Numerical simulation of laminar-turbulent transition in a supersonic boundary layer under the action of acoustic disturbances

In low disturbance environment, laminar-turbulent transition (LTT) is associated with excitation of unstable normal modes of small initial amplitudes (receptivity problem). These modes grow exponentially to a critical amplitude in accord with the linear stability theory (LST) and trigger the nonlinear breakdown. In the current study numerical simulation of laminar-turbulent transition (LTT) in the boundary layer on the upper surface of a flat plate in a supersonic free stream of Mach number M∞=3 and Reynolds number Re∞=2 × 107 is carried out. The flow is perturbed by fast or slow acoustic waves of low intensity, which excite unstable waves of the first mode. The latter have frequencies corresponding to the integral amplification N ≈ 9.16 typical for flight conditions. Two cases are considered: the angle of attack AoA=0° at which acoustic waves pass through a weak shock induced by viscous-inviscid interaction; AoA=5° at which acoustic waves pass through the expansion fan emanating from the plate leading edge. A holistic modeling of all stages of the transition from receptivity to the birth of turbulent spots is performed using direct numerical simulations. Linear stability theory is used to interpret the results. Feasibility of practical implementation of the amplitude method for predictions of the LTT onset in the considered and similar cases is discussed. It has been shown that to realize the amplitude method in the considered and similar cases, it is sufficient: to calculate the initial amplitudes of instability in a small vicinity of the leading edge and the propagation of instability from the leading edge to the station where the instability reaches the critical amplitude u′max≈4%. Analysis of known numerical and experimental data showed that this criterion weakly depends on the local Mach number in the range 0