Alfred Ritter, Yung-Huai Kuo

The present paper is concerned with the phenomena encountered when a plane oblique shock wave is incident upon the boundary layer of a flat plate. In an effort to simplify the problem, the flow field was divided into a viscous layer near the wall and a supersonic potential outer flow. The pressure disturbances due to the incident wave would be propagated upstream and downstream in the subsonic portion of the boundary layer, thus giving rise to perturbations of the boundary layer. By restricting the study to infinitesimal incident compression waves, only small perturbations were encountered and hence the ordinary linearized theory could be applied to the outer flow. In the laminar case, the boundary layer treatment was based upon a momentum-integral equation previously derived by Howarth. The two flows must be compatible; hence, the deflection of the streamlines near the boundary layer was expressed in terms of the vertical velocity component along the edge of the boundary layer and this relation was used as a boundary condition for the outer flow. The boundary condition determined the form of solution upstream and downstream of the point of incidence. Determination of the constants of integration was accomplished by a consideration of conditions at infinity and a matching of the two flows at the point of incidence. With the outer flow thus determined, boundary-layer growth and pressure distribution were computed and results for the laminar case were obtained as follows:

1. The pressure disturbance along the wall decreased exponentially from a definite value at the point of incidence to zero far upstream of the point of incidence. Downstream of the point of incidence, the pressure rose to a maximum value and then dropped off to the value corresponding to regular reflection.
2. The disturbances produced by the interaction decayed exponentially upstream; for a free-stream Mach number of approximately 2 and a Reynolds number of approximately 1500 in the undisturbed boundary-layer displacement thickness the upstream influence was of the order of 30 boundary-layer displacement thicknesses.
3. The “self-induced” pressure gradient along the wall was such that the boundary layer might separate ahead of the point of incidence. If separation occurred, the separation point moved upstream as the shock strength was increased. With increasing Reynolds number, the separation point also moved upstream, whereas for increasing Mach number, the separation point moved downstream.

In the turbulent case the upstream influence was quite small and the incident wave must be reflected as a shock wave.

弱激波从沿平板的边界层的反射 I.

用动量积分方法分析弱激波与层流和湍流边界层的相互作用

Alfred Ritter, 郭永怀

本文研究当一个平面斜激波入射到平板边界层时所遇到的现象。为了简化问题，将流场划分为近壁面的粘性层和超声速位势外流。由于入射波引起的压力扰动在边界层的亚声速区会向上游和下游传播，从而导致边界层的扰动。若仅限于研究无限小的入射压缩波的情况，则只发生小扰动，因而通常的线化理论适用于外流。在层流的情况下，可以基于Howarth原先导出的动量积分方程来处理边界层。因为两个区域的流动应该是相容的，因此，边界层附近的流线偏转角可用边界层外缘处法向速度分量来表达，而这一关系就可以作为外流的边界条件。边界条件决定了入射点上游和下游解的形式，积分常数则是通过考虑无穷远处的条件并在入射点匹配两个区域的流动来确定。用这种方法确定外流后，再来计算边界层发展和压力分布，对层流情况得到的结果如下：

1. 沿壁面的压力扰动，从入射点的某一定值向上游以指数律下降到很远处的零。在入射点的下游，压力先上升到最大值，然后下降到对应于正规反射之值。
2. 相互作用产生的扰动向上游以指数律衰减；当来流马赫数近似为2，基于未扰边界层排挤厚度的雷诺数近似为1500时，对上游影响范围的量级是30倍边界层位移厚度。
3. 沿壁面的“自诱导”压力梯度会使边界层在入射点前发生分离。如果分离发生，激波强度增加可使分离点向上游移动，随着雷诺数的增加，分离点也向上游运动，而马赫数增加时分离点向下游移动。

在湍流情况，对上游的影响是相当小的，而入射波应有如激波一样的反射。

原文发表于National Advisory Committee For Aeronautics Technical Note 2868. 见《郭永怀文集》北京：科学出版社出版，pp.265-312, 2009.