一种高空高超声速非定常气动力近似模型

AN APPROXIMATE MODEL OF UNSTEADY AERODYNAMICS FOR HYPERSONIC PROBLEMS AT HIGH ALTITUDE

针对高空高马赫数飞行环境和强黏性干扰的物理特性，在当地流活塞理论的基础上引入有效外形修正，发展了黏性修正当地流活塞理论，结合定常N—S方程解给出了高空高马赫数下针对该方法的有效外形的判据，并通过数值算例对该判据进行了验证．通过对典型尖头薄翼和典型钝头翼的一系列二维非定常算例，将该方法与一阶活塞理论、基于欧拉（Euler）方程的当地流活塞理论和非定常N—S方程数值解进行了对比．结果显示在高度为40—70km、马赫数为10—20范围内，通过该方法计算得到的非定常气动力与非定常N—s方程数值解吻合较好，明显优于活塞理论和基于Euler方程的当地流活塞理论．该方法克服了传统的活塞理论和当地流活塞理论不能用于高空高马赫数这类强黏性效应情况的弊端，在较宽的马赫数、攻角、飞行高度范围内都有良好的适用性，同时其计算效率远高于非定常N-S方程．

The paper introduces a local piston theory with viscous correction for the prediction of hypersonic unsteady aerodynamic loads at high altitude where viscous interaction cannot be ignored. A semi-empirical relation for the determination of effective shape for this method at high Mach number and high altitude is presented based on steady Navier-Stokes equations, and validation of the relation is also completed by numerical method. Furthermore, a series of two-dimensional numerical examples with various Mach numbers, angles of attack and operating altitudes for typical thin airfoil and typical blunt airfoil are provided. The unsteady aerodynamic force coefficients are in well agreement with the unsteady Navier-Stokes predictions with altitude in the range of 40 to 70km and Mach number in the range of 10 to 20. Compared with classical piston theory and local piston theory based on steady Euler equations, this model performs much better at high Mach number and high altitudes when the viscous interaction effects are strong. This model can be applied in supersonic/hypersonic problems with wide range of Mach number, angle of attack and altitude, and has much higher computational efficiency than unsteady Navier-Stokes equations.