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Calculation of unsteady linearized Euler flows in cascades using harmonically deforming grids

机译:用谐波变形网格计算级联中的非定常线性欧拉流。

摘要

A method for calculating unsteady, inviscid, compressible flows in cascades is presented. Using the linearized Euler technique, the flow is decomposed into a steady or mean flow plus a harmonically varying small disturbance flow. The equations that describe the small disturbance flow are linear variable coefficient equations, and are solved using a pseudo-time time marching Lax-Wendroff technique. Unlike previous linearized methods, however, the solution is computed on a harmonically deforming computational grid that conforms to the motion of the vibrating airfoils. The mean flow and perturbation flow solutions are defined in the deforming coordinate system rather than in a coordinate system fixed in space. Hence, no extrapolation terms are required to implement the upwash boundary conditions at the airfoil surfaces, significantly improving the accuracy of the method. For transonic flow calculations, unsteady shock motions are modelled using shock capturing. The unsteady loads due to the shock motion are then seen as pressure impulses. Representative computational results are presented for transonic channel flows and subsonic and transonic cascade flows.
机译:提出了一种计算叶栅中不稳定,无粘性,可压缩流动的方法。使用线性欧拉技术,将流量分解为稳定流量或平均流量,再加上谐波变化的小扰动流量。描述小扰动流的方程是线性可变系数方程,并且使用伪时间行进Lax-Wendroff技术进行求解。但是,与以前的线性化方法不同,该解决方案是在符合振动翼型运动的谐波变形计算网格上计算的。平均流量和摄动流解是在变形坐标系中定义的,而不是在固定在空间中的坐标系中定义的。因此,不需要外推项即可在机翼表面实施上冲边界条件,从而大大提高了方法的准确性。对于跨音速流计算,使用冲击捕捉对不稳定冲击运动进行建模。然后将由于冲击运动而产生的非恒定载荷视为压力脉冲。给出了跨音速通道流以及亚音速和跨音速级联流的代表性计算结果。

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