Laminar Subsonic, Supersonic, and Transonic Boundary-Layer Flow past a Flat Plate

Abstract

A boundary-layer formulation is developed for the low-Mach-number limit. Self-similar low-Mach-number Falkner-Skan solutions are found for flow past a wedge. From computation of both this low-Mach-number-limit solution and the full compressible boundary-layer equations, it is shown that laminar transonic boundary-layer flow past a constant temperature flat plate may be accurately calculated using the simpler low-Mach-number-limit solution. Nomenclaturetemperatures with and without Mach number heating J = total enthalpy M ∞ = freestream Mach number m ∞ = parameter relating τ and M ∞ Pr = Prandtl number Re = Reynolds number T c= temperature within the boundary layer scaled using |T e − T w | for a flat plate T e , J e = temperature and total enthalpy at the edge of the boundary layer T * e = dimensional temperature at the edge of the boundary layer T w = nondimensional wall temperaturê T ,R = nondimensional perturbation temperature and density within the boundary layer U, V = streamwise and wall-normal velocities U e = velocity at the edge of the boundary layer β = pressure gradient parameter T * = dimensional temperature difference between the freestream and the wall ρ = density within the boundary layer ρ e , µ e = density and viscosity at the edge of the boundary layer ρ w = nondimensional wall density τ = freestream air temperature perturbation from wall temperature ψ, ,ˆ , f = stream functions Subscripts e = property at the edge of the boundary layer s, N = derivatives in boundary-layer equations w = property at the wall ξ, η = derivatives in boundary-layer equations in transformed coordinates

Instability of stagnation and attachment line icing

“…In the low Mach number stagnation flow of this study, the heat flux does not vary with streamwise distance. However, in the boundary layer formulation of Rothmayer [48] (also see Otta and Rothmayer [56]), a cooling effect of the heat flux from airflow wing. These ice structures are called "scallops", "cups" or "lobster tails" (see Vargas [57]).…”