Control of flow using genetic algorithm for a circular cylinder executing rotary oscillation Tapan K. Sengupta a, * , Kalyanmoy Deb b , Srikanth B. Talla a a CFD Laboratory, Department of Aerospace Engineering, Indian Institute of Technology Kanpur, Kanpur 208 016, India b Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur 208 016, India Received 19 July 2005; received in revised form 20 December 2005; accepted 7 March 2006 Available online 30 June 2006 Abstract 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 [Sengupta TK. Fundamentals of computational fluid dynamics. Hyderabad, India: University Press; 2004] 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 equa- tion subject to discrete changes of decision variables. The objective function – the time-averaged drag – is optimized using a real-coded genetic algorithm [Deb K. Multi-objective optimization using evolutionary algorithms. Chichester, UK: Wiley; 2001] for the two decision variables, the maximum rotation rate and the forcing frequency of the rotary oscillation. Various approaches to optimal decision vari- ables have been explored for the purpose of drag reduction and the collection of results are self-consistent and furthermore match well with the experimental values reported in [Tokumaru PT, Dimotakis PE. Rotary oscillation control of a cylinder wake. J Fluid Mech 1991;224:77]. Ó 2006 Elsevier Ltd. All rights reserved. 1. Introduction The problem of bluff-body flow control is of significant interest to research community due to its importance in many practical application areas. It is also of considerable theoretical interest to flow control and optimization. Flow past a circular cylinder is a canonical problem often used to understand the bluff-body flows. Modifications of the wake of cylinders by means of mechanical oscillatory excitations that alters vortex shedding pattern have been studied and reported in literature. However, study of flow over oscillat- ing circular cylinder has mainly focused on in-line or trans- verse linear oscillations as reviewed by [4–6] and in [7].A large number of studies also exist for flow past steadily rotating circular cylinders – as reported in [8–11] and other references contained therein. For high steady rotation rates and Reynolds numbers, vortex shedding was shown to have been suppressed in [12]. While steady state rotation can effectively reduce drag and unsteadiness for flow past a circular cylinder, it does not work for all geometries. It is in this context, rotary oscillation becomes important – as it can alter vortex shedding beneficially for bodies with 0045-7930/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.compfluid.2006.03.002 * Corresponding author. Tel.: +91 512 259 7945; fax: +91 512 259 7561. E-mail addresses: tksen@iitk.ac.in (T.K. Sengupta), deb@iitk.ac.in (K. Deb), tsbabu@iitk.ac.in (S.B. Talla). www.elsevier.com/locate/compfluid Computers & Fluids 36 (2007) 578–600