A Nonlinear Sub-grid Scale Model for Compressible Turbulent Flow

本文采用直接过滤的Navier-Stokes方程组作为可压缩湍流大涡模拟控制方程组。方程组中因过滤产生的高阶相关项用Taylor级数展开近似,但仅保留级数的一阶导数项。这样产生的误差相当于丢失了模型的部分耗散作用,本文用一种动力学非线性亚格子模型来补偿丢失的耗散影响。本文根据Caylay-Hamilton定理导出了一个非线性亚格子模型,模型中包含的系数由动力学模式确定。与传统的动力学Smagorinsky模式相比,这种动力学非线性模型(DNM)稳定性更好,且不需要在统计均匀方向进行统计平均来计算模型系数,因此减少了计算开销。本文用这种非线性亚格子模型对绕双椭球高超声速湍流进行了模拟,并将所得结果与实验值、计算值及理论值进行了对比。结果表明,本文模型可以有效地模拟可压缩湍流流场。

A Nonlinear Sub-grid Scale Model for Compressible Turbulent Flow

The governing equations for large eddy simulation (LES) are obtained by filtering the Navier-Stokes (N-S) equations with standard (non-Favre filtering) spatial filter function. The filtered scale stress due to the standard filtering is then reconstructed by using the Taylor series expansion. The loss of information due to truncating the expansion up to the first derivative term is modeled by a dynamic nonlinear model (DNM), which is free from any empirical constant and wall damping function. The DNM avoids the singularity of the model and shows good local stability. Unlike the conventional dynamic Smagorinsky model (DSM), the DNM does not require the plane averaging and reduces the computational cost. The turbulent flow over a double ellipsoid for Reynolds number of 4.25 × 106 and Mach number of 8.02 is simulated numerically to validate the proposed approach. The results are compared with experiment data, as well as the data of Reynolds averaged numerical simulation (RANS).