THE DESIGN OF SYMMETRICAL, OPTIMAL SUPERSONIC AND HYPERSONIC FLOW PROFILES FOR ARBITRARY ISOPERIMETRIC CONDITIONS

A simple and accurate approach to the design of symmetric profiles whi ch are optimal in the supersonic and hypersonic flow with an attached shock is developed. Besides dimensional constraints, the bodies being optimized can satisfy arbitrary isoperimetric conditions. The approach which has been developed uses a modification of the ''shock-expansion '' method (SEM). The modified shock-expansion method (MSEM), unlike SE M, does not lead to a physically absurd result, that is, to a finite c hange in the flow parameters when the slope of the contour is solely c hanged at the leading point of the body. This makes MSEM suitable for solving two-dimensional variational problems in gas dynamics, by reduc ing any of them to a certain extension of the Lagrange problem for sys tems which are described by ordinary differential equations. The possi bilities of the approach which has been developed re illustrated using examples of profiles which achieve a minimum wave drag coefficient, C -x. Profiles designed using the MSEM are compared with those obtained using the Newtonian model and linear theory and with wedges while the C-x values found for them using the above-mentioned approximate models and MSEM are compared with the results of the numerical integration o f Euler's equations. (C) 1998 Elsevier Science Ltd. All rights reserve d.