Compressible Isotropic Turbulence Research Articles

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 a963grid using Fourier collocation methods. Extensive comparisons between the direct and modelled 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 coarse323grid – 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.

Direct simulation of compressible turbulence in a shear flow

The purpose of this study is to investigate compressibility effects on the turbulence in homogeneous shear flow. Physical experiments have not been and perhaps cannot be performed for homogeneous shear flows at flow speeds which are sufficiently high to introduce compressible effects on the turbulence. However, direct numerical simulation (DNS) of this problem could provide meaningful data, especially since DNS for the incompressible problem ([1], [2]) has been successful in giving realistic flow fields akin to those obtained in physical experiments. The present simulations of the homogeneous shear problem augment and extend our previous results ([3], [4]) for compressible isotropic turbulence. The compressible Navier-Stokes equations are written in a frame of reference moving with the mean flow u. We use a Fourier collocation method for the spatial discretization of the governing equations. A third order, low storage Runge-Kutta scheme is used for advancing the solution in time. Up to 1283 points are used for the simulations. The simulated turbulent fields have Taylor microscale Reynolds numbers Re? up to 35 and turbulent Mach numbers Mt up to 0.6. The results are summarized below. We find that an increase in initial compressibility level, either due to increased turbulent Mach number or increased dilatational fraction of the velocity field decreases the growth of turbulent kinetic energy (and all its components) in the case of homogeneous shear flow. This is reminiscent of the reduction in turbulent velocity intensities observed in experiments on supersonic free shear

Subgrid-scale backscatter in turbulent and transitional flows

Most subgrid-scale (SGS) models for large-eddy simulations (LES) are absolutely dissipative (that is, they remove energy from the large scales at each point in the physical space). The actual SGS stresses, however, may transfer energy to the large scales (backscatter) at a given location. Recent work on the LES of transitional flows [Piomelli et al., Phys. Fluids A 2, 257 (1990)] has shown that failure to account for this phenomenon can cause inaccurate prediction of the growth of the perturbations. Direct numerical simulations of transitional and turbulent channel flow and compressible isotropic turbulence are used to study the backscatter phenomenon. In all flows considered roughly 50% of the grid points were experiencing backscatter when a Fourier cutoff filter was used. The backscatter fraction was less with a Gaussian filter, and intermediate with a box filter in physical space. Moreover, the backscatter and forward scatter contributions to the SGS dissipation were comparable, and each was often much larger than the total SGS dissipation. The SGS dissipation (normalized by total dissipation) increased with filter width almost independently of filter type. The amount of backscatter showed an increasing trend with Reynolds number. In the near-wall region of the channel, events characterized by strong Reynolds shear stress correlated fairly well with areas of high SGS dissipation (both forward and backward). In compressible isotropic turbulence similar results were obtained, independent of fluctuation Mach number.

The subgrid-scale modeling of compressible turbulence

A subgrid-scale model recently derived by Yoshizawa [Phys. Fluids 29, 2152 (1986)] 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 only applicable 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.

On the Construction and Comparison of Difference Schemes

On the Construction and Comparison of Difference Schemes