Flat-Plate Interaction with the Near Wake of a Square Cylinder

Abstract

B LUFF bodies are integral components of aircraft, high-speed trains, automobiles, and many forms of industrial equipment. The minimization of mean and fluctuating force levels generated by bluff bodieswhen placed in afluid streamhas the benefits of reducing drag, vibration, and radiated sound. It is therefore very important that a good understanding of the flowfield about bluff bodies be obtained to achieve these aims. This Note explores how lowReynolds number bluff-body wake interference can affect the generation of unsteady flowand force. The case chosen for study is the interaction of a square cylinder and an infinitely thin flat plate. A rigid square cylinder is one of the most basic forms of a bluff body and when placed in a uniform fluid stream has been shown to exhibit strong vortex shedding, resulting in fluctuating forces and the radiation of sound in the form of an aeolian tone. Previous fluid dynamic experimental studies [1,2] exhibit this strong vortex shedding over a wide range of Reynolds number (10–10). Numerical studies investigating the fluid dynamics [3–6] also confirm this behavior. Despite the wealth of experimental data available for circular cylinders, experimental or numerical data for square cylinders are rare. Available studies include the work of Inoue [7], who performs a numerical simulation of compressible flow about a square cylinder at Re 150. Zhou et al. [8] use an upstream plate to suppress fluctuating lift on a square cylinder. They find that there is an optimal position and size for the upstream plate for effective lift suppression. Studies concerning the control of noise from a circular cylinder are more common. Recent numerical studies [9,10] investigate the use of a splitter plate attached to the base of a circular cylinder. These studies show that vortex shedding can disappear once the splitter plate achieves a certain length. Numerical solutions of the compressible unsteady Navier–Stokes equations for tandem square cylinders [11] show that significant force and noise reduction can occur if the cylinders are placed at a critical spacing in a region in which vortex shedding from the upstream cylinder is suppressed. If this separation distance is increased, the force and noise increase rapidly, due to the reestablishment of upstream vortex shedding and the associated vortex impingement on the downstream cylinder. Other work includes the experimental time-resolved force measurements of tandem bluff bodies by Sakamoto et al. [12] and Alam and Zhou [13], which were used to investigate the phase difference between the aerodynamic forces of each body in the vortex-shedding regime (i.e., the interbody spacing was such that vortex shedding was allowed to occur from each body). In each case, the phase varied linearly with separation distance. Further, Alam and Zhou developed a theoretical model based on the convective properties of isolated bluff-body wakes that agrees reasonably with experimental results. This Note will consider the case of an infinitely thin flat plate placed in the near wake of a square cylinder at a Reynolds number of Re 150. To the author’s knowledge, there have been no previous investigations of the interaction of a thin flat plate with the near wake of a square cylinder. The Note is structured as follows. After outlining the numerical approach (Sec. II), a solution of the incompressible Navier–Stokes equations for the single square cylinder case is presented and validated against available experimental and numerical results (Sec. III). A second solution is then presented that includes the downstream plate (Sec. IV), and the flow and force results are analyzed. The Note concludes with a summary of the key results.