Numerical simulation of the control of wave packet disturbances in the boundary layer on a flat plate.

Abstract

The control of the transition from laminar to turbulent flow in a boundary layer of a flat plate is investigated using numerical simulations. The numerical model is based on the incompressible Navier-Stokes equations, which is coupled with the energy equation through the temperature dependent viscosity. A fully implicit finite difference spectral method was used to solve the governing equations. The numerical model allows for the spatial evolution of the disturbances in a non-parallel boundary layer. Active control of wave packet disturbances in the non-isothermal boundary layer is studied in detail. Wave packet disturbances are created in the flow field by simulating the effect of thermally activated heater elements on the plate surface. Through a controlled spanwise variation of the temperature of the heater elements, two- and three-dimensional wave packet disturbances can be studied. The propagation and amplification of the wave packet disturbances in the boundary layer is examined. The heater elements on the plate surface act as locally strong heat sources causing thermal wakes within the boundary layer that spread in the downstream direction. A transfer function technique is used for the control strategy. The transfer function is based on the vorticity response to a finite temperature fluctuation at the heater strip and is obtained from the numerical simulations. With additional heater segments (controller) located downstream of an excitation source, the possibility of attenuating wave packet disturbances is investigated. With the numerical transfer function, a successful control strategy for the wave packet cancellation could be developed. Initially, for the low amplitude, two-dimensional disturbances in the transition process with the implemented control strategy the wave packet disturbances could be almost completely cancelled. For the attentuation of three-dimensional wave packet disturbances, the transfer function technique was extended to allow for spanwise variations. The attenuation of three-dimensional wave packets with the modified transfer function technique was almost equally as successful as for the purely two-dimensional flow disturbances. For the simulation of the three-dimensional flow development with no control applied, nonlinear interaction of wave components of the wave packet first appeared for the oblique modes in the low frequency range, which was also observed in experimental investigations. The attenuation of only the two-dimensional components of a three-dimensional wave packet disturbance delays the onset of the nonlinear interaction of the oblique spanwise modes in the lower frequency range.