A novel interface method for two-dimensional multiphase SPH: Interface detection and surface tension formulation

2021 ◽  
Vol 431 ◽  
pp. 110119
Author(s):  
B.X. Zheng ◽  
L. Sun ◽  
P. Yu
Keyword(s):  
Surface Tension ◽  
Two Dimensional

scholarly journals Nonlinear two-dimensional free surface solutions of flow exiting a pipe and impacting a wedge

2021 ◽  
Vol 126 (1) ◽  
Author(s):  
Alex Doak ◽  
Jean-Marc Vanden-Broeck
Keyword(s):  
Surface Tension ◽  
Integral Equation ◽  
Free Surface ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Two Dimensional ◽  
Numerical Schemes ◽  
Additional Advantage ◽  
Infinite Wedge ◽  
Good Agreement

AbstractThis paper concerns the flow of fluid exiting a two-dimensional pipe and impacting an infinite wedge. Where the flow leaves the pipe there is a free surface between the fluid and a passive gas. The model is a generalisation of both plane bubbles and flow impacting a flat plate. In the absence of gravity and surface tension, an exact free streamline solution is derived. We also construct two numerical schemes to compute solutions with the inclusion of surface tension and gravity. The first method involves mapping the flow to the lower half-plane, where an integral equation concerning only boundary values is derived. This integral equation is solved numerically. The second method involves conformally mapping the flow domain onto a unit disc in the s-plane. The unknowns are then expressed as a power series in s. The series is truncated, and the coefficients are solved numerically. The boundary integral method has the additional advantage that it allows for solutions with waves in the far-field, as discussed later. Good agreement between the two numerical methods and the exact free streamline solution provides a check on the numerical schemes.

scholarly journals Kelvin-Helmholtz discontinuity in two superposed viscous conducting fluids in a horizontal magnetic field

2008 ◽  
Vol 12 (3) ◽  
pp. 103-110 ◽  
Author(s):  
Aiyub Khan ◽  
Neha Sharma ◽  
P.K. Bhatia
Keyword(s):  
Magnetic Field ◽  
Surface Tension ◽  
Growth Rate ◽  
Unstable Mode ◽  
Two Dimensional ◽  
Horizontal Magnetic Field ◽  
Streaming Velocity ◽  
The Stability ◽  
Conducting Fluids ◽  
Streaming Motion

The Kelvin-Helmholtz discontinuity in two superposed viscous conducting fluids has been investigated in the taking account of effects of surface tension, when the whole system is immersed in a uniform horizontal magnetic field. The streaming motion is assumed to be two-dimensional. The stability analysis has been carried out for two highly viscous fluid of uniform densities. The dispersion relation has been derived and solved numerically. It is found that the effect of viscosity, porosity and surface tension have stabilizing influence on the growth rate of the unstable mode, while streaming velocity has a destabilizing influence on the system.

Upward ‘falling’ jets and surface tension

1957 ◽  
Vol 2 (2) ◽  
pp. 201-203 ◽  
Author(s):  
Joseph B. Keller ◽  
Mortimer L. Weitz
Keyword(s):  
Surface Tension ◽  
Incompressible Fluid ◽  
Two Dimensional ◽  
Parabolic Shape ◽  
Parabolic Trajectory ◽  
Hydraulic Theory

According to the simple hydraulic theory of jets, each particle of a jet moves independently along a parabolic trajectory. Therefore a steady jet has a parabolic shape. We wish to consider how these results are modified by surface tension. For simplicity we will consider a two-dimensional jet of incompressible fluid.

Asymptotic expansions for solitary gravity-capillary waves in two and three dimensions

2009 ◽  
Vol 465 (2109) ◽  
pp. 2725-2749 ◽  
Author(s):  
M. J. Ablowitz ◽  
T. S. Haut
Keyword(s):  
Surface Tension ◽  
Solitary Wave ◽  
Solitary Waves ◽  
Asymptotic Series ◽  
High Order ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Small Surface ◽  
Petviashvili Equation ◽  
Dimensional Series

High-order asymptotic series are obtained for two- and three-dimensional gravity-capillary solitary waves. In two dimensions, the first term in the asymptotic series is the well-known sech 2 solution of the Korteweg–de Vries equation; in three dimensions, the first term is the rational lump solution of the Kadomtsev–Petviashvili equation I. The two-dimensional series is used (with nine terms included) to investigate how small surface tension affects the height and energy of large-amplitude waves and waves close to the solitary version of Stokes’ extreme wave. In particular, for small surface tension, the solitary wave with the maximum energy is obtained. For large surface tension, the two-dimensional series is also used to study the energy of depression solitary waves. Energy considerations suggest that, for large enough surface tension, there are solitary waves that can get close to the fluid bottom. In three dimensions, analytic solutions for the high-order perturbation terms are computed numerically, and the resulting asymptotic series (to three terms) is used to obtain the speed versus maximum amplitude curve for solitary waves subject to sufficiently large surface tension. Finally, the above asymptotic method is applied to the Benney–Luke (BL) equation, and the resulting asymptotic series (to three terms) is verified to agree with the solitary-wave solution of the BL equation.

scholarly journals Two-dimensional Hertzian contact problem with surface tension

2012 ◽  
Vol 49 (13) ◽  
pp. 1588-1594 ◽  
Author(s):  
J.M. Long ◽  
G.F. Wang ◽  
X.Q. Feng ◽  
S.W. Yu
Keyword(s):  
Surface Tension ◽  
Contact Problem ◽  
Hertzian Contact ◽  
Two Dimensional

THE CONCENTRATIONS OF OIL IN SEA WATER RESULTING FROM NATURAL AND CHEMICALLY INDUCED DISPERSION OF OIL SLICKS

1977 ◽  
Vol 1977 (1) ◽  
pp. 381-385 ◽  
Author(s):  
D. Cormack ◽  
J.A. Nichols
Keyword(s):  
Surface Tension ◽  
Oil Recovery ◽  
Oil Spills ◽  
Sea Water ◽  
The Other ◽  
Viscous Drag ◽  
Two Dimensional ◽  
Drag Forces ◽  
Chemically Induced ◽  
Low Toxicity

ABSTRACT Results are presented on the factors relating to the dissipation of oil spills at sea, including evaporation, emulsion formation, spreading, and natural dispersion into the water column. For Ekofisk oil, 20% evaporates in about 7.5 hours and, while emulsion formation is as rapid as for Kuwait crude, the resulting viscosity is low and insufficient to allow interference with the natural spreading and dispersion rates. Spreading has two components. One is controlled by surface tension-viscous drag forces and the other is wind-induced. Together they contribute to the two dimensional dissipation of the oil so that subsequent oil concentrations in the sea are of necessity, low. These concentrations were measured for naturally dispersing and chemically dispersed slicks. The chemically-dispersed slicks were of two kinds. One was previously weathered for three hours, the other was of controlled thickness and was dispersed immediately upon being laid. Resulting concentrations of oil in the sea are low and of short duration compared with those required to give observable effects in laboratory toxicity studies. No significant deleterious effects were found to result from the dispersion of oil slicks at sea using low toxicity dispersant chemicals; also it was noted that, in any case, substantial quantities of oil can be expected to enter the sea before oil recovery operations can be mounted.

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