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Stabilization of two-dimensional Rayleigh-Bénard convection by means of optimal feedback control. (English) Zbl 1036.76015
Summary: We consider the problem of suppressing the Rayleigh-Bénard convection in a finite domain by adjusting the heat flux profile at the bottom of the system while keeping the heat input the same. The appropriate profile of heat flux at the bottom is determined by the optimal feedback control. When most of the convection modes are taken into consideration in the construction of the feedback controller, the suppressed state is found to be stable for all range of Rayleigh number investigated. With the feedback controller constructed by employing only the dominant convection modes, however, there exists a threshold Rayleigh number beyond which a new convective state emerges due to the hydrodynamic instability. The threshold Rayleigh number is found to increase with the number of modes taken in the feedback controller.

76E06Convection (hydrodynamic stability)
76D55Flow control and optimization
80A20Heat and mass transfer, heat flow
Full Text: DOI
[1] S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Oxford University Press, Oxford, 1969.
[2] P.G. Drazin, W.H. Reid, Hydrodynamic Stability, Cambridge University Press, Cambridge, 1981.
[3] Series, R. W.; Hurle, D. T.: The use of magnetic fields in semiconductor crystal growth. J. cryst. Growth 113, 305-328 (1991)
[4] B.D.O. Anderson, J.B. Moore, Optimal Control: Linear Quadratic Methods, Prentice-Hall, Englewood Cliffs, NJ, 1989.
[5] Tang, J.; Bau, H. H.: Feedback control stabilization of the no-motion state of a fluid confined in a horizontal, porous layer heated from below. J. fluid mech. 257, 485-505 (1993) · Zbl 0789.76033
[6] Tang, J.; Bau, H. H.: Stabilization of the no-motion state in Rayleigh--Bénard convection through the use of feedback control. Phys. rev. Lett. 70, 1795-1798 (1993)
[7] Bewley, T.; Temam, R.; Ziane, M.: A general framework for robust control in fluid mechanics. Physica D 138, 360-392 (2000) · Zbl 0981.76026
[8] L. Baramov, O. Tutty, E. Rogers, Robust control of plane Poiseuille flow, AIAA paper no. 2000-2684, AIAA, 2000.
[9] Joshi, S.; Speyer, J.; Kim, J.: Finite-dimensional optimal control of Poiseuille flow. J. guid. Contr. dyn. 22, 340-348 (1999)
[10] Ku, H. C.; Taylor, T. D.; Hirsh, R. S.: Pseudospectral methods for solution of the incompressible Navier--Stokes equation. Comput. fluids 15, 195-214 (1987) · Zbl 0622.76028
[11] Park, H. M.; Ryu, D. H.: A solution method of nonlinear convection stability problems in finite domains. J. comput. Phys. 170, 141-160 (2001) · Zbl 1046.76035
[12] D.G. Luenberger, Linear and Nonlinear Programming, 2nd ed., Addison-Wesley, Reading, MA, 1984. · Zbl 0571.90051