Simple Physics-Based Model for the Prediction of Shock-Train Location

Abstract

A simple physics-based model was developed for the prediction of shock-train location in constant-area scramjet isolators. The shock train was shown to manifest at the location within the isolator that possesses the Mach number required to match the isolator pressure ratio, the ratio of isolator exit pressure to inlet pressure. The model assumes that the Mach-number gradient along the isolator is due to boundary-layer growth. Using the normal-shock and quasi-one-dimensional isentropic-flow equations, a relation was derived for determining the location of the leading shock of the shock train. The model must be calibrated to obtain some measure of the boundary-layer thickness and growth. The model accuracy depends upon the amount of calibration data used. The model performed well using only the Mach-number-gradient information in a Mach 1.8 cold-flow direct-connect isolator, but not as well in a combusting Mach 2.2 direct-connect dual-mode scramjet tunnel. Improved performance of the model for both tunnels was achieved with the use of more calibration data. This simple model is useful for gaining physical insight into isolator dynamics and implementing closed-loop control schemes that seek to control the shock-train location in the isolator. Particularly, it demonstrates the importance of the isolator Mach-number gradient in determining the range of isolator pressure ratios the isolator can sustain.