Control of flow using genetic algorithm for a circular cylinder executing rotary oscillation. (English) Zbl 1177.76114

Summary: We propose here a new approach to optimally control incompressible viscous flow past a circular cylinder for drag minimization by rotary oscillation. The flow at \(Re = 15000\) is simulated by solving 2D Navier-Stokes equations in stream function-vorticity formulation. High accuracy compact scheme for space discretization and four stage Runge-Kutta scheme for time integration makes such simulation possible. While numerical solution for this flow field has been reported using a fast viscous-vortex method, to our knowledge, this has not been done at such a high Reynolds number by computing the Navier-Stokes equation before. The importance of scale resolution, aliasing problem and preservation of physical dispersion relation for such vortical flows of the used high accuracy schemes is highlighted.
For the dynamic problem, a novel genetic algorithm (GA) based optimization technique has been adopted, where solutions of Navier-Stokes equations are obtained using small time-horizons at every step of the optimization process, called a GA generation. Then the objective functions is evaluated that is followed by GA determined improvement of the decision variables. This procedure of time advancement can also be adopted to control such flows experimentally, as one obtains time-accurate solution of the Navier-Stokes equation subject to discrete changes of decision variables. The objective function - the time-averaged drag - is optimized using a real-coded genetic algorithm for the two decision variables, the maximum rotation rate and the forcing frequency of the rotary oscillation. Various approaches to optimal decision variables have been explored for the purpose of drag reduction and the collection of results are self-consistent and furthermore match well with experimental values.


76D55 Flow control and optimization for incompressible viscous fluids
92D99 Genetics and population dynamics
Full Text: DOI


[1] Sengupta, T.K., Fundamentals of computational fluid dynamics, (2004), University Press Hyderabad, India
[2] Deb, K., Multi-objective optimization using evolutionary algorithms, (2001), Wiley Chichester, UK · Zbl 0970.90091
[3] Tokumaru, P.T.; Dimotakis, P.E., Rotary oscillation control of a cylinder wake, J fluid mech, 224, 77, (1991)
[4] Berger, E.; Willie, R., Periodic flow phenomenon, Ann rev fluid mech, 4, 313, (1972)
[5] Bearman, P.W., Vortex shedding from oscillating bluff bodies, Ann rev fluid mech, 16, 195, (1984) · Zbl 0605.76045
[6] Griffin, O.M.; Hall, M., Vortex shedding lock-on and flow control in bluff body wakes, Trans ASME J fluids engng, 113, 526, (1991)
[7] Sümer, B.M.; Fredsøe, J., Hydrodynamics around cylindrical structures, (1997), World Scientific Singapore · Zbl 0964.76001
[8] Badr, H.M.; Coutanceau, M.; Dennis, S.C.R.; Menard, C., Unsteady flow past a rotating circular cylinder at Reynolds numbers 10^{3} and 104, J fluid mech, 220, 459, (1990)
[9] Chang, C.-C.; Chern, R.-L., Vortex shedding from an impulsively started rotating and translating circular cylinder, J fluid mech, 233, 265, (1991) · Zbl 0739.76049
[10] Chen, Y.-M.; Ou, Y.-R.; Pearlstein, A., Development of the wake behind a circular cylinder impulsively started into rotatory and rectilinear motion, J fluid mech, 253, 449, (1993) · Zbl 0809.76024
[11] Nair, M.T.; Sengupta, T.K.; Chauhan, U.S., Flow past rotating cylinders at high Reynolds numbers using higher order upwind scheme, Comput fluids, 27, 47, (1998) · Zbl 0906.76052
[12] Diaz, F.; Gavalda, J.; Kawall, J.; Keffer, J.; Giralt, F., Vortex shedding from a spinning cylinder, Phys fluids, 26, 3454, (1983)
[13] Taneda, S., Visual observations of the flow past a circular cylinder performing a rotatory oscillation, J phys soc jpn, 45, 1038, (1978)
[14] Okajima A, Takata H, Asanuma T. Viscous flow around a rotationally oscillating cylinder. Tech Rep Rept 532, Inst Space and Aero Sci (U. Tokyo), 1981.
[15] Wu, J.; Mo, J.; Vakili, A., On the wake of a cylinder with rotational oscillations, AIAA paper, 89, 1024, (1989)
[16] Filler, J.R.; Marston, P.L.; Mih, W., Response of the shear layers separating from a circular cylinder to small-amplitude rotational oscillations, J fluid mech, 231, 481, (1991)
[17] Lu, X.-Y.; Sato, J., A numerical study of flow past a rotationally oscillating circular cylinder, J fluids struct, 10, 829, (1996)
[18] Baek, S.-J.; Sung, H., Numerical simulations of the flow behind a rotary oscillating circular cylinder, Phys fluids, 10, 869, (1998)
[19] Dennis, S.C.R.; Nguyen, P.; Kocabiyik, S., The flow induced by a rotationally oscillating and translating circular cylinder, J fluid mech, 407, 123, (2000) · Zbl 0969.76095
[20] Choi, S.; Choi, H.; Kang, S., Characteristics of flow over a rotationally oscillating cylinder at low Reynolds number, Phys fluids, 14, 8, 2767, (2002) · Zbl 1185.76086
[21] Cheng, M.; Chew, Y.; Luo, S., Numerical investigation of a rotationally oscillating cylinder in Mean flow, J fluids struct, 15, 981, (2001)
[22] Shiels, D.; Leonard, A., Investigation of a drag reduction on a circular cylinder in rotary oscillation, J fluid mech, 431, 297, (2001) · Zbl 1017.76024
[23] Sengupta, T.K.; Ganeriwal, G.; De, S., Analysis of central and upwind compact schemes, J comput phys, 192, 677, (2003) · Zbl 1038.65082
[24] Sengupta, T.K.; Guntaka, A.; De, S., Incompressible navier – stokes solution by new compact schemes, J sci comput, 21, 3, 269, (2004) · Zbl 1071.76041
[25] Sengupta, T.K.; Dipankar, A., A comparative study of time advancement methods for solving navier – stokes equations, J sci comput, 21, 2, 225, (2004) · Zbl 1060.76084
[26] Williamson, C.H.K., The existence of two stages in the transition to three-dimensionality of a cylinder wake, Phys fluids, 31, 3165-3168, (1988)
[27] Sengupta, T.K.; De, S.; Sarkar, S., Vortex-induced instability of incompressible wall-bounded shear layer, J fluid mech, 493, 277, (2003) · Zbl 1068.76023
[28] Braza, M.; Chassaing, P.; Haminh, H., Numerical study and analysis of the pressure and velocity fields in the near wake of a cylinder, J fluid mech, 165, 79-130, (1986) · Zbl 0596.76047
[29] Kawamura, T.; Takami, H.; Kuwahara, K., A new higher order upwind scheme for incompressible navier – stokes equation, Fluid dynam res, 1, 145-162, (1985)
[30] Sengupta, T.K.; Sengupta, R., Flow past an impulsively started circular cylinder at high Reynolds number, Comput mech, 14, 298-310, (1994) · Zbl 0800.76280
[31] He, J.-W.; Glowinski, R.; Metcalfe, R.; Nordlander, A.; Periaux, J., Active control and drag optimization for flow past a circular cylinder, J comput phys, 163, 83, (2000) · Zbl 0977.76021
[32] Protas, B.; Styczek, A., Optimal rotary control of the cylinder wake in the laminar regime, Phys fluids, 14, 7, 2073, (2002) · Zbl 1185.76304
[33] Milano, M.; Koumoutsakos, P., A clustering genetic algorithm for cylinder drag optimization, J comput phys, 175, 79, (2002) · Zbl 1168.74470
[34] Mittal, R.; Balachander, S., Effect of three-dimensionality on the lift and drag of nominally two-dimensional cylinders, Phys fluids, 7, 8, 1841, (1995) · Zbl 1032.76530
[35] Morrison, R.W., Designing evolutionary algorithms for dynamic environment, (2004), Springer-Verlag Berlin-Heidelberg · Zbl 1070.68130
[36] Branke J. Evolutionary approaches to dynamic optimization problems – updated survey. In: GECCO workshop on evolutionary algorithms for dynamic optimization problems, 2001. p. 27.
[37] Ursem, R.K.; Filipic, B.; Krink, T., Exploring the performance of an evolutionary algorithm for greenhouse control, J comput inform technol, 10, 3, 195, (2002)
[38] Orlanski, I., A simple boundary condition for unbounded hyperbolic flows, J comput phys, 21, 251, (1976) · Zbl 0403.76040
[39] Esposito, P.G.; Verzicco, R.; Orlandi, P., Boundary condition influence on the flow around a circular cylinder, ()
[40] der Vorst, H.A.V., Bi-CGSTAB: A fast and smoothly converging variant of bi-CG for the solution of non-symmetric linear systems, SIAM J sci stat comput, 12, 631, (1992) · Zbl 0761.65023
[41] Saad, Y., Iterative methods for sparse linear systems, (2003), SIAM USA · Zbl 1002.65042
[42] Haras, Z.; Ta’asan, S., Finite difference scheme for long time integration, J comput phys, 114, 265, (1994) · Zbl 0808.65083
[43] Deb, K.; Agrawal, R.B., Simulated binary crossover for continuous search space, Complex syst, 9, 2, 115-148, (1995) · Zbl 0843.68023
[44] Deb K, Beyer H-G. Self-adaptation in real-parameter genetic algorithms with simulated binary crossover. In: Proceedings of the genetic and evolutionary computation conference (GECCO-99), 1999. p. 172-9.
[45] Goldberg, D.E., Genetic algorithms for search, optimization, and machine learning, (1989), Addison-Wesley Reading, MA · Zbl 0721.68056
[46] Vose, M.D., Simple genetic algorithm: foundation and theory, (1999), MIT Press Ann Arbor, MI · Zbl 0952.65048
[47] Beyer, H.-G., The theory of evolution strategies, (2001), Springer Berlin, Germany · Zbl 1001.68186
[48] Goldberg, D.E.; Deb, K.; Clark, J.H., Genetic algorithms, noise, and the sizing of populations, Complex syst, 6, 4, 333-362, (1992) · Zbl 0800.68600
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.