The trend towards ultra compact thermal power generation, is constrained by the unavailability of fluid-machinery adequate for supersonic flow conditions. Conventional turbine designs exhibit unacceptable performances related to large aerodynamic losses and a narrow operation range. This paper provides for the first time in the open literature the design procedure, and subsequent analysis of the turbine performance of a turbine adequate for supersonic axial pulsating flows, as those encountered in innovative combustors. The design approach considers the most adverse condition, a steady inlet axial Mach number equal to 3.5. The possible turbine families were classified by the velocity triangles and discussed. A fundamental issue in supersonic passages is to ensure the normal shock at the start of the engine is swallowed through the turbine passages, namely the turbine passage is started. To ensure self-starting capability the turning is restricted to lower values than in the conventional subsonic turbines. The design procedure was based on the method of characteristics, converting the inlet uniform flow into a vortex flow field, such that the adequate deflection is inflicted to the supersonic flow. The performance of the supersonic passage was first assessed and then compared to conventional designs. The present design procedure and analysis of unconventional supersonic turbines provides guidelines for the design and optimization of efficient high supersonic passages, suitable to future tightly packed fluid machinery

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.