Bimodal control of three-dimensional wakes
Résumé
This paper investigates control strategies for drag reduction of three-dimensional wake generated by a circular cylinder at Reynolds number Re = 300, such flows presenting mode B instabilities whose main feature is streamwise finger-shaped eddies. The control is performed thanks to a field of tangential velocities on the cylinder. One first focuses on two-dimensional velocity fiels (spanwise invariant), using both a clustering genetic algorithm (see [7]) and Newton algorithm in Fourier space with five Fourier modes. Besically the same field comes out, whatever the control technique used. A square-root regression of the drag reduction versus amplitude of the control leads to the formulation of an efficiency criterion. One then considers a class of spanwise harmonic perturbation of this quasi-optimal profile, leading to a two paramater optimization problem, involving amplitude and wavelength of the perturbation. A cartography of the efficiency with respect to these two parameters is finally obtained, showing regions of interest. 1 Methodology One considers the full three-dimensional Navier-Stokes equations in their velocity-vorticity (u, ω) formulation and in the context of external flows : ∂ω ∂t + u · ∇ω − ω · ∇u − ν∆ω = 0 (1) with ∇ · u = 0 and ∇ × u = ω in the domain, and u = 0 on boundaries, ν being the kinematic viscosity and the velocity u satisfying far field condition lim |x|→∞ u(x) = U ∞ e x with e x being the streamwise basis vector. The numerical scheme used is an hybrid vortex in cell method, fully described in [5, 3], performing direct numerical simulation of equation (1). As a summary, a time splitting algorithm is used in order to split apart convective and diffusive effects. The diffusive part is solved using a large finite-difference stencil based on particle
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