Leading-edge vortices and shock-detachment flow over delta wings.

Abstract

A review of the pertinent literature and a discussion of various flow phenomena, how they arise, and their relevance to highly swept wings at cruise conditions, is presented. The relative significance of each of these flow phenomena, their interaction, and their variation with the wing operating conditions have been examined. Also established is an understanding of the reasons for the differences between experiment and theory with regard to the reduction in drag due to the lift of supersonic wings by the use of wing camber and twist. Failure to attain experimentally the reductions in drag due to the lift is traced to the inadequacy of the theory for predicting wing pressure distributions. The linear theory neglects such significant influences as 1) three-dimensional separation and subsequent vortex formation, 2) detachment of the leading-edge shock waves, and 3) the presence of shock waves on the wing surfaces, etc. It is suggested that an effort be undertaken to develop analytical repre- sentations of the essential features of the flow which are observed in the experiments. OME form of flow separation is encountered over a wing- in flight which is not accounted for in the theory and thus is responsible for large discrepancies between the theory and experiment. The linear theory is based on the assumption of small disturbances, but the wing twist and camber predicted by the optimization procedures which utilize linear theory is so extreme that it causes the flow to violate this assumption. Discrepancies between the linear theory and experimental results occur for flat wings as well as for other wings. Love1 and Lampert2 have independently tested families of delta wings at supersonic Mach numbers. Both indicate that the lift slope becomes low relative to the theoretical values as the Mach number normal to the leading edge approaches one. An experimental investigation which reveals how the leading-edge vortex phenomenon influences the wing pressure distribution is reported by Drougge and Larson.3 The results clearly indicate the existence of three-dimensi onal flow sep- aration from the upper surface and the formation of relatively concentrated regions of vorticity streaming back above the wing surface. A very good insight into the various flow phe- nomena which can occur on the three-dimensional wings is provided by Rogers and Hall.4 Kuchemann5 provides addi- tional insight into the various flow phenomena which can become significant in the flow of a supersonic freestream about three-dimensional bodies. Maskell6 concluded that, when separation occurs, there are two basic viscous flow elements which can exist in the resulting flow. These flow elements are the free vortex layer and the separation bubbles, each of which is identifiable by characteristi c flow patterns in the family of limiting streamlines on the solid surface. Lock and Rogers7 present a semiempirical procedure for designing transonic wingbody combinations which are reasonably free from surface shocks and flow separations. The idea is to maintain quasi-two-dimensional flow over the wing with specified chordwise pressure distributions known to be attain- able without developing surface shocks. Lee8 has tested a series of delta wing models with cross sections designed to capitalize on the separated vortex flow pressure distribution