Numerical investigation of three-dimensional active control of boundary-layer transition

A numerical model is developed for the investigation of boundary-layer transition control of spatially evolving instability waves. Active control of a periodically forced boundary layer in an incompressible fluid is simulated using surface heating techniques. The Navier-Stokes and energy equations are solved using a fully implicit finite-difference/spectral method. Temperature perturbations are introduced locally along finite heater strips to directly attenuate instability waves in the flow. A feedback control loop is employed in which a downstream sensor is used to monitor wall shear stress fluctuations. Active control of small-amplitude two-dimensional and three-dimensional disturbances is shown. Both wave reinforcement and wave attenuation are demonstrated. Active control of the early stages of the nonlinear fundamental breakdown process is also numerically investigated. The high three-dimensional growth rates that are characteristic of the secondary instability process are significantly reduced using either two-dimensional or three-dimensional control inputs to the heater strips. A receptivity study of the processes by which the localized temperature perturbations generate instability waves in the boundary layer is made. It is shown that the boundary layer is more receptive to narrow heater strips in that they maximize the amplitude level of the disturbances in the boundary layer.