Numerical investigation of suction in a transitional flat-plate boundary layer

Abstract

Direct Numerical Simulations (DMS) of the incompressible Navier-Stokes equations are used to investigate the effect of wall suction on transition in a flat-plate boundary layer. The Navier-Stokes equations are cast in vorticity-velocity formulation. The streamwise and wall-normal derivatives are discretized with compact differences, with a pseudospectral treatment of the spanwise derivatives. Two different methods are used for the time integration. In most calculations, an explicit four-stage Runge Kutta method is used. In some cases, a semi-implicit combination of a three-stage Runge-Kutta- and a Crank-Nicolson method is used. Several case studies are performed. The first case treats the effect of a single row of suction holes, aligned in the spanwise direction, on the evolution of a Tollmien-Schlichting wave. It is found that suction through small holes leads to noticeable nonlinear effects on disturbances with large spanwise wavenumbers. The effect of suction on secondary instability with regards to a large-amplitude Tollmien-Schlichting wave is investigated in the second case study. The suction configurations here are a permeable wall, spanwise slots, and streamwise slots. It is found that sufficiently strong suction suppresses the secondary instability. The different suction configurations are equally effective. The role of the Klebanoff-mode in boundary layer transition is the subject of the third case study. A numerical model of the Klebanoff-mode is presented that agrees well with experimental observations. It is shown how the interaction between the Klebanoff-mode and a Tollmien-Schlichting wave can cause transition. Wall suction is found to be an effective means to prevent transition and maintain laminar flow even in the presence of high-amplitude Klebanoff-mode fluctuations. In the last case study, the limit of very strong suction through holes is investigated. It is shown how the suction holes generate streamwise vortices that can become unstable and lead to bypass transition.