Two parallel expansions for improving supersonic axisymmetric nozzle performance

Abstract

The aim of this work is to develop a numerical computation program allowing designing new contours of a supersonic axisymmetric nozzle having two expansions at the throat, named by DEN (Dual Expansion Nozzle). This new nozzle gives a uniform and parallel flow at the exit section, to improve considerably the performances compared to the conventional Minimum Length Nozzle (MLN), and the Best Performances Nozzle (BPN). The present nozzle has a two unknowns external and central body curved walls. Each of them is started by an initial expansion angle to give a uniform and horizontal flow at the exit section. Two others transition regions are calculated in parallel with the contours points to give the desired exit Mach number. The walls are determined point by point by the High Temperature Method of Characteristics (HT MOC) model. The resolution of the four compatibility and characteristics equations is done numerically by the finite difference predictor corrector algorithm. The validation of the results is controlled by the convergence of the calculated critical sections ratio to that given by the theory. The design depends on four parameters, where MLN and BPN become special cases of DEN. A comparison is made with MLN, since it is currently used in the aerospace propulsion and with BPN aiming to improve their performances. The comparison is made for the same critical mass flow rate. The results demonstrate a remarkable reduction up of 45 %, and 52 % in the mass of DEN when the exit Mach number ME = 3.00 and the stagnation temperature T0 = 2000 K. The application is made for air and for future aerospace missiles in order to improve their trajectory parameters. The chosen example demonstrates an improvement of 13 % and 16 % on the missile range compared, respectively to MLN, and BPN.