Boundary-layer receptivity to two-dimensional acoustic and vortical disturbances for hypersonic flows over two-dimensional and axi-symmetric geometries were numerically investigated. The role of bluntness, wall cooling, and pressure gradients on the receptivity and stability were analyzed and compared with the sharp nose cases. It was found that for flows over sharp nose geometries in adiabatic wall conditions the instability waves are generated in the leading-edge region and that the boundary layer is much more receptive to slow acoustic waves as compared to the fast waves. The computations confirmed the stabilizing effect of nose bluntness and the role of the entropy layer in the delay of boundarylayer transition. The receptivity coefficients in flows over blunt bodies are orders of magnitude smaller than that for the sharp cone cases. Wall cooling stabilizes the first mode strongly and destabilizes the second mode. However, the receptivity coefficients are also much smaller compared to the adiabatic case. The adverse pressure gradients increased the unstable second mode regions.
Nomenclaturea = speed of sound C recpt = receptivity coefficient c v = specific heat E = total energy e = internal energy F = flux vector in the x-direction, non-dimensional frequency f = frequency in Hz G = flux vector in the r-direction k = thermal conductivity M = Mach number N = N factor Pr = Prandtl number p = pressure p s = surface pressure Q = conserved flow variables vector R = gas constant Re = Reynolds number, per meter Re s = Reynolds number based on the distance s, per meter r = radial coordinate r 0 = nose radius S = source term s = distance along the surface T = temperature t = time U = mean axial velocity u = axial velocity 1 Research Scientist, AIAA Associate Fellow Downloaded by CARLETON UNIVERSITY LIBRARY on July 17, 2015 | http://arc.aiaa.org | American Institute of Aeronautics and Astronautics 2 V = radial velocity X = axial coordinate x 0 = reference x location α = wavenumber in the x-direction η = curvilinear coordinate in the radial direction, boundary-layer similarity coordinate δ = boundary layer thickness µ = viscosity ξ = curvilinear coordinate in the axial direction ρ = density ω = frequency in radian Subscripts ac = acoustic e = boundary-layer edge conditions max = maximum n = normal to the surface, neutral point ∞ = freestream quantities