Boundary layer calculations are performed around an airfoil and its wake. Smith-van Ingen transition prediction method is employed to find the transition from laminar to turbulent flow. First, potential flow around the airfoil is solved with the Hess-Smith panel method. The resulting velocity distribution is input to the boundary layer equations in order to find a so called blowing velocity distribution. The output of the boundary layer equations are also used to compute the location of onset of transition using the Smith-van Ingen en transition prediction method. The obtained blowing velocity distribution is fed back to the panel method to find a velocity distribution which includes the effects of viscosity. The procedure described is repeated until convergence is observed. A computer program is developed using the theory. Results obtained are in good accord with measurements

Disturbances introduced in wall-bounded flows can grow and lead to transition from laminar to turbulent flow. In order to reduce losses or enhance mixing in energy systems, a fundamental understanding of the flow stability and transition mechanism is important. In the present thesis, the stability, transition mechanism and early turbulent evolution of wall-bounded flows are studied. The stability is investigated by means of linear stability equations and the transition mechanism and turbulence are studied using direct numerical simulations. Three base flows are considered, the Falkner-Skan boundary layer, boundary layers subjected to wall suction and the Blasius wall jet. The stability with respect to the exponential growth of waves and the algebraic growth of optimal streaks is studied for the Falkner-Skan boundary layer. For the algebraic growth, the optimal initial location, where the optimal disturbance is introduced in the boundary layer, is found to move downstream with decreased pressure gradient. A unified transition prediction method incorporating the influences of pressure gradient and free-stream turbulence is suggested. The algebraic growth of streaks in boundary layers subjected to wall suction is calculated. It is found that the spatial analysis gives larger optimal growth than temporal theory. Furthermore, it is found that the optimal growth is larger if the suction begins a distance downstream of the leading edge. Thresholds for transition of periodic and localized disturbances as well as the spreading of turbulent spots in the asymptotic suction boundary layer are investigated for Reynolds number Re=500, 800 and 1200 based on the displacement thickness and the free-stream velocity. It is found that the threshold amplitude scales like Re^-1.05 for transition initiated by streamwise vortices and random noise, like Re^-1.3 for oblique transition and like Re^-1.5 for the localized disturbance. The turbulent spot is found to take a bullet-shaped form that becomes more distinct and increases its spreading rate for higher Reynolds number. The Blasius wall jet is matched to the measured flow in an experimental wall-jet facility. Both the linear and nonlinear regime of introduced waves and streaks are investigated and compared to measurements. It is demonstrated that the streaks play an important role in the breakdown process where they suppress pairing and enhance breakdown to turbulence. Furthermore, statistics from the early turbulent regime are analyzed and reveal a reasonable self-similar behavior, which is most pronounced with inner scaling in the near-wall region. / QC 20101025

<p>Disturbances introduced in wall-bounded flows can grow and lead to transition from laminar to turbulent flow. In order to reduce losses or enhance mixing in energy systems, a fundamental understanding of the flow stability and transition mechanism is important. In the present thesis, the stability, transition mechanism and early turbulent evolution of wall-bounded flows are studied. The stability is investigated by means of linear stability equations and the transition mechanism and turbulence are studied using direct numerical simulations. Three base flows are considered, the Falkner-Skan boundary layer, boundary layers subjected to wall suction and the Blasius wall jet. The stability with respect to the exponential growth of waves and the algebraic growth of optimal streaks is studied for the Falkner-Skan boundary layer. For the algebraic growth, the optimal initial location, where the optimal disturbance is introduced in the boundary layer, is found to move downstream with decreased pressure gradient. A unified transition prediction method incorporating the influences of pressure gradient and free-stream turbulence is suggested. The algebraic growth of streaks in boundary layers subjected to wall suction is calculated. It is found that the spatial analysis gives larger optimal growth than temporal theory. Furthermore, it is found that the optimal growth is larger if the suction begins a distance downstream of the leading edge. Thresholds for transition of periodic and localized disturbances as well as the spreading of turbulent spots in the asymptotic suction boundary layer are investigated for Reynolds number Re=500, 800 and 1200 based on the displacement thickness and the free-stream velocity. It is found that the threshold amplitude scales like Re^-1.05 for transition initiated by streamwise vortices and random noise, like Re^-1.3 for oblique transition and like Re^-1.5 for the localized disturbance. The turbulent spot is found to take a bullet-shaped form that becomes more distinct and increases its spreading rate for higher Reynolds number. The Blasius wall jet is matched to the measured flow in an experimental wall-jet facility. Both the linear and nonlinear regime of introduced waves and streaks are investigated and compared to measurements. It is demonstrated that the streaks play an important role in the breakdown process where they suppress pairing and enhance breakdown to turbulence. Furthermore, statistics from the early turbulent regime are analyzed and reveal a reasonable self-similar behavior, which is most pronounced with inner scaling in the near-wall region.</p>

Cette thèse propose la reformulation et l'implantation d'une méthode simplifiée de prévision de la transition laminaire-turbulent naturelle, la méthode des paraboles. Elle s'appuie sur une base de donnée pour fournir une expression analytique des taux d'amplification de perturbations modales de la couche limite. Ces perturbations prennent naissance dans la couche limite à travers un mécanisme de réceptivité, puis connaissent une croissance linéaire suivie d'interactions non-linéaires qui conduisent à la transition vers la turbulence.La méthode du facteur-N permet la prévision de la position de transition en supposant qu'elle a lieu quand l'amplification linéaire totale d'un mode des perturbations a atteint une amplitude critique.L'amplification totale est obtenue en intégrant les taux d'amplifications des perturbations le long de la ligne de courant extérieure à la couche limite.Cette formulation intégrale n'est pas adaptée aux codes RANS et ces travaux proposent une reformulation de la méthode du facteur-N sous forme d'équation de transport, dont le terme source dépend du taux d'amplification des perturbations donné par la méthode des paraboles.Le modèle qui en résulte (N-sigma-P ou NSP) permet de déterminer si un point donné est en amont ou en aval du point de transition et ainsi de prévoir la position de transition, pour des configurations où la transition est déclenchée par des modes longitudinaux (ondes de Tollmien-Schlichting) ou transverses (crossflow). / A simplified laminar-turbulent transition prediction method (the so-called parabolas method) is recast into a RANS compatible formulation.The parabolas method is a database approach that gives an estimation of the growth rates of modal perturbations growing in the boundary layer.These perturbations rise through a process called receptivity and undergo a linear modal growth, followed by non-linear interactions that lead to a breakdown to transition. The N-factor (or e-to-N) method predicts the transition location under the assumption that transition occurs when the total linear growth of a mode reaches a prescribed threshold. This total growth is obtained via an integration of a mode's growth rate along the boundary-layer edge streamline. This classical integral formulation is not suitable in a RANS context and is therefore recast into a set of transport equations whose source terms depend on the growth rates given by the parabolas method.The resulting model (N-sigma-P or NSP) predicts if a given point in the flow field is up- or downstream of the transition location. It has been validated for cases where transition was triggered by longitudinal (Tollmien-Schlichting) and crossflow modes.

<p>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–Skan boundary layer subject tofavorable, adverse and zero pressure gradients and the Blasiuswall jet. For the Falkner–Skan 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.</p><p>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.</p>

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–Skan boundary layer subject tofavorable, adverse and zero pressure gradients and the Blasiuswall jet. For the Falkner–Skan 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 20140805