MINISTRY OF AVIATION AERONAUTICAL RESEARCH COUNCIL CURRENT PAPERS Some Calculations by the Crocco-Lees and Other Methods of Interactions between Shock Waves and Laminar Boundary Layers, including Effects of Heat Transfer and Suction

SUMMARY The Crocco-Lees method is applied to interactions between shocks and boundary layers that remain laminar throughout. The underlying assumptions of the method are critically reviewed, and the mathematical analysis imolved is presented. Results obtained by solving the resulting equations with the aid of the N.P.L. DEUCE computer are discussed. They are found to agree qualitatively with those of a more recent method. Cooling the wall and the use of distributed'suction are both found to reduce the extent of regions of separation. I. The Type of Problem to be Considered Interactions between shock waves and boundary layers frequently occur in practice, but often the flow configuration is complicated. A basic understanding of such practical instances can, however, be gained by studying relatively simple cases. The cases to be considered in the present paper are those shown in Figs.1 and 2. It is assumed that the flow is two-dimensional, and that the boundary layer remains laminar throughout the region of interaction. This latter is an important assumption, since it is known that if transition occurs within the region of interaction it greatly affects the flow. However entirely laminar interactions are far from academic, since high-speed aircraft usually fly high, wi,th correspondingly low Reynolds numbers. Heat transfer between the airstream and the surface often arises in practice, and it can have a large effect on the interaction. Hence cases with heat transfer are studied in the present paper. Distributed suction is also considered as it may be of practical interest in the future. The theoretical method used in. the major part of the paper is that due to Crocco and Lees1r2, 394. An account will be given in this section of the underlying approximations and physical assumptions of the method. Consider the cases shown in Fig.1 or Fig.2. Here the pressure rise imposed on the boundary layer by the incident shock, or by the change of wall slope, has an influence on the flow upstream of the shock or corner. The pressure begins to rise above its upstream value, and this causes the boundary layer to thicken, because near to the wall there is a region of-2-low-speed subsonic flow. The thickening of the boundary layer deflects the external flow outwards from its original direction, so generating a.ba.nd of compression waves. Clearly the boundary-layer thickening must be matched to the assOciatea compression waves, and finding the conditions under which the two processes can …