Mathematical Modeling of Heat and Mass Transfer During Aerodynamic Heating of the Nose Parts of Hypersonic Aircraft

Abstract

The study focuses on heat and mass transfer on the side surfaces of blunt nose cones of hypersonic aircraft under aerodynamic heating conditions and formulates the problem of viscous flow and heat and mass transfer in dynamic, thermal, and diffusion boundary layers. After minor simplifications, we found approximate analytical solutions related to the gas-dynamic, thermal, and diffusion characteristics of the dissociating flow and obtained closed analytical expressions for the distribution of enthalpy and concentrations of the gas mixture components over the thickness of the boundary layers. Furthermore, by the derivatives of the enthalpies and concentrations distributions with respect to the vertical variable on the wall, we determined convective and diffusion heat fluxes to the aircraft surface. Using the balance between the supplied convective-diffusion heat fluxes and the fluxes removed due to radiation and heat elimination into the body, we obtained a nonlinear equation for the wall temperature, which is solved numerically. Numerical results are obtained and analyzed on convective-diffusion heat fluxes and wall temperatures of hypersonic aircraft, depending on the Mach number and flight altitude in a wide range of values, which make it possible to determine the boundaries of speeds and altitudes at which the mass of the heat-shielding coating is not removed. Finally, we investigated the influence of the catalytic properties of the aircraft surface on heat transfer in the same ranges of the Mach number and flight altitude