一种EASM k-ω两方程湍流模型的应用研究

On Exploring Predicting Precision of an EASM k-ω Two-Equation Turbulence Model

显式代数应力 ( EASM)模型是一种比线性涡粘模型 ( LEVM)更高级的非线性构成模型。这类构成模型用平均速度梯度、平均应变率和旋转应变率张量 ,给出了更高级的湍流剪应力表达式。通过把 EASM构成模型和 k- ω两方程模型耦合到一起 ,可得到一种更高级的 EASM k- ω两方程湍流模型。采用这种非线性的构成模型后 ,可以极大地拓展湍流模型的应用范围 ,提高数值计算精度。在求解湍流流场时 ,Navier- Stokes( N- S)方程和 EASM k-ω两方程湍流模型的控制方程采用非耦合方法求解 ,通过对平板、RAE 2 82 2超临界翼型、ONERA M6机翼等标准算例的计算 ,验证了此种湍流模型对湍流流场的预测能力 。

EASM two-equation turbulence models have been gaining widespread attention recently. This class of models belongs to the class of nonlinear eddy viscosity models (NEVM), but unlike some nonlinear models they obtain their expansion coefficients through their rigorous relationship with differential Reynolds stress equations. EASM (explicit algebraic stress model) assumes a higher-order tensor representation involving either powers of the mean velocity gradient or combinations of the mean strain rate and rotation rate tensors; so EASM models can predict the differences in the turbulent normal stresses and they look promising for attaining higher precision in simulating flow fields and for being more widely applicable. In this paper we explain in detail how the EASM model is coupled with k-ω two-equation turbulence model to form an EASM k-ω two-equation turbulence model. The Reynolds averaged Navier-Stokes (N-S) equations are advanced in time with an implicit approximate-factorization (AF) method, and EASM k-ω turbulence model equations are solved uncoupled from N-S equations with the same AF method. Three numerical examples are given. The first is the turbulent flow field over a zero-pressure gradient flat plate; the simulating results obtained with EASM k-ω two-equation turbulence model shows excellent agreement with theoretical solution. The second and third numerical cases are the full turbulent flow around RAE2822 airfoil and ONERA M6 wing respectively; results obtained with this turbulence model agree well with experimental data.