Thrust and gravity centers for axisymmetric supersonic nozzles

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 / P 0 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 / P 0 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 ( T 0 ), nozzle throat ratio ( λ ), the truncate of the nozzle, and the effect of NPR . The x GC changes also with M E , T 0 , 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 / P 0 distribution, where it is on the middle of the nozzle, in accordance with the exact solution. One makes the application for air.