后掠翼可压缩三维边界层稳定性计算

 采用可压缩线化稳定性理论对后掠机翼的层流边界层稳定性进行了计算研究。对三维边界层中三维扰动波的可压缩稳定性方程组特征问题采用相关两步格式求解。与常用的初值法相比,具有不需预估特征值和快速收敛的特点。为得到渐近边界条件的准确表达式,导出了外边界上方程的解析解,这对精确的特征值计算和分析至关重要。为避免出现伪不稳定模态,选择了合适的稳定性方程组形式。最后,通过层流控制机翼和自然层流机翼的算例,研究了后掠翼上典型Tollmien-Schlichting(T-S)型扰动和横流(C-F)扰动稳定性问题,其结果与已有计算结果符合甚好。

THE CALCULATION OF THREE-DLMENSIONAL COMPRESSIBLE BOUNDARY LAYER STABILITY ON SWEPT WINGS

The boundary layer stability on swept wings is investigated computationally by using three-dimensional compressible laminar stability theory. For a threedime-nsional disturbance wave in a three-dimensional boundary layer, an eigenvalue of an eighth-order system of compressible stability equations is computed by highly efficient correlative two-steps method. Compared with initial-value method used commonly, the two-steps method makes a feature of no eigenvalue guess and rapid rate of convergence, and therefore it is extremely efficient for the computation. The analytical solutions of equations at the outer edge of boundary layers are derived, and the correct asymptotic boundary condition is very important for an exact eigenvalue computation and analysis; spurious unstable modes are avoided by choosing available form of stability equations in the present research. The examples of the laminar-flow-control (LFC) wing and the natural-laminar-flow (NLF) wing are given and used to study typical stability problems of Tollmien-Schlichting(T-S) type disturbance and crossflow (C-F) disturbance on the swept wing. The results are quite consistent with available calculations.