## THERMAL SCIENCE

International Scientific Journal

### Thermal Science - Online First

online first only
### Computational fluid dynamics modeling patterns and force characteristics of flow over in-line four square cylinders

**ABSTRACT**

The Flow over four square cylinders in an in-line, square arrangement was numerically investigated by using the finite volume method with Computational Fluid Dynamics (CFD) techniques. The working fluid is an incompressible ideal gas. The length of the sides of the array (L) are equal. The analysis is carried out for a Reynolds number of 300, with center-to-center distance ratios, L/D, ranging from 1.5 to 8.0. To fully understand the flow mechanism, details in terms of lift and drag coefficients and Strouhal numbers of the unsteady wake frequencies are analyzed, and the vortex shedding patterns around the four square cylinders are described. It is concluded that L/D has important effects on the drag and lift coefficients, vortex shedding frequencies, and flow field characteristics.

**KEYWORDS**

PAPER SUBMITTED: 2017-02-11

PAPER REVISED: 2017-02-13

PAPER ACCEPTED: 2017-02-25

PUBLISHED ONLINE: 2017-03-03

- Sumner, D., Two Circular Cylinders in Cross-Flow: A review, Journal of Fluids and Structures, 26 (2010), 6, pp. 849-899.
- Han, Z. L., et al., Flow Past two Tandem Circular Cylinders Using Spectral Element Method, The Seventh International Colloquium on Bluff Body Aerodynamics and Applications (BBAA7), Shanghai, China, September 2-6, 2012, pp. 546-554.
- Mittal, S., Kumar, V. A., Unsteady Incompressible Flows Past two Cylinders in Tandem and Staggered Arrangements, International Journal of Numerical Methods in Fluids, 25 (1997), 11, pp. 1315-1344.
- Huang, G., et al., Simulation of Flow Past two Tandem Cylinders Using Deterministic Vortex Method, Thermal Science, 16 (2012), 5, pp. 1460-1464.
- Agrawal, A., et al., Investigation of Flow Around a Pair of Side-by-Side Square Cylinders Using the Lattice Boltzmann Method, Computer and Fluids, 35 (2006), 10, pp. 1093-1107.
- Sumner, D., et al., Flow-Pattern Identification for two Staggered Circular Cylinders in Cross-Flow, Journal of Fluid Mechanics, 411 (2000), pp. 263-303.
- Nikolay, P. M., Jakgrit, S., Numerical Simulation of Heat Transfer and Fluid Flow Over Two Rotating Circular Cylinders at Low Reynolds Number, Heat Transfer Asian Research, 39 (2010), 4, pp. 246-261.
- Mohammad, S. V., Ariyan, Z. G., Numerical Investigation of Fluid Flow and Heat Transfer Around a Solid Circular Cylinder Utilizing Nanofluid, International Communications in Heat and Mass Transfer, 38 (2011), 9, pp. 1296-1304.
- Afshin, M., et al., Convective Cooling of Tandem Heated Triangular Cylinders Placed in a Channel, Thermal Science, 14 (2010), 1, pp. 183-197.
- Chang, B. H., Mills, A. F., Effect of Aspect Ratio on Forced Convection Heat Transfer from Cylinders, International Journal of Heat and Mass Transfer, 47 (2004), 6, pp. 1289-1296.
- Sayers, A. T., Flow Interference Between four Equispaced Cylinders when Subjected to a Cross Flow, Journal of Wind Engineering and Industrial Aerodynamics, 31 (1988), 1, pp. 9-28.
- Ladjedel, O., et al., Experimental Investigation of Turbulent Flow Past four Grooved and Smooth Cylinders in an In-Line Square Arrangement, EPJ Web of Conference, 2015, Vol. 92, pp. 02046-1-02046-4.
- Waqas, S. A., et al., Effect of Reynolds Numbers on Flow Past four Square Cylinders in an In-Line Square Configuration for Different Gap Spacing, Journal of Mechanical Science and Technology, 28 (2014), 2, pp. 539-552.
- Lam, K., Lam, K., Lam, K., Lam, K., Zou, L., Experimental and Numerical Study for the Cross Zou, L., Experimental and Numerical Study for the Cross Zou, L., Experimental and Numerical Study for the CrossZou, L., Experimental and Numerical Study for the Cross Zou, L., Experimental and Numerical Study for the Cross Zou, L., Experimental and Numerical Study for the Cross Zou, L., Experimental and Numerical Study for the CrossZou, L., Experimental and Numerical Study for the CrossZou, L., Experimental and Numerical Study for the Cross Zou, L., Experimental and Numerical Study for the Cross Zou, L., Experimental and Numerical Study for the CrossZou, L., Experimental and Numerical Study for the Cross Zou, L., Experimental and Numerical Study for the CrossZou, L., Experimental and Numerical Study for the Cross Zou, L., Experimental and Numerical Study for the Cross Zou, L., Experimental and Numerical Study for the CrossZou, L., Experimental and Numerical Study for the Cross Zou, L., Experimental and Numerical Study for the Cross Zou, L., Experimental and Numerical Study for the CrossZou, L., Experimental and Numerical Study for the CrossZou, L., Experimental and Numerical Study for the Cross Zou, L., Experimental and Numerical Study for the CrossZou, L., Experimental and Numerical Study for the Cross Zou, L., Experimental and Numerical Study for the CrossZou, L., Experimental and Numerical Study for the CrossZou, L., Experimental and Numerical Study for the Cross -Flow Around four Flow Around four Flow Around four Flow Around four Flow Around four Flow Around four Cylinders in an In Cylinders in an In Cylinders in an In Cylinders in an In Cylinders in an In Cylinders in an InCylinders in an In Cylinders in an In -Line Square Configuration Line Square Configuration Line Square Configuration Line Square Configuration Line Square Configuration Line Square Configuration Line Square Configuration Line Square Configuration, Journal of Mechanical Science and Technology, 21 (2007), (2007), (2007), 9, pp. 1338 -1343. 1343.
- Zou, L., et al., Flow Patterns and Force Characteristics of Laminar Flow Past four Cylinders in Diamond Arrangement, Journal of Hydrodynamics, 23 (2011), 1, pp. 55-64.
- Lam, K., et al., Flow Pattern and Velocity Field Distribution of Cross-Flow Around four Cylinders in a Square Configuration at Low Reynolds Number, Journal of Fluids and Structures, 17 (2003), 5, pp. 579-665.
- Lam, K., et al., Force Coefficient and Strouhal Numbers of four Cylinders in Cross Flow, Journal of Fluids and Structures, 18 (2003), 3, pp. 305-324.
- Lam, K., et al., Numerical Simulation of Cross-Flow around Four Cylinders in an In-Line Square Configuration, Journal of Fluids and Structures, 24 (2008), 1, pp. 34-57.
- Huang, L. Z., Nie, D. M., Vortex Shedding Patterns in Flow Past Inline Oscillating Elliptical Cylinders, Thermal Science, 16 (2012), 5, pp. 1395-1399.
- Alam, M. M., et al., The Wake of two Side-by-Side Square Cylinders, Journal of Fluid Mechanics, 669 (2011), pp. 432-471.
- Yen, S. C., et al., Interactions of Tandem Square Cylinders at Low Reynolds Numbers, Experimental Thermal and Fluid Science, 32 (2008), 4, pp. 927-938.
- Saha, A. K., et al., Transition and Chaos in a 2-D Flow Past a Square Cylinder, ASME Journal of Engineering Mechanics, 136 (2000), 5, pp. 523-532
- Davis, R., Moore, E. F., A Numerical Study of Vortex Shedding from Rectangles, Journal of Fluid Mechanics, 116 (1982), 5, pp. 475-506.
- Franke, R., et al., Numerical Calculation of Laminar Vortex Shedding for Flow Past Cylinders, Journal of Wind Engineering and Industrial Aerodynamics, 35 (1990), pp. 237-257.
- Lam, K., Lo, S. C., A Visualization Study of Cross-Flow around Four Cylinders in a Square Configuration, Journal of Fluids and Structures, 6 (1992), 1, pp. 109-131.
- K ang, X. Y., Su, Y. P., Lattice Boltzmann Simulation of Flow around two, three and four Circular Cylinders in Close Proximity, Science China, Physics, Mechanics & Astronomy, 55 (2012), 10, pp. 1873-1885.
- Lam, K., Fang, X., The Effect of Interference of four Equi-Spaced Cylinders in Cross Flow on Pressure and Force Coefficients, Journal of Fluids and Structures, 9 (1995), 2, pp. 195-214.