Computations of turbulent lean premixed combustion using conditional moment closure
NASA Astrophysics Data System (ADS)
Amzin, Shokri; Swaminathan, Nedunchezhian
2013-12-01
Conditional Moment Closure (CMC) is a suitable method for predicting scalars such as carbon monoxide with slow chemical time scales in turbulent combustion. Although this method has been successfully applied to non-premixed combustion, its application to lean premixed combustion is rare. In this study the CMC method is used to compute piloted lean premixed combustion in a distributed combustion regime. The conditional scalar dissipation rate of the conditioning scalar, the progress variable, is closed using an algebraic model and turbulence is modelled using the standard k-ɛ model. The conditional mean reaction rate is closed using a first order CMC closure with the GRI-3.0 chemical mechanism to represent the chemical kinetics of methane oxidation. The PDF of the progress variable is obtained using a presumed shape with the Beta function. The computed results are compared with the experimental measurements and earlier computations using the transported PDF approach. The results show reasonable agreement with the experimental measurements and are consistent with the transported PDF computations. When the compounded effects of shear-turbulence and flame are strong, second order closures may be required for the CMC.
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.
Second moment closure modeling for rotating stably stratified turbulent shear flow
NASA Astrophysics Data System (ADS)
Ji, Minsuk
The general linear second moment closure (SMC) turbulence model is considered for flows subjected to buoyancy and rotation. Model response to external forces are analyzed with the aid of structural equilibrium analysis. A closed form equilibrium solution for the anisotropy tensor bij, dispersion tensor Kij, dimensionless scalar variance q2 /k(S/Stheta )2, and the ratio of mean to turbulent time scale epsilon/ Sk is obtained. The variable of particular interest to bifurcation analysis, epsilon/Sk is shown as a function of the parameters characterizing the body forces: O/S (the ratio of the rotation rate to the mean shear rate) for rotation and Rig (the gradient Richardson number) for buoyancy; it determines the bifurcation surface in the epsilon/Sk-O/S-Rig space. It is shown, with the use of the closed form solution, that the conventional general linear models do not have a real and stable equilibrium solution when rotational and buoyant forces of certain magnitudes are simultaneously imposed on the flow. When this occurs, time integration of the turbulence model results in a diverging solution. A new model is proposed that removes this unphysical behavior. It ensures the existence of stable, real solutions for all combinations of rotation and buoyancy. Further improvements to the model are made through bifurcation analysis. Model constants are adjusted such that the model's bifurcation characteristics are in agreement with the physically observed onset of turbulence stabilization due to stable stratification. Experimental data and numerical simulation results for stably stratified homogeneous shear flow suggest the critical gradient Richardson number of Ricrg = 0.25, and the new model is able to predict it correctly. In connection with the bifurcation analysis of SMC models, rapid distortion theory (RDT) of turbulence is applied to rotating, stably stratified shear flow to provide the stability characteristics of such flows. It is shown that the RDT predictions are
Prediction of turbulent flow through a transition duct using a second-moment closure
NASA Astrophysics Data System (ADS)
Sotiropoulos, F.; Patel, V. C.
1994-11-01
The near-wall, full Reynolds-stress closure of Launder and Shima is employed to calculate the three-dimensional turbulent flow through a circular-to-rectangular transition duct. The solutions are compared with the recent experimental data of Davis and Gessner. The comparisons reveal that the computed streamwise velocity and vorticity fields are in remarkable agreement with the measurements. Downstream of the transition region, however, the computed Reynolds stresses appear to decay at a much faster rate than observed in the measurements. These results point to the need for further refinement of Reynolds-stress models to correctly predict the relaxation of rapidly strained turbulence towards equilibrium.
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 Astrophysics Data System (ADS)
Vie, Aymeric; Masi, Enrica; Simonin, Olivier; Massot, Marc; EM2C/Ecole Centrale Paris Team; IMFT Team
2012-11-01
To simulate particulate flows, a convenient formalism for HPC is to use Eulerian moment methods, which describe the evolution of velocity moments instead of tracking directly the number density function (NDF) of the droplets. By using a conditional PDF approach, the Mesoscopic Eulerian Formalism (MEF) of Février et al. 2005 offers a solution for the direct numerical simulation of turbulent particulate flows, even at relatively high Stokes number. Here, we propose to compare to existing approaches used to solved for this formalism: the Algebraic-Closure-Based Moment method (Kaufmann et al. 2008, Masi et al. 2011), and the Kinetic-Based Moment Method (Yuan et al. 2010, Chalons et al. 2010, Vié et al. 2012). Therefore, the goal of the current work is to evaluate both strategies in turbulent test cases. For the ACBMM, viscosity-type and non-linear closures are envisaged, whereas for the KBMM, isotropic and anisotropic closures are investigated. A main aspect of the current methodology for the comparison is that the same numerical methods are used for both approaches. Results show that the new non-linear closure and the Anisotropic Gaussian closures are both accurate in shear flows, whereas viscosity-type and isotropic closures lead to wrong results.
Conditional Moment Closure of Mixing and Reaction in Turbulent Nonpremixed Combustion
NASA Technical Reports Server (NTRS)
Smith, Nigel S. A.
1996-01-01
Nonpremixed combustion is the process whereby fuel and oxidizer species, which are each nonflammable in isolation, concurrently mix to burn a flammable mixture, and chemically react in the flammable mixture. In cases of practical industrial interest, the bulk of nonpremixed combustion occurs in a turbulent mixing regime where enhanced mass transfer rates flow the maximum power density to be achieved in any given thermochemical device.
Milford, A.; Devaud, C.B.
2010-08-15
The present paper examines the case of autoignition of high pressure methane jets in a shock tube over a range of pre-heated air temperatures in engine-relevant conditions. The two objectives of the present paper are: (i) to examine the effect of the inhomogeneous mixing model on the autoignition predictions relative to the results obtained using homogeneous mixing models and (ii) to see if the magnitude of the change can explain the discrepancy between the predictions of ignition delay previously obtained with homogeneous mixing models and the experimental data. The governing equation of the scalar dissipation rate is solved for transient conditions and two different formulations of the same model are tested and compared: one using the linear model for the conditional velocity and one including the gradient diffusion model. The predicted ignition kernel location and time delay over a range of pre-combustion air temperatures are compared with results obtained using two homogeneous turbulent mixing models and available experimental data. The profiles of conditional velocity and the conditional scalar dissipation rate are examined. Issues related to the conditional velocity model are discussed. It is found that the differences in the predictions are due to the mixing model only. The inhomogeneous model using the gradient conditional velocity model produces much larger ignition delays compared to the other models, whereas the inhomogeneous form including the linear model does not produce any significant differences. The effect of the turbulent inhomogeneous model is larger at high air temperatures and decreases with decreasing air temperatures. In comparison with the measured ignition delays, the inhomogeneous-Gradient model brings a small improvement at high air temperatures over the results from the turbulent homogeneous models. At low air temperatures, other parameters need to be investigated in order to bring the predicted ignition delays and locations within the
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.
Turbulence closure modeling near rigid boundaries
NASA Technical Reports Server (NTRS)
Durbin, Paul A.
1991-01-01
The near-wall region plays an essential role in turbulent boundary layers: it is a region of high shear; the peak rate of production and peak intensity of turbulence occurs there; and the peak rate of dissipation occurs right at the wall. Nevertheless, this region has received less attention from modelers than have more nearly homogeneous flows. One reason for this is that when the boundary layer is near equilibrium, experimental data can be used to prescribe the flow in the wall layer. Another reason is that most turbulence models are developed under assumptions of near homogeneity. This is a poor approximation in the wall region. A single-point moment closure model for the strongly non-homogeneous A turbulent flow near a rigid boundary is developed.
Quasi-explicit algebraic turbulence closures for compressible reacting flows
NASA Astrophysics Data System (ADS)
Adumitroaie, Virgil
A consistent and complete set of quasi-explicit algebraic closures for turbulent reacting flows is proposed as approximate solutions to the full second order moment equations. Quasi-explicit algebraic scalar flux models that are valid for three-dimensional turbulent flows are derived from a hierarchy of second-order moment closures. The mathematical procedure is based on the Cayley-Hamilton theorem and is an extension of the scheme developed by Taulbee (1992). Several closures for the pressure-scalar gradient correlations are considered and explicit algebraic relations are provided for the velocity-scalar correlations in both non-reacting and reacting flows. In the latter, the role of the Damkohler number is exhibited in isothermal turbulent flows with nonpremixed reactants. The relationship between these closures and traditional models based on the linear gradient diffusion approximation is theoretically established. The results of model predictions are assessed via comparison with available laboratory data in turbulent jet flows. The development of the quasi-explicit algebraic models for Reynolds stresses, temperature fluxes and reacting scalar fluxes is extended to high-speed turbulent reacting flows under a density weighted average formalism. New closures are proposed for the pressure-strain and the pressure-scalar gradient correlations. These accommodate compressibility corrections subject to the magnitude of the turbulent Mach number, the density gradient, the pressure gradient and the mean dilatation effects. Non-reacting and reacting flows with heat release are considered. In the latter, a second-order irreversible chemical reactions in turbulent flows with initially segregated reactants is considered. The models are tested in simple compressible free-shear flows. Comparisons are made between the full second order moment computations and the algebraic closure predictions. For a mixing layer, experimental data are used to validate the predicted results.
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.
Moment Closures on Two-Dimensional Cartesian Grids
Garrett, Charles K.
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.
Approximate maximum-entropy moment closures for gas dynamics
NASA Astrophysics Data System (ADS)
McDonald, James G.
2016-11-01
Accurate prediction of flows that exist between the traditional continuum regime and the free-molecular regime have proven difficult to obtain. Current methods are either inaccurate in this regime or prohibitively expensive for practical problems. Moment closures have long held the promise of providing new, affordable, accurate methods in this regime. The maximum-entropy hierarchy of closures seems to offer particularly attractive physical and mathematical properties. Unfortunately, several difficulties render the practical implementation of maximum-entropy closures very difficult. This work examines the use of simple approximations to these maximum-entropy closures and shows that physical accuracy that is vastly improved over continuum methods can be obtained without a significant increase in computational cost. Initially the technique is demonstrated for a simple one-dimensional gas. It is then extended to the full three-dimensional setting. The resulting moment equations are used for the numerical solution of shock-wave profiles with promising results.
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.
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.
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.
Development of Turbulent Biological Closure Parameterizations
2011-09-30
the role of TIBI term in the ADR equation a simple example, that of upwelling of seed nutrients and phytoplankton into a turbulent optically active...overall role that turbulence plays in determining the mean phytoplankton profile and in contributing to total phytoplankton production . As indicated... nutrients , phytoplankton , and zooplankton embedded in the turbulent field. Contrast the TIBI terms with the biological turbulent flux terms ’ , ’ , ’i
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.
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.
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.
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.
Conditional Moment Closure Schemes for Studying Stochastic Dynamics of Genetic Circuits.
Soltani, Mohammad; Vargas-Garcia, Cesar Augusto; Singh, Abhyudai
2015-08-01
Inside individual cells, stochastic expression drives random fluctuations in gene product copy numbers, which corrupts functioning of both natural and synthetic genetic circuits. Dynamic models of genetic circuits are formulated stochastically using the chemical master equation framework. Since obtaining probability distributions can be computationally expensive in these models, noise is typically investigated through lower-order statistical moments (mean, variance, correlation, skewness, etc.) of mRNA/proteins levels. However, due to the nonlinearities in genetic circuits, this moment dynamics is typically not closed, in the sense that the time derivative of the lower-order statistical moments depends on high-order moments. Moment equations are closed by expressing higher-order moments as nonlinear functions of lower-order moments, a technique commonly referred to as moment closure. We provide a new moment closure scheme for studying stochastic dynamics of genetic circuits, where genes randomly toggle between transcriptionally active and inactive states. The method is based on conditioning protein levels on active states of genes and then expressing higher-order moments as functions of lower-order conditional moments. The conditional closure scheme is illustrated on different circuit motifs and found to outperform existing closure techniques. Rapid computation of stochasticity through closure methods will enable improved characterization and design of synthetic circuits that exhibit robust performance in spite of noisy expression of underlying genes.
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.
Second moment closure analysis of the backstep flow database
NASA Technical Reports Server (NTRS)
Parneix, S.; Laurence, D.; Durbin, P.
1996-01-01
A Second Moment Closure computation (SMC) is compared in detail with the Direct Numerical Simulation (DNS) data of Le and Moin for the backstep flow at Re = 5,000 in an attempt to understand why the intensity of the backflow and, consequently, the friction coefficient in the recirculation bubble are severely underestimated. The data show that this recirculation bubble is far from being laminar except in the very near wall layer. A novel 'differential a priori' procedure was used, in which the full transport equation for one isolated component of the Reynolds stress tensor was solved using DNS data as input. Conclusions are then different from what would have been deduced by comparing a full simulation to a DNS. One cause of discrepancy was traced back to insufficient transfer of energy to the normal stress by pressure strain, but was not cured. A significant finding, confirmed by the DNS data in the core region of a channel flow, is that the coefficient that controls destruction of dissipation, C epsilon(sub 2), should be decreased by a factor of 2 when production is vanishing. This is also the case in the recirculation bubble, and a new formulation has cured 25% of the backflow discrepancy.
Prediction of the turbulent wake with second-order closure
NASA Technical Reports Server (NTRS)
Taulbee, D. B.; Lumley, J. L.
1981-01-01
A turbulence was envisioned whose energy containing scales would be Gaussian in the absence of inhomogeneity, gravity, etc. An equation was constructed for a function equivalent to the probability density, the second moment of which corresponded to the accepted modeled form of the Reynolds stress equation. The third moment equations obtained from this were simplified by the assumption of weak inhomogeneity. Calculations are presented with this model as well as interpretations of the results.
Interpolative Hyperbolic Realizable Moment Closures for Non-Equilibrium Flows with Heat Transfer
NASA Astrophysics Data System (ADS)
Tensuda, Boone Rudy
The predictive capabilities of a novel, 14-moment, maximum-entropy-based, interpolative closure are explored for multi-dimensional non-equilibrium flows of a monatomic gas with heat transfer. Unlike the maximum-entropy closure on which it is based, the interpolative closure provides closed-form expressions for the closing fluxes while retaining a large region of hyperbolicity. Properties of the moment system are explored via a dispersion analysis and an implicit finite-volume solution procedure is proposed. Multi-dimensional applications of the closure are then examined for several canonical non-equilibrium flow problems in order to provide an assessment of its capabilities. The predictive capabilities of the closure were found to surpass those of the 10-moment Gaussian closure. It was also found to predict interesting non-equilibrium phenomena, such as counter-gradient heat flux. The proposed implicit solver showed improved computational performance compared to the previously studied semi-implicit technique.
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.
NASA Astrophysics Data System (ADS)
Yu, R.; Lipatnikov, A. N.; Bai, X. S.
2014-08-01
In order to gain further insight into (i) the use of conditioned quantities for characterizing turbulence within a premixed flame brush and (ii) the influence of front propagation on turbulent scalar transport, a 3D Direct Numerical Simulation (DNS) study of an infinitely thin front that self-propagates in statistically stationary, homogeneous, isotropic, forced turbulence was performed by numerically integrating Navier-Stokes and level set equations. While this study was motivated by issues relevant to premixed combustion, the density was assumed to be constant in order (i) to avoid the influence of the front on the flow and, therefore, to know the true turbulence characteristics as reference quantities for assessment of conditioned moments and (ii) to separate the influence of front propagation on turbulent transport from the influence of pressure gradient induced by heat release. Numerical simulations were performed for two turbulence Reynolds numbers (50 and 100) and four ratios (1, 2, 5, and 10) of the rms turbulent velocity to the front speed. Obtained results show that, first, the mean front thickness is decreased when a ratio of the rms turbulent velocity to the front speed is decreased. Second, although the gradient diffusion closure yields the right direction of turbulent scalar flux obtained in the DNS, the diffusion coefficient Dt determined using the DNS data depends on the mean progress variable. Moreover, Dt is decreased when the front speed is increased, thus, indicating that the front propagation affects turbulent scalar transport even in a constant-density case. Third, conditioned moments of the velocity field differ from counterpart mean moments, thus, disputing the use of conditioned velocity moments for characterizing turbulence when modeling premixed turbulent combustion. Fourth, computed conditioned enstrophies are close to the mean enstrophy in all studied cases, thus, suggesting the use of conditioned enstrophy for characterizing turbulence
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.
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
Conditional Second Order Closure for Turbulent Shear Flows.
1985-07-22
measurements in several shear flows and satisfactory agreement between calculation and experiment is obtained. S Ps *s ~ J j~~- p .’* % LX- W-Vvw.n W...which allows calculation of the intermittency factor and statistical moments characterizing the fluctuations in the individual zones. The closure model...The resulting model is then compared with measurements in several shear flows and satisfactory agreement between calculation and experiment is
Magnetic moment conservation and particles acceleration in turbulence
NASA Astrophysics Data System (ADS)
Dalena, S.; Greco, A.; Matthaeus, W. H.
2010-12-01
The present work concerns the study of particle magnetic moment conservation in the presence of turbulent magnetic fields. As we know from the particle orbit theory, for slow temporal and spatial magnetic field variations(i.e. if their characteristic length and time are greater than the particle orbit diameter and the time spent by a particle to execute one orbit, respectively), the magnetic moment, defined as μ = (v^2⊥ /B) (averaged over the particle gyroperiod) is an adiabatic invariant and remains constant during particle motion. But in presence of a well developed magnetic turbulence μ can undergo rapid variations and might not be constant anymore. Of course, this fact could influence particle acceleration and could have a considerable implications in many astrophysical problems, such as coronal heating. In order to reproduce and extend some of the results obtained by Karimabadi et al. 1992, we study the interaction between ions and a single or a couple of electromagnetic waves. We varied both the wave frequency and the cosine of pitch angle at which particles are injected, in order to observe in this very simple case which is the limit for magnetic moment conservation. We also will reconsider the results of Dmitruk and Matthaeus (2006) regarding particle acceleration in turbulence, taking into account statistics of the magnetic moment (see also Lehe et al., 2010). Later we will add more waves to obtain a complete turbulent spectrum. The final aim of this research work is the understanding the behavior of particles magnetic moment during magnetic reconnection phenomena. H. Karimabadi, D. Krauss-Varban and T. Teresawa, JGR, 97, 13853, 1992. P. Dmitruk and W. H. Matthaeus, JGR, 11, A12110, 2006. R. Lehe, I. J. Parrish and E. Quataert, Astrophys. J. 707, 404, 2009.
Variational approach to the closure problem of turbulence theory
NASA Astrophysics Data System (ADS)
Qian, J.
1983-08-01
A new method is proposed to solve the closure problem of turbulence theory and to drive the Kolmogorov law in an Eulerian framework. Instead of using complex Fourier components of velocity field as modal parameters, a complete set of independent real parameters and dynamic equations are worked out to describe the dynamic states of a turbulence. Classical statistical mechanics is used to study the statistical behavior of the turbulence. An approximate stationary solution of the Liouville equation is obtained by a perturbation method based on a Langevin-Fokker-Planck (LFP) model. The dynamic damping coefficient eta of the LFP model is treated as an optimum control parameter to minimize the error of the perturbation solution; this leads to a convergent integral equation for eta to replace the divergent response equation of Kraichnan's direct-interaction (DI) approximation, thereby solving the closure problem without appealing to a Lagrangian formulation. The Kolmogorov constant Ko is evaluated numerically, obtaining Ko = 1.2, which is compatible with the experimental data given by Gibson and Schwartz, (1963).
Multi-dimensional validation of a maximum-entropy-based interpolative moment closure
NASA Astrophysics Data System (ADS)
Tensuda, Boone R.; McDonald, James G.; Groth, Clinton P. T.
2016-11-01
The performance of a novel maximum-entropy-based 14-moment interpolative closure is examined for multi-dimensional flows via validation of the closure for several established benchmark problems. Despite its consideration of heat transfer, this 14-moment closure contains closed-form expressions for the closing fluxes, unlike the maximum-entropy models on which it is based. While still retaining singular behaviour in some regions of realizable moment space, the interpolative closure proves to have a large region of hyperbolicity while remaining computationally tractable. Furthermore, the singular nature has been shown to be advantageous for practical simulations. The multi-dimensional cases considered here include Couette flow, heat transfer between infinite parallel plates, subsonic flow past a circular cylinder, and lid-driven cavity flow. The 14-moment predictions are compared to analytical, DSMC, and experimental results as well the results of other closures. For each case, a range of Knudsen numbers are explored in order to assess the validity and accuracy of the closure in different regimes. For Couette flow and heat transfer between flat plates, it is shown that the closure predictions are consistent with the expected analytical solutions in all regimes. In the cases of flow past a circular cylinder and lid-driven cavity flow, the closure is found to give more accurate results than the related lower-order maximum-entropy Gaussian and maximum-entropy-based regularized Gaussian closures. The ability to predict important non-equilibrium phenomena, such as a counter-gradient heat flux, is also established.
Application of Gaussian Moment Closures to Three-Dimensional Micro-Scale Flows
NASA Astrophysics Data System (ADS)
Lam, Christopher
A parallel, implicit, adaptive mesh refinement (AMR), finite-volume scheme is described for the solution of the standard and regularized Gaussian moment closures on three-dimensional, multi-block, body-fitted, hexahedral meshes. The standard Gaussian closure has been shown to accurately predict non-equilibrium phenomena at moderate Knudsen numbers through an anisotropic treatment of pressure. The regularized closure builds on these advantages and includes the effects of non-equilibrium heat transfer by means of a first-order correction to the standard Gaussian closure. The combined moment closure treatment / numerical method is applied to the prediction of three-dimensional, non-equilibrium, micro-scale, gaseous flows. Unlike other regularized moment closures, the underlying closure is the standard maximum-entropy Gaussian closure which provides a fully-realizable and strictly hyperbolic description of non-equilibrium gaseous flows that is valid from the continuum limit, through the transition regime, and up to the free-molecular flow limit. The proposed finite-volume scheme uses Riemann-solver-based flux functions and limited linear reconstruction to provide accurate and monotonic solutions, even in the presence of large solution gradients and/or under-resolved solution content. A rather effective and highly scalable parallel implicit time-marching scheme based on a Jacobian-free inexact Newton-Krylov-Schwarz (NKS) approach with additive Schwarz preconditioning and domain partitioning following from the multi-block AMR mesh is used to obtain solutions to the non-linear ordinary-differential equations that result from finite-volume spatial discretization procedure. Details are given of the standard and regularized Gaussian closure, extensions for diatomic gases, and slip-flow boundary treatment. Numerical results for several canonical flow problems demonstrate the potential of the closures, that when combined with an efficient parallel solution method, provide an
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.
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.
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.
NASA Technical Reports Server (NTRS)
Cheng, A.; Xu, K.-M.; Golaz, J.-C.
2004-01-01
A hierarchy of third-order turbulence closure models are used to simulate boundary-layer cumuli in this study. An unrealistically strong liquid-water oscillation (LWO) is found in the fully prognostic model, which predicts all third moments. The LWO propagates from cloud base to cloud top with a speed of 1 m/s. The period of the oscillation is about 1000 s. Liquid-water buoyancy terms in the third-moment equations contribute to the LWO. The LWO mainly affects the vertical profiles of cloud fraction, mean liquid-water mixing ratio and the fluxes of liquid-water potential temperature and total water, but has less impact on the vertical profiles of other second-moments and third-moments. In order to minimize the LWO, a moderate large diffusion coefficient and a large turbulent dissipation at its originating level are needed. However, this approach distorts the vertical distributions of cloud fraction and liquid-water mixing ratio. A better approach is to parameterize liquid-water buoyancy more reasonably. A minimally prognostic model, which diagnoses all third moments except for vertical velocity, is shown to produce better results, compared to a fully prognostic model.
An alternative assessment of second-order closure models in turbulent shear flows
NASA Technical Reports Server (NTRS)
Speziale, Charles G.; Gatski, Thomas B.
1994-01-01
The performance of three recently proposed second-order closure models is tested in benchmark turbulent shear flows. Both homogeneous shear flow and the log-layer of an equilibrium turbulent boundary layer are considered for this purpose. An objective analysis of the results leads to an assessment of these models that stands in contrast to that recently published by other authors. A variety of pitfalls in the formulation and testing of second-order closure models are uncovered by this analysis.
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.
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.
Direct numerical simulation-based Reynolds-averaged closure for bubble-induced turbulence
NASA Astrophysics Data System (ADS)
Ma, Tian; Santarelli, Claudio; Ziegenhein, Thomas; Lucas, Dirk; Fröhlich, Jochen
2017-03-01
Budgets of the turbulent kinetic energy from direct numerical simulations (DNSs) of disperse bubbly channel flows are used to develop a model for bubble-induced turbulence in the Euler-Euler Reynolds-averaged framework. First, an appropriate time scale is selected. Second, links between the unclosed terms in the transport equations of the turbulence quantities and the DNS data for small bubbles are established. Third, a suitably chosen iterative procedure employing the full Reynolds-averaged model provides suitable coefficients for the closure of the terms resulting from bubble-induced turbulence while largely removing the influence of others. At the same time these results validate the closure, exhibiting very good agreement with the DNS and better performance than the standard closures. The model is now ready for use and can be employed in practical Euler-Euler simulations.
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
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
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.
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.
NASA Astrophysics Data System (ADS)
Laplante, Jérémie; Groth, Clinton P. T.
2016-11-01
The Navier-Stokes-Fourier (NSF) equations are conventionally used to model continuum flow near local thermodynamic equilibrium. In the presence of more rarefied flows, there exists a transitional regime in which the NSF equations no longer hold, and where particle-based methods become too expensive for practical problems. To close this gap, moment closure techniques having the potential of being both valid and computationally tractable for these applications are sought. In this study, a number of five-moment closures for a model one-dimensional kinetic equation are assessed and compared. In particular, four different moment closures are applied to the solution of stationary shocks. The first of these is a Grad-type moment closure, which is known to fail for moderate departures from equilibrium. The second is an interpolative closure based on maximization of thermodynamic entropy which has previously been shown to provide excellent results for 1D gaskinetic theory. Additionally, two quadrature methods of moments (QMOM) are considered. One method is based on the representation of the distribution function in terms of a combination of three Dirac delta functions. The second method, an extended QMOM (EQMOM), extends the quadrature-based approach by assuming a bi-Maxwellian representation of the distribution function. The closing fluxes are analyzed in each case and the region of physical realizability is examined for the closures. Numerical simulations of stationary shock structures as predicted by each moment closure are compared to reference kinetic and the corresponding NSF-like equation solutions. It is shown that the bi-Maxwellian and interpolative maximum-entropy-based moment closures are able to closely reproduce the results of the true maximum-entropy distribution closure for this case very well, whereas the other methods do not. For moderate departures from local thermodynamic equilibrium, the Grad-type and QMOM closures produced unphysical subshocks and were
NASA Astrophysics Data System (ADS)
Hendrickson, Kelli; Yue, Dick
2016-11-01
This work presents the development and a priori testing of closure models for the incompressible highly-variable density turbulent (IHVDT) flow in the near wake region of a transom stern. This complex, three-dimensional flow includes three regions with distinctly different flow behavior: (i) the convergent corner waves that originate from the body and collide on the ship center plane; (ii) the "rooster tail" that forms from the collision; and (iii) the diverging wave train. The characteristics of these regions involve violent free-surface flows and breaking waves with significant turbulent mass flux (TMF) at Atwood number At = (ρ2 -ρ1) / (ρ2 +ρ1) 1 for which there is little guidance in turbulence closure modeling for the momentum and scalar transport along the wake. Utilizing datasets from high-resolution simulations of the near wake of a canonical three-dimensional transom stern using conservative Volume-of-Fluid (cVOF), implicit Large Eddy Simulation (iLES), and Boundary Data Immersion Method (BDIM), we develop explicit algebraic turbulent mass flux closure models that incorporate the most relevant physical processes. Performance of these models in predicting the turbulent mass flux in all three regions of the wake will be presented. Office of Naval Research.
Elliptic blending model: A new near-wall Reynolds-stress turbulence closure
NASA Astrophysics Data System (ADS)
Manceau, Rémi; Hanjalić, Kemal
2002-02-01
A new approach to modeling the effects of a solid wall in one-point second-moment (Reynolds-stress) turbulence closures is presented. The model is based on the relaxation of an inhomogeneous (near-wall) formulation of the pressure-strain tensor towards the chosen conventional homogeneous (far-from-a-wall) form using the blending function α, for which an elliptic equation is solved. The approach preserves the main features of Durbin's Reynolds-stress model, but instead of six elliptic equations (for each stress component), it involves only one, scalar elliptic equation. The model, called "the elliptic blending model," offers significant simplification, while still complying with the basic physical rationale for the elliptic relaxation concept. In addition to model validation against direct numerical simulation in a plane channel for Reτ=590, the model was applied in the computation of the channel flow at a "real-life" Reynolds number of 106, showing a good prediction of the logarithmic profile of the mean velocity.
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.
Allam, A.M.; Crichlow, H.B.; Soliman, M.Y.
1981-01-01
A numerical technique for analyzing the behavior of a fractured gas reservoir system is presented. The reservoir is simulated by a fully implicit three-dimensional model that incorporates the effects of turbulent flow and closure stress in a finite conductivity fracture. The model utilizes the real gas pseudo-pressure, two-point upstream transmissibilities and a stable iterative process based on a sparse matrix approach to solving the equation systems. This paper presents a description of the model and applications to various reservoirs to illustrate the effects of fracture heights, turbulence and closure pressure on well performance. 16 refs.
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.
NASA Astrophysics Data System (ADS)
Fabijonas, Bruce R.; Holm, Darryl D.
2004-04-01
The Craik-Criminale class of exact solutions is examined for a nonlinear-reactive fluids theory that includes a family of turbulence closure models. These may be formally regarded as either large eddy simulation or Reynolds-averaged Navier-Stokes models of turbulence. All of the turbulence closure models in the class under investigation preserve the existence of elliptic instability, although they shift its angle of critical stability as a function of the rotation rate Ω of the coordinate system, the wave number β of the Kelvin wave, and the model parameter α, the turbulence correlation length. Elliptic instability allows a comparison among the properties of these models. It is emphasized that the physical mechanism for this instability is not wave-wave interaction, but rather wave, mean-flow interaction as governed by the choice of a model's nonlinearity.
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.
Closure of a kinetic model of plasma in strong turbulence by relaxation
NASA Technical Reports Server (NTRS)
Tchen, C. M.
1978-01-01
A Fokker-Planck kinetic equation for a turbulent plasma is derived by a repeated cascade decomposition. Calculation of the propagator and the kinetic equation determine the transport coefficients (diffusivity and turbulent viscosity) by means of a closure based on a relaxation procedure governing the approach to equilibrium. The k to the minus third power spectral law is obtained, which governs the coupling between the velocity and the electrostatic field fluctuations.
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.
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.
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.
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.
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.
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.
Evaluation of Maximum Entropy Moment Closure for Solution To Radiative Heat Transfer Equation
NASA Astrophysics Data System (ADS)
Fan, Doreen
The maximum entropy moment closure for the two-moment approximation of the radiative transfer equation is presented. The resulting moment equations, known as the M1 model, are solved using a finite-volume method with adaptive mesh refinement (AMR) and two Riemann-solver based flux function solvers: a Roe-type and a Harten-Lax van Leer (HLL) solver. Three different boundary schemes are also presented and discussed. When compared to the discrete ordinates method (DOM) in several representative one- and two-dimensional radiation transport problems, the results indicate that while the M1 model cannot accurately resolve multi-directional radiation transport occurring in low-absorption media, it does provide reasonably accurate solutions, both qualitatively and quantitatively, when compared to the DOM predictions in most of the test cases involving either absorbing-emitting or scattering media. The results also show that the M1 model is computationally less expensive than DOM for more realistic radiation transport problems involving scattering and complex geometries.
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.
LES-Modeling of a Partially Premixed Flame using a Deconvolution Turbulence Closure
NASA Astrophysics Data System (ADS)
Wang, Qing; Wu, Hao; Ihme, Matthias
2015-11-01
The modeling of the turbulence/chemistry interaction in partially premixed and multi-stream combustion remains an outstanding issue. By extending a recently developed constrained minimum mean-square error deconvolution (CMMSED) method, to objective of this work is to develop a source-term closure for turbulent multi-stream combustion. In this method, the chemical source term is obtained from a three-stream flamelet model, and CMMSED is used as closure model, thereby eliminating the need for presumed PDF-modeling. The model is applied to LES of a piloted turbulent jet flame with inhomogeneous inlets, and simulation results are compared with experiments. Comparisons with presumed PDF-methods are performed, and issues regarding resolution and conservation of the CMMSED method are examined. The author would like to acknowledge the support of funding from Stanford Graduate Fellowship.
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
Inference of turbulence parameters from a ROMS simulation using the k-ε closure scheme
NASA Astrophysics Data System (ADS)
Thyng, Kristen M.; Riley, James J.; Thomson, Jim
2013-12-01
Comparisons between high resolution turbulence data from Admiralty Inlet, WA (USA), and a 65-meter horizontal grid resolution simulation using the hydrostatic ocean modelling code, Regional Ocean Modeling System (ROMS), show that the model's k-ε turbulence closure scheme performs reasonably well. Turbulent dissipation rates and Reynolds stresses agree within a factor of two, on average. Turbulent kinetic energy (TKE) also agrees within a factor of two, but only for motions within the observed inertial sub-range of frequencies (i.e., classic approximately isotropic turbulence). TKE spectra from the observations indicate that there is significant energy at lower frequencies than the inertial sub-range; these scales are not captured by the model closure scheme nor the model grid resolution. To account for scales not present in the model, the inertial sub-range is extrapolated to lower frequencies and then integrated to obtain an inferred, diagnostic total TKE, with improved agreement with the observed total TKE. The realistic behavior of the dissipation rate and Reynolds stress, combined with the adjusted total TKE, imply that ROMS simulations can be used to understand and predict spatial and temporal variations in turbulence. The results are suggested for application to siting tidal current turbines.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Ralston, David K.; Cowles, Geoffrey W.; Geyer, W. Rockwell; Holleman, Rusty C.
2017-01-01
The Connecticut River is a tidal salt wedge estuary, where advection of sharp salinity gradients through channel constrictions and over steeply sloping bathymetry leads to spatially heterogeneous stratification and mixing. A 3-D unstructured grid finite-volume hydrodynamic model (FVCOM) was evaluated against shipboard and moored observations, and mixing by both the turbulent closure and numerical diffusion were calculated. Excessive numerical mixing in regions with strong velocities, sharp salinity gradients, and steep bathymetry reduced model skill for salinity. Model calibration was improved by optimizing both the bottom roughness (z0), based on comparison with the barotropic tidal propagation, and the mixing threshold in the turbulence closure (steady state Richardson number, Rist), based on comparison with salinity. Whereas a large body of evidence supports a value of Rist ˜ 0.25, model skill for salinity improved with Rist ˜ 0.1. With Rist = 0.25, numerical mixing contributed about 1/2 the total mixing, while with Rist = 0.10 it accounted for ˜2/3, but salinity structure was more accurately reproduced. The combined contributions of numerical and turbulent mixing were quantitatively consistent with high-resolution measurements of turbulent mixing. A coarser grid had increased numerical mixing, requiring further reductions in turbulent mixing and greater bed friction to optimize skill. The optimal Rist for the fine grid case was closer to 0.25 than for the coarse grid, suggesting that additional grid refinement might correspond with Rist approaching the theoretical limit. Numerical mixing is rarely assessed in realistic models, but comparisons with high-resolution observations in this study suggest it is an important factor.
Critical examination of two-equation turbulence closure models
NASA Technical Reports Server (NTRS)
Chambers, T. L.; Wilcox, D. C.
1976-01-01
Comparison of the Jones-Launder, Ng-Spalding, Saffman-Wilcox, and Wilcox-Traci two-equation turbulence models has been conducted. It was shown that the Saffman-Wilcox and Wilcox-Traci dissipation-rate formulations admit straightforward integration through the viscous sublayer, whereas integration through the viscous sublayer is a more difficult issue with the Jones-Launder dissipation-function and the Ng-Spalding length-scale formulations. Numerical computations were conducted in which the models were applied to four equilibrium boundary layer flows including adverse, zero, and favorable pressure gradients. Computations of zero pressure gradient flow over a convex wall composed the final part of the comparison.
NASA Astrophysics Data System (ADS)
Wang, Minghuai; Larson, Vincent E.; Ghan, Steven; Ovchinnikov, Mikhail; Schanen, David P.; Xiao, Heng; Liu, Xiaohong; Rasch, Philip; 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 Multiscale 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 short-wave cloud forcing in better agreement with observations, while CLUBB with single-moment cloud microphysics overestimates short-wave 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.
Mao, Haidan; Zhao, Daomu
2010-01-18
Based on the intensity moments and Wigner distribution function, the second-order moments for broadband partially coherent flat-topped (BPCFT) beams in atmospheric turbulence are studied. The beam width of BPCFT beams in atmospheric turbulence is larger than that in free space. The beam width of BPCFT beams in atmospheric turbulence is larger than that of broadband fully coherent flat-topped (BFCFT) beams in atmospheric turbulence. The broader the bandwidth is, the larger the beam width of BPCFT beams becomes. Similar conclusion can be obtained by analyzing the divergence angle and beam propagation factor of BPCFT beams. The beam width of BPCFT beams in atmospheric turbulence is less affected by the broad spectral bandwidth than that in free space. The beam width of BFCFT beams in atmospheric turbulence is less affected by the broad spectral bandwidth than that of BPCFT beams in atmospheric turbulence.
Three-Dimensional Shallow Water Adaptive Hydraulics (ADH-SW3): Turbulence Closure
2015-06-01
ER D C/ CH L CR -1 5- 1 Three-Dimensional Shallow Water Adaptive Hydraulics (ADH-SW3): Turbulence Closure Co as ta l a nd H yd ra ul ic...military engineering, geospatial sciences, water resources, and environmental sciences for the Army, the Department of Defense, civilian agencies, and our...library at http://acwc.sdp.sirsi.net/client/default. ERDC/CHL CR-15-1 June 2015 Three-Dimensional Shallow Water Adaptive Hydraulics (ADH-SW3
A comparison of turbulence closure models for transonic flows about airfoils
NASA Technical Reports Server (NTRS)
King, Lyndell S.
1987-01-01
Navier-Stokes transonic airfoil calculations using three different turbulence closure models are presented and compared with available experimental data. Two of the models, Cebeci-Smith and Baldwin-Lomax, are equilibrium models in the sense that the turbulent shear stress is assumed to depend only on the local properties of the mean flow. The third model, Johnson and King, is a nonequilibrium model in which an ordinary differential equation is employed to account for the streamwise development of the maximum Reynolds shear stress. An eddy viscosity distribution across the boundary layer is assumed which is functionally dependent on this stress. For attached flows with little inviscid-viscous interaction, little difference in the results with the different models is noted. With stronger interactions and with separation occurring on the airfoils, the nonequilibrium model is shown to perform better.
Anomalous scaling from controlled closure in a shell model of turbulence
NASA Astrophysics Data System (ADS)
L'vov, Victor S.; Pierotti, Daniela; Pomyalov, Anna; Procaccia, Itamar
2000-04-01
We present a model of hydrodynamic turbulence for which the program of computing the scaling exponents from first principles can be developed in a controlled fashion. The model consists of N suitably coupled copies of the "Sabra" shell model of turbulence. The couplings are chosen to include two components: random and deterministic, with a relative importance that is characterized by a parameter called ɛ. It is demonstrated, using numerical simulations of up to 25 copies and 28 shells that in the N→∞ limit but for 0<ɛ⩽1 this model exhibits correlation functions whose scaling exponents are anomalous. The theoretical calculation of the scaling exponents follows verbatim the closure procedure suggested recently for the Navier-Stokes problem, with the additional advantage that in the N→∞ limit the parameter ɛ can be used to regularize the closure procedure. The main result of this paper is a finite and closed set of scale-invariant equations for the 2nd and 3rd order statistical objects of the theory. This set of equations takes into account terms up to order ɛ4 and neglects terms of order ɛ6. Preliminary analysis of this set of equations indicates a K41 normal scaling at ɛ=0, with a birth of anomalous exponents at larger values of ɛ, in agreement with the numerical simulations.
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.
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.
NASA Technical Reports Server (NTRS)
Eggleston, John M; Diederich, Franklin W
1957-01-01
The correlation functions and power spectra of the rolling and yawing moments on an airplane wing due to the three components of continuous random turbulence are calculated. The rolling moments to the longitudinal (horizontal) and normal (vertical) components depend on the spanwise distributions of instantaneous gust intensity, which are taken into account by using the inherent properties of symmetry of isotropic turbulence. The results consist of expressions for correlation functions or spectra of the rolling moment in terms of the point correlation functions of the two components of turbulence. Specific numerical calculations are made for a pair of correlation functions given by simple analytic expressions which fit available experimental data quite well. Calculations are made for four lift distributions. Comparison is made with the results of previous analyses which assumed random turbulence along the flight path and linear variations of gust velocity across the span.
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.
Modelling complex draft-tube flows using near-wall turbulence closures
Ventikos, Y.; Sotiropoulos, F.; Patel, V.C.
1996-12-31
This paper presents a finite-volume method for simulating flows through complex hydroturbine draft-tube configurations using near-wall turbulence closures. The method employs the artificial-compressibility pressure-velocity coupling approach in conjunction with multigrid acceleration for fast convergence on very fine grids. Calculations are carried out for a draft tube with two downstream piers on a computational mesh consisting of 1.2x10{sup 6} nodes. Comparisons of the computed results with measurements demonstrate the ability of the method to capture most experimental trends with reasonable accuracy. Calculated three-dimensional particle traces reveal very complex flow features in the vicinity of the piers, including horse-shoe longitudinal vortices and and regions of flow reversal.
Experimental Investigation of Statistical Moments of Travel Time in Grid-Generated Turbulence
NASA Astrophysics Data System (ADS)
Durgin, William; Meleschi, Shangari; Andreeva, Tatiana
2003-11-01
Experimental Investigation of Statistical Moments of Travel Time in Grid-Generated Turbulence W.W. Durgin, S.B. Meleschi and T.A. Andreeva ABSTRACT. An experimental technique for investigation of the behavior of acoustic waves propagation through a turbulent medium is discussed. The present study utilizes the ultrasonic travel-time technique to diagnose a grid-generated turbulence. The statistics of the travel-time variations of ultrasonic wave propagation along a path are used to determine some metrics of the turbulence. Experimental investigation is performed under well-controlled laboratory conditions using a data acquisition and control system featuring a high-speed analog to digital conversion card that enables fine resolution of ultrasonic signals. Experimental data confirm numerical and theoretical predictions of a nonlinear increase of the first-order travel time variance with propagation distance. This behavior seems to be closely related to the occurrence of first caustics [Kulkarny and White, Blanc-Benon et al, 1991, 1995]. With increased turbulent intensity the distance at which the first caustic occurs, decreases. Numerically the phenomena was explored by Blanc-Benon and Juvé [1990], Juvé et al, 1991; Karweit et al [1991]; and their probability of appearance in a random field theoretically by Kulkarny and White [1982], Klyatskin [1993], Blanc-Benon et al, [1995]. Current work seeks to illustrate the correspondence between flow parameters and the first appearance of non-linearity in the travel time variance. Expansion of experimental controls to include flow temperature references and rigid transducer supports adds to the integrity of the determined travel times.
Eigenspace perturbations for uncertainty estimation of single-point turbulence closures
NASA Astrophysics Data System (ADS)
Iaccarino, Gianluca; Mishra, Aashwin Ananda; Ghili, Saman
2017-02-01
Reynolds-averaged Navier-Stokes (RANS) models represent the workhorse for predicting turbulent flows in complex industrial applications. However, RANS closures introduce a significant degree of epistemic uncertainty in predictions due to the potential lack of validity of the assumptions utilized in model formulation. Estimating this uncertainty is a fundamental requirement for building confidence in such predictions. We outline a methodology to estimate this structural uncertainty, incorporating perturbations to the eigenvalues and the eigenvectors of the modeled Reynolds stress tensor. The mathematical foundations of this framework are derived and explicated. Thence, this framework is applied to a set of separated turbulent flows, while compared to numerical and experimental data and contrasted against the predictions of the eigenvalue-only perturbation methodology. It is exhibited that for separated flows, this framework is able to yield significant enhancement over the established eigenvalue perturbation methodology in explaining the discrepancy against experimental observations and high-fidelity simulations. Furthermore, uncertainty bounds of potential engineering utility can be estimated by performing five specific RANS simulations, reducing the computational expenditure on such an exercise.
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 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.
Generalized higher order two-point moments in turbulent boundary layers.
NASA Astrophysics Data System (ADS)
Yang, Xiang; Marusic, Ivan; Meneveau, Charles
2015-11-01
Generalized higher order two-point moments such as
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.
From Markovian to pairwise epidemic models and the performance of moment closure approximations.
Taylor, Michael; Simon, Péter L; Green, Darren M; House, Thomas; Kiss, Istvan Z
2012-05-01
Many if not all models of disease transmission on networks can be linked to the exact state-based Markovian formulation. However the large number of equations for any system of realistic size limits their applicability to small populations. As a result, most modelling work relies on simulation and pairwise models. In this paper, for a simple SIS dynamics on an arbitrary network, we formalise the link between a well known pairwise model and the exact Markovian formulation. This involves the rigorous derivation of the exact ODE model at the level of pairs in terms of the expected number of pairs and triples. The exact system is then closed using two different closures, one well established and one that has been recently proposed. A new interpretation of both closures is presented, which explains several of their previously observed properties. The closed dynamical systems are solved numerically and the results are compared to output from individual-based stochastic simulations. This is done for a range of networks with the same average degree and clustering coefficient but generated using different algorithms. It is shown that the ability of the pairwise system to accurately model an epidemic is fundamentally dependent on the underlying large-scale network structure. We show that the existing pairwise models are a good fit for certain types of network but have to be used with caution as higher-order network structures may compromise their effectiveness.
Allam, A.M.
1982-01-01
Although techniques for designing a fracture treatment are available, the intended results of these techniques are often not attained. The evaluation of fracturing treatments on low permeability gas wells is required to both optimize the fracturing design and form prediction calculations of a treatments effect. This study primarily investigates the effect of fracture height on the performance of vertically fractured wells. The effects of layered media, turbulance, and closure pressure are included in this work. Consider that a well, intercepted by a vertical fracture, is in the center of a squared drainage system with closed outer boundary. Any increase in well productivity will be determined by fracture parameters, which are: fracture length, height, fracture conductivity, and location of the fracture in the formaton. On the basis of the analysis of fluid flow in porous media, the problem solving technique used in this study is the numerical method. A three-dimensional finite difference fully implicit model was written for this. In addition, the Sparse Matrix technique was used as a solver. Furthermore, Slices Source Over Relaxation was used as an iterative method for solving routines. Presented here are the numerical results of the three-dimensional model for a well intercepting a vertical fracture wth finite conductivity. The results are presented in the general form of dimensionless variables. Type curves considering the effect of fracture height on well performance are included. In addition, type curves for turbulent flow in the fracture are also obtained. Finally, other important contributions of this work are the data showing the effect of layered formation on fractured well performance.
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
A second-order closure model for the effect of averaging time on turbulent plume dispersion
Sykes, R.I.; Gabruk, R.S.
1996-12-31
Turbulent dispersion in the atmosphere is a result of chaotic advection by a wide spectrum of eddy motions. In genera, the larger scale motions behave like a time-dependent, spatially inhomogeneous mean wind and produce coherent meandering of a pollutant cloud or plume, while the smaller scale motions act to diffuse the pollutant and mix it with the ambient air. The distinction between the two types of motion is dependent on both the sampling procedure and the scale of the pollutant cloud. For the case of a continuous plume of material, the duration of the sampling time (the time average period) determines the effective size of the plume. The objective is the development of a practical scheme for representing the effect of time-averaging on plume width. The model must describe relative dispersion in the limit of short-term averages, and give the absolute, or ensemble, dispersion rate for long-term sampling. The authors shall generalize the second-order closure ensemble dispersion model of Sykes et al. to include the effect of time-averaging, so they first briefly review the basic model.
NASA Astrophysics Data System (ADS)
Talamelli, Alessandro; Segalini, Antonio; Örlü, Ramis; Schlatter, Philipp; Alfredsson, P. Henrik
2013-04-01
Spatial averaging, resulting from the finite size of a hot-wire probe, significantly affects the accuracy of velocity measurements in turbulent flows close to walls. Here, we extend the theoretical model, introduced in Segalini et al. (Meas Sci Technol 22:104508, 2011) quantifying the effect of a linear spatial filter of hot-wire probes on the mean and the variance of the streamwise velocity in turbulent wall-bounded flows, to describe the effect of the spatial filtering on the third- and fourth-order moments of the same velocity component. The model, based on the three-(four) point velocity-correlation function for the third-(fourth-) order moment, shows that the filtering can be related to a characteristic length scale which is an equivalent of the Taylor transverse microscale for the second-order moment. The capacity of the model to accurately describe the attenuation is validated against direct numerical simulation (DNS) data of a zero pressure-gradient turbulent boundary layer. The DNS data allow the filtering effect to be appraised for different wire lengths and for the different moments. The model shows good accuracy except for the third-order moment in the region where a zero-crossing of the third-order function is observed and where the equations become ill-conditioned. An "a posteriori" correction procedure, based on the developed model, to correct the measured third- and fourth-order velocity moments is also presented. This procedure, based on combining the measured data by two single hot-wire sensors with different wire lengths, is a natural extension of the one introduced by Segalini et al. (Exp Fluids 51:693-700, 2011) to evaluate both the turbulence intensity and the transverse Taylor microscale in turbulent flows. The technique is validated against spatially averaged simulation data showing a good capacity to correct the actual profiles over the entire height of the boundary layer except, as expected, for the third-order moment in the region where
Podesta, J. J.; Forman, M. A.; Smith, C. W.
2007-09-15
Laws governing the behavior of statistical third-order moments in the inertial range are among the few rigorous results in the theory of statistically homogeneous incompressible magnetohydrodynamic turbulence. These fundamental laws apply to both isotropic and anisotropic turbulence. Assuming that the turbulence is stationary in time and statistically axisymmetric under proper rotations about the direction of the mean magnetic field, it is shown that the general mathematical form of the tensor quantities appearing in these laws is constrained by symmetry to have a particular form. Using these forms, the general solutions of the law for the vector and pseudovector third-order moments F and F{sub C} are obtained in the limit of large kinetic Reynolds number and large magnetic Reynolds number. The physical meaning of the different terms in F and F{sub C} are investigated and a method for obtaining the cascade rates of energy {epsilon} and cross-helicity {epsilon}{sub C} from experimental data is described. The results show that the measurement of the cascade rates goes hand-in-hand with the measurement of the spatial anisotropy of the third-order moments F and F{sub C}. The theory developed here can be applied to measure the turbulent cascade rates of energy and cross-helicity in laboratory plasma experiments, numerical simulations, and the solar wind.
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 Astrophysics Data System (ADS)
Ezhova, E. V.; Zilitinkevitch, S. S.; Rybushkina, G. V.; Soustova, I. A.; Troitskaya, Yu. I.
2016-05-01
The self-similar turbulent density jump evolution has been studied in the scope of a turbulence closure modernized theory which takes into account the anisotropy and mutual transformation of the turbulent fluctuation kinetic and potential energy for a stably stratified fluid. The numerical calculation, performed using the equations for the average density and kinetic and potential energies of turbulent fluctuations, indicates that the vertical profiles of the buoyancy frequency, turbulence scale, and kinetic and potential energies drastically change when the turbulence anisotropy is strong. The vertical profiles of the corresponding energy and spatial discontinuity parameters, calculated at a weaker anisotropy, indicate that similar drastic changes are absent and a qualitative agreement exists with the known analytical solution, which describes the density jump evolution in a freshwater basin and was obtained previously [5, 8] in the scope of a turbulence local-similarity hypothesis applied in combination with the budget equation for the turbulent fluctuation kinetic energy.
Two-point closure method for turbulence with reacting and mixing chemical elements of type A+B→ C
NASA Astrophysics Data System (ADS)
Meshram, M. C.
2010-12-01
Turbulence with reacting and mixing chemical elements of type A+B→C was investigated by using the two-point closure method, For implementation of this method, two-point correlation functions and two-point triple correlation functions are defined first. Equations describing the turbulence under study that describe the dynamical behaviour are written in terms of two-point correlation functions and two-point triple correlation functions. These describe the dynamical behaviour of two-point double-reactant fluctuation correlation functions. In each of these equations, two-point triple correlation functions appear. Thus, the characteristic difficulty of indeterminacy in turbulence theory is noticed in these equations too. A simple closure hypothesis for two-point triple correlation functions is proposed with a view to overcoming the indeterminacy. This hypothesis enables one to obtain the closed set of equations for double correlation functions, as desired. The resulting equations for double correlation functions provide theoretical information about the turbulence under investigation. Having obtained the closed set of equations for double correlation functions, the relationships for reactants' eddy diffusivity functions are derived. Also, the reactants' energy and transfer functions in fluid space are obtained. Having expressed the Karman-Howarth equations for the present investigation in dimensionless form, these are rewritten in terms of energy functions in fluid space. The system of equations for scales of segregation related to reactants A and B is derived. Various length scales involved in this study can be evaluated on integration of these equations, which in turn generates theoretical information about the turbulence under investigation.
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.
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.
Navier-Stokes computation of compressible turbulent flows with a second order closure
NASA Technical Reports Server (NTRS)
Dingus, C.; Kollmann, W.
1991-01-01
The objective was the development of a complete second order closure for wall bounded flows, including all components of the dissipation rate tensor and a numerical solution procedure for the resulting system of equations. The main topics discussed are the closure of the pressure correlations and the viscous destruction terms in the dissipation rate equations and the numerical solution scheme based on a block-tridiagonal solver for the nine equations required for the prediction of plane or axisymmetric flows.
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.
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.
NASA Astrophysics Data System (ADS)
Bou-Zeid, Elie; Huang, Jing; Golaz, Jean-Christophe
2011-11-01
A disconnect remains between our improved physical understanding of boundary layers stabilized by buoyancy and how we parameterize them in coarse atmospheric models. Most operational climate models require excessive turbulence mixing in such conditions to prevent decoupling of the atmospheric component from the land component, but the performance of such a model is unlikely to be satisfactory under weakly and moderately stable conditions. Using Large-eddy simulation, we revisit some of the basic challenges in parameterizing stable atmospheric boundary layers: eddy-viscosity closure is found to be more reliable due to an improved alignment of vertical Reynolds stresses and mean strains under stable conditions, but the dependence of the magnitude of the eddy viscosity on stability is not well represented by several models tested here. Thus, we propose a new closure that reproduces the different stability regimes better. Subsequently, tests of this model in the GFDL's single-column model (SCM) are found to yield good agreement with LES results in idealized steady-stability cases, as well as in cases with gradual and sharp changes of stability with time.
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.
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)
Macole, Sabat; Vié, Aymeric; Larat, Adam; Doisneau, Francois; Chalons, Christophe; Massot, Marc
2014-11-01
The simulation of particle-laden flows is a challenging topic due to their multiscale character. Lagrangian particle tracking methods are classically used. However, for high performance computing, such approaches deteriorate with the disperse phase inhomogeneities. Moment methods bypass this issue through an Eulerian framework allowing to use the same parallelization paradigm as the gas phase. We present recent developments for DNS and LES based on a Kinetic-Based Moment Method. The moment system is closed by assuming a presumed shape for the NDF. The selected NDF is an Anisotropic Gaussian giving the following properties: 1/hyperbolicity; 2/realizability of the moments; 3/maximization of entropy; 4/H-theorem. The method is evaluated on configurations of increasing complexity that exhibit its potential and drawbacks. This method extends towards LES by means of a full kinetic-based filtering technique instead of filtering the moment equations. Thus realizability conditions are easily derived, and the main properties of the DNS system are preserved. The subgrid terms are closed following the work of Zaichik et al. 2009. The resulting LES strategy is evaluated based on filtered DNS results.
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
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.
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).
NASA Astrophysics Data System (ADS)
Dunn, Dennis; Squires, Kyle
2015-11-01
Modeling dispersions of particles in multiphase flows is especially challenging in gas-solid suspensions. Lagrangian methods are suitable for dilute particle mediums, but are not cost effective at denser concentrations and impose additional modeling challenges. A moderately dense particle phase is neither sufficiently dense for a continuum limit assumption (collisional equilibrium) nor sufficiently dilute for a Lagrangian method, and resides in the intermediate regime under consideration in the current work. A quadrature-based moment method (QBMM) is chosen to simulate a particle-laden turbulent channel flow considering inter-particle collision effects. In quadrature-based approaches similarly behaving particles may be grouped together and treated in a stochastic manner within an Eulerian framework. Specifically, the Conditional Quadrature Method of Moments (CQMOM) is implemented to discretize a fully 3-D velocity space and capture particle trajectory crossing (PTC). This has the potential for large computational savings as compared to Lagrangian methods, especially when dense collisions are prominent. The probability density function is discretized with a two-point-quadrature in each dimension - the minimum requirement to capture PTC and enforce collisions. Predictions of the channel flow demonstrate that the collision treatment leads to the expected effects (e.g., redistribution of kinetic energy) and also offer improved accuracy relative to simpler approaches.
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)
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.
Yoshimatsu, Katsunori
2012-06-01
The four-fifths law for third-order longitudinal moments is examined, using direct numerical simulation (DNS) data on three-dimensional (3D) forced incompressible magnetohydrodynamic (MHD) turbulence without a uniformly imposed magnetic field in a periodic box. The magnetic Prandtl number is set to one, and the number of grid points is 512(3). A generalized Kármán-Howarth-Kolmogorov equation for second-order velocity moments in isotropic MHD turbulence is extended to anisotropic MHD turbulence by means of a spherical average over the direction of r. Here, r is a separation vector. The viscous, forcing, anisotropic and nonstationary terms in the generalized equation are quantified. It is found that the influence of the anisotropic terms on the four-fifths law is negligible at small scales, compared to that of the viscous term. However, the influence of the directional anisotropy, which is measured by the departure of the third-order moments in a particular direction of r from the spherically averaged ones, on the four-fifths law is suggested to be substantial, at least in the case studied here.
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
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.
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.
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 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.
NASA Astrophysics Data System (ADS)
Manickam, B.; Franke, J.; Muppala, S. P. R.; Dinkelacker, F.
In this LES study, an algebraic flame surface wrinkling model based on the progress variable gradient approach is validated for lean premixed turbulent propane/air flames measured on VOLVO test rig. These combustion results are analyzed for uncertainty in the solution using two quality assessment techniques.
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.
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
Mechanics of Turbulence of Multicomponent Gases
NASA Astrophysics Data System (ADS)
Marov, Mikhail Ya.; Kolesnichenko, Aleksander V.
2002-02-01
Turbulence in multicomponent reacting gas mixtures is an important mechanism underlying numerous natural phenomena closely related to the study of our space environment. This book develops a new mathematical approach for modelling multicomponent gas turbulence that adequately describes the combined processes of dynamics and heat and mass transfer when chemical kinetics and turbulent mixing are equally important. The developed models include the evolutionary transfer equations for the single-point second correlation moments of turbulent fluctuations of thermohydrodynamical parameters. The phenomenological approach to the closure problem in hydrodynamic equations of mean motion at the level of the first order moments is based on the thermodynamics of irreversible processes and enables defining relationships in a more general form as compared to those conventionally deduced using the mixing path concept. Based on the developed approach, turbulent exchange factors for a planetary upper atmosphere are evaluated, and a turbulent model of a protoplanetary accretion gas-dust disk involving heat and mass transfer and coagulation is also considered. As compared to previously published books on the problem of turbulence, this book deals, for the first time, with the complicated models of reacting gas mixtures. It is intended for graduate and postgraduate students in the fields of fluid gas dynamics, astrophysics, space physics, planetary sciences, and aeronomy, and especially for those dealing with computer modelling of the processes in such natural media. The book may also be of interest to specialists in the relevant fields of ecology, engineering, and material processing.
Ahmed, Khurshid; Munawar, Muhammad; Chakraborty, Rabin; Hartono, Beny; Yusri, Achmad
2015-01-01
Rupture of sinus of Valsalva (SV) is a rare occurrence with a wide spectrum of presentation, ranging from an asymptomatic murmur to cardiogenic shock or even sudden cardiac death. We hereby report a case which was successfully closed by transcatheter technique. In this case, ruptured SV was entered from the aorta, an arteriovenous loop was created and device was implanted using a venous approach. The procedure was safe, effective and uncomplicated, obviating the need for surgery. In this case, the authors report for the first time the use of echo color Doppler turbulent flow jet diameter as a reference value for sizing the device.
NASA Astrophysics Data System (ADS)
Leitch, A. S.; Nesic, Z.; Christen, A.; Black, T. A.
2010-12-01
opposing gradient in manual chamber-measured soil CO2 effluxes. The additional CO2 difference measurement period at the 2.6-m height (with IRGAs measuring at 2 Hz) also included 5 CSAT3 sonic anemometers measuring at the same locations at 10 Hz. The setup permits back-of-the-envelope calculation of horizontal turbulent CO2 flux divergence along the 73.5-m transect, a term in the scalar conservation equation which has received much interest but little quantification in the literature. The IRGAs also measured high frequency water vapour concentrations, permitting the calculation of (horizontal) turbulent and (horizontal and vertical) advective H2O fluxes. H2O fluxes other than the vertical turbulent flux are not routinely calculated, but may have the potential to shed light on the energy-balance closure problem in the same manner as advective CO2 fluxes comment on the friction velocity correction procedure. Horizontal turbulent carbon dioxide flux divergence and energy balance closure will be discussed, along with final conclusions for advective carbon dioxide fluxes at DF49.
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
PDF modeling of turbulence-radiation interactions
Mazumder, S.; Modest, M.F.
1997-07-01
The interactions between turbulence and radiation, although acknowledged and qualitatively understood over the last several decades, are extremely difficult to model. Traditional Eulerian turbulence models are incapable of addressing the closure problem for any realistic reactive flow situation, because of the large number of unknown turbulent moments that need to be modeled. A novel approach, based on the velocity-composition joint probability density function (PDF) method, is presented. This approach is Lagrangian in nature and provides an elegant and feasible alternative to turbulence closure. A mixed Monte Carlo/finite-volume technique is used to simulate a bluff-body-stabilized methane-air diffusion flame in a two-dimensional planar recirculating combustor, and enables treatment of turbulence in recirculating flows, finite-rate chemistry, and multiple-band radiation calculations within the CPU limitations of a standard single-processor workstation. Results demonstrate the role of radiation and turbulence-radiation interactions in altering the overall flame structure, the wall heat loads, and the overall heat emission by the flame at various Reynolds numbers and equivalence ratios.
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
CFD Simulation of the Turbulent Flow and Heat Transfer in a Bare Rod Bundle
In, W.K.; Shin, C.H.; Oh, D.S.; Chun, T.H.
2004-07-01
A computational fluid dynamics(CFD) analysis has been performed to investigate the turbulent flow and heat transfer in a triangular rod bundle with pitch-to-diameter ratios(P/D) of 1.06 and 1.12. The CFD predictions using various turbulence models were compared with the experimental results. Anisotropic turbulence models(nonlinear k - {epsilon} and second-moment closure models) predicted the turbulence-driven secondary flow in the triangular subchannel and the distributions of the time mean velocity and temperature showing a significantly improved agreement with the measurements from the linear standard k - {epsilon} model. The anisotropic turbulence models predicted the turbulence structure for a rod bundle with a large P/D fairly well but could not predict the very high turbulent intensity of the azimuthal velocity observed in the narrow flow region(gap) for a rod bundle with a small P/D. (authors)
Mizuno, Y; Ohi, K; Sogabe, T; Yamamoto, Y; Kaneda, Y
2010-09-01
A numerical analysis is made on the four-point correlation function in a similarity range of a model of two-dimensional passive scalar field ψ advected by a turbulent velocity field with infinitely small correlation time. The model yields an exact closure equation for the four-point correlation Ψ{4} of ψ, which may be casted into the form of an eigenvalue problem in the similarity range. The analysis of the eigenvalue problem gives not only the scale dependence of Ψ{4} , but also the dependence on the configuration of the four points. The numerical analysis gives S4(R)∝R{ζ{4}} in the similarity range in which S2(R)∝R{ζ{2}} , where S_{N} is the structure function defined by S{N}(R)≡⟨[ψ(x+R)-ψ(x)]{N} and ζ{4}≠2ζ{2} . The estimate of ζ_{4} by the numerical analysis of the eigenvalue problem is in good agreement with numerical simulations so far reported. The agreement supports the idea of universality of the exponent ζ{4} in the sense that ζ_{4} is insensitive to conditions of ψ outside the similarity range. The numerical analysis also shows that the correlation C(R,r)≡[ψ(x+R)-ψ(x)]{2}[ψ(x+r)-ψ(x)]{2}> is stronger than that given by the joint-normal approximation, and scales like C(R,r)∝(r/R){χ} for r/R<1 with R and r in the similarity range, where χ is a constant depending on the angle between R and r .
Analytical theories of turbulence and the epsilon expansion
NASA Astrophysics Data System (ADS)
Dannevik, William P.; Yakhot, Victor; Orszag, Steven A.
1987-07-01
The fixed-point form of hydrodynamic equations emerging from renormalization group (RNG) analysis of strong turbulence is analyzed using perturbation expansion in powers of the renormalized coupling constant. The stochastic models adopted to describe the universality of small scales and the basics of the RNG analysis are outlined. The properties of the analytical closures for the moment hierarchy derived by simple perturbation expansion are explored, and the Kolmogorov constant is computed. The procedure for diffusion of a passive scalar is outlined, and the derivation of turbulent diffusivity and the Batchelor constant is presented.
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.
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.
NASA Astrophysics Data System (ADS)
Varma, A. K.; Sandri, G.; Donaldson, C. Dup.
1980-01-01
Models for the scalar probability density function (pdf) have to be developed to achieve closure of turbulent transport equations for mixing and reacting flows. The best statistical bounds on a number of moments for two and three species flows have been derived and have been used to construct and test a delta function 'typical eddy' pdf model. It has been proven that for two species a rational pdf composed only of delta functions can always be constructed at any point within the statistically valid moment space. The delta function model and a canonical pdf model have been directly compared to experimental pdf measurements and both the models show good agreement for higher-order moments, but the delta function model is simpler to construct and is recommended for closure of the transport equations for mixing flows.
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.
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).
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).
Simulating a Cold-Air Outbreak with SHOC (Simplified Higher-Order Closure)
NASA Astrophysics Data System (ADS)
Krueger, S. K.; Bogenschutz, P.
2013-12-01
The Grey Zone Project aims to systematically explore convective transport and cloud processes in weather and climate models at various resolutions, ranging from high resolution turbulent resolving scales all the way to coarse resolutions that require full parameterized descriptions of these processes. The first Grey Zone intercomparison case is based on observations of a cold air outbreak during the CONSTRAIN field campaign. The purpose of the intercomparison is two-fold: First, through systematically varying the horizontal resolution, the intercomparison will aim to assess the relative contributions of the resolved and the subgrid-scale (SGS) cloud and convective processes in the Grey Zone for the present CONSTRAIN case. Second, the intercomparison is interesting in its own right as it is the first time that a comprehensive mid-latitude cold-air outbreak case has been organized. We will participate by using a version of a cloud-resolving model, SAM (System for Atmospheric Modeling), that 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
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.
Lattice Boltzmann Representations of MHD Turbulence
NASA Astrophysics Data System (ADS)
Vahala, George; Vahala, Linda; Soe, Min; Flint, Christopher
2013-10-01
Lattice Botlzmann algorithms are an ideally parallelized method for the solutions of macroscopic nonlinear equations of physics - like resistive MHD. In its simplest LB representation one introduces a scalar distribution for the density-velocity fields and a vector distribution for the magnetic field. An important feature is that gradients of certain macroscopic fields can be represented by local moments of the mesoscopic distribution functions. In particular, div B = 0 can be exactly enforced to machine accuracy, without any divergence cleaning. One of the problems facing the explicit LB code is numerical instabilities. Methods to permit strong turbulence simulations include: (a) moving from a single BGK to multiple collisional relaxation, (b) quasi-equilibria and central moment enhanced LB representations. The LB turbulence modeling of Ansumali et al. to Navier-Stokes turbulence will be extended to MHD in which in its noted that filtering and Chapman-Enskog limits do not commute. In the NS-case, it leads to unique Samgorinsky closure scheme, with definite filter width.
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.
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…
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.
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.
Closure phase and lucky imaging.
Rhodes, William T
2009-01-01
Since its introduction by Jennison in 1958, the closure-phase method for removing the effects of electrical path-length errors in radio astronomy and of atmospheric turbulence in optical astronomy has been based on the non-redundant-spacing triple interferometer. It is shown that through application of lucky imaging concepts it is possible to relax this condition, making closure-phase methods possible with redundantly spaced interferometer configurations and thereby widening their range of application. In particular, a quadruple-interferometer can, under lucky imaging conditions, be treated as though it were a triple interferometer. The slit-annulus aperture is investigated as a special case.
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.
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.
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.
Multiphase Turbulence Modeling for Computational Ship Hydrodynamics
2014-05-30
to the SGS model as bubbles become under-resolved, passing through the numerical Hinze scale. 3 iii. URANS closure modeling by analysis of the...variable density turbulence) for URANS models have been developed and tested a priori for turbulent mass flux and kinetic energy. The iLES...well as established the importance of turbulent mass flux and anisotropy in the wake that has guided the development of URANS closure models. This
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.
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.
Sable, D. E.
1985-06-11
A closure device connectible to a well head through which the polished rod of a rod string extends into a well tubing for operating pump means for moving well fluids to a surface flow conductor, the closure device having a tubular ram provided with a packing or plug for closing an annular passage between the polished rod and a tubular body connected to the well head above a lateral port of the tubular body, the tubular ram and the tubular body having thread means for moving the plug between an operative lower position wherein it closes the annular passage when the rod string is stationary and on inoperative upper position; seal means between the ram and the polished rod spaced above the plug; and a plurality of independent seal means between the ram and the tubular body operative when the plug is in its inoperative position. The plug of the closure device is especially adapted to operate under high temperature and pressure conditions of the well, as during steam injection operations when the rod string is stationary, to protect the seal means from high pressures and temperatures as well as any fluids which may be corrosive or otherwise deleterious to the substance of which the seal means are made.
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
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.
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.
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.
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
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.
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.
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.
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.
A nonlocal fluid closure for antiparallel reconnection
NASA Astrophysics Data System (ADS)
Ng, Jonathan; Hakim, A.; Bhattacharjee, A.
2016-10-01
The integration of kinetic effects in fluid models is an important problem in global simulations of the Earth's magnetosphere and space weather modelling. In particular, it has been shown that ion kinetics play an important role in the dynamics of large reconnecting systems, and that fluid models can account of some of these effects. Here we introduce a new fluid model and closure for collisionless magnetic reconnection and more general applications. Taking moments of the kinetic equation, we evolve the full pressure tensor for electrons and ions, which includes the off diagonal terms necessary for reconnection. Kinetic effects are recovered by using a nonlocal heat flux closure, which approximates linear Landau damping in the fluid framework. Using the island coalescence problem as a test, we show how the nonlocal ion closure improves on the typical collisional closures used for ten-moment models and circumvents the need for a colllisional free parameter. Finally, we extend the closure to study guide-field reconnection and discuss the implementation of a twenty-moment model. Supported by: NSF Grant No. AGS-1338944, DOE Contract DE-AC02-09CH11466.
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.
Physics-Preserving Turbulent Closure Models
2001-08-01
REQUIREMENTS (2) AND (3) 2.1.1. q - v relation Theorem 1. f is independent of v. Proof From the principle of observer transformations ( Geankoplis 1983...constraints on large-eddy simulations, Theoret. Comput. Fluid Dynamics, 9, 85-102. Geankoplis , C. J. (1983) Transport Processes: Momentum, Heat, and Mass
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.
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.
Filtering skill for turbulent signals for a suite of nonlinear and linear extended Kalman filters
NASA Astrophysics Data System (ADS)
Branicki, M.; Gershgorin, B.; Majda, A. J.
2012-02-01
The filtering skill for turbulent signals from nature is often limited by errors due to utilizing an imperfect forecast model. In particular, real-time filtering and prediction when very limited or no a posteriori analysis is possible (e.g. spread of pollutants, storm surges, tsunami detection, etc.) introduces a number of additional challenges to the problem. Here, a suite of filters implementing stochastic parameter estimation for mitigating model error through additive and multiplicative bias correction is examined on a nonlinear, exactly solvable, stochastic test model mimicking turbulent signals in regimes ranging from configurations with strongly intermittent, transient instabilities associated with positive finite-time Lyapunov exponents to laminar behavior. Stochastic Parameterization Extended Kalman Filter (SPEKF), used as a benchmark here, involves exact formulas for propagating the mean and covariance of the augmented forecast model including the unresolved parameters. The remaining filters use the same nonlinear forecast model but they introduce model error through different moment closure approximations and/or linear tangent approximation used for computing the second-order statistics of the augmented stochastic forecast model. A comprehensive study of filter performance is carried out in the presence of various moment closure errors which are enhanced by additional model errors due to incorrect parameters inducing additive and multiplicative stochastic biases. The estimation skill of the unresolved stochastic parameters is also discussed and it is shown that the linear tangent filter, despite its popularity, is completely unreliable in many turbulent regimes for both parameter estimation and filtering; moreover, regimes of filter divergence for the linear tangent filter are identified. The results presented here provide useful guidelines for filtering turbulent, high-dimensional, spatially extended systems with more general model errors, as well as
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.
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.
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).
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.
Exact statistical results for binary mixing and reaction in variable density turbulence
NASA Astrophysics Data System (ADS)
Ristorcelli, J. R.
2017-02-01
We report a number of rigorous statistical results on binary active scalar mixing in variable density turbulence. The study is motivated by mixing between pure fluids with very different densities and whose density intensity is of order unity. Our primary focus is the derivation of exact mathematical results for mixing in variable density turbulence and we do point out the potential fields of application of the results. A binary one step reaction is invoked to derive a metric to asses the state of mixing. The mean reaction rate in variable density turbulent mixing can be expressed, in closed form, using the first order Favre mean variables and the Reynolds averaged density variance, ⟨ρ2⟩ . We show that the normalized density variance, ⟨ρ2⟩ , reflects the reduction of the reaction due to mixing and is a mix metric. The result is mathematically rigorous. The result is the variable density analog, the normalized mass fraction variance ⟨c2⟩ used in constant density turbulent mixing. As a consequence, we demonstrate that use of the analogous normalized Favre variance of the mass fraction, c″ 2˜ , as a mix metric is not theoretically justified in variable density turbulence. We additionally derive expressions relating various second order moments of the mass fraction, specific volume, and density fields. The central role of the density specific volume covariance ⟨ρ v ⟩ is highlighted; it is a key quantity with considerable dynamical significance linking various second order statistics. For laboratory experiments, we have developed exact relations between the Reynolds scalar variance ⟨c2⟩ its Favre analog c″ 2˜ , and various second moments including ⟨ρ v ⟩ . For moment closure models that evolve ⟨ρ v ⟩ and not ⟨ρ2⟩ , we provide a novel expression for ⟨ρ2⟩ in terms of a rational function of ⟨ρ v ⟩ that avoids recourse to Taylor series methods (which do not converge for large density differences). We have derived
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.
Hinton, F. L.; Waltz, R. E.
2006-10-15
Expressions for particle and energy fluxes and heating rates due to turbulence are derived. These fluxes and heating rates are identified from moments of an extended drift-kinetic equation for the equilibrium distribution function. These include neoclassical as well as turbulent diffusion and heating. Phase-space conservation is demonstrated, allowing the drift-kinetic equation to be expressed in conservative form. This facilitates taking moments with few approximations, mainly those consistent with drift kinetics for the equilibrium distribution function and the relative smallness of the fluctuations. The turbulent heating is uniquely defined by choosing the standard gyrokinetic definition for the energy flux. With this definition, most of the heating can be expressed in the form of ohmic heating from turbulent parallel and perpendicular current density perturbations. The latter current is identified with grad-B and curvature drifts, plus terms involving magnetic perturbations (which are smaller for low beta). A small contribution to the heating comes from the divergence of an energy flux that is dependent on the finite gyroradius of the ions. The fluxes and heating rates are expressed in a form that can be easily evaluated from gyrokinetic turbulence simulations.
A closure scheme for chemical master equations.
Smadbeck, Patrick; Kaznessis, Yiannis N
2013-08-27
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.
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
A comparison of three algebraic stress closures for combustor flow calculations
NASA Technical Reports Server (NTRS)
Nikjooy, M.; So, R. M. C.; Hwang, B. C.
1985-01-01
A comparison is made of the performance of two locally nonequilibrium and one equilibrium algebraic stress closures in calculating combustor flows. Effects of four different pressure-strain models on these closure models are also analyzed. The results show that the pressure-strain models have a much greater influence on the calculated mean velocity and turbulence field than the algebraic stress closures, and that the best mean strain model for the pressure-strain terms is that proposed by Launder, Reece and Rodi (1975). However, the equilibrium algebraic stress closure with the Rotta return-to-isotropy model (1951) for the pressure-strain terms gives as good a correlation with measurements as when the Launder et al. mean strain model is included in the pressure-strain model. Finally, comparison of the calculations with the standard k-epsilon closure results show that the algebraic stress closures are better suited for simple turbulent flow calculations.
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
Turbulence Model Discovery with Data-Driven Learning and Optimization
NASA Astrophysics Data System (ADS)
King, Ryan; Hamlington, Peter
2016-11-01
Data-driven techniques have emerged as a useful tool for model development in applications where first-principles approaches are intractable. In this talk, data-driven multi-task learning techniques are used to discover flow-specific optimal turbulence closure models. We use the recently introduced autonomic closure technique to pose an online supervised learning problem created by test filtering turbulent flows in the self-similar inertial range. The autonomic closure is modified to solve the learning problem for all stress components simultaneously with multi-task learning techniques. The closure is further augmented with a feature extraction step that learns a set of orthogonal modes that are optimal at predicting the turbulent stresses. We demonstrate that these modes can be severely truncated to enable drastic reductions in computational costs without compromising the model accuracy. Furthermore, we discuss the potential universality of the extracted features and implications for reduced order modeling of other turbulent flows.
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.
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),…
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.
Pandit, Narendra; Singh, Harjeet; Kumar, Hemanth; Gupta, Rajesh; Verma, G R
2016-11-01
Intestinal loop stoma is a common surgical procedure performed for various benign and malignant abdominal problems, but it rarely undergoes spontaneous closure, without surgical intervention. Two male patients presented to our emergency surgical department with acute abdominal pain. One of them was diagnosed as having rectosigmoid perforation and underwent diversion sigmoid loop colostomy after primary closure of the perforation. The other was a known case of carcinoma of the rectum who had already undergone low anterior resection with covering loop ileostomy; the patient underwent second loop ileostomy, this time for complicated intestinal obstruction. To our surprise, both the loop colostomy and ileostomy closed spontaneously at 8 weeks and 6 weeks, respectively, without any consequences. Spontaneous stoma closure is a rare and interesting event. The exact etiology for spontaneous closure remains unknown, but it may be hypothesized to result from slow retraction of the stoma, added to the concept of a tendency towards spontaneous closure of enterocutaneous fistula.
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.
Magnetohydrodynamic Turbulence and the Geodynamo
NASA Technical Reports Server (NTRS)
Shebalin, John V.
2016-01-01
Recent research results concerning forced, dissipative, rotating magnetohydrodynamic (MHD) turbulence will be discussed. In particular, we present new results from long-time Fourier method (periodic box) simulations in which forcing contains varying amounts of magnetic and kinetic helicity. Numerical results indicate that if MHD turbulence is forced so as to produce a state of relatively constant energy, then the largest-scale components are dominant and quasistationary, and in fact, have an effective dipole moment vector that aligns closely with the rotation axis. The relationship of this work to established results in ideal MHD turbulence, as well as to models of MHD turbulence in a spherical shell will also be presented. These results appear to be very pertinent to understanding the Geodynamo and the origin of its dominant dipole component. Our conclusion is that MHD turbulence, per se, may well contain the origin of the Earth's dipole magnetic field.
NASA Astrophysics Data System (ADS)
Jin, F.; Pan, L.; Watanabe, M.
2005-05-01
The two-way interaction between synoptic eddy and low-frequency flow (SELF), which we will refer to as the SELF interaction, has been recognized for decades to play an important role in the dynamics of the low-frequency variability of the atmospheric circulation. We propose a new framework for studying the dynamics of the SELF interaction and the low-frequency variability in a stormy background flow. By considering a Gaussian flow as a surrogate for the stormy background flow, we expand the traditional climatological basic flow to a synthetic stochastic basic flow. Its ensemble mean is the observed climatological mean flow while its prescribed variance/covariance fields represent the climatological variance/covariance fields of the observed synoptic eddies. Low-frequency anomalies in the traditional month-to-seasonal mean flow and in the variance/covariance fields of the transient eddy flow are viewed as equivalent to the anomalies in the first and second moments of the quasi-stationary stochastic flow ensemble. The linear dynamics of SELF interaction are described by the coupling among the anomalies in first and second moments. Under the assumption that slow changes in the second moments are in quasi-equilibrium with the anomalies in the first moment, an analytical non-local dynamical closure for SELF interaction is obtained. Using this framework, we show that leading low-frequency modes earn their dominance because they can effective organizing the turbulent synoptic flow such that they get reinforced by positive SELF interaction.
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.
Numerical Investigation of a Statistically Stationary Turbulent Reacting Flow
NASA Astrophysics Data System (ADS)
Overholt, Matthew R.; Pope, Stephen B.
1997-11-01
Direct numerical simulation (DNS) has been very useful in the study of inert scalar mixing in turbulent flows, and has recently become feasible for studies of reacting scalars. We have formulated an accessible inhomogeneous nonpremixed turbulent reactive flow for investigating the effects of mixing on reaction and testing mixing models. The mixture fraction-progress variable approach is used with a model single-step reversible finite-rate thermochemistry, yielding non-trivial stationary solutions corresponding to stable reaction and allowing local extinction to occur. A mean gradient in the mixture fraction gives rise to stationarity without forcing, as well as a flame brush. A range of reaction zone thicknesses and Damkohler numbers are examined, yielding a broad spectrum of behavior, ranging from thick to thin flames, and from local extinction to near equilibrium. Based on this study results from full probability density function (PDF) simulations using the IEM and EMST mixing models are evaluated. Conditional moment closure (CMC) results are evaluated as well.
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.
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.
Joint PDF Modelling of Turbulent Flow and Dispersion in an Urban Street Canyon
NASA Astrophysics Data System (ADS)
Bakosi, J.; Franzese, P.; Boybeyi, Z.
2009-05-01
The joint probability density function (PDF) of turbulent velocity and concentration of a passive scalar in an urban street canyon is computed using a newly developed particle-in-cell Monte Carlo method. Compared to moment closures, the PDF methodology provides the full one-point one-time PDF of the underlying fields containing all higher moments and correlations. The small-scale mixing of the scalar released from a concentrated source at the street level is modelled by the interaction by exchange with the conditional mean (IECM) model, with a micro-mixing time scale designed for geometrically complex settings. The boundary layer along no-slip walls (building sides and tops) is fully resolved using an elliptic relaxation technique, which captures the high anisotropy and inhomogeneity of the Reynolds stress tensor in these regions. A less computationally intensive technique based on wall functions to represent the boundary layers and its effect on the solution are also explored. The calculated statistics are compared to experimental data and large-eddy simulation. The present work can be considered as the first example of computation of the full joint PDF of velocity and a transported passive scalar in an urban setting. The methodology proves successful in providing high level statistical information on the turbulence and pollutant concentration fields in complex urban scenarios.
Parallel closures in an inhomogeneous magnetic field
NASA Astrophysics Data System (ADS)
Lee, Hankyu; Ji, Jeong-Young
2016-10-01
We solve a reduced drift kinetic equation with a Krook-type model collision operator to obtain parallel closures. Grid points in the velocity space are chosen for Gauss-Laguerre quadrature to take closure moments. For trapped and passing regimes, analytical solutions are expressed as kernel-weighted integrals of thermodynamic drives. The analytical sloutions are compared to numerical solutions obtained from a finite difference method. Inverting the free streaming operator near a bouncing point is investigated to improve accuracy of solutions. Research supported by the U.S. DOE under Grant Nos. DE-SC0014033, DE-FG02-04ER54746, DE-FC02-04ER54798, and DE-FC02-05ER54812.
NASA Technical Reports Server (NTRS)
Chandler, C. L.
1987-01-01
In order to forecast turbulence, one needs to have an understanding of the cause of turbulence. Therefore, an attempt is made to show the atmospheric structure that often results when aircraft encounter moderate or greater turbulence. The analysis is based on thousands of hours of observations of flights over the past 39 years of aviation meteorology.
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.
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)
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.
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.
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.
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.
NASA Technical Reports Server (NTRS)
Ahmed, S.; Tannehill, J. C.
1990-01-01
A new nonequilibrium turbulence closure model has been developed for computing wall bounded two-dimensional turbulent flows. This two-layer eddy viscosity model was motivated by the success of the Johnson-King model in separated flow regions. The influence of history effects are described by an ordinary differential equation developed from the turbulent kinetic energy equation. The performance of the present model has been evaluated by solving the flow around three airfoils using the Reynolds time-averaged Navier-Stokes equations. Excellent results were obtained for both attached and separated turbulent flows about the NACA 0012 airfoil, the RAE 2822 airfoil, and the Integrated Technology A 153W airfoil. Based on the comparison of the numerical solutions with the available experimental data, it is concluded that the new nonequilibrium turbulence model accurately captures the history effects of convection and diffusion on turbulence.
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.
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.
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.
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.
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.
The higher moments in the Lundgren model conform with Kolmogorov scaling
NASA Astrophysics Data System (ADS)
Segel, Daniel
1995-12-01
We calculate the structure functions of the higher moments of the vorticity in the framework of Lundgren's spiral model of turbulence. We show that they conform to the scaling expected from Kolmogorov's scaling hypothesis of 1941, and explain the result.
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.
NASA Astrophysics Data System (ADS)
Schneider, Florian
2016-10-01
This paper provides a generalization of the realizability-preserving discontinuous-Galerkin scheme given in [3] to general full-moment models that can be closed analytically. It is applied to the class of Kershaw closures, which are able to provide a cheap closure of the moment problem. This results in an efficient algorithm for the underlying linear transport equation. The efficiency of high-order methods is demonstrated using numerical convergence tests and non-smooth benchmark problems.
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)
Lucey, Paula A
2002-01-01
Hospital closures have become more common. The challenges facing a nursing leader in this situation are complex and difficult. This author suggests that looking for new beginnings rather than focusing on endings created an approach to closing a public hospital. The article includes approaches to employee morale, staffing, and patient care.
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.
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.
Ring closure in actin polymers
NASA Astrophysics Data System (ADS)
Sinha, Supurna; Chattopadhyay, Sebanti
2017-03-01
We present an analysis for the ring closure probability of semiflexible polymers within the pure bend Worm Like Chain (WLC) model. The ring closure probability predicted from our analysis can be tested against fluorescent actin cyclization experiments. We also discuss the effect of ring closure on bend angle fluctuations in actin polymers.
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.
Regularization of turbulence - a comprehensive modeling approach
NASA Astrophysics Data System (ADS)
Geurts, B. J.
2011-12-01
Turbulence readily arises in numerous flows in nature and technology. The large number of degrees of freedom of turbulence poses serious challenges to numerical approaches aimed at simulating and controlling such flows. While the Navier-Stokes equations are commonly accepted to precisely describe fluid turbulence, alternative coarsened descriptions need to be developed to cope with the wide range of length and time scales. These coarsened descriptions are known as large-eddy simulations in which one aims to capture only the primary features of a flow, at considerably reduced computational effort. Such coarsening introduces a closure problem that requires additional phenomenological modeling. A systematic approach to the closure problem, know as regularization modeling, will be reviewed. Its application to multiphase turbulent will be illustrated in which a basic regularization principle is enforced to physically consistently approximate momentum and scalar transport. Examples of Leray and LANS-alpha regularization are discussed in some detail, as are compatible numerical strategies. We illustrate regularization modeling to turbulence under the influence of rotation and buoyancy and investigate the accuracy with which particle-laden flow can be represented. A discussion of the numerical and modeling errors incurred will be given on the basis of homogeneous isotropic turbulence.
Bubble-induced turbulence study in homogeneous turbulent flow using DNS approach
NASA Astrophysics Data System (ADS)
Feng, Jinyong; Bolotnov, Igor
2015-11-01
The effect of a single bubble on the energy transfer to a homogeneous turbulent flow using DNS approach is investigated for various conditions. The single-phase turbulence is numerically generated by pressure-gradient driven uniform flow through a fully resolved turbulence generating grid. The turbulent intensity measured is uniform normal to the flow direction. The decay rate of the turbulent kinetic energy is validated against analytical power law. The collected instantaneous velocity is used as inflow condition for single-bubble simulations to study the bubble-induced turbulence (BIT). In interface-resolved two-phase simulation the bubble is kept at fixed positions by using a proportional-integral-derivative controller. This simulation set allows estimating the turbulent kinetic energy before and after the bubble, quantifying the BIT. Effects of bubble deformability, velocity and turbulent intensity are separately studied. We observe that for a nearly spherical bubble, the bubble-induced turbulence is positive, increasing the level of turbulent kinetic energy in the liquid phase. BIT is influenced by the other studied parameters and the presented work will contribute to the closure BIT model development in multiphase computational fluid dynamics modeling. The work is supported by NSF-CBET-Fluid Dynamics, Award #1333993.
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.
Hospital closure and economic efficiency.
Capps, Cory; Dranove, David; Lindrooth, Richard C
2010-01-01
We present a new framework for assessing the effects of hospital closures on social welfare and the local economy. While patient welfare necessarily declines when patients lose access to a hospital, closures also tend to reduce costs. We study five hospital closures in two states and find that urban hospital bailouts reduce aggregate social welfare: on balance, the cost savings from closures more than offset the reduction in patient welfare. However, because some of the cost savings are shared nationally, total surplus in the local community may decline following a hospital closure.
Quasisteady turbulence driven by runaway electrons
Muschietti, L.; Appert, K.; Vaclavik, J.
1982-07-01
The evolution of the turbulence driven by runaway electrons has been followed by means of a computer code based on the quasilinear equations. The evolution is not characterized by periodic relaxations as claimed in previous works but ends in a quasisteady turbulent, yet very persistent state, accessible from different initial conditions. This discrepancy is clarified as being due to the excessive stiffness of the moment equations used to demonstrate the relaxations. Moreover, a theory is developed to interpret the quasisteady state found.
Recommendations for managing hospital closure.
van der Wal, R; Bouthillette, F; Havlovic, S J
1998-01-01
An acute care hospital was closed by the British Columbia Ministry of Health in 1993. A research study was conducted to investigate the ways closure of the hospital affected hospital employees and to identify ways to facilitate the closure/reorganization process. Unstructured interviews were conducted with 25 employees around the time of closure and six months after the closure. In the category Living with Closure, six themes arose from the qualitative analysis. They related to (1) provision of information; (2) effect of closure on the working environment and colleagues; (3) perceived stress; (4) recognition of one's worth; (5) provision of support services; and (6) the process of having a new job. The authors offer recommendations stemming from the analysis, which are intended to assist others planning for future hospital reorganizations or closures.
NASA Astrophysics Data System (ADS)
Tsubota, Makoto
2008-11-01
The present article reviews the recent developments in the physics of quantum turbulence. Quantum turbulence (QT) was discovered in superfluid 4He in the 1950s, and the research has tended toward a new direction since the mid 90s. The similarities and differences between quantum and classical turbulence have become an important area of research. QT is comprised of quantized vortices that are definite topological defects, being expected to yield a model of turbulence that is much simpler than the classical model. The general introduction of the issue and a brief review on classical turbulence are followed by a description of the dynamics of quantized vortices. Then, we discuss the energy spectrum of QT at very low temperatures. At low wavenumbers, the energy is transferred through the Richardson cascade of quantized vortices, and the spectrum obeys the Kolmogorov law, which is the most important statistical law in turbulence; this classical region shows the similarity to conventional turbulence. At higher wavenumbers, the energy is transferred by the Kelvin-wave cascade on each vortex. This quantum regime depends strongly on the nature of each quantized vortex. The possible dissipation mechanism is discussed. Finally, important new experimental studies, which include investigations into temperature-dependent transition to QT, dissipation at very low temperatures, QT created by vibrating structures, and visualization of QT, are reviewed. The present article concludes with a brief look at QT in atomic Bose-Einstein condensates.
NASA Technical Reports Server (NTRS)
Webbon, B. W.; Vykukal, H. C. (Inventor)
1978-01-01
A simple, economical and reliable entry closure is described for joining opposite halves of a torso section for a pressure suit in a manner which simplifies self-donning. A single coupling joins coaxially aligned, axially separable, tubular segments of a hard spacesuit along an angulated zone of separation, adapted to be mated in an hermetrically sealing relation. A releasable C section clamp secures the members in their mated relationship.
Moment estimation for chemically reacting systems by extended Kalman filtering.
Ruess, J; Milias-Argeitis, A; Summers, S; Lygeros, J
2011-10-28
In stochastic models of chemically reacting systems that contain bimolecular reactions, the dynamics of the moments of order up to n of the species populations do not form a closed system, in the sense that their time-derivatives depend on moments of order n + 1. To close the dynamics, the moments of order n + 1 are generally approximated by nonlinear functions of the lower order moments. If the molecule counts of some of the species have a high probability of becoming zero, such approximations may lead to imprecise results and stochastic simulation is the only viable alternative for system analysis. Stochastic simulation can produce exact realizations of chemically reacting systems, but tends to become computationally expensive, especially for stiff systems that involve reactions at different time scales. Further, in some systems, important stochastic events can be very rare and many simulations are necessary to obtain accurate estimates. The computational cost of stochastic simulation can then be prohibitively large. In this paper, we propose a novel method for estimating the moments of chemically reacting systems. The method is based on closing the moment dynamics by replacing the moments of order n + 1 by estimates calculated from a small number of stochastic simulation runs. The resulting stochastic system is then used in an extended Kalman filter, where estimates of the moments of order up to n, obtained from the same simulation, serve as outputs of the system. While the initial motivation for the method was improving over the performance of stochastic simulation and moment closure methods, we also demonstrate that it can be used in an experimental setting to estimate moments of species that cannot be measured directly from time course measurements of the moments of other species.
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.
Turbulent transport in premixed flames
NASA Technical Reports Server (NTRS)
Rutland, C. J.; Cant, R. S.
1994-01-01
Simulations of planar, premixed turbulent flames with heat release were used to study turbulent transport. Reynolds stress and Reynolds flux budgets were obtained and used to guide the investigation of important physical effects. Essentially all pressure terms in the transport equations were found to be significant. In the Reynolds flux equations, these terms are the major source of counter-gradient transport. Viscous and molecular terms were also found to be significant, with both dilatational and solenoidal terms contributing to the Reynolds stress dissipation. The BML theory of premixed turbulent combustion was critically examined in detail. The BML bimodal pdf was found to agree well with the DNS data. All BML decompositions, through the third moments, show very good agreement with the DNS results. Several BML models for conditional terms were checked using the DNS data and were found to require more extensive development.
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.
A stochastic subgrid model for sheared turbulence
NASA Astrophysics Data System (ADS)
Bertoglio, J. P.
A new subgrid model for homogeneous turbulence is proposed. The model is used in a method of Large Eddy Simulation coupled with an E.D.Q.N.M. prediction of the statistical properties of the small scales. The model is stochastic in order to allow a 'disaveraging' of the informations provided by the E.D.Q.N.M. closure. It is based on stochastic amplitude equations for two-point closures. It allows backflow of energy from the small scales, introduces stochasticity into L.E.S., and is well adapted to nonisotropic fields. A few results are presented here.
On the Lundgren-Townsend model of turbulent fine scales
NASA Astrophysics Data System (ADS)
Pullin, D. I.; Saffman, P. G.
1993-01-01
Vorticity and velocity-derivative moments for homogeneous isotropic turbulence are calculated using the strained-spiral vortex model of turbulent fine scales given by Lundgren (1982). A specific form of the relaxing spiral vortex is proposed, modeled by a rolling-up vortex layer embedded in a background containing opposite signed vorticity and with zero total circulation at infinity.
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.
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.
Statistics of High Atwood Number Turbulent Mixing Layers
NASA Astrophysics Data System (ADS)
Baltzer, Jon; Livescu, Daniel
2015-11-01
The statistical properties of incompressible shear-driven planar mixing layers between two miscible streams of fluids with different densities are investigated by means of Direct Numerical Simulations. The simulations begin from a thin interface perturbed by a thin broadband random disturbance, and the mixing layers are allowed to develop to self-similar states. The temporal simulations are performed in unprecedented domain sizes, with grid sizes up to 6144 x 2048 x 1536, which allows turbulent structures to grow and merge naturally. This allows the flow to reach states far-removed from the initial disturbances, thereby enabling high-quality statistics to be obtained for higher moments, pdfs, and other quantities critical to developing closure models. A wide range of Atwood numbers are explored, ranging from nearly constant density to At=0.87. The consequences of increasing the density contrast are investigated for global quantities, such as growth rates, and asymmetries that form in statistical profiles. Additional simulations in smaller domains are performed to study the effects of domain size.
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.
NASA Technical Reports Server (NTRS)
Ringnes, E. A.; Frost, W.
1986-01-01
The influence of spanwise turbulence on airplane dynamic behavior is determined. Calculations are based on data collected from test flights with the NASA B-57 research aircraft. The approach is to first compute aerodynamic forces and moments due to a spanwise distribution of angle of attack and airspeed. Secondly, these quantities are incorporated into the equations of motion. Simulation of flights done with the effects of spanwise turbulence included are compared to simulations without any spanwise turbulence. The findings of the study are that the moments developed by turbulence along the span are significant and that more realistic flight simulation can be achieved by including the spanwise turbulence terms.
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.
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
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
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.
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
Large eddy simulation and direct numerical simulation of high speed turbulent reacting flows
NASA Astrophysics Data System (ADS)
Adumitroaie, V.; Frankel, S. H.; Madnia, C. K.; Givi, P.
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
Analysis of surface energy balance closure over heterogeneous surfaces
NASA Astrophysics Data System (ADS)
Kim, Soojin; Lee, Young-Hee; Kim, Kyu Rang; Park, Young-San
2014-11-01
Surface energy balance closure has been examined using eddy covariance measurements and other observations at one industrial and three agricultural sites near the Nakdong River during daytime. Energy balance closure was evaluated by calculating the long-term averaged energy balance ratio (EBR), the ratio of turbulent energy fluxes to available energy, and the statistical regression of turbulent energy fluxes against available energy using half-hourly data. The EBR of all sites ranges from 0.46 to 0.83 while the coefficient of determination ( R 2) ranges from 0.37 to 0.77. The energy balance closure was relatively poor compared to homogeneous sites, indicating the influence of surface heterogeneity. Unmeasured heat storage terms also seem to play a role in the surface energy budget at the industrial and irrigated sites. The energy balance closure was better in conditions of high wind speed, low downward short wave radiation, and high friction velocity, which suggests the role of heat storage term and surface heterogeneity in surface energy balance at these sites. Spectrum analysis shows a sharp roll-off at the low frequency in co-spectrum, which indicates that low-frequency motions do not significantly contribute to turbulent fluxes. Both the spectra and cospectra in unstable conditions show a broad peak indicating the influence of multiple sizes of large eddies over heterogeneous sites. Most of ogive curves for the kinematic latent and sensible heat fluxes reach an asymptote within 30 minutes regardless of the EBR value, indicating that low frequency motion is not a main factor for energy imbalance. However, stationary eddies due to landscape heterogeneity still remains as a possible cause for energy imbalance.
Hybrid Gyrofluid/Gyrokinetic Modeling of Tokamak Turbulence with GryfX
NASA Astrophysics Data System (ADS)
Mandell, Noah; Dorland, Bill; Highcock, Edmund; Hammett, Greg
2016-10-01
Gyrofluid models are more efficient than gyrokinetic models, but have a disadvantage in their potential lack of physics fidelity. Here we present three major improvements to the physics fidelity and speed of gyrofluid models, which we encapsulate in the GryfX gyrofluid turbulence code. First, we implement a new nonlinear closure to model the cascade of free energy simultaneously in k⊥ and v⊥ via nonlinear phase-mixing (NLPM). Second, we use a hybrid algorithm that improves zonal flow physics by simulating zonal flow modes with a fully gyrokinetic model. These two improvements bring heat flux predictions from nonlinear GryfX simulations into agreement with the gyrokinetic code GS2. Third, we implement the equations on modern heterogeneous computing platforms, both as a standalone simulation tool that exploits the power of GPUs and as a component of TRINITY (a transport modeling code for tokamaks). GryfX has a roughly 1,200 times performance advantage over GS2 due to the combination of GPU acceleration and the reduction of hundreds of velocity space grid points to six gyrofluid moments. This makes GryfX ideal for large parameter scans, and enables the use of the TRINITY-GryfX system for efficient multi-scale analysis of tokamak turbulence on transport time scales. Present address: Chalmers University, Gothenburg, Sweden.
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.
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)
Acres, W. R.
1980-01-01
Safe reentry of the shuttle orbiter requires that the payload bay doors be closed and securely latched. Since a malfunction in the door drive or bulkhead latch systems could make safe reentry impossible, the requirement to provide tools to manually close and secure the doors was implemented. The tools would disconnect a disabled door or latch closure system and close and secure the doors if the normal system failed. The tools required to perform these tasks have evolved into a set that consists of a tubing cutter, a winch, a latching tool, and a bolt extractor. The design, fabrication, and performance tests of each tool are described.
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.
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…
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
Espinoza, Roberta
2012-01-01
Educators can have a powerful influence on the future of low-income and minority students whose paths might appear uncertain. By developing trusting relationships, acting as mentors, and sharing information about the education system, teachers, counselors, and other adults can create pivotal moments that transform students' lives. Espinoza shares…
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.
NASA Astrophysics Data System (ADS)
Colucci, Paul John
A methodology termed the "filtered density function" (FDF) is developed and implemented for large eddy simulation (LES) of chemically reacting turbulent flows. In this methodology, the effects of the unresolved scalar fluctuations are taken into account by considering the probability density function (PDF) of the subgrid scale (SGS) scalar quantities. The transport equation governing the evolution of the FDF is derived in which the effect of chemical reaction appears in a closed form. The influences of scalar mixing and convection within the subgrid are modeled. The generalization to variable density flows is made through consideration of the filtered mass density function (FMDF). The FDF and FMDF transport equations are solved numerically via a Lagrangian Monte Carlo scheme in which the solutions of equivalent stochastic differential equations (SDEs) are obtained. The consistency of the approach, the convergence of the Monte Carlo solution, and the performance of the closures employed in the FDF and FMDF transport equations are assessed by comparisons with results obtained by direct numerical simulation (DNS) and by conventional LES procedures in which the first two SGS scalar moments are obtained by a finite difference method (LES-FD). In non-reacting flows, the Monte Carlo solution yields results similar to those via LES-FD for the first two SGS moments. The advantage of the methodology is demonstrated by its use in LES of reacting flows. In the absence of a closure for the SGS scalar fluctuations, the LES-FD results are significantly different from those based on DNS. Comparatively, the FDF and FMDF yield much better agreement with filtered DNS results. The methodology is also tested by comparative assessments against experimental data for a heat releasing hydrogen-fluorine reacting mixing layer.
Streamline curvature effects on turbulent boundary layers
NASA Technical Reports Server (NTRS)
Wilcox, D. C.; Chambers, T. L.
1976-01-01
A theoretical tool has been developed for predicting, in a nonempirical manner, effects of streamline curvature and coordinate-system rotation on turbulent boundary layers. The second-order closure scheme developed by Wilcox and Traci has been generalized for curved streamline flow and for flow in a rotating coordinate system. A physically based straightforward argument shows that curvature/rotation primarily affects the turbulent mixing energy; the argument yields suitable curvature/rotation terms which are added to the mixing-energy equation. Singular-perturbation solutions valid in the wall layer of a curved-wall boundary layer and a fully developed rotating channel flow demonstrate that, with the curvature/rotation terms, the model predicts the curved-wall and the rotating coordinate system laws of the wall. Results of numerical computations of curved-wall boundary layers and of rotating channel flow show that curvature/rotation effects can be computed accurately with second-order closure.
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.
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.
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
NASA Astrophysics Data System (ADS)
Skrbek, L.
2011-12-01
We review physical properties of quantum fluids He II and 3He-B, where quantum turbulence (QT) has been studied experimentally. Basic properties of QT in these working fluids are discussed within the phenomenological two-fluid model introduced by Landau. We consider counterflows in which the normal and superfluid components flow against each other, as well as co-flows in which the direction of the two fluids is the same. We pay special attention to the important case of zero temperature limit, where QT represents an interesting and probably the simplest prototype of three-dimensional turbulence in fluids. Experimental techniques to explore QT such as second sound attenuation, Andreev reflection, NMR, ion propagation are briefly introduced and results of various experiments on so-called Vinen QT and Kolmogorov QT both in He II and 3He are discussed, emphasizing similarities and differences between classical and quantum turbulence.
Kinematics of velocity and vorticity correlations in turbulent flow
NASA Astrophysics Data System (ADS)
Bernard, P. S.
1983-08-01
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.
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.
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.
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.
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.
Representation of the Essential Flame-Turbulence Dynamics using Specific Flame-Vortex Interactions
NASA Astrophysics Data System (ADS)
Paes, Paulo L. K.; Brasseur, James; Xuan, Yuan
2016-11-01
Many engineering applications involve turbulent reacting flows, where nonlinear, multi-scale turbulence-combustion couplings are important. Directly resolving the complex fluid dynamics involved in these applications is associated with prohibitive computational costs, which makes it necessary to employ turbulent closure models and turbulent combustion models to account for the effects of unresolved scales on resolved scales. Most of these existent closure models rely on some assumptions about the turbulence dynamics and the scale separation between turbulence and the different combustion processes. A better understanding of the turbulence-combustion interactions is required for the development of more accurate, physics-based sub-grid-scale models for turbulent reacting flows. Instead of developing an extreme-resolution, high Reynolds number turbulent flame simulation that is limited to a localized part of the regime diagram, in this work, we propose to develop a series of numerical experiments of simplified interactions between a laminar premixed flame and specified vortex distributions of varying strengths and scales to capture the essential flame-turbulence dynamics over distinct premixed turbulent combustion regimes. The response of the laminar flame to different vortex time and length scales is investigated and the physical relevance of each dataset to practical turbulent premixed flames is discussed.
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.
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
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.
Local isotropy in buoyancy-generated turbulence
NASA Astrophysics Data System (ADS)
Chasnov, Jeffrey R.
1991-12-01
Batchelor et al. (1992) recently considered the turbulent motion generated by buoyancy forces acting on random fluctuations in the density of an infinite fluid. This homogeneous buoyancy-generated flow field with zero mean density gradient was conceived as an idealized system which, like isotropic turbulence, may be useful as a vehicle for the general study of turbulence. The Batchelor et al. study relied partly on theoretical analysis and partly on direct and large-eddy numerical simulations of the flow field. To this mix, we add here a two-point closure study based on the eddy-damped quasi-normal Markovian (EDQNM) closure model applied to axisymmetric turbulence. The EDQNM model has been shown to yield reasonably accurate quantitative results for a variety of problems in homogeneous turbulence (Lesieur 1987). The main advantage here in applying EDQNM to the buoyancy-driven flow field is the wide range of wavenumbers over which a solution of the EDQNM equations may be solved. Whereas a typical large-eddy simulation using 128(exp 3) grid points has a wavenumber range of only 60, the EDQNM calculation can be easily run with a wavenumber range of several decades. Because of the growth in length scales in the buoyancy-driven flow field, this large wavenumber range allows for a solution of the flow field well into its asymptotic regime. Recent comparisons between large-eddy simulations and closure theory (Herring 1990) indicate that a time longer than that attainable by current large-eddy simulations is required to reach flow asymptotics and that conclusions based on large-eddy simulation results may be based only on an intermediate transient state. We briefly introduce the EDQNM equations for the buoyancy-generated flow field. We then present a Kolmogorov-like theoretical argument on the scaling of the small-scale spectra. This scaling is then confirmed by numerical solution of the EDQNM equations. We briefly conclude with possible future research directions.
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.
1991-10-01
and complexity of thermochemistry . Accordingly a practical viewpoint is required to meet near-term work required for use in advanced CFD codes...teachers the opportunity to learn/explore/ teach turbulence issues. While such a product could be an invaluable eductaional tool (university), it also
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.
Assessment of dynamic closure for premixed combustion large eddy simulation
NASA Astrophysics Data System (ADS)
Langella, Ivan; Swaminathan, Nedunchezhian; Gao, Yuan; Chakraborty, Nilanjan
2015-09-01
Turbulent piloted Bunsen flames of stoichiometric methane-air mixtures are computed using the large eddy simulation (LES) paradigm involving an algebraic closure for the filtered reaction rate. This closure involves the filtered scalar dissipation rate of a reaction progress variable. The model for this dissipation rate involves a parameter βc representing the flame front curvature effects induced by turbulence, chemical reactions, molecular dissipation, and their interactions at the sub-grid level, suggesting that this parameter may vary with filter width or be a scale-dependent. Thus, it would be ideal to evaluate this parameter dynamically by LES. A procedure for this evaluation is discussed and assessed using direct numerical simulation (DNS) data and LES calculations. The probability density functions of βc obtained from the DNS and LES calculations are very similar when the turbulent Reynolds number is sufficiently large and when the filter width normalised by the laminar flame thermal thickness is larger than unity. Results obtained using a constant (static) value for this parameter are also used for comparative evaluation. Detailed discussion presented in this paper suggests that the dynamic procedure works well and physical insights and reasonings are provided to explain the observed behaviour.
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.
NASA Astrophysics Data System (ADS)
Lee, Young J.; Huh, Kang Y.
2012-02-01
Simulation is performed to analyse the characteristics of turbulent spray combustion in conventional low and high speed diesel engine conditions. Turbulence-chemistry interaction is resolved by the Conditional Moment Closure (CMC) model in the spatially integrated form of an Incompletely Stirred Reactor (ISR). After validation against measured pressure traces, characteristic length and time scales and dimensionless numbers are estimated at the locations of sequentially injected fuel groups. Conditional flame structures are calculated for sequentially evaporated fuel groups to consider different available periods for ignition chemistry. Injection overlaps the combustion period in the high rpm engine, while most combustion occurs after injection and evaporation are complete in the low rpm engine. Ignition occurs in rich premixture with the initial peak temperature at the equivalence ratio around 2-4 as observed in Dec [2]. It corresponds to the most reactive mixture fraction of the minimum ignition delay for the given mixture states. Combustion proceeds to lean and rich sides in the mixture fraction space as a diffusion process by turbulence. The mean scalar dissipation rates (SDRs) are lower than the extinction limit to show stability of diffusion flames throughout the combustion period.
Angle closure in younger patients.
Chang, Brian M; Liebmann, Jeffrey M; Ritch, Robert
2002-01-01
PURPOSE: Angle-closure glaucoma is rare in children and young adults. Only scattered cases associated with specific clinical entities have been reported. We evaluated the findings in patients in our database aged 40 or younger with angle closure. METHODS: Our database was searched for patients with angle closure who were 40 years old or younger. Data recorded included age at initial consultation; age at the time of diagnosis; gender; results of slit-lamp examination, gonioscopy, and ultrasound biomicroscopy (from 1993 onward); clinical diagnosis; and therapy. Patients with previous incisional surgery were excluded, as were patients with anterior chamber proliferative mechanisms leading to angle closure. RESULTS: Sixty-seven patients (49 females, 18 males) met entry criteria. Mean age (+/- SD) at the time of consultation was 34.4 +/- 9.4 years (range, 3-68 years). Diagnoses included plateau iris syndrome (35 patients), iridociliary cysts (8 patients), retinopathy of prematurity (7 patients), uveitis (5 patients), isolated nanophthalmos (3 patients), relative pupillary block (2 patients), Weill-Marchesani syndrome (3 patients), and 1 patient each with Marfan syndrome, miotic-induced angle closure, persistent hyperplastic primary vitreous, and idiopathic lens subluxation. CONCLUSION: The etiology of angle closure in young persons is different from that in the older population and is typically associated with structural or developmental ocular anomalies rather than relative pupillary block. Following laser iridotomy, these eyes should be monitored for recurrent angle closure and the need for additional laser or incisional surgical intervention. PMID:12545694
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.
Calculation of turbulent free mixing: Status and problems
NASA Technical Reports Server (NTRS)
Bushnell, D. M.
1973-01-01
An overview of turbulence closure methods is presented along with discussions concerning which method works where and which approaches deserve further development. A table is given which lists the various computational techniques together with their prime usage areas. In addition, free mixing phenomena which were not specifically included in the basic data considered for the conference are summarized.
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.
Helicity statistics in homogeneous and isotropic turbulence and turbulence models
NASA Astrophysics Data System (ADS)
Sahoo, Ganapati; De Pietro, Massimo; Biferale, Luca
2017-02-01
We study the statistical properties of helicity in direct numerical simulations of fully developed homogeneous and isotropic turbulence and in a class of turbulence shell models. We consider correlation functions based on combinations of vorticity and velocity increments that are not invariant under mirror symmetry. We also study the scaling properties of high-order structure functions based on the moments of the velocity increments projected on a subset of modes with either positive or negative helicity (chirality). We show that mirror symmetry is recovered at small scales, i.e., chiral terms are subleading and they are well captured by a dimensional argument plus anomalous corrections. These findings are also supported by a high Reynolds numbers study of helical shell models with the same chiral symmetry of Navier-Stokes equations.
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
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, 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, 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...
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...
Pfannenstiel incision closure: a review of current skin closure techniques.
Altman, Alon D; Allen, Victoria M; McNeil, Shelly A; Dempster, Jeffrey
2009-06-01
The goal of any skin closure technique is to produce appropriate skin approximation and adequate healing while minimizing pain, wound complications, cost, and scarring; the technique should be quick, cost-effective, and simple, while maximizing wound cosmesis and patient satisfaction. Although many studies have shown the superiority of staples for speed of closure, it is unclear if staples give a superior cosmetic result or reduce pain. Several randomized controlled trials have found that sutures are superior for cosmesis and that they decrease postoperative pain and are more cost-effective. There remains a paucity of data on wound infections and complications associated with closure technique. This review summarizes studies to date evaluating outcomes associated with wound closure using staples and sutures in repairing abdominal incisions and, in particular, assesses outcomes in the obstetric population with a Pfannenstiel incision.
NASA Astrophysics Data System (ADS)
Lewandowski, M. T.; Pozorski, J.
2016-10-01
The present work reports on the assessment of different turbulence-chemistry interaction closures for the modelling of turbulent non-premixed combustion. Two-dimensional axisymmetric simulations have been carried out based on three different laboratory flames. The methane fueled, piloted jet flame Sandia D, the simple jet syngas flame and the so-called Delft Jet-in-Hot Coflow flame are studied. All the flames can be characterised as non-premixed but differ by some features which are taken into account through appropriate modelling approach.
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.
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
Modeling variable density turbulence in the wake of an air-entraining transom stern
NASA Astrophysics Data System (ADS)
Hendrickson, Kelli; Yue, Dick
2015-11-01
This work presents a priori testing of closure models for the incompressible highly-variable density turbulent (IHVDT) flows in the near wake region of a transom stern. This three-dimensional flow is comprised of convergent corner waves that originate from the body and collide on the ship center plane forming the ``rooster tail'' that then widens to form the divergent wave train. These violent free-surface flows and breaking waves are characterized by significant turbulent mass flux (TMF) at Atwood number At = (ρ2 -ρ1) / (ρ2 +ρ1) ~ 1 for which there is little guidance in turbulence closure modeling for the momentum and scalar transport along the wake. To whit, this work utilizes high-resolution simulations of the near wake of a canonical three-dimensional transom stern using conservative Volume-of-Fluid (cVOF), implicit Large Eddy Simulation (iLES), and Boundary Data Immersion Method (BDIM) to capture the turbulence and large scale air entrainment. Analysis of the simulation results across and along the wake for the TMF budget and turbulent anisotropy provide the physical basis of the development of multiphase turbulence closure models. Performance of isotropic and anisotropic turbulent mass flux closure models will be presented. Sponsored by the Office of Naval Research.
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.
THOR Turbulence Electron Analyser: TEA
NASA Astrophysics Data System (ADS)
Fazakerley, Andrew; Moore, Tom; Owen, Chris; Pollock, Craig; Wicks, Rob; Samara, Marilia; Rae, Jonny; Hancock, Barry; Kataria, Dhiren; Rust, Duncan
2016-04-01
Turbulence Heating ObserveR (THOR) is the first mission ever flown in space dedicated to plasma turbulence. The Turbulence Electron Analyser (TEA) will measure the plasma electron populations in the mission's Regions of Interest. It will collect a 3D electron velocity distribution with cadences as short as 5 ms. The instrument will be capable of measuring energies up to 30 keV. TEA consists of multiple electrostatic analyser heads arranged so as to measure electrons arriving from look directions covering the full sky, i.e. 4 pi solid angle. The baseline concept is similar to the successful FPI-DES instrument currently operating on the MMS mission. TEA is intended to have a similar angular resolution, but a larger geometric factor. In comparison to earlier missions, TEA improves on the measurement cadence. For example, MMS FPI-DES routinely operates at 30 ms cadence. The objective of measuring distributions at rates as fast as 5 ms is driven by the mission's scientific requirements to resolve electron gyroscale size structures, where plasma heating and fluctuation dissipation is predicted to occur. TEA will therefore be capable of making measurements of the evolution of distribution functions across thin (a few km) current sheets travelling past the spacecraft at up to 600 km/s, of the Power Spectral Density of fluctuations of electron moments and of distributions fast enough to match frequencies with waves expected to be dissipating turbulence (e.g. with 100 Hz whistler waves).
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.
New dynamical mean-field dynamo theory and closure approach.
Blackman, Eric G; Field, George B
2002-12-23
We develop a new nonlinear mean field dynamo theory that couples field growth to the time evolution of the magnetic helicity and the turbulent electromotive force, E. We show that the difference between kinetic and current helicities emerges naturally as the growth driver when the time derivative of E is coupled into the theory. The solutions predict significant field growth in a kinematic phase and a saturation rate/strength that is magnetic Reynolds number dependent/independent in agreement with numerical simulations. The amplitude of early time oscillations provides a diagnostic for the closure.
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.
Wittmann, Marc
2011-01-01
It has been suggested that perception and action can be understood as evolving in temporal epochs or sequential processing units. Successive events are fused into units forming a unitary experience or “psychological present.” Studies have identified several temporal integration levels on different time scales which are fundamental for our understanding of behavior and subjective experience. In recent literature concerning the philosophy and neuroscience of consciousness these separate temporal processing levels are not always precisely distinguished. Therefore, empirical evidence from psychophysics and neuropsychology on these distinct temporal processing levels is presented and discussed within philosophical conceptualizations of time experience. On an elementary level, one can identify a functional moment, a basic temporal building block of perception in the range of milliseconds that defines simultaneity and succession. Below a certain threshold temporal order is not perceived, individual events are processed as co-temporal. On a second level, an experienced moment, which is based on temporal integration of up to a few seconds, has been reported in many qualitatively different experiments in perception and action. It has been suggested that this segmental processing mechanism creates temporal windows that provide a logistical basis for conscious representation and the experience of nowness. On a third level of integration, continuity of experience is enabled by working memory in the range of multiple seconds allowing the maintenance of cognitive operations and emotional feelings, leading to mental presence, a temporal window of an individual’s experienced presence. PMID:22022310
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
[Turbulent characteristics in forest canopy under atmospheric neutral condition].
Diao, Yi-Wei; Guan, De-Xin; Jin, Chang-Jie; Wang, An-Zhi; Pei, Tie-Fan
2010-02-01
Based on the micrometeorological data of broad-leaved Korean pine forest in Changbai Mountain in 2003, a second-order closure model was employed to calculate and analyze the turbulent characteristics within and above the canopy of the forest. The calculated mean wind profile was coincident with the measured one. The Reynolds stress within the forest was significantly attenuated. The turbulent strength, velocity flux, and skew were the largest at forest-atmosphere interface, as well the wind shear. With the increase of velocity skew, the turbulent intermittence became more significant, and the downward turbulent eddy within the canopy was limited. Most of the turbulent deeply within the forest canopy was produced by the non-local contributions above the canopy.
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
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.
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
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.
Inverse cascade of magnetic helicity in magnetohydrodynamic turbulence.
Müller, Wolf-Christian; Malapaka, Shiva Kumar; Busse, Angela
2012-01-01
The nonlinear dynamics of magnetic helicity HM, which is responsible for large-scale magnetic structure formation in electrically conducting turbulent media, is investigated in forced and decaying three-dimensional magnetohydrodynamic turbulence. This is done with the help of high-resolution direct numerical simulations and statistical closure theory. The numerically observed spectral scaling of HM is at variance with earlier work using a statistical closure model [Pouquet et al., J. Fluid Mech. 77, 321 (1976)]. By revisiting this theory, a universal dynamical balance relation is found that includes the effects of kinetic helicity as well as kinetic and magnetic energies on the inverse cascade of HM and explains the above-mentioned discrepancy. Consideration of the result in the context of mean-field dynamo theory suggests a nonlinear modification of the α-dynamo effect, which is important in the context of magnetic-field excitation in turbulent plasmas.
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.
Doppler lidar signal and turbulence study
NASA Technical Reports Server (NTRS)
Frost, W.; Huang, K. H.
1983-01-01
Wind fields were measured with the ground-based NASA/MSFC lidar are compared with the in situ NASA RB-57 aircraft measurements. The mean wind fields, the turbulence intensities, and the turbulence spectra determined from measurements by both systems are in very good agreement. Turbulence intensities and spectra were calculated from the fluctuations with time in the radial wind speed component. The second moment or Doppler frequency spectral width of the lidar measurements was also compared with turbulence intensities measured by the aircraft. These second moments could only be resolved at the very low altitudes (in three range bins). Turbulence intensities estimated from the spectral width data were an order of magnitude higher than those measured by the aircraft. An interesting boundary layer evolved during the progress of the experiment. The breakup of a stable boundary layer resulted in winds blowing in one direction above 600 m msl and in the opposite direction below that level. Both the aircraft and the lidar systems clearly identified this unusual boundary layer flow and showed the identical trends.
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.
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
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.
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.
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.
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.
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).
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.
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.
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
Aspects of Turbulent / Non-Turbulent Interfaces
NASA Technical Reports Server (NTRS)
Bisset, D. K.; Hunt, J. C. R.; Rogers, M. M.; Koen, Dennis (Technical Monitor)
1999-01-01
A distinct boundary between turbulent and non-turbulent regions in a fluid of otherwise constant properties is found in many laboratory and engineering turbulent flows, including jets, mixing layers, boundary layers and wakes. Generally, the flow has mean shear in at least one direction within t he turbulent zone, but the non-turbulent zones have no shear (adjacent laminar shear is a different case, e.g. transition in a boundary layer). There may be purely passive differences between the turbulent and non-turbulent zones, e.g. small variations in temperature or scalar concentration, for which turbulent mixing is an important issue. The boundary has several major characteristics of interest for the present study. Firstly, the boundary advances into the non-turbulent fluid, or in other words, nonturbulent fluid is entrained. Secondly, the change in turbulence properties across the boundary is remarkably abrupt; strong turbulent motions come close to the nonturbulent fluid, promoting entrainment. Thirdly, the boundary is irregular with a continually changing convoluted shape, which produces statistical intermittency. Its shape is contorted at all scales of the turbulent motion.
Turbulence and turbulent mixing in natural fluids
NASA Astrophysics Data System (ADS)
Gibson, Carl H.
2010-12-01
Turbulence and turbulent mixing in natural fluids begin with big bang turbulence powered by spinning combustible combinations of Planck particles and Planck antiparticles. Particle prograde accretions on a spinning pair release 42% of the particle rest mass energy to produce more fuel for turbulent combustion. Negative viscous stresses and negative turbulence stresses work against gravity, extracting mass-energy and space-time from the vacuum. Turbulence mixes cooling temperatures until strong-force viscous stresses freeze out turbulent mixing patterns as the first fossil turbulence. Cosmic microwave background temperature anisotropies show big bang turbulence fossils along with fossils of weak plasma turbulence triggered as plasma photon-viscous forces permitting gravitational fragmentation on supercluster to galaxy mass scales. Turbulent morphologies and viscous-turbulent lengths appear as linear gas-protogalaxy-clusters in the Hubble ultra-deep field at z~7. Protogalaxies fragment into Jeans mass clumps of primordial-gas planets at decoupling: the dark matter of galaxies. Shortly after the plasma-to-gas transition, planet mergers produce stars that explode on overfeeding to fertilize and distribute the first life.
Cabled butterfly closure: a novel technique for sternal closure.
Jolly, Shashank; Flom, Beau; Dyke, Cornelius
2012-10-01
Impaired sternal wound healing remains problematic after median sternotomy and can lead to significant morbidity after cardiac surgical procedures. Although metal plating systems exist for closing the sternum, their use is limited by expense and practicality, and simple wire closure remains the most common technique to close the sternum. We describe a cabling technique for sternal closure that is secure, uses standard sternal wire, and may be used on every patient. We have used the technique routinely in 291 patients with no sternal dehiscence or wound healing problems.
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…
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 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.
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.
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.
Turbulence dynamics in unsteady atmospheric flows
NASA Astrophysics Data System (ADS)
Momen, Mostafa; Bou-Zeid, Elie
2016-11-01
Unsteady pressure-gradient forcing in geophysical flows challenges the quasi-steady state assumption, and can strongly impact the mean wind and higher-order turbulence statistics. Under such conditions, it is essential to understand when turbulence is in quasi-equilibrium, and what are the implications of unsteadiness on flow characteristics. The present study focuses on the unsteady atmospheric boundary layer (ABL) where pressure gradient, Coriolis, buoyancy, and friction forces interact. We perform a suite of LES with variable pressure-gradient. The results indicate that the dynamics are mainly controlled by the relative magnitudes of three time scales: Tinertial, Tturbulence, and Tforcing. It is shown that when Tf Tt , the turbulence is no longer in a quasi-equilibrium state due to highly complex mean-turbulence interactions; consequently, the log-law and turbulence closures are no longer valid in these conditions. However, for longer and, surprisingly, for shorter forcing times, quasi-equilibrium is maintained. Varying the pressure gradient in the presence of surface buoyancy fluxes primarily influences the buoyant destruction in the stable ABLs, while under unstable conditions it mainly influences the transport terms. NSF-PDM under AGS-10266362. Cooperative Institute for Climate Science, NOAA-Princeton University under NA08OAR4320752. Simulations performed at NCAR, and Della server at Princeton University.
Spectral formulation of turbulent flame speed with consideration of hydrodynamic instability.
Chaudhuri, Swetaprovo; Akkerman, V'yacheslav; Law, Chung K
2011-08-01
Effects of Darrieus-Landau (DL) instability on the structure and propagation of turbulent premixed flame fronts are considered. By first hypothesizing separation of time scales of instability and turbulence, we estimate whether the instability can develop in the presence of turbulence of given flow rms-velocity and integral length scale. As a result, we modify the standard turbulent premixed combustion regime diagram by introducing new boundaries, limiting the domain where the instability influences the global flame shape and speed. Based on this analysis, a "turbulence-induced DL cutoff" as a function of turbulence and instability parameters is introduced, which when combined with a turbulent flame speed without DL instability yields the turbulent flame speed accounting for the instability. The consumption turbulent flame speed for no DL instability is formulated from the spectral closure of the G equation, thus accounting for the scale-dependent "turbulent" nature of the problem. Finally, an analytical form of the turbulent flame speed is derived, which is found to agree well with the corresponding experimentally measured turbulent flame speed from literature over wide ranges of normalized turbulence intensities and length scales.
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.
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.
Turbulent Transport in a Three-dimensional Solar Wind
NASA Astrophysics Data System (ADS)
Shiota, D.; Zank, G. P.; Adhikari, L.; Hunana, P.; Telloni, D.; Bruno, R.
2017-03-01
Turbulence in the solar wind can play essential roles in the heating of coronal and solar wind plasma and the acceleration of the solar wind and energetic particles. Turbulence sources are not well understood and thought to be partly enhanced by interaction with the large-scale inhomogeneity of the solar wind and the interplanetary magnetic field and/or transported from the solar corona. To investigate the interaction with background inhomogeneity and the turbulence sources, we have developed a new 3D MHD model that includes the transport and dissipation of turbulence using the theoretical model of Zank et al. We solve for the temporal and spatial evolution of three moments or variables, the energy in the forward and backward fluctuating modes and the residual energy and their three corresponding correlation lengths. The transport model is coupled to our 3D model of the inhomogeneous solar wind. We present results of the coupled solar wind-turbulence model assuming a simple tilted dipole magnetic configuration that mimics solar minimum conditions, together with several comparative intermediate cases. By considering eight possible solar wind and turbulence source configurations, we show that the large-scale solar wind and IMF inhomogeneity and the strength of the turbulence sources significantly affect the distribution of turbulence in the heliosphere within 6 au. We compare the predicted turbulence distribution results from a complete solar minimum model with in situ measurements made by the Helios and Ulysses spacecraft, finding that the synthetic profiles of the turbulence intensities show reasonable agreement with observations.
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.
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.
[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.
Closure of Building 624 incinerator
Ridley, M.N.; Hallisey, M.L.; Terusaki, S.; Steverson, M.
1992-06-01
The Building 624 incinerator was a Resource Conservation Recovery Act (RCRA) mixed waste incinerator at Lawrence Livermore National Laboratory (LLNL). This incinerator was in operation from 1978 to 1989. The incinerator was to be closed as a mixed waste incinerator, but was to continue burning classified nonhazardous solid waste. The decision was later made to discontinue all use of the incinerator. Closure activities were performed from June 15 to December 15, 1991, when a clean closure was completed. The main part of the closure was the characterization, which included 393 samples and 30 blanks. From these 393 samples, approximately 13 samples indicated the need for further investigation, such as an isotopic scan; however, none of the samples was concluded to be hazardous or radioactive.
Reynolds stress closure in jet flows using wave models
NASA Technical Reports Server (NTRS)
Morris, P. J.
1987-01-01
Numerical methods were developed that will form the computational part of the turbulence closure scheme. A wave model was developed for the two-dimensional shear layer. This configuration is being used as a test case for the closure schemes. Various numerical schemes were examined to give efficient solutions of the Rayleigh equation for this geometry. These include both spectral and finite difference methods. Secondly, numerical methods are under development to solve the non-separable Rayleigh equation. This solution is required for the closure scheme in more complex geometries. A model problem was used to assist in the algorithm development. Two-dimensional spectral methods and a hybrid spectral/finite difference technique were developed. An analytic solution of the Rayleigh equation for a basic elliptic flow was obtained. This will be used to verify the stability codes developed for arbitrary geometries. Other numerical methods for solving the Rayleigh equation based on the boundary element technique were also examined. These solutions are forming the basis of a model for the shock structure in jets of arbitrary geometry.
NASA Astrophysics Data System (ADS)
Kaufmann, A.; Moreau, M.; Simonin, O.; Helie, J.
2008-06-01
The purpose of this paper is to evaluate the accuracy of the mesoscopic approach proposed by Février et al. [P. Février, O. Simonin, K.D. Squires, Partitioning of particle velocities in gas-solid turbulent flows into a continuous field and a spatially uncorrelated random distribution: theoretical formalism and numerical study, J. Fluid Mech. 533 (2005) 1-46] by comparison against the Lagrangian approach for the simulation of an ensemble of non-colliding particles suspended in a decaying homogeneous isotropic turbulence given by DNS. The mesoscopic Eulerian approach involves to solve equations for a few particle PDF moments: number density, mesoscopic velocity, and random uncorrelated kinetic energy (RUE), derived from particle flow ensemble averaging conditioned by the turbulent fluid flow realization. In addition, viscosity and diffusivity closure assumptions are used to compute the unknown higher order moments which represent the mesoscopic velocity and RUE transport by the uncorrelated velocity component. A detailed comparison between the two approaches is carried out for two different values of the Stokes number based on the initial fluid Kolmogorov time scale, St=0.17 and 2.2. In order to perform reliable comparisons for the RUE local instantaneous distribution and for the mesoscopic kinetic energy spectrum, the error due to the computation method of mesoscopic quantities from Lagrangian simulation results is evaluated and minimized. A very good agreement is found between the mesoscopic Eulerian and Lagrangian predictions for the small particle Stokes number case corresponding to the smallest particle inertia. For larger particle inertia, a bulk viscous term is included in the mesoscopic velocity governing equation to avoid spurious spatial oscillation that may arise due to the inability of the numerical scheme to resolve sharp number density gradients. As a consequence, for St=2.2, particle number density and RUE spatial distribution predicted by the
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.
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.
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.
40 CFR 265.113 - Closure; time allowed for closure.
Code of Federal Regulations, 2010 CFR
2010-07-01
... section, at a hazardous waste management unit or facility, or within 90 days after approval of the closure...) The hazardous waste management unit or facility has the capacity to receive additional hazardous... another person will recommence operation of the hazardous waste management unit or the facility within...
40 CFR 265.113 - Closure; time allowed for closure.
Code of Federal Regulations, 2013 CFR
2013-07-01
... section, at a hazardous waste management unit or facility, or within 90 days after approval of the closure...) The hazardous waste management unit or facility has the capacity to receive additional hazardous... another person will recommence operation of the hazardous waste management unit or the facility within...
NASA Astrophysics Data System (ADS)
Venaille, Antoine; Nadeau, Louis-Philippe; Vallis, Geoffrey
2014-12-01
We investigate the non-linear equilibration of a two-layer quasi-geostrophic flow in a channel with an initial eastward baroclinically unstable jet in the upper layer, paying particular attention to the role of bottom friction. In the limit of low bottom friction, classical theory of geostrophic turbulence predicts an inverse cascade of kinetic energy in the horizontal with condensation at the domain scale and barotropization in the vertical. By contrast, in the limit of large bottom friction, the flow is dominated by ribbons of high kinetic energy in the upper layer. These ribbons correspond to meandering jets separating regions of homogenized potential vorticity. We interpret these results by taking advantage of the peculiar conservation laws satisfied by this system: the dynamics can be recast in such a way that the initial eastward jet in the upper layer appears as an initial source of potential vorticity levels in the upper layer. The initial baroclinic instability leads to a turbulent flow that stirs this potential vorticity field while conserving the global distribution of potential vorticity levels. Statistical mechanical theory of the 1 1/2 layer quasi-geostrophic model predicts the formation of two regions of homogenized potential vorticity separated by a minimal interface. We explain that cascade phenomenology leads to the same result. We then show that the dynamics of the ribbons results from a competition between a tendency to reach the equilibrium state and baroclinic instability that induces meanders of the interface. These meanders intermittently break and induce potential vorticity mixing, but the interface remains sharp throughout the flow evolution. We show that for some parameter regimes, the ribbons act as a mixing barrier which prevents relaxation toward equilibrium, favouring the emergence of multiple zonal (eastward) jets.
A turbulence model for pulsatile arterial flows.
Younis, B A; Berger, S A
2004-10-01
Difficulties in predicting the behavior of some high Reynolds number flows in the circulatory system stem in part from the severe requirements placed on the turbulence model chosen to close the time-averaged equations of fluid motion. In particular, the successful turbulence model is required to (a) correctly capture the "nonequilibrium" effects wrought by the interactions of the organized mean-flow unsteadiness with the random turbulence, (b) correctly reproduce the effects of the laminar-turbulent transitional behavior that occurs at various phases of the cardiac cycle, and (c) yield good predictions of the near-wall flow behavior in conditions where the universal logarithmic law of the wall is known to be not valid. These requirements are not immediately met by standard models of turbulence that have been developed largely with reference to data from steady, fully turbulent flows in approximate local equilibrium. The purpose of this paper is to report on the development of a turbulence model suited for use in arterial flows. The model is of the two-equation eddy-viscosity variety with dependent variables that are zero-valued at a solid wall and vary linearly with distance from it. The effects of transition are introduced by coupling this model to the local value of the intermittency and obtaining the latter from the solution of a modeled transport equation. Comparisons with measurements obtained in oscillatory transitional flows in circular tubes show that the model produces substantial improvements over existing closures. Further pulsatile-flow predictions, driven by a mean-flow wave form obtained in a diseased human carotid artery, indicate that the intermittency-modified model yields much reduced levels of wall shear stress compared to the original, unmodified model. This result, which is attributed to the rapid growth in the thickness of the viscous sublayer arising from the severe acceleration of systole, argues in favor of the use of the model for the
Paradigm for Subgrid Scale Closure Modeling in Multiphase Geophysical Flows
NASA Astrophysics Data System (ADS)
Calantoni, J.; Simeonov, J.; Penko, A. M.; Bateman, S. P.; Palmsten, M. L.; Holland, K.
2012-12-01
We present a new paradigm for modeling multiphase geophysical flows to produce highly accurate and highly efficient forecasting of the complexity of the natural environment across the full range of relevant length and time scales. The assumption that computing technology will never allow us to perform direct numerical simulations (DNS) of the natural environment often limits our ambition in forward thinking model development and produces only incremental improvements in the state-of-the-art technology. Regional and global forecasting models for earth, ocean, and atmospheric processes based on averaged equations (e.g. RANS) must advance beyond simple closures relations obtained for single-phase fluid turbulence (e.g., k-epsilon, k-omega, and Mellor-Yamada). We propose using a hierarchy of computationally intensive, high fidelity simulations to resolve subgrid processes across a range of cascading length and time scales in the model domain to generate numerical interpolations for the unresolved physical processes. Further, we believe that it is possible to use the cumulative results of these subgrid scale simulations to develop a Bayesian network, for example, which may eventually replace the computationally intensive simulations with a highly efficient probabilistic closure model for the unresolved physical processes. The success of our approach will be greatly enhanced through rigorous validation of our subgrid scale models using three-dimensional laboratory and field measurements of fluid-particle turbulence at the scales of interest. Recent advances in optical imaging techniques have made it possible to make highly resolved three-dimensional measurements of fluid-particle turbulent interactions in the laboratory with spatial and temporal resolutions at or near the Kolmogorov scales. Additional work must be done to transition these technologies for use in the field. As a pilot test case we introduce our new paradigm using a hierarchy of models we have developed
Three-dimensional modelling of coastal circulations with different k- ɛ closures
NASA Astrophysics Data System (ADS)
Verdier-Bonnet, C.; Angot, Philippe; Fraunie, Philippe; Coantic, M.
1999-06-01
The actual tendency in 3D turbulent closure models for stratified shallow water flows is to come back to closure models with two transport equations for turbulent variables or to algebraic flux models. We retain the simpler k- ɛ closure model. For a simplified coastal upwelling circulation, we studied the relevance of the isotropic eddy viscosity assumption of the standard k-ɛ model for stratified and shallow-water flows submitted to the Coriolis force with two corrected k-ɛ models: STRAT-COR and ASPECT. We considered two mean sources of coastal turbulence production: the surface current shear generated by wind and the bottom shear. In order to understand the processes involved, we have modelled academic configurations such as constant depth ones or one-dimensional vertical problems. For a simplified coastal upwelling circulation, we have studied the pertinence of the isotropic eddy viscosity assumption of the standard k-ɛ model for stratified and shallow-water flows submitted to the Coriolis force. In order to take into account those non-isotropic behaviour of turbulence, we have used two corrected k-ɛ models: STRAT-COR and ASPECT. But, the mean deficiency of this model is the isotropic eddy viscosity assumption. In order to take into account the non-isotropic behaviour of turbulence due to buoyancy and Coriolis forces, a hybrid turbulence model (STRAT-COR) combining the standard k- ɛ and algebraic Reynolds stress models, is used. For shallow-water flows ( δ=( L)/( H)≫1) two eddies length scales can be pointed out: L for the large horizontal structures and H for the smaller but 3D ones. These effects are represented by a correction to the standard k- ɛ model, based on the separation of two turbulence scales, respectively associated to L and H. We focus our study onto two main sources of turbulent oceanic energy: the surface current shear induced by wind and the bottom stress due to tidal circulation. The k- ɛ closure model corrected to account for non
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.
DNAPL Remediation: Selected Projects Approaching Regulatory Closure
This paper is a status update on the use of DNAPL source reduction remedial technologies, and provides information about recent projects where regulatory closure has been reached or projects are approaching regulatory closure, following source reduction.
Hamiltonian reductions of the one-dimensional Vlasov equation using phase-space moments
NASA Astrophysics Data System (ADS)
Chandre, C.; Perin, M.
2016-03-01
We consider Hamiltonian closures of the Vlasov equation using the phase-space moments of the distribution function. We provide some conditions on the closures imposed by the Jacobi identity. We completely solve some families of examples. As a result, we show that imposing that the resulting reduced system preserves the Hamiltonian character of the parent model shapes its phase space by creating a set of Casimir invariants as a direct consequence of the Jacobi identity. We exhibit three main families of Hamiltonian models with two, three, and four degrees of freedom aiming at modeling the complexity of the bunch of particles in the Vlasov dynamics.
Björck, Martin; D'Amours, Scott K; Hamilton, A E Ricardo
2011-07-01
The open abdomen is a valuable tool in the management of patients with intra-abdominal hypertension and abdominal compartment syndrome. The longer an abdomen is left open, the greater the potential morbidity, however. From the very start, specific measures should be considered to increase the likelihood of definitive closure and prevent the development of visceral adhesions, lateralization, and/or loss of skin and fascia, ileus, fistulae, and malnutrition. Early definitive closure of all abdominal wall layers is the short-term goal of management once the need for the open abdomen has resolved. Several devices and strategies improve the chances for definitive closure. If a frozen abdomen develops, split-thickness skin grafting of a granulating open abdominal wound base is an alternative. Early coverage of the exposed viscera and acceptance of a large abdominal hernia permit earlier reversal of the catabolic state and lower the risk of fistula formation. When a stoma is required, sealing and separation can become problematic. If a fistula develops, a more complex situation prevails, requiring specific techniques to isolate its output and a longer-term strategy to restore intestinal continuity. Planning the closure of an open abdomen is a process that starts on the first day that the abdomen is opened. Multiple factors need to be addressed, optimized, and controlled to achieve the best outcome.
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.
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.
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.
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.
Flamelet Regime Diagram for Turbulent Combustion Simulations
NASA Astrophysics Data System (ADS)
Chan, Wai Lee; Ihme, Matthias; Kolla, Hemanth; Chen, Jacqueline
2016-11-01
The flamelet model has been widely used in numerical combustion investigations, particularly for the closure of large-eddy simulations (LES) of turbulent reacting flows. In most cases, the simulation results demonstrated good agreements with their experimental counterparts. However, a systematic analysis of the flamelet model's applicability, as well as its potential limitations, is seldom conducted, and the model performance is usually based only on a-posteriori comparisons. The objective of this work is to derive a metric that can formally quantify the suitability of the flamelet model in different flame configurations. For this purpose, a flamelet regime diagram has been developed and studied in the context of direct numerical simulations (DNS) of a turbulent lifted jet flame. The implementation of the regime diagram in LES has been investigated through explicit filtering of the DNS results.
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
Leith diffusion model for homogeneous anisotropic turbulence
Rubinstein, Robert; Clark, Timothy T.; Kurien, Susan
2016-07-19
Here, a proposal for a spectral closure model for homogeneous anisotropic turbulence. The systematic development begins by closing the third-order correlation describing nonlinear interactions by an anisotropic generalization of the Leith diffusion model for isotropic turbulence. The correlation tensor is then decomposed into a tensorially isotropic part, or directional anisotropy, and a trace-free remainder, or polarization anisotropy. The directional and polarization components are then decomposed using irreducible representations of the SO(3) symmetry group. Under the ansatz that the decomposition is truncated at quadratic order, evolution equations are derived for the directional and polarization pieces of the correlation tensor. Here, numerical simulation of the model equations for a freely decaying anisotropic flow illustrate the non-trivial effects of spectral dependencies on the different return-to-isotropy rates of the directional and polarization contributions.
Leith diffusion model for homogeneous anisotropic turbulence
Rubinstein, Robert; Clark, Timothy T.; Kurien, Susan
2016-07-19
Here, a proposal for a spectral closure model for homogeneous anisotropic turbulence. The systematic development begins by closing the third-order correlation describing nonlinear interactions by an anisotropic generalization of the Leith diffusion model for isotropic turbulence. The correlation tensor is then decomposed into a tensorially isotropic part, or directional anisotropy, and a trace-free remainder, or polarization anisotropy. The directional and polarization components are then decomposed using irreducible representations of the SO(3) symmetry group. Under the ansatz that the decomposition is truncated at quadratic order, evolution equations are derived for the directional and polarization pieces of the correlation tensor. Here, numericalmore » simulation of the model equations for a freely decaying anisotropic flow illustrate the non-trivial effects of spectral dependencies on the different return-to-isotropy rates of the directional and polarization contributions.« less
Leith diffusion model for homogeneous anisotropic turbulence
NASA Astrophysics Data System (ADS)
Rubinstein, Robert; Clark, Timothy; Kurien, Susan
2016-11-01
A new spectral closure model for homogeneous anisotropic turbulence is proposed. The systematic development begins by closing the third-order correlation describing nonlinear interactions by an anisotropic generalization of the Leith diffusion model for isotropic turbulence. The correlation tensor is then decomposed into a tensorially isotropic part, or directional anisotropy, and a trace-free remainder, or polarization anisotropy. The directional and polarization components are then decomposed using irreducible representations of the SO(3) symmetry group. Under the ansatz that the decomposition is truncated at quadratic order, evolution equations are derived for the directional and polarization pieces of the correlation tensor. Numerical simulation of the model equations for a freely decaying anisotropic flow illustrate the non-trivial effects of spectral dependencies on the different return-to-isotropy rates of the directional and polarization contributions.
40 CFR 258.61 - Post-closure care requirements.
Code of Federal Regulations, 2010 CFR
2010-07-01
... 40 Protection of Environment 24 2010-07-01 2010-07-01 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, 2010 CFR
2010-07-01
... 40 Protection of Environment 25 2010-07-01 2010-07-01 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, 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 §...
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.
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.
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.
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.
Vorticity statistics and the time scales of turbulent strain.
Moriconi, L; Pereira, R M
2013-07-01
Time scales of turbulent strain activity, denoted as the strain persistence times of first and second order, are obtained from time-dependent expectation values and correlation functions of Lagrangian rate-of-strain eigenvalues taken in particularly defined statistical ensembles. Taking into account direct numerical simulation data, our approach relies on heuristic closure hypotheses which allow us to establish a connection between the statistics of vorticity and strain. It turns out that softly divergent prefactors correct the usual "1/s" strain time-scale estimate of standard turbulence phenomenology, in a way which is consistent with the phenomenon of vorticity intermittency.
Generalized Convective Quasi-Equilibrium Closure
NASA Astrophysics Data System (ADS)
Yano, Jun-Ichi; Plant, Robert
2016-04-01
Arakawa and Schubert proposed convective quasi-equilibrium as a basic principle for closing their spectrum mass-flux convection parameterization. In deriving this principle, they show that the cloud work function is a key variable that controls the growth of convection. Thus, this closure hypothesis imposes a steadiness of the cloud work function tendency. This presentation shows how this principle can be generalized so that it can also encompasses both the CAPE and the moisture-convergence closures. Note that the majority of the current mass-flux convection parameterization invokes a CAPE closure, whereas the moisture-convergence closure was extremely popular historically. This generalization, in turn, includes both closures as special cases of convective quasi-equilibrium. This generalization further suggests wide range of alternative possibilities for convective closure. In general, a vertical integral of any function depending on both large-scale and convective-scale variables can be adopted as an alternative closure variables, leading to an analogous formulation as Arakawa and Schubert's convective quasi-equilibrium formulation. Among those, probably the most fascinating possibility is to take a vertical integral of the convective-scale moisture for the closure. Use of a convective-scale variable for closure has a particular appeal by not suffering from a loss of predictability of any large-scale variables. That is a main problem with any of the current convective closures, not only for the moisture-convergence based closure as often asserted.
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.
Consideration of Turbulence Effects in One-Dimensional Laminar Flamelet Equations
NASA Astrophysics Data System (ADS)
Chan, Wai Lee; Ihme, Matthias
2014-11-01
The laminar flamelet formulation has been used as a fundamental building block for the construction of turbulent combustion closures. By assuming that turbulence only leads to a deformation and straining of the local flame structure, the turbulence/chemistry interaction is then considered through a presumed shape probability density function (PDF) approach. However, the consistency of this approach remains unclear in the context of large-eddy simulations (LES), and the objective of this study is to examine the representation of turbulent scalar fluxes and turbulence/chemistry coupling on the flame structure. To this end, a detailed numerical simulation of a turbulent counterflow diffusion flame is performed, and the simulation results are used to analyze the limitations of the classic laminar flamelet formulation and explore a possible alternative approach. Financial support through the Air Force Office of Scientific Research under Award No. FA9550-11-1-0031 is gratefully acknowledged.
Turbulence and Star Formation in Interacting Galaxies
NASA Astrophysics Data System (ADS)
Auge, Connor; Chien, Lisa
2017-01-01
We investigate the turbulent gas motion in the tidal bridges and tails of colliding galaxies to see if there is a relation between this phenomenon and star formation within these galaxies. Previous studies have shown that the higher-order statistical moments, i.e. skewness and kurtosis, of the neutral hydrogen (HI) gas are linked to their turbulent motion in a galaxy. Such turbulences are considered to be potentially crucial in enhancing star formation at regions where the gas density is low, for example, the outer disk of a spiral galaxy, a dwarf galaxy, and tidal tails in an interacting system. Here we present these studies on a sample of colliding galaxy systems in detail. We create skewness and kurtosis maps representing the distribution of turbulent gas in these galaxies as a whole system and of the individual regions we are interested in. These maps also inform us as to whether the gas motion in these regions is sub-sonic or super-sonic. In order to investigate the relation between the turbulent gas motion and the star formation in low-density regions such as tidal tails, we compare these maps to far-ultraviolet images taken by GALEX space telescope.
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
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.
Repository Closure and Sealing Approach
A.T. Watkins
2000-06-28
The scope of this analysis will be to develop the conceptual design of the closure seals and their locations in the Subsurface Facilities. The design will be based on the recently established program requirements for transitioning to the Site Recommendation (SR) design as outlined by ''Approach to Implementing the Site Recommendation Baseline'' (Stroupe 2000) and the ''Monitored Geologic Repository Project Description Document'' (CRWMS M&O 1999b). The objective of this analysis will be to assist in providing a description for the Subsurface Facilities System Description Document, Section 2 and finally to document any conclusions reached in order to contribute and provide support to the SR. This analysis is at a conceptual level and is considered adequate to support the SR design. The final closure barriers and seals for the ventilation shafts, and the north and south ramps will require these openings to be permanently sealed to limit excessive air and water inflows and prevent human intrusion. The major tasks identified with closure in this analysis are: (1) Developing the overall subsurface seal layout and identifying design and operational interfaces for the Subsurface Facilities. (2) Summarizing the general site conditions and general rock characteristic with respect to seal location and describing the seal selected. (3) Identify seal construction materials, methodology of construction and strategic locations including design of the seal and plugs. (4) Discussing methods to prevent human intrusion.
Sampling and monitoring for closure
McLemore, V.T.; Russell, C.C.; Smith, K.S.
2004-01-01
The Metals Mining Sector of the Acid Drainage Technology Initiative (ADTI-MMS) addresses technical drainage-quality issues related to metal mining and related metallurgical operations, for future and active mines, as well as, for historical mines and mining districts. One of the first projects of ADTI-MMS is to develop a handbook describing the best sampling, monitoring, predicting, mitigating, and modeling of drainage from metal mines, pit lakes and related metallurgical facilities based upon current scientific and engineering practices. One of the important aspects of planning a new mine in today's regulatory environment is the philosophy of designing a new or existing mine or expansion of operations for ultimate closure. The holistic philosophy taken in the ADTI-MMS handbook maintains that sampling and monitoring programs should be designed to take into account all aspects of the mine-life cycle. Data required for the closure of the operation are obtained throughout the mine-life cycle, from exploration through post-closure.
Space-Time Correlations and Dynamic Coupling in Turbulent Flows
NASA Astrophysics Data System (ADS)
He, Guowei; Jin, Guodong; Yang, Yue
2017-01-01
Space-time correlation is a staple method for investigating the dynamic coupling of spatial and temporal scales of motion in turbulent flows. In this article, we review the space-time correlation models in both the Eulerian and Lagrangian frames of reference, which include the random sweeping and local straining models for isotropic and homogeneous turbulence, Taylor's frozen-flow model and the elliptic approximation model for turbulent shear flows, and the linear-wave propagation model and swept-wave model for compressible turbulence. We then focus on how space-time correlations are used to develop time-accurate turbulence models for the large-eddy simulation of turbulence-generated noise and particle-laden turbulence. We briefly discuss their applications to two-point closures for Kolmogorov's universal scaling of energy spectra and to the reconstruction of space-time energy spectra from a subset of spatial and temporal signals in experimental measurements. Finally, we summarize the current understanding of space-time correlations and conclude with future issues for the field.
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.
Kershaw closures for linear transport equations in slab geometry I: Model derivation
NASA Astrophysics Data System (ADS)
Schneider, Florian
2016-10-01
This paper provides a new class of moment models for linear kinetic equations in slab geometry. These models can be evaluated cheaply while preserving the important realizability property, that is the fact that the underlying closure is non-negative. Several comparisons with the (expensive) state-of-the-art minimum-entropy models are made, showing the similarity in approximation quality of the two classes.
An Oriented-Eddy Collision Model for Turbulence Prediction
2007-06-15
kinetic energy, K, and dissipation rate, E). There is also a hypothesized algebraic constitutive equation relating these two scalar quantities and the...elliptic relaxation ( Durbin ) have even expanded the predictive scope of these models. Nevertheless, it is well understood at this time, even by CFD users...Publisher, 1993 P.A. Durbin , Near-wall turbulence closure modeling without ’damping functions’, Theoret. Comput. Fluid Dynamics 3, 1-13, 1991. W. C
Hierarchical structures in fully developed turbulence
NASA Astrophysics Data System (ADS)
Liu, Li
Analysis of the probability density functions (PDFs) of the velocity increment dvl and of their deformation is used to reveal the statistical structure of the intermittent energy cascade dynamics of turbulence. By analyzing a series of turbulent data sets including that of an experiment of fully developed low temperature helium turbulent gas flow (Belin, Tabeling, & Willaime, Physica D 93, 52, 1996), of a three-dimensional isotropic Navier-Stokes simulation with a resolution of 2563 (Cao, Chen, & She, Phys. Rev. Lett. 76, 3711, 1996) and of a GOY shell model simulation (Leveque & She, Phys. Rev. E 55, 1997) of a very big sample size (up to 5 billions), the validity of the Hierarchical Structure model (She & Leveque, Phys. Rev. Lett. 72, 366, 1994) for the inertial-range is firmly demonstrated. Furthermore, it is shown that parameters in the Hierarchical Structure model can be reliably measured and used to characterize the cascade process. The physical interpretations of the parameters then allow to describe differential changes in different turbulent systems so as to address non-universal features of turbulent systems. It is proposed that the above study provides a framework for the study of non-homogeneous turbulence. A convergence study of moments and scaling exponents is also carried out with detailed analysis of effects of finite statistical sample size. A quantity Pmin is introduced to characterize the resolution of a PDF, and hence the sample size. The fact that any reported scaling exponent depends on the PDF resolution suggests that the validation (or rejection) of a model of turbulence needs to carry out a resolution dependence analysis on its scaling prediction.
Turbulence and Star Formation in a Sample of Spiral Galaxies
NASA Astrophysics Data System (ADS)
Maier, Erin; Chien, Li-Hsin; Hunter, Deidre A.
2016-11-01
We investigate turbulent gas motions in spiral galaxies and their importance to star formation in far outer disks, where the column density is typically far below the critical value for spontaneous gravitational collapse. Following the methods of Burkhart et al. on the Small Magellanic Cloud, we use the third and fourth statistical moments, as indicators of structures caused by turbulence, to examine the neutral hydrogen (H i) column density of a sample of spiral galaxies selected from The H i Nearby Galaxy Survey. We apply the statistical moments in three different methods—the galaxy as a whole, divided into a function of radii and then into grids. We create individual grid maps of kurtosis for each galaxy. To investigate the relation between these moments and star formation, we compare these maps with their far-ultraviolet images taken by the Galaxy Evolution Explorer satellite.We find that the moments are largely uniform across the galaxies, in which the variation does not appear to trace any star-forming regions. This may, however, be due to the spatial resolution of our analysis, which could potentially limit the scale of turbulent motions that we are sensitive to greater than ∼700 pc. From comparison between the moments themselves, we find that the gas motions in our sampled galaxies are largely supersonic. This analysis also shows that the Burkhart et al. methods may be applied not just to dwarf galaxies but also to normal spiral galaxies.
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
Response of a wind turbine blade to seismic and turbulent wind excitations
NASA Astrophysics Data System (ADS)
Hong, R. C. Y.
The purpose was to investigate the dynamic behavior of a wind turbine blade under seismic and turbulent wind excitations. Toward this goal a procedure was developed in which the Markov process theory and its stochastic differential equation are used to obtain equations for statistical moments of blade response variables. Such equations then can be used to determine certain moment stability conditions for any given set of parameters and moment responses if the system is stable. The results show that for a constant rpm wind turbine generator the uncoupled flapping, coupled flap lagging and coupled flap lag torsion of a wind turbine blade are very stable under normal operating conditions, and that torsion has little influence on the dynamic behavior of flapping and leadlagging motions. If the system is stable, the effect of turbulence on moment responses is greater than that of an earthquake, therefore, turbulence is likely the main cause for structural fatigue of wind turbine blades.
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.
A statistical state dynamics approach to wall turbulence.
Farrell, B F; Gayme, D F; Ioannou, P J
2017-03-13
This paper reviews results obtained using statistical state dynamics (SSD) that demonstrate the benefits of adopting this perspective for understanding turbulence in wall-bounded shear flows. The SSD approach used in this work employs a second-order closure that retains only the interaction between the streamwise mean flow and the streamwise mean perturbation covariance. This closure restricts nonlinearity in the SSD to that explicitly retained in the streamwise constant mean flow together with nonlinear interactions between the mean flow and the perturbation covariance. This dynamical restriction, in which explicit perturbation-perturbation nonlinearity is removed from the perturbation equation, results in a simplified dynamics referred to as the restricted nonlinear (RNL) dynamics. RNL systems, in which a finite ensemble of realizations of the perturbation equation share the same mean flow, provide tractable approximations to the SSD, which is equivalent to an infinite ensemble RNL system. This infinite ensemble system, referred to as the stochastic structural stability theory system, introduces new analysis tools for studying turbulence. RNL systems provide computationally efficient means to approximate the SSD and produce self-sustaining turbulence exhibiting qualitative features similar to those observed in direct numerical simulations despite greatly simplified dynamics. The results presented show that RNL turbulence can be supported by as few as a single streamwise varying component interacting with the streamwise constant mean flow and that judicious selection of this truncated support or 'band-limiting' can be used to improve quantitative accuracy of RNL turbulence. These results suggest that the SSD approach provides new analytical and computational tools that allow new insights into wall turbulence.This article is part of the themed issue 'Toward the development of high-fidelity models of wall turbulence at large Reynolds number'.
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.
Reynolds stress closure in jet flows using wave models
NASA Technical Reports Server (NTRS)
Morris, Philip J.
1990-01-01
A collection of papers is presented. The outline of this report is as follows. Chapter three contains a description of a weakly nonlinear turbulence model that was developed. An essential part of the application of such a closure scheme to general geometry jets is the solution of the local hydrodynamic stability equation for a given jet cross-section. Chapter four describes the conformal mapping schemes used to map such geometries onto a simple computational domain. Chapter five describes a solution of a stability problem for circular, elliptic, and rectangular geometries. In chapter six linear models for the shock shell structure in non-circular jets is given. The appendices contain reprints of papers also published during this study including the following topics: (1) instability of elliptic jets; (2) a technique for predicting the shock cell structure in non-circular jets using a vortex sheet model; and (3) the resonant interaction between twin supersonic jets.
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.
Maximum entropy reconstruction method for moment-based solution of the BGK equation
NASA Astrophysics Data System (ADS)
Summy, Dustin; Pullin, D. I.
2016-11-01
We describe a method for a moment-based solution of the BGK equation. The starting point is a set of equations for a moment representation which must have even-ordered highest moments. The partial-differential equations for these moments are unclosed, containing higher-order moments in the flux terms. These are evaluated using a maximum-entropy reconstruction of the one-particle velocity distribution function f (x , t) , using the known moments. An analytic, asymptotic solution describing the singular behavior of the maximum-entropy construction near to the local equilibrium velocity distribution is presented, and is used to construct a complete hybrid closure scheme for the case of fourth-order and lower moments. For the steady-flow normal shock wave, this produces a set of 9 ordinary differential equations describing the shock structure. For a variable hard-sphere gas these can be solved numerically. Comparisons with results using the direct-simulation Monte-Carlo method will be presented. Supported partially by NSF award DMS 1418903.
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
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
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.
Turbulent Spots Inside the Turbulent Boundary Layer
NASA Astrophysics Data System (ADS)
Skarda, Jinhie; Wu, Xiaohua; Moin, Parviz; Lozano-Duran, Adrian; Wallace, James; Hickey, Jean-Pierre
2016-11-01
We present evidence that the buffer region of the canonical turbulent boundary layer is populated by locally generated turbulent spots, which cause strong indentations on the near-wall low-momentum streaks. This evidence is obtained from a spatially-developing direct numerical simulation carrying the inlet Blasius boundary layer through a bypass transition to the turbulent boundary layer state over a moderate Reynolds number range. The turbulent spots are structurally analogous to their transitional counter-parts but without any direct causality connection. High-pass filtered time-history records are used to calculate the period of turbulent spot detection and this period is compared to the boundary layer bursting period reported in hot-wire experiments. The sensitivity of the results to parameters such as the high pass filter frequency and the amplitude discriminator level is examined. The characteristics of these turbulent spots are also quantified using a spatial connectivity based conditional sampling technique. This evidence seems to be at odds with the notion that the buffer region is dominated by quasi-streamwise vortices, and contributes to the potential unification of the studies on near-wall turbulent boundary layer dynamics.
Fluid electrons with kinetic closure for long wavelength energetic particles driven modes
Chen Yang; Parker, Scott E.
2011-05-15
A kinetic electron closure scheme is presented for the fluid electron model that has been implemented in the GEM code [J. Lang, Y. Chen, S. E. Parker, and G.-Y. Fu, Phys. Plasmas 16, 102101 (2009)]. The most important element of the closure scheme is a complete Ohm's law for the parallel electric field E{sub ||}, derived by combining the quasineutrality condition, the Ampere's equation and the v{sub ||} moment of the gyrokinetic equations. A discretization method for the closure scheme is presented and studied in detail for a three-dimensional shearless slab plasma. It is found that for long wavelength shear Alfven waves the kinetic closure scheme is both more accurate and more robust than the previous GEM algorithm [Y. Chen and S. E. Parker, J. Comput. Phys. 189, 463 (2003)], whereas for the ion-gradient-driven instability the previous algorithm is more efficient. The fluid electron model with kinetic electron closure is useful for studying energetic particles driven modes with electron kinetic damping effects.
Clamshell closure for metal drum
Blanton, Paul S
2014-09-30
Closure ring to retain a lid in contact with a metal drum in central C-section conforming to the contact area between a lid and the rim of a drum and further having a radially inwardly directed flange and a vertically downwardly directed flange attached to the opposite ends of the C-section. The additional flanges reinforce the top of the drum by reducing deformation when the drum is dropped and maintain the lid in contact with the drum. The invention is particularly valuable in transportation and storage of fissile material.
Closure constraints for hyperbolic tetrahedra
NASA Astrophysics Data System (ADS)
Charles, Christoph; Livine, Etera R.
2015-07-01
We investigate the generalization of loop gravity's twisted geometries to a q-deformed gauge group. In the standard undeformed case, loop gravity is a formulation of general relativity as a diffeomorphism-invariant SU(2) gauge theory. Its classical states are graphs provided with algebraic data. In particular, closure constraints at every node of the graph ensure their interpretation as twisted geometries. Dual to each node, one has a polyhedron embedded in flat space {{{R}}3}. One then glues them, allowing for both curvature and torsion. It was recently conjectured that q-deforming the gauge group SU(2) would allow us to account for a non-vanishing cosmological constant Λ \
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
Turbulence, Turbulence Control, and Drag Reduction.
1987-08-01
Onsager (1945) and Weizs~cker (1948). has made remarkable strides in advancing our understanding of turbulent flows. It is this description of turbulent...tujrbuilce Inl thle lar to thle Intermiittenit trans’ition to turbulence lus.t ,iedipen itlik. N\\N.tern onI the other. O pen0 * ~ ~ h 1 ~ kdinition10 po...Some Studies of Non-Simple Pipe Flows K R SREENIVASAN 2.AR’ .\\ variety o phenooena occrs ’.5’, ,sTecla’., f we stray,’ away from straight circ- lar i es a
A study of crack closure in fatigue
NASA Technical Reports Server (NTRS)
Shih, T. T.; Wei, R. P.
1973-01-01
Crack closure phenomenon in fatigue was studied by using a Ti-6Al-4V titanium alloy. The occurrence of crack closure was directly measured by an electrical-potential method, and indirectly by load-strain measurement. The experimental results showed that the onset of crack closure depends on both the stress ratio, and the maximum stress intensity factor. No crack closure was observed for stress ratio, greater than 0.3 in this alloy. A two-dimensional elastic model was used to explain the behavior of the recorded load-strain curves. Closure force was estimated by using this model. Yield level stress was found near the crack tip. Based on this estimated closure force, the crack opening displacement was calculated. This result showed that onset of crack closure detected by electrical-potential measurement and crack-opening-displacement measurement is the same. The implications of crack closure on fatigue crack are considered. The experimental results show that crack closure cannot fully account for the effect of stress ratio, on crack growth, and that it cannot be regarded as the sole cause for delay.
100-D Ponds closure plan. Revision 1
Petersen, S.W.
1997-09-01
The 100-D Ponds is a Treatment, Storage, and Disposal (TSD) unit on the Hanford Facility that received both dangerous and nonregulated waste. This Closure Plan (Rev. 1) for the 100-D Ponds TSD unit consists of a RCRA Part A Dangerous Waste Permit Application (Rev. 3), a RCRA Closure Plan, and supporting information contained in the appendices to the plan. The closure plan consists of eight chapters containing facility description, process information, waste characteristics, and groundwater monitoring data. There are also chapters containing the closure strategy and performance standards. The strategy for the closure of the 100-D Ponds TSD unit is clean closure. Appendices A and B of the closure plan demonstrate that soil and groundwater beneath 100-D Ponds are below cleanup limits. All dangerous wastes or dangerous waste constituents or residues associated with the operation of the ponds have been removed, therefore, human health and the environment are protected. Discharges to the 100-D Ponds, which are located in the 100-DR-1 operable unit, were discontinued in June 1994. Contaminated sediment was removed from the ponds in August 1996. Subsequent sampling and analysis demonstrated that there is no contamination remaining in the ponds, therefore, this closure plan is a demonstration of clean closure.
Comment on: The current status of turbulence modeling in CFD and its future prospects
NASA Technical Reports Server (NTRS)
Bushnell, D. M.
1992-01-01
Information is given in viewgraph form on computational fluid dynamics (CFD). Topics covered include the fundamental problem with conventional turbulence modeling, the fundamental problems with the state-of-the-art turbulence modeling approach of 'eddy viscosity', major problems with Reynolds stress equation (RSE) closures, RSE challenges that are probably addressable within the context of Reynolds averaging, RSE challenges which may require theoretical/numerical spectral adjuncts for satisfactory solutions, tools available to aid RSE modeling, and a simplex view of the status of turbulence modeling.
Influence of Gas Turbulence on the Instability of an Air-Water Mixing Layer.
Matas, Jean-Philippe; Marty, Sylvain; Dem, Mohamed Seydou; Cartellier, Alain
2015-08-14
We present the first evidence of the direct influence of gas turbulence on the shear instability of a planar air-water mixing layer. We show with two different experiments that increasing the level of velocity fluctuations in the gas phase continuously increases the frequency of the instability, up to a doubling of frequency for the largest turbulence intensity investigated. A modified spatiotemporal stability analysis taking turbulence into account via a simple Reynolds stress closure provides the right trend and magnitude for this effect.
The effect of journal misalignment on the operation of a turbulent flow hydrostatic bearing
NASA Astrophysics Data System (ADS)
San Andres, Luis
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.
The effects of atmospheric turbulence on a quadrotor heavy lift airship
NASA Technical Reports Server (NTRS)
Tischler, M. B.; Jex, H. R.
1982-01-01
The response of a quadrotor heavy lift airship to atmospheric turbulence is evaluated using a four-point input model. Results show interaction between gust inputs and the characteristic modes of the vehicle's response. Example loop closures demonstrate tradeoffs between response regulation and structural loads. Vehicle responses to a tuned discrete wave front compare favorably with the linear results and illustrate characteristic HLA motion.
Moment tensor mechanisms from Iberia
NASA Astrophysics Data System (ADS)
Stich, D.; Morales, J.
2003-12-01
New moment tensor solutions are presented for small and moderate earthquakes in Spain, Portugal and the westernmost Mediterranean Sea for the period from 2002 to present. Moment tensor inversion, to estimate focal mechanism, depth and magnitude, is applied at the Instituto Andaluz de Geof¡sica (IAG) in a routine manner to regional earthquakes with local magnitude larger then or equal 3.5. Recent improvements of broadband network coverage contribute to relatively high rates of success: Since beginning of 2002, we could obtain valuable solutions, in the sense that moment tensor synthetic waveforms fit adequately the main characteristics of the observed seismograms, for about 50% of all events of the initial selection. Results are available on-line at http://www.ugr.es/~iag/tensor/. To date, the IAG moment tensor catalogue contains 90 solutions since 1984 and gives a relatively detailed picture of seismotectonics in the Ibero-maghrebian region, covering also low seismicity areas like intraplate Iberia. Solutions are concentrated in southern Spain and the Alboran Sea along the diffuse African-Eurasian plate boundary. These solutions reveal characteristics of the transition between the reverse faulting regime in Algeria and predominately normal faulting on the Iberian Peninsula. Further we discuss the available mechanisms for intermediate deep events, related to subcrustal tectonic processes at the plate contact.
Unteachable Moments and Pedagogical Relationships
ERIC Educational Resources Information Center
Wang, Hongyu
2016-01-01
This paper discusses how Julia Kristeva's theory can inform our understanding of unteachable moments. It proposes a pedagogical relationship that can contain breakdowns of meanings and work toward breakthroughs to new awareness, particularly related to social justice pedagogy in teacher education. First, one example from the author's own teaching…
Moment generation in wheelchair propulsion.
Guo, Lan-Yuen; Zhao, K D; Su, Fong-Chin; An, Kai-Nan
2003-01-01
Wheelchair propulsion is a man machine interaction in which chair design and fit affect the relative positions and orientations of the upper extremity relative to the handrim and wheel axle. To understand these relationships better, experimental data were collected in five hand positions from five subjects exerting maximal effort to propel an instrumented wheelchair with its wheel in a locked position. The results of experiments revealed that the progression moment was greater at both initial and terminal propulsion positions and smaller in the mid-propulsion position. The vertical and horizontal force components were directed radially away from the wheel axle posterior to the dead centre position and radially towards the wheel axle anterior to top dead centre. Subsequently, a subject-specific quasi-static model of the upper extremity which maximized wheel progression moment was developed to augment our understanding of experimental measures. Model-predicted trends in progression moments and hand force direction were similar to experiment. Model predictions revealed that the optimal progression moment generation could potentially be affected by an individual's anthropometric parameters, joint strengths and also the direction of force applied by the hand on the handrim. Through wheelchair fitting and training of wheelchair users, it may be possible to improve propulsion technique.
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
NASA Astrophysics Data System (ADS)
Miller, Arthur I.; Williams, Paul; Palmer, Tim; O'Shea, Michael; Neale, Ron; Reed, Cameron
2016-11-01
In October Philip Ball reported on the “Physics Imagination Retreat” workshop held in June at the University of Cambridge in the UK, at which a number of prominent scientists recounted their moments of sudden insight that led to scientific discoveries.
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…
On the modeling of low-Reynolds-number turbulence
NASA Technical Reports Server (NTRS)
So, R. M. C.; Yoo, G. J.
1986-01-01
A full Reynolds-stress closure that is capable of describing the flow all the way to the wall was formulated for turbulent flow through circular pipe. Since viscosity does not appear explicitly in the pressure redistribution terms, conventional high-number models for these terms are found to be applicable. However, the models for turbulent diffusion and viscous dissipation have to be modified to account for viscous diffusion near a wall. Two redistribution and two diffusion models are investigated for their effects on the model calculations. Wall correction to pressure redistribution modeling is also examined. Diffusion effects on calculated turbulent properties are further investigated by simplifying the transport equations to algebraic equations for Reynolds stress. Two approximations are explored. These are the equilibrium and nonequilibrium turbulence assumptions. Finally, the two-equation closure is also used to calculate the flow in question and the results compared with all the other model calculations. Fully developed pipe flows at two moderate Reynolds numbers are used to validate these model calculations.
40 CFR 264.112 - Closure plan; amendment of plan.
Code of Federal Regulations, 2010 CFR
2010-07-01
... 40 Protection of Environment 25 2010-07-01 2010-07-01 false Closure plan; amendment of plan. 264... Closure and Post-Closure § 264.112 Closure plan; amendment of plan. (a) Written plan. (1) The owner or operator of a hazardous waste management facility must have a written closure plan. In addition,...
40 CFR 264.112 - 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. 264... Closure and Post-Closure § 264.112 Closure plan; amendment of plan. (a) Written plan. (1) The owner or operator of a hazardous waste management facility must have a written closure plan. In addition,...
40 CFR 264.112 - 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. 264... Closure and Post-Closure § 264.112 Closure plan; amendment of plan. (a) Written plan. (1) The owner or operator of a hazardous waste management facility must have a written closure plan. In addition,...
A new approach to the formulation of scalar flux closure
NASA Technical Reports Server (NTRS)
Shabany, Y.; Durbin, P.
1995-01-01
This report shows that if a stochastic differential equation (Langevin equation) for velocity fluctuation vector is known, it is possible to derive the equations for scalar flux transport. Durbin and Speziale (1994) showed that the second moment of this stochastic differential equation gives an equation for the evolution of Reynolds stress tensor. Similarly, the stochastic equation will give an equation for scalar flux. Therefore, a coupling between these two is present. The basis for the present work is that there should be Langevin equations that can produce acceptable models for both the Reynolds stress tensor and the scalar flux vector. Having found this basic Langevin equation, the amount of work needed to model the second order closure problems is reduced; using the well developed models for Reynolds stress equations, it will be possible to derive corresponding models for scalar flux equation.
ERIC Educational Resources Information Center
Gross, Rosalind L.; White, Harry E.
This publication describes a selected group of child-resistant closures used in packaging five categories of medicine and household products. The material in the document was collected to train survey personnel to identify closures for a planned household study of the effectiveness of child-resistant packaging. The 39 closures described are of…
40 CFR 265.1202 - Closure and post-closure care.
Code of Federal Regulations, 2010 CFR
2010-07-01
... post-closure care. (a) At closure of a magazine or unit which stored hazardous waste under this subpart... estimates for closure, and financial responsibility for magazines or units must meet all of the requirements... as long as it remains in service as a munitions or explosives magazine or storage unit. (b) If,...
Accelerating cleanup: Paths to closure
Edwards, C.
1998-06-30
This document was previously referred to as the Draft 2006 Plan. As part of the DOE`s national strategy, the Richland Operations Office`s Paths to Closure summarizes an integrated path forward for environmental cleanup at the Hanford Site. The Hanford Site underwent a concerted effort between 1994 and 1996 to accelerate the cleanup of the Site. These efforts are reflected in the current Site Baseline. This document describes the current Site Baseline and suggests strategies for further improvements in scope, schedule and cost. The Environmental Management program decided to change the name of the draft strategy and the document describing it in response to a series of stakeholder concerns, including the practicality of achieving widespread cleanup by 2006. Also, EM was concerned that calling the document a plan could be misconstrued to be a proposal by DOE or a decision-making document. The change in name, however, does not diminish the 2006 vision. To that end, Paths to Closure retains a focus on 2006, which serves as a point in time around which objectives and goals are established.
A study of turbulent flow with sensitivity analysis
NASA Astrophysics Data System (ADS)
Dwyer, H. A.; Peterson, T.
1980-07-01
In this paper a new type of analysis is introduced that can be used in numerical fluid mechanics. The method is known as sensitivity analysis and it has been widely used in the field of automatic control theory. Sensitivity analysis addresses in a systematic way to the question of 'how' the solution to an equation will change due to variations in the equation's parameters and boundary conditions. An important application is turbulent flow where there exists a large uncertainty in the models used for closure. In the present work the analysis is applied to the three-dimensional planetary boundary layer equations, and sensitivity equations are generated for various parameters in turbulence model. The solution of these equations with the proper techniques leads to considerable insight into the flow field and its dependence on turbulence parameters. Also, the analysis allows for unique decompositions of the parameter dependence and is efficient.
Characterisation of turbulence downstream of a linear compressor cascade
NASA Astrophysics Data System (ADS)
di Mare, Luca; Jelly, Thomas; Day, Ivor
2014-11-01
Characterisation of turbulence in turbomachinery remains one of the most complex tasks in fluid mechanics. In addition, current closure models required for Reynolds-averaged Navier-Stokes computations do not accurately represent the action of turbulent forces against the mean flow. Therefore, the statistical properties of turbulence in turbomachinery are of significant interest. In the current work, single- and two-point hot-wire measurements have been acquired downstream of a linear compressor cascade in order to examine the properties of large-scale turbulent structures and to assess how they affect turbulent momentum and energy transfer in compressor passages. The cascade has seven controlled diffusion which are representative of high-pressure stator blades found in turbofan engines. Blade chord, thickness and camber are 0.1515 m, 9.3% and 42 degrees, respectively. Measurements were acquired at a chord Reynolds number of 6 . 92 ×105 . Single-point statistics highlight differences in turbulence structure when comparing mid-span and end-wall regions. Evaluation of two-point correlations and their corresponding spectra reveal the length-scales of the energy-bearing eddies in the cascade. Ultimately, these measurements can be used to calibrate future computational models. The authors gratefully acknowledge Rolls-Royce plc for funding this work and granting permission for its publication.
Numerical Simulation of the Nocturnal Turbulence Characteristics over Rattlesnake Mountain.
NASA Astrophysics Data System (ADS)
Heilman, W. E.; Takle, E. S.
1991-08-01
A two4Mensional second-order turbulence-closure model based on Mellor-Yamada level 3 is used to examine the nocturnal turbulence characteristics over Rattlesnake Mountain in Washington. Simulations of mean horizontal velocities and potential temperatures agree well with data. The equations for the components of the turbulent kinetic energy (TKE) show that anisotropy contributes in ways that are counter to our intuition developed from mean now considerations: shear production under stable conditions forces the suppression of the vertical component proportion of loud TKE, while potential-temperature variance under stable conditions leads to a positive (countergradient) contribution to the heat flux that increases the vertical component proportion of total TKE. This paper provides a qualitative analysis of simulated turbulence fields, which indicates significant variation over the windward and leeward slopes. From the simulation results, turbulence anisotropy is seen to develop in the katabatic flow region where vertical wind shears and atmospheric stability are large. An enhancement of the vertical component proportion of the total TKE takes place over the leeward slope as the downslope distance increases. The countergradient portion of the turbulent heat flux plays an important role in producing regions of anisotropy.
A moment-convergence method for stochastic analysis of biochemical reaction networks
NASA Astrophysics Data System (ADS)
Zhang, Jiajun; Nie, Qing; Zhou, Tianshou
2016-05-01
Traditional moment-closure methods need to assume that high-order cumulants of a probability distribution approximate to zero. However, this strong assumption is not satisfied for many biochemical reaction networks. Here, we introduce convergent moments (defined in mathematics as the coefficients in the Taylor expansion of the probability-generating function at some point) to overcome this drawback of the moment-closure methods. As such, we develop a new analysis method for stochastic chemical kinetics. This method provides an accurate approximation for the master probability equation (MPE). In particular, the connection between low-order convergent moments and rate constants can be more easily derived in terms of explicit and analytical forms, allowing insights that would be difficult to obtain through direct simulation or manipulation of the MPE. In addition, it provides an accurate and efficient way to compute steady-state or transient probability distribution, avoiding the algorithmic difficulty associated with stiffness of the MPE due to large differences in sizes of rate constants. Applications of the method to several systems reveal nontrivial stochastic mechanisms of gene expression dynamics, e.g., intrinsic fluctuations can induce transient bimodality and amplify transient signals, and slow switching between promoter states can increase fluctuations in spatially heterogeneous signals. The overall approach has broad applications in modeling, analysis, and computation of complex biochemical networks with intrinsic noise.
A moment-convergence method for stochastic analysis of biochemical reaction networks.
Zhang, Jiajun; Nie, Qing; Zhou, Tianshou
2016-05-21
Traditional moment-closure methods need to assume that high-order cumulants of a probability distribution approximate to zero. However, this strong assumption is not satisfied for many biochemical reaction networks. Here, we introduce convergent moments (defined in mathematics as the coefficients in the Taylor expansion of the probability-generating function at some point) to overcome this drawback of the moment-closure methods. As such, we develop a new analysis method for stochastic chemical kinetics. This method provides an accurate approximation for the master probability equation (MPE). In particular, the connection between low-order convergent moments and rate constants can be more easily derived in terms of explicit and analytical forms, allowing insights that would be difficult to obtain through direct simulation or manipulation of the MPE. In addition, it provides an accurate and efficient way to compute steady-state or transient probability distribution, avoiding the algorithmic difficulty associated with stiffness of the MPE due to large differences in sizes of rate constants. Applications of the method to several systems reveal nontrivial stochastic mechanisms of gene expression dynamics, e.g., intrinsic fluctuations can induce transient bimodality and amplify transient signals, and slow switching between promoter states can increase fluctuations in spatially heterogeneous signals. The overall approach has broad applications in modeling, analysis, and computation of complex biochemical networks with intrinsic noise.
Flight-crash events in turbulence.
Xu, Haitao; Pumir, Alain; Falkovich, Gregory; Bodenschatz, Eberhard; Shats, Michael; Xia, Hua; Francois, Nicolas; Boffetta, Guido
2014-05-27
The statistical properties of turbulence differ in an essential way from those of systems in or near thermal equilibrium because of the flux of energy between vastly different scales at which energy is supplied and at which it is dissipated. We elucidate this difference by studying experimentally and numerically the fluctuations of the energy of a small fluid particle moving in a turbulent fluid. We demonstrate how the fundamental property of detailed balance is broken, so that the probabilities of forward and backward transitions are not equal for turbulence. In physical terms, we found that in a large set of flow configurations, fluid elements decelerate faster than accelerate, a feature known all too well from driving in dense traffic. The statistical signature of rare "flight-crash" events, associated with fast particle deceleration, provides a way to quantify irreversibility in a turbulent flow. Namely, we find that the third moment of the power fluctuations along a trajectory, nondimensionalized by the energy flux, displays a remarkable power law as a function of the Reynolds number, both in two and in three spatial dimensions. This establishes a relation between the irreversibility of the system and the range of active scales. We speculate that the breakdown of the detailed balance characterized here is a general feature of other systems very far from equilibrium, displaying a wide range of spatial scales.
Flight–crash events in turbulence
Xu, Haitao; Pumir, Alain; Falkovich, Gregory; Bodenschatz, Eberhard; Shats, Michael; Xia, Hua; Francois, Nicolas; Boffetta, Guido
2014-01-01
The statistical properties of turbulence differ in an essential way from those of systems in or near thermal equilibrium because of the flux of energy between vastly different scales at which energy is supplied and at which it is dissipated. We elucidate this difference by studying experimentally and numerically the fluctuations of the energy of a small fluid particle moving in a turbulent fluid. We demonstrate how the fundamental property of detailed balance is broken, so that the probabilities of forward and backward transitions are not equal for turbulence. In physical terms, we found that in a large set of flow configurations, fluid elements decelerate faster than accelerate, a feature known all too well from driving in dense traffic. The statistical signature of rare “flight–crash” events, associated with fast particle deceleration, provides a way to quantify irreversibility in a turbulent flow. Namely, we find that the third moment of the power fluctuations along a trajectory, nondimensionalized by the energy flux, displays a remarkable power law as a function of the Reynolds number, both in two and in three spatial dimensions. This establishes a relation between the irreversibility of the system and the range of active scales. We speculate that the breakdown of the detailed balance characterized here is a general feature of other systems very far from equilibrium, displaying a wide range of spatial scales. PMID:24794529
Turbulence and Star Formation in Dwarf Galaxies
NASA Astrophysics Data System (ADS)
Hollyday, Gigja; Hunter, Deidre Ann; Little Things Team
2015-01-01
We are interested in understanding the nature and role of turbulence in the interstellar medium of dwarf irregular galaxies. Turbulence, resulting from a variety of processes, is a potential source for cloud formation, and thus star formation. We have undertaken an indirect analysis of turbulence via the third (skewness) and fourth (kurtosis) moments of the distribution of atomic hydrogen gas densities using the LITTLE THINGS data for a 40-count sample of nearby (<10.3 Mpc) dwarf galaxies. We followed the formulism used by Burkhart et al. (2010) in a study of the SMC. We found that there is evidence of turbulence in dwarf galaxies at a level comparable to that found in the SMC, but we have found no correlation between integrated star formation rates and integrated kurtosis values nor a clear correlation between kurtosis as a function of radius with gas surface density and star formation profiles. We are grateful for a summer internship provided by the Research Experiences for Undergraduates program at Northern Arizona University, run by Dr. Kathy Eastwood and Dr. David Trilling and funded by the National Science Foundation through grant AST-1004107.
Analysis of homogeneous turbulent reacting flows
NASA Technical Reports Server (NTRS)
Leonard, A. D.; Hill, J. C.; Mahalingam, S.; Ferziger, J. H.
1988-01-01
Full turbulence simulations at low Reynolds numbers were made for the single-step, irreversible, bimolecular reaction between non-premixed reactants in isochoric, decaying homogeneous turbulence. Various initial conditions for the scalar field were used in the simulations to control the initial scalar dissipation length scale, and simulations were also made for temperature-dependent reaction rates and for non-stoichiometric and unequal diffusivity conditions. Joint probability density functions (pdf's), conditional pdf's, and various statistical quantities appearing in the moment equations were computed. Preliminary analysis of the results indicates that compressive strain-rate correlates better than other dynamical quantities with local reaction rate, and the locations of peak reaction rates seem to be insensitive to the scalar field initial conditions.
A statistical state dynamics approach to wall turbulence
NASA Astrophysics Data System (ADS)
Farrell, B. F.; Gayme, D. F.; Ioannou, P. J.
2017-03-01
This paper reviews results obtained using statistical state dynamics (SSD) that demonstrate the benefits of adopting this perspective for understanding turbulence in wall-bounded shear flows. The SSD approach used in this work employs a second-order closure that retains only the interaction between the streamwise mean flow and the streamwise mean perturbation covariance. This closure restricts nonlinearity in the SSD to that explicitly retained in the streamwise constant mean flow together with nonlinear interactions between the mean flow and the perturbation covariance. This dynamical restriction, in which explicit perturbation-perturbation nonlinearity is removed from the perturbation equation, results in a simplified dynamics referred to as the restricted nonlinear (RNL) dynamics. RNL systems, in which a finite ensemble of realizations of the perturbation equation share the same mean flow, provide tractable approximations to the SSD, which is equivalent to an infinite ensemble RNL system. This infinite ensemble system, referred to as the stochastic structural stability theory system, introduces new analysis tools for studying turbulence. RNL systems provide computationally efficient means to approximate the SSD and produce self-sustaining turbulence exhibiting qualitative features similar to those observed in direct numerical simulations despite greatly simplified dynamics. The results presented show that RNL turbulence can be supported by as few as a single streamwise varying component interacting with the streamwise constant mean flow and that judicious selection of this truncated support or `band-limiting' can be used to improve quantitative accuracy of RNL turbulence. These results suggest that the SSD approach provides new analytical and computational tools that allow new insights into wall turbulence.
Ihme, Matthias; Pitsch, Heinz
2008-10-15
An extension of the flamelet/progress variable (FPV) model for the prediction of extinction and reignition is applied in large-eddy simulation (LES) of flames D and E of the Sandia piloted turbulent jet flame series. This model employs a presumed probability density function (PDF), in which the marginal PDF of a reactive scalar is modeled by a statistically most likely distribution. This provides two advantages. First of all, the shape of the distribution depends on chemical and mixing time-scale information, and second, an arbitrary number of moments can be enforced. This model was analyzed in an a priori study in the first part of this work. In the present LES application, the first two moments of mixture fraction and reaction progress variable are used to constrain the shape of the presumed PDF. Transport equations for these quantities are solved, and models for the residual scalar dissipation rates, which appear as unclosed terms in the equations for the scalar variances, are provided. Statistical flow field quantities for axial velocity, mixture fraction, and temperature, obtained from the extended FPV model, are in good agreement with experimental data. Mixture-fraction-conditioned data, conditional PDFs, and burning indices are computed and compared with the delta-function flamelet closure model, which employs a Dirac distribution as a model for the marginal PDF of the reaction progress parameter. The latter model considerably underpredicts the amount of local extinction, which shows that the consideration of second-moment information in the presumed PDF of the reaction progress parameter is important for the accurate prediction of extinction and reignition. Mixture-fraction-conditioned results obtained from the extended FPV model are in good agreement with experimental data; however, the overprediction of the consumption of fuel and oxidizer on the fuel-rich side results in an overprediction of minor species. The predictions for the conditional PDFs and
Turbulence generation by waves
Kaftori, D.; Nan, X.S.; Banerjee, S.
1995-12-31
The interaction between two-dimensional mechanically generated waves, and a turbulent stream was investigated experimentally in a horizontal channel, using a 3-D LDA synchronized with a surface position measuring device and a micro-bubble tracers flow visualization with high speed video. Results show that although the wave induced orbital motion reached all the way to the wall, the characteristics of the turbulence wall structures and the turbulence intensity close to the wall were not altered. Nor was the streaky nature of the wall layer. On the other hand, the mean velocity profile became more uniform and the mean friction velocity was increased. Close to the free surface, the turbulence intensity was substantially increased as well. Even in predominantly laminar flows, the introduction of 2-D waves causes three dimensional turbulence. The turbulence enhancement is found to be proportional to the wave strength.
Kerstein, A.R.
1996-12-31
One-Dimensional Turbulence is a new turbulence modeling strategy involving an unsteady simulation implemented in one spatial dimension. In one dimension, fine scale viscous and molecular-diffusive processes can be resolved affordably in simulations at high turbulence intensity. The mechanistic distinction between advective and molecular processes is thereby preserved, in contrast to turbulence models presently employed. A stochastic process consisting of mapping {open_quote}events{close_quote} applied to a one-dimensional velocity profile represents turbulent advection. The local event rate for given eddy size is proportional to the velocity difference across the eddy. These properties cause an imposed shear to induce an eddy cascade analogous in many respects to the eddy cascade in turbulent flow. Many scaling and fluctuation properties of self-preserving flows, and of passive scalars introduced into these flows, are reproduced.
Bilateral angle closure glaucoma following general anaesthesia.
Raj, K Mohan; Reddy, P Arun Subhash; Kumar, Vikram Chella
2015-04-01
Angle closure glaucoma is one of the ophthalmic emergencies and treatment has to be given at the earliest. It is a rare complication of general anesthesia. A female patient underwent Hysterectomy under general anesthesia. Following this, patient developed bilateral angle closure glaucoma. This patient was treated with antiglaucoma medications followed by YAG laser iridotomy and patient regained vision.
Hospital closure: Phoenix, Hydra or Titanic?
Dunne, T; Davis, S
1996-01-01
Very little has been published about the effects of hospital closure in terms of the service, financial or management issues of the process. Attempts through a case-study format to redress the balance and as such represents the reflections of practitioners who have recently undergone the experience of hospital closure and the often neglected issues arising both during and after the process.
Code of Federal Regulations, 2011 CFR
2011-07-01
... STANDARDS FOR OWNERS AND OPERATORS OF HAZARDOUS WASTE TREATMENT, STORAGE, AND DISPOSAL FACILITIES Thermal Treatment § 265.381 Closure. At closure, the owner or operator must remove all hazardous waste and hazardous waste residues (including, but not limited to, ash) from the thermal treatment process or equipment....
Code of Federal Regulations, 2010 CFR
2010-07-01
... STANDARDS FOR OWNERS AND OPERATORS OF HAZARDOUS WASTE TREATMENT, STORAGE, AND DISPOSAL FACILITIES Thermal Treatment § 265.381 Closure. At closure, the owner or operator must remove all hazardous waste and hazardous waste residues (including, but not limited to, ash) from the thermal treatment process or equipment....
50 CFR 20.26 - Emergency closures.
Code of Federal Regulations, 2010 CFR
2010-10-01
... wildlife conservation agency, and announcement on local radio and television. (b) Any such closure or... 50 Wildlife and Fisheries 6 2010-10-01 2010-10-01 false Emergency closures. 20.26 Section 20.26 Wildlife and Fisheries UNITED STATES FISH AND WILDLIFE SERVICE, DEPARTMENT OF THE INTERIOR...
Code of Federal Regulations, 2010 CFR
2010-07-01
... Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) SOLID WASTES (CONTINUED) INTERIM STATUS STANDARDS FOR OWNERS AND OPERATORS OF HAZARDOUS WASTE TREATMENT, STORAGE, AND DISPOSAL FACILITIES Chemical, Physical, and Biological Treatment § 265.404 Closure. At closure, all hazardous waste and hazardous...
Code of Federal Regulations, 2013 CFR
2013-07-01
... Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) SOLID WASTES (CONTINUED) INTERIM STATUS STANDARDS FOR OWNERS AND OPERATORS OF HAZARDOUS WASTE TREATMENT, STORAGE, AND DISPOSAL FACILITIES Chemical, Physical, and Biological Treatment § 265.404 Closure. At closure, all hazardous waste and hazardous...
Code of Federal Regulations, 2014 CFR
2014-07-01
... Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) SOLID WASTES (CONTINUED) INTERIM STATUS STANDARDS FOR OWNERS AND OPERATORS OF HAZARDOUS WASTE TREATMENT, STORAGE, AND DISPOSAL FACILITIES Chemical, Physical, and Biological Treatment § 265.404 Closure. At closure, all hazardous waste and hazardous...
Code of Federal Regulations, 2011 CFR
2011-07-01
... Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) SOLID WASTES (CONTINUED) INTERIM STATUS STANDARDS FOR OWNERS AND OPERATORS OF HAZARDOUS WASTE TREATMENT, STORAGE, AND DISPOSAL FACILITIES Chemical, Physical, and Biological Treatment § 265.404 Closure. At closure, all hazardous waste and hazardous...
Code of Federal Regulations, 2012 CFR
2012-07-01
... Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) SOLID WASTES (CONTINUED) INTERIM STATUS STANDARDS FOR OWNERS AND OPERATORS OF HAZARDOUS WASTE TREATMENT, STORAGE, AND DISPOSAL FACILITIES Chemical, Physical, and Biological Treatment § 265.404 Closure. At closure, all hazardous waste and hazardous...
2005 Base Closure and Realignment Commission Report
The 2005 Defense Base Closure and Realignment Commission is proud to present its Final Report for your consideration. As required by law, the Commission thoroughly and objectively reviewed the domestic installation closure and realignment recommendations proposed by the Secretary of Defense on May 13, 2005.
NASA Astrophysics Data System (ADS)
Lee, Kurnchul; Girimaji, Sharath S.; Kerimo, Johannes
2008-08-01
G. I. Taylor’s postulate [Proc. R. Soc. APRLAAZ0080-4630 151, 421 (1935)10.1098/rspa.1935.0158] that dissipation is independent of viscosity at high Reynolds numbers is the foundation of many single-fluid turbulence theories and closure models. The validity of this key postulate in an important class of flows, turbulent mixtures, is not yet clearly established. We devise a simple numerical experiment of decaying turbulence in a mixture of two fluids of vastly different viscosities to examine dissipation scaling. Initially, the two fluids are segregated, and dissipation is directly proportional to viscosity. As turbulence evolves and fluids mix, the velocity gradients rapidly adapt to the viscosity field, and within one-half eddy turnover time, dissipation-viscosity independence is established. Viscosity-weighted velocity-gradient skewness is shown to be constant, leading to the validity of Taylor’s postulate in turbulent mixtures.
Characterizing Magnetohydrodynamic Turbulence in the Small Magellanic Cloud
NASA Astrophysics Data System (ADS)
Burkhart, Blakesley K.
2010-01-01
We investigate the nature of turbulence in the Small Magellanic Cloud (SMC) using several diagnostics known to provide information on magnetohydrodynamic sonic and Alfven Mach numbers. We calculated the 2nd, 3rd and 4th statistical moments of the SMC, i.e. variance, skewness and kurtosis, respectively. It is known that a strong dependence of variance, skewness and kurtosis with Ms exists. An analysis of 3rd and 4th order moments give us a average Ms=3-4 for the SMC. We explore moments of smaller scale features in the SMC by making 'moment maps’ with a circular beam aperture. These maps indicate large turbulence in star forming regions and at regions on the interface of supershells. We also investigate how the spatial power spectral slope, which is known to get shallower with increasing sonic Mach number, of the SMC compares with that of simulations. We find that this method gives Ms 3 and suggests the SMC may be super-Alfvenic. We also calculate the sonic Mach number of the SMC using the ratio of kinetic to spin temperature, and obtain a median value for the cold gas of Ms = 7.12 ± 3.41. In addition to these techniques we apply the bispectrum, a new tool for statistical studies of the interstellar medium, in order to study turbulence wave-wave interactions. Unlike the ordinary power spectrum, the bispectrum preserves phase information in the stochastic field. We compare the bispectrum of the SMC with that of 3D isothermal simulations. We explore the bispectrum of the SMC for a variety of velocity channel samplings. We compare the bispectrum of the SMC to bispectrum of simulations of strong and weakly magnetized turbulence and find that the bispectrum of the SMC shows similar properties to supersonic turbulence. This work was in part supported by the NSF Graduate Research Fellowship
Remote visualization and scale analysis of large turbulence datatsets
NASA Astrophysics Data System (ADS)
Livescu, D.; Pulido, J.; Burns, R.; Canada, C.; Ahrens, J.; Hamann, B.
2015-12-01
Accurate simulations of turbulent flows require solving all the dynamically relevant scales of motions. This technique, called Direct Numerical Simulation, has been successfully applied to a variety of simple flows; however, the large-scale flows encountered in Geophysical Fluid Dynamics (GFD) would require meshes outside the range of the most powerful supercomputers for the foreseeable future. Nevertheless, the current generation of petascale computers has enabled unprecedented simulations of many types of turbulent flows which focus on various GFD aspects, from the idealized configurations extensively studied in the past to more complex flows closer to the practical applications. The pace at which such simulations are performed only continues to increase; however, the simulations themselves are restricted to a small number of groups with access to large computational platforms. Yet the petabytes of turbulence data offer almost limitless information on many different aspects of the flow, from the hierarchy of turbulence moments, spectra and correlations, to structure-functions, geometrical properties, etc. The ability to share such datasets with other groups can significantly reduce the time to analyze the data, help the creative process and increase the pace of discovery. Using the largest DOE supercomputing platforms, we have performed some of the biggest turbulence simulations to date, in various configurations, addressing specific aspects of turbulence production and mixing mechanisms. Until recently, the visualization and analysis of such datasets was restricted by access to large supercomputers. The public Johns Hopkins Turbulence database simplifies the access to multi-Terabyte turbulence datasets and facilitates turbulence analysis through the use of commodity hardware. First, one of our datasets, which is part of the database, will be described and then a framework that adds high-speed visualization and wavelet support for multi-resolution analysis of
Structures and scaling laws of turbulent Couette flow
NASA Astrophysics Data System (ADS)
Oberlack, Martin; Avsarkisov, Victor; Hoyas, Sergio; Rosteck, Andreas; Garcia-Galache, Jose P.; Frank, Andy
2014-11-01
We conducted a set of large scale DNS of turbulent Couette flow with the two key objectives: (i) to better understand large scale coherent structures and (ii) to validate new Lie symmetry based turbulent scaling laws for the mean velocity and higher order moments. Though frequently reported in the literature large scale structures pose a serious constraint on our ability to conduct DNS of turbulent Couette flow as the largest structures grow with increasing Re#, while at the same time Kolmogorov scale decreases. Other than for the turbulent Poiseuille flow a too small box is immediately visible in low order statistics such as the mean and limited our DNS to Reτ = 550 . At the same time we observed that scaling of the mean is peculiar as it involves a certain statistical symmetry which has never been observed for any other parallel wall-bounded turbulent shear flow. Symmetries such as Galilean group lie at the heart of fluid dynamics, while for turbulence statistics due to the multi-point correlation equations (MPCE) additional statistical symmetries are admitted. Most important, symmetries are the essential to construct exact solutions to the MPCE, which with the new above-mentioned special statistical symmetry led to a new turbulent scaling law for the Couette flow. DFG Grant No; KH 257/2-1.
Superconductivity from Emerging Magnetic Moments.
Hoshino, Shintaro; Werner, Philipp
2015-12-11
Multiorbital Hubbard models are shown to exhibit a spatially isotropic spin-triplet superconducting phase, where equal-spin electrons in different local orbitals are paired. This superconducting state is stabilized in the spin-freezing crossover regime, where local moments emerge in the metal phase, and the pairing is substantially assisted by spin anisotropy. The phase diagram features a superconducting dome below a non-Fermi-liquid metallic region and next to a magnetically ordered phase. We suggest that this type of fluctuating-moment-induced superconductivity, which is not originating from fluctuations near a quantum critical point, may be realized in spin-triplet superconductors such as strontium ruthenates and uranium compounds.
NASA Technical Reports Server (NTRS)
Canuto, V. M.
1990-01-01
Some of the astrophysical scenarios in which turbulence plays an important role are discussed in view of the comparative advantages of currently available models of turbulence phenomena; attention is given to a specific model that has undergone continuous refinement since 1985. The desideratum in this inquiry is a turbulence model which incorporates the best features of an a priori deterministic model, as well as a redundant set of results from full numerical simulations for a wide variety of turbulent flows; there should also be a simplification of the former, and an enlargement of the complexities of the latter.
Tactical missile turbulence problems
NASA Technical Reports Server (NTRS)
Dickson, Richard E.
1987-01-01
Of particular interest is atmospheric turbulence in the atmospheric boundary layer, since this affects both the launch and terminal phase of flight, and the total flight for direct fire systems. Brief discussions are presented on rocket artillery boost wind problems, mean wind correction, turbulent boost wind correction, the Dynamically Aimed Free Flight Rocket (DAFFR) wind filter, the DAFFR test, and rocket wake turbulence problems. It is concluded that many of the turbulence problems of rockets and missiles are common to those of aircraft, such as structural loading and control system design. However, these problems have not been solved at this time.
NASA Astrophysics Data System (ADS)
Jejjala, Vishnu; Minic, Djordje; Ng, Y. Jack; Tze, Chia-Hsiung
We propose a string theory of turbulence that explains the Kolmogorov scaling in 3+1 dimensions and the Kraichnan and Kolmogorov scalings in 2+1 dimensions. This string theory of turbulence should be understood in light of the AdS/CFT dictionary. Our argument is crucially based on the use of Migdal's loop variables and the self-consistent solutions of Migdal's loop equations for turbulence. In particular, there is an area law for turbulence in 2+1 dimensions related to the Kraichnan scaling.
NASA Astrophysics Data System (ADS)
Taitano, William; Knoll, Dana; Chacon, Luis; Chen, Guangye; Daughton, Bill
2012-10-01
[1][2] pioneered the implicit moment method (IMM) for kinetic plasma simulation. In the classic IMM approach, upon convergence of the discrete kinetic and fluid moment system within a timestep, a discretization truncation inconsistency between the two systems can exist. Additionally, when using the total stress tensor from the kinetic system as closure for the moment system, the stiff hyperbolic waves are not effectively decoupled from the kinetic system and accelerated in the moment system. In this presentation, we advance the original IMM approach by 1) addressing the discrete truncation consistency between the kinetic and moment system, and 2) improve the IMM approach by introducing the idea of density normalized stress tensor to efficiently isolate and implicitly step over the stiff hyperbolic isothermal wave in the moment system. We will present the significance of these improvements on the IMM method by discussing energy conservation and nonlinear convergence rate of the method for a multiscale two species ion acoustic shockwave problem. Additional results of the method accelerated via Anderson acceleration will be presented. [4pt][1] R.J. Mason, J. Comp. Phys., 1981. [2] J.U. Brackbill et al. J. Comp. Phys., 1982. [3] W.T. Taitano et al. SISC, 2012 in review.
Plank, Michael J; Law, Richard
2015-04-01
Mathematical models of dynamical systems in the life sciences typically assume that biological systems are spatially well mixed (the mean-field assumption). Even spatially explicit differential equation models typically make a local mean-field assumption. In effect, the assumption is that diffusive movement is strong enough to destroy spatial structure or that interactions between individuals are sufficiently long-range that the effects of spatial structure are weak. However, many important biophysical processes, such as chemical reactions of biomolecules within cells, disease transmission among humans, and dispersal of plants, have characteristic spatial scales that can generate strong spatial structure at the scale of individuals, with important effects on the behaviour of biological systems. This calls for mathematical methods that incorporate spatial structure. Here, we focus on one method, spatial-moment dynamics, which is based on the idea that important information about a spatial point process is held in its low-order spatial moments. The method goes beyond the dynamics of the first moment, i.e. the mean density or concentration of agents in space, in which no information about spatial structure is retained. By including the dynamics of at least the second moment, the method retains some information about spatial structure. Whereas mean-field models effectively use a closure assumption for the second moment, spatial-moment models use a closure assumption for the third (or a higher-order) moment. The aim of the paper was to provide a parsimonious and intuitive derivation of spatial-moment dynamic equations that is accessible to non-specialists. The derivation builds naturally from the first moment to the second, and we show how it can be extended to higher-order moments. Rather than tying the model to a specific biological example, we formulate a general model of movement, birth, and death of multiple types of interacting agents. This model can be applied to
Mass and Momentum Turbulent Transport Experiments with Confined Coaxial Jets
NASA Technical Reports Server (NTRS)
Johnson, B. V.; Bennett, J. C.
1981-01-01
Downstream mixing of coaxial jets discharging in an expanded duct was studied to obtain data for the evaluation and improvement of turbulent transport models currently used in a variety of computational procedures throughout the propulsion community for combustor flow modeling. Flow visualization studies showed four major shear regions occurring; a wake region immediately downstream of the inlet jet inlet duct; a shear region further downstream between the inner and annular jets; a recirculation zone; and a reattachment zone. A combination of turbulent momentum transport rate and two velocity component data were obtained from simultaneous measurements with a two color laser velocimeter (LV) system. Axial, radial and azimuthal velocities and turbulent momentum transport rate measurements in the r-z and r-theta planes were used to determine the mean value, second central moment (or rms fluctuation from mean), skewness and kurtosis for each data set probability density function (p.d.f.). A combination of turbulent mass transport rate, concentration and velocity data were obtained system. Velocity and mass transport in all three directions as well as concentration distributions were used to obtain the mean, second central moments, skewness and kurtosis for each p.d.f. These LV/LIF measurements also exposed the existence of a large region of countergradient turbulent axial mass transport in the region where the annular jet fluid was accelerating the inner jet fluid.
Closure for milliliter scale bioreactor
Klein, David L.; Laidlaw, Robert D.; Andronaco, Gregory; Boyer, Stephen G.
2010-12-14
A closure for a microreactor includes a cap that is configured to be inserted into a well of the microreactor. The cap, or at least a portion of the cap, is compliant so as to form a seal with the well when the cap is inserted. The cap includes an aperture that provides an airway between the inside of the well to the external environment when the cap is inserted into the well. A porous plug is inserted in the aperture, e.g., either directly or in tube that extends through the aperture. The porous plug permits gas within the well to pass through the aperture while preventing liquids from passing through to reduce evaporation and preventing microbes from passing through to provide a sterile environment. A one-way valve may also be used to help control the environment in the well.
NASA Technical Reports Server (NTRS)
Abid, R.; Speziale, C. G.
1992-01-01
Turbulent channel flow and homogeneous shear flow have served as basic building block flows for the testing and calibration of Reynolds stress models. A direct theoretical connection is made between homogeneous shear flow in equilibrium and the log-layer of fully-developed turbulent channel flow. It is shown that if a second-order closure model is calibrated to yield good equilibrium values for homogeneous shear flow it will also yield good results for the log-layer of channel flow provided that the Rotta coefficient is not too far removed from one. Most of the commonly used second-order closure models introduce an ad hoc wall reflection term in order to mask deficient predictions for the log-layer of channel flow that arise either from an inaccurate calibration of homogeneous shear flow or from the use of a Rotta coefficient that is too large. Illustrative model calculations are presented to demonstrate this point which has important implications for turbulence modeling.
Why turbulence sustains in supercritically stratified free atmosphere?
NASA Astrophysics Data System (ADS)
Zilitinkevich, Sergej
2016-04-01
It is widely believed that in very stable stratifications, at Richardson numbers (Ri) exceeding critical value Ric ˜ 0.25 turbulence decays and flow becomes laminar. This is so at low Reynolds numbers (Re), e.g., in lab experiments; but this is not true in very-high-Re geophysical flows. Free atmosphere and deep ocean are turbulent in spite of strongly supercritical stratifications: 1 << Ri < 103. Until recently, this paradox remained unexplained. The Energy- and Flux-Budget (EFB) turbulence-closure (Zilitinkevich et al., 2013) has disclosed the following turbulence self-control mechanisms. Until recently, the role of negative buoyancy flux, Fb > 0, in turbulence energetics was treated in terms of the turbulent kinetic energy (TKE) budget equation and understood as just consumption of TKE by the buoyancy forces. This has led to the conclusion that sufficiently strong static stability causes the negative buoyancy flux sufficiently strong to exceed the TKE generation rate and thus to kill turbulence. However, considering TKE equation together with budget equation for turbulent potential energy (TPE proportional to the squared buoyancy fluctuations) shows that the role of Fb in turbulence energetics is nothing but conversion of TKE into TPE (Fb just quantifies the rate of this conversion); so that Fb does not affect total turbulent energy (TTE = TKE + TPE). Moreover, as follows from the buoyancy-flux budget equation, TPE generates positive (directed upward) buoyancy flux irrespective of the sign of the buoyancy gradient. Indeed, the warmer fluid particles (with positive buoyancy fluctuation) rise up, whereas the cooler particles sink down, so that both contribute to the positive buoyancy flux opposing to the usual, negative flux generated by mean buoyancy gradient. In this context, strengthening the negative buoyancy flux leads to decreasing TKE and increasing TPE. The latter enhances the counter-gradient share of the total flux, thus reduces |Fb| and, eventually
Properties of turbulence in natural gas-oxygen diffusion flames
Sautet, J.C.; Ditaranto, M. ); Samaniego, J.M.; Charon, O. )
1999-07-01
Measurements of turbulent flow field velocities, including first and second order velocity moments and the shear stress are carried out by laser Doppler velocimetry in five different, 25 kW, turbulent natural gas-oxygen diffusion flames. The mean flow behavior is described including the velocity half value radius as well as centerline velocity. Mean radial velocity profiles are fitted by a Gaussian function. According to the initial momentum ratio, different jet dynamic behaviors are pointed out by the description of the fluctuating velocity field.
NASA Technical Reports Server (NTRS)
Ha Minh, H.; Viegas, J. R.; Rubesin, M. W.; Spalart, P.; Vandromme, D. D.
1989-01-01
The turbulent boundary layer under a freestream whose velocity varies sinusoidally in time around a zero mean is computed using two second order turbulence closure models. The time or phase dependent behavior of the Reynolds stresses are analyzed and results are compared to those of a previous SPALART-BALDWIN direct simulation. Comparisons show that the second order modeling is quite satisfactory for almost all phase angles, except in the relaminarization period where the computations lead to a relatively high wall shear stress.
Nuclear Quadrupole Moments and Nuclear Shell Structure
DOE R&D Accomplishments Database
Townes, C. H.; Foley, H. M.; Low, W.
1950-06-23
Describes a simple model, based on nuclear shell considerations, which leads to the proper behavior of known nuclear quadrupole moments, although predictions of the magnitudes of some quadrupole moments are seriously in error.
Factors Associated with Increasing Nursing Home Closures
Castle, Nicholas G; Engberg, John; Lave, Judith; Fisher, Andrew
2009-01-01
Purpose We determine the rate of nursing home closures for 7 years (1999–2005) and examine internal (e.g., quality), organizational (e.g., chain membership), and external (e.g., competition) factors associated with these closures. Design and Method The names of the closed facilities and dates of closure from state regulators in all 50 states were obtained. This information was linked to the Online Survey, Certification, and Reporting data, which contains information on internal, organizational, and market factors for almost all nursing homes in the United States. Results One thousand seven hundred and eighty-nine facilities closed over this time period (1999–2005). The average annual rate of closure was about 2 percent of facilities, but the rate of closure was found to be increasing. Nursing homes with higher rates of deficiency citations, hospital-based facilities, chain members, small bed size, and facilities located in markets with high levels of competition were more likely to close. High Medicaid occupancy rates were associated with a high likelihood of closure, especially for facilities with low Medicaid reimbursement rates. Implications As states actively debate about how to redistribute long-term care services/dollars, our findings show that they should be cognizant of the potential these decisions have for facilitating nursing home closures. PMID:19674434
NASA Technical Reports Server (NTRS)
Montgomery, David
1988-01-01
Three areas of study in MHD turbulence are considered. These are the turbulent relaxation of the toroidal Z pinch, density fluctuations in MHD fluids, and MHD cellular automata. A Boolean computer game that updates a cellular representation in parallel and that has macroscopic averages converging to solutions of the two-dimensional MHD equations is discussed.
Defining moments in leadership character development.
Bleich, Michael R
2015-06-01
Critical moments in life define one's character and clarify true values. Reflective leadership is espoused as an important practice for transformational leaders. Professional development educators can help surface and explore defining moments, strengthen leadership behavior with defining moments as a catalyst for change, and create safe spaces for leaders to expand their leadership capacity.
Galerkin POD Model Closure with Triadic Interactions by the Maximum Entropy Method
NASA Astrophysics Data System (ADS)
Hérouard, Nicolas; Niven, Robert K.; Noack, Bernd R.; Abel, Markus W.; Schlegel, Michael
2016-11-01
The maximum entropy method of Jaynes provides a method to infer the expected or most probable state of a system, by maximizing the relative entropy subject to physical constraints such as conservation of mass, energy and power. A maximum entropy closure for reduced-order models of fluid flows based on principal orthogonal decomposition (POD) is developed, to infer the probability density function for the POD modal amplitudes. This closure takes into account energy transfers by triadic interactions between modes, by extension of a theoretical model of these interactions in incompressible flow. The framework is applied to several incompressible flow systems including the cylinder wake, both at low and high Reynolds number (oscillatory and turbulent flow conditions), with important implications for the triadic structure and power balance (energy cascade) in the system. Australian Research Council Discovery Projects Grant DP140104402.
Samanta, Devranjan; Dubief, Yves; Holzner, Markus; Schäfer, Christof; Morozov, Alexander N.; Wagner, Christian; Hof, Björn
2013-01-01
Turbulence is ubiquitous in nature, yet even for the case of ordinary Newtonian fluids like water, our understanding of this phenomenon is limited. Many liquids of practical importance are more complicated (e.g., blood, polymer melts, paints), however; they exhibit elastic as well as viscous characteristics, and the relation between stress and strain is nonlinear. We demonstrate here for a model system of such complex fluids that at high shear rates, turbulence is not simply modified as previously believed but is suppressed and replaced by a different type of disordered motion, elasto-inertial turbulence. Elasto-inertial turbulence is found to occur at much lower Reynolds numbers than Newtonian turbulence, and the dynamical properties differ significantly. The friction scaling observed coincides with the so-called “maximum drag reduction” asymptote, which is exhibited by a wide range of viscoelastic fluids. PMID:23757498
Esquivel, A.; Lazarian, A.; Benjamin, R.A.; Cho, J.; Leitner, S.N.
2005-09-28
Turbulent mixing layers have been proposed to explain observations of line ratios of highly ionized elements in the interstellar medium. We present preliminary results of numerical simulations of turbulent mixing layers in a magnetized medium. We developed a MHD code with radiative cooling. The magnetic field is expected to be a controlling factor by suppressing instabilities that lead to the turbulent mixing. Our results suggest that the difference in turbulent mixing in the unmagnetized case as compared to the case of a weak magnetic field, {beta} = Pgas/Pmag {approx} 10, is insignificant. With a more thorough exploration of parameter space, this work will provide more reliable diagnostics of turbulent mixing layers than those available today.
Yucca Mountain Waste Package Closure System
Herschel Smartt; Arthur Watkins; David Pace; Rodney Bitsoi; Eric Larsen; Timothy McJunkin; Charles Tolle
2006-04-01
The current disposal path for high-level waste is to place the material into secure waste packages that are inserted into a repository. The Idaho National Laboratory has been tasked with the development, design, and demonstration of the waste package closure system for the repository project. The closure system design includes welding three lids and a purge port cap, four methods of nondestructive examination, and evacuation and backfill of the waste package, all performed in a remote environment. A demonstration of the closure system will be performed with a full-scale waste package.
Yucca Mountain Waste Package Closure System
shelton-davis; Colleen Shelton-Davis; Greg Housley
2005-10-01
The current disposal path for high-level waste is to place the material into secure waste packages that are inserted into a repository. The Idaho National Laboratory has been tasked with the development, design, and demonstration of the waste package closure system for the repository project. The closure system design includes welding three lids and a purge port cap, four methods of nondestructive examination, and evacuation and backfill of the waste package, all performed in a remote environment. A demonstration of the closure system will be performed with a full-scale waste package.
Moments of catchment storm area
NASA Technical Reports Server (NTRS)
Eagleson, P. S.; Wang, Q.
1985-01-01
The portion of a catchment covered by a stationary rainstorm is modeled by the common area of two overlapping circles. Given that rain occurs within the catchment and conditioned by fixed storm and catchment sizes, the first two moments of the distribution of the common area are derived from purely geometrical considerations. The variance of the wetted fraction is shown to peak when the catchment size is equal to the size of the predominant storm. The conditioning on storm size is removed by assuming a probability distribution based upon the observed fractal behavior of cloud and rainstorm areas.
Fermion dipole moment and holography
NASA Astrophysics Data System (ADS)
Kulaxizi, Manuela; Rahman, Rakibur
2015-12-01
In the background of a charged AdS black hole, we consider a Dirac particle endowed with an arbitrary magnetic dipole moment. For non-zero charge and dipole coupling of the bulk fermion, we find that the dual boundary theory can be plagued with superluminal modes. Requiring consistency of the dual CFT amounts to constraining the strength of the dipole coupling by an upper bound. We briefly discuss the implications of our results for the physics of holographic non-Fermi liquids.
Perception and Haptic Rendering of Friction Moments.
Kawasaki, H; Ohtuka, Y; Koide, S; Mouri, T
2011-01-01
This paper considers moments due to friction forces on the human fingertip. A computational technique called the friction moment arc method is presented. The method computes the static and/or dynamic friction moment independent of a friction force calculation. In addition, a new finger holder to display friction moment is presented. This device incorporates a small brushless motor and disk, and connects the human's finger to an interface finger of the five-fingered haptic interface robot HIRO II. Subjects' perception of friction moment while wearing the finger holder, as well as perceptions during object manipulation in a virtual reality environment, were evaluated experimentally.
Predicting Robust Learning with the Visual Form of the Moment-by-Moment Learning Curve
ERIC Educational Resources Information Center
Baker, Ryan S.; Hershkovitz, Arnon; Rossi, Lisa M.; Goldstein, Adam B.; Gowda, Sujith M.
2013-01-01
We present a new method for analyzing a student's learning over time for a specific skill: analysis of the graph of the student's moment-by-moment learning over time. Moment-by-moment learning is calculated using a data-mined model that assesses the probability that a student learned a skill or concept at a specific time during learning (Baker,…
Two phenomenological constants explain similarity laws in stably stratified turbulence.
Katul, Gabriel G; Porporato, Amilcare; Shah, Stimit; Bou-Zeid, Elie
2014-02-01
In stably stratified turbulent flows, the mixing efficiency associated with eddy diffusivity for heat, or equivalently the turbulent Prandtl number (Pr(t)), is fraught with complex dynamics originating from the scalewise interplay between shear generation of turbulence and its dissipation by density gradients. A large corpus of data and numerical simulations agree on a near-universal relation between Pr(t) and the Richardson number (R(i)), which encodes the relative importance of buoyancy dissipation to mechanical production of turbulent kinetic energy. The Pr(t)-R(i) relation is shown to be derivable solely from the cospectral budgets for momentum and heat fluxes if a Rotta-like return to isotropy closure for the pressure-strain effects and Kolmogorov's theory for turbulent cascade are invoked. The ratio of the Kolmogorov to the Kolmogorov-Obukhov-Corrsin phenomenological constants, and a constant associated with isotropization of the production whose value (= 3/5) has been predicted from Rapid Distortion Theory, explain all the macroscopic nonlinearities.
A minimal model of self-sustaining turbulence
Thomas, Vaughan L.; Gayme, Dennice F.; Farrell, Brian F.; Ioannou, Petros J.
2015-10-15
In this work, we examine the turbulence maintained in a Restricted Nonlinear (RNL) model of plane Couette flow. This model is a computationally efficient approximation of the second order statistical state dynamics obtained by partitioning the flow into a streamwise averaged mean flow and perturbations about that mean, a closure referred to herein as the RNL{sub ∞} model. The RNL model investigated here employs a single member of the infinite ensemble that comprises the covariance of the RNL{sub ∞} dynamics. The RNL system has previously been shown to support self-sustaining turbulence with a mean flow and structural features that are consistent with direct numerical simulations (DNS). Regardless of the number of streamwise Fourier components used in the simulation, the RNL system’s self-sustaining turbulent state is supported by a small number of streamwise varying modes. Remarkably, further truncation of the RNL system’s support to as few as one streamwise varying mode can suffice to sustain the turbulent state. The close correspondence between RNL simulations and DNS that has been previously demonstrated along with the results presented here suggest that the fundamental mechanisms underlying wall-turbulence can be analyzed using these highly simplified RNL systems.
Turbulence-particle interactions under surface gravity waves
NASA Astrophysics Data System (ADS)
Paskyabi, Mostafa Bakhoday
2016-11-01
The dispersion and transport of single inertial particles through an oscillatory turbulent aquatic environment are examined numerically by a Lagrangian particle tracking model using a series of idealised test cases. The turbulent mixing is incorporated into the Lagrangian model by the means of a stochastic scheme in which the inhomogeneous turbulent quantities are governed by a one-dimensional k- ɛ turbulence closure scheme. This vertical mixing model is further modified to include the effects of surface gravity waves including Coriolis-Stokes forcing, wave breaking, and Langmuir circulations. To simplify the complex interactions between the deterministic and the stochastic phases of flow, we assume a time-invariant turbulent flow field and exclude the hydrodynamic biases due to the effects of ambient mean current. The numerical results show that the inertial particles acquire perturbed oscillations traced out as time-varying sinking/rising orbits in the vicinity of the sea surface under linear and cnoidal waves and acquire a non-looping single arc superimposed with the high-frequency fluctuations beneath the nonlinear solitary waves. Furthermore, we briefly summarise some recipes through the course of this paper on the implementation of the stochastic particle tracking models to realistically describe the drift and suspension of inertial particles throughout the water column.
Rubinstein, Robert; Kurien, Susan; Cambon, Claude
2015-06-22
The representation theory of the rotation group is applied to construct a series expansion of the correlation tensor in homogeneous anisotropic turbulence. The resolution of angular dependence is the main analytical difficulty posed by anisotropic turbulence; representation theory parametrises this dependence by a tensor analogue of the standard spherical harmonics expansion of a scalar. As a result, the series expansion is formulated in terms of explicitly constructed tensor bases with scalar coefficients determined by angular moments of the correlation tensor.
Closure and transport theory for high-collisionality electron-ion plasmas
NASA Astrophysics Data System (ADS)
Ji, Jeong-Young; Held, Eric D.
2013-04-01
Systems of algebraic equations for a high-collisionality electron-ion plasma are constructed from the general moment equations with linearized collision operators [J.-Y. Ji and E. D. Held, Phys. Plasmas 13, 102103 (2006) and J.-Y. Ji and E. D. Held, Phys. Plasmas 15, 102101 (2008)]. A systematic geometric method is invented and applied to solve the system of equations to find closure and transport relations. It is known that some closure coefficients of Braginskii [S. I. Braginskii, Reviews of Plasma Physics (Consultants Bureau, New York, 1965), Vol. 1] are in error up to 65% for some finite values of x (cyclotron frequency × electron-ion collision time) and have significant error in the large-x limit [E. M. Epperlein and M. G. Haines, Phys. Fluids 29, 1029 (1986)]. In this work, fitting formulas for electron coefficients are obtained from the 160 moment (Laguerre polynomial) solution, which converges with increasing moments for x ≤100 and from the asymptotic solution for large x-values. The new fitting formulas are practically exact (less than 1% error) for arbitrary x and Z (the ion charge number, checked up to Z = 100). The ion coefficients for equal electron and ion temperatures are moderately modified by including the ion-electron collision operator. When the ion temperature is higher than the electron temperature, the ion-electron collision and the temperature change terms in the moment equations must be kept. The ion coefficient formulas from 3 moment (Laguerre polynomial) calculations, precise to less than 0.4% error from the convergent values, are explicitly written.
Dissipation in non-equilibrium turbulence
NASA Astrophysics Data System (ADS)
Bos, Wouter; Rubinstein, Robert
2016-11-01
For about a decade, experimental and numerical studies have reported on the existence of an anomalous behaviour of the viscous dissipation rate in unsteady turbulence (see for instance Vassilicos, Annu. Rev. Fluid Mech. 2015). It appears that the short-time transient dynamics can be described by a universal power law, incompatible with Taylor's 1935 dissipation rate estimate. We show that these results can be explained using a non-equilibrium energy distribution, obtained from a low-frequency perturbative expansion of simple spectral closure. The resulting description is fairly simple. In particular, during the transient, according to the predictions, the normalized dissipation rate Cɛ evolves as a function of the Taylor-scale Reynolds number Rλ following the relation Cɛ Rλ- 15 / 14 , in close agreement with experimental and numerical observations.
Collapse of higher-order solute concentration moments in groundwater transport
NASA Astrophysics Data System (ADS)
Srzic, Veljko; Andricevic, Roko; Gotovac, Hrvoje; Cvetkovic, Vladimir
2013-08-01
In this paper, we use numerical simulations based on a Lagrangian framework to study contaminant transport through highly heterogeneous porous media due to advection and local diffusion (under local diffusion, we assume coupled effect of mechanical dispersion and molecular diffusion). The analysis of the concentration field is done for the case of a two-dimensional hydraulic conductivity domain representing the aquifer, with three log-conductivity structures that differ in spatial correlation. In addition to different conductivity structures, we focus our investigation on mild and highly heterogeneous porous media characterized by the values of hydraulic log-conductivity variance >(σY2>) being equal to 1 and 8. In the concentration moment analysis, we show that a linear relationship exists between higher-order to second-order normalized concentration moments on a log-log scale up to the fourth-order moment. This leads to the important finding that moments of a higher than the second order can be derived based on information about the first two concentration moments only. Such a property has been observed previously for boundary-layer water channels, wind tunnels, and turbulent diffusion in open terrain and laboratory experiments. Normalized moments are shown to collapse for different types of hydraulic conductivity structures, Peclet (Pe) numbers and σY2 values. In the case of local diffusion absence, a linear log-log relationship is derived analytically and is set as a lower limit. The deviation from the lower limit is explained to be predominantly caused by the local diffusion, which needs time to evolve. In the case of local diffusion presence, we define the moment deriving function (MDF) to describe the linear log-log relationship between higher-order concentration moments to the second-order normalized one. Finally, the comparison between numerical results and those obtained from the Columbus Air Force Base Macrodispersion Experiment (MADE 1) is used to