Spatial simulation of channel flow instability and control

Abstract

AbstractA direct numerical simulation is performed on the full time-dependent three-dimensional Navier–Stokes equations in a spatially developing plane-channel flow at a Reynolds number of 10 000. Two-dimensional eigenfunctions based on the solution of the Orr–Sommerfeld equation are introduced at the inflow with random noise added to simulate a vibrating ribbon transition experiment. The flow is allowed to choose a natural path to secondary instability, either K-type (after Klebanoff) or H-type (after Herbert), depending on the amplitude of the two-dimensional disturbance. For low-amplitude two-dimensional disturbances (1 % of the centreline velocity), H-type modes are found to dominate, while a doubling of the amplitude (2 % of the centreline velocity) produces a mixed H-type/K-type disturbance field with explosive growth of the secondary modes. In addition, the use of a suction/blowing slot that is phase lagged with respect to a fixed wall pressure signal is demonstrated to significantly reduce the energy in the primary mode owing to the destruction of phase between the streamwise and wall-normal velocity components. The use of forward finite-time Lyapunov exponents to generate Lagrangian coherent structures as a means of flow visualization is also presented, showing qualitative agreement with previous experimental visualizations, and represents a viable means of identifying characteristic vortical flow structures.