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Intern rapport

Optimal disturbances in suction boundary layers

Författare Dokumenttyp År Nerladdning Filstorlek
Martin Byström, Ori Levin, Dan Henningson Examensarbetesrapport 2005 Inte tillgänglig
Id
ISSN 0348-467X
ISRN KTH/MEK/TR--05/02--SE

Abstract

The transition point is an important parameter in all applications where the minimization of friction drag is an objective, such as wing design. One method to delay transition from laminar to turbulent flow is to apply suction at the wall. In the present work the algebraic growth in the asymptotic suction boundary layer and the semi suction boundary layer is studied. In the semi suction boundary layer the suction is only applied over the downstream part of the interval, allowing a Blasius profile to develop from the leading edge to the point where the suction starts. The suction rate is set to 0.29% of the free-stream velocity. An adjoint-based optimization procedure is used to find the optimal disturbance, i.e. the initial disturbance that maximizes the energy growth over the streamwise interval. Furthermore, the spanwise wave number and angular frequency of the disturbance as well as the streamwise interval length are optimized. It is found that the optimal disturbance consists of streamwise vortices that develop into streamwise streaks. Furthermore, it is found that the optimal growth and spanwise wave number decrease when the streamwise interval is prolonged, the optimal angular frequency is however zero for all intervals. A comparison shows that the semi suction boundary layer gives significantly higher growth than the asymptotic suction boundary layer in short intervals, but for long intervals the growth is the same. Furthermore a comparison with experimental results is carried out. It is shown that the optimal spanwise wave number of the semi suction boundary layer lies close to the experimentally observed values, closer than the optimal wave number of the asymptotic suction boundary layer.