Supersonic nozzle design for viscous fluids

Abstract

A method is presented for including the effects of viscosity in the design of supersonic wind tunnel nozzles, the effect being presented in the form of a modification to the non-viscous, or perfect fluid, nozzle shapes. The modification essentially consists of providing additional expansion area to compensate for the retarded flow near the wall, and is estimated from considerations of possible boundary layer growth along a heat insulated flat well with a pressure gradient, when both the velocity profile and friction coefficient are assumed. It is shown that the modification to the perfect fluid shape becomes very pronounced for design Mach numbers above five and results in a shorter nozzle length for a given test section size than that predicted from perfect fluid theory. At a Mach number of 10, this method results in a nozzle length reduction of 50% indicating that the boundary layer occupies this percentage of the test section for the shortened nozzle. Design curves are presented from which the modification to a specific perfect fluid nozzle shape may be computed for Mach numbers up to 10.