| The main goal of the present investigation is the study of the hypersonic laminar boundary layer, in equilibrium, with the consideration of real gas effects. The full understanding of the physical characteristics and behavior of the laminar boundary layer at the high Mach numbers and stagnation temperatures encountered in hypersonic flow will be an important information for the feasibility of the National Aerospace Plane (NASP) and other hypersonic vehicles.; The computer simulations developed complement the previous investigations and the experimental research in progress and provide information on the behavior of hypersonic laminar boundary layer, an area where only limited publications are available in the literature for hypersonic Mach numbers at high stagnation temperatures.; The Prandtl laminar boundary layer equations for a flat plate are solved using a finite element method with symbolic evaluation of element matrices for three different assumptions: (i) perfect gas with constant properties and unity Prandtl number; (ii) perfect gas with viscosity and thermal conductivity variation with temperature; and (iii) real gas with equilibrium air properties. The laminar boundary layer was also analyzed for two different wall conditions for real gas flows: (i) constant wall temperature of 1,000 K; and (ii) adiabatic wall. Results for each flow regime include streamwise and transverse velocity profiles, temperature and density distributions, and gas property distributions to Mach 30. The solutions included results for air considered as an equilibrium real gas with effects of vibrational excitation, dissociation, ionization, and chemical reactions.; The computer codes developed to solve the partial differential equations of the problem, use a semi-discrete finite element Galerkin method with a piecewise linear polynomial basis, with possible extension to higher degree polynomials. Symbolic computation was used to evaluate elemental inner products and Jacobians, providing an improvement in computational performance.; The calculated results agree reasonably well with available numerical and experimental solutions for hypersonic boundary layers at low stagnation temperatures. It was possible, for instance, to update the previous solutions for Mach numbers to 20, by Van Driest, where the Crocco transformation resulted in a singularity at the boundary layer outer edge. The approach used in the present investigation proved to be more suitable for higher Mach numbers than the Mangler-Levy-Lees transformation and Runge-Kutta integration. |
