任意曲线坐标系Euler方程S2流面的计算方法

Euler S2 Stream Surface Calculation for Arbitrary Curvilinear Coordinate System

为提高S2流面计算方法对涡轮复杂几何的适应性和计算能力,详细推导了任意正交曲线坐标系下应用于流道中心S2流面计算的Euler方程,提出了任意曲线坐标系Euler方程S2流面的计算方法,发展了适用于三阶精度总变差减小的差分格式的数学模型,结合了隐格式时间推进、Riemann问题求解等技术。在应用于带弧形凸起的流道及某直叶栅气动参数计算,并对某三级低压涡轮进行性能预测的结果表明:所提方法对激波具有较高的捕捉精度,能够较准确地获得叶栅气动参数分布,且与实验结果吻合良好;对于多级涡轮总性能参数和气动参数分布均有较高的计算精度,是一种可为涡轮设计提供快速、可靠的计算方法。

To adapt the complex geometry of the turbine profile and improve the computing capability, an Euler S2 stream surface calculation strategy is proposed in the body-fitted coordinate system, the governing equation for Euler S2 stream surface calculation in the arbitrary orthogonal curvilinear coordinate system is derived in detail, and the mathematical model for the third order total variation diminishing （TVD） difference scheme is developed. The implicit time marching method and the Riemann solver are also employed to solve the aerodynamic parameters of a flow channel with bump and a linear cascade, and to predict the performance of a 3-stage low pressure turbine. The results show that the proposed strategy is able to capture the shock wave with high resolution. The solution to the linear cascade coincides well with the experimental data with a credible accuracy for the flow field calculation.