叶轮机转子内流动的三维跨声Navier-Stokes方程组数值计算

Numerical Simulation and Test Verification of 3-Dimensional Transonic Navier-Stokes Equations Appliedto Turbomachinery Rotor Internal Flow

应用有限体积法及Baldwin-Lomax代数紊流模型求解叶轮机转子内流动的三维可压缩非定常薄层Navier-Stokes方程组,计算一个绕X轴等转速旋转的转子内流场问题,用当地时间步长方法来加速收敛。采用隐式算法对对流通量进行求解,而扩散通量采用显式算法。采用高阶TVD下的Roe格式计算对流通量,采用中心差分格式计算扩散通量。关于守恒变量Q的非线性方程组,采用牛顿迭代方法求解,线化后的方程用对称的Gauss-Seidle方法求其渐近解。应用该算法模拟了转子NASARotor67流场,与试验做了大量的对比研究,包括性能、等马赫线以及总压和总温等等。在最高效率点附近计算与试验比较接近,但在靠近失速点时计算与试验略有差别。

A method of three-dimensional numerical simulation for the transonic turbomachinery rotor internal flow field by solving three-dimensional unsteady compressible thin-layer Navier-Stokes equations in rotating frame using finite volume method and Baldwin-Lomax algebraic turbulent model is presented. The local time step was used to accelerate the iteration process. Implicit treatment of convective fluxes was combined with the explicit treatment of diffusive fluxes. Roe's method with three-order TVD scheme was used for the evaluation of convective fluxes, and central difference scheme was used for diffusive fluxes. Newton's sub-iterations were applied to reduce the non-linear equations of conservative variable into linear one. The linear equations were solved using symmetric Gauss-Seidle iterative method. The case used for examining was NASA Rotor 67. Calculated performance, relative Mach number contours at different span location, spanwise total pressure and temperature distribution at rotor exit, etc., were compared with the experimental data. Computation results agree well with experimental data at peak efficient point, but there is a little discrepancy at near stall point.