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Research Papers: Multiphase Flows

# Large Eddy Simulation of Flow Past Free Surface Piercing Circular Cylinders

[+] Author and Article Information
G. Yu

Department of Engineering, Queen Mary University of London, Mile End Road, London E1 4NS, UKg.yu@qmul.ac.uk

E. J. Avital

Department of Engineering, Queen Mary University of London, Mile End Road, London E1 4NS, UKe.avital@qmul.ac.uk

J. J. Williams

Department of Engineering, Queen Mary University of London, Mile End Road, London E1 4NS, UKj.j.r.williams@qmul.ac.uk

J. Fluids Eng 130(10), 101304 (Sep 08, 2008) (9 pages) doi:10.1115/1.2969462 History: Received January 29, 2008; Revised June 03, 2008; Published September 08, 2008

## Abstract

Flows past a free surface piercing cylinder are studied numerically by large eddy simulation at Froude numbers up to $FrD=3.0$ and Reynolds numbers up to $ReD=1×105$. A two-phase volume of fluid technique is employed to simulate the air-water flow and a flux corrected transport algorithm for transport of the interface. The effect of the free surface on the vortex structure in the near wake is investigated in detail together with the loadings on the cylinder at various Reynolds and Froude numbers. The computational results show that the free surface inhibits the vortex generation in the near wake, and as a result, reduces the vorticity and vortex shedding. At higher Froude numbers, this effect is stronger and vortex structures exhibit a 3D feature. However, the free surface effect is attenuated as Reynolds number increases. The time-averaged drag force on the unit height of a cylinder is shown to vary along the cylinder and the variation depends largely on Froude number. For flows at $ReD=2.7×104$, a negative pressure zone is developed in both the air and water regions near the free surface leading to a significant increase of drag force on the cylinder in the vicinity of the free surface at about $FrD=2.0$. The mean value of the overall drag force on the cylinder increases with Reynolds number and decreases with Froude number but the reduction is very small for $FrD=1.6–2.0$. The dominant Strouhal number of the lift oscillation decreases with Reynolds number but increases with Froude number.

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## Figures

Figure 1

Schematic description of the cylindrical coordinates (a) and the configurations of the computational domain (b). The inflow region covers an arc of 90deg.

Figure 2

(a) Instantaneous evolution of the interface surface (c=0.5), ReD=2.7×104, and FrD=0.8. (b) Contours of the time-averaged air-water interface height corresponding to c=0.5, ReD=2.7×104, and FrD=0.8.

Figure 3

Energy spectrum of the flow in the near wake of the cylinder; the solid straight line has a slope of −5∕3; the dashed line represents the grid cutoff

Figure 4

Comparison of the time-averaged streamwise velocity profiles at x=4.5D, y=0 in the wake, ReD=2.7×104, and FrD=0.8. (◻) Experimental results of Inoue (2), (△) numerical simulation of Kawamura (5), (—) current simulation with grid size of 161×161×131, and (---) current simulation with grid size of 129×129×99.

Figure 5

Time-averaged air-water interface surface with a fountain generated in front of the cylinder; the initial still water height is 4D, ReD=2.7×104, and FrD=0.8

Figure 6

Normalized fountain height by D versus Froude number. (a) Experimental observation of Wickramasinghe and Wilkinson (1) and (b) current simulation results.

Figure 7

Contours of the instantaneous vorticity magnitude for Case 1 in Table 1 on the plane adjacent to the bed (a), at the midplane (b), and near the free surface (c)

Figure 8

Power spectral density of the lift for Case 1 in Table 1 on the plane adjacent to the bed (a), at the midplane (b), and near the free surface (c)

Figure 9

Contours of time-averaged vorticity magnitude for Case 1 in Table 1 on the plane adjacent to the bed (a), at the midplane (b), and near the free surface (c)

Figure 10

Contours of the Reynolds stress ⟨u′v′⟩ for Case 1 in Table 1 on the plane adjacent to the bed (a), at the midplane (b), and near the free surface (c)

Figure 11

Instantaneous vortex structure in the near wake at ReD=2.7×104 and FrD=0.8; the view is taken on the plane cross the cylinder center in the inflow direction (λ=−5)

Figure 12

Instantaneous vortex structure in the near wake at ReD=2.7×104 and FrD=2.0; the view is taken on the plane cross the cylinder center in the inflow direction (λ=−5)

Figure 13

Instantaneous vortex structure in the near wake at ReD=1.0×105 and FrD=0.8; the view is taken on the plane cross the cylinder center in the inflow direction (λ=−5)

Figure 14

Power spectral density of the lift at FrD=0.8, on the plane adjacent to the bed (a), at the midplane (b), and near the free surface (c)

Figure 15

Overall drag coefficient C¯d as a function of time tU∕d at the same FrD=0.8 but various Reynolds numbers (a) and the same Reynolds number ReD=2.7×104 but various Froude numbers (b)

Figure 16

Time-averaged sectional drag coefficient distribution along the cylinder at the same FrD=0.8 but various Reynolds numbers (a) and the same Reynolds number ReD=2.7×104 but various Froude numbers (b)

Figure 17

Time-averaged air-water interface (c=0.5) at ReD=2.7×104 and FrD=2.0 (a), and ReD=2.7×104 and FrD=0.8 (b). Water flows in the x direction.

Figure 18

Time-averaged pressure distribution on the plane 3.4D above the bed at ReD=2.7×104 and FrD=2.0. There are 20 levels between −0.34 and 0.59. The dashed lines represent negative values.

## Errata

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