Thin flat bodies of minimum wave drag in nonequilibrium supersonic flow

Abstract

In [1] the problem of optimal profiling of the contours of plane and axisymmetric bodies in supersonic nonequilibrium flow without the formation of a shock wave (these bodies include, in particular, the contours of base sections and nozzles) is reduced to the boundary value problem for a hyperbolic system of equations, which includes the flow equations and the equations for the Lagrange multipliers (there is an error in Eq. (4.5) of [1]; there should be a minus sign in front of the third term in the braces). In view of the solution complexity, in [2] the construction of the optimum nozzle contour is based on the one-dimensional approximation. Although this approach does permit establishing the order of the possible gain, the conclusions concerning the contour shape which result from this approach are basically qualitative. In the following the construction of thin plane bodies of minimal wave drag in a nonequilibrium supersonic flow is carried out in the linear approximation, which leads to a more complete picture of the form of the optimum contours. Numerous examples of the use of linear theory for optimizing body shape in supersonic perfect gas flow are given in [3].