Rotating detonation combustors (RDCs) offer theoretically a significant total pressure increase, which may result in enhanced cycle efficiency. The fluctuating exhaust of RDC, however, induces low supersonic flow and large flow angle fluctuations at several kHz, which affects the performance of the downstream turbine. In this paper, a numerical methodology is proposed to characterize a supersonic turbine exposed to fluctuations from RDC without any dilution. The inlet conditions of the turbine were extracted from a three-dimensional (3D) unsteady Reynolds-averaged Navier–Stokes simulation of a nozzle attached to a rotating detonation combustor, optimized for minimum flow fluctuations and a mass-flow averaged Mach number of 2 at the nozzle outlet. In a first step, a supersonic turbine able to handle steady Mach 2 inflow was designed based on a method of characteristics solver and total pressure loss was assessed. Afterward, unsteady simulations of eight stator passages exposed to periodic oblique shocks were performed. Total pressure loss was evaluated for several oblique shock frequencies and amplitudes. The unsteady stator outlet profile was extracted and used as inlet condition for the unsteady rotor simulations. Finally, a full stage unsteady simulation was performed to characterize the flow field across the entire turbine stage. Power extraction, airfoil base pressure, and total pressure losses were assessed, which enabled the estimation of the loss mechanisms in supersonic turbine exposed to large unsteady inlet conditions.

The pressure gain across a rotating detonation combustor offers an efficiency rise and potential architecture simplification of compact gas turbine engines. However, the combustor walls of the rotating detonation combustor are periodically swept by both detonation and oblique shock waves at several kilohertz, disrupting the boundary layer, resulting in a rather complex convective heat transfer between the fluid and the solid walls. A computationally fast procedure is presented to calculate this extraordinary convective heat flux along the detonation combustor. First, a numerical model combining a two-dimensional method of characteristics approach with a monodimensional reaction model is used to compute the combustor flow field. Then, an integral boundary layer routine is used to predict the main boundary layer parameters. Finally, an empirical correlation is adopted to predict the convective heat-transfer coefficient to obtain the bulk and local heat flux. The procedure has been applied to a combustor operating with premixed hydrogen–air fuel. The results of this approach compare well with high-fidelity unsteady Reynolds-averaged Navier–Stokes three-dimensional simulations, which included wall refinement in an unrolled combustor. The model demonstrates that total pressure has an important influence on heat flux within the combustor and is less dependent on the inlet total temperature. For an inlet total pressure of 0.5 MPa and an inlet total temperature of 300 K, a peak time-averaged heat flux of 6 MW/m² was identified at the location of the triple point, followed by a decrease downstream of the oblique shock, to about 4 MW/m². Maximum discrepancy between the reduced-order model and the high-fidelity solver was 16%, but the present reduced-order model required a computational time of only 200 s, that is, about 7000 times faster than the high-fidelity three-dimensional unsteady solver. Therefore, the present tool can be used to optimize the combustor cooling system.