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NASA NTRS1987

Toward the large-eddy simulations of compressible turbulent flows

New subgrid-scale models for the large-eddy simulation of compressible turbulent flows are developed based on the Favre-filtered equations of motion for an ideal gas. A compressible generalization of the linear combination of the Smagorinsky model and scale-similarity model (in terms of Favre-filtered fields) is obtained for the subgrid-scale stress tensor. An analogous thermal linear combination model is also developed for the subgrid-scale heat flux vector. The three dimensionless constants associated with these subgrid-scale models are obtained by correlating with the results of direct numerical simulations of compressible isotropic turbulence performed on a 96 to the third power grid using Fourier collocation methods. Extensive comparisons between the direct and modeled subgrid-scale fields are provided in order to validate the models. Future applications of these compressible subgrid-scale models to the large-eddy simulation of supersonic aerodynamic flows are discussed briefly.

Erlebacher, G.↗

NASA NTRS1990

Toward the large-eddy simulation of compressible turbulent flows

New subgrid-scale models for the large-eddy simulation of compressible turbulent flows are developed and tested based on the Favre-filtered equations of motion for an ideal gas. A compressible generalization of the linear combination of the Smagorinsky model and scale-similarity model, in terms of Favre-filtered fields, is obtained for the subgrid-scale stress tensor. An analogous thermal linear combination model is also developed for the subgrid-scale heat flux vector. The two dimensionless constants associated with these subgrid-scale models are obtained by correlating with the results of direct numerical simulations of compressible isotropic turbulence performed on a 96(exp 3) grid using Fourier collocation methods. Extensive comparisons between the direct and modeled subgrid-scale fields are provided in order to validate the models. A large-eddy simulation of the decay of compressible isotropic turbulence (conducted on a coarse 32(exp 3) grid) is shown to yield results that are in excellent agreement with the fine grid direct simulation. Future applications of these compressible subgrid-scale models to the large-eddy simulation of more complex supersonic flows are discussed briefly.

Erlebacher, G.↗

NASA NTRS1992

Toward the large-eddy simulation of compressible turbulent flows

New subgrid-scale models for the large-eddy simulation of compressible turbulent flows are developed and tested based on the Favre-filtered equations of motion for an ideal gas. A compressible generalization of the linear combination of the Smagorinsky model and scale-similarity model, in terms of Favre-filtered fields, is obtained for the subgrid-scale stress tensor. An analogous thermal linear combination model is also developed for the subgrid-scale heat flux vector. The two dimensionless constants associated with these subgrid-scale models are obtained by correlating with the results of direct numerical simulations of compressible isotropic turbulence performed on a 96 (exp 3) grid using Fourier collocation methods. Extensive comparisons between the direct and modeled subgrid-scale fields are provided in order to validate the models. A large-eddy simulation of the decay of compressible isotropic turbulence (conducted on a coarse 32(exp 3) grid) is shown to yield results that are in excellent agreement with the fine-grid direct simulation. Future applications of these compressible subgrid-scale models to the large-eddy simulation of more complex supersonic flows are discussed briefly.

Erlebacher, G.↗

NASA NTRS1989

On the large-eddy simulation of transitional wall-bounded flows

The structure of the subgrid scale fields in plane channel flow has been studied at various stages of the transition process to turbulence. The residual stress and subgrid scale dissipation calculated using velocity fields generated by direct numerical simulations of the Navier-Stokes equations are significantly different from their counterparts in turbulent flows. The subgrid scale dissipation changes sign over extended areas of the channel, indicating energy flow from the small scales to the large scales. This reversed energy cascade becomes less pronounced at the later stages of transition. Standard residual stress models of the Smagorinsky type are excessively dissipative. Rescaling the model constant improves the prediction of the total (integrated) subgrid scale dissipation, but not that of the local one. Despite the somewhat excessive dissipation of the rescaled Smagorinsky model, the results of a large eddy simulation of transition on a flat-plate boundary layer compare quite well with those of a direct simulation, and require only a small fraction of the computational effort. The inclusion of non-dissipative models, which could lead to further improvements, is proposed.

Piomelli, Ugo↗

NASA NTRS1990

On the large-eddy simulation of transitional wall-bounded flows

Piomelli, Ugo↗

NASA NTRS1988

Model consistency in large eddy simulation of turbulent channel flows

Combinations of filters and subgrid scale stress models for large eddy simulation of the Navier-Stokes equations are examined by a priori tests and numerical simulations. The structure of the subgrid scales is found to depend strongly on the type of filter used, and consistency between model and filter is essential to ensure accurate results. The implementation of consistent combinations of filter and model gives more accurate turbulence statistics than those obtained in previous investigations in which the models were chosen independently from the filter. Results and limitations of the a priori test are discussed. The effect of grid refinement is also examined.

Piomelli, Ugo↗

NASA NTRS2002

Properties of the Residual Stress of the Temporally Filtered Navier-Stokes Equations

The development of a unifying framework among direct numerical simulations, large-eddy simulations, and statistically averaged formulations of the Navier-Stokes equations, is of current interest. Toward that goal, the properties of the residual (subgrid-scale) stress of the temporally filtered Navier-Stokes equations are carefully examined. Causal time-domain filters, parameterized by a temporal filter width 0 less than Delta less than infinity, are considered. For several reasons, the differential forms of such filters are preferred to their corresponding integral forms; among these, storage requirements for differential forms are typically much less than for integral forms and, for some filters, are independent of Delta. The behavior of the residual stress in the limits of both vanishing and in infinite filter widths is examined. It is shown analytically that, in the limit Delta to 0, the residual stress vanishes, in which case the Navier-Stokes equations are recovered from the temporally filtered equations. Alternately, in the limit Delta to infinity, the residual stress is equivalent to the long-time averaged stress, and the Reynolds-averaged Navier-Stokes equations are recovered from the temporally filtered equations. The predicted behavior at the asymptotic limits of filter width is further validated by numerical simulations of the temporally filtered forced, viscous Burger's equation. Finally, finite filter widths are also considered, and a priori analyses of temporal similarity and temporal approximate deconvolution models of the residual stress are conducted.

Pruett, C. D.↗

NASA NTRS1993

A local dynamic model for large eddy simulation

The dynamic model is a method for computing the coefficient C in Smagorinsky's model for the subgrid-scale stress tensor as a function of position from the information already contained in the resolved velocity field rather than treating it as an adjustable parameter. A variational formulation of the dynamic model is described that removes the inconsistency associated with taking C out of the filtering operation. This model, however, is still unstable due to the negative eddy-viscosity. Next, three models are presented that are mathematically consistent as well as numerically stable. The first two are applicable to homogeneous flows and flows with at least one homogeneous direction, respectively, and are, in fact, a rigorous derivation of the ad hoc expressions used by previous authors. The third model in this set can be applied to arbitrary flows, and it is stable because the C it predicts is always positive. Finally, a model involving the subgrid-scale kinetic energy is presented which attempts to model backscatter. This last model has some desirable theoretical features. However, even though it gives results in LES that are qualitatively correct, it is outperformed by the simpler constrained variational models. It is suggested that one of the constrained variational models should be used for actual LES while theoretical investigation of the kinetic energy approach should be continued in an effort to improve its predictive power and to understand more about backscatter.

Ghosal, Sandip↗

NASA NTRS1999

On Taylor-Series Approximations of Residual Stress

Although subgrid-scale models of similarity type are insufficiently dissipative for practical applications to large-eddy simulation, in recently published a priori analyses, they perform remarkably well in the sense of correlating highly against exact residual stresses. Here, Taylor-series expansions of residual stress are exploited to explain the observed behavior and "success" of similarity models. Until very recently, little attention has been given to issues related to the convergence of such expansions. Here, we re-express the convergence criterion of Vasilyev [J. Comput. Phys., 146 (1998)] in terms of the transfer function and the wavenumber cutoff of the grid filter.

Pruett, C. David↗

DOE OSTI2023

Differentiable physics-enabled closure modeling for Burgers’ turbulence

Abstract Data-driven turbulence modeling is experiencing a surge in interest following algorithmic and hardware developments in the data sciences. We discuss an approach using the differentiable physics paradigm that combines known physics with machine learning to develop closure models for Burgers’ turbulence. We consider the one-dimensional Burgers system as a prototypical test problem for modeling the unresolved terms in advection-dominated turbulence problems. We train a series of models that incorporate varying degrees of physical assumptions on an a posteriori loss function to test the efficacy of models across a range of system parameters, including viscosity, time, and grid resolution. We find that constraining models with inductive biases in the form of partial differential equations that contain known physics or existing closure approaches produces highly data-efficient, accurate, and generalizable models, outperforming state-of-the-art baselines. Addition of structure in the form of physics information also brings a level of interpretability to the models, potentially offering a stepping stone to the future of closure modeling.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1987

Model consistency in the large eddy simulation of turbulent channel flows

Various combinations of filters and subgrid scale stress models for large eddy simulation of the Navier-Stokes equations are studied by a priori tests and numerical simulations. Consistency between model and filter is found to be essential to ensure accurate results. Results and limitations of the a priori test are discussed. The effect of grid refinement is also examined.

Moin, Parviz↗

NASA NTRS1994

Developments and applications of dynamic models for large eddy simulation of complex flows

The dynamic modeling procedure for large eddy simulation of turbulent flows is reviewed and recent developments in the theoretical aspects and applications are described. Methods for inclusion of backscatter of energy from small to large scale motions are presented. New formulations of the dynamic procedure are proposed which are optimized based on the subgrid scale flux vector or the energy dissipation rate instead of the subgrid scale stress tensor. Recent results from application of the model to forced isotropic turbulence with an inertial subrange, flow over a backward facing step at Reynolds number of 28000, and flow over a concave curved surface are presented.

Moin, P.↗

NASA NTRS1999

Scale-Similar Models for Large-Eddy Simulations

Scale-similar models employ multiple filtering operations to identify the smallest resolved scales, which have been shown to be the most active in the interaction with the unresolved subgrid scales. They do not assume that the principal axes of the strain-rate tensor are aligned with those of the subgrid-scale stress (SGS) tensor, and allow the explicit calculation of the SGS energy. They can provide backscatter in a numerically stable and physically realistic manner, and predict SGS stresses in regions that are well correlated with the locations where large Reynolds stress occurs. In this paper, eddy viscosity and mixed models, which include an eddy-viscosity part as well as a scale-similar contribution, are applied to the simulation of two flows, a high Reynolds number plane channel flow, and a three-dimensional, nonequilibrium flow. The results show that simulations without models or with the Smagorinsky model are unable to predict nonequilibrium effects. Dynamic models provide an improvement of the results: the adjustment of the coefficient results in more accurate prediction of the perturbation from equilibrium. The Lagrangian-ensemble approach [Meneveau et al., J. Fluid Mech. 319, 353 (1996)] is found to be very beneficial. Models that included a scale-similar term and a dissipative one, as well as the Lagrangian ensemble averaging, gave results in the best agreement with the direct simulation and experimental data.

Sarghini, F.↗

NASA NTRS2001

Statistical Ensemble of Large Eddy Simulations

A statistical ensemble of large eddy simulations (LES) is run simultaneously for the same flow. The information provided by the different large scale velocity fields is used to propose an ensemble averaged version of the dynamic model. This produces local model parameters that only depend on the statistical properties of the flow. An important property of the ensemble averaged dynamic procedure is that it does not require any spatial averaging and can thus be used in fully inhomogeneous flows. Also, the ensemble of LES's provides statistics of the large scale velocity that can be used for building new models for the subgrid-scale stress tensor. The ensemble averaged dynamic procedure has been implemented with various models for three flows: decaying isotropic turbulence, forced isotropic turbulence, and the time developing plane wake. It is found that the results are almost independent of the number of LES's in the statistical ensemble provided that the ensemble contains at least 16 realizations.

Carati, Daniele↗

NASA NTRS1997

Large-Eddy Simulation of Transition to Turbulence in Boundary Layers

Large-eddy simulation results for laminar-to-turbulent transition in a spatially developing boundary layer are presented. The disturbances are ingested into a laminar flow through an unsteady suction-and-blowing strip. The filtered, three-dimensional time- dependent Navier-Stokes equations are integrated numerically using spectral, high-order finite-difference, and three-stage low-storage Runge-Kutta methods. The buffer-domain technique is used for the outflow boundary condition. The localized dynamic model used to parameterize the subgrid-scale stresses begins to have a significant impact at the beginning of the nonlinear transition (or intermittency) region. The flow structures commonly found in experiments are also observed in the present simulation; the computed linear instability modes and secondary instability lambda-vortex structures are in agreement with the experiments, and the streak-like-structures and turbulent statistics compare with both the experiments and the theory. The physics captured in the present LES are consistent with the experiments and the full Navier-Stokes simulation (DNS), at a significant fraction of the DNS cost. A comparison of the results obtained with several SGS models shows that the localized model gives accurate results both in a statistical sense and in terms of predicting the dynamics of the energy-carrying eddies, without ad hoc adjustments.

Huai, Xiao-Li↗

NASA NTRSDate not supplied

Surrogate Modeling of Subgrid Turbulent Transport Based on 3D Radiative Hydrodynamic Simulations of the Quiet Sun

Turbulent Transport: Plays a critical role in astrophysical plasmas, such as the solar interior, spanning multiple scales and challenging traditional modeling approaches. Objective: Develop machine learning (ML) models—MLP and CNN—to predict subgrid Reynolds stress tensors from StellarBox 3D simulations of the solar atmosphere. Benchmarking: Compare ML-driven models against physics-based Gradient and Smagorinsky approaches.

SMD↗

NASA NTRS1979

Large Eddy Simulation of turbulent shear flows

The conceptual foundation underlying Large Eddy Simulation (LES) is summarized, and the numerical methods developed for simulation of the time-developing turbulent mixing layer and turbulent plane Poiseuille flow are discussed. Computational results show that the average Reynolds stress profile nearly attains the equilibrium shape which balances the downstream mean pressure gradient in the regions away from the walls. In the vicinity of the walls, viscous stresses are shown to be significant; together with the Reynolds stresses, these stresses balance the mean pressure gradient. It is stressed that the subgrid scale contribution to the total Reynolds stress is significant only in the vicinity of the walls. The continued development of LES is urged.

Moin, P.↗

NASA NTRS1993

On the large eddy simulation of turbulent flows in complex geometry

Application of the method of Large Eddy Simulation (LES) to a turbulent flow consists of three separate steps. First, a filtering operation is performed on the Navier-Stokes equations to remove the small spatial scales. The resulting equations that describe the space time evolution of the 'large eddies' contain the subgrid-scale (sgs) stress tensor that describes the effect of the unresolved small scales on the resolved scales. The second step is the replacement of the sgs stress tensor by some expression involving the large scales - this is the problem of 'subgrid-scale modeling'. The final step is the numerical simulation of the resulting 'closed' equations for the large scale fields on a grid small enough to resolve the smallest of the large eddies, but still much larger than the fine scale structures at the Kolmogorov length. In dividing a turbulent flow field into 'large' and 'small' eddies, one presumes that a cut-off length delta can be sensibly chosen such that all fluctuations on a scale larger than delta are 'large eddies' and the remainder constitute the 'small scale' fluctuations. Typically, delta would be a length scale characterizing the smallest structures of interest in the flow. In an inhomogeneous flow, the 'sensible choice' for delta may vary significantly over the flow domain. For example, in a wall bounded turbulent flow, most statistical averages of interest vary much more rapidly with position near the wall than far away from it. Further, there are dynamically important organized structures near the wall on a scale much smaller than the boundary layer thickness. Therefore, the minimum size of eddies that need to be resolved is smaller near the wall. In general, for the LES of inhomogeneous flows, the width of the filtering kernel delta must be considered to be a function of position. If a filtering operation with a nonuniform filter width is performed on the Navier-Stokes equations, one does not in general get the standard large eddy equations. The complication is caused by the fact that a filtering operation with a nonuniform filter width in general does not commute with the operation of differentiation. This is one of the issues that we have looked at in detail as it is basic to any attempt at applying LES to complex geometry flows. Our principal findings are summarized.

Ghosal, Sandip↗