| The flight conditions of a hypersonic vehicle on an ascent trajectory are computed and Reynolds-averaged Navier-Stokes (RANS) simulations of the turbulent boundary layers are performed across a Mach number range of 0.3 up to 16 using the computational fluid dynamics (CFD) software, VULCAN. The boundary conditions and leading edge geometry are varied from the simple case of adiabatic and sharp to cooled and blunted to reveal the physics of how these effects impact the results of flat plate boundary layer methods as applied to practical aerospace systems. The law of the wall, the Van Driest transformation, and a shear stress preserving transformation's ability to collapse boundary layer velocity profiles under the conditions of variable wall boundary condition and leading edge geometry is explored.;Boundary layer related quantities examined include the boundary layer thickness, local skin friction coefficient, displacement thickness, momentum thickness, heat flux, and integrated loads. It is found that cooling the surface serves to increase the density of the boundary layer, making it thinner. This thinning of the boundary layer thickness increases the velocity gradients, thus increasing the shear stresses and the local skin friction coefficient. The effects on turbulent boundary layers of blunting the leading edge are explained by the difference in properties, particularly viscosity, caused by a detached bow shock instead of a Mach wave that comes off of a sharp nose plate. Heat flux into a vehicle is found to be insignificant at low speeds, but increases drastically as the Mach number rises into the supersonic and hypersonic regimes. It is observed that the integrated skin friction coefficient decreases as Mach number increases and the leading edge becomes blunted, however, it increases as more cooling is applied at the boundary. The integrated heat flux computed from a sharp leading edge geometry is greater compared to a blunted leading edge due to greater temperature gradients in the sharp nose case relative to the blunt nose case.;The shear stress preserving transformation, derived with the inclusion of a stress balance condition, is found to produce a better collapse of the velocity profile data than the Van Driest transformation and the incompressible law of the wall regardless of Mach number, boundary condition or leading edge geometry. The normalized untransformed velocity gradients are compared to the velocity gradients resulting from the Van Driest and shear stress preserving tranformation. It is shown that the velocity gradients from the shear stress preserving match the normalized untransformed velocity gradients more closely than the Van Driest velocity gradients do. The advantages, disadvantages, and limitations of each transformation are discussed. |
