Publications Details

Numerical considerations of slow acoustic mode in high-velocity boundary layers

Harris, Shaun R.; Wagnild, Ross M.

Direct numerical simulations (DNS) were conducted of a high-velocity flat plate boundary layer with time-periodic fluctuating inflow. The DNS fluctuation growth and evolution over the plate is then compared to the solution as computed using classical linear stability theory (LST) and the parabolized stability equations (PSE) of a second mode eigen function. The decay rate of the free stream perturbations is also compared to LST and the choice of shock-capturing method and the associated dissipation rate is characterized. The agreement observed between the eigen function from LST and the fundamental harmonic of the temporal Fourier transform (FT) of the DNS simulation demonstrates the ability of the solver to capture the initiation and linear growth of a hypersonic boundary layer instability. The work characterizes the shock-capturing numerical dissipation for slow and second mode growth as well as provides confidence in the numerical solver to study further development towards non-linear growth and eventual transition to turbulence.