【作者】 李慧；

【导师】 黄章峰；

【作者基本信息】 天津大学 ， 流体力学， 2014， 硕士

【摘要】 本文采用直接数值模拟和线性稳定性分析相结合的方法研究了单个粗糙元对可压缩平板边界层稳定性的影响。首先通过求解Navier-Stokes (N-S)方程得到来流马赫数为4.5的可压缩平板中包含不同高度的余弦凸起时的二维基本流,其次基于线性稳定性理论对基本流进行稳定性分析,然后通过求解扰动方程研究不同频率的Tollmien-Schlichting (T-S)扰动波在不同高度的粗糙单元影响时的幅值演化情况,最后定义了穿透系数来定量刻画粗糙单元对扰动波幅值演化的影响。通过对共42种工况计算结果的研究,可以得到如下结论：1、粗糙单元对基本流的影响范围是有限的。在粗糙单元附近会产生一道马赫波,在远离粗糙单元的地方,基本流恢复到与原来平行流相似的状态。粗糙单元高度越高,对基本流的影响范围越大,程度越深。2、不同高度粗糙单元对不同频率扰动波的影响情况不同。对相同频率的扰动波,粗糙单元高度越高,对扰动波的影响程度越大。相同高度的粗糙单元能使增强低频扰动波的不稳定性,对高频扰动波有稳定作用。3、穿透系数△N(ω,h)定量刻画了粗糙单元对流动稳定性的影响。通过穿透系数可以快速看出高度为h的粗糙单元对频率为ω的扰动波稳定性的影响：穿透系数△N(ω,h)为正,表示该高度的粗糙单元使该频率的扰动波更加不稳定；穿透系数△N(ω,h)为负,表示该高度的粗糙单元对该频率的扰动波有稳定作用。穿透系数的绝对值大小,表示粗糙单元对该频率的扰动波对应的N值的修正大小。利用穿透系数可使工程师快速、有效地实现对有粗糙单元工况的转捩预测。更多还原

【Abstract】 To get the effect of the roughness elements to the instability of the boundary layer, the method which combined direct numerical simulation and stability analysis was adopted to investigate the influence of the roughness elements of various heights on the Tollmien-Schlichting (T-S) disturbance waves of different frequencies. At first, mean flow at Mach number of4.5was obtained by solving the Navier-Stokes (N-S) equations, of which was performed on the two-dimensional compressible boundary layer of a flat plate with a roughness element of different heights. Stability analysis was employed to investigating the mean flow according to linear stability theory (LST). Then the perturbation equations was used to analyzing the interaction of disturbance waves of different frequencies and roughness elements of various heights. Finally, a transmission coefficient was settled to characterize the effect of roughness elements on the instability.Investigating of the results of42kinds of working conditions, conclusions can be drawn as follow:1、The roughness elements affects the mean flow locally, a mach wave was appeared near the roughness element, the mean flow gets back to the original state of parallel flow away from the roughness element. The higher the roughness element is, the impact on the mean flow is greater.2、The influence of different heights roughness elements of work on the disturbance waves is different at various frequencies. When the disturbance waves are at the same frequencies, the higher the roughness element is, the affect it impacts on the disturbance waves is more obvious. When the heights of the roughness elements are the same, the roughness element destabilizes the low-frequency disturbances and stabilizes the high-frequency disturbances.3、Transmission coefficient AN(ω,h) describes the impact of roughness element on the flow instability quantitatively. With transmission coefficient, we can quickly know the influence of the roughness element of height h on the disturbance wave of frequency ω:when transmission coefficient AN(ω, h) is positive, the roughness element destabilizes the disturbance wave; transmission coefficient AN (ω,h) is negative, the roughness element stabilizes the disturbance wave. The absolute value of the transmission coefficient quantifies the correction of N the roughness element works on the disturbance wave. Transmission coefficient can be used to predict the transition location on the flow with roughness element effectively and efficiently.更多还原