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187 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Measuring scale-dependent shape anisotropy by coarse-graining: Application to inhomogeneous Rayleigh-Taylor turbulence

Here, we generalize the “filtering spectrum” to probe scales along different directions by spatial coarse-graining. This multidimensional filtering spectrum quantifies the spectral content of flows that are not necessarily homogeneous. From multidimensional spectral information, we propose a simple metric for shape anisotropy at various scales. The method is applied to simulations of two-dimensional (2D) and 3D Rayleigh-Taylor (RT) turbulence, which is inhomogeneous and anisotropic. We show that 3D RT has clear shape anisotropy at large scales with approximately 4:3 vertical to horizontal aspect ratio but tends toward isotropy at small scales as expected. In sharp contrast, we find that RT in 2D simulations, which are still the main modeling framework for many applications, is isotropic at large scales and its shape anisotropy increases at smaller scales where structures tend to be horizontally elongated. While this may be surprising, it is consistent with recent results that large-scale isotropy in 2D RT is due to the generation of a large-scale overturning circulation via an upscale cascade, while small-scale anisotropy is due to the stable stratification resultant from such overturning and the inefficient mixing in 2D.

42 ENGINEERING↗
NASA NTRS1996

Evaluation of Subgrid-Scale Models for Large Eddy Simulation of Compressible Flows

The objective of this project was to evaluate and develop subgrid-scale (SGS) turbulence models for large eddy simulations (LES) of compressible flows. During the first phase of the project results from LES using the dynamic SGS model were compared to those of direct numerical simulations (DNS) of compressible homogeneous turbulence. The second phase of the project involved implementing the dynamic SGS model in a NASA code for simulating supersonic flow over a flat-plate. The model has been successfully coded and a series of simulations has been completed. One of the major findings of the work is that numerical errors associated with the finite differencing scheme used in the code can overwhelm the SGS model and adversely affect the LES results. Attached to this overview are three submitted papers: 'Evaluation of the Dynamic Model for Simulations of Compressible Decaying Isotropic Turbulence'; 'The effect of the formulation of nonlinear terms on aliasing errors in spectral methods'; and 'Large-Eddy Simulation of a Spatially Evolving Compressible Boundary Layer Flow'.

Blaisdell, Gregory A.↗
NASA NTRS1987

Rossby waves and two-dimensional turbulence in a large-scale zonal jet

Homogeneous barotropic beta-plane turbulence is investigated, taking into account the effects of spatial inhomogeneity in the form of a zonal shear flows. Attention is given to the case of zonal flows that are barotropically stable and of larger scale than the resulting transient eddy field. Numerical simulations reveal that large-scale zonal flows alter the picture of classical beta-plane turbulence. It is found that the disturbance field penetrates to the largest scales of motion, that the larger disturbance scales show a tendency to meridional rather than zonal anisotropy, and that the initial spectral transfer rate away from an isotropic intermediate-scale source is enhanced by the shear-induced transfer associated with straining by the zonal flow.

Shepherd, Theodor G.↗
NASA NTRS1993

A Realizable Reynolds Stress Algebraic Equation Model

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

Shih, Tsan-Hsing↗
NASA NTRS1988

Scaling laws for homogeneous turbulent shear flows in a rotating frame

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.

Speziale, Charles G.↗
NASA NTRS1989

Scaling laws for homogeneous turbulent shear flows in a rotating frame

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.

Speziale, Charles G.↗
NASA NTRS2003

DNS and LES of a Shear-Free Mixing Layer

The purpose of this work is twofold. First, given the computational resources available today, it is possible to reach, using DNS, higher Reynolds numbers than in Briggs et al.. In the present study, the microscale Reynolds numbers reached in the low- and high-energy homogeneous regions are, respectively, 32 and 69. The results reported earlier can thus be complemented and their robustness in the presence of increased turbulence studied. The second aim of this work is to perform a detailed and documented LES of the shear-free mixing layer. In that respect, the creation of a DNS database at higher Reynolds number is necessary in order to make meaningful LES assessments. From the point of view of LES, the shear-free mixing-layer is interesting since it allows one to test how traditional LES models perform in the presence of an inhomogeneity without having to deal with difficult numerical issues. Indeed, as argued in Briggs et al., it is possible to use a spectral code to study the shear-free mixing layer and one can thus focus on the accuracy of the modelling while avoiding contamination of the results by commutation errors etc. This paper is organized as follows. First we detail the initialization procedure used in the simulation. Since the flow is not statistically stationary, this initialization procedure has a fairly strong influence on the evolution. Although we will focus here on the shear-free mixing layer, the method proposed in the present work can easily be used for other flows with one inhomogeneous direction. The next section of the article is devoted to the description of the DNS. All the relevant parameters are listed and comparison with the Veeravalli & Warhaft experiment is performed. The section on the LES of the shear-free mixing layer follows. A detailed comparison between the filtered DNS data and the LES predictions is presented. It is shown that simple eddy viscosity models perform very well for the present test case, most probably because the flow seems to be almost isotropic in the small-scale range that is not resolved by the LES.

Knaepen, B.↗