使用PAFV湍流模型对叶栅流动的数值研究

为进一步发展更有效的湍流模型，提高对高负荷跨声速压气机流动的数值计算精度，以侧偏平均脉动速度和应变率张量为基础构造了新的侧偏平均脉动速度(partial average fluctuation velocity, PAFV)湍流模型。在使用Python计算机语言进行编程计算过程中，将流动控制方程在一般曲线坐标系下变换后，采用有限差分方法进行空间离散。方程对流项采用Steger-Warming通量向量分裂法，扩散项采用中心差分格式离散，时间导数项采用具有TVD(total variation diminishing)性质的二阶Runge-Kutta法离散。使用该湍流模型对德国航空航天研究试验院的L030-4叶栅亚声速和超声速流动进行了计算，在进行网格无关性研究基础上，获得了流场压力等值线云图、马赫数等值线云图，压力系数分布等结果。计算显示侧偏平均脉动速度在激波附近区域受到明显抑制，避免了激波附近区域出现过大的湍流黏性。数值计算结果与实验符合比较好，初步验证了PAFV湍流模型可以有效地模拟该类型的叶栅流动。

Numerical study of cascade flow with PAFV turbulence model

In order to further develop an effective turbulence model and improve the accuracy of numerical calculation for high load transonic compressor flow, a new turbulence model PAFV is constructed based on the fluctuation velocity and strain rate tensor. The governing equation is transformed into a generalized curvilinear coordinate and discretized by the finite difference method. The numerical calculation is programmed with Python language. The convection term is discretized by Steger-warming splitting method, the diffusion term is discretized by the central difference scheme, and the time derivative term is discretized by the second-order Runge-Kutta method with TVD property. The subsonic and supersonic flows in L030-4 cascade are simulated and the pressure contour, Mach number contour and pressure coefficient distribution are obtained, respectively. The turbulent viscosity coefficient constructed with the fluctuation velocity as the turbulent velocity scale avoids the excessive turbulent viscosity near the shock wave region. The calculation is in good agreement with the experimental data, which illustrates PAFV turbulence model can effectively simulate this type of cascade flow.