旋转体跨音速零升波阻和压力的差分计算

应用Murman-Cole的有限差分法,求解具有纵向大扰动而横向小扰动的跨音速轴对称速势方程,由此计算旋转体跨音速零升力时的压力分布和波阻力,以及激波位置。物面边界条件被转移到物体轴上。远场边界条件由无穷远处的条件近似代替。计算物面压力系数时,用细长体理论进行物面速势插值。 速势的差分方程用沿半径方向线超松弛改进迭代求解。网格取62×16,迭代初场取零,达到收敛的迭代次数对M_∞<1,M_∞>1以及M_∞≈1分别大约为150,40和300次。松弛因子取为:M_∞<1时,0.9≤ω_b≤1.7,0.9≤ω_p<1.0;M_∞≥1时,0.8≤ω_b≤0.9,0.8≤ω_p≤0.9,这里ω_b,ω_p分别为局部亚音速点和超音速点的松弛因子。 算例为七种不同外形的细长体,计算结果与实验符合尚好。 文中对网格、初场、迭代方法、松弛因子等有关收敛性、收敛速度问题进行了探讨。在局部线化条件下,对定常小扰动轴对称势流的差分方程,进行了线超松弛迭代的稳定性和收敛性分析。数值计算经验与理论分析所得结论相符。

FINITE DIFFERENCE COMPUTATION OF WAVE DRAG AND PRESSURE ON SLENDER BODIES OF REVOLUTION AT TRANSONIC SPEEDS WITH ZERO-LIFT

A transonic axisymmetrical potential equation with large disturbance in the free stream direction and small disturbance in the transverse direction is solved by using the Murman-Cole schemes of finite differences.The boundary condition on the body is transfered to body axis.The boundary condition at farfield is approximated by that at infinite.Finite difference equations for the potential are solved by line-overrela-xation along the radius with Seidel iteration.In order to calculate the pre-ssure on the body surface,the potential is interpolated by the slender-body theory.The pressure coefficient is calculated by the exact Bernoulli's equation.The zero-lift wave-drag coefficients are obtained by integrating the pressure coefficients on the body surface.The computational results for seven different configurations agree well with the known wind tunnel test data as shown In Fig.2 to Fig.6.The experiences obtained from investigation of mesh spacings,initial-fields,iterative methods,relaxation factors etc.in relation to the convergence and convergent rate may be interesting to engineers.A linearized analysis of the stability and the convergence in line overrelaxation of difference equations for steady axisymmetric small perturbation potential flow is carried out and the conclusions are shown in table 1.The numerical computations do agree with the theoretical conclusions.It must be pointed out that as M∞ is very close to unit or the mesh spacing is shortened,the iterative computation does not converge to the usual degree of accuracy.This fact might be explained by vanishing of the artificial viscosity in the potential difference equation at locally supersonic points.