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Volume of fluid method

About: Volume of fluid method is a research topic. Over the lifetime, 5338 publications have been published within this topic receiving 116760 citations.


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TL;DR: In this paper, the authors analyzed the flow of viscous fluid from a point or line source on an inclined plane using the equations of lubrication theory in which surface tension is neglected.
Abstract: The flow of a viscous fluid from a point or line source on an inclined plane is analysed using the equations of lubrication theory in which surface tension is neglected. At short times, when the gradient of the interfacial thickness is much greater than that of the plane, the fluid is shown to spread symmetrically from the source, as on a horizontal plane. At long times, the flow is predominantly downslope, with some cross-slope spreading for the case of a point source. Similarity solutions for the long-time behaviour of the governing nonlinear partial differential equations are found for the case in which the volume of fluid increases with time like tα, where α is a constant. The two-dimensional equations appropriate to a line source are hyperbolic in the self-similar regime and the similarity profile is found analytically to end abruptly at a downslope position which increases like t(2α+1)/3. Inclusion of higher-order terms in the analysis resolves this frontal shock into a boundary-layer structure of width comparable to the thickness of the current. Owing to the term representing cross-slope spreading, the mathematical structure of the equations is considerably more complex for flow from a point source and the similarity form is found numerically in this case. Though the downslope and cross-slope extents of the current again increase with time according to a power-law if α > 0, they also depend on a power of In t if α = 0. The leading-order near-source structure is shown to be that of steady flow from a constant-flux source of strength given by the instantaneous flow rate. For sources with α > 1, the contact line advances at all points on the perimeter of the flow and the entire plane is eventually covered by the flow; for sources with 0 < α < 1, only a portion of the contact line is advancing at any time and only that part of the plane with |y| [les ] cx3α/(4α+3) is eventually covered, where x and y are the downslope and cross-slope coordinates and c is a constant. The theoretical spreading relationships and planforms are found to be in good agreement with experimental measurements of constant-volume and constant-flux flows of viscous fluids from a point source on a plane. At very long times, however, the experimental flows are observed to be unstable to the formation of a capillary rivulet at the nose of the current.

145 citations

Journal ArticleDOI
TL;DR: In this paper, the authors compare the shallow water approach to fully three-dimensional simulations based on the solution of the complete set of Reynolds-Averaged Navier-Stokes (RANS) equations coupled to the volume of fluid (VOF) method.
Abstract: . This paper presents numerical simulations of free surface flows induced by a dam break comparing the shallow water approach to fully three-dimensional simulations. The latter are based on the solution of the complete set of Reynolds-Averaged Navier-Stokes (RANS) equations coupled to the Volume of Fluid (VOF) method. The methods assessment and comparison are carried out on a dam break over a flat bed without friction, a dam break over a triangular bottom sill and a dam break flow over a 90° bend. Experimental and numerical literature data are compared to present results. The results demonstrate that the shallow water approach, even if able to sufficiently reproduce the main aspects of the fluid flows, loses some three-dimensional phenomena, due to the incorrect shallow water idealization that neglects the three-dimensional aspects related to the gravity force.

144 citations

Journal ArticleDOI
TL;DR: In this paper, the authors deal with finite element analysis of closed membrane structures that contain an enclosed fluid such as air, and the change in the fluid pressure resulting from the application of external forces is evaluated and taken into account in the formulation of the equilibrium equations.

141 citations

Journal ArticleDOI
TL;DR: In this paper, butadiene polymers containing 70% or more of 1,2-structure and a relatively low melting point are produced by polymerizing 1,3-butadiene in the presence of a catalyst which has been prepared by admixing (a) an organic solvent solution containing 1, 3-Butadiene, a cobalt compound and an organoaluminium compound; (b) an amide compound of the formula (2, or (3): (2) or(3), wherein R1, R2 and R3 are
Abstract: Butadiene polymers containing 70% or more of 1,2-structure and a relatively low melting point are produced by polymerizing 1,3-butadiene in the presence of a catalyst which has been prepared by admixing (A) an organic solvent solution containing 1,3-butadiene, a cobalt compound and an organoaluminium compound; (B) an amide compound of the formula (2) or (3): (2) or (3) wherein R1, R2 and R3 are respectively an H atom, aliphatic hydrocarbon radical of 1 to 7 carbon atoms or aromatic hydrocarbon radical of 6 or 7 carbon atoms, R3 is H or an aliphatic hydrocarbon radical of 1 to 3 carbon atoms and n is 2 to 5, and; (C) carbon disulfide.

141 citations

Journal ArticleDOI
TL;DR: In this article, a coupled level-set and volume-of-fluid method is presented for modeling incompressible two-phase flows with surface tension, which conserves mass and captures the complicated interfaces very accurately.
Abstract: A coupled level-set and volume-of-fluid method is presented for modeling incompressible two-phase flows with surface tension. The coupled algorithm conserves mass and captures the complicated interfaces very accurately. A planar simulation of bubble growth is performed in water at near critical pressure for different degrees of superheat. The effect of superheat on the frequency of bubble formation has been analyzed. In addition, simulation of film boiling and bubble formation is performed in refrigerant R134a at near critical and far critical pressures. The effect of saturation pressure on the frequency of bubble formation has also been studied. A deviation from the periodic bubble release is observed in the case of superheat beyond 15 K in water. The effect of heat flux on the instability has also been analyzed. It is found that for water at near critical condition, a decrease in superheat from 15 to 10 K leads to oscillations with subharmonics influencing the time period of the ebullition cycle.

141 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023315
2022655
2021352
2020345
2019341
2018323