Hypersonic flow past delta wings of a certain class at angle of attack with an attached shock

We study the hypersonic flow of an inviscid ideal gas past a delta wing of small aspect ratio at a finite angle of attack. Increasing the Mach number M of the approaching flow to infinity for a constant geometric parameter characterizing the stream disturbance (for example, the body relative thickness or angle of attack), we obtain the limiting hypersonic flow pattern about the body, when the very strong compression shock approaches close to the body, forming a thin compressed layer of disturbed gas flow. Such a flow may be studied using the method of the small parameter, which characterizes the density ratio across the compression shock 1, 2].In 3,4] an analysis is made of the flow past conical wings whose aspect ratio is of order unity. In this case the compression shock will be attached to the leading edge. In 5] a study is made of the flow past wings of small aspect ratio which diminishes along with the small parameter in such a way that the wing half-apex angle has the same order of magnitude as the Mach cone angle within the compressed layer.In this case the angle of attack remains finite (of order unity) so that as M the hypersonic law of plane sections for slender bodies at large angles of attack 6] is satisfied, which together with the additional limit passage0 leads to the similarity law established in 5]. In this case both the case of the detached shock (when the similarity parameter <2), considered in 5, 7], and the case of the attached compression shock (>2) are possible.The monograph 2] reproduces the results of these studies with certain extensions, and also considers the direct problem of flow past a flat delta plate with attached shock, whose solution was found to contain several singular points which require further investigation.In the present study, considering the inverse problem, we were able to construct a closed pattern of the flow past wings of a certain class with thickness and with an attached compression shock, where the field of the gas-dynamic parameters and the shape of the wing surface and of the shock wave are everywhere continuous and do not contain any singular points with the exception of the known thin entropy layer near the stagnation point, which shows up only in the higher approximations 2, 4].In conclusion I would like to thank V. V. Sychev and V. Ya. Neiland for discussions of the subject and of the results, and I would also like to thank V. P. Kolgan for assistance in making the calculations.