二维非定常跨音速时间线化积分方程的推导

1.引言 求解非定常跨音速流动的主要困难是非线性问题。对于微幅翼型振动问题(同时引起激波的微幅振动)可做时间线化简化处理,得到时间线化微分方程定解问题。时间线化积分方程是由时间线化微分方程推导出来的。

DERIVATION OF THE TWO DIMENSIONAL TRANSONIC TIME LINERIZED INTEGRAL EQUATION

Abstract The study on unsteady transonic flows over wings is important for the analyses of the aeroelasticity of wings. In the case of low-frequency, small disturbance transonic flows around harmonically oscillating airfoils, a time-linearized low-frequency integral equation was derived by Nixon.Later a time-linearized integral equation available for arbitary reduced frequency was presented by Lamah and Harris. But the integral equation is limited to the case of two dimensional subcritical flows. Recently further work was done with the method used by the present authors. Through introducing artificial viscosity, a time-linearized two dimensional integral equation available for transonic flows with shock was derived. In the present paper, an alternative approach on the time linearized integral equations are derived, and the far field characteristics of the two-dimensional transonic unsteady flow are analyzed. Unlike in the steady flows, the order of the unsteady flow quantities in the far field are of 0(1 r), lower than the counter parts in the steady flow, and the differentiation does not increase the orders of the magnitude of the far field quantities. Finally, an analytical expression for the far field is presented.