Self-induced separation
Self-induced separation
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DOI：
10.1098/rspa.1969.0148
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发表时间：
1969-09
期刊：
影响因子：
--
通讯作者：
K. Stewartson;P. Williams
中科院分区：
文献类型：
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作者：
K. Stewartson;P. Williams
发展了一个合理的理论来解释层流边界层与中强激波相互作用时的初始压力上升和随后的分离。该理论以Lighthill(1953)的线性化理论为基础，将感兴趣的区域划分为三个部分：边界层的主要部分，在很大的无粘力作用下发生变化；紧邻边界层的超音速主流，其中压力变化很小；以及靠近壁面的区域，在边界层尺度上，速度的相对变化很大，但受不可压缩边界层方程的控制，加上新的边界条件。我们发现，前两部分可以直接处理，而自诱导分离问题本质上归结为不可压缩边界层理论中的单个问题的解。结果表明，该问题有三种解，一种对应于无扰动流动，另一种描述了一个边界层，它自发地产生一个逆压梯度和一个减小的表面摩擦，最终消失，然后在下游建立一个反向流动。第三种解决方案产生有利的压力梯度，与本研究无关。虽然到目前为止还没有有效的数值方法来积分边界层和反向流动，但我们发现特别的方法似乎可以得到一个稳定的解，它具有分离边界层所期望的一些性质。与实验结果比较，定性吻合较好，但定量误差约为20%。人们认为，这些误差的产生是因为实验时的雷诺数太小。
A rational theory is developed to explain the initial pressure rise and consequent separation of a laminar boundary layer when it interacts with a moderately strong shock. In this theory, which is firmly based on the linearized theory of Lighthill (1953), the region of interest is divided into three parts: the major part of the boundary layer, which is shown to change under largely inviscid forces, the supersonic main stream just adjacent to the boundary layer in which the pressure variation is small; and a region close to the wall, on boundary-layer scale, in which the relative variation of the velocity is large but is controlled by the incompressible boundary-layer equations, together with novel boundary conditions. We find that the first two parts can be handled in a straightforward way and the problem of self-induced separation reduces, in its essentials, to the solution of a single problem in the theory of incompressible boundary layers. It is found that this problem has three solutions, one of which corresponds to undisturbed flow and another describes a boundary layer which, spontaneously, generates an adverse pressure gradient and a decreasing skin friction which eventually vanishes and then downstream a reversed flow is set up. The third solution generates a favourable pressure gradient and is not relevant to the present study. Although there has hitherto been no valid numerical method of integrating a boundary layer with reversed flow, we find that an ad hoc method seems to lead to a stable solution which has a number of the properties to be expected of a separated boundary layer. Comparison with experiment gives qualitatively good agreement, but quantitatively errors of the order of 20% are found. It is believed that these errors arise because the Reynolds numbers at which the experiments were carried out are too small.