Supersonic Nozzle Flowfields: a Comparison of Fully Viscous and Navier-Stokes Solutions

Abstract

The conventional method for the analysis of supersonic nozzle flowfields is to assume the flow to be inviscid everywhere except near the wall where a thin viscous layer grows. The inviscid core is described by Euler’s equations and the wall layer by boundary layer equations. This technique is universally used to design contoured supersonic nozzles for specified exit flow conditions. The determination of flowfields in given nozzles with known initial and boundary conditions becomes substantially more complicated. The difficulties arise because of the coupling between the inviscid core and the viscous wall layer. The expansion rate of the core depends on the boundary layer displacement which in turn depends on the core and wall conditions. Such a coupling inevitably needs a tedious iterative numerical scheme for flowfield computations. In general the following simplifying assumptions are made

• i) the neglect of the transverse curvature of the wall;

• ii) the use of flat plate thin boundary layer theory along with local similarity;

• iii) simple modelling of the flowfield such as one dimensional inviscid flow, upstream of the throat.