DNS OF INJECTION-INDUCED TRANSITION IN HYPERSONIC FLOW OVER POROUS SURFACES FOR TRANSPIRATION COOLING APPLICATIONS

Flow at hypersonic speeds is characterised by severe heat loads at the wall that can lead to the failure of the vehicle structure. Most passive-cooling thermal protection systems (TPS) make use of a low-density porous material to decrease the thermal conductivity and the heat transfer in the inner structure. Porosity plays an important role in active-cooling systems, allowing the coolant gas to be injected into the hot boundary layer, as in the case of transpiration cooling. However, the influence of cooling on transition needs to be investigated, as an induced earlier transition can dramatically increase the wall heat flux, thus causing the loss of the wall-cooling benefits. Reliable simulations of such a system require capability of modeling and meshing the porous structure, to capture the main flow features at a multiscale level, i.e. within the porous layer, in the mixing layer and in the downstream boundary layer.

The transition mechanism is affected by the physical properties and main flow features of the injected fluid, which, in turn, depend on the main parameters determining the characteristics of the flowfield through a porous medium, namely porosity, Reynolds number, pore size and shape, arrangement of the pores, and tortuosity. The latter is a measure of the average path length of the streamlines within the pores up to the upper surface, compared to the thickness of the sample, which determines, along with the porosity, the permeability of the porous structure. Different models of permeability and tortuosity have been proposed by researchers, but none is universal, and a change in the characteristics of the porous medium can lead to significant errors in the estimation of the main features of the injected flow (e.g. the hydraulic discharge) if one relies on a particular model. The difficulty in predicting the physical properties of the flow through a porous medium by means of a reliable universal model lies in the many above-mentioned independent parameters involved. Thus, accurate numerical simulations of the flow through a porous medium are needed for evaluating the relative weight of each of the relevant factors on the solution of the injected flow as well as on the downstream boundary-layer flow.

In our study, we perform direct numerical simulations (DNS) of injection through a porous layer in hypersonic flow over a flat plate for a prescribed pressure ratio between the lower and upper surface of the sample. The method used to carry out the simulations is a 6th-order hybrid central differencing / weighted essentially nonoscillatory (WENO-CD) scheme. First, a local (short) domain is considered, where the porous structure is modelled by filling its volume with distributed solid spherical elements, and a parametric study is carried out based on different sizes and arrangements of the solid particles, as well as different porosity percentages, to evaluate the effects on the outer flow. This will provide indications of how the fluid flowing through the porous layer is affected by the geometrical structure of the pores, for different porosity levels, thus allowing an assessment of the tortuosity (and hence the permeability) dependence on the particular porous structure. The effect of the presence of a hypersonic crossflow on top of the porous sample is investigated as well. Then, a wider flat-plate domain will be considered, in which the effect of injection on the boundary-layer stability properties and the transition mechanism will be studied and compared with the results obtained for different configurations, namely a flat plate with slots, and a flat plate with modelled blowing on the surface.

This work will lead to future accurate modelling of the flow through porous media in a hypersonic environment, allowing a semi-empirical model of the permeability of the porous layer to be made, based on the DNS data. Moreover, the present study will provide important insights in the physics of blowing through a porous layer in hypersonic flow and its effects on the transition mechanism.