后掠机翼跨音速绕流的二级近似方法

本文采用TSDH方程计算三维后掠机翼的跨音速绕流,考虑了适用于机翼钝前缘的前缘边界条件和前缘速势方程。采用Jameson格式在不等步长格网中的推广形式,把TSDH方程离散化为差分方程组。然后,在整个计算空间内布置稀网,在机翼附近再布置密网,进行稀密网的交替迭代,以加速收敛和提高计算精度。对ONERA M6机翼的超临界无激波和有激波情况的计算表明,TSDH解与FVP解和风洞试验符合良好。

SECOND ORDER APPROXIMATION METHOD FOR TRANSONIC FLOWS OVER SWEPT WINGS

In order to compute the pressure distribution on a swept wing,a transonic small disturbance equation retaining all second and several third order terms,i.e.TSDH equation（1）,with μ=1 is proposed so as to overcome the shortcomings inherent in the classical transonic small disturbance equation,i.e,TSD equation.At the blunt leading edge,a simplified full velocity potential equation（5）and the exact blunt leading edge boundary condition（3）are employed so that the computational results near there are improved.An extended nonrotated Jameson difference scheme for the non-uniform rectangular grids in the physical plane is applied to discretization of the TSDH equation.For example,at the supersonic points,the formulas of this scheme are expressed in eq.（9）and eq.（10）.For the blunt leading edge potential equation（5）,the one-sided scheme is adopted for ψxx,ψxy and ψxx in order to satisfy the boundary condition（3）.To speed up convergence rate and reduce computer storage,Boppe's grid embedded technique is used for solving the difference equations.However,a distinct feature of author's work lies in the procedure that this technique is only applied to solving the TSD equation,then its converged solution serves as the starting flowfield for solving TSDH equation（1）and the blunt leading edge equation（5）,finally the TSDH solution is obtained in the finest grid near the wing.Thus the computing effort is reduced.The computation of supercritical pressure distributions for ONERA M6 wing with and without shock waves has been completed.The results show that TSDH solutions agree well with the FVP solution and test data,and give a fine expression of the complicated shock pattern.On the contrary,the agreement of TSD solution with test data is not satisfactory.