Optimization of contoured hypersonic scramjet inlets with a least-squares parabolized Navier-Stokes procedure

Abstract

A new optimization procedure, in which a parabolized Navier-Stokes solver is coupled with a non-linear least-squares optimization algorithm, is applied to the design of a Mach 14, laminar two-dimensional hypersonic subscale flight inlet with an internal contraction ratio of 15:1 and a length-to-throat half-height ratio of 150:1. An automated numerical search of multiple geometric wall contours, which are defined by polynomial splines, results in an optimal geometry that yields the maximum total-pressure recovery for the compression process. Optimal inlet geometry is obtained for both inviscid and viscous flows, with the assumption that the gas is either calorically or thermally perfect. The analysis with a calorically perfect gas results in an optimized inviscid inlet design that is defined by two cubic splines and yields a mass-weighted total-pressure recovery of 0.787, which is a 23% improvement compared with the optimized shock-canceled two-ramp inlet design. Similarly, the design procedure obtains the optimized contour for a viscous calorically perfect gas to yield a mass-weighted total-pressure recovery value of 0.749. Additionally, an optimized contour for a viscous thermally perfect gas is obtained to yield a mass-weighted total-pressure recovery value of 0.768. The design methodology incorporates both complex fluid dynamic physics and optimal search techniques without an excessive compromise of computational speed; hence, this methodology is a practical technique that is applicable to optimal inlet design procedures.