This paper experimentally examines the internal and external flow characteristics of porous zirconium diboride (Z r B 2 ), an Ultra-High-Temperature-Ceramic (UHTC) and a potential candidate for transpiration cooling of hypersonic vehicles. This is performed for both partially sintered material and fully densified material with cast features. The Darcy and Forchheimer permeability coefficients of these samples are determined using an ISO standard test rig. The outflow of the transpiring porous samples is investigated where no hypersonic cross-flow is involved using hot-wire anemometry and focused Schlieren visualisation. The velocity maps obtained from the hot-wire data show significant non-uniformities across the UHTC's outflow region, both at low and high differential pressures. The focused Schlieren using carbon dioxide as the injected gas reveals unsteady structures at high differential pressures as the outflowing gas interacts with the surrounding air.

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 paper, 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 $$0.295\%$$ 0.295 % . The unit Reynolds number of the flow is $$12.9\times 10^6\;\mathrm {m^{-1}}$$ 12.9 × 10 6 m - 1 . A coolant concentration of up to $$95\%$$ 95 % is achieved immediately (2 mm) downstream of the injector. The film concentration drops in a monotonic fashion farther downstream; however, a constant film coverage of 5–20 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. 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. Finally, a collapse of the thermal effectiveness is achieved and a modified analytical correlation is proposed. Graphical abstract

Porous Ultra-High-Temperature-Ceramics (UHTC) 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 work experimentally examines the internal and external flow behaviour of porous UHTC made of zirconium diboride (ZrB 2 ) 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.

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The design of a transpiration cooled system requires detailed local heat transfer information on and in the vicinity of the porous injector; however, limited spatially resolved experimental studies exist, particularly in hypersonic flows. In this work experiments were conducted in the Oxford High Density Tunnel at Mach 6.1 in both laminar and turbulent regimes. Spatially resolved 2D surface heat transfer measurements were acquired by imaging directly on and downstream of two micro-porous transpiration cooled injectors (METAPOR CE170 and Zirconia) using high-speed infra-thermography. Whilst injection in the laminar regime results in a steady, monotonic reduction in heat transfer from the start of the injector, a flatter profile is present for the turbulent cases where turbulent mixing inhibits surface heat transfer reduction.

This paper presents a semi-analytical solution of the coupled differential equations for fluid and solid phase in a one-dimensional porous medium in thermal non-equilibrium. The thermal impulse response of the fluid and solid phases is used to determine the pressure loss over the thickness of the material. Experimental data obtained from surface heating of porous ZrB2 samples is compared to the theoretical model. The plenum pressure, surface temperature and backside temperature are measured using pressure sensors, thermographic imaging and thermocouple instrumentation The non-integer system identification (NISI) approach is used to obtain the thermal impulse response which is then compared with the model prediction. Plenum pressure rise and thermal impulse response of the heating experiments are used to assess the volumetric heat transfer coefficient of the sample. Good agreement is found between the simulated and experimental data for the temperature and pressure measurements. The obtained heat transfer coefficients are between 2.1 • 10 4 and 6.8 • 10 4 W m −3 K −1 for mass fluxes of 10 to 244 g m −2 s −1 .

Two-dimensional simulations of transpiration cooling in a laminar, hypersonic boundarylayer were performed using the Thermochemical Implicit Non-Equilibrium Algorithm (TINA) -a Navier-Stokes solver. Coolant concentration and heat flux results are compared to data obtained from laminar transpiration cooling experiments conducted in the Oxford High Density Tunnel (HDT) employing a flat-plate geometry at Mach 7. 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.

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