American Journal of Applied Mathematics and Statistics, 2013, Vol. 1, No. 1, 11-20 Available online at http://pubs.sciepub.com/ajams/1/1/3 DOI:10.12691/ajams-1-1-3 Numerical Simulation of Flow around Diamond-Shaped Obstacles at Low to Moderate Reynolds Numbers Seyed Reza Djeddi, Ali Masoudi, Parviz Ghadimi * Department of Marine Technology, Amirkabir University of Technology, Tehran, Iran *Corresponding author: pghadimi@aut.ac.ir Received January 14, 2013; Revised February 04, 2013; Accepted February 28, 2013 Abstract In this paper, viscous fluid flow over an unconventional diamond-shaped obstacle in a confined channel is simulated in low to moderate Reynolds numbers. The diamond-shaped obstacle is altered geometrically in order to represent different blockage coefficients based on the channel height and different aspect ratios based on the length to height ratios of the obstacle. An in-house finite difference Navier-Stokes solver using staggered grid arrangement and Chorin’s projection method is developed for the simulation of the laminar viscous flow. The numerical solver is validated against numerical results that are presented in the literature for the flow over rectangular cylinders and good agreement is observed. Grid resolution has been studied within a mesh convergence test and as a result, suitable grid dimension is achieved. A series of simulations have been carried out for each set of geometry and configuration in order to find the critical Reynolds number for each case in which the vortex shedding will occur. Therefore, simulations are divided into two groups of steady and unsteady flows. In the case of unsteady flow, non- dimensional Strouhal Number (St) is investigated and results prove the dependency of St on the blockage coefficient and aspect ratio. It is shown that the Strouhal number will increase with the rise of blockage ratio and the local maximum of St will occur at lower Re for geometries with lower aspect ratios (bluff bodies) than geometries with higher aspect ratios, i.e. with more streamlined bodies. Keywords: flow around obstacle, diamond-shaped, finite difference, Chorin’s projection method, Strouhal number 1. Introduction Flow around bluff and streamlined bodies has attracted many scientists and researchers for long period of time. The importance of this problem can be sought in its vast applications in engineering problems. Separation and vortex shedding are the common phenomena which happen at relatively low Reynolds numbers as a result of high positive pressure gradients. Vortex shedding causes fluctuation of pressure distribution on the body surface. Due to the vortex-induced forces, the body oscillates with a definite frequency. This may cause damages to structures such as suspended bridges and offshore oil platforms. Despite of many studies which have been done on flow around circular cylinders, rectangular shaped obstacles have been studied less experimentally and numerically, however, these shapes have many applications in analysis of aerodynamics of structures and fluid-structure interaction (FSI) problems. In the problem of flow around a confined cylinder in addition to the common parameters such as Reynolds number, another parameter called blockage coefficient (which is defined as the ratio of square side length to the channel height) should be considered [1]. Based on Reynolds number, different regimes of flow can be observed for the problem of flow around confined rectangular cylinder [2]. At very low Reynolds numbers (Re << 1), viscous forces dominate the flow. In this creeping flow, no separation occurs. With the increase of Reynolds number, flow separates at trailing edge and forms a recirculation region which consists of two symmetric vortices. Size of recirculation zone increases with an increase of Reynolds number and by reaching the critical Reynolds number, Von Kármán vortex street with periodic vortex shedding happens. With further increase of Reynolds number beyond this critical value, separation will occur in the leading edge, but the range of Re for this phenomenon has not been studied clearly and only the range of 100-150 is reported [2,3]. Okajima [3] has investigated the Strouhal number for aspect ratios (ratio of cylinder’s length to height) of 1 to 4 and a range of Reynolds numbers and stated the commence of periodic vortex motion at Reynolds number of 70 leading to an upper limit of critical Reynolds number at Re ≈ 70. A smaller value of critical Reynolds number Re ≈ 54 was determined by Klekar and Patankar [4] based on a stability analysis of the flow. Davis et al. [5] interpreted flow around a rectangular cylinder for a wide range of Reynolds numbers and aspect ratios of 1/4 and 1/6. Two-dimensional study of this problem for Reynolds numbers of 90 to 1200 and aspect ratios of 1/8 and 1/4 has been done by Mukhopadhyay et al. [6]. Also, Suzuki et al. [7] has investigated this problem for a range of Reynolds numbers from 56.3 to 225 and aspect ratios of 1/20 to 1/5. Sohankar et al. [8] have studied the effects of blockage coefficient on an unsteady 2-D laminar flow at different angles of incident for Reynolds numbers of 100 and 200. Moreover, experimental and numerical analyses have been