“Tutorial on Feedback Control of Flows, Part II: Diagnostics and Feedback Control of Mixing”
Authors: Ole M. Aamo and Thor I. Fossen,Affiliation: NTNU, Department of Engineering Cybernetics
Reference: 2002, Vol 23, No 4, pp. 275-298.
Keywords: Flow control, feedback, mixing
Abstract: Control of fluid flows span a wide variety of specialities. In Part II of this tutorial, we focus on diagnostics of mixing and the problem of enhancing mixing by boundary feedback control. Diagnostic tools from dynamical systems theory are presented that enable detection and quantification of chaotic transport in periodically perturbed systems. However, real systems are generally not periodic, and available measurements or simulations are finite in time. A method for quantifying mixing in finite-time velocity fields is discussed, and applied to data obtained from simulations of the 2D controlled channel flow. Mixing has traditionally been brought on by open-loop control strategies, such as stirring, jet injection or mixing valves. Applications of active feedback to mixing problems are scarce in the literature, but the idea is currently drawing attention from various research groups. Feedback laws for the purpose of mixing enhancement in 2D and 3D pipe flow are presented, and simulations show that they induce strong mixing.
PDF (2847 Kb)
DOI: 10.4173/mic.2002.4.3References:
[1] AAMO, O.M., KRSTIC, M. BEWLEY, T.R. (2002). Control of Mixing by Boundary Feedback in 2D Channel Flow, Submitted.
[2] AAMO, O.M. (2002). Tutorial on Feedback Control of Flows, Part I: Stabilization of Fluid Flows in Channels and Pipes, Modelling, Identification and Control, 2.3.
[3] ANNASWAMY, A.M. GHONIEM A.F. (1995). Active Control in Combustion Systems, IEEE Control Systems, 1.6, 49-63 doi:10.1109/37.476386
[4] AREF, H. (1984). Stirring by chaotic advection, Journal of Fluid Mechanics, 143, 1-21 doi:10.1017/S0022112084001233
[5] AREF, H. TRYGGVASON, G. (1984). Vortex dynamics of passive and active interfaces, Physica, 12D, 59-70.
[6] BALOGH, A., AAMO, O.M. KRSTIC, M. (2002). Optimal Mixing Enhancement in 3D Pipe Flow, Submitted.
[7] BAMIEH, B., MEZIC, I. FARDAD, M. (2001). A framework for destabilization of dynamical systems and mixing enhancement, In Proceedings of the 49th IEEE Conference on Decision and Control, Orlando, Florida USA.
[8] CHIEN, W-L., RISING, H. OTTINO, J.M. (1986). Laminar mixing and chaotic mixing in several cavity flows, Journal of Fluid Mechanics, 170, 355-377 doi:10.1017/S0022112086000927
[9] D´ALESSANDRO, D., DAHLEH, M. MEZIC, I. (1998). Control of Fluid Mixing Using Entropy Methods, In Proceedings of the American Control Conference, Philadelphia, Pennsylvania.
[10] D´ALESSANDRO, D., DAHLEH, M. MEZIC, I. (1999). Control of Mixing in Fluid Flow: A Maximum Entropy Approach, IEEE Transactions on Automatic Control, 4.10, 1852-1863 doi:10.1109/9.793724
[11] FRANJIONE, J.G. OTTINO, J.M. (1987). Feasibility of numerical tracking of material lines and surfaces in chaotic flows, Phys. Fluids, 30, 3641-3 doi:10.1063/1.866449
[12] GHONIEM, A.F. NG, K.K. (1987). Numerical study of the dynamics of a forced shear layer, Phys. Fluids, 3.3, 706-721 doi:10.1063/1.866321
[13] GUCKENHEIMER, J. HOLMES, P (1983). Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag.
[14] HALLER, G. POJE, A.C. (1998). Finite time transport in aperiodic flows, Physica D, 119,352-380 doi:10.1016/S0167-2789(98)00091-8
[15] HALLER, G. (2000). Finding finite-time invariant manifolds in two-dimensional velocity fields, Chaos, 1.1 doi:10.1063/1.166479
[16] HALLER, G. YUAN, G. (2000). Lagrangian coherent structures and mixing in two-dimensional turbulence, Physica D, 147, 352-370 doi:10.1016/S0167-2789(00)00142-1
[17] HALLER, G. (2001). Distinguished material surfaces and coherent structures in three-dimensional fluid flows, Physica D, 149. 248-277 doi:10.1016/S0167-2789(00)00199-8
[18] KHAKHAR, D.V., RISING, H. OTTINO, J.M. (1986). Analysis of chaotic mixing in two model systems, Journal of Fluid Mechanics, 172, 419-451 doi:10.1017/S0022112086001805
[19] KRASNAPOLSKAYA, T.S., MELESHKO V.V., PETERS, G.W.M. MEIJER, H.E.H. (1999). Mixing in Stokes flow in an annular wedge cavity, Eur. J. Mech. B/Fluids, 18, 793-822 doi:10.1016/S0997-7546(99)00119-3
[20] LEONG, C.W. OTTINO, J.M. (1989). Experiments on mixing due to chaotic advection in a cavity, Journal of Fluid Mechanics, 209, 463-499 doi:10.1017/S0022112089003186
[21] MALHOTRA, N., MEZIC, I. WIGGINS, S. (1998). Patchiness: A new diagnostic for Lagrangian trajectory analysis in time-dependent fluid flows, International Journal of Bifurcation and Chaos, .6, 1053-1093 doi:10.1142/S0218127498000875
[22] MEZIC, C. (1994). On Geometrical and Statistical Properties of Dynamical Systems: Theory and Applications, Ph.D. thesis, California Institute of Technology.
[23] MEZIC, I. WIGGINS, S. (1999). A method for visualization of invariant sets of dynamical systems based on the ergodic partition, Chaos, .1, 213-218 doi:10.1063/1.166399
[24] MILLER, P.D., JONES, C.K.R.T., ROGERSON, A.M. PRATT, L.J. (1997). Quantifying transport in numerically generated velocity fields, Physica D, 110, 105-122 doi:10.1016/S0167-2789(97)00115-2
[25] NOACK, B.R., MEZIC, I. BANASZUK, A. (2000). Controlling vortex motion and chaotic advection, In Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia, 11-15 December, 2000.
[26] OTTINO, J.M. (1989). The Kinematics of Mixing: Stretching, Chaos, and Transport, Cambridge University Press.
[27] OTTINO, J.M. (1990). Mixing, chaotic advection, and turbulence, Annu. Rev. Fluid Mech. 22, 207-53 doi:10.1146/annurev.fl.22.010190.001231
[28] POJE, A.C., HALLER, G. MEZIC, I. (1999). The geometry and statistics of mixing in aperiodic flows, Physics of Fluids, 1.10 doi:10.1063/1.870155
[29] POJE, A.C. HALLER, G. (1999). Geometry of Cross-Stream Mixing in a Double-Gyre Ocean Model, Journal of Physical Oceanography, 29, 1469-1665.
[30] ROM-KEDAR, V., LEONARD, A. WIGGINS, S. (1990). An analytical study of transport, mixing and chaos in an unsteady vortical flow, Journal of Fluid Mechanics, 214, 347-394 doi:10.1017/S0022112090000167
[31] SWANSON, P.D. OTTINO, J.M. (1990). A comparative computational and experimental study of chaotic mixing of viscous fluids, Journal of Fluid Mechanics, 213, 227-249 doi:10.1017/S0022112090002300
[32] TEN, A.A., PODLADCHIKOV, Y.Y., YUEN, D.A., LARSEN, T.B. MALEVSKY, A.V. (1998). Comparison of Mixing Properties in Convection with the Particle-Line Method, Geophys. Res. Lett., 25, 3205-3208 doi:10.1029/98GL51991
[33] WIGGINS, S. (1990). Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer-Verlag.
[34] WIGGINS, S. (1990). Chaotic Transport in Dynamical Systems, Springer-Verlag.
BibTeX:
@article{MIC-2002-4-3,
title={{Tutorial on Feedback Control of Flows, Part II: Diagnostics and Feedback Control of Mixing}},
author={Aamo, Ole M. and Fossen, Thor I.},
journal={Modeling, Identification and Control},
volume={23},
number={4},
pages={275--298},
year={2002},
doi={10.4173/mic.2002.4.3},
publisher={Norwegian Society of Automatic Control}
};