DNS of turbulent flat-plate flow with transpiration cooling. (August 2020) - Christopher, Nicholas; Peter, Johannes M.F.; Kloker, Markus J.; Hickey, Jean-Pierre
Highlights: Direct Numerical Simulations of turbulent boundary layers with transpiration cooling was conducted. The effects of the transpirative cooling efficiency was investigated under different blowing regimes. A model is proposed to account for the heat advection and film accumulation effects in transpiration cooling. Turbulence is generated at the coolant-gas injection locations and impact the heat transfer to the wall. The effect of the type of injection (uniform or strip injection) on the heat transfer to the wall is assessed . Abstract: Transpiration cooling in a turbulent boundary layer on a flat plate is investigated using direct numerical simulations (DNS). The simulations are performed by solving the compressible Navier-Stokes equations at low Mach number conditions ( M ∞ = 0.3 ). Both the coolant and the hot gas are air, with isothermal walls and coolant at a temperature of T w / T ∞ = 0.5, while the blowing ratio and boundary conditions have been varied. These simulations elucidate the turbulence and heat-flux alterations due to the interaction of the coolant with the hot-gas boundary layer. By increasing the blowing ratio, the peak turbulent kinetic energy moves away from the wall to a region of shear between the low-momentum coolant and high-momentum hot gas. The reduction of the wall heat transfer is caused by the combined effects of heat advection due to the non-zero wall-normal velocity at the wall, and the reduction of the average boundary-layer temperature due to the accumulation of coolant. A new model for the latter effect is proposed which is physically realistic in the limit cases. The proposed combined model accounts for both heat advection and film accumulation and shows good agreement with the DNS data. An increase in turbulent transport of heat with increasing blowing rate is caused by the production of vortices between the coolant and hot gas. This causes a reduction in the cooling effectiveness, and can be seen near the leading edge of the transpiration region. In order to investigate wall modelling effects, simulations with uniform coolant injection have been compared to simulations with injection via many small strips. It is observed that as the strips get smaller (at fixed total mass flow rate and fixed wall porosity), the results trend towards the uniform injection case. Therefore, it is hypothesized that for small pore sizes, neglecting the effects of the individual pores in the wall boundary condition is physically justifiable.