【作者】 李翠萍；

【导师】 方一红；

【作者基本信息】 天津大学 ， 流体力学， 2013， 硕士

【摘要】 本文采用抛物化稳定性方程(PSE)研究了超音速边界层对慢声波的感受性。首先，根据有粘和无粘流场中慢声波的传播特性和色散关系，得到符合慢声波特点的计算网格和上边界条件。采用非线性抛物化稳定性方程(LPSE)计算单个慢声波在非均匀流场中的演化，分别使用改进网格和均匀网格，两者计算结果一致。对计算结果投影分析发现单个慢声波无法激发T-S波。另外依据感受性理论，用非线性抛物化稳定性方程(NPSE)研究边界层中T-S波的演化，结果表明：1.相对于T-S波，计算慢声波的网格及上边界条件需要修正。法向网格在边界层内由密到稀，到边界层外趋于均匀。上边界条件需要考虑慢声波的入射和反射特点。2.采用线性抛物化稳定性方程分别计算相同频率的慢声波和T-S波向下游的演化。当两者相速度最接近时，将慢声波向T-S波投影，发现慢声波中所含T-S波成分极少，表明单个慢声波很难激发T-S波。3.基于感受性理论给出初始扰动，采用非线性抛物化稳定性方程计算扰动向下游的演化。在演化过程中，发现扰动幅值增长与频率和展向波长有关。频率大、展向波长小的波更容易激发高频不稳定波，通过分解这些由非线性作用所产生的高频不稳定波，发现它们不完全是第二模态不稳定波。更多还原

【Abstract】 In this paper, we studied the mechanisms of the receptivity of the supersonicflat-plate boundary layer to slow acoustic waves by using parabolized stabilityequations (PSE). Firstly, based on the characteristics of the slow acoustic wave bothin viscous and inviscid flow field as well as the dispersion relation, The calculationgrid and boundary conditions are adapted. The evolution of a single slow acousticwave was calculated using linear parabolized stability equations (LPSE) in thenon-uniform flow field, whereas the modified non-uniform grid and uniform grid areemployed. The results of two different grids are consistent respectively. Projectionmethod show a single slow acoustic wave cannot induce T-S wave.Otherwise,according to the receptivity theory, the evolution of T-S waves in a flat-plateboundary layer using nonlinear parabolized stability equations, the results are listedbelow:1. The grid and upper boundary conditions need to be amended whencalculating slow acoustic wave. The grid in normal direction should be fromdense to sparse within boundary layer, and uniform outside the boundarylayer. The upper boundary conditions should include the incident andreflected.2. The downstream evolution of the slow acoustic wave and T-S wave withsame frequency were calculated by linear parabolized stability equations.When the two waves have the closest phase velocity, the projection methodis used to analysis the slow acoustic wave. It is indicated that there is seldomT-S wave in slow acoustic wave. It showed that slow acoustic wave is unableto induce the T-S wave.3. The initial disturbance was chosen under the receptivity theory, the evolutionof disturbances were calculated using nonlinear parabolized stabilityequations. The growth of disturbance amplitude varies with frequency andspanwise wavelength. The higher frequency and smaller spanwisewavelength wave are in favor of stimulating high-frequency instability waves.It is found that there are only a small part second mode waves in thehigh-frequency disturbances waves. The result demonstrates that the high-frequency disturbances waves do not belong to the second modeinstability waves.更多还原