Distinctive Features of Heat Transfer on a Permeable Plate in Supersonic Flow under Injection of Extraneous Gas
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inctive Features of Heat Transfer on a Permeable Plate in Supersonic Flow under Injection of Extraneous Gas V. G. Lushchika,* and M. S. Makarovaa,** aMoscow
State University, Institute of Mechanics, Moscow, 119991 Russia *e-mail: [email protected] **e-mail: [email protected]
Received March 1, 2020; revised March 12, 2020; accepted March 12, 2020
Abstract—The laminar and turbulent compressible boundary layer on a permeable plate under injection of helium in supersonic xenon flow is investigated numerically. The regimes in which the injected gas temperature is lower than the adiabatic impermeable wall temperature are considered. It is shown that at a certain distance from the start of injection the permeable-wall temperature becomes lower than the injected-gas temperature. The regimes of homogeneous injection, when He(5%)–Xe mixture with the Prandtl number Pr = 0.18 is injected, and extraneous injection, when homogeneous helium is injected in a xenon stream, are compared between themselves in the case of the injected-gas or gasmixture temperatures equal to the adiabatic impermeable wall temperature in the corresponding regime. Keywords: permeable plate, injection of extraneous gas, homogeneous injection, boundary layer, supersonic flow, differential turbulence model DOI: 10.1134/S0015462820050109
The use of permeable surfaces in various technical devices is caused by the necessity of wall heat protection by means of injection. The topicality of the heat protection problem can be estimated from the large number of publications devoted to investigation of the boundary layer with injection and reviewed in [1, 2]. For certain applied problems [3], of interest are heat-transfer agents with low Prandtl numbers (Pr < 0.7) which can be implemented in mixtures, for example, mixtures of hydrogen or helium with argon or xenon. In [4, 5] for the turbulent boundary layer on a permeable plate in supersonic air flow under air injection (Pr = 0.7) at a given cooler temperature it was found that the wall temperature can be lower than the injected gas temperature Tj at certain values of Tj. In order to eliminate the possible influence of turbulence on the heat transfer characteristics in boundary layer flow and to confirm this effect, in [6] the laminar compressible boundary layer on the permeable plate with injection was investigated numerically at low Prandtl numbers. The calculations carried out for a gas with constant Prandtl number Pr = 0.3 at the injected-gas temperatures less than the adiabatic impermeable-wall temperature have confirmed the existence of a range of permeable-wall temperatures significantly lower than the injected gas temperature. In this case the maximum difference between the injected-gas and wall temperatures is reached at the injected gas temperature equal to the adiabatic impermeable wall temperature. It is also of interest to investigate the influence of variability of the Prandtl number on the temperature difference. This can be implemented by means of injection of an extraneous gas, in particular,
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