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The combustion mode in a steady-flow propulsion system has a strong influence on the overall efficiency of the system. To evaluate the relative merits of different modes, we propose that it is most appropriate to keep the upstream stagnation state fixed and the wave stationary within the combustor. Because of the variable wave speed and upstream stagnation state, the conventional Hugoniot analysis of combustion waves is inappropriate for this purpose. To remedy this situation, we propose a new formulation of the analysis of stationary combustion waves for a fixed initial stagnation state, which we call the stagnation Hugoniot. For a given stagnation enthalpy, we find that stationary detonation waves generate a higher entropy rise than deflagration waves. The combustion process generating the lowest entropy increment is found to be constant-pressure combustion. These results clearly demonstrate that the minimum entropy property of detonations derived from the conventional Hugoniot analysis does not imply superior performance in all propulsion systems. This finding reconciles previous analysis of flowpath performance analysis of detonation-based ramjets with the thermodynamic cycle analysis of detonation-based propulsion systems. We conclude that the thermodynamic analysis of propulsion systems based on stationary detonation waves must be formulated differently than for propagating waves, and the two situations lead to very different results.

Stagnation Hugoniot Analysis for Steady Combustion Waves in Propulsion Systems