平面叶栅非定常响应函数及声辐射分析

Unsteady response function and acoustic radiation analysis of Cascade

[目的]针对叶栅在湍流中的脉动压力和声辐射问题,介绍并推导叶栅响应函数理论。[方法]该理论假设叶栅叶片无厚度,通过Wiener-Hopf方法求解叶栅散射场积分表达式,得到叶栅散射场速度势的解析表达式和叶栅表面非定常压力系数,再进一步得到叶栅外部流域的辐射声功率。采用解析公式计算叶栅的压力系数和辐射声功率,并与数值法进行对比,然后进一步将该函数推广应用至水下计算,对叶栅响应函数与Sears函数预报的叶栅表面非定常力进行比较。[结果]结果表明,采用解析法与数值法计算得到的结果吻合较好,叶栅响应函数与Sears函数计算得到的叶栅非定常升力系数频谱曲线趋势一致。[结论]在幅值上叶栅响应函数计算结果略低于Sears函数的结果,但相对于叶栅响应函数,单波数域的Sears函数无法考虑安放角、纵倾和侧斜对叶栅非定常升力的影响。

[Objective]To solve the problems of the fluctuating pressure and acoustic radiation of a cascade in turbulence,the theory of the cascade response function is introduced and analyzed.[Methods]The the-ory assumes that cascade blades have no thickness,and the integral expression of the cascade scattering field is solved by the Wiener-Hopf method,so that the analytical expression of the velocity potential of the cascade scattering field and the unsteady pressure coefficient of the cascade surface can be obtained,and the radiated sound power of the outer watershed of the cascade can be further obtained.The pressure coefficient and radi-ated sound power of the cascade are calculated by the analytical formula and compared with the results of the numerical method.The function is further extended to underwater,and the unsteady forces predicted by the cascade response function and Sears function are compared.[Results]The results obtained by the analytic-al method and numerical method are consistent.The frequency spectrum curves of the cascade unsteady lift coefficient calculated by the cascade response function and Sears function have the same trend.[Conclusion]The calculated results of the cascade response function are slightly lower than those of the Sears function in amplitude.However,compared with the cascade response function,the Sears function in a single wavenumber domain cannot take into account the effects of the placement angle,trim and sideslope on the unsteady lift of the cascade.