Drag reduction strategies for the turbulent flow around a D-shaped body are examined experimentally and theoretically. A reduced-order vortex model describes the interaction between the shear layer and wake dynamics and guides a path to an efficient feedback control design. The derived feedback controller desynchronizes shear-layer and wake dynamics, thus postponing vortex formation. This actuation is tested in a wind tunnel. The Reynolds number based on the height of the body ranges from 23000 to 70000. We achieve a 40% increase in base pressure associated with a 15% drag reduction employing zero-net-mass-flux actuation. Our controller outperforms other approaches based on open-loop forcing and extremum-seeking feedback strategies in terms of drag reduction, adaptivity, and the required actuation energy.
Active control of separated flows has become an attractive approach enabling the designer to meet increased performance demands for various systems. Whereas a significant part of the work published so far in the area of closed-loop flow control is based on simulation studies, this paper presents an example of a successful application of a multivariable controller in wind tunnel experiments. A robust H 1 controller is used to control the spanwise variable reattachment length downstream of a benchmark problem, the backward-facing step. To reduce the conservatism of this approach, a nonlinear static precompensation is included, first. The synthesis of the controller is based on a family of identified linear black-box models, which describe the compensated input/output behavior of the plant. Tracking performance and disturbance rejection of the controller are tested in wind tunnel experiments and shown in this paper.actuation frequency f s = sampling frequency f shear = instability frequency of the shear layer Gs = model of the plant G N s = nominal model H = step height I = unit matrix i = index j = imaginary unit K S = static gain Ls = open-loop transfer function l M ! = minimum distance to all identified models N = cost functional p 0 rms = root-mean-square value of pressure fluctuations q act t = maximum velocity vector at the actuator slot Re H = Reynolds number based on step height, Re H Hu 1 = Re 2 = Reynolds number based on boundary layer momentum thickness, Re 2 2 u 1 = rt = reference variable vector Ss = sensitivity transfer function St H = Strouhal number based on step height, St H Hf a =u 1 St x Rm = Strouhal number based on reattachment length, St x Rm x Rm f a =u 1 St 2 = Strouhal number based on boundary layer momentum thickness, St 2 2 f a =u 1 s = Laplace variable Ts = complementary sensitivity transfer function t = time t rms = averaging time of rms values t 0 = time delay vector ut = manipulated variable or control input ux; y; z; t = flow velocity in streamwise direction u 1 = freestream velocity W = step width W CS s, W S s, W T s = weights for H 1 minimization w s = width of actuator slots x, y, z = streamwise, transverse, and spanwise coordinates, respectively x R t = reattachment length vector using rms method x Rm = time-averaged reattachment length vector x Rm 0 = time-averaged reattachment length vector for the unactuated flow yt = control variables or output vector M s = multiplicative uncertainty 2 = boundary layer momentum thickness 99 = boundary layer thickness = viscosity = kinematic viscosity min , max = minimal and maximal singular values W = wall-shear stress ! B= bandwidth ! C = crossover frequency
To speed up gradient estimation in a slope-seeking controller two different modifications are proposed in this study. In a first approach, the gradient estimation is based on a locally identified black-box model. A further improvement is obtained by applying an extended Kalman filter to estimate the local gradient of an input-output map. Moreover, a simple method is outlined to adapt the search radius in the classical extremum-and slopeseeking approach to reduce the perturbations near the optimal state. To show the versatility of the slope-seeking controller for flow control applications two different wind tunnel experiments are considered, namely with a two-dimensional bluff body and a generic threedimensional car model (Ahmed body).
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