School of Mathematics, University of Manchester, Manchester M13 9PL, UK
School of Mathematics, University of Manchester, Manchester M13 9PL, UK.
Philos Trans A Math Phys Eng Sci. 2014 Jul 28;372(2020). doi: 10.1098/rsta.2013.0342.
The instability of supersonic compression ramp flow is investigated. It is assumed that the Reynolds number is large and that the governing equations are the unsteady triple-deck equations. The mean flow is first calculated by solving the steady equations for various scaled ramp angles α, and the numerical results suggest that there is no singularity for increasing ramp angles. The stability of the flow is investigated using two approaches, first by solving the linearized unsteady equations and looking for global modes proportional to e(λt). In the second approach, the linearized unsteady equations are solved numerically with various initial conditions. Whereas no globally unsteady modes could be found for the range of ramp angles studied, the numerical simulations show the formation of wavepacket type disturbances which grow and convect and reach large amplitudes. However, the numerical results show large variations with grid size even on very fine grids.
研究了超声速压缩斜坡流的不稳定性。假设雷诺数很大，控制方程是不稳定的三层方程。首先通过求解不同标度斜坡角α的定常方程来计算平均流，数值结果表明，随着斜坡角的增加，不存在奇点。通过两种方法来研究流的稳定性，首先通过求解线性非定常方程，并寻找与 e(λt)成正比的全局模式。在第二种方法中，通过求解不同初始条件的数值线性非定常方程。虽然在所研究的斜坡角范围内没有发现全局非定常模式，但数值模拟显示了波包类型的干扰的形成，这些干扰会增长和对流，并达到很大的幅度。然而，即使在非常细的网格上，数值结果也显示出与网格大小的大的变化。
