Experiments and Simulations of Free-Surface Flow behind a Finite Height Rigid Vertical Cylinder

Valentin Ageorges,Vincent Moureau,Ghislain Lartigue,Jorge Peixinho,Gaële Perret

doi:10.3390/fluids6100367

Abstract

We present the results of a combined experimental and numerical study of the free-surface flow behind a finite height rigid vertical cylinder. The experiments measure the drag and the wake angle on cylinders of different diameters for a range of velocities corresponding to 30,000 <Re< 200,000 and 0.2<Fr<2 where the Reynolds and Froude numbers are based on the diameter. The three-dimensional large eddy simulations use a conservative level-set method for the air-water interface, thus predicting the pressure, the vorticity, the free-surface elevation and the onset of air entrainment. The deep flow looks like single phase turbulent flow past a cylinder, but close to the free-surface, the interaction between the wall, the free-surface and the flow is taking place, leading to a reduced cylinder drag and the appearance of V-shaped surface wave patterns. For large velocities, vortex shedding is suppressed in a layer region behind the cylinder below the free surface. The wave patterns mostly follow the capillary-gravity theory, which predicts the crest lines cusps. Interestingly, it also indicates the regions of strong elevation fluctuations and the location of air entrainment observed in the experiments. Overall, these new simulation results, drag, wake angle and onset of air entrainment, compare quantitatively with experiments.

Highlights

IntroductionThe turbulent flow around a fully immersed cylinder has been the object of numerous experimental [1] and numerical studies [2,3]
We presented experimental and numerical results of three-dimensional simulations on the drag, the wake angles, the pressure fields, the vorticity fields and the free-surface elevation of a vertical finite height rigid cylinder in turbulent free-surface flow
The simulations were performed for D = 5 cm in the range of parameters 30,000 < Re < 70,000 or 0.86 < Fr < 2, which coincides with the occurrence of the V-shaped pattern on the free surface and the onset of air entrainment

Summary

Introduction

The turbulent flow around a fully immersed cylinder has been the object of numerous experimental [1] and numerical studies [2,3]. Turbulent free-surface flows are well documented for vertical flat plates [5,6], hull shapes [7] and hydrofoils [8]. The simple configuration of a finite height vertical rigid cylinder partially immersed in water flow has been less studied in the recent years. In 1947, Hay [9] reported an extensive investigation on the flow around a semi-submerged cylinder and provided many photographs from above and below the free surface for a wide range of velocities and diameters. The data uncovered the scaling relationship for the dimension of the various waves ahead and downstream of the cylinder; the wave dimensions seemed proportional to the square of the translating velocity [10,11]

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Conclusion