discussed, namely, the five-moment limit that evolves a scalar pressures for each species and the ten-moment limit that evolves the full anisotropic, non-gyrotropic pressure tensor for each species. We first demonstrate analytically and numerically that the five-moment model reduces to the widely used Hall magnetohydrodynamics (Hall MHD) model under the assumptions of vanishing electron inertia, infinite speed of light, and quasi-neutrality. Then, we compare ten-moment and fully kinetic particle-in-cell (PIC) simulations of a large scale Harris sheet reconnection problem, where the ten-moment equations are closed with a local linear collisionless approximation for the heat flux. The ten-moment simulation gives reasonable agreement with the PIC results regarding the structures and magnitudes of the electron flows, the polarities and magnitudes of elements of the electron pressure tensor, and the decomposition of the generalized Ohm's law. Possible ways to improve the simple local closure towards a nonlocal fully three-dimensional closure are also discussed.
NASA Astrophysics Data System (ADS)
Wang, Liang; Hakim, Ammar H.; Bhattacharjee, A.; Germaschewski, K.
2015-01-01
We introduce an extensible multi-fluid moment model in the context of collisionless magnetic reconnection. This model evolves full Maxwell equations and simultaneously moments of the Vlasov-Maxwell equation for each species in the plasma. Effects like electron inertia and pressure gradient are self-consistently embedded in the resulting multi-fluid moment equations, without the need to explicitly solving a generalized Ohm's law. Two limits of the multi-fluid moment model are discussed, namely, the five-moment limit that evolves a scalar pressures for each species and the ten-moment limit that evolves the full anisotropic, non-gyrotropic pressure tensor for each species. We first demonstrate analytically and numerically that the five-moment model reduces to the widely used Hall magnetohydrodynamics (Hall MHD) model under the assumptions of vanishing electron inertia, infinite speed of light, and quasi-neutrality. Then, we compare ten-moment and fully kinetic particle-in-cell (PIC) simulations of a large scale Harris sheet reconnection problem, where the ten-moment equations are closed with a local linear collisionless approximation for the heat flux. The ten-moment simulation gives reasonable agreement with the PIC results regarding the structures and magnitudes of the electron flows, the polarities and magnitudes of elements of the electron pressure tensor, and the decomposition of the generalized Ohm's law. Possible ways to improve the simple local closure towards a nonlocal fully three-dimensional closure are also discussed.
A Study of Low Cloud Climate Feedbacks Using a Generalized Higher-Order Closure Subgrid Model
NASA Astrophysics Data System (ADS)
Firl, Grant J.
One of the biggest uncertainties in projections of future climate is whether and how low cloudiness will change and whether that change will feed back on the climate system. Much of the uncertainty revolves around the difference in scales between the processes that govern low cloudiness and the processes that can be resolved in climate models, a fact that relegates shallow convection to the parameterization realm with varying levels of success. A new subgrid-scale parameterization, named THOR, has been developed in an effort to improve the representation of low cloudiness via parameterization in climate models. THOR uses the higher-order closure approach to determine the statistics describing subgrid-scale processes. These statistics are used to determine a trivariate double-Gaussian PDF among vertical velocity, ice-liquid water potential temperature, and total water specific humidity. With this information, one can diagnose what portion of the grid cell is cloudy, subgrid-scale cloud water content, and subgrid-scale vertical cloud water flux. In addition, samples are drawn from the trivariate PDF in order to drive the microphysics and radiation schemes. Although schemes similar to THOR have been developed over the past decade, THOR includes several novel concepts, like the generalization of the saturation curve to include condensation over both ice and liquid substrates, the determination of the PDF parameters from the given turbulence statistics, the introduction of a stochastic parcel entrainment process for the turbulence length scale, and a sub-column approach for calculating radiative transfer using the PDF. The new model is validated by simulating five test cases spanning a wide range of boundary layer cloud types, from stratocumulus to cumulus and the transition between the two. The results are compared to an ensemble of LES models running the same cases, with particular attention paid to turbulence statistics and cloud structure. For all cloud types tested
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.
Modeling extinction and reignition in turbulent flames
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.
Reynolds stress closure in jet flows using wave models
NASA Technical Reports Server (NTRS)
Morris, P. J.
1988-01-01
Ways of implementing the turbulence closure scheme based on modeling the large scale coherent structures as instability waves were sought. The computational tools necessary to apply this scheme to jets of arbitrary geometry were developed. The model, developed earlier, was extended to the shock structure of supersonic jets of arbitrary geometry and multiple jets. It was found that though the qualititate features of the unsteady flow field could be predicted there were always difficulties with some of the quantitative features. This led to the new formation of the closure scheme. The schemes for computations tools which were developed are efficient and represent the application of the very powerful mathematical tools to the problems of practical significance.
NASA Technical Reports Server (NTRS)
Hsu, Andrew T.
1992-01-01
Turbulent combustion can not be simulated adequately by conventional moment closure turbulent models. The probability density function (PDF) method offers an attractive alternative: in a PDF model, the chemical source terms are closed and do not require additional models. Because the number of computational operations grows only linearly in the Monte Carlo scheme, it is chosen over finite differencing schemes. A grid dependent Monte Carlo scheme following J.Y. Chen and W. Kollmann has been studied in the present work. It was found that in order to conserve the mass fractions absolutely, one needs to add further restrictions to the scheme, namely alpha(sub j) + gamma(sub j) = alpha(sub j - 1) + gamma(sub j + 1). A new algorithm was devised that satisfied this restriction in the case of pure diffusion or uniform flow problems. Using examples, it is shown that absolute conservation can be achieved. Although for non-uniform flows absolute conservation seems impossible, the present scheme has reduced the error considerably.
Magnetohydrodynamic Turbulence
NASA Astrophysics Data System (ADS)
Montgomery, David C.
2004-01-01
Magnetohydrodynamic (MHD) turbulence theory is modeled on neutral fluid (Navier-Stokes) turbulence theory, but with some important differences. There have been essentially no repeatable laboratory MHD experiments wherein the boundary conditions could be controlled or varied and a full set of diagnostics implemented. The equations of MHD are convincingly derivable only in the limit of small ratio of collision mean-free-paths to macroscopic length scales, an inequality that often goes the other way for magnetofluids of interest. Finally, accurate information on the MHD transport coefficients-and thus, the Reynolds-like numbers that order magnetofluid behavior-is largely lacking; indeed, the algebraic expressions used for such ingredients as the viscous stress tensor are often little more than wishful borrowing from fluid mechanics. The one accurate thing that has been done extensively and well is to solve the (strongly nonlinear) MHD equations numerically, usually in the presence of rectangular periodic boundary conditions, and then hope for the best when drawing inferences from the computations for those astrophysical and geophysical MHD systems for which some indisputably turbulent detailed data are available, such as the solar wind or solar prominences. This has led to what is perhaps the first field of physics for which computer simulations are regarded as more central to validating conclusions than is any kind of measurement. Things have evolved in this way due to a mixture of the inevitable and the bureaucratic, but that is the way it is, and those of us who want to work on the subject have to live with it. It is the only game in town, and theories that have promised more-often on the basis of some alleged ``instability''-have turned out to be illusory.
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.
MEANS: python package for Moment Expansion Approximation, iNference and Simulation
Fan, Sisi; Geissmann, Quentin; Lakatos, Eszter; Lukauskas, Saulius; Ale, Angelique; Babtie, Ann C.; Kirk, Paul D. W.; Stumpf, Michael P. H.
2016-01-01
Motivation: Many biochemical systems require stochastic descriptions. Unfortunately these can only be solved for the simplest cases and their direct simulation can become prohibitively expensive, precluding thorough analysis. As an alternative, moment closure approximation methods generate equations for the time-evolution of the system’s moments and apply a closure ansatz to obtain a closed set of differential equations; that can become the basis for the deterministic analysis of the moments of the outputs of stochastic systems. Results: We present a free, user-friendly tool implementing an efficient moment expansion approximation with parametric closures that integrates well with the IPython interactive environment. Our package enables the analysis of complex stochastic systems without any constraints on the number of species and moments studied and the type of rate laws in the system. In addition to the approximation method our package provides numerous tools to help non-expert users in stochastic analysis. Availability and implementation: https://github.com/theosysbio/means Contacts: m.stumpf@imperial.ac.uk or e.lakatos13@imperial.ac.uk Supplementary information: Supplementary data are available at Bioinformatics online. PMID:27153663
40 CFR 265.280 - Closure and post-closure.
Code of Federal Regulations, 2014 CFR
2014-07-01
... contaminants caused by wind erosion; and (4) Compliance with § 265.276 concerning the growth of food-chain... unit as appropriate for its post-closure use; (3) Assure that growth of food chain crops complies...
40 CFR 265.280 - Closure and post-closure.
Code of Federal Regulations, 2011 CFR
2011-07-01
... contaminants caused by wind erosion; and (4) Compliance with § 265.276 concerning the growth of food-chain... unit as appropriate for its post-closure use; (3) Assure that growth of food chain crops complies...
40 CFR 265.280 - Closure and post-closure.
Code of Federal Regulations, 2010 CFR
2010-07-01
... contaminants caused by wind erosion; and (4) Compliance with § 265.276 concerning the growth of food-chain... unit as appropriate for its post-closure use; (3) Assure that growth of food chain crops complies...
40 CFR 265.280 - Closure and post-closure.
Code of Federal Regulations, 2012 CFR
2012-07-01
... contaminants caused by wind erosion; and (4) Compliance with § 265.276 concerning the growth of food-chain... unit as appropriate for its post-closure use; (3) Assure that growth of food chain crops complies...
40 CFR 265.280 - Closure and post-closure.
Code of Federal Regulations, 2013 CFR
2013-07-01
... contaminants caused by wind erosion; and (4) Compliance with § 265.276 concerning the growth of food-chain... unit as appropriate for its post-closure use; (3) Assure that growth of food chain crops complies...
A GLOBAL TURBULENCE MODEL FOR NEUTRINO-DRIVEN CONVECTION IN CORE-COLLAPSE SUPERNOVAE
Murphy, Jeremiah W.; Meakin, Casey
2011-12-01
Simulations of core-collapse supernovae (CCSNe) result in successful explosions once the neutrino luminosity exceeds a critical curve, and recent simulations indicate that turbulence further enables explosion by reducing this critical neutrino luminosity. We propose a theoretical framework to derive this result and take the first steps by deriving the governing mean-field equations. Using Reynolds decomposition, we decompose flow variables into background and turbulent flows and derive self-consistent averaged equations for their evolution. As basic requirements for the CCSN problem, these equations naturally incorporate steady-state accretion, neutrino heating and cooling, non-zero entropy gradients, and turbulence terms associated with buoyant driving, redistribution, and dissipation. Furthermore, analysis of two-dimensional (2D) CCSN simulations validate these Reynolds-averaged equations, and we show that the physics of turbulence entirely accounts for the differences between 1D and 2D CCSN simulations. As a prelude to deriving the reduction in the critical luminosity, we identify the turbulent terms that most influence the conditions for explosion. Generically, turbulence equations require closure models, but these closure models depend upon the macroscopic properties of the flow. To derive a closure model that is appropriate for CCSNe, we cull the literature for relevant closure models and compare each with 2D simulations. These models employ local closure approximations and fail to reproduce the global properties of neutrino-driven turbulence. Motivated by the generic failure of these local models, we propose an original model for turbulence which incorporates global properties of the flow. This global model accurately reproduces the turbulence profiles and evolution of 2D CCSN simulations.
Closure in Knee Replacement Surgery
Kharat, Kiran
2012-01-01
Total Knee replacement (TKR) is one of the commonest arthroplasty surgeries performed. Various techniques of closures in TKR are described. This technical note describes an useful technique of achieving water tight closure in TKR. An optimal tension watertight closure also reduces the chances of dead space hematomas and infection. The author has described his technique where the soft tissues are never unduly compromised. In his experience the patient can be mobilized freely in bed and even allowed to sleep prone after first wound check.
Not Available
1994-01-01
This report has been prepared to satisfy Section 3156(b) of Public Law 101-189 (Reports in Connection with Permanent Closures of Department of Energy Defense Nuclear Facilities), which requires submittal of a Closure Report to Congress by the Secretary of Energy upon the permanent cessation of production operations at a US Department of Energy (DOE) defense nuclear facility (Watkins 1991). This closure report provides: (1) A complete survey of the environmental problems at the facility; (2) Budget quality data indicating the cost of environmental restoration and other remediation and cleanup efforts at the facility; (3) A proposed cleanup schedule.
[Angle-closure chronic glaucoma].
Lachkar, Y
2003-10-01
The incidence of chronic angle closure glaucoma is considerably greater than the incidence of the acute type. This type of glaucoma may mimic primary open angle glaucoma with visual field deterioration, optic nerve alteration and intraocular pressure elevation with a quiet painless eye. Its diagnosis is based on indentation gonioscopy showing peripheral anterior synechiae. The mechanisms of angle closure are the pupillary block, the plateau iris configuration and the creeping form. The treatment of chronic angle closure glaucoma is based on laser peripheral iridotomy. PMID:14646832
Explosive turbulent magnetic reconnection.
Higashimori, K; Yokoi, N; Hoshino, M
2013-06-21
We report simulation results for turbulent magnetic reconnection obtained using a newly developed Reynolds-averaged magnetohydrodynamics model. We find that the initial Harris current sheet develops in three ways, depending on the strength of turbulence: laminar reconnection, turbulent reconnection, and turbulent diffusion. The turbulent reconnection explosively converts the magnetic field energy into both kinetic and thermal energy of plasmas, and generates open fast reconnection jets. This fast turbulent reconnection is achieved by the localization of turbulent diffusion. Additionally, localized structure forms through the interaction of the mean field and turbulence. PMID:23829741
Turbulence Heating ObserveR - THOR
NASA Astrophysics Data System (ADS)
Retino, Alessandro; Marcucci, Maria FedericaFederica; Vaivads, Andris; Escoubet, C. Philippe; Khotyaintsev, Yuri; Fazakerley, Andrew; Soucek, Jan; Gehler, Martin; Lavraud, Benoit; Vainio, Rami; Valentini, Francesco; Chen, Christopher H. K.; Narita, Yasuhito; Wielders, Arno
2016-07-01
Turbulent fluctuations are ubiquitous in astrophysical plasmas and reach up to scales as large as stars, bubbles or clouds blown out by stellar winds, or even entire galaxies. However, most of the irreversible energy dissipation produced by turbulent fluctuations occurs at very small scales, the so-called kinetic scales, where the plasma no longer behaves as a fluid and the properties of individual plasma species (electrons, protons, and other ions) become important. The heating of different plasma species as well as the acceleration of particles to high energies are governed by kinetic processes which determine how the turbulent electromagnetic fluctuations dissipate. Thus, processes at kinetic scales directly affect the large-scale properties of astrophysical plasmas. Turbulence Heating ObserveR (THOR) is the first mission ever flown in space fully dedicated to study plasma turbulent fluctuations and associated energization mechanisms. It will explore the kinetic plasma processes that determine the fundamental behavior of the majority of baryonic matter in the universe. THOR will lead to an understanding of the basic plasma heating and particle acceleration mechanisms, of their effect on different plasma species and of their relative importance in different turbulent regimes. THOR will provide closure of these fundamental questions by making detailed in situ measurements of the closest available dilute and turbulent magnetized plasmas at unprecedented temporal and spatial resolution. THOR focuses on particular regions in space: the pristine solar wind, the Earth's bow shock and interplanetary shocks, and the compressed solar wind regions downstream of shocks. These regions are selected because of their different turbulence properties, and reflect similar astrophysical environments. THOR is a candidate for selection as the next ESA M4 mission. Here we present THOR's science as well as the results of the ongoing mission study, currently undertaken at ESA.
Neglected ends: clinical ethics consultation and the prospects for closure.
Fiester, Autumn
2015-01-01
Clinical ethics consultations (CECs) are sometimes deemed complete at the moment when the consultants make a recommendation. In CECs that involve actual ethical conflict, this view of a consult's endpoint runs the risk of overemphasizing the conflict's resolution at the expense of the consult's process, which can have deleterious effects on the various parties in the conflict. This overly narrow focus on reaching a decision or recommendation in consults that involve profound moral disagreement can result in two types of adverse, lingering sequelae: moral distress or negative moral emotions. The problem, succinctly named, is that such consults have insufficient "closure" for patients, families, and providers. To promote closure, and avoid the ills of moral distress and the moral emotions, I argue that CECs need to prioritize assisted conversation between the different stakeholders in these conflicts, what is often referred to as "bioethics mediation." PMID:25562222
Inquiry-Based Science: Turning Teachable Moments into Learnable Moments
ERIC Educational Resources Information Center
Haug, Berit S.
2014-01-01
This study examines how an inquiry-based approach to teaching and learning creates teachable moments that can foster conceptual understanding in students, and how teachers capitalize upon these moments. Six elementary school teachers were videotaped as they implemented an integrated inquiry-based science and literacy curriculum in their…
NASA Astrophysics Data System (ADS)
Corsini, A.; Rispoli, F.; Santoriello, A.; Tezduyar, T. E.
2006-09-01
Recent advances in turbulence modeling brought more and more sophisticated turbulence closures (e.g. k-ɛ, k-ɛ - v 2- f, Second Moment Closures), where the governing equations for the model parameters involve advection, diffusion and reaction terms. Numerical instabilities can be generated by the dominant advection or reaction terms. Classical stabilized formulations such as the Streamline Upwind/Petrov Galerkin (SUPG) formulation (Brook and Hughes, comput methods Appl Mech Eng 32:199 255, 1982; Hughes and Tezduyar, comput methods Appl Mech Eng 45: 217 284, 1984) are very well suited for preventing the numerical instabilities generated by the dominant advection terms. A different stabilization however is needed for instabilities due to the dominant reaction terms. An additional stabilization term, called the diffusion for reaction-dominated (DRD) term, was introduced by Tezduyar and Park (comput methods Appl Mech Eng 59:307 325, 1986) for that purpose and improves the SUPG performance. In recent years a new class of variational multi-scale (VMS) stabilization (Hughes, comput methods Appl Mech Eng 127:387 401, 1995) has been introduced, and this approach, in principle, can deal with advection diffusion reaction equations. However, it was pointed out in Hanke (comput methods Appl Mech Eng 191:2925 2947) that this class of methods also need some improvement in the presence of high reaction rates. In this work we show the benefits of using the DRD operator to enhance the core stabilization techniques such as the SUPG and VMS formulations. We also propose a new operator called the DRDJ (DRD with the local variation jump) term, targeting the reduction of numerical oscillations in the presence of both high reaction rates and sharp solution gradients. The methods are evaluated in the context of two stabilized methods: the classical SUPG formulation and a recently-developed VMS formulation called the V-SGS (Corsini et al. comput methods Appl Mech Eng 194:4797 4823, 2005
Near-wall response in turbulent shear flows subjected to imposed unsteadiness
NASA Technical Reports Server (NTRS)
Mankbadi, Reda R.; Liu, Joseph T. C.
1992-01-01
Rapid-distortion theory is adapted to introduce a truly unsteady closure into a simple phenomenological turbulence model in order to describe the unsteady response of a turbulent wall layer exposed to a temporarily oscillating pressure gradient. The closure model is built by taking the ratio of turbulent shear stress to turbulent kinetic energy to be a function of the effective strain. The latter accounts for the history of the flow. The computed unsteady velocity fluctuations and modulated turbulent stresses compare favorably in the 'non-quasi-steady' frequency range, where quasi-steady assumptions would fail. This suggests that the concept of rapid distortion is especially appropriate for unsteady flows. This paper forms the basis for acoustical studies of the problem to be reported elsewhere.
Progress in turbulence modeling for complex flow fields including effects of compressibility
NASA Technical Reports Server (NTRS)
Wilcox, D. C.; Rubesin, M. W.
1980-01-01
Two second-order-closure turbulence models were devised that are suitable for predicting properties of complex turbulent flow fields in both incompressible and compressible fluids. One model is of the "two-equation" variety in which closure is accomplished by introducing an eddy viscosity which depends on both a turbulent mixing energy and a dissipation rate per unit energy, that is, a specific dissipation rate. The other model is a "Reynolds stress equation" (RSE) formulation in which all components of the Reynolds stress tensor and turbulent heat-flux vector are computed directly and are scaled by the specific dissipation rate. Computations based on these models are compared with measurements for the following flow fields: (a) low speed, high Reynolds number channel flows with plane strain or uniform shear; (b) equilibrium turbulent boundary layers with and without pressure gradients or effects of compressibility; and (c) flow over a convex surface with and without a pressure gradient.
Afeyan, B. B.; Boley, C. D.; Estabrook, K. G.; Kirkwood, R. K.; Milam, D.; Murray, J. E.; Nielsen, N. D.; Sell, W. D.; Zakharenkov, Y. A.
1998-07-20
Spatial-filter pinholes and knife-edge samples were irradiated in vacuum by 1053-nm, 5-20 ns pulses at intensities to 500 GW/cm
Latson, L A
1998-01-01
Per-catheter devices for atrial septal defect (ASD) closure have been evolving since 1974. The four major devices available for use on a limited basis in early 1997 are reviewed. These include (in alphabetical order) the Angel Wing device, the ASDOS device, the Buttoned device, and the CardioSeal device (successor to the Clamshell). Sufficient data have been collected to indicate that transcatheter ASD closure is a viable alternative to surgery in selected patients. The advantages of the concept of per-catheter closure over surgical closure should lead to the continued development of devices and techniques for per-catheter treatment of ASD and other septal defects in the years to come. PMID:9396853
40 CFR 258.60 - Closure criteria.
Code of Federal Regulations, 2012 CFR
2012-07-01
... 40 Protection of Environment 26 2012-07-01 2011-07-01 true Closure criteria. 258.60 Section 258.60 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) SOLID WASTES CRITERIA FOR MUNICIPAL SOLID WASTE LANDFILLS Closure and Post-Closure Care § 258.60 Closure criteria. (a) Owners or operators of all MSWLF units must install a...
40 CFR 258.60 - Closure criteria.
Code of Federal Regulations, 2011 CFR
2011-07-01
... 40 Protection of Environment 25 2011-07-01 2011-07-01 false Closure criteria. 258.60 Section 258.60 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) SOLID WASTES CRITERIA FOR MUNICIPAL SOLID WASTE LANDFILLS Closure and Post-Closure Care § 258.60 Closure criteria. (a) Owners or operators of all MSWLF units must install a...
40 CFR 258.60 - Closure criteria.
Code of Federal Regulations, 2014 CFR
2014-07-01
... 40 Protection of Environment 25 2014-07-01 2014-07-01 false Closure criteria. 258.60 Section 258.60 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) SOLID WASTES CRITERIA FOR MUNICIPAL SOLID WASTE LANDFILLS Closure and Post-Closure Care § 258.60 Closure criteria. (a) Owners or operators of all MSWLF units must install a...
27 CFR 19.662 - Affixing closures.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Affixing closures. 19.662 Section 19.662 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE BUREAU, DEPARTMENT OF THE TREASURY LIQUORS DISTILLED SPIRITS PLANTS Closures § 19.662 Affixing closures. Closures...
Generalized kinetic-neoclassical closure for parallel viscosity in a tokamak.
NASA Astrophysics Data System (ADS)
Smolyakov, A.; Callen, J. D.; Hegna, C.
2000-10-01
We develop a drift-kinetic equation for a Chapman Enskog-type calculations of the parallel viscosity in a tokamak. This approach allows us to uniformly obtain closure relations for the parallel viscosity that include the kinetic effects of wave-particle interactions, such as those of Hammet-Perkins closures, as well as standard neoclassical moment closures induced by collisions and the magnetic field strength variation along field lines. Closures for both these cases can be obtained from our expressions; also, their mutual influences can be investigated. The developed equations allow calculation of parallel vicosity in general kinetic-neoclassical regimes while the main conservation properties remain correct even with an approximate treatment of the collisional operator.
Understanding the basis of space closure in Orthodontics for a more efficient orthodontic treatment
Ribeiro, Gerson Luiz Ulema; Jacob, Helder B.
2016-01-01
ABSTRACT Introduction: Space closure is one of the most challenging processes in Orthodontics and requires a solid comprehension of biomechanics in order to avoid undesirable side effects. Understanding the biomechanical basis of space closure better enables clinicians to determine anchorage and treatment options. In spite of the variety of appliance designs, space closure can be performed by means of friction or frictionless mechanics, and each technique has its advantages and disadvantages. Friction mechanics or sliding mechanics is attractive because of its simplicity; the space site is closed by means of elastics or coil springs to provide force, and the brackets slide on the orthodontic archwire. On the other hand, frictionless mechanics uses loop bends to generate force to close the space site, allowing differential moments in the active and reactive units, leading to a less or more anchorage control, depending on the situation. Objective: This article will discuss various theoretical aspects and methods of space closure based on biomechanical concepts. PMID:27275623
NASA Astrophysics Data System (ADS)
Shatskii, I. P.; Makoviichuk, N. V.
2011-05-01
The problem of closure of collinear cracks during bending of a shallow shell is considered within the framework of the Kirchhoff theory. Crack closure is described using the model of contact along a line on one of the shell faces. Strain and moment intensity factors and fracture load are studied as functions of shell curvature and defect location, and the distribution of contact forces along the cracks is investigated.
Closure and Sealing Design Calculation
T. Lahnalampi; J. Case
2005-08-26
The purpose of the ''Closure and Sealing Design Calculation'' is to illustrate closure and sealing methods for sealing shafts, ramps, and identify boreholes that require sealing in order to limit the potential of water infiltration. In addition, this calculation will provide a description of the magma that can reduce the consequences of an igneous event intersecting the repository. This calculation will also include a listing of the project requirements related to closure and sealing. The scope of this calculation is to: summarize applicable project requirements and codes relating to backfilling nonemplacement openings, removal of uncommitted materials from the subsurface, installation of drip shields, and erecting monuments; compile an inventory of boreholes that are found in the area of the subsurface repository; describe the magma bulkhead feature and location; and include figures for the proposed shaft and ramp seals. The objective of this calculation is to: categorize the boreholes for sealing by depth and proximity to the subsurface repository; develop drawing figures which show the location and geometry for the magma bulkhead; include the shaft seal figures and a proposed construction sequence; and include the ramp seal figure and a proposed construction sequence. The intent of this closure and sealing calculation is to support the License Application by providing a description of the closure and sealing methods for the Safety Analysis Report. The closure and sealing calculation will also provide input for Post Closure Activities by describing the location of the magma bulkhead. This calculation is limited to describing the final configuration of the sealing and backfill systems for the underground area. The methods and procedures used to place the backfill and remove uncommitted materials (such as concrete) from the repository and detailed design of the magma bulkhead will be the subject of separate analyses or calculations. Post-closure monitoring will not
Lagrangian statistics in laboratory 2D turbulence
NASA Astrophysics Data System (ADS)
Xia, Hua; Francois, Nicolas; Punzmann, Horst; Shats, Michael
2014-05-01
Turbulent mixing in liquids and gases is ubiquitous in nature and industrial flows. Understanding statistical properties of Lagrangian trajectories in turbulence is crucial for a range of problems such as spreading of plankton in the ocean, transport of pollutants, etc. Oceanic data on trajectories of the free-drifting instruments, indicate that the trajectory statistics can often be described by a Lagrangian integral scale. Turbulence however is a state of a flow dominated by a hierarchy of scales, and it is not clear which of these scales mostly affect particle dispersion. Moreover, coherent structures often coexist with turbulence in laboratory experiments [1]. The effect of coherent structures on particle dispersion in turbulent flows is not well understood. Recent progress in scientific imaging and computational power made it possible to tackle this problem experimentally. In this talk, we report the analysis of the higher order Lagrangian statistics in laboratory two-dimensional turbulence. Our results show that fluid particle dispersion is diffusive and it is determined by a single measurable Lagrangian scale related to the forcing scale [2]. Higher order moments of the particle dispersion show strong self-similarity in fully developed turbulence [3]. Here we introduce a new dispersion law that describes single particle dispersion during the turbulence development [4]. These results offer a new way of predicting dispersion in turbulent flows in which one of the low energy scales are persistent. It may help better understanding of drifter Lagrangian statistics in the regions of the ocean where small scale coherent eddies are present [5]. Reference: 1. H. Xia, H. Punzmann, G. Falkovich and M. Shats, Physical Review Letters, 101, 194504 (2008) 2. H. Xia, N. Francois, H. Punzmann, and M. Shats, Nature Communications, 4, 2013 (2013) 3. R. Ferrari, A.J. Manfroi , W.R. Young, Physica D 154 111 (2001) 4. H. Xia, N. Francois, H. Punzmann and M. Shats, submitted (2014
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.
40 CFR 264.1202 - Closure and post-closure care.
Code of Federal Regulations, 2013 CFR
2013-07-01
... 40 Protection of Environment 27 2013-07-01 2013-07-01 false Closure and post-closure care. 264... FACILITIES Hazardous Waste Munitions and Explosives Storage § 264.1202 Closure and post-closure care. (a) At... or decontaminated, he or she must close the facility and perform post-closure care in accordance...
40 CFR 265.1102 - Closure and post-closure care.
Code of Federal Regulations, 2013 CFR
2013-07-01
... 40 Protection of Environment 27 2013-07-01 2013-07-01 false Closure and post-closure care. 265..., STORAGE, AND DISPOSAL FACILITIES Containment Buildings § 265.1102 Closure and post-closure care. (a) At... practicably removed or decontaminated, he must close the facility and perform post-closure care in...
B.B. Rokhman
2007-09-15
This article considers the Eulerian continuum description of turbulent transfer of momentum and moment of momentum in a solid phase on the basis of the equations of transfer of the second and third moments of pulsations of the linear and angular velocities of particles. The pulsating characteristics of a gas are computed using the two-parameter model of turbulence generalized to the case of gas-dispersed turbulent flows.
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.
RCRA closure of mixed waste impoundments
Blaha, F.J.; Greengard, T.C.; Arndt, M.B.
1989-11-01
A case study of a RCRA closure action at the Rocky Flats Plant is presented. Closure of the solar evaporation ponds involves removal and immobilization of a mixed hazardous/radioactive sludge, treatment of impounded water, groundwater monitoring, plume delineation, and collection and treatment of contaminated groundwater. The site closure is described within the context of regulatory negotiations, project schedules, risk assessment, clean versus dirty closure, cleanup levels, and approval of closure plans and reports. Lessons learned at Rocky Flats are summarized.
A Multiscale Morphing Continuum Description for Turbulence
NASA Astrophysics Data System (ADS)
Chen, James; Wonnell, Louis
2015-11-01
Turbulence is a flow physics phenomena invlolving multiple length scales. The popular Navier- Stokes equations only possess one length/time scale. Therefore, extremely fine mesh is needed for DNS attempting to resolve the small scale motion, which comes with a burden of excessive computational cost. For practical application with complex geometries, the research society rely on RANS and LES, which requre turbulence model or subgrid scale (SGS) model for closure problems. Different models not only lead to different results but usually are invalidated on solid physical grounds, such as objectivity and entropy principle.The Morphing Continuum Theory (MCT) is a high-order continuum theory formulated under the framework of thermalmechanics for physics phenomena involving microstructure. In this study, a theoretical perspective for the multiscale nature of the Morphing Continuum Theory is connected with the multiscale nature of turbulence physics. The kinematics, balance laws, constitutive equations and a Morphing Continuum description of turbulence are introduced. The equations were numerically implemented for a zero pressure gradient flat plate. The simulations are compate with the laminar, transitional and turbulence cases.
Disturbance Dynamics in Transitional and Turbulent Flows
NASA Technical Reports Server (NTRS)
Grosch, Chester E.
1999-01-01
In order to expand the predictive capability of single-point turbulence closure models to account for the early-stage transition regime, a methodology for the formulation and calibration of model equations for the ensemble-averaged disturbance kinetic energy and energy dissipation rate is presented. First the decay of laminar disturbances and turbulence in mean shear-free flows is studied. In laminar flows, such disturbances are linear superpositions of modes governed by the Orr-Sommerfeld equation. In turbulent flows, disturbances are described through transport equations for representative mean quantities. The link between a description based on a deterministic evolution equation and a probability based mean transport equation is established. Because an uncertainty in initial conditions exists in the laminar as well as the turbulent regime, a probability distribution must be defined even in the laminar case. Using this probability distribution, it is shown that the exponential decay of the linear modes in the laminar regime can be related to a power law decay of both the (ensemble) mean disturbance kinetic energy and the dissipation rate. The evolution of these mean disturbance quantities is then described by transport equations similar to those for the corresponding turbulent decaying flow. Second, homogeneous shear flow, where disturbances can be described by rapid distortion theory (RDT), is studied. The relationship between RDT and linear stability theory is exploited in order to obtain a closed set of modeled equations. The linear disturbance equations are solved directly so that the numerical simulation yields a database from which the closure coefficients in the ensemble-averaged disturbance equations can be determined.
Perturbation Methods and Closure Approximations in Nonlinear Systems.
NASA Astrophysics Data System (ADS)
Dubin, Daniel Herschel Eli
In the first section of this thesis, Hamiltonian theories of guiding center and gyro-center motion are developed using modern symplectic methods and Lie transformations. Littlejohn's techniques, combined with the theory of resonant interaction and island overlap, are used to explore the problem of adiabatic invariance and onset of stochasticity. As an example, we consider the breakdown of invariance due to resonance between drift motion and gyromotion in a tokamak. A Hamiltonian is developed for motion in a straight magnetic field with electrostatic perturbations in the gyrokinetic ordering, from which nonlinear gyrokinetic equations are constructed which have the property of phase space preservation, useful for computer simulation. Energy invariants are found and various limits of the equations are considered. For small Larmor radius the equations are similar to those of Lee. Several new effects appear which are absent from conventional theories. We show that the wave kinetic equation of Galeev and Sagdeev neglects several important gyrokinetic effects. In the second section, statistical closure theories are applied to simple dynamical systems. We use the logistic map as an example because of its universal properties and simple quadratic nonlinearity. The first closure considered is the Direct Interaction Approximation of Kraichnan, which is found to fail when applied to the logistic map because it cannot approximate the bounded support of the map's equilibrium distribution. By imposing a periodicity constraint on a Langevin form of the D.I.A. a new stable closure is developed. The relation between the predictability theory of Kraichnan and the theory of Liapunov exponents is considered. Realizability constraints on the moments of a distribution are formulated using Kuhn-Tucker multipliers. Results are related to the work of Sandri and Kraichnan, but the variational technique employed allows for a more elegant and general approach. The realizability criteria are
Macroscopic approximation to relativistic kinetic theory from a nonlinear closure
NASA Astrophysics Data System (ADS)
Peralta-Ramos, J.; Calzetta, E.
2013-02-01
We use a macroscopic description of a system of relativistic particles based on adding a nonequilibrium tensor to the usual hydrodynamic variables. The nonequilibrium tensor is linked to relativistic kinetic theory through a nonlinear closure suggested by the entropy production principle; the evolution equation is obtained by the method of moments and together with energy-momentum conservation closes the system. Transport coefficients are chosen to reproduce second-order fluid dynamics if gradients are small. We compare the resulting formalism to exact solutions of Boltzmann’s equation in 0+1 dimensions and show that it tracks kinetic theory better than second-order fluid dynamics.
Turbulence Modeling Effects on the Prediction of Equilibrium States of Buoyant Shear Flows
NASA Technical Reports Server (NTRS)
Zhao, C. Y.; So, R. M. C.; Gatski, T. B.
2001-01-01
The effects of turbulence modeling on the prediction of equilibrium states of turbulent buoyant shear flows were investigated. The velocity field models used include a two-equation closure, a Reynolds-stress closure assuming two different pressure-strain models and three different dissipation rate tensor models. As for the thermal field closure models, two different pressure-scrambling models and nine different temperature variance dissipation rate, Epsilon(0) equations were considered. The emphasis of this paper is focused on the effects of the Epsilon(0)-equation, of the dissipation rate models, of the pressure-strain models and of the pressure-scrambling models on the prediction of the approach to equilibrium turbulence. Equilibrium turbulence is defined by the time rate (if change of the scaled Reynolds stress anisotropic tensor and heat flux vector becoming zero. These conditions lead to the equilibrium state parameters. Calculations show that the Epsilon(0)-equation has a significant effect on the prediction of the approach to equilibrium turbulence. For a particular Epsilon(0)-equation, all velocity closure models considered give an equilibrium state if anisotropic dissipation is accounted for in one form or another in the dissipation rate tensor or in the Epsilon(0)-equation. It is further found that the models considered for the pressure-strain tensor and the pressure-scrambling vector have little or no effect on the prediction of the approach to equilibrium turbulence.
Turbulence radiation interaction modeling in hydrocarbon pool fire simulations
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.
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.
An experimental Lagrangian study of inhomgeneous turbulence
NASA Astrophysics Data System (ADS)
Stelzenmuller, Nickolas; Mordant, Nicolas
2015-11-01
We investigate experimentally the Lagrangian properties of inhomogeneous turbulence in the general scope of dispersion studies in natural and industrial flows. Lagrangian studies of homogeneous turbulence are becoming common, but very little Lagrangian experimental data exists for inhomogeneous turbulence despite the vast range of applications. Particle tracking velocimetry using a very high speed camera in a fully developed turbulent channel flow in water is achieved at ReH = 33 , 000 . This technique provides Lagrangian velocity and acceleration statistics fully resolved at the smallest turbulent scales near the wall. These statistics, conditioned by the distance to the wall, allow the the investigation of the inhomogeneity of the statistical properties of this flow. Autocorrelations of velocity and acceleration show increasing Lagrangian turbulent scales as distance from the wall increases, as well as decreasing anisotropy. PDF's and moments of Lagrangian quantities are presented by showing the evolution of structure functions across the boundary layer. These results are compared to direct numerical simulation results from a similar flow, and their implications for stochastic models of inhomogeneous flows are discussed.
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.
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.
Toward a Turbulence Constitutive Relation for Rotating Flows
NASA Technical Reports Server (NTRS)
Ristorcelli, J. R.
1996-01-01
In rapidly rotating turbulent flows the largest scales of the motion are in approximate geostrophic balance. Single-point turbulence closures, in general, cannot attain a geostrophic balance. This article addresses and resolves the possibility of constitutive relation procedures for single-point second order closures for a specific class of rotating or stratified flows. Physical situations in which the geostrophic balance is attained are described. Closely related issues of frame-indifference, horizontal nondivergence, Taylor-Proudman theorem and two-dimensionality are, in the context of both the instantaneous and averaged equations, discussed. It is shown, in the absence of vortex stretching along the axis of rotation, that turbulence is frame-indifferent. A derivation and discussion of a geostrophic constraint which the prognostic equations for second-order statistics must satisfy for turbulence approaching a frame-indifferent limit is given. These flow situations, which include rotating and nonrotating stratified flows, are slowly evolving flows in which the constitutive relation procedures are useful. A nonlinear non-constant coefficient representation for the rapid-pressure strain covariance appearing in the Reynolds stress and heat flux equations consistent with the geostrophic balance is described. The rapid-pressure strain model coefficients are not constants determined by numerical optimization but are functions of the state of the turbulence as parameterized by the Reynolds stresses and the turbulent heat fluxes. The functions are valid for all states of the turbulence attaining their limiting values only when a limit state is achieved. These issues are relevant to strongly vortical flows as well as flows such as the planetary boundary layers, in which there is a transition from a three-dimensional shear driven turbulence to a geostrophic or horizontal turbulence.
Onsager's-principle-consistent 13-moment transport equations
NASA Astrophysics Data System (ADS)
Singh, Narendra; Agrawal, Amit
2016-06-01
A new set of generalized transport equations is derived for higher-order moments which are generated in evolution equation for stress tensor and heat flux vector in 13-moment equations. The closure we employ satisfies Onsager's symmetry principle. In the derivation, we do not employ a phase density function based on Hermite polynomial series in terms of higher-order moments, unlike Grad's approach. The distribution function is rather chosen to satisfy collision invariance, and H-theorem and capture relatively strong deviations from equilibrium. The phase density function satisfies the linearized Boltzmann equation and provides the correct value of the Prandtl number for monatomic gas. The derived equations are compared with Grad's 13-moments equations for gas modeled as Maxwellian molecule. The merits of the proposed equations against Grad's and R13 equations are discussed. In particular, it is noted that the proposed equations contain higher-order terms compared to these equations but require a fewer number of boundary conditions as compared to the R13 equations. The Knudsen number envelope which can be covered to describe flows with these equations is therefore expected to be larger as compared to the earlier equations.
Linearly exact parallel closures for slab geometry
Ji, Jeong-Young; Held, Eric D.; Jhang, Hogun
2013-08-15
Parallel closures are obtained by solving a linearized kinetic equation with a model collision operator using the Fourier transform method. The closures expressed in wave number space are exact for time-dependent linear problems to within the limits of the model collision operator. In the adiabatic, collisionless limit, an inverse Fourier transform is performed to obtain integral (nonlocal) parallel closures in real space; parallel heat flow and viscosity closures for density, temperature, and flow velocity equations replace Braginskii's parallel closure relations, and parallel flow velocity and heat flow closures for density and temperature equations replace Spitzer's parallel transport relations. It is verified that the closures reproduce the exact linear response function of Hammett and Perkins [Phys. Rev. Lett. 64, 3019 (1990)] for Landau damping given a temperature gradient. In contrast to their approximate closures where the vanishing viscosity coefficient numerically gives an exact response, our closures relate the heat flow and nonvanishing viscosity to temperature and flow velocity (gradients)
Linearly exact parallel closures for slab geometry
NASA Astrophysics Data System (ADS)
Ji, Jeong-Young; Held, Eric D.; Jhang, Hogun
2013-08-01
Parallel closures are obtained by solving a linearized kinetic equation with a model collision operator using the Fourier transform method. The closures expressed in wave number space are exact for time-dependent linear problems to within the limits of the model collision operator. In the adiabatic, collisionless limit, an inverse Fourier transform is performed to obtain integral (nonlocal) parallel closures in real space; parallel heat flow and viscosity closures for density, temperature, and flow velocity equations replace Braginskii's parallel closure relations, and parallel flow velocity and heat flow closures for density and temperature equations replace Spitzer's parallel transport relations. It is verified that the closures reproduce the exact linear response function of Hammett and Perkins [Phys. Rev. Lett. 64, 3019 (1990)] for Landau damping given a temperature gradient. In contrast to their approximate closures where the vanishing viscosity coefficient numerically gives an exact response, our closures relate the heat flow and nonvanishing viscosity to temperature and flow velocity (gradients).
Finite-element analysis of enclosed turbulent diffusion flames
NASA Astrophysics Data System (ADS)
Benim, A. C.
A FEM formulation is presented for the turbulent diffusion flames encountered in such important technical fields as thermal power plant furnaces, industrial furnaces, and gas turbine combustors; these involve a powerful interaction among fluid mechanics, heat transfer, and chemical kinetics. Turbulence is an important feature of the flow, which is responsible for mixing and convective transport processes. A k-epsilon model is used to define the state of such turbulence. The inclusion of radiative heat transfer considerably complicates problems of this sort and entails the use of the FEM 'moment' method.
DNS of aerosol evolution in a turbulent jet
NASA Astrophysics Data System (ADS)
Zhou, Kun; Attili, Antonio; Bisetti, Fabrizio
2011-11-01
The effects of turbulence on the evolution of aerosols are not well understood. In this work, the interaction of aerosol dynamics and turbulence are studied in a canonical flow configuration by numerical means. The configuration consists of a hot nitrogen stream saturated with dibutyl phthalate (DBP) vapor mixing with cool air in a shear layer. A direct numerical simulation (DNS) for the momentum and scalar fields is coupled with the direct quadrature method of moments (DQMOM) for the condensing liquid phase. The effects of turbulent mixing on aerosol processes (nucleation, condensation, and coagulation) are quantified by analyzing the statistics of number density and droplet sizes.
Fast-Tracking Colostomy Closures.
Nanavati, Aditya J; Prabhakar, Subramaniam
2015-12-01
There have been very few studies on applying fast-track principles to colostomy closures. We believe that outcome may be significantly improved with multimodal interventions in the peri-operative care of patients undergoing this procedure. A retrospective study was carried out comparing patients who had undergone colostomy closures by the fast-track and traditional care protocols at our centre. We intended to analyse peri-operative period and recovery in colostomy closures to confirm that fast-track surgery principles improved outcomes. Twenty-six patients in the fast-track arm and 24 patients in the traditional care arm had undergone colostomy closures. Both groups were comparable in terms of their baseline parameters. Patients in the fast-track group were ambulatory and accepted oral feeding earlier. There was a significant reduction in the duration of stay (4.73 ± 1.43 days vs. 7.21 ± 1.38 days, p = 0.0000). We did not observe a rise in complications or 30-day re-admissions. Fast-track surgery can safely be applied to colostomy closures. It shows earlier ambulation and reduction in length of hospital stay. PMID:27011527
NASA Astrophysics Data System (ADS)
Bolla, Michele; Farrace, Daniele; Wright, Yuri M.; Boulouchos, Konstantinos; Mastorakos, Epaminondas
2014-03-01
The influence of the turbulence-chemistry interaction (TCI) for n-heptane sprays under diesel engine conditions has been investigated by means of computational fluid dynamics (CFD) simulations. The conditional moment closure approach, which has been previously validated thoroughly for such flows, and the homogeneous reactor (i.e. no turbulent combustion model) approach have been compared, in view of the recent resurgence of the latter approaches for diesel engine CFD. Experimental data available from a constant-volume combustion chamber have been used for model validation purposes for a broad range of conditions including variations in ambient oxygen (8‑21% by vol.), ambient temperature (900 and 1000 K) and ambient density (14.8 and 30 kg/m3). The results from both numerical approaches have been compared to the experimental values of ignition delay (ID), flame lift-off length (LOL), and soot volume fraction distributions. TCI was found to have a weak influence on ignition delay for the conditions simulated, attributed to the low values of the scalar dissipation relative to the critical value above which auto-ignition does not occur. In contrast, the flame LOL was considerably affected, in particular at low oxygen concentrations. Quasi-steady soot formation was similar; however, pronounced differences in soot oxidation behaviour are reported. The differences were further emphasised for a case with short injection duration: in such conditions, TCI was found to play a major role concerning the soot oxidation behaviour because of the importance of soot-oxidiser structure in mixture fraction space. Neglecting TCI leads to a strong over-estimation of soot oxidation after the end of injection. The results suggest that for some engines, and for some phenomena, the neglect of turbulent fluctuations may lead to predictions of acceptable engineering accuracy, but that a proper turbulent combustion model is needed for more reliable results.
Point estimates for probability moments
Rosenblueth, Emilio
1975-01-01
Given a well-behaved real function Y of a real random variable X and the first two or three moments of X, expressions are derived for the moments of Y as linear combinations of powers of the point estimates y(x+) and y(x-), where x+ and x- are specific values of X. Higher-order approximations and approximations for discontinuous Y using more point estimates are also given. Second-moment approximations are generalized to the case when Y is a function of several variables. PMID:16578731
Spectral moments of fullerene cages
NASA Astrophysics Data System (ADS)
Zhang, Hongxing; Balasubramanian, K.
Based on the symmetric method, analytical expression or recursive relations for the spectral moments of the C20, C24, C26, C28, C30, C32, C36, C38, C40, C42, C44, C50 and C60 fullerene cage clusters are obtained by factoring the original graphs and the corresponding characteristic polynomials into their smaller subgraphs and subpolynomials. We also give numerical results for the spectral moments. It is demonstrated that the symmetric method is feasible in enumerating the moments as well as factoring the characteristic polynomials for fullerene cages.
Turbulent structures and budgets behind permeable ribs
Panigrahi, P.K.; Schroeder, A.; Kompenhans, J.
2008-02-15
Different rib geometries are traditionally used to improve heat transfer and enhance mixing in different industrial applications, i.e. heat exchangers, cooling passages of gas turbine blades and fuel elements of nuclear reactors, etc. Permeable ribs have been proposed in literature for passive control of the reattaching flow past surface mounted ribs leading to superior performance. The flow past different surface mounted permeable rib geometries, i.e. solid, slit, split-slit and inclined split-slit ribs have been investigated in this study. Both two components and stereo particle image velocimetry (PIV) have been used in streamwise and cross stream planes to study the underlying flow structures. The detailed turbulent statistics, i.e. mean and rms velocity, higher order moments, quadrant decomposition of turbulent shear stress producing motions, skewness and components of the turbulent kinetic energy budgets have been compared for different rib geometries. Coherent structures are identified based on the invariant of velocity gradient tensor invariant and wavelet transform. The skewness results demonstrate the intermittency of quadrant motions. The reattachment length of the inclined split-slit rib is lowest among all rib geometries. The average Reynolds stresses and the production of turbulent kinetic energy are highest for the inclined split-slit rib. The pressure transport calculated as residual of the turbulent kinetic energy budget equation is highest for the inclined split-slit rib. This is attributed to the smaller reattachment length leading to greater adverse pressure gradient for the inclined split-slit rib. The quadrant motions, turbulent fluxes, skewness and kinetic energy budgets at post reattachment region compares well with that of flat plate turbulent boundary layer from hot wire measurements in literature. Overall, this study demonstrates the effectiveness of PIV technique for the detailed turbulent structures characterization of complex flows
A twenty-moment model for collisionless guide field reconnection
NASA Astrophysics Data System (ADS)
Ng, Jonathan; Hakim, Ammar; Bhattacharjee, Amitava
2015-11-01
The integration of kinetic effects in fluid models is an important problem in global simulations of the Earth's magnetosphere and space weather modelling. Here we introduce a new fluid model and closure for collisionless magnetic reconnection and more general applications. It has recently been shown that electron pressure anisotropy is important in setting the structure of the reconnection region, and a closure based on the drift kinetic equation using a distribution of trapped and passing particles has been derived. We extend the model and present a general expression for moments of the distribution function. By evolving the heat flux tensor and closing at the fourth velocity moment, we obtain a self-consistent set of fluid equations, which includes the evolution of the off-diagonal elements of the pressure tensor. The model is implemented in a two-fluid code and the results are compared to PIC simulations of guide field reconnection. This work was supported by NSF Grant No. AGS-1338944, DOE Contract DE-AC02-09CH11466.
Turbulence generation in homogeneous dilute particle- laden flows
NASA Astrophysics Data System (ADS)
Chen, Jeng-Horng
Homogeneous turbulence generated by the motion of particles in dispersed multiphase flows was studied both theoretically and experimentally, motivated by applications to sprays, particle-laden jets, bubble plumes and rainstorms, among others. The experiments involved uniform fluxes of monodisperse spherical particles falling through a slow upflow of air. Particle fluxes and phase velocities were measured by sampling and phase-discriminating laser Doppler velocimetry (LDV), respectively. Measured particle velocities included mean and fluctuating streamwise and cross-stream velocities and probability density functions (PDF's). Measured continuous-phase velocities included mean and fluctuating streamwise and cross-stream velocities, PDF's and the higher moments of velocity fluctuations such as skewness and kurtosis, energy spectra of velocity fluctuations and integral length scales based on streamwise velocity fluctuations. Continuous-phase velocity measurements included conditional averages for particle wake disturbances and the turbulent inter-wake region surrounding these disturbances as well as overall flow properties. Present and earlier results in the literature provided particle Reynolds numbers of 38-990, particle volume fractions less than 0.01% and turbulence intensities (normalized by mean particle relative velocities) of 0.1-10.0%. Theory included characterization of particle wake disturbances as laminar-like turbulent wakes observed for intermediate particle Reynolds numbers in turbulent environments, characterization of the turbulent inter-wake region by analogy to grid-generated isotropic turbulence, and estimation of overall flow properties by conditional averaging of the properties of the wake disturbances and the turbulent inter-wake region. Present measurements showed that particle wake disturbances during turbulence generation were properly characterized by the properties of laminar-like turbulent wakes. The turbulent inter-wake region was
Direct numerical simulation of turbulent H2-O2 combustion using reduced chemistry
NASA Technical Reports Server (NTRS)
Montgomery, Christopher J.; Kosaly, George; Riley, James J.
1993-01-01
Results of direct numerical simulations of hydrogen-oxygen combustion using a partial-equilibrium chemistry scheme in constant density, decaying, isotropic turbulence are reported. The simulations qualitatively reproduce many features of experimental results, such as superequilibrium radical species mole fractions, with temperature and major species mole fractions closer to chemical equilibrium. It was also observed that the peak reaction rates occur in narrow zones where the stoichiometric surface intersects regions of high scalar dissipation, as might be expected for combustion conditions close to chemical equilibrium. Another finding was that high OH mole fraction correspond more closely to the stoichiometric surface than to areas of high reaction rate for conditions of the simulations. Simulation results were compared to predictions of the Conditional Moment Closure model. This model was found to give good results for all quantities of interest when the conditionally averaged scalar dissipation was used in the prediction. When the nonconditioned average dissipation was used, the predictions compared well to the simulations for most of the species and temperature, but not for the reaction rate. The comparison would be expected to improve for higher Reynolds number flows, however.
Fundamental base closure environmental principles
Yim, R.A.
1994-12-31
Military base closures present a paradox. The rate, scale and timing of military base closures is historically unique. However, each base itself typically does not present unique problems. Thus, the challenge is to design innovative solutions to base redevelopment and remediation issues, while simultaneously adopting common, streamlined or pre-approved strategies to shared problems. The author presents six environmental principles that are fundamental to base closure. They are: remediation not clean up; remediation will impact reuse; reuse will impact remediation; remediation and reuse must be coordinated; environmental contamination must be evaluated as any other initial physical constraint on development, not as an overlay after plans are created; and remediation will impact development, financing and marketability.
[Endoscopic vacuum-assisted closure].
Wedemeyer, J; Lankisch, T
2013-03-01
Anastomotic leakage in the upper and lower intestinal tract is associated with high morbidity and mortality. Within the last 10 years endoscopic treatment options have been accepted as sufficient treatment option of these surgical complications. Endoscopic vacuum assisted closure (E-VAC) is a new innovative endoscopic therapeutic option in this field. E-VAC transfers the positive effects of vacuum assisted closure (VAC) on infected cutaneous wounds to infected cavities that can only be reached endoscopically. A sponge connected to a drainage tube is endoscopically placed in the leakage and a continuous vacuum is applied. Sponge and vacuum allow removal of infected fluids and promote granulation of the leakage. This results in clean wound grounds and finally allows wound closure. Meanwhile the method was also successfully used in the treatment of necrotic pancreatitis. PMID:23430199
Organisational closure in biological organisms.
Mossio, Matteo; Moreno, Alvaro
2010-01-01
The central aim of this paper consists in arguing that biological organisms realize a specific kind of causal regime that we call "organisational closure"; i.e., a distinct level of causation, operating in addition to physical laws, generated by the action of material structures acting as constraints. We argue that organisational closure constitutes a fundamental property of biological systems since even its minimal instances are likely to possess at least some of the typical features of biological organisation as exhibited by more complex organisms. Yet, while being a necessary condition for biological organization, organisational closure underdetermines, as such, the whole set of requirements that a system has to satisfy in order to be taken as a paradigmatic example of organism. As we suggest, additional properties, as modular templates and control mechanisms via dynamical decoupling between constraints, are required to get the complexity typical of full-fledged biological organisms. PMID:21162371
Humid site stabilization and closure
Cutshall, N.H.
1981-01-01
The purpose of the work described here is to identify and evaluate the importance of factors that are expected to dictate the nature of site stabilization and closure requirements. Subsequent efforts will plan for implementation of such requirements. Two principal areas of site stabilization and closure effort will be pursued initially - geological management and vegetation management. The geological effort will focus on chemical weathering and surficial erosion. Such catastrophic geologic events as landslides, flooding, earthquakes, volcanos, etc. are already considered in site selection and operation and these factors will not be emphasized initially. Vegetation management will be designed to control erosion, to minimize nuclide mobilization by roots and to be compatible with natural successional pressures. It is anticipated that the results of this work will be important both to site selection and operation as well as the actual stabilization and closure procedure.
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.
Nonlinear Trapped Electron Mode Pinch in Strong Turbulence Regime
NASA Astrophysics Data System (ADS)
Hatch, David; Terry, P. W.
2006-10-01
Recent work has shown that there is an inward flux component in collisionless trapped electron mode turbulence produced by a nonlinear cross phase^2. The result was obtained for a weak turbulence regime, consistent with near threshold conditions. We extend this work to the strong turbulence regime, applying asymptotic analysis to the nonlinear frequency expressions generated from self-consistent statistical closure theory. We first check to see if there is a consistent strong turbulence regime for the previously considered threshold ordering^2, and examine the properties and scalings of the inward flux components. We then examine other orderings that are further above the instability threshold. The orderings will be compared with experimental profiles to determine likely regimes and nonlinear pinch properties. ^2P.W. Terry and R. Gatto, Phys. Plasmas 13, 062309 (2006).
Radiation reaction of multipole moments
NASA Astrophysics Data System (ADS)
Kazinski, P. O.
2007-08-01
A Poincaré-invariant description is proposed for the effective dynamics of a localized system of charged particles in classical electrodynamics in terms of the intrinsic multipole moments of the system. A relativistic-invariant definition for the intrinsic multipole moments of a system of charged particles is given. A new generally covariant action functional for a relativistic perfect fluid is proposed. In the case of relativistic charged dust, it is proven that the description of the problem of radiation reaction of multipole moments by the model of particles is equivalent to the description of this problem by a hydrodynamic model. An effective model is obtained for a pointlike neutral system of charged particles that possesses an intrinsic dipole moment, and the free dynamics of this system is described. The bound momentum of a point dipole is found.
A Self-Contained Mapping Closure Approximation for Scalar Mixing
NASA Technical Reports Server (NTRS)
He, Guo-Wei; Zhang, Zi-Fan
2003-01-01
Scalar turbulence exhibits interplays of coherent structures and random fluctuations over a broad range of spatial and temporal scales. This feature necessitates a probabilistic description of the scalar dynamics, which can be achieved comprehensively by using probability density functions (PDFs). Therefore, the challenge is to obtain the scalar PDFs (Lundgren 1967; Dopazo 1979). Generally, the evolution of a scalar is governed by three dynamical processes: advection, diffusion and reaction. In a PDF approach (Pope 1985), the advection and reaction can be treated exactly but the effect of molecular diffusion has to be modeled. It has been shown (Pope 1985) that the effect of molecular diffusion can be expressed as conditional dissipation rates or conditional diffusions. The currently used models for the conditional dissipation rates and conditional diffusions (Pope 1991) have resisted deduction from the fundamental equations and are unable to yield satisfactory results for the basic test cases of decaying scalars in isotropic turbulence, although they have achieved some success in a variety of individual cases. The recently developed mapping closure approach (Pope 1991; Chen, Chen & Kraichnan 1989; Kraichnan 1990; Klimenko & Pope 2003) provides a deductive method for conditional dissipation rates and conditional di usions, and the models obtained can successfully describe the shape relaxation of the scalar PDF from an initial double delta distribution to a Gaussian one. However, the mapping closure approach is not able to provide the rate at which the scalar evolves. The evolution rate has to be modeled. Therefore, the mapping closure approach is not closed. In this letter, we will address this problem.
Alarm sensor apparatus for closures
Carlson, James A.; Stoddard, Lawrence M.
1986-01-01
An alarm sensor apparatus for closures such as doors and windows, and particularly for closures having loose tolerances such as overhead doors, garage doors or the like, the sensor apparatus comprising a pair of cooperating bracket members, one being attached to the door facing or frame work and the other to the door member, two magnetic sensor elements carried by said bracket members, the bracket members comprising a pair of cooperating orthogonal guide slots and plates and a stop member engageable with one of the sensors for aligning the sensors with respect to each other in all three orthogonal planes when the door is closed.
Alarm sensor apparatus for closures
Carlson, J.A.; Stoddard, L.M.
1984-01-31
An alarm sensor apparatus for closures such as doors and windows, and particularly for closures having loose tolerances such as overhead doors, garage doors or the like, the sensor apparatus comprising a pair of cooperating bracket members, one being attached to the door facing or framework and the other to the door member, two magnetic sensor elements carried by said bracket members, the bracket members comprising a pair of cooperating orthogonal guide slots and plates and a stop member engageable with one of the sensors for aligning the sensors with respect to each other in all three orthogonal planes when the door is closed.
Not Available
1993-05-01
The Resource Conservation and Recovery Act (RCRA) requires that hazardous waste management facilities operate in accordance with permits granted by the US Environmental Protection Agency (EPA) or a State authorized to carry out the RCRA Subtitle C program. Several categories of permits (including treatment, storage, and disposal permits; research, development, and demonstration permits; post-closure permits; emergency permits; permits-by-rule; and trial burn and land treatment demonstration permits) are issued under the RCRA Subtitle C program. This Information Brief focuses on post-closure permitting requirements under 40 CFR 270.1(c).
New Third-Order Moments for the PBL
NASA Technical Reports Server (NTRS)
Canuto, V. M.; Cheng, Y.; Howard, A.; Hansen, James E. (Technical Monitor)
2000-01-01
Turbulent convection is inherently non-local and a primary condition for a successful treatment of the PBL is a reliable model of non-locality. In the dynamic equations governing the convective flux, turbulent kinetic energy, etc, non-locality enters through the third-order moments, TOMs. Since the simplest form, the so-called down gradient approximation (DGA , severely underestimates the TOMs (by up to an order of magnitude), a more physical model is needed. In 1994, an analytical model was presented which was derived directly from the dynamical equations for the TOMs. It considerably improved the DGA but was a bit cumbersome to use. Here, we present a new analytic expression for the TOMs which is considerably simpler than the 1994 expression and which at the same time yields a much better fit to the LES data.
Second moments and rotational spectroscopy
NASA Astrophysics Data System (ADS)
Bohn, Robert K.; Montgomery, John A.; Michels, H. Harvey; Fournier, Joseph A.
2016-07-01
Although determining molecular structure using microwave spectroscopy is a mature technique, there are still simple but powerful insights to analysis of the data which are not generally appreciated. This paper summarizes three applications of second (or planar) moments which quickly and easily provide insights and conclusions about a molecule's structure not easily obtained from the molecule's rotational constants. If the molecule has a plane of symmetry, group second moments can verify that property and determine which groups are located on that plane. Common groups contribute predictable values to second moments. This study examines the contribution and transferability of CH2/CH3, CF2/CF3, isopropyl, and phenyl groups to molecular constants. Structures of related molecules can be critically compared using their second moments. A third application to any molecule, even those whose structures have only the identity symmetry element, determines bond lengths and angles which exactly reproduce experimentally determined 2nd moments, rotational constants, and moments of inertia. Approximate least squares methods are not needed.
Elliott, Mark A; Giersch, Anne
2015-01-01
There has been evidence for the very brief, temporal quantization of perceptual experience at regular intervals below 100 ms for several decades. We briefly describe how earlier studies led to the concept of "psychological moment" of between 50 and 60 ms duration. According to historical theories, within the psychological moment all events would be processed as co-temporal. More recently, a link with physiological mechanisms has been proposed, according to which the 50-60 ms psychological moment would be defined by the upper limit required by neural mechanisms to synchronize and thereby represent a snapshot of current perceptual event structure. However, our own experimental developments also identify a more fine-scaled, serialized process structure within the psychological moment. Our data suggests that not all events are processed as co-temporal within the psychological moment and instead, some are processed successively. This evidence questions the analog relationship between synchronized process and simultaneous experience and opens debate on the ontology and function of "moments" in psychological experience. PMID:26779059
Energy balance and non-turbulent fluxes
NASA Astrophysics Data System (ADS)
Moderow, Uta; Feigenwinter, Christian; Bernhofer, Christian
2010-05-01
Often, the sum of the turbulent fluxes of sensible heat and latent heat from eddy covariance (EC) measurements does not match the available energy (sum of net radiation, ground heat flux and storage changes). This is referred to as energy balance closure gap. The reported imbalances vary between 0% and 50% (Laubach 1996). In various publications, it has been shown that the uncertainty of the available energy itself does not explain the gap (Vogt et al. 1996; Moderow et al. 2009). Among other reasons, the underestimation is attributed to an underestimation of turbulent fluxes and undetected non-turbulent transport processes, i.e. advection (e.g. Foken et al. 2006). The imbalance is typically larger during nighttime than during daytime as the EC method fails to capture non-turbulent transports that can be significant during night (e.g. Aubinet 2008). Results for the budget of CO2 showed that including non-turbulent fluxes can change the budgets considerably. Hence, it is interesting to see how the budget of energy is changed. Here, the consequences of including advective fluxes of sensible heat and latent heat in the energy balance are explored with focus on nighttime conditions. Non-turbulent fluxes will be inspected critically regarding their plausibility. Following Bernhofer et al. (2003), a ratio similar to Bowen's ratio of the turbulent fluxes are defined for the non-turbulent fluxes and compared to each other. This might have implications for the partitioning of the available energy into sensible heat and latent heat. Data of the ADVEX-campaigns (Feigenwinter et al. 2008) of three different sites across Europe are used and selected periods are inspected. References Aubinet M (2008) Eddy covariance CO2-flux measurements in nocturnal conditions: An analysis of the problem. Ecol Appl 18: 1368-1378 Bernhofer C, Grünwald T, Schwiebus A, Vogt R (2003) Exploring the consequences of non-zero energy balance closure for total surface flux. In: Bernhofer C (ed
Ohira, Yutaka
2013-04-10
We consider particle acceleration by large-scale incompressible turbulence with a length scale larger than the particle mean free path. We derive an ensemble-averaged transport equation of energetic charged particles from an extended transport equation that contains the shear acceleration. The ensemble-averaged transport equation describes particle acceleration by incompressible turbulence (turbulent shear acceleration). We find that for Kolmogorov turbulence, the turbulent shear acceleration becomes important on small scales. Moreover, using Monte Carlo simulations, we confirm that the ensemble-averaged transport equation describes the turbulent shear acceleration.
Geophysical and astrophysical turbulence
NASA Astrophysics Data System (ADS)
Moffatt, H. K.
Spiral structures in two-dimensional turbulence are studied and a theory (Moffatt, 1985, 1986) which regards fully three-dimensional turbulence as an agglomeration of 'random vortex sheets and coherent helical structures' is reviewed. Consideration is given to the process by which current-sheet discontinuities may appear during magnetic relaxation. Within the framework of dynamo theory, the determination of the generation coefficient and the turbulent diffusivity in mean-field electrodynamics for turbulence with helicity in the limit of a large magnetic Reynolds number is discussed. Certain features of 'chromospheric turbulence' (i.e., turbulence in the solar atmosphere outside the photosphere) are also examined.
Properties of Interstellar Turbulence from Gradients of Linear Polarization Maps
NASA Astrophysics Data System (ADS)
Burkhart, Blakesley; Lazarian, A.; Gaensler, B. M.
2012-04-01
Faraday rotation of linearly polarized radio signals provides a very sensitive probe of fluctuations in the interstellar magnetic field and ionized gas density resulting from magnetohydrodynamic (MHD) turbulence. We used a set of statistical tools to analyze images of the spatial gradient of linearly polarized radio emission (|∇P|) for both observational data from a test image of the Southern Galactic Plane Survey (SGPS) and isothermal three-dimensional simulations of MHD turbulence. Visually, in both observations and simulations, a complex network of filamentary structures is seen. Our analysis shows that the filaments in |∇P| can be produced both by interacting shocks and random fluctuations characterizing the non-differentiable field of MHD turbulence. The latter dominates for subsonic turbulence, while the former is only present in supersonic turbulence. We show that supersonic and subsonic turbulence exhibit different distributions as well as different morphologies in the maps of |∇P|. Particularly, filaments produced by shocks show a characteristic "double jump" profile at the sites of shock fronts resulting from delta function-like increases in the density and/or magnetic field, while those produced by subsonic turbulence show a single jump profile. In order to quantitatively characterize these differences, we use the topology tool known as the genus curve as well as the probability distribution function moments of the image distribution. We find that higher values for the moments correspond to cases of |∇P| with larger sonic Mach numbers. The genus analysis of the supersonic simulations of |∇P| reveals a "swiss cheese" topology, while the subsonic cases have characteristics of a "clump" topology. Based on the analysis of the genus and the higher order moments, the SGPS test region data have a distribution and morphology that match subsonic- to transonic-type turbulence, which confirms what is now expected for the warm ionized medium.
PROPERTIES OF INTERSTELLAR TURBULENCE FROM GRADIENTS OF LINEAR POLARIZATION MAPS
Burkhart, Blakesley; Lazarian, A.; Gaensler, B. M.
2012-04-20
Faraday rotation of linearly polarized radio signals provides a very sensitive probe of fluctuations in the interstellar magnetic field and ionized gas density resulting from magnetohydrodynamic (MHD) turbulence. We used a set of statistical tools to analyze images of the spatial gradient of linearly polarized radio emission (|{nabla}P|) for both observational data from a test image of the Southern Galactic Plane Survey (SGPS) and isothermal three-dimensional simulations of MHD turbulence. Visually, in both observations and simulations, a complex network of filamentary structures is seen. Our analysis shows that the filaments in |{nabla}P| can be produced both by interacting shocks and random fluctuations characterizing the non-differentiable field of MHD turbulence. The latter dominates for subsonic turbulence, while the former is only present in supersonic turbulence. We show that supersonic and subsonic turbulence exhibit different distributions as well as different morphologies in the maps of |{nabla}P|. Particularly, filaments produced by shocks show a characteristic 'double jump' profile at the sites of shock fronts resulting from delta function-like increases in the density and/or magnetic field, while those produced by subsonic turbulence show a single jump profile. In order to quantitatively characterize these differences, we use the topology tool known as the genus curve as well as the probability distribution function moments of the image distribution. We find that higher values for the moments correspond to cases of |{nabla}P| with larger sonic Mach numbers. The genus analysis of the supersonic simulations of |{nabla}P| reveals a 'swiss cheese' topology, while the subsonic cases have characteristics of a 'clump' topology. Based on the analysis of the genus and the higher order moments, the SGPS test region data have a distribution and morphology that match subsonic- to transonic-type turbulence, which confirms what is now expected for the warm ionized
Second Moments (planar Moments) and Their Application in Spectroscopy
NASA Astrophysics Data System (ADS)
Bohn, Robert K.; Montgomery, John A., Jr.; Michels, H. Harvey; Byrd, Jason N.
2013-06-01
Second moments, also called planar moments (P_{ii} = Σ m_{i}^{} x_{i}^{2}), are the spectroscopic parameters used to determine substitution structures (r_{s}) ) by Kraitchman''s method from spectra of a molecule and its isotopologs. They are also useful for discussing other molecular structural properties. Just as bond lengths and angles are considered transferable among similar molecules, second moments of many common groups are also transferable. This paper discusses applications of second moments of methylene/methyl groups, singly or multiply, isopropyl/tert-butyl groups, phenyl groups, per{f}{l}uoro methylene/methyl groups, combinations of any of them, and planarity of molecules, the historically most common application of second moments. The inertial defect is Δ = (I_{c} - I_{a} - I_{b}) or -2P_{cc}. Some authors err by assuming each isotopolog provides three independent rotational constants, but in some cases they are not all independent. J. Kraitchman, Am. J. Phys. {21 (17), 1953.}
Inquiry-Based Science: Turning Teachable Moments into Learnable Moments
NASA Astrophysics Data System (ADS)
Haug, Berit S.
2014-02-01
This study examines how an inquiry-based approach to teaching and learning creates teachable moments that can foster conceptual understanding in students, and how teachers capitalize upon these moments. Six elementary school teachers were videotaped as they implemented an integrated inquiry-based science and literacy curriculum in their classrooms. In this curriculum, science inquiry implies that students search for evidence in order to make and revise explanations based on the evidence found and through critical and logical thinking. Furthermore, the curriculum material is designed to address science key concepts multiple times through multiple modalities (do it, say it, read it, write it). Two types of teachable moments were identified: planned and spontaneous. Results suggest that the consolidation phases of inquiry, when students reinforce new knowledge and connect their empirical findings to theory, can be considered as planned teachable moments. These are phases of inquiry during which the teacher should expect, and be prepared for, student utterances that create opportunities to further student learning. Spontaneous teachable moments are instances when the teacher must choose to either follow the pace of the curriculum or adapt to the students' need. One implication of the study is that more teacher support is required in terms of how to plan for and effectively utilize the consolidation phases of inquiry.
AN EXPERIMENTAL STUDY OF TURBULENCE IN AN URBAN ENVIRONMENT
The structure of turbulence in the urban surface boundary layer is discussed. Wind and temperature fluctuations were measured with fast-response sensors at a height of 31 m at a rural and three urban sites in the St. Louis environs. The second moments of the fluctuations were com...
Relaxation approximation in the theory of shear turbulence
NASA Technical Reports Server (NTRS)
Rubinstein, Robert
1995-01-01
Leslie's perturbative treatment of the direct interaction approximation for shear turbulence (Modern Developments in the Theory of Turbulence, 1972) is applied to derive a time dependent model for the Reynolds stresses. The stresses are decomposed into tensor components which satisfy coupled linear relaxation equations; the present theory therefore differs from phenomenological Reynolds stress closures in which the time derivatives of the stresses are expressed in terms of the stresses themselves. The theory accounts naturally for the time dependence of the Reynolds normal stress ratios in simple shear flow. The distortion of wavenumber space by the mean shear plays a crucial role in this theory.
The behaviour of turbulence anisotropy through shock waves and expansions
NASA Technical Reports Server (NTRS)
Minh, H. H.; Kollmann, W.; Vandromme, D.
1985-01-01
A second order closure has been implemented in an implicit Navier-Stokes solver to study the behavior of the Reynolds stresses under the influence of severe pressure gradients. In the boundary layer zone, the strongly sheared character of the mean flow dominates the turbulence generation mechanisms. However, the pressure gradients play also a very important role for these processes, but at different locations within the boundary layer. This aspect may be emphasized by the analysis of turbulence anisotropy through shock waves and expansions.
LES, DNS and RANS for the analysis of high-speed turbulent reacting flows
NASA Technical Reports Server (NTRS)
Givi, Peyman
1994-01-01
The objective of this research is to continue our efforts in advancing the state of knowledge in Large Eddy Simulation (LES), Direct Numerical Simulation (DNS), and Reynolds Averaged Navier Stokes (RANS) methods for the analysis of high-speed reacting turbulent flows. In the first phase of this research, conducted within the past six months, focus was in three directions: RANS of turbulent reacting flows by Probability Density Function (PDF) methods, RANS of non-reacting turbulent flows by advanced turbulence closures, and LES of mixing dominated reacting flows by a dynamics subgrid closure. A summary of our efforts within the past six months of this research is provided in this semi-annual progress report.
Moments of probable seas: statistical dynamics of Planet Ocean
NASA Astrophysics Data System (ADS)
Holloway, Greg
The ocean is too big. From the scale of planetary radius to scales of turbulent microstructure, the range of length scales is 109. Likewise for time scales. Classical geophysical fluid dynamics does not have an apparatus for dealing with such complexity, while `brute force' computing on the most powerful supercomputers, extant or presently foreseen, barely scratches this complexity. Yet the everywhere-swirling-churning ocean interacts unpredictably in climate history and climate future - against which we attempt to devise planetary stewardship. Can we better take into account the unpredictability of oceans to improve upon present ocean/climate forecasting? What to do? First, recognize that our goal is to comprehend probabilities of possible oceans. Questions we would ask are posed as moments (expectations). Then the dynamical goal is clear: we seek equations of motion of moments of probable oceans. Classical fluid mechanics offers part of the answer but fails to recognize statistical dynamical aspects (missing the arrow of time as past==>future). At probabilities of oceans, the missing physics emerges: moments are forced by gradients of entropy with respect to moments. Time regains its arrow, and first (simplest) approximations to entropy-gradient forces enhance the fidelity of ocean theories and practical models.
CIRSE Vascular Closure Device Registry
Reekers, Jim A.; Mueller-Huelsbeck, Stefan; Libicher, Martin; Atar, Eli; Trentmann, Jens; Goffette, Pierre; Borggrefe, Jan; Zelenak, Kamil; Hooijboer, Pieter; Belli, Anna-Maria
2011-02-15
Purpose: Vascular closure devices are routinely used after many vascular interventional radiology procedures. However, there have been no major multicenter studies to assess the safety and effectiveness of the routine use of closure devices in interventional radiology. Methods: The CIRSE registry of closure devices with an anchor and a plug started in January 2009 and ended in August 2009. A total of 1,107 patients were included in the registry. Results: Deployment success was 97.2%. Deployment failure specified to access type was 8.8% [95% confidence interval (95% CI) 5.0-14.5] for antegrade access and 1.8% (95% CI 1.1-2.9) for retrograde access (P = 0.001). There was no difference in deployment failure related to local PVD at the access site. Calcification was a reason for deployment failure in only <0.5% of patients. Postdeployment bleeding occurred in 6.4%, and most these (51.5%) could be managed with light manual compression. During follow-up, other device-related complications were reported in 1.3%: seven false aneurysms, three hematoma >5.9 cm, and two vessel occlusions. Conclusion: The conclusion of this registry of closure devices with an anchor and a plug is that the use of this device in interventional radiology procedures is safe, with a low incidence of serious access site complications. There seems to be no difference in complications between antegrade and retrograde access and other parameters.
Statistical theory of turbulent incompressible multimaterial flow
Kashiwa, B.
1987-10-01
Interpenetrating motion of incompressible materials is considered. ''Turbulence'' is defined as any deviation from the mean motion. Accordingly a nominally stationary fluid will exhibit turbulent fluctuations due to a single, slowly moving sphere. Mean conservation equations for interpenetrating materials in arbitrary proportions are derived using an ensemble averaging procedure, beginning with the exact equations of motion. The result is a set of conservation equations for the mean mass, momentum and fluctuational kinetic energy of each material. The equation system is at first unclosed due to integral terms involving unknown one-point and two-point probability distribution functions. In the mean momentum equation, the unclosed terms are clearly identified as representing two physical processes. One is transport of momentum by multimaterial Reynolds stresses, and the other is momentum exchange due to pressure fluctuations and viscous stress at material interfaces. Closure is approached by combining careful examination of multipoint statistical correlations with the traditional physical technique of kappa-epsilon modeling for single-material turbulence. This involves representing the multimaterial Reynolds stress for each material as a turbulent viscosity times the rate of strain based on the mean velocity of that material. The multimaterial turbulent viscosity is related to the fluctuational kinetic energy kappa, and the rate of fluctuational energy dissipation epsilon, for each material. Hence a set of kappa and epsilon equations must be solved, together with mean mass and momentum conservation equations, for each material. Both kappa and the turbulent viscosities enter into the momentum exchange force. The theory is applied to (a) calculation of the drag force on a sphere fixed in a uniform flow, (b) calculation of the settling rate in a suspension and (c) calculation of velocity profiles in the pneumatic transport of solid particles in a pipe.
Discrete models of fluids: spatial averaging, closure and model reduction
Panchenko, Alexander; Tartakovsky, Alexandre M.; Cooper, Kevin
2014-04-15
We consider semidiscrete ODE models of single-phase fluids and two-fluid mixtures. In the presence of multiple fine-scale heterogeneities, the size of these ODE systems can be very large. Spatial averaging is then a useful tool for reducing computational complexity of the problem. The averages satisfy exact balance equations of mass, momentum, and energy. These equations do not form a satisfactory continuum model because evaluation of stress and heat flux requires solving the underlying ODEs. To produce continuum equations that can be simulated without resolving microscale dynamics, we recently proposed a closure method based on the use of regularized deconvolution. Here we continue the investigation of deconvolution closure with the long term objective of developing consistent computational upscaling for multiphase particle methods. The structure of the fine-scale particle solvers is reminiscent of molecular dynamics. For this reason we use nonlinear averaging introduced for atomistic systems by Noll, Hardy, and Murdoch-Bedeaux. We also consider a simpler linear averaging originally developed in large eddy simulation of turbulence. We present several simple but representative examples of spatially averaged ODEs, where the closure error can be analyzed. Based on this analysis we suggest a general strategy for reducing the relative error of approximate closure. For problems with periodic highly oscillatory material parameters we propose a spectral boosting technique that augments the standard deconvolution and helps to correctly account for dispersion effects. We also conduct several numerical experiments, one of which is a complete mesoscale simulation of a stratified two-fluid flow in a channel. In this simulation, the operation count per coarse time step scales sublinearly with the number of particles.
A preliminary compressible second-order closure model for high speed flows
NASA Technical Reports Server (NTRS)
Speziale, Charles G.; Sarkar, Sutanu
1989-01-01
A preliminary version of a compressible second-order closure model that was developed in connection with the National Aero-Space Plane Project is presented. The model requires the solution of transport equations for the Favre-averaged Reynolds stress tensor and dissipation rate. Gradient transport hypotheses are used for the Reynolds heat flux, mass flux, and turbulent diffusion terms. Some brief remarks are made about the direction of future research to generalize the model.
Distinguishing ichthyogenic turbulence from geophysical turbulence
NASA Astrophysics Data System (ADS)
Pujiana, Kandaga; Moum, James N.; Smyth, William D.; Warner, Sally J.
2015-05-01
Measurements of currents and turbulence beneath a geostationary ship in the equatorial Indian Ocean during a period of weak surface forcing revealed unexpectedly strong turbulence beneath the surface mixed layer. Coincident with the turbulence was a marked reduction of the current speeds registered by shipboard Doppler current profilers, and an increase in their variability. At a mooring 1 km away, measurements of turbulence and currents showed no such anomalies. Correlation with the shipboard echo sounder measurements indicate that these nighttime anomalies were associated with fish aggregations beneath the ship. The fish created turbulence by swimming against the strong zonal current in order to remain beneath the ship, and their presence affected the Doppler speed measurements. The principal characteristics of the resultant ichthyogenic turbulence are (i) low wave number roll-off of shear spectra in the inertial subrange relative to geophysical turbulence, (ii) Thorpe overturning scales that are small compared with the Ozmidov scale, and (iii) low mixing efficiency. These factors extend previous findings by Gregg and Horne (2009) to a very different biophysical regime and support the general conclusion that the biological contribution to mixing the ocean via turbulence is negligible.
Nuclear Electric Dipole Moment Calculations
NASA Astrophysics Data System (ADS)
Haxton, Wick
2010-11-01
One of the most important constraints on CP violation in the nucleon and NN interaction is provided by electric dipole moment (EDM) limits for neutral diamagnetic atoms, particularly 199Hg. To extract CP-violating couplings from experiment, one must relate the atomic EDM to the underlying nuclear CP-odd moments, a task complicated by the atomic response, which largely shields the nucleus from the applied external electric field. The residual response -- the Schiff moment -- depends on corrections such as the finite size of the nucleus. Conventional Schiff-moment calculations have largely ignored one consequence of the screening: the cancellation between direct and polarization diagrams, which yields an answer that is suppressed by two powers of RN/RA, where RN and RA are the nuclear and atomic sizes, requires one to identify all other terms that contribute to the same order in the RN/RA power counting. We show that such terms arise from nuclear excitations associated with the dipole charge and transverse electric multipole operators, and discuss the consequences. We also describe higher T-odd moments that contribute up to the same order in the counting, and point out interesting nuclear structure and experimental consequences.
Fundamental Statistical Descriptions of Plasma Turbulence in Magnetic Fields
John A. Krommes
2001-02-16
A pedagogical review of the historical development and current status (as of early 2000) of systematic statistical theories of plasma turbulence is undertaken. Emphasis is on conceptual foundations and methodology, not practical applications. Particular attention is paid to equations and formalism appropriate to strongly magnetized, fully ionized plasmas. Extensive reference to the literature on neutral-fluid turbulence is made, but the unique properties and problems of plasmas are emphasized throughout. Discussions are given of quasilinear theory, weak-turbulence theory, resonance-broadening theory, and the clump algorithm. Those are developed independently, then shown to be special cases of the direct-interaction approximation (DIA), which provides a central focus for the article. Various methods of renormalized perturbation theory are described, then unified with the aid of the generating-functional formalism of Martin, Siggia, and Rose. A general expression for the renormalized dielectric function is deduced and discussed in detail. Modern approaches such as decimation and PDF methods are described. Derivations of DIA-based Markovian closures are discussed. The eddy-damped quasinormal Markovian closure is shown to be nonrealizable in the presence of waves, and a new realizable Markovian closure is presented. The test-field model and a realizable modification thereof are also summarized. Numerical solutions of various closures for some plasma-physics paradigms are reviewed. The variational approach to bounds on transport is developed. Miscellaneous topics include Onsager symmetries for turbulence, the interpretation of entropy balances for both kinetic and fluid descriptions, self-organized criticality, statistical interactions between disparate scales, and the roles of both mean and random shear. Appendices are provided on Fourier transform conventions, dimensional and scaling analysis, the derivations of nonlinear gyrokinetic and gyrofluid equations
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.
Anisotropy in turbulent flows and in turbulent transport
NASA Astrophysics Data System (ADS)
Biferale, Luca; Procaccia, Itamar
2005-07-01
The problem of anisotropy and its effects on the statistical theory of high Reynolds number (Re) turbulence (and turbulent transport) is intimately related and intermingled with the problem of the universality of the (anomalous) scaling exponents of structure functions. Both problems had seen tremendous progress in the last 5 years. In this review we present a detailed description of the new tools that allow effective data analysis and systematic theoretical studies such as to separate isotropic from anisotropic aspects of turbulent statistical fluctuations. Employing the invariance of the equations of fluid mechanics to all rotations, we show how to decompose the (tensorial) statistical objects in terms of the irreducible representation of the SO(d) symmetry group (with d being the dimension, d=2 or 3). This device allows a discussion of the scaling properties of the statistical objects in well-defined sectors of the symmetry group, each of which is determined by the “angular momenta” sector numbers (j,m). For the case of turbulent advection of passive scalar or vector fields, this decomposition allows rigorous statements to be made: (i) the scaling exponents are universal, (ii) the isotropic scaling exponents are always leading, (iii) the anisotropic scaling exponents form a discrete spectrum which is strictly increasing as a function of j. This emerging picture offers a complete understanding of the decay of anisotropy upon going to smaller and smaller scales. Next, we explain how to apply the SO(3) decomposition to the statistical Navier-Stokes theory. We show how to extract information about the scaling behavior in the isotropic sector. Doing so furnishes a systematic way to assess the universality of the scaling exponents in this sector, clarifying the anisotropic origin of the many measurements that claimed the opposite. A systematic analysis of direct numerical simulations (DNS) of the Navier-Stokes equations and of experiments provides a strong support
Statistical energy conservation principle for inhomogeneous turbulent dynamical systems.
Majda, Andrew J
2015-07-21
Understanding the complexity of anisotropic turbulent processes over a wide range of spatiotemporal scales in engineering shear turbulence as well as climate atmosphere ocean science is a grand challenge of contemporary science with important societal impact. In such inhomogeneous turbulent dynamical systems there is a large dimensional phase space with a large dimension of unstable directions where a large-scale ensemble mean and the turbulent fluctuations exchange energy and strongly influence each other. These complex features strongly impact practical prediction and uncertainty quantification. A systematic energy conservation principle is developed here in a Theorem that precisely accounts for the statistical energy exchange between the mean flow and the related turbulent fluctuations. This statistical energy is a sum of the energy in the mean and the trace of the covariance of the fluctuating turbulence. This result applies to general inhomogeneous turbulent dynamical systems including the above applications. The Theorem involves an assessment of statistical symmetries for the nonlinear interactions and a self-contained treatment is presented below. Corollary 1 and Corollary 2 illustrate the power of the method with general closed differential equalities for the statistical energy in time either exactly or with upper and lower bounds, provided that the negative symmetric dissipation matrix is diagonal in a suitable basis. Implications of the energy principle for low-order closure modeling and automatic estimates for the single point variance are discussed below. PMID:26150510
Statistical energy conservation principle for inhomogeneous turbulent dynamical systems
Majda, Andrew J.
2015-01-01
Understanding the complexity of anisotropic turbulent processes over a wide range of spatiotemporal scales in engineering shear turbulence as well as climate atmosphere ocean science is a grand challenge of contemporary science with important societal impact. In such inhomogeneous turbulent dynamical systems there is a large dimensional phase space with a large dimension of unstable directions where a large-scale ensemble mean and the turbulent fluctuations exchange energy and strongly influence each other. These complex features strongly impact practical prediction and uncertainty quantification. A systematic energy conservation principle is developed here in a Theorem that precisely accounts for the statistical energy exchange between the mean flow and the related turbulent fluctuations. This statistical energy is a sum of the energy in the mean and the trace of the covariance of the fluctuating turbulence. This result applies to general inhomogeneous turbulent dynamical systems including the above applications. The Theorem involves an assessment of statistical symmetries for the nonlinear interactions and a self-contained treatment is presented below. Corollary 1 and Corollary 2 illustrate the power of the method with general closed differential equalities for the statistical energy in time either exactly or with upper and lower bounds, provided that the negative symmetric dissipation matrix is diagonal in a suitable basis. Implications of the energy principle for low-order closure modeling and automatic estimates for the single point variance are discussed below. PMID:26150510
NASA Astrophysics Data System (ADS)
Vlaykov, Dimitar G.; Grete, Philipp; Schmidt, Wolfram; Schleicher, Dominik R. G.
2016-06-01
Compressible magnetohydrodynamic (MHD) turbulence is ubiquitous in astrophysical phenomena ranging from the intergalactic to the stellar scales. In studying them, numerical simulations are nearly inescapable, due to the large degree of nonlinearity involved. However, the dynamical ranges of these phenomena are much larger than what is computationally accessible. In large eddy simulations (LESs), the resulting limited resolution effects are addressed explicitly by introducing to the equations of motion additional terms associated with the unresolved, subgrid-scale dynamics. This renders the system unclosed. We derive a set of nonlinear structural closures for the ideal MHD LES equations with particular emphasis on the effects of compressibility. The closures are based on a gradient expansion of the finite-resolution operator [W. K. Yeo (CUP, 1993)] and require no assumptions about the nature of the flow or magnetic field. Thus, the scope of their applicability ranges from the sub- to the hyper-sonic and -Alfvénic regimes. The closures support spectral energy cascades both up and down-scale, as well as direct transfer between kinetic and magnetic resolved and unresolved energy budgets. They implicitly take into account the local geometry, and in particular, the anisotropy of the flow. Their properties are a priori validated in Paper II [P. Grete et al., Phys. Plasmas 23, 062317 (2016)] against alternative closures available in the literature with respect to a wide range of simulation data of homogeneous and isotropic turbulence.
40 CFR 258.61 - Post-closure care requirements.
Code of Federal Regulations, 2013 CFR
2013-07-01
... 40 Protection of Environment 26 2013-07-01 2013-07-01 false Post-closure care requirements. 258.61... FOR MUNICIPAL SOLID WASTE LANDFILLS Closure and Post-Closure Care § 258.61 Post-closure care requirements. (a) Following closure of each MSWLF unit, the owner or operator must conduct post-closure...
40 CFR 265.112 - Closure plan; amendment of plan.
Code of Federal Regulations, 2012 CFR
2012-07-01
... 40 Protection of Environment 27 2012-07-01 2012-07-01 false Closure plan; amendment of plan. 265... DISPOSAL FACILITIES Closure and Post-Closure § 265.112 Closure plan; amendment of plan. (a) Written plan... have a written closure plan. Until final closure is completed and certified in accordance with §...
40 CFR 265.112 - Closure plan; amendment of plan.
Code of Federal Regulations, 2014 CFR
2014-07-01
... 40 Protection of Environment 26 2014-07-01 2014-07-01 false Closure plan; amendment of plan. 265... DISPOSAL FACILITIES Closure and Post-Closure § 265.112 Closure plan; amendment of plan. (a) Written plan... have a written closure plan. Until final closure is completed and certified in accordance with §...
40 CFR 265.112 - Closure plan; amendment of plan.
Code of Federal Regulations, 2013 CFR
2013-07-01
... 40 Protection of Environment 27 2013-07-01 2013-07-01 false Closure plan; amendment of plan. 265... DISPOSAL FACILITIES Closure and Post-Closure § 265.112 Closure plan; amendment of plan. (a) Written plan... have a written closure plan. Until final closure is completed and certified in accordance with §...
40 CFR 258.61 - Post-closure care requirements.
Code of Federal Regulations, 2012 CFR
2012-07-01
... 40 Protection of Environment 26 2012-07-01 2011-07-01 true Post-closure care requirements. 258.61... FOR MUNICIPAL SOLID WASTE LANDFILLS Closure and Post-Closure Care § 258.61 Post-closure care requirements. (a) Following closure of each MSWLF unit, the owner or operator must conduct post-closure...
40 CFR 258.61 - Post-closure care requirements.
Code of Federal Regulations, 2014 CFR
2014-07-01
... 40 Protection of Environment 25 2014-07-01 2014-07-01 false Post-closure care requirements. 258.61... FOR MUNICIPAL SOLID WASTE LANDFILLS Closure and Post-Closure Care § 258.61 Post-closure care requirements. (a) Following closure of each MSWLF unit, the owner or operator must conduct post-closure...
A Two-length Scale Turbulence Model for Single-phase Multi-fluid Mixing
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.
Neutron star moments of inertia
NASA Technical Reports Server (NTRS)
Ravenhall, D. G.; Pethick, C. J.
1994-01-01
An approximation for the moment of inertia of a neutron star in terms of only its mass and radius is presented, and insight into it is obtained by examining the behavior of the relativistic structural equations. The approximation is accurate to approximately 10% for a variety of nuclear equations of state, for all except very low mass stars. It is combined with information about the neutron-star crust to obtain a simple expression (again in terms only of mass and radius) for the fractional moment of inertia of the crust.
S. Dartevelle
2005-09-05
The objective of this manuscript is to fully derive a geophysical multiphase model able to ''accommodate'' different multiphase turbulence approaches; viz., the Reynolds Averaged Navier-Stokes (RANS), the Large Eddy Simulation (LES), or hybrid RANSLES. This manuscript is the first part of a larger geophysical multiphase project--lead by LANL--that aims to develop comprehensive modeling tools for large-scale, atmospheric, transient-buoyancy dusty jets and plume (e.g., plinian clouds, nuclear ''mushrooms'', ''supercell'' forest fire plumes) and for boundary-dominated geophysical multiphase gravity currents (e.g., dusty surges, diluted pyroclastic flows, dusty gravity currents in street canyons). LES is a partially deterministic approach constructed on either a spatial- or a temporal-separation between the large and small scales of the flow, whereas RANS is an entirely probabilistic approach constructed on a statistical separation between an ensemble-averaged mean and higher-order statistical moments (the so-called ''fluctuating parts''). Within this specific multiphase context, both turbulence approaches are built up upon the same phasic binary-valued ''function of presence''. This function of presence formally describes the occurrence--or not--of any phase at a given position and time and, therefore, allows to derive the same basic multiphase Navier-Stokes model for either the RANS or the LES frameworks. The only differences between these turbulence frameworks are the closures for the various ''turbulence'' terms involving the unknown variables from the fluctuating (RANS) or from the subgrid (LES) parts. Even though the hydrodynamic and thermodynamic models for RANS and LES have the same set of Partial Differential Equations, the physical interpretations of these PDEs cannot be the same, i.e., RANS models an averaged field, while LES simulates a filtered field. In this manuscript, we also demonstrate that this multiphase model fully fulfills the second law of
Introduction to quantum turbulence.
Barenghi, Carlo F; Skrbek, Ladislav; Sreenivasan, Katepalli R
2014-03-25
The term quantum turbulence denotes the turbulent motion of quantum fluids, systems such as superfluid helium and atomic Bose-Einstein condensates, which are characterized by quantized vorticity, superfluidity, and, at finite temperatures, two-fluid behavior. This article introduces their basic properties, describes types and regimes of turbulence that have been observed, and highlights similarities and differences between quantum turbulence and classical turbulence in ordinary fluids. Our aim is also to link together the articles of this special issue and to provide a perspective of the future development of a subject that contains aspects of fluid mechanics, atomic physics, condensed matter, and low-temperature physics. PMID:24704870
Modeling Compressed Turbulence
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.
Introduction to quantum turbulence
Barenghi, Carlo F.; Skrbek, Ladislav; Sreenivasan, Katepalli R.
2014-01-01
The term quantum turbulence denotes the turbulent motion of quantum fluids, systems such as superfluid helium and atomic Bose–Einstein condensates, which are characterized by quantized vorticity, superfluidity, and, at finite temperatures, two-fluid behavior. This article introduces their basic properties, describes types and regimes of turbulence that have been observed, and highlights similarities and differences between quantum turbulence and classical turbulence in ordinary fluids. Our aim is also to link together the articles of this special issue and to provide a perspective of the future development of a subject that contains aspects of fluid mechanics, atomic physics, condensed matter, and low-temperature physics. PMID:24704870
Turbulent transport in the atmospheric boundary layer with application to wind farm dynamics
NASA Astrophysics Data System (ADS)
Waggy, Scott B.
-equation closure model, used to model the third and fourth velocity-temperature moments, performed well for the unstable cases. Optimal model coefficients found for the DNS data are shown to agree with atmospheric observations as well as LES data. Finally, the effects of top-down diffusion (entrainment-induced flux at the temperature inversion) and bottom-up diffusion (non-zero surface flux) were studied and improvements to correlation functions are suggested. This thesis concludes by analyzing the neutral and unstable cases under the effects of wind turbine wakes. A unique means of converting a periodic simulation into a spatially evolving flow in the wake of a turbine is demonstrated; present results under neutral stratification are shown to agree with wind tunnel experiments under similar conditions. By introducing a scalar (humidity) into the flow field, the effect of a turbine wake on scalar transport in a wind farm is uncovered. The results show a clear drying effect under both neutral and unstable stratification given a wet surface. An investigation of energy and flux budgets gives guidance as to why such a phenomena occurs.
New Third-Order Moments for the CBL
NASA Technical Reports Server (NTRS)
Canuto, V. M.; Cheng, Y.; Howard, A.; Hansen, James E. (Technical Monitor)
2001-01-01
Turbulent convection is an inherently non-local phenomenon and a primary condition for a successful treatment of the CBL (convective boundary layer) is a reliable model of non-locality. In the dynamic equations governing the convective flux, the turbulent kinetic energy, etc., non-locality is represented by the third-order moments, TOMs. Since the simplest form, the so-called down gradient approximation (DGA), severely underestimates the TOMs (up to an order of magnitude), a more physical model is needed. In 1994, an analytical model was presented which was derived directly from the dynamical equations for the TOMs. It considerably improved the DGA but was a bit cumbersome to use and, more importantly, it was based on the quasi-normal (QN) approximation for the fourth-order moments. Here, we present a new analytic expression for the TOMs which is structurally simpler than the 1994 expression and which avoids the QN approximation. The resulting fit to the LES data is superior to that of the 1994 model.
Atrioventricular block after ASD closure
Asakai, Hiroko; Weskamp, Sofia; Eastaugh, Lucas; d'Udekem, Yves; Pflaumer, Andreas
2016-01-01
Objective Secundum atrial septal defect (ASD) is a common congenital heart defect. There is limited data on both early and late atrioventricular (AV) block post ASD closure. The aim of this study was to determine the incidence and risk factors of AV block associated with ASD closure. Methods A retrospective analysis of all patients who underwent ASD closure either with a device or surgical method at the Royal Children's Hospital Melbourne between 1996 and 2010 was performed. Baseline demographics, procedural details and follow-up data were collected from medical records. Results A total of 378 patients were identified; 242 in the device group and 136 in the surgical group. Fourteen patients (3.7%) had AV block (1 with second degree and 13 with first degree) at a median follow-up of 28 months; 11/242 (4.5%) in the device group and 3/135 (2.2%) in the surgical group (p=0.39). Six patients had new-onset AV block after ASD closure. In the device subgroup, patients with AV block at follow-up had a larger indexed device size compared with those without (22 (15–31) vs 18(7–38), p=0.02). Multivariate analysis revealed the presence of AV block either pre procedure or post procedure to be the only variables associated with late AV block. Conclusions Late AV block in patients with repaired ASD is rare and most likely independent of the technique used. In the device subgroup, the only risk factor identified to be associated with late AV block was the presence of either preprocedural or postprocedural AV block, so long-term follow-up for these patients should be provided. PMID:27540418
Elliott, Mark A.; Giersch, Anne
2016-01-01
There has been evidence for the very brief, temporal quantization of perceptual experience at regular intervals below 100 ms for several decades. We briefly describe how earlier studies led to the concept of “psychological moment” of between 50 and 60 ms duration. According to historical theories, within the psychological moment all events would be processed as co-temporal. More recently, a link with physiological mechanisms has been proposed, according to which the 50–60 ms psychological moment would be defined by the upper limit required by neural mechanisms to synchronize and thereby represent a snapshot of current perceptual event structure. However, our own experimental developments also identify a more fine-scaled, serialized process structure within the psychological moment. Our data suggests that not all events are processed as co-temporal within the psychological moment and instead, some are processed successively. This evidence questions the analog relationship between synchronized process and simultaneous experience and opens debate on the ontology and function of “moments” in psychological experience. PMID:26779059
[Great moments in renal transplantation].
Ghossain, Antoine
2015-01-01
A selective review of some great moments in renal transplantation experienced or witnessed with some of the great architects of this epic. The path was strewn with hazards, sometimes halts or changes of attitude that harmed or helped some patients. PMID:26591188
Measuring the Moment of Inertia
ERIC Educational Resources Information Center
Lehmberg, George L.
1978-01-01
Two physics experiments are described, One, involving a laboratory cart accelerated along a level surface, examines the concept of inertial mass in translation and the other, using a solid cylinder, measures the moment of inertia of a wheel. Equations and illustrations are included. (MA)
Moment of Inertia by Differentiation
ERIC Educational Resources Information Center
Rizcallah, Joseph A.
2015-01-01
The calculation of the moment of inertia of an extended body, as presented in standard introductory-level textbooks, involves the evaluation of a definite integral--an operation often not fully mastered by beginners, let alone the conceptual difficulties it presents, even to the advanced student, in understanding and setting up the integral in the…
Brief, Amazing Moments of Inclusion
ERIC Educational Resources Information Center
Fialka, Janice
2005-01-01
"Real inclusion" of kinds with special needs occurs everywhere, inside the classroom as well as outside. This is a fairly basic principle, however, it is not always easy to achieve. In this article, the author describes how her family have had to "fight" for inclusive education and shares some amazing moments of inclusion with her son Micah.
NASA Astrophysics Data System (ADS)
Heilman, Warren Emanuel
A two-dimensional second-order turbulence-closure model based on level three of the Mellor-Yamada turbulence hierarchy has been developed and used to examine the nocturnal and early morning turbulence characteristics over Rattlesnake Mountain in Washington. The model includes radiation, soil, canopy, and slope parameterizations for calculating mean and turbulence variables over two-dimensional terrain features. Simulations of mean horizontal velocities and potential temperatures show good agreement with data obtained over Rattlesnake Mountain during nocturnal drainage-flow conditions. Qualitative analysis of simulated turbulence fields during these conditions indicates significant variations over the windward and leeward slopes. Turbulence anisotropy develops in the drainage-flow region where vertical wind shears and atmospheric stability are large. The buoyant portion of the turbulent heat flux enhances the vertical component of turbulent kinetic energy, especially over the leeward slope. Derived turbulent diffusivities reflect the developed anisotropic turbulence conditions. Simulations of the atmospheric conditions over Rattlesnake Mountain during the early morning hours indicate significant growth of the convective boundary layer when the initial stability over the entire depth of the modeled region is very weak. Upslope flow develops when no ambient wind is present. The buoyancy-generated turbulence inhibits the formation of large upslope velocity maxima when ambient winds are present. Spatial variations in the turbulent kinetic energy develop over the mountain, but they are less than the variations during nocturnal drainage-flow conditions. Turbulence anisotropy is significant in the convective boundary layer. However, the developed anisotropy plays a minor role in affecting turbulent diffusivity magnitudes. The transition from nocturnal drainage-flow conditions to convective conditions is characterized by a redistribution of energy among the turbulent
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.
Particle Deposition During Airway Closure
NASA Astrophysics Data System (ADS)
Tai, Cheng-Feng; Halpern, David; Grotberg, James B.
2011-11-01
Inhaled aerosol particles deposit in the lung and may be from environmental, toxic, or medical therapy sources. While much research focuses on inspiratory deposition, primarily at airway bifurcations due to inertial impaction, there are other mechanisms that allow the particles to reach the airway surface, such as gravitational settling and diffusion depending on particle size. We introduce a new mechanism not previously studied, i.e. aerosol deposition from airway closure. The airways are lined with a liquid layer. Due to the surface tension driven instability, a liquid plug can form from this layer which blocks the airway. This process of airway closure tends to occur toward the end of expiration. In this study, the efficiency of the impaction of the particles during airway closure will be investigated. The particles will be released from the upstream of the airway and convected by the air flow and deposited onto the closing liquid layer. We solve the governing equations using a finite volume approach in conjunction with a sharp interface method for the interfaces. Once the velocity field of the gas flow is obtained, the path of the particles will be calculated and the efficiency of the deposition can be estimated. We acknowledge support from the National Institutes of Health grant number NIH HL85156.
The effect of journal misalignment on the operation of a turbulent flow hydrostatic bearing
San Andres, L. )
1993-07-01
An analysis for calculation of the dynamic force and moment response in turbulent flow, orifice compensated hydrostatic journal bearings is presented. The fully developed flow of a barotropic liquid is described by variable properties, bulk-flow equations and local turbulent friction factors based on bearing surface condition. Bearing load and moments and, dynamic force and moment coefficients are calculated for perturbations in journal center displacements and misaligned journal axis rotations. Numerical results for the effect of static misalignment angles in the plane of the eccentricity vector are presented for a water lubricated hydrostatic bearing. The predictions show that journal axis misalignment causes a reduction in load capacity due to loss in film thickness, increases the flow rate and produces significant restoring moments (couples). Force and moment coefficients due to dynamic journal axis rotations are also discussed. 37 refs.
Observations of turbulence in a partially stratified estuary
Stagey, M.T.; Monismith, Stephen G.; Burau, J.R.
1999-01-01
The authors present a field study of estuarine turbulence in which profiles of Reynolds stresses were directly measured using an ADCP throughout a 25-h tidal day. The dataset that is discussed quantifies turbulent mixing for a water column in northern San Francisco Bay that experiences a sequence of states that includes a weak ebb and flood that are stratified, followed by a strong, and eventually unstratified, ebb and flood. These measurements show that energetic turbulence is confined to a bottom mixed layer by the overlying stratification. Examination of individual Reynolds stress profiles along with profiles of Richardson number and turbulent Froude number shows that the water column can be divided into regions based on the relative importance of buoyancy effects. Using the measured turbulence production rate P, the dissipation rate e. is estimated. The observed turbulence had values of e/vN2 > 20 all of the time and e/vN2 > 200 most of the time, suggesting that the observed motions were buoyancy affected turbulence rather than internal waves. However, at times, turbulent Froude numbers in much of the upper-water column were less than one, indicating important stratification effects. Taken as a whole, the data show that stratification affects the turbulent velocity variance q2 most severely; that is, observed reductions in u'w' are largely associated with small values of q2 rather than with a dramatic reduction in the efficiency with which turbulent motions produce momentum fluxes. Finally, the dataset is compared to predictions made using the popular Mellor-Yamada level 2.5 closure. These comparisons show that the model tends to underestimate the turbulent kinetic energy in regions of strong stratification where the turbulence is strongly inhomogeneous and to overestimate the turbulent kinetic energy in weakly stratified regions. The length scale does not appear to compensate for these errors, and, as a result, similar errors are seen in the eddy viscosity
Analysis of Extensive Cross-Flow Separation using Higher-Order RANS Closure Models
NASA Technical Reports Server (NTRS)
Morrison, J. H.; Panaras, A. G.; Gatski, T. B.; Georgantopoulos, G. A.
2003-01-01
The turbulent flow fields associated with the incompressible flow over a 6:1 prolate spheroid at high angle of attack, and the supersonic flow over an ogive cylinder are studied. Both these flows are characterized by large separation and vortical flow regions and therefore provide a challenging database for comparison of turbulent closure models. Of interest is the ability to predict the effects of separation and associated vortical motion common to both flows. Two turbulent models are investigated that each represent the class of linear eddy-viscosity models (LEVMs) and explicit algebraic stress models (EASMs). Since the EASM accounts for anisotropic effects, the influence of these effects on flow field predictions can be assessed. The EASM model is shown to both improve the separation location prediction and pressure trough under the secondary vortex on the 6:l prolate spheroid at high angle of attack and high Reynolds number, and improve the prediction of the separation location on a supersonic ogive cylinder.
Scaling of turbulence and turbulent mixing using Terascale numerical simulations
NASA Astrophysics Data System (ADS)
Donzis, Diego A.
Fundamental aspects of turbulence and turbulent mixing are investigated using direct numerical simulations (DNS) of stationary isotropic turbulence, with Taylor-scale Reynolds numbers (Rlambda) ranging from 8 to 650 and Schmidt numbers (Sc) from 1/8 to 1024. The primary emphasis is on important scaling issues that arise in the study of intermittency, mixing and turbulence under solid-body rotation. Simulations up to 20483 in size have been performed using large resource allocations on Terascale computers at leading supercomputing centers. Substantial efforts in algorithmic development have also been undertaken and resulted in a new code based on a two-dimensional domain decomposition which allows the use of very large number of processors. Benchmark tests indicate very good parallel performance for resolutions up to 40963 on up to 32768 processors, which is highly promising for future simulations at higher resolutions and processor counts eventually to approach Petascale levels. Investigation of intermittency through the statistics of dissipation and enstrophy in a series of simulations at the same Reynolds number but different resolution indicate that accurate results in high-order moments require a higher degree of fine-scale resolution than commonly practiced. However, statistics up to fourth order are satisfactory if the grid spacing is not larger than Komogorov scale, without the requirement of a clear analytic range for corresponding structure functions as suggested by recent theories. Results from highly resolved simulations provide support for a modified resolution criterion derived in this work for structure functions of different orders and as a function of Rlambda. At the highest Reynolds number in our simulations (400 and 650) dissipation and enstrophy exhibit extreme fluctuations of O(1000) the mean which have not been studied in the literature before. The far tails of the probability density functions of dissipation and enstrophy appear to coincide