Investigations of laminar-turbulent transition on a sharp cone with localized heating or cooling in high-speed flow

Abstract

A localized heating or cooling effect on stability and transition of the boundary layer flow on a sharp cone at zero angle of attack at the free-stream Mach number 6 is analyzed using the linear stability theory. Three different locations of the heating/cooling strip are considered. The steady-state laminar flow solution is calculated using the axisymmetric Navier-Stokes equations to provide the mean flow field. The spatial stability analysis is performed for two-dimensional disturbances associated with the Mack first and second modes. The transition onset points are estimated using the e N method. In this framework, the heating/cooling effect on the transition onset is inconclusive. The heater (or cooler) may cause earlier or later transition depending on the choice of critical N-factor. Direct numerical simulations and experiments are needed to clarify this situation. Nomenclature M = Mach number Re = Reynolds number p = pressure T = temperature , u v = longitudinal and vertical velocity components Superscripts * = dimensional Subscripts ∞ = free stream w = wall surface e = upper edge of the boundary layer

Effect of the local wall cooling/heating on the hypersonic boundary layer stability and transition

“…Investigation of physical mechanisms associated with the foregoing thermal e¨ects will help to design advanced TPS providing capabilities of transition control. The only work devoted to the in §uence of localized heating/cooling on hypersonic boundary layer stability is computational data [13].…”