Flow patterns and force characteristics of laminar flow past four cylinders in diamond arrangement

A three-dimensional numerical investigation of cross-flow past four circular cylinders in a diamond arrangement at Reynolds number of 200 is carried out. With the spacing ratios (L/D) ranging from 1.2 to 5.0, the flow patterns can be classified into three basic regimes. The critical spacing ratio for the transition from narrow gap flow pattern to vortex impingement flow pattern around the cylinders is found to be L/D = 3.0, while a single bluff-body flow pattern is observed at L/D = 1.2. The relationship between the three-dimensional flow patterns and force characteristics around the four cylinders shows that the variation of forces and Strouhal numbers against L/D are generally governed by these three kinds of flow patterns. It is concluded that the spacing ratio has important effects on the development of the free shear layers about the cylinders and hence has significant effects on the force and pressure characteristics of the four cylinders with different spacing ratios.