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This paper presents a numerical-simulation study of transient flow over a blunt compression cone under the effect of freestream hotspot perturbations. This study is motivated by concurrent wind-tunnel laser-spot experiments carried out at Purdue University. The flow conditions used in the simulation are based on the experimental conditions. The simulation is performed using a high-order shock-fitting finite-difference scheme. The simulation results show that the hotspot is able to excite second-mode instability, where the instability growth is found to be dominant in the boundary layer. The receptivity mechanism is investigated by comparing the simulated results with linear-stability theory. Fast acoustic waves generated by hotspot-shock interaction excite the boundary-layer disturbances. Also, the synchronization of mode F and mode S leads to the dominance of boundary-layer disturbances by the growing second mode. Nomenclature a = phase speed c v = specific heat in a constant-volume process d = perturbation of a variable e = total energy per unit volume F = frequency F j = inviscid flux vector in jth direction F vj = viscous flux vector in jth direction H = local height from the wall L = length scale of the boundary-layer thickness M ∞ = freestream Mach number P = pressure P ∞ = freestream pressure Pr = Prandtl number q j = heat flux due to thermal conduction R = local Reynolds number R = gas constant Re ∞ = freestream Reynolds number per unit length S = entropy S ∞ = freestream entropy s = natural coordinate along the body surface T = temperature T o = total temperature T r = reference temperature T s = Sutherland's temperature T wall = temperature at wall T ∞ = freestream temperature t = time u 1 , u 2 , u 3 = velocity components u ∞ = freestream velocity y n = normalized local normal distance from the wall α = streamwise complex wave number α i = local growth rate α r = local wave number γ = ratio of specific heat ζ = coordinate in azimuthal direction η = coordinate in the direction normal to the wall κ = heat conductivity coefficient μ = viscosity coefficient μ ∞ = freestream viscosity coefficient μ r = reference viscosity coefficient ξ = coordinate in streamwise direction ρ = mass density ρ ∞ = freestream density τ = time in computational domain τ ij = shear-stress tensor φ = phase angle ω = circular frequency Superscripts = dimensional variable 0 = perturbation of a variable

This paper presents the direct numerical simulation (DNS) study of the boundary layer receptivity for blunt compression cones in Mach-6 flow with freestream laser-spot (hotspot) perturbation. The flow conditions are the same as the Boeing/AFOSR Mach-6 Quiet tunnel (BAM6QT) in Purdue University. Compression-cone geometry is expected to cause laminar/turbulence transition in shorter stream-wise distance than straight-wedged cone geometry due to adverse pressure gradient occurs along the body. Therefore, using compression cones is advantageous to study the transition mechanisms. The DNS will be carried out in two parts: simulation of the steady flow behind the bow-shock, and simulation of the unsteady flow behind the bow-shock. The aim of the DNS is to generate the results that are agreeable with Purdue's laser induced hotspot experiment for compression cones.

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This work considers a theoretical approach to analyzing receptivity of a realistic geometry in hypersonic flow to a freestream entropy disturbance. Receptivity coefficients and phase angles are determined at a variety of locations by applying multimode decomposition to direct numerical simulation (DNS) data. The multimode decomposition scheme is implemented and rigorous verification performed against results from previous works. The method is then applied to the DNS results characterized by a freestream hotspot perturbation interacting with the bow-shock of Purdue's blunt compression cone in a Mach-6 freestream. The DNS data is decomposed into elements of the discrete and continuous spectra at various locations and frequencies, and the results compared to a prior, qualitative LST analysis. The previous analysis' conclusions are confirmed, showing that in the region downstream of the mode F / S synchronization location for the most unstable frequency, mode S is amplified and becomes the dominant mechanism of transition. The results upstream of this location are shown to be dominated by low frequency mode F perturbations. Receptivity coefficients are computed and examined for the branch I/II neutral frequencies at several locations. Brief continuous spectrum analysis is performed, showing agreement with previous work in the limited contribution from the entropy and vorticity spectra.