Inviscid Design of Hypersonic Wind Tunnel Nozzles for a Real Gas

A straightforward procedure has been developed to quickly determine an inviscid design of a hypersonic wind tunnel nozzle when the test gas is both calorically and thermally imperfect. This real gas procedure divides the nozzle into four distinct parts: subsonic, throat to conical, conical, and turning flow regions. The design process is greatly simplified by treating the imperfect gas effects only in the source flow region. This simplification can be justified for a large class of hypersonic wind tunnel nozzle design problems. The final nozzle design is obtained either by doing a classical boundary layer correction or by using this inviscid design as the starting point for a viscous design optimization based on computational fluid dynamics. An example of a real gas nozzle design is used to illustrate the method. The accuracy of the real gas design procedure is shown to compare favorably with an ideal gas design based on computed flow field solutions. Nomenclature C1 = constant in Eq. (1) Cd = contraction coefficient M = Mach number r* = nozzle throat radius or height Rc = throat radius of curvature/r* S = Rc + 1 x = axial coordinate X a = start of subsonic contour with Eq.(1) y = radial coordinate yw = nozzle wall radial coordinate yw ' = nozzle wall slope γ = gamma, ratio of specific heats θa = subsonic approach angle θsuper = nozzle inflection angle