Force coefficients and Strouhal numbers of four cylinders in cross flow

This paper presents the measurements of force coefficients and Strouhal numbers (St) on four cylinders in a square configuration at subcritical Reynolds numbers (Re) using a piezo-electric load cell in a wind tunnel. Six spacing ratios (L/D) varying from 1.69 to 3.83 and 13 angles of incidence a ranging from 0degrees to 180degrees at a 15degrees interval covering all orientations were investigated. With the help of a laser-induced fluorescence visualization technique, it is found that the variation of forces and Strouhal numbers with L/D are governed by three distinct flow patterns. They are: (a) free oscillations of shear layers and vortex formation at large L/D; (b) reattachment of shear layer or shielding flow for intermediate L/D and (c) narrow gap flows for small L/D. Two major causes for large fluctuating forces are discussed in this paper and the force results are compared with other measurements. It is concluded that the flow patterns, i.e., the development and the interferences of the free shear layers and the distribution of the wake vortices of the cylinders play a key role in the variation of the forces and shedding frequencies. Consequently, the downstream cylinders are usually subjected to more serious fluctuating forces under the influence of unsteady wake vortices. Also, the upstream cylinders normally experience larger mean drags than the downstream ones. (C) 2003 Elsevier Ltd. All rights reserved.