Fluid-Solid Heat Exchange in Porous Media for Transpiration Cooling Systems

Abstract

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 .

Thermal Impulse Response in Porous Media for Transpiration-Cooling Systems

“…Porous ZrB 2 is simulated with the respective measured thermophysical parameters summarized in Table 1. These simulated impulse responses have been obtained with a =−2.71 • 10 4 W m −3 K −1 and h v = 3.5 • 10 4 W m −3 K −1 which have been determined as the best fit to the measurement data [40].…”

“…10 and 11which show a number of different blowing cases for experiment and simulation respectively. As the volumetric heat transfer coefficient of the material is unknown, each simulated impulse response has been fitted to its experimental counterpart by varying the volumetric heat transfer coefficient which is in the order of 5 • 10 4 W m −3 K −1[40]. The strong dependence of the impulse response on the fluid mass flux clearly shows the importance to incorporate the coupling between solid and fluid phases into the determination of the impulse response.…”

Performance of Transpiration-Cooled Heat Shields for Reentry Vehicles

“…The cooling effect of local heat flux mitigation and downstream film effectiveness is taken into account using semi-empirical models [20,48,49]. The temperature of the fluid and solid phases in the heat shield material are calculated based on an impulse response convolution approach that solves the coupled fluid-solid heat conduction problem assuming an adiabatic back-wall of the plenum structure behind the transpiration cooled segment [44].…”

“…Another drawback is that these regions do not benefit significantly from internal convective cooling. This mechanism is dependent on the absolute coolant density in the porous material whereas the external film cooling is dependent on the ratio of coolant to free stream mass flux [11,44]. The low mass fluxes of this region lead to low coolant densities and hence to a relatively poor internal convective heat transfer.…”

“…Conversely, regions in the parameter space and types of re-entry trajectories are identified where the effectiveness of transpiration cooling is impaired. For this purpose, a simulation tool has been developed that allows for the efficient calculation of the material temperature of a porous wall for a given flight trajectory [44]. Two different materials are considered to assess the general performance of this cooling technique in various hypersonic flow regimes.…”