平板の非定常空力加熱

Abstract

Abstract The problems of the aerodynamic heating through the turbulent boundary layer of a thin flat plate is discussed in view of the unsteady temperature distribution along the surface. The fundamental system of equations for a turbulent boundary layer of a compressible fluid consists of the conservation equations for mass, momentum and energy, the equation of state and the equations describing the transport properties of air. The solutions depend upon the boundary conditions on the surface of a plate. For the temperature distribution in the boundary layer, either the adiabatic-wall assumption or the equitemperature-wall condition has usually been postulated, simply for the convenience of analysis. But strictly speaking, the temperature is hardly regarded as uniform. On the other hand, the wall temperature should be determined by solving the equations of heat conduction in the plate which is under the influence of aerodynamic heating through the boundary layer. However, because the rate of aerodynamic heating depends on the boundary layer flow, the heating rate itself turns out to be dependent on the wall temperature. This means that the boundary layer over a plate and the heat conduction in a plate must be solved simultaneously. Since we are interested in the temperature distribution over the wall, the problem will be reduced to that of determining the surface temperature by introducing the heat transfer rate through the boundary layer with arbitrary temperature distribution in the equation of heat conduction. Using FERRARI's formula for the aerodynamic heat of the turbulent boundary layer, we obtained numerical results for a thin steel plate of 10 mm thick. The theoretical unsteady temperature distributions are compared with the experimental results.