The temperature recovery factor in a boundary layer on a permeable plate

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A numerical investigation of the boundary layer on a permeable wall in a supersonic gas flow is performed using a differential turbulence model. Temperature recovery factors are obtained for a series of Prandtl numbers and gas suction or injection in a wide range of the permeability factor from critical injection to asymptotic suction. With the example of air injection into a supersonic air flow, two methods for determining the temperature of a heat-insulated permeable wall are considered. The first is to solve the problem with a boundary condition of zero heat flux to the wall. The second is similar to an experimental method when the temperature of the gas injected at a section along the plate length becomes equal to the wall temperature. The heat-insulated wall temperatures and temperature recovery factors obtained by these two methods for injection below the critical one are close to each other. In case of critical injection, these two methods yield different results.