Numerical Simulation of Flow around Diamond-Shaped Obstacles at Low to Moderate Reynolds Numbers

Seyed Reza Djeddi¹, Ali Masoudi¹ and Parviz Ghadimi^1,

¹Department of Marine Technology, Amirkabir University of Technology, Tehran, Iran

Cite this paper:
Seyed Reza Djeddi, Ali Masoudi and Parviz Ghadimi. Numerical Simulation of Flow around Diamond-Shaped Obstacles at Low to Moderate Reynolds Numbers. American Journal of Applied Mathematics and Statistics. 2013; 1(1):11-20. doi: 10.12691/ajams-1-1-3

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

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