Stability analysis and transition prediction of wall-bounded flows

Disturbances introduced in wall-bounded .ows can grow andlead to transition from laminar to turbulent .ow. In order toreduce losses or enhance mixing in energy systems, afundamental understanding of the .ow stability is important. Inlow disturbance environments, the typical path to transition isan exponential growth of modal waves. On the other hand, inlarge disturbance environments, such as in the presence of highlevels of free-stream turbulence or surface roughness,algebraic growth of non-modal streaks can lead to transition.In the present work, the stability of wall-bounded .ows isinvestigated by means of linear stability equations valid bothfor the exponential and algebraic growth scenario. Anadjoint-based optimization technique is used to optimize thealgebraic growth of streaks. The exponential growth of waves ismaximized in the sense that the envelope of the most ampli.edeigenmode is calculated. Two wall-bounded .ows areinvestigated, the Falkner\u96Skan boundary layer subject tofavorable, adverse and zero pressure gradients and the Blasiuswall jet. For the Falkner\u96Skan boundary layer, theoptimization is carried out over the initial streamwiselocation as well as the spanwise wave number and the angularfrequency. Furthermore, a uni.ed transition-prediction methodbased on available experimental data is suggested. The Blasiuswall jet is matched to the measured .ow in an experimentalwall-jet facility. Linear stability analysis with respect tothe growth of two-dimensional waves and streamwise streaks areperformed and compared to the experiments. The nonlinearinteraction of introduced waves and streaks and the .owstructures preceding the .ow breakdown are investigated bymeans of direct numerical simulations. Descriptors: Boundary layer, wall jet, algebraic growth,exponential growth, lift-up e.ect, streamwise streaks,Tollmien-Schlichting waves, free-stream turbulence, roughnesselement, transition prediction, Parabolized StabilityEquations, Direct Numerical Simulation.NR 2014080