Abstract
This paper presents the application of an interconnected systems approach to the flow transition control problem. The control system consists of a network of local controllers with dedicated actuators and sensors. The measured feedback signals used by the controllers are the local changes in wall shear force, and the generated control action is a local change in fluid wall normal velocities. The approach presented here does not require periodicity of the channel as was required by most earlier approaches. Thus, in contrast to previously proposed control schemes which operate in Fourier domain, this approach works in physical domain. Secondly it does not restrict the number of interacting units, thus allowing the application of MEMS arrays. In order to synthesize such controllers, first the dynamics of the fluid is converted into interconnected system form. The model is validated using a non-linear simulation environment developed in FLUENT, and by analysing the growth in the transient energy. The model is then used to synthesize an interconnected controller. The simulated closed-loop response shows that the controller can delay the transition by reducing the transient energy.
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References
el Hak, M.G.: Modern developments in flow control. Applied Mechanics Review 49, 365–379 (1996)
Chughtai, S., Werner, H.: Transition control of plane Poiseuille flow - a spatially interconnected model. In: Proc. of 47th IEEE Conference on Decision and Control, Cancun, Mexico (2008)
Baramov, L., Tutty, O., Rogers, E.: H  ∞  control of nonperiodic two-dimensional channel flow. IEEE Transactions on Control Systems Technology 12(1), 111–122 (2004)
Fasel, H.: Investigation of the stability of boundary layers by a finite-difference model of the Navier-Stokes equations. Journal of Fluid Mechanics 78, 355–383 (1976)
Daube, O.: Resolution of the 2D Navier-Stokes equations in velocity-vorticity forms by means of an influence matrix technique. Journal of Computational Physics 103, 402–414 (1992)
Butler, K., Farrell, B.: Three dimensional optimal disturbances in viscous shear flow. Physics of Fluids 4(8), 1637–1650 (1992)
Trefethen, L., Trefethen, A., Reddy, S., Driscoll, T.: Hydrodynamic stability without eigenvalues. Science 261(30), 578–584 (1993)
Bewley, T., Liu, S.: Optimal and robust control and estimation of linear paths to transition. Journal of Fluid Mechanics 365(12), 305–349 (1998)
McKernan, J., Whidborne, J., Papadakis, G.: Linear quadratic control of plane Poiseuille flow-transient behaviour. International Journal of Control 80(12), 1912–1930 (2007)
Jovanovic, M., Bamieh, B.: Componentwise energy amplification in channel flows. Journal of Fluid Mechanics 534, 145–183 (2005)
King, R., Aleksic, K., Gelbert, G., Losse, N., Muminovic, R., Brunn, A., Nitsche, W., Bothien, M., Moeck, J., Paschereit, C., Noack, B., Rist, U., Zeng, M.: Model predictive flow control. In: Proc. of 4th Flow Control Conference, Seattle, USA (2008)
Krstic, M., Smyshlyaev, A.: Boundary control of PDEs: A course on backstepping design. SIAM (2008)
el Hak, M.G., Tsai, H.: Transition and turbulence control. Lecture notes. World Scientific Publishing Co. Ltd. (2006)
King, R.: Active Flow Control. NNFM, vol. 95. Springer, Heidelberg (2007)
Peyret, R.: Spectral methods for incompressible viscous flow. Applied Mathematical Science. Springer, Berlin (2002)
Orszag, S.: Accurate solution of the Orr-Sommerfeld stability equation. Journal of Fluid Mechanics 50(4), 689–703 (1971)
Kim, J., Bewley, T.R.: A linear systems approach to flow control. Ann. Rev. Fluid Mech. (39), 39–383 (2007)
Sipp, D., Marquet, O., Meliga, P., Barbagallo, A.: Dynamics and control of global instabilities in open-flows: a linearized approach. Appl. Mech. Rev. 3(63), 30801 (2010)
Bagheri, S., Henningson, D.S.: Transition delay using control theory. Philos. Trans. R. Soc. (369), 1365–1381 (2011)
McKernan, J.: Control of plane Poiseuille flow: A theoretical and computational investigation. PhD thesis, Cranfield University, Dept. of Aerospace Siences, School of Engineering (2006)
Fluent, I.: FLUENT 6.3 User’s Guide. FLUENT Inc. (2006)
Boyd, J.: Chebyshev and Fourier Spectral Methods. Dover Publications Inc., New York (2001)
Schmid, P., Henningson, D.: Stability and transition in shear flows. Springer, New York (2001)
Trefethen, L.: Pseudospectra of linear operators. SIAM Review 39(3), 383–406 (1997)
Ali, M., Ali, A., Chughtai, S., Werner, H.: Consisitent identification of spatially interconnected systems. In: Proc. American Control Conference, San Francisco, CA, USA, pp. 3583–3588 (2011)
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Chughtai, S.S., Werner, H. (2015). An Interconnected Systems Approach to Flow Transition Control. In: King, R. (eds) Active Flow and Combustion Control 2014. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 127. Springer, Cham. https://doi.org/10.1007/978-3-319-11967-0_9
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DOI: https://doi.org/10.1007/978-3-319-11967-0_9
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-11966-3
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