Closed-form analytical method for conceptual design and optimization of scramjet combustor

A closed-form analytical method is presented to predict a Mach number, pressure, and temperature for a scramjet combustor where variable area, friction, and heat addition effects are simultaneously present. The method was verified against classical solutions of quasi one-dimensional isentropic flow, Fanno flow, and Rayleigh flow. The Mach number predicted by the analytical method agreed to within 0.45%, 0.01%, and 0.83% with the classical solutions, respectively. The closed-form analytical results were compared against the Reynolds Averaged Navier–Stoke based computational fluid dynamics (CFD) model prediction for a scramjet isolator-combustor operating at an inlet Mach number of 2 and fueled by Hydrogen–air combustion at an equivalence ratio of 0.2. The two results demonstrated a good agreement with within 1.02%, 1.76%, 3.38%, and 0.95% for the Mach number, density, static pressure, and static temperature distribution, respectively. An optimization of the combustor exit height using the analytical method was carried out to achieve a 35% reduction in stagnation pressure loss. The analytically based optimization demonstrated that the method is highly attractive for the scramjet combustor design and optimization during the conceptual design stage as it allows an extremely rapid evaluation of multitude of design concepts at a fraction of a time as compared to what a CFD simulation and/or an experimental test would have taken.