旋成体轴对称跨声速全位势流的高效差分算法

本文用守恒型全位势方程,贴体坐标网格,对旋成体轴对称跨声速绕流的差分数值计算方法进行了研究;根据最佳收敛准则,提出了轴对称情形的AF2迭代算法,并将此算法应用于半球头柱体、弹体等各种外形的旋成体。与一般方法仅适用于亚声速自由流不同,本计算可从亚声速、跨声速自由流一直到低超声速自由流。计算结果表明,本文方法收敛快,与实验及其它方法的结果符合较好。

AN EFFICIENT FINITE DIFFERENCE SCHEME FOR COMPUTATION OF AXISYMMETRIC , TRANSONIC FULL-POTENTIAL FLOWS OVER BODIES OF REVOLUTION

Fast and accurate estimations of pressure distributions and wave drags around blunt or pointed bodies of revolution in transonic flow are of practical importance for the aerodynamic design of aircraft, missile and many shapes of classical and practical interest. This paper studies the finite difference numerical method for the solution of conservative full potential equation with exact boundary conditions for general axisymmetric bodies in inviscid, steady transonic flow. The nearly orthogonal body-fitted "C" grids, obtained by the combination of conformal mapping technique and sheared coordinate transformation, are used in the computation. It is found that the difference between governing equations of axisymmetric flow and 2-D planar flow is that p in governing equation of 2-D planar flow is replaced by py, where p is isentropic density and y is the radial distance from the body axis. But, if we do the same as 2-D iteration scheme AF2 to get axisymmetric AF2 scheme, the iteration will be divergent. In this paper, the reasons for divergence are analyzed and a highly efficient algorithm of finite difference method AF2 designed to solve conservative full potential equation for axisymmetric transonic flow has been developed according to the optimum "convergence conditions. This axisymmetric AF2 scheme developed has been applied to hemisphere-cylinder, missile forebody and a wide variety of blunt and pointed bodies of revolution. Unlike other methods which can only be applied to subsonic free streams, the present method can treat subsonic, transonic and low supersonic free streams. Numerical results of the surface pressure distribution , including subsonic, transonic and supersonic cases, are presented for hermisphere-cylinder and missile forebody. All calculated examples show that the present AF2 scheme yields very good convergence rate and that the results obtained agree very well with avilable experiments and other theories.