Direct numerical simulation of supersonic turbulent flow with film cooling by wall-parallel blowing

An advanced film-cooling application is the thermal protection of the nozzle extension of high-performance rocket engines. The extension wall needs be protected from the hot supersonic thrust gas, very much like the combustion chamber or nozzle throat region, where the flow is, however, sub- or transonic. A reliable cooling modeling for practical applications requires benchmark results for generic cases with accurate flow-field details. To this end, fundamental investigations of the interaction between the thrust and cooling gas have been performed for flat-plate flow using high-order direct numerical simulations for the first time. A cool secondary gas is injected through a vertical slot of height s in a backward-facing step. The thrust-gas flow is steam (gaseous H₂O) at Mach 3.3 with a turbulent boundary layer, and a laminar supersonic stream of cool helium is injected. The influence of the coolant mass flow rate is investigated by varying the blowing ratio F or the injection height s at a fixed cooling-gas temperature and Mach number. Several previously unknown effects are found fostering correlation model evolution of the film cooling, inter alia that the upstream wall temperature needs be taken into account and how the turbulent Prandtl and Schmidt number distributions are in the field, essential for improved Reynolds-averaged Navier–Stokes simulations.