Linear stability analysis of hypersonic boundary layers computed by a kinetic approach: a semi-infinite flat plate at 4.5≤M_∞≤9

Linear stability analysis is performed using a combination of two-dimensional direct simulation Monte Carlo (DSMC) (Bird in Molecular gas dynamics and the direct simulation of gas flows, Oxford University Press, Oxford, 1994) method for the computation of the basic state and solution of the pertinent eigenvalue problem, as applied to the canonical boundary layer on a semi-infinite flat plate. Three different gases are monitored, namely nitrogen, argon and air, the latter as a mixture of 79% N ₂ and 21% O ₂ at a range of free-stream Mach numbers corresponding to flight at an altitude of ∼55km. A neural network has been utilized to predict and smooth the raw DSMC data; the steady laminar profiles obtained are in very good agreement with those computed by (self-similar) boundary layer theory, under isothermal or adiabatic wall conditions, subject to the appropriate slip corrections computed in the DSMC method (Beskok and Karniadakis in Microscale Thermophys Eng 3(1):43–77, 1999; Beskok et al. in J Fluids Eng 118(3):448–456, 1996). The leading eigenmode results pertaining to the unsmoothed DSMC profiles are compared against those of the classic boundary layer theory (Mack in Boundary layer stability theory, Jet Propulsion Laboratory, Pasadena, 1969). Small quantitative, but no significant qualitative differences between the results of the two classes of steady base flows have been found at all parameters examined. The frequencies of the leading eigenmodes at all conditions examined are practically identical, while perturbations corresponding to the DSMC profiles are found to be systematically more damped than their counterparts arising in the boundary layer at the conditions examined, when the correct velocity slip and temperature jump boundary conditions are imposed in the base flow profiles; by contrast, when the classic no-slip boundary conditions are used, less damped/more unstable profiles are obtained, which would lead the flow to earlier transition. On the other hand, the DSMC profiles smoothed by the neural network are marginally more stable than their unsmoothed counterparts. A vortex generator (VG) introduced into the boundary layer downstream of the leading edge and pulsed at rather large momentum coefficient, C_μ= 0.27 , and scaled frequency F⁺≈ 0.98 (Greenblatt and Wygnanski in Prog Aerosp Sci 36:487–545, 2000), is used to generate linear perturbations that decay along the plate, as expected from the low value of the Reynolds number, Re _δ= 290 , in this numerical experiment. The damping rate diminishes monotonically as the VG is placed at successive downstream positions along the plate. The characteristics of the oscillation generated in the boundary layer are predicted accurately by linear stability analysis of the undisturbed profile at the location of VG placement. Most interestingly, the effect of the generated perturbation is felt well outside of the boundary layer, generating oscillations of the leading edge shock that synchronize with linear perturbations inside the boundary layer.