Characteristic velocity analysis of the total pressure gain of rotating detonation combustors

Recently extensive efforts have been made on the evidence of the total pressure gain (TPG) in rotating detonation combustors (RDCs), but no positive TPGs have been obtained experimentally so far. To further reveal the mechanism of the TPG in the RDC, the characteristic velocity analysis is performed through numerical simulation and theoretical modelling. The distribution of the characteristic velocity in the RDC flow field is obtained and the functional relationships between the TPG and the outlet-to-inlet area ratio are derived, for both RDCs and ideal isobaric combustors. The 2D numerical simulation results show that the characteristic velocity of the detonation products closely following the rotating detonation wave is higher than the ideal isobaric value. However, after expansion, the characteristic velocity of the detonation products approaches a value lower than the ideal isobaric value. Via area-averaging (also time-averaging in the RDC), the characteristic velocity at the RDC exit is close to that of ideal isobaric combustion products. Further discussion indicates that the gain in characteristic velocity does not play a primary role in the TPG of the RDC. Compared with the published numerical and experimental results, it shows that the TPGs in experiments have not exceeded that of ideal isobaric combustors. When the outlet-to-inlet area ratio decreases, the differences between the TPGs of experiments and the theoretical TPG upper limit of the RDC increase. This suggests that to achieve the TPG, it is required not only to design the profiles between different stations to enable stable rotating detonation but also to minimize the injection area blocked by the detonation wave, thereby increasing the average inlet Mach number.