Numerical Analysis of Transpiration Cooling on a Turbulent Flat Plate
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Date
2020-01-14
Authors
Christopher, Nicholas
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Publisher
University of Waterloo
Abstract
Transpiration cooling is a promising thermal protection system for gas turbines, atmospheric re-entry heat shields, and rocket engine combustion chambers. Design of transpiration cooling systems must rely on numerical simulation in order to reduce costs. The purpose of this work it to better understand the physical phenomena which effect turbulence and heat transfer in a turbulent boundary layer with transpiration cooling, in order to inform models of the system. Towards this goal, direct numerical simulations (DNS) of transpiration cooling in a turbulent flat-plate boundary layer at a freestream mach number of 0.3 have been performed. The coolant and the hot gas are both air, and isothermal walls and coolant at a temperature ratio of Tw/T∞ = 0.5 have been prescribed. The blowing ratio (which is the mass flux ratio between the coolant and the freestream gas), and the coolant injection boundary conditions have been varied to investigate their effects on the flow. It is found that 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. As the blowing ratio is increased, there is also a reduction in heat transfer to the porous wall. This reduction of 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. Log law scaling of the velocity profile with blowing walls is analyzed, and found to only be applicable for modest blowing rates. Reasons for the failure of scaling laws at high blowing rates are proposed based on the x-momentum balance of the Navier-Stokes equations. In order to investigate wall modelling effects, simulations with uniform coolant injection have been compared to simulations with injection via many small slits. It is observed that as the slits 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.
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Keywords
rocket, thermal protection system, transpiration cooling, direct numerical simulation