zbMATH — the first resource for mathematics

Energy efficiency and performance limitations of linear adaptive control for transition delay. (English) Zbl 1383.76135
Summary: A reactive control technique with localised actuators and sensors is used to delay the transition to turbulence in a flat-plate boundary-layer flow. Through extensive direct numerical simulations, it is shown that an adaptive technique, which computes the control law on-line, is able to significantly reduce skin-friction drag in the presence of random three-dimensional perturbation fields with linear and weakly nonlinear behaviour. An energy budget analysis is performed in order to assess the net energy saving capabilities of the linear control approach. When considering a model of the dielectric-barrier-discharge (DBD) plasma actuator, the energy spent to create appropriate actuation force inside the boundary layer is of the same order as the energy gained from reducing skin-friction drag. With a model of an ideal actuator a net energy gain of three orders of magnitude can be achieved by efficiently damping small-amplitude disturbances upstream. The energy analysis in this study thus provides an upper limit for what we can expect in terms of drag-reduction efficiency for linear control of transition as a means for drag reduction.

76D55 Flow control and optimization for incompressible viscous fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
76F06 Transition to turbulence
76F70 Control of turbulent flows
Full Text: DOI
[1] Ardekani, I. T.; Abdulla, W., Theoretical convergence analysis of fxlms algorithm, Signal Process., 90, 12, 3046-3055, (2010) · Zbl 1197.94020
[2] Aström, K. J.; Wittenmark, B., Adaptive Control, (1995), Addison Wesley · Zbl 0217.57903
[3] Bagheri, S.; Brandt, L.; Henningson, D. S., Input – output analysis, model reduction and control of the flat-plate boundary layer, J. Fluid Mech., 620, 263-298, (2009) · Zbl 1156.76374
[4] Belson, B. A.; Semeraro, O.; Rowley, C. W.; Henningson, D. S., Feedback control of instabilities in the two-dimensional Blasius boundary layer: the role of sensors and actuators, Phys. Fluids, 25, (2013)
[5] Cattafesta, L. N.; Sheplak, M., Actuators for Active Flow Control, Annu. Rev. Fluid Mech., 43, 247-272, (2010) · Zbl 1299.76108
[6] Chevalier, M., Schlatter, P., Lundbladh, A. & Henningson, D. S.2007 A pseudo-spectral solver for incompressible boundary layer flows. Tech. Rep. TRITA-MEK 2007:07. KTH Mechanics, Stockholm, Sweden.
[7] Dadfar, R.; Fabbiane, N.; Bagheri, S.; Henningson, D. S., Centralised versus decentralised active control of boundary layer instabilities, Flow Turbul. Combust., 93, 4, 537-553, (2014)
[8] Dadfar, R.; Semeraro, O.; Hanifi, A.; Henningson, D. S., Output feedback control of blasius flow with leading edge using plasma actuator, AIAA J., 51, 9, 2192-2207, (2013)
[9] Fabbiane, N., Bagheri, S. & Henningson, D. S.2015aAdaptive control of finite-amplitude 3D disturbances in 2D boundary-layer flows. In International Symposium on Turbulence and Shear Flow Phenomena (TSFP-9): http://www.tsfp-conference.org/proceedings/proceedings-of-tsfp-9-2015-melbourne.html. · Zbl 1383.76135
[10] Fabbiane, N.; Semeraro, O.; Bagheri, S.; Henningson, D. S., Adaptive and model-based control theory applied to convectively unstable flows, Appl. Mech. Rev., 66, 6, (2014)
[11] Fabbiane, N.; Simon, B.; Fischer, F.; Grundmann, S.; Bagheri, S.; Henningson, D. S., On the role of adaptivity for robust laminar-flow control, J. Fluid Mech., 767, R1, (2015)
[12] Jeong, J.; Hussain, F., On the identification of a vortex, J. Fluid Mech., 285, 69-94, (1995) · Zbl 0847.76007
[13] Jolibois, J.; Moreau, E., Enhancement of the electromechanical performances of a single dielectric barrier discharge actuator, IEEE Trans. Dielec. Elec. Insul., 16, 3, 758-767, (2009)
[14] Juillet, F.; Mckeon, B. J.; Schmid, P. J., Experimental control of natural perturbations in channel flow, J. Fluid Mech., 752, 296-309, (2014)
[15] Kachanov, Y. S., Physical mechanisms of laminar-boundary-layer transition, Annu. Rev. Fluid Mech., 26, 1, 411-482, (1994)
[16] Kotsonis, M.; Shukla, R. K.; Pröbsting, S., Control of natural Tollmien-Schlichting waves using dielectric barrier discharge plasma actuators, Intl J. Flow Control, 7, 1-2, 37-54, (2015)
[17] Kriegseis, J.; Möller, B.; Grundmann, S.; Tropea, C., Capacitance and power consumption quantification of dielectric barrier discharge (DBD) plasma actuators, J. Electrostat., 69, 4, 302-312, (2011)
[18] Kriegseis, J.; Schwarz, C.; Tropea, C.; Grundmann, S., Velocity-information-based force-term estimation of dielectric-barrier discharge plasma actuators, J. Phys. D, 46, 5, (2013)
[19] Kurz, A.; Goldin, N.; King, R.; Tropea, C. D.; Grundmann, S., Hybrid transition control approach for plasma actuators, Exp. Fluids, 54, 11, 1-4, (2013)
[20] Li, Y.; Gaster, M., Active control of boundary-layer instabilities, J. Fluid Mech., 550, 185-205, (2006) · Zbl 1222.76044
[21] Nordström, J.; Nordin, N.; Henningson, D. S., The fringe region technique and the Fourier method used in the direct numerical simulation of spatially evolving viscous flows, SIAM J. Sci. Comput., 20, 4, 1365-1393, (1999) · Zbl 0930.35015
[22] Schlatter, P.; Li, Q.; Brethouwer, G.; Johansson, A. V.; Henningson, D. S., Simulations of spatially evolving turbulent boundary layers up to Re_𝜃 = 4300, Intl J. Heat Fluid Flow, 31, 3, 251-261, (2010)
[23] Schlatter, P.; Stolz, S.; Kleiser, L., LES of transitional flows using the approximate deconvolution model, Intl J. Heat Fluid Flow, 25, 3, 549-558, (2004)
[24] Schultz-Grunow, F., Neues Widerstandgesetz für glatte Flatten, Luftfahrtforsch, 17, 239, (1940) · JFM 66.1074.01
[25] Semeraro, O.; Bagheri, S.; Brandt, L.; Henningson, D. S., Transition delay in a boundary layer flow using active control, J. Fluid Mech., 731, 288-311, (2013) · Zbl 1294.76093
[26] Simon, B.; Nemitz, T.; Rohlfing, J.; Fischer, F.; Mayer, D.; Grundmann, S., Active flow control of laminar boundary layers for variable flow conditions, Intl J. Heat Fluid Flow, 56, 344-354, (2015)
[27] Snyder, S. D.; Hansen, C. H., The effect of transfer function estimation errors on the filtered-x LMS algorithm, IEEE Trans. Signal Process., 42, 4, 950-953, (1994)
[28] Stroh, A.; Frohnapfel, B.; Schlatter, P., A comparison of opposition control in turbulent boundary layer and turbulent channel flow, Phys. Fluids, 27, (2015)
[29] Sturzebecher, D.; Nitsche, W., Active cancellation of Tollmien-Schlichting instabilities on a wing using multi-channel sensor actuator systems, Intl J. Heat Fluid Flow, 24, 572-583, (2003)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.