用可压缩流涡方法模拟叶轮机动静叶的相互作用

Numerical Simulation of Rotor/Stator Interaction in Turbomachinery by Use of a Disturbance Vortex Method for Compressible Flow

本课题组发展了一种扰动涡方法,用以研究叶轮机内动、静叶相互作用[1,2]。其优点是物理图画清楚,计算收敛快。它采用了一个重要假设:扰动胀量为零,从而大大简化了计算过程。文章的目的是研究此假设的影响,并取消此假设,使扰动涡方法建立在完全严格的数学基础上。由于取消了“扰动胀量为零”的假设,需要耦合求解扰动质量方程、扰动涡量输运方程和扰动能量输运方程。这是文章与文献[1,2]的主要区别。文献[1,2]对NASA67压气机第一级内由于动、静叶间的相互作用引起的非定常流动过程作了数值模拟,并与试验结果作了对比。文章也作了同样的算例,以研究扰动胀量为零的影响。数值模拟结果表明,在引入了扰动胀量后,用扰动涡方法模拟动静干涉仍保持较好的收敛性和收敛速度,且与试验的符合程度更好。文章强调指出,即使对于非定常可压流,为满足无渗透边界条件所需的运动分量也是用椭圆类的拉普拉斯方程描述,而不是用双曲类的方程描述。“扰动胀量为零”

A disturbance vortex method for simulating rotor/stator interaction in turbomachinery was developed [1,2] .This method has some obvious advantages in simulating unsteady flow in turbomachinery,such as understandable physical picture and good convergency.However,there is an important simplification in reference 1,which ignores the disturbance expansion.As a result,the computational process is greatly simplified.The main purpose of the present paper is to take the disturbance expansion into consideration with the aim to lay down a solid mathematical and physical foundation for the disturbance vortex method.Since the disturbance expansion has been taken into account,one has to solve the mass,vorticity transport and energy transport equations for disturbance motion in a coupled way.These are the main differences between the present paper and reference 1. To validate the computational method,the unsteady flows caused by rotor/stator interaction in the first stage of NASA67 compressor were simulated in reference 1.And unsteady velocity correlation parameters at several locations inside the passage were compared with the experimental data.In order to find out the influence of ignoring the disturbance expansion on computational results,the same example was studied in the present paper.From the simulation results it can seen that the disturbance vortex method still converges fast even the disturbance expansion is taken into consideration. It is noted that the additional velocity component which is needed to meet the nonpenetrate condition on the body surface is expressed by an elliptic type Laplace equation rather than a hyperbolic type equation even the flow is unsteady and compressible.It is also noted that setting the disturbance expansion to be zero is not equivalent to an incompressible disturbance motion.[