A Relation for Specific Impulse versus Back Pressure Changes and Optimum Conical Nozzle Expansion Ratio Algorithm

The main objective of utilizing nozzles is to convert the chemical energy to kinetic energy producing thrust. Wide variety of parameters make significant impact on nozzle performance; one of which produces significant effect is back pressure or ambient pressure. Basically, a nozzle designed for a specific back pressure does not work properly when the engine is ascending. Consequently, designing of nozzles needs knowledge of full effect of back pressure on engine performance. In this study, numerical simulation of three solid propellant nozzles have been conducted in several flight conditions. In other words, simulations have done in some ambient pressures which represents specific flight altitudes. Numerical modeling has been conducted aiding commercial code FLUENT. k-ϵ RNG turbulence model has been used for calculating turbulence interactions with the flow. Mass flow rate, chemical species, and chamber temperature have been used as the inlet boundary conditions based on engine specifications. Numerical results show a reasonable accuracy in comparison with experimental measurements. Estimating nozzle thrust level as a function of altitude increment is the primary goal of this study. Furthermore, with the aid of this relation and a MATLAB code for computing average specific impulse, optimum expansion ratio can be achieved based on a specified mission.