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OPTIMAL DISTURBANCES OF FLOW ABOVE A FLAT PLATE WITH AN ELLIPTIC LEADING EDGE

Antonios Monokrousos
Linne Flow Centre, KTH Mechanics Osquars Backe 18, SE-100 44 Stockholm, Sweden

Luca Brandt
Linné Flow Centre, KTH Mechanics, Osquars backe 18, SE-100 44 Stockholm, Sweden

Catherine Mavriplis
Department of Mechanical Engineering, University of Ottawa, ON, Canada, K1N 6N5

Dan S. Henningson
Linne FLOW Centre and Swedish e-Science Research Centre (SeRC) KTH Mechanics, Royal Institute of Technology SE-100 44 Stockholm, Sweden

Аннотация

Adjoint-based iterative methods are employed in order to compute linear optimal disturbances in the case of a spatially growing boundary layer around an elliptic leading edge. The Lagrangian approach is used where an objective function is chosen and constraints are assigned. The optimization problem is solved using power iterations combined with a matrix-free formulation, where the state is marched forward in time with a standard DNS solver and backward with the adjoint solver until a chosen criterion is fulfilled. We consider the global and the upstream localized optimal initial condition leading to the largest possible energy amplification at time T. We find that the two-dimensional initial condition with the largest potential for growth is a Tollmien-Schichtinglike wave packet that includes the Orr mechanism and is located inside the boundary layer, downstream of the leading edge. The localized optimal initial condition method allows a more precise systematic study of leading edge effects; we propose it a new method to study receptivity. We find the two-dimensional disturbances are inefficient at triggering an unstable eigenmode. The three-dimensional disturbances exploit the lift up mechanism; both the global and upstream localized disturbances give significant growth. These findings support the hypothesis of high receptivity to three-dimensional disturbances.