Finite Element Simulations of Free Surface Flows With Surface Tension in Complex Geometries

2002 ◽  
Vol 124 (3) ◽  
pp. 584-594 ◽  
Author(s):  
Gang Wang
Keyword(s):  
Surface Tension ◽  
Finite Element ◽  
Free Surface ◽  
Surface Force ◽  
Free Surface Flows ◽  
Complex Geometries ◽  
Finite Element Program ◽  
Surface Flows ◽  
Static Contact ◽  
Element Program

The finite-element program, ANSYS/FLOTRAN, has been enhanced at Release 5.7 to predict free surface flows with surface tension in complex geometries. The two-dimensional incompressible Navier-Stokes and energy equations are solved in both Cartesian and axisymmetric coordinate systems. At Release 5.6, the free surface capabilities have been incorporated into ANSYS/FLOTRAN using the CLEAR-VOF algorithm. The main contribution of this work is to implement a surface tension model into ANSYS/FLOTRAN to study free surface flows with surface tension in complex geometries. Both normal and tangential components of surface tension forces are modeled at the interface through a continuum surface force (CSF) model. This new algorithm is first validated with two model problems: a droplet in equilibrium and an oscillating droplet. For the first problem, the computed pressure value is compared with the theoretical value, whereas for the second problem, the oscillation frequency is compared with both the analytical solution and experimental data. The computer program is then applied to thermocapillary flows in two types of trapezoidal cavities to investigate the interesting flow and heat transfer characteristics. Systematic calculations are performed to study the influence of Marangoni number, capillary number and static contact angle on Marangoni convection.

The solution of viscous incompressible jet and free-surface flows using finite-element methods

1974 ◽  
Vol 65 (1) ◽  
pp. 189-206 ◽  
Author(s):  
R. E. Nickell ◽  
R. I. Tanner ◽  
B. Caswell
Keyword(s):  
Surface Tension ◽  
Finite Element ◽  
Free Surface ◽  
Transient Flow ◽  
Reynolds Numbers ◽  
Free Surface Flows ◽  
Stick Slip ◽  
Finite Element Program ◽  
Viscous Forces ◽  
Element Program

We discuss the creation of a finite-element program suitable for solving incompressible, viscous free-surface problems in steady axisymmetric or plane flows. For convenience in extending program capability to non-Newtonian flow, non-zero Reynolds numbers, and transient flow, a Galerkin formulation of the governing equations is chosen, rather than an extremum principle. The resulting program is used to solve the Newtonian die-swell problem for creeping jets free of surface tension constraints. We conclude that a Newtonian jet expands about 13%, in substantial agreement with experiments made with both small finite Reynolds numbers and small ratios of surface tension to viscous forces. The solutions to the related ‘stick-slip’ problem and the tube inlet problem, both of which also contain stress singularities, are also given.

Finite Element Simulations of Gas-Liquid Flows With Surface Tension

2000 ◽  
Author(s):  
Gang Wang
Keyword(s):  
Surface Tension ◽  
Finite Element ◽  
Marangoni Convection ◽  
Surface Force ◽  
Rigid Wall ◽  
Navier Stokes ◽  
Finite Element Program ◽  
Element Program ◽  
Energy Equations ◽  
Liquid Flows

Abstract The finite-element program, ANSYS/FLOTRAN, has been enhanced at Release 5.7 to predict gas-liquid flows with surface tension. The two-dimensional incompressible Navier-Stokes and energy equations are solved in both Cartesian and axisymmetric geometry. The location of the interface is computed and tracked with the CLEAR-VOF algorithm. Normal and tangential boundary conditions at the interface are enforced through a continuum surface force (CSF) model. This new algorithm is first validated with two model problems: a droplet in equilibrium and an oscillating droplet. For the first problem, the computed pressure value is compared with the theoretical value, whereas for the second problem, the oscillation frequency is compared with both the analytical solution and the experimental data. The computer program is then applied to a number of interesting free surface problems: droplet impacting on a rigid wall, binary droplet collision, flow induced by wall adhesion, and marangoni convection in a rectangular cavity.

scholarly journals Modeling Free Surface Flows Using Stabilized Finite Element Method

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Deepak Garg ◽  
Antonella Longo ◽  
Paolo Papale
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Surface ◽  
Numerical Scheme ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Computer Code ◽  
Free Surface Flows ◽  
Surface Flows ◽  
Element Method

This work aims to develop a numerical wave tank for viscous and inviscid flows. The Navier-Stokes equations are solved by time-discontinuous stabilized space-time finite element method. The numerical scheme tracks the free surface location using fluid velocity. A segregated algorithm is proposed to iteratively couple the fluid flow and mesh deformation problems. The numerical scheme and the developed computer code are validated over three free surface problems: solitary wave propagation, the collision between two counter moving waves, and wave damping in a viscous fluid. The benchmark tests demonstrate that the numerical approach is effective and an attractive tool for simulating viscous and inviscid free surface flows.

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