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将抛物化稳定性方程(PSE)方法应用到可压缩单股剪切混合流的稳定性研究中。采用并发展了适用于自由剪切流的高精度数值方法,包括六阶紧致格式、坐标变换以及渐近边界条件等,对PSE进行有效求解。通过求解相似边界层方程得到更准确的剪切层内基本流;求解线性稳定性理论(LST)控制方程得到扰动的初始条件,并通过流向空间推进方法对扰动的空间不稳定性进行求解。计算并分析了在不同马赫数和温度比情况下,不同频率、波数等参数的扰动波线性发展过程。计算结果表明:在弱压缩性情况下,二维扰动最不稳定,随着压缩性增强三维扰动变得比二维扰动更不稳定,对流动不稳定性起主导作用;在流动的上游,温度比的增加对流动起稳定作用,而在下游,温度比的增加起不稳定作用;当频率增加或波角增大时,扰动的流向不稳定区减小;PSE方法是单股剪切混合流稳定性快速有效的分析方法。
The Parabolic Stability Equation (PSE) method is applied to the stability study of compressible single-shear shear flow. The high-precision numerical method for free shear flow is adopted and developed, including the sixth-order compact scheme, coordinate transformation and asymptotic boundary conditions to effectively solve PSE. By solving the equations of similar boundary layer, a more accurate shear flow in the shear layer is obtained. The initial conditions for the disturbance of the linear stability theory (LST) control equation are obtained. The space instability of the disturbance is solved by the flow-space propulsion method. The linear development of the perturbation wave with different frequencies, wave number and other parameters under different Mach number and temperature ratio is calculated and analyzed. The results show that in the case of weak compressibility, the two-dimensional disturbances are the most unstable, and the three-dimensional disturbances become more unstable than the two-dimensional disturbances as the compressibility enhances, leading to the instability of the flow. In the upstream of the flow, the temperature The increase of the ratio can stabilize the flow, but it is unstable in the downstream and the increase of the temperature ratio. When the frequency increases or the wave angle increases, the disturbance instability decreases. The PSE method is single shear mixed flow Fast and effective analysis of stability.