Theoretical analysis on the total pressure gain of rotating detonation systems

Abstract

To achieve the positive total pressure gain of the aerospace propulsion system is one of the critical issues for the application of rotating detonation. This study conducts a theoretical analysis on the total pressure gain (PG) of a rotating detonation system (RDS) composed of the isolator, anti-backflow zone and detonation combustor, with the system inlet Mach number of Ma2. The impact of the reverse oblique shock wave (ROSW) on the system performance is emphasized. The definition of PG is based on the mass-weighted average pressure (MAP). An estimation method for PG is proposed, which is related to the inlet parameters and system anti-backflow capability. The approximate range of PG for the typical RDS and the parameter influence law are thus obtained. Results show that there is no guarantee that a positive PG can be achieved for the RDS. The theoretical upper limit PGmax is obtained when the ideal detonation cycle is realized, and its value mainly depends the reactant activity. The theoretical lower limit PGmin is mainly related to Ma2 and the area ratio of system inlet and outlet, and a specific range of Ma2 exists so that PGmin ≥ 0. When the ideal check valve (ICV) is employed, which can completely suppress the ROSW and cause no total pressure loss in the anti-backflow zone, the PGICV first increases and then decreases with the increase of Ma2, and reaches a maximum value when Ma2 approaches 1. For a general RDS, PG is always less than PGICV. The calculation example shows that for the stoichiometric C10H20/air mixture, the range of PG is ranged in (-1, 3). Eventually, two key approaches are needed to realize the positive PG of RDS, namely employing the ideal check valve, and making Ma2 approach 1 that is achieving the maximum inlet mass flux. The present study is guidable for the RDS design in practice.