Receptivity of crossflow-dominated boundary layers

Abstract: This thesis deals with receptivity mechanisms of three-dimensional, crossflow-dominated boundary layers. The receptivity of two model problems, a swept-flat-plate and a swept-wing boundary layer, is investigated by solving the parabolised stability equations (PSE) as well as by performing direct numerical simulations (DNS).Both flow cases are known to exhibit strong inflectional instabilities, the crossflow disturbances, whose excitation by external disturbances such as surface roughness or free-stream vorticity is studied. One focus is on worst-case scenarios. This involves the determination of optimal conditions, i.e. those disturbance environments yielding the largest possible response inside the boundary layer. A new method on the basis of the PSE is presented which allows to study optimal disturbances of swept-flat-plate boundary layers. These take the form of tilted streamwise vortices. While convected downstream they develop into streamwise streaks experiencing strong non-modal growth. Eventually, they turn into crossflow disturbances and undergo exponential growth. Non-modal growth is thus found to optimally excite crossflow disturbances and can be related to a receptivity mechanism of three-dimensional boundary layers. Evaluating effects of compressibility reveals that the potential for both non-modal and modal growth increases for higher Mach numbers. It is shown that wall cooling has diverse effects on disturbances of non-modal and modal nature. While destabilising the former it attenuates the growth of modal disturbances. Concave curvature on the other hand is found to be equally destabilising for both types of disturbances. The adjoint of the linearised Navier-Stokes equations is solved for a swept-wing boundary layer by means of DNS. The adjoint solution of a steady crossflow disturbance is computed in the boundary layer as well as in the free-stream upstream of the leading edge. This allows to determine receptivity to incoming free-stream disturbances and surface roughness as well as the corresponding worst-case scenarios. Upstream of a swept wing the optimal initial free-stream disturbance is found to be of streak-type which convects downstream towards the leading edge. It entrains the boundary layer a short distance downstream of the stagnation line. While minor streamwise vorticity is present the streak component is dominant all the way into the boundary layer where the optimal disturbance turns into a crossflow mode. Futher, the worst-case surface roughness is determined. It takes a wavy shape and is distributed in the chordwise direction. It is shown that, under such optimal conditions, the swept-wing boundary layer is more receptive to surface roughness than to free-stream disturbances. Another focus of this work has been the development and evaluation of tools for receptivity prediction. Both DNS and direct and adjoint solutions of the PSE are used to predict the receptivity of a swept-wing boundary layer to localised surface roughness. The configuration conforms to wind tunnel experiments performed by Saric and coworkers at the Arizona State University. Both the DNS and the PSE are found to predict receptivity amplitudes which are in excellent agreement with each other. Though the predicted disturbance amplitudes are slightly lower than experimental measurements the overall agreement with experimental results is very satisfactory. Finally, a DNS of the stabilisation of a transitional swept-wing boundary layer by means of discrete roughness elements is presented. This control approach is found to completely suppress transition to turbulence within the domain studied and confirms experimental results by Saric & coworkers.