Design of Planar Supersonic Wind Tunnel Nozzle

Abstract

This thesis revisits the design of a planar supersonic nozzle for a supersonic wind tunnel using the method of characteristics (MOC) and Computational Fluid Dynamics (CFD). While design of a converging-diverging (CD) nozzle is in principle thought to be the outcome of a relatively straightforward procedure, the practical challenge is to design a nozzle that is free of waves in the test section of the wind tunnel. This thesis in particular studies how the waves generated due to the curvature discontinuity at the so-called point of inflection in the graphical method of MOC get modified and influenced by various aspects such as the growth of boundary layers in the nozzle and the test section, the curved nature of sonic line at the throat, the length of the initial expansion curve, the effect of various parameters of the subsonic contraction section upstream of the throat. The main objective of this effort was to design by MOC and validate using CFD a Mach 2 wind tunnel nozzle contour that results in a wave-free test section. First, the Subsonic and near sonic Mach number conditions are achieved by the use of an Error function profile for the contraction section using a procedure given by Ho and Emanuel [11] that can be used in conjunction with the divergent section of C-D Nozzle. The divergent section contour design consists firstly finding the Prandtl-Meyer angle ( ) corresponding to the Mach number at test section and then, starting at the throat and proceeding downstream, determining the flow field in terms of the local Prandtl-Meyer angle and wall angle ( and ), by MOC. MOC is based on the mathematical theory of characteristics of non-linear differential equations of the velocity potential for two-dimensional, steady, isentropic, irrotational compressible flow. The present graphical method determines the contour of the divergent walls that would transform a uniform sonic flow at the throat to a uniform shock-free flow at a desired supersonic speed. A MATLAB code was developed to calculate the nozzle wall coordinates based on MOC. The boundary layer correction was applied to the profiles to account for viscous effects which cause a Mach number reduction from the desired test section Mach number using a formulation given by Tucker [20]. The outcome of the present work is a realization of a CD nozzle with uniform and shock-free flow such that the Mach number variation on the center line of the test section was negligibly small that it can be deemed to be a constant. The design is assessed by numerical simulation using CFD software HiFUN. The final results are presented in terms of center line Mach number in the test section, which is the most significant parameters related to tunnel performance.