Quasi-one-dimensional modeling of pressure effects in supersonic nozzles

In this paper, a quasi-one-dimensional approach to account for the effects of contour on pressure profiles in supersonic nozzles is presented. The isentropic pressure equation is coupled with Stodola's area-Mach number equation, the normal shock relations, and the geometric profile to evaluate the pressure profile for a variety nozzle designs. The present study utilizes fundamental fluid relations which normally only vary with the area ratio; however, through the reintroduction of the axial coordinate, the effect of the nozzle contour on the pressure profile can be evaluated. To demonstrate the method, the pressure profiles in planar ramp, conical, and planar trumpet-bell nozzles are calculated. The planar trumpet-bell nozzle results are compared to a computational simulation with good agreement in both the subsonic and supersonic pressure profiles. An adjustment to the pressure ratio model is proposed which increases the agreement with the simulation results.