The Effect of Surface Tension on Free-Surface Flow Induced by a Point Sink

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

doi:10.1017/s1446181116000018

Cited by 3 publications

(3 citation statements)

References 26 publications

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“…The flow phenomena observed in this experiment is similar to the one observed by Lubin and Springer [2] and Hocking et al [8,9]. At a certain entrainment depth and at a certain flow rate a dip forms above the point sink on the surface of the lower fluid.…”

Section: B Inviscid Flow Model Using Bernoulli's Principlesupporting

confidence: 88%

“…The critical draw-down Froude number based on the depth of the withdrawn fluid layer, for conditions in which interfacial waves was not a significant factor, is approximately 1. Later, Hocking et al [9] included the surface tension effect due to the curvature of the interface and concluded that the Froude number, based on the sink depth from the interface, represented the complete flow phenomenon and the surface tension adds a resistance to the withdrawal force. However, no predictive relationship between the submergence depth and the critical flow rate was found.…”

Section: Introductionmentioning

confidence: 99%

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Predicting transition from selective withdrawal to entrainment in two-fluid stratified systems

2022

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Selective withdrawal is a desired phenomenon in transferring oil from large caverns in US Strategic petroleum reserve (SPR), because entrainment of oil at the time during withdrawal poses a risk of contaminating the environment. Motivated to understand selective withdrawal in an SPR-like orientation, experiments were performed in order to investigate the critical submergence depth as a function of critical flow rate. For the experiments, a tube was positioned through a liquid-liquid interface that draws the lower liquid upwards, avoiding entrainment of the upper fluid. Analysis of the normal stress balance across the interface produced a Weber number, utilizing dynamic pressure scaling, that predicted the transition to entrainment. Additionally, an inviscid flow analysis was performed assuming an ellipsoidal control volume surface that produced a linear relationship between the Weber number and the scaled critical submergence depth. This analytical model was validated using the experimental data resulting in a robust model for predicting transition from selective withdrawal to entrainment.

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Section: B Inviscid Flow Model Using Bernoulli's Principlesupporting

confidence: 88%

Section: Introductionmentioning

confidence: 99%

Predicting transition from selective withdrawal to entrainment in two-fluid stratified systems

2022

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“…al. [10,11] who examined some problems in the solutions of the model equations in that case, and for unsteady flows in Stokes et. al.…”

Section: Introductionmentioning

confidence: 99%

Potential flow of fluid from an elevated, two-dimensional source

Shraida

Hocking

2019

Applied Mathematical Modelling

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When fluid is pumped from an elevated source it flows downward and then outward once it hits the base. In this paper we consider a simple two dimensional model of flow from a single line source elevated above a horizontal base and consider its downward flow into a spreading layer on the bottom. A hodograph solution and linear solutions are obtained for high flow rates and full nonlinear solutions are obtained over a range of parameter space. It is found that there is a minimum flow rate beneath which no steady solutions exist. Overhanging surfaces are found for a range of parameter values. This flow serves as a model for a two-dimensional water fountain, or approximates a similar flow in a density stratified environment.

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