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The authors study two-dimensional, steady, irrotational flow of an inviscid incompressible fluid through solid walls, focusing on how surface tension affects the free-surface shape while neglecting gravity. Using a numerical series truncation method, they compute solutions across different wall angles (β), vertical wall lengths (BC), and Weber numbers, mostly with N=50 terms, and report approximate solutions for α > 3, while validating results against other numerical methods and special-angle exact solutions. A stated limitation is that the work is presented as a preprint and not peer reviewed, and gravitational effects are not included. The paper does not explicitly discuss endometriosis or adenomyosis; it was included in the corpus via a keyword match in the upstream search index.
Abstract
We examine the two-dimensional, steady, and irrotational flow of an inviscid and incompressible fluid emerging from certain cases of flow through solid walls. Surface tension (T) is considered, while gravitational effects are neglected. This problem is complicated by the non-linear boundary condition imposed by the Bernoulli equation on the free surface, which presents challenges when adapting numerical methods used by many researchers. We employ a series truncation method for numerical solution. We computed solutions for various values of the angle (β) between the walls AB and the horizontal, the length of the vertical wall BC, and different Weber numbers. For determining the shape of the free surface, most of the calculations were performed for N=50. We were able to find approximate solutions for α > 3 To validate our results, they were compared with studies using other numerical methods and in special cases of the angle β, compared with the exact solution in the limit of
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This is a preprint and has not been peer reviewed. Data may be preliminary.
Two-dimensional free surface flow through solid walls with Surface Tension Effects
Abstract
We examine the two-dimensional, steady, and irrotational flow of an inviscid and incompressible fluid emerging from certain cases of flow through solid walls. Surface tension (T) is considered, while gravitational effects are neglected. This problem is complicated by the non-linear boundary condition imposed by the Bernoulli equation on the free surface, which presents challenges when adapting numerical methods used by many researchers. We employ a series truncation method for numerical solution. We computed solutions for various values of the angle (β) between the walls AB and the horizontal, the length of the vertical wall BC, and different Weber numbers. For determining the shape of the free surface, most of the calculations were performed for N=50. We were able to find approximate solutions for α > 3 To validate our results, they were compared with studies using other numerical methods and in special cases of the angle β, compared with the exact solution in the limit of
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Zineb GUELLATI, Abdelkader GASMI.
Two-dimensional free surface flow through solid walls with Surface Tension Effects. Authorea. 02 March 2025.
DOI: https://doi.org/10.22541/au.174094212.28359777/v1
DOI: https://doi.org/10.22541/au.174094212.28359777/v1
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