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NASA NTRS2022

A Dynamic Nonlinear Subgrid-Scale Model for Large-Eddy Simulation of Complex Turbulent Flows

We present a new dynamic nonlinear subgrid-scale (SGS) model for large-eddy simulations (LES) and apply it to compute a flow involving pressure gradients, surface curvature and separation, for which data from a direct numerical simulation are available for comparison. The model, inspired by the triple model idea of Bardina et al. (“Improved Turbulence Models Based on Large Eddy Simulation of Homogeneous, Incompressible, Turbulent Flows,” Report No. TF-19, Thermosciences Division, Department of Mechanical Engineering, Stanford University, 1983), includes a Galilean-invariant term called the modified Leonard stress tensor, and two nonlinear terms comprised of the products of the strain-rate and rotation-rate tensors for an improved representation of the subgrid-scale dissipation, backscatter and anisotropy effects. The model does not employ any ad hoc averaging or clipping procedures, and does not require the specification of a characteristic length scale; hence, it naturally avoids the ambiguities associated with defining a proper length scale for anisotropic grids. Results from the wall-resolved LES of flow past a Gaussian bump using the new model demonstrate improved prediction of skin-friction, flow separation, mean flow profiles and turbulent quantities when compared to implicit LES as well as explicit LES using the Vreman SGS model on the same grid.

Turbulence↗

NASA NTRS1979

Evaluation of subgrid-scale models using an accurately simulated turbulent flow

A calculation of periodic homogeneous isotropic turbulence is used to simulate the experimental decay of grid turbulence. The calculation is found to match the experiment in a number of important aspects and the computed flow field is then treated as a realization of a physical turbulent flow. From this flow, a calculation is conducted of the large eddy field and the various averages of the subgrid-scale turbulence that occur in the large eddy simulation equations. These quantities are compared with the predictions of the models that are usually applied in large eddy simulation. The results show that the terms which involve the large-scale field are accurately modeled but the subgrid-scale Reynolds stresses are only moderately well modeled. It is also possible to use the method to predict the constants of the models without reference to experiment. Attempts to find improved models have not met with success.

Clark, R. A.↗

NASA NTRS1987

Analysis of subgrid-scale eddy viscosity with use of results from direct numerical simulations

Without resort to any modeling, subgrid-scale eddy viscosity is computed from the results of high-resolution (64 cubed and 128 cubed grid points) direct numerical simulations of three-dimensional homogeneous isotropic decaying turbulence. In these simulations the eddy viscosity peaks sharply at the cutoff wavenumber, in rough agreement with the results of Kraichnan (1976). In addition, in the low-wavenumber range the eddy viscosity may be negative, contrary to the generally accepted concept of subgrid-scale eddy viscosity. Some possible explanations of this behavior are discussed.

Domaradzki, J. Andrzej↗

NASA NTRS1989

Land surface hydrology parameterization for atmospheric general circulation models including subgrid scale spatial variability

Parameterizations are developed for the representation of subgrid hydrologic processes in atmospheric general circulation models. Reasonable a priori probability density functions of the spatial variability of soil moisture and of precipitation are introduced. These are used in conjunction with the deterministic equations describing basic soil moisture physics to derive expressions for the hydrologic processes that include subgrid scale variation in parameters. The major model sensitivities to soil type and to climatic forcing are explored.

Entekhabi, D.↗

NASA NTRS1993

Stratified turbulence in the atmosphere and oceans - A new subgrid model

Turbulence in stably and unstably stratified media is studied, and the results are used to construct a subgrid simulation (SGS) model for use in large eddy simulation (LES). It was found that, although the assumption of inertiality of the subgrid scales is reasonable for the case of unstable stratification, it ceases to be so in the case of stable stratification, where gravity removes kinetic energy from the eddies: the generation of gravity waves becomes the dominant physical process, with dissipation relegated to higher wavenumbers. Preliminary results show that the total kinetic energy dissipation length scale increases with stability, in accordance with LES results but in disagreement with Deardorff's model that suggests a decrease of all dissipation scales in presence of stratification.

Canuto, V. M.↗

NASA NTRS1993

A normal stress subgrid-scale eddy viscosity model in large eddy simulation

The Smagorinsky subgrid-scale eddy viscosity model (SGS-EVM) is commonly used in large eddy simulations (LES) to represent the effects of the unresolved scales on the resolved scales. This model is known to be limited because its constant must be optimized in different flows, and it must be modified with a damping function to account for near-wall effects. The recent dynamic model is designed to overcome these limitations but is compositionally intensive as compared to the traditional SGS-EVM. In a recent study using direct numerical simulation data, Horiuti has shown that these drawbacks are due mainly to the use of an improper velocity scale in the SGS-EVM. He also proposed the use of the subgrid-scale normal stress as a new velocity scale that was inspired by a high-order anisotropic representation model. The testing of Horiuti, however, was conducted using DNS data from a low Reynolds number channel flow simulation. It was felt that further testing at higher Reynolds numbers and also using different flows (other than wall-bounded shear flows) were necessary steps needed to establish the validity of the new model. This is the primary motivation of the present study. The objective is to test the new model using DNS databases of high Reynolds number channel and fully developed turbulent mixing layer flows. The use of both channel (wall-bounded) and mixing layer flows is important for the development of accurate LES models because these two flows encompass many characteristic features of complex turbulent flows.

Horiuti, K.↗

NASA NTRS1993

Large-eddy simulation of laminar-turbulent breakdown at high speeds with dynamic subgrid-scale modeling

The laminar-turbulent breakdown of a boundary-layer flow along a hollow cylinder at Mach 4.5 is investigated with large-eddy simulation. The subgrid scales are modeled dynamically, where the model coefficients are determined from the local resolved field. The behavior of the dynamic-model coefficients is investigated through both an a priori test with direct numerical simulation data for the same case and a complete large-eddy simulation. Both formulations proposed by Germano et al. and Lilly are used for the determination of unique coefficients for the dynamic model and their results are compared and assessed. The behavior and the energy cascade of the subgrid-scale field structure are investigated at various stages of the transition process. The investigations are able to duplicate a high-speed transition phenomenon observed in experiments and explained only recently by the direct numerical simulations of Pruett and Zang, which is the appearance of 'rope-like' waves. The nonlinear evolution and breakdown of the laminar boundary layer and the structure of the flow field during the transition process were also investigated.

El-Hady, Nabil M.↗

NASA NTRS1995

The importance of mesoscale circulations generated by subgrid-scale landscape heterogeneities in general circulation models

A mesoscale atmospheric model was used to evaluate the impact of subgrid-scale landscape discontinuities on the vertical profiles of resolved temperature, moisture, and moist static energy in the planetary boundary layer (PBL) of general circulation models (GCMs). These profiles were produced with a 3D version of the model (using a horizontal grid resolution of 7.5 km and 13 vertical layers in the PBL) by averaging horizontally the various atmospheric variables over a 180 x 180 sq km domain-about the size of the horizontal domain represented by a single grid element in a GCM. They were compared to corresponding vertical profiles produced with a 1D version of the model, which simulates the PBL, as in a GCM, over a single horizontal grid element. Differences obtained between the horizontally averaged atmospheric variables produced with the 3D simulations and the 1D simulations emphasize the impact of subgrid-scale landscape discontinuities on GCM-resolved variables. Various types of landscape discontinuities, characterized by horizontal contrasts of surface wetness and size of land patches, were simulated under various background-wind conditions. Differences of temperature, specific humidity, and moist static energy as large as 4 K, 6 g/kg, and 10 kJ/kg were obtained in some cases. These differences were not affected significantly by moderate winds but were sensitive to the spatial distribution of surface wetness. These results emphasize the need to parameterize mesoscale processes induced by landscape discontinuities in GCMss.

Lynn, Barry H.↗

NASA NTRS1995

On why dynamic subgrid-scale models work

Dynamic subgrid models have proved to be remarkably successful in predicting the behavior of turbulent flows. Part of the reasons for their success are well understood. Since they are constructed to generate an effective viscosity which is proportional to some measure of the turbulent energy at the high wavenumber end of the spectrum, their eddy viscosity vanishes as the flow becomes laminar. This alone would justify their use over simpler models. But beyond this obvious advantage, which is confined to inhomogeneous and evolving flows, the reason why they also work better in simpler homogeneous cases, and how they do it without any obvious adjustable parameter, is not clear. This lack of understanding of the internal mechanisms of a useful tool is disturbing, not only as an intellectual challenge, but because it raises the doubt of whether it will work in all cases. This note is an attempt to clarify those mechanisms. We will see why dynamic models are robust and how they can get away with even comparatively gross errors in their formulations. This will suggest that they are only particular cases of a larger family of robust models, all of which would be relatively insensitive to large simplifications in the physics of the flow. We will also construct some such models, although mostly as research tools. It will turn out, however, that the standard dynamic formulation is not only robust to errors, but also behaves as if it were substantially well formulated. The details of why this is so will still not be clear at the end of this note, specially since it will be shown that the 'a priori' testing of the stresses gives, as is usual in most subgrid models, very poor results. But it will be argued that the basic reason is that the dynamic formulation mimics the condition that the total dissipation is approximately equal to the production measured at the test filter level.

Jimenez, J.↗

NASA NTRS1996

A priori testing of subgrid-scale models for the velocity-pressure and vorticity-velocity formulations

Subgrid-scale models for Large Eddy Simulation (LES) in both the velocity-pressure and the vorticity-velocity formulations were evaluated and compared in a priori tests using spectral Direct Numerical Simulation (DNS) databases of isotropic turbulence: 128(exp 3) DNS of forced turbulence (Re(sub(lambda))=95.8) filtered, using the sharp cutoff filter, to both 32(exp 3) and 16(exp 3) synthetic LES fields; 512(exp 3) DNS of decaying turbulence (Re(sub(Lambda))=63.5) filtered to both 64(exp 3) and 32(exp 3) LES fields. Gaussian and top-hat filters were also used with the 128(exp 3) database. Different LES models were evaluated for each formulation: eddy-viscosity models, hyper eddy-viscosity models, mixed models, and scale-similarity models. Correlations between exact versus modeled subgrid-scale quantities were measured at three levels: tensor (traceless), vector (solenoidal 'force'), and scalar (dissipation) levels, and for both cases of uniform and variable coefficient(s). Different choices for the 1/T scaling appearing in the eddy-viscosity were also evaluated. It was found that the models for the vorticity-velocity formulation produce higher correlations with the filtered DNS data than their counterpart in the velocity-pressure formulation. It was also found that the hyper eddy-viscosity model performs better than the eddy viscosity model, in both formulations.

Winckelmans, G. S.↗

NASA NTRS1999

A Priori Subgrid Analysis of Temporal Mixing Layers with Evaporating Droplets

Subgrid analysis of a transitional temporal mixing layer with evaporating droplets has been performed using three sets of results from a Direct Numerical Simulation (DNS) database, with Reynolds numbers (based on initial vorticity thickness) as large as 600 and with droplet mass loadings as large as 0.5. In the DNS, the gas phase is computed using a Eulerian formulation, with Lagrangian droplet tracking. The Large Eddy Simulation (LES) equations corresponding to the DNS are first derived, and key assumptions in deriving them are first confirmed by computing the terms using the DNS database. Since LES of this flow requires the computation of unfiltered gas-phase variables at droplet locations from filtered gas-phase variables at the grid points, it is proposed to model these by assuming the gas-phase variables to be the sum of the filtered variables and a correction based on the filtered standard deviation; this correction is then computed from the Subgrid Scale (SGS) standard deviation. This model predicts the unfiltered variables at droplet locations considerably better than simply interpolating the filtered variables. Three methods are investigated for modeling the SGS standard deviation: the Smagorinsky approach, the Gradient model and the Scale-Similarity formulation. When the proportionality constant inherent in the SGS models is properly calculated, the Gradient and Scale-Similarity methods give results in excellent agreement with the DNS.

Okongo, Nora↗

NASA NTRS2003

Large-eddy Simulation of Stratocumulus-topped Atmospheric Boundary Layers with Dynamic Subgrid-scale Models

The objective of the present study is to evaluate the dynamic procedure in LES of stratocumulus topped atmospheric boundary layer and assess the relative importance of subgrid-scale modeling, cloud microphysics and radiation modeling on the predictions. The simulations will also be used to gain insight into the processes leading to cloud top entrainment instability and cloud breakup. In this report we document the governing equations, numerical schemes and physical models that are employed in the Goddard Cumulus Ensemble model (GCEM3D). We also present the subgrid-scale dynamic procedures that have been implemented in the GCEM3D code for the purpose of the present study.

Senocak, Inane↗

NASA NTRS1999

A Priori Subgrid Analysis of Temporal Mixing Layers with Evaporating Droplets

subgrid↗

NASA NTRS1980

Improved subgrid-scale models for large-eddy simulation

The paper analyzes models for subgrid-scale turbulence. The analysis indicates that there is sufficient information in the resolved scales to determine some characteristics of the complete flow field. The kinetic energy of the small-scale motions can be decomposed into two parts: one results from the large scales and is correlated with them, and the other part is uncorrelated which leads to a two-component eddy-viscosity model. The 'production equals dissipation' argument does not apply to the small scales in the decay of turbulence because it does not account for the uncorrelated component. The exchange between the large and small scales takes place mainly between the smallest scales of the former and the largest scales of the latter; this argument is the basis of a new model shown to be superior to the Smagorinsky model (1963).

Bardina, J.↗

NASA NTRS1987

On the subgrid-scale modeling of compressible turbulence

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

Speziale, C. G.↗

NASA NTRS1987

Validation of EDQNM for subgrid and supergrid models

From preliminary calculations it was concluded that the two-point Eddy Damping Quasi-Normal Markovian (EDQNM) closure accurately describes the behavior of second order moments. This closure can be applied as subgrid and supergrid models for Large Eddy Simulations at higher Reynolds numbers. In the case of homogeneous anisotropic turbulence, when the nonlinear terms are introduced the calculation becomes quite onerous but is still considerably less expensive than the calculation of a DS. The major merit of two-point closure models is that they can be easily applied to flows at Reynolds numbers that are unreachable by a DS. Work is in progress to derive expressions for the nonlinear terms that give good global conservation properties.

Orlandi, P.↗

NASA NTRS1988

The subgrid-scale modeling of compressible turbulence

Speziale, C. G.↗

NASA NTRS1991

Renormalization group analysis of reduced magnetohydrodynamics with application to subgrid modeling

The technique for obtaining a subgrid model for Navier-Stokes turbulence, based on renormalization group analysis (RNG), is extended to the reduced magnetohydrodynamic (RMND) equations. It is shown that a RNG treatment of the Alfven turbulence supported by the RMHD equations leads to effective values of the viscosity and resistivity at large scales, k yields 0, dependent on the amplitude of turbulence. The effective viscosity and resistivity become independent of the molecular quantities when the RNG analysis is augmented by the Kolmogorov argument for energy cascade. A self-contained system of equations is derived for the range of scales, k = 0-K, where K = pi/Delta is the maximum wave number for a grid size Delta. Differential operators, whose coefficients depend upon the amplitudes of the large-scale quantities, represent in this system the resistive and viscous dissipation.

Longcope, D. W.↗