Transpiration cooling of a hypersonic vehicle

In this thesis, a porous Ultra-High-Temperature-Ceramic (UHTC) made of zirconium diboride (ZrB2) is qualified for the purpose for transpiration cooling for the first time. Subsequently, the mixing mechanism between the coolant and a laminar, hypersonic boundary-layer gas at the wall downstream of a transpiration-cooled injector is investigated. This has led to understanding the mixing process at the wall in a laminar boundary layer.
Porous UHTCs are a candidate group of materials for transpiration cooling of hypersonic vehicles due to their exceptionally high melting point, typically above 3000 K. Their high operating temperature permits a higher amount of radiative cooling than that achievable with conventional materials, which reduces the required coolant mass flow rate to cool the surface. This thesis experimentally examines the internal and external flow behaviour of porous UHTC made of zirconium diboride (ZrB2) for the purpose of transpiration cooling. A dedicated ISO standard permeability test rig was built. The outflow velocity distribution was acquired employing miniature hot-wire anemometry. The data obtained for the pressure loss across the porous samples agree with the Darcy-Forchheimer model for flow in porous media; respective Darcy and Forchheimer permeability coefficients are calculated and reported. Cleaning the surface of the samples using sandpaper or an ultrasonic bath raised the permeability coefficient by up to 19%. The outflow velocity maps exhibit a good flow uniformity with an average standard deviation of 25.1% with respect to the mean value. Individual jets are absent, and the velocity varies within the same order of magnitude.
The mixing between the coolant and the boundary-layer gas downstream of an injector – for transpiration/film cooling – has been extensively studied for turbulent flows; however, only a handful of studies concerning laminar mixing exist, particularly in hypersonic flows. In this thesis, the concentration of the coolant gas at the wall and the heat flux reduction downstream of a transpiring injector in a hypersonic, laminar flow are experimentally measured and examined. Experiments are performed in the Oxford High Density Tunnel at Mach 7. A flat-plate model is coated with Pressure-sensitive Paint (PSP) to spatially resolve the film and obtain a film effectiveness based on coolant concentration. Thin-film arrays are installed to measure the heat flux reduction. Six different cases are studied featuring Nitrogen and Helium as the coolant gas, where the blowing ratio is varied from 0.0406% to 0.295%. The unit Reynolds number of the flow is 12.9 × 10ˆ6 1/m. A coolant concentration of up to 95% is achieved immediately downstream of the injector. The film concentration drops in a monotonic fashion farther downstream; however, a constant film coverage of 5 mm to 20 mm immediately downstream of the injector is observed in cases with a higher blowing ratio. A film coverage above 15% over three injector-lengths is present even for the lowest blowing ratio. Heat flux reduction is achieved in all cases; an onset of boundary-layer transition is not promoted. The concentration effectiveness obtained from PSP is compared with the thermal film effectiveness calculated from the heat flux reduction. The latter is found to be higher than the former for all data points. Subsequently, a collapse of the thermal effectiveness is achieved and a modified analytical correlation is proposed.
A two-dimensional simulation study of transpiration cooling in a laminar, hypersonic boundary-layer using the Thermochemical Implicit Non-Equilibrium Algorithm (TINA) – a Navier-Stokes solver was undertaken. Coolant concentration and heat flux results are compared to data obtained from the experiments. TINA successfully predicts the mixing rate at the wall as a function of the stream-wise direction for all blowing ratios. The simulations are more successful in predicting the mixing downstream of the injector compared to the mixing on the injector, especially at low blowing ratios. A collapse of the thermal effectiveness values calculated from simulation data is achieved, which agrees with laminar correlations within an absolute value of ±10%. It is shown that, when the concentration effectiveness is close to 1 at the injector, the temperature gradient becomes negative at locations immediately downstream of the injector, resulting in a negative heat flux. The acceleration of the coolant in the stream-wise direction downstream promotes dissipation of energy, which results in a reduction in the temperature of the coolant and thereby induces a negative temperature gradient close to the injector.
Finally, an analytical model based on one-dimensional diffusion is proposed to predict the mixing between the coolant gas and boundary-layer gas at the wall downstream of a transpiring injector in a laminar flow. The model is validated against the experimentally obtained coolant concentration data. It successfully predicts the mixing at the wall downstream within 17% of the experimental data. It is shown that this mixing mechanism at the wall in laminar flows is fully described by the process of diffusion. The coolant coverage at a given downstream location is promoted when the stream-wise velocity decreases, the blowing ratio increases, or the diffusion coefficient drops. Subsequently, a mass budget calculation is performed for a transpiration-cooled hypersonic vehicle employing the analytical model. The model predicts a 3.6 times less coolant mass requirement when Helium is used as the coolant gas as opposed to Nitrogen for the chosen trajectory. However, Helium requires twice the storage volume compared to Nitrogen.

Keywords: hypersonics
active cooling
boundary layer
analytical modelling
laminar mixing
ultra high temperature ceramics
PSP
thermal protection system
heat flux
laminar boundary layer
reusable TPS
reusable rockets
reusable thermal protection system
navier stokes solver
pressure sensitive paint
aerodynamics
mixing mechanism
porous media flow
porous UHTC
concentration
darcy forchheimer equation
diffusion
fluid mechanics
uhtc
aerothermodynamics
boundary-layer mixing
mixing
TPS
fluid dynamics
zirconium diboride
hypersonic wind tunnel
thin-film gauges
ZrB2
reentry vehicle
hypersonic vehicle
transpiration cooling
Advisor: McGilvray, M
Hermann, T