Aerodynamic design of axisymmetric hypersonic wind-tunnel nozzles using a least-squares/parabolized Navier-Stokes procedure

A new procedure, which unifies the best of current classical design practices, computational fluid dynamics (CFD), and optimization procedures, is demonstrated for designing the aerodynamic lines of hypersonic wind-tunnel nozzles. The new procedure can be used to design wind-tunnel nozzles with thick boundary layers where the classical design procedure has been shown to break down. An efficient CFD code, which solves the parabolized Navier-Stokes (PNS) equations, is coupled to a least-squares (LS) optimization procedure. An LS problem is formulated to minimize the difference between the computed flowfield and the objective function, consisting of the centerline Mach number distribution and the exit Mach number and flow angle profiles. The aerodynamic lines of the nozzle are defined using a cubic spline, the slopes of which are optimized with the design procedure. The advantages of the hew procedure are that it allows full use of CFD codes in the design process, it can be used to design new nozzles or improve sections of existing nozzles, and it automatically compensates the nozzle contour for viscous effects. The computed flowfield for a Mach 15 helium LS/PNS designed nozzle is compared with the classically designed nozzle and demonstrates a significant improvement in the flow expansion process and uniform core region.

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