Analytical and Numerical Design of a High Performance Double–Throated Supersonic Blowdown Windtunnel

Abstract

In this publication the focus lies on the design process of the full supersonic double throated wind tunnel. Starting with the fundamental equations of gas dynamics in combination with an analytical model of the pressure reservoir, the area of the throat at the nozzle and the runtime of the blowdown wind tunnel were computed. Based on these results, the shape of a shock free nozzle was calculated by the method of characteristics. For this purpose, a nozzle design program was developed using Python. In order to validate the results of the method of characteristics program, these results were compared with the area-Mach number relation, which is the exact analytical solution of the isentropic flow through supersonic nozzles. The convergent part of the nozzle, which initially accelerates the flow to sonic speed, cannot be calculated by the method of characteristics, since it applies to supersonic flows only. Hence the subsonic convergent section of the nozzle was designed directly with 2D CFD using CD Adapco Star-CCM+ v. 10.06. A parametric model of the convergent nozzle section was used to find the optimum nozzle shape, i.e. a nozzle which results in a maximum mass flow rate in order to have an undisturbed flow field and Mach number in the following test section. In order to decelerate the flow again from supersonic to subsonic flow after the test section and minimize the total pressure losses, an oblique shock diffuser was used [1]. As for the convergent subsonic nozzle, the optimum shape of a diffusor was found by 2D CFD analysis. Putting all these elements together, i.e. nozzle, test section and diffuser the optimum supersonic wind tunnel shape was found. Finally, a full 3D simulation of the supersonic wind tunnel was performed in order to validate the complete design procedure and computations and also to include the viscous effect of the side walls. These results and the whole design process are presented and analyzed in the paper.