The effect of surface tension on free surface flow induced by a point sink in a fluid of finite depth

Hocking, Graeme C.; Nguyen, Ha H. N.; Stokes, Tim; Forbes, Lawrence K.

doi:10.1016/j.compfluid.2017.08.015

Cited by 2 publications

(1 citation statement)

References 26 publications

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“…Steady or unsteady withdrawal from a fluid of finite or infinite depth through a line sink or point sink including surface-tension effects has been the subject of considerable study. Hocking et al [12][13][14], and Forbes and Hocking [10] found that the inclusion of even a small amount of surface tension has a big influence on the final values of the maximum flow rate. They were also able to show nonuniqueness in the solution domain.…”

Section: Introductionmentioning

confidence: 99%

Flow induced by a line sink near a vertical wall in a fluid with a free surface Part I: infinite depth

2022

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The two-dimensional, steady flow of an inviscid fluid induced by a line sink located near a vertical wall in a region of infinite depth is computed. The effects of surface tension are investigated. The solution in the limit of small Froude number is obtained analytically, and numerically for the nonlinear problem. The asymptotic solution is found to have a property that if the horizontal location of the sink, $$x_\mathrm{{s}} < 1$$ x s < 1 , there is only one stagnation point on the surface, at the wall. However, if the horizontal location $$x_{\mathrm{s}} > 1$$ x s > 1 , a second stagnation point forms on the free surface. Numerical solution for the nonlinear problem confirms these properties. The effect of moving the sink horizontally has also been considered. The maximum Froude numbers at which steady solutions exist are computed and compared with the previous work.

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Section: Introductionmentioning

confidence: 99%

Flow induced by a line sink near a vertical wall in a fluid with a free surface Part I: infinite depth

2022

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Flow induced by a line sink near a vertical wall in a fluid with a free surface, Part II: finite depth

2022

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Flow caused by a line sink near a vertical wall in an otherwise stagnant fluid with a free surface is studied. A linear solution for small flow rates is obtained and a numerical method based on fundamental singularities techniques is applied to the full nonlinear problem. The sink is located at an arbitrary location away from all boundaries and the fluid is of finite depth. Steady solutions are presented for various flow rates and sink location. It is shown that the numerical results and linear solutions are in good agreement for small flow rates. The results suggest that steady nonlinear solutions are limited to flow rates below some critical value. Some interesting surface shapes are obtained depending on the location of the sink.

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The effect of surface tension on free surface flow induced by a point sink in a fluid of finite depth

Abstract: The effect of surface tension on free surface flow induced by a point sink in a fluid of finite depth. Computers & Fluids, 156. pp. 526-533.

Cited by 2 publications

References 26 publications

Flow induced by a line sink near a vertical wall in a fluid with a free surface Part I: infinite depth

Flow induced by a line sink near a vertical wall in a fluid with a free surface Part I: infinite depth

Flow induced by a line sink near a vertical wall in a fluid with a free surface, Part II: finite depth

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