Artificial fluid properties for large-eddy simulation of compressible turbulent mixing

Abstract

An alternative methodology is described for Large-Eddy Simulation of flows involving shocks, turbulence and mixing. In lieu of filtering the governing equations, it is postulated that the large-scale behavior of an "LES" fluid, i.e., a fluid with artificial properties, will be similar to that of a real fluid, provided the artificial properties obey certain constraints. The artificial properties consist of modifications to the shear viscosity, bulk viscosity, thermal conductivity and species diffusivity of a fluid. The modified transport coefficients are designed to damp out high wavenumber modes, close to the resolution limit, without corrupting lower modes. Requisite behavior of the artificial properties is discussed and results are shown for a variety of test problems, each designed to exercise different aspects of the models. When combined with a 10th-order compact scheme, the overall method exhibits excellent resolution characteristics for turbulent mixing, while capturing shocks and material interfaces in crisp fashion.

Simulations of Turbulent Flows with Strong Shocks and Density Variations: Final Report

“…• The modified artificial diffusivity methods that use dilatation rather than strain-rate magnitude to activate the artificial bulk viscosity are substantial improvements over the originial method of Cook (17), and make the method suitable for compressible turbulence calculations.…”

“…• WENO and the original artificial diffusivity method of Cook (17) in their standard forms are not suitable for high-fidelity computations of compressible turbulence. If used, they must be accompanied with convincing grid refinement studies clearly showing sufficient grid resolution.…”

“…The Taylor scale Reynolds number Re λ is 45 and the turbulent Mach number M t is 0.4. The shock is captured by 4 grid points, a characteristic of the artificial viscosity method employed here (see (17)), giving a shock thickness l s = 3∆ and a shock thickness to turbulence length scale ratio l s /l 0 of 0.05, i.e the shock length scale is much smaller than turbulence. All shocks including eddy shocklets in the isotropic turbulence field are captured, and not resolved.…”

Facilitating the Adoption of Unstructured High-Order Methods Amongst a Wider Community of Fluid Dynamicists

“…Another high-wavenumber biased scheme is that of Cook and Cabot [25], who employ a mesh dependent artificial shear viscosity scaled by the gradient (or higher derivatives) of the solution. This approach was extended by the same authors to include both artificial shear and bulk viscosity terms (so called hyperviscosity) [26], and then further extended by Cook [24] to include an artificial thermal conductivity term. Recently, the work of Cook and Cabot [25,26], and Cook [24], has been extended to non-uniform curvilinear grids by Kawai and Lele [73], and further extended by Bhagatwala and Lele [10] to include an additional flow sensor, which allows artificial viscosity to be focused in regions of strong negative dilatation (likely coincident with shock structures).…”

“…This approach was extended by the same authors to include both artificial shear and bulk viscosity terms (so called hyperviscosity) [26], and then further extended by Cook [24] to include an artificial thermal conductivity term. Recently, the work of Cook and Cabot [25,26], and Cook [24], has been extended to non-uniform curvilinear grids by Kawai and Lele [73], and further extended by Bhagatwala and Lele [10] to include an additional flow sensor, which allows artificial viscosity to be focused in regions of strong negative dilatation (likely coincident with shock structures). Even more recently, the work of Kawai and Lele [73] and Bhagatwala and Lele [10] has been adapted by Premasuthan, Liang and Jameson [106,107] for use in a fully unstructured SD flow solver.…”