J. Fluid Mech. (2008), vol. 606, pp. 369–397. c  2008 Cambridge University Press doi:10.1017/S0022112008001924 Printed in the United Kingdom 369 Simulation of flow around a row of square cylinders SHASHI RANJAN KUMAR, ATUL SHARMA AND AMIT AGRAWAL Department of Mechanical Engineering, Indian Institute of Technology – Bombay, Powai, Mumbai, 400076, India (Received 18 March 2007 and in revised form 19 March 2008) In this paper, the low-Reynolds number (Re =80) flow around a row of nine square cylinders placed normal to the oncoming flow is investigated using the lattice- Boltzmann method. The effects of the cylinder spacing on the flow are studied for spacing to diameter ratios of 0.3 to 12. No significant interaction between the wakes is observed with spacings greater than six times the diameter. At smaller spacings, the flow regimes as revealed by vorticity field and drag coefficient signal are: synchronized, quasi-periodic and chaotic. These regimes are shown to result from the interaction between primary (vortex shedding) and secondary (cylinder interaction) frequencies; the strength of the latter frequency in turn depends on the cylinder spacing. The secondary frequency is also related to transition between narrow and wide wakes behind a cylinder. The mean drag coefficient and Strouhal number are found to increase rapidly with a decrease in spacing; correlations of these parameters with spacing are proposed. The Strouhal number based on gap velocity becomes approximately constant for a large range of spacings, highlighting the significance of gap velocity for this class of flows. It is also possible to analyse the vortex pattern in the synchronized and quasi-periodic regimes with the help of vorticity dynamics. These results, most of which have been obtained for the first time, are of fundamental significance. 1. Introduction The flow downstream of a row of cylinders placed normal to the flow has many practical engineering applications. A row of cylinders is often used to screen strong and sudden winds in order to change them to weak and gentle ones (Mizushima & Takemoto 1996). Cascades of cylinders, with a narrow spacing between the cylinders, are often used in wind tunnels to obtain a uniform velocity distribution; but the velocity distribution is prevented from becoming uniform when cylinders are put too close to each other (Bradshaw 1965). The flow past a row of cylinders is of interest in situations such as turning vanes in duct elbows, multi-slotted airfoils, and flow around closely spaced electrical power poles (Cheng & Moretti 1988). The flow around multiple cylinders is a spatially developing flow problem, where several rich phenomena are observed. In this paper, we numerically study flow around a row of square cylinders placed side-by-side, at low Reynolds number. Square cylinders were chosen for the present study because they can be described on a Cartesian grid with a higher accuracy as compared to circular cylinders. The cylinders are assumed to be of equal size (d ) and the distance between two consecutive cylinders (s ) is the same. For a row of cylinders,