Flow past a square cylinder at low Reynolds numbers.

*(English)*Zbl 1426.76303Summary: Results are presented for the flow past a stationary square cylinder at zero incidence for Reynolds number, \(Re \leqslant 150\). A stabilized finite-element formulation is employed to discretize the equations of incompressible fluid flow in two-dimensions. For the first time, values of the laminar separation Reynolds number, \(Re_{s}\), and separation angle, \(\theta _{s}\), at \(Re_{s}\) are predicted. Also, the variation of \(\theta _{s}\) with Re is presented. It is found that the steady separation initiates at Re = 1.15. Contrary to the popular belief that separation originates at the rear sharp corners, it is found to originate from the base point, i.e. \(\theta _{s}=180^{\circ }\) at \(Re = Re_{s}\). For \(Re > 5, \theta _{s}\) approaches the limit of \(135 ^{\circ }\). The length of the separation bubble increases approximately linearly with increasing Re. The drag coefficient varies as \(Re^{ - 0.66}\). Flow characteristics at \(Re \leqslant 40\) are also presented for elliptical cylinders of aspect ratios 0.2, 0.5, 0.8 and 1 (circle) having the same characteristic dimension as the square and major axis oriented normal to the free-stream. Compared with a circular cylinder, the flow separates at a much lower Re from a square cylinder leading to the formation of a bigger wake (larger bubble length and width). Consequently, at a given Re, the drag on a square cylinder is more than the drag of a circular cylinder. This suggests that a cylinder with square section is more bluff than the one with circular section. Among all the cylinder shapes studied, the square cylinder with sharp corners generates the largest amount of drag.

##### MSC:

76M10 | Finite element methods applied to problems in fluid mechanics |

76D25 | Wakes and jets |

76D05 | Navier-Stokes equations for incompressible viscous fluids |

PDF
BibTeX
XML
Cite

\textit{S. Sen} et al., Int. J. Numer. Methods Fluids 67, No. 9, 1160--1174 (2011; Zbl 1426.76303)

Full Text:
DOI

##### References:

[1] | Okajima, Strouhal numbers of rectangular cylinders, Journal of Fluid Mechanics 123 pp 379– (1982) |

[2] | Davis, A numerical-experimental study of confined flow around rectangular cylinders, Physics of Fluids 27 pp 46– (1984) |

[3] | Davis, A numerical study of vortex shedding from rectangles, Journal of Fluid Mechanics 116 pp 475– (1982) · Zbl 0491.76042 |

[4] | Franke, Numerical calculation of laminar vortex-shedding flow past cylinders, Journal of Wind Engineering and Industrial Aerodynamics 35 pp 237– (1990) |

[5] | Mukhopadhaya, Numerical investigation of confined wakes behind a square cylinder in a channel, International Journal for Numerical Methods in Fluids 14 pp 1473– (1984) · Zbl 0825.76163 |

[6] | Sohankar, Low-Reynolds-number flow around a square cylinder at incidence: study of blockage, onset of vortex shedding and outlet boundary condition, International Journal for Numerical Methods in Fluids 26 pp 39– (1998) · Zbl 0910.76067 |

[7] | Robichaux, Three-dimensional floquet instability of the wake of square cylinder, Physics of Fluids 11 pp 560– (1999) · Zbl 1147.76482 |

[8] | Saha, Three-dimensional study of flow past a square cylinder at low Reynolds numbers, International Journal of Heat and Fluid Flow 24 pp 54– (2003) |

[9] | Sheard, Cylinders with square cross-section: wake instabilities with incidence angle variation, Journal of Fluid Mechanics 630 pp 43– (2009) · Zbl 1181.76069 |

[10] | Breuer, Accurate computations of the laminar flow past a square cylinder based on two different methods: lattice-Boltzmann and finite-volume, International Journal of Heat and Fluid Flow 21 pp 186– (2000) |

[11] | Taneda, Experimental investigation of the wakes behind cylinders and plates at low Reynolds numbers, Journal of Physical Society of Japan 11 pp 302– (1956) |

[12] | Sen, Steady separated flow past a circular cylinder at low Reynolds numbers, Journal of Fluid Mechanics 620 pp 89– (2009) · Zbl 1156.76381 |

[13] | Gupta, Two-dimensional steady flow of a power-law fluid past a square cylinder in a plane channel: momentum and heat-transfer characteristics, Industrial and Engineering Chemistry Research 42 pp 5674– (2003) |

[14] | Paliwal, Power law fluid flow past a square cylinder: momentum and heat transfer characteristics, Chemical Engineering Science 58 pp 5315– (2003) |

[15] | Sharma, Heat and fluid flow across a square cylinder in the two-dimensional laminar flow regime, Numerical Heat Transfer A 45 pp 247– (2004) |

[16] | Dhiman, Effects of Reynolds and Prandtl numbers on heat transfer across a square cylinder in the steady flow regime, Numerical Heat Transfer A 49 pp 717– (2006) |

[17] | Sohankar, Simulation of three-dimensional flow around a square cylinder at moderate Reynolds numbers, Physics of Fluids 11 pp 288– (1999) · Zbl 1147.76502 |

[18] | Tezduyar, Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements, Computer Methods in Applied Mechanics and Engineering 95 pp 221– (1992) · Zbl 0756.76048 |

[19] | Saad, GMRESS: a generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM Journal on Scientific and Statistical Computing 7 pp 856– (1986) · Zbl 0599.65018 |

[20] | Sen S Mittal S Biswas G Finite-element simulation of steady flow past elliptic cylinders · Zbl 1356.76065 |

[21] | Lighthill, Laminar Boundary Layers pp 46– (1963) |

[22] | Darekar, Flow past a square-section cylinder with a wavy stagnation face, Journal of Fluid Mechanics 426 pp 263– (2001) · Zbl 1016.76015 |

[23] | Singh, Flow past a transversely oscillating square cylinder in free stream at low Reynolds numbers, International Journal for Numerical Methods in Fluids 61 pp 658– (2009) · Zbl 1172.76012 |

[24] | Sahu, Two-dimensional unsteady laminar flow of a power law fluid across a square cylinder, Journal of Non-Newtonian Fluid Mechanics 160 pp 157– (2009) · Zbl 1274.76063 |

[25] | Vorobieff, Onset of the second wake: dependence on the Reynolds number, Physics of Fluids 14 pp L53– (2002) · Zbl 1185.76382 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.