Thrust and gravity centers for axisymmetric supersonic nozzles

Abstract

The purpose of this paper is to develop a new numerical calculation program allowing determining the position of the gravity (x _GC ) and thrust (x _TC ) centers of an axisymmetric supersonic nozzle, aiming to relate them, and with the nozzle pressure ratio (NPR). However, the x _TC changes position with the change in NPR and x _GC does not change with the flow. First, one designs the nozzle to determine numerically point by point its contour, and P/P₀ distribution along the wall, giving a uniform flow and parallel to the exit section. One made the design by HT MOC. One made the distribution of P/P₀ in the case of adaptation. The position of x _TC and x _GC are determined with the variation of exit Mach number (M _E ), stagnation temperature (T₀), nozzle throat ratio (λ), the truncate of the nozzle, and the effect of NPR. The x _GC changes also with M _E , T₀, λ, truncate of the nozzle, and do not change with NPR. One made application on MLN given its current aerospace application, and with BPN and DEN, aiming to make a comparison and improvement for our latest DEN. One has done the validation of the results by calculating x _GC of BPN central body, where it is on the middle of the nozzle according to the exact solution. For the x _TC , one made the validation for a nozzle having a constant section and P/P₀ distribution, where it is on the middle of the nozzle, in accordance with the exact solution. One makes the application for air.