16 fsurf

Information about 16 fsurf

Published on January 1, 2008

Author: Mikhail

Source: authorstream.com

Content

Lecture 16 - Free Surface Flows Applied Computational Fluid Dynamics:  Lecture 16 - Free Surface Flows Applied Computational Fluid Dynamics Instructor: André Bakker © André Bakker (2002) © Fluent Inc. (2002) Example: spinning bowl:  Example: spinning bowl Example: flow in a spinning bowl. Re = 1E6 At startup, the bowl is partially filled with water. The water surface deforms once the bowl starts spinning. The animation covers three full revolutions. Example: splashing droplet:  Example: splashing droplet Example: pouring water:  Example: pouring water A bucket of water is poured through the air into a container of kerosene. This disrupts the kerosene, and air bubbles formed soon rise to the surface and break. The three liquids in this simulation do not mix, and after a time the water collects at the bottom of the container. The sliding mesh model is used to model the tipping of the bucket. VOF Model:  VOF Model Volume of fluid (VOF) model overview. VOF is an Eulerian fixed-grid technique. Interface tracking scheme. Application: modeling of gravity current. Surface tension and wall adhesion. Solution strategies. Summary. Modeling techniques:  Modeling techniques Lagrangian methods: The grid moves and follows the shape of the interface. Interface is specifically delineated and precisely followed. Suited for viscous, laminar flows. Problems of mesh distortion, resulting in instability and internal inaccuracy. Eulerian methods: Fluid travels between cells of the fixed mesh and there is no problem with mesh distortion. Adaptive grid techniques. Fixed grid techniques, e.g. volume of fluid (VOF) method. Volume of fluid model:  Volume of fluid model Immiscible fluids with clearly defined interface. Shape of the interface is of interest. Typical problems: Jet breakup. Motion of large bubbles in a liquid. Motion of liquid after a dam break. Steady or transient tracking of any liquid-gas interface. Inappropriate if bubbles are small compared to a control volume (bubble columns). VOF:  Assumes that each control volume contains just one phase (or the interface between phases). Solves one set of momentum equations for all fluids. Surface tension and wall adhesion modeled with an additional source term in momentum equation. For turbulent flows, single set of turbulence transport equations solved. Solves a volume fraction conservation equation for the secondary phase. VOF Volume fraction:  Defines a step function  equal to unity at any point occupied by fluid and zero elsewhere such that: For volume fraction of kth fluid, three conditions are possible: k = 0 if cell is empty (of the kth fluid). k = 1 if cell is full (of the kth fluid). 0 < k < 1 if cell contains the interface between the fluids. Volume fraction Volume fraction (2):  Tracking of interface(s) between phases is accomplished by solution of a volume fraction continuity equation for each phase: Mass transfer between phases can be modeled by using a user-defined subroutine to specify a nonzero value for Sk. Multiple interfaces can be simulated. Cannot resolve details of the interface smaller than the mesh size. Volume fraction (2) Interface tracking schemes:  Example of free surface Donor-Acceptor Scheme Linear slope reconstruction Interface tracking schemes Slide12:  2nd order upwind. Interface is not tracked explicitly. Only a volume fraction is calculated for each cell. Donor - Acceptor Geometric reconstruction Comparing different interface tracking schemes Surface tension:  Surface tension Surface tension along an interface arises from attractive forces between molecules in a fluid (cohesion). Near the interface, the net force is radially inward. Surface contracts and pressure increases on the concave side. At equilibrium, the opposing pressure gradient and cohesive forces balance to form spherical bubbles or droplets. Surface tension example:  Surface tension example Cylinder of water (5 x 1 cm) is surrounded by air in no gravity. Surface is initially perturbed so that the diameter is 5% larger on ends. The disturbance at the surface grows by surface tension. Surface tension - when important:  Surface tension - when important To determine significance, first evaluate the Reynolds number. For Re << 1, evaluate the Capillary number. For Re >> 1, evaluate the Weber number. Surface tension important when We >>1 or Ca<< 1. Surface tension modeled with an additional source term in momentum equation. Wall adhesion :  Wall adhesion Large contact angle (> 90°) is applied to water at bottom of container in zero-gravity field. An obtuse angle, as measured in water, will form at walls. As water tries to satisfy contact angle condition, it detaches from bottom and moves slowly upward, forming a bubble. Modeling of the gravity current:  Brine: m=0.001 r=1005.1 Water: m=0.001 r=1000 g =9.8 Modeling of the gravity current Mixing of brine and fresh water. 190K cells with hanging nodes. Domain: length 1m, height 0.15m. Time step: 0.002 s. PISO algorithm. Geometric reconstruction scheme. QUICK scheme for momentum. Run time ~8h on an eight-processor (Ultra2300) network. Gravity current (1):  Gravity current (1) T = 0 s T = 1 s T = 2 s Gravity current (2):  Gravity current (2) T = 5 s T = 4 s T = 3 s Gravity current (3):  Gravity current (3) T = 10 s T = 7 s T = 9 s Visco-elastic fluids - Weissenberg effect:  Visco-elastic fluids - Weissenberg effect Visco-elastic fluids, such as dough and certain polymers, tend to climb up rotating shafts instead of drawing down a vortex. This is called the Weissenberg effect and is very difficult to model. The photograph shows the flow of a solution of polyisobutylene. Visco-elastic fluids - blow molding:  Visco-elastic fluids - blow molding Blow molding is a commonly used technique to manufacture bottles, canisters, and other plastic objects. Important parameters to model are local temperature and material thickness. VOF model formulations - steady state:  VOF model formulations - steady state Steady-state with implicit scheme: Used to compute steady-state solution using steady-state method. More accurate with higher order discretization scheme. Must have distinct inflow boundary for each phase. Example: flow around ship’s hull. VOF model formulations - time dependent:  VOF model formulations - time dependent Time-dependent with explicit schemes: Use to calculate time accurate solutions. Geometric linear slope reconstruction. Most accurate in general. Donor-acceptor. Best scheme for highly skewed hex mesh. Euler explicit. Use for highly skewed hex cells in hybrid meshes if default scheme fails. Use higher order discretization scheme for more accuracy. Example: jet breakup. Time-dependent with implicit scheme: Used to compute steady-state solution when intermediate solution is not important and the final steady-state solution is dependent on initial flow conditions. There is not a distinct inflow boundary for each phase. More accurate with higher order discretization scheme. Example: shape of liquid interface in centrifuge. VOF solution strategies: time dependence:  Time-stepping for the VOF equation: Automatic refinement of the time step for VOF equation using Courant number C: t is the minimum transit time for any cell near the interface. Calculation of VOF for each time-step: Full coupling with momentum and continuity (VOF updated once per iteration within each time-step): more CPU time, less stable. No coupling (default): VOF and properties updated once per time step. Very efficient, more stable but less accurate for very large time steps. VOF solution strategies: time dependence VOF solution strategies (continued):  VOF solution strategies (continued) To reduce the effect of numerical errors, specify a reference pressure location that is always in the less dense fluid, and (when gravity is on) a reference density equal to the density of the less dense fluid. For explicit formulations for best and quick results: Always use geometric reconstruction or donor-acceptor. Use PISO algorithm. Increase all under-relaxation factors up to 1.0. Lower timestep if it does not converge. Ensure good volume conservation: solve pressure correction equation with high accuracy (termination criteria to 0.001 for multigrid solver). Solve VOF once per time-step. For implicit formulations: Always use QUICK or second order upwind difference scheme. May increase VOF under-relaxation from 0.2 (default ) to 0.5. Summary:  Summary Free surface flows are encountered in many different applications: Flow around a ship. Blow molding. Extrusion. Mold filling. There are two basic ways to model free surface flows: Lagrangian: the mesh follows the interface shape. Eulerian: the mesh is fixed and a local volume fraction is calculated. The most common method used in CFD programs based on the finite volume method is the volume-of-fluid (VOF) model.

Related presentations


Other presentations created by Mikhail

Pune Contr QM 05
28. 11. 2007
0 views

Pune Contr QM 05

Feeling tired presentation
28. 11. 2007
0 views

Feeling tired presentation

IOC
26. 10. 2007
0 views

IOC

2006Harmonization
31. 10. 2007
0 views

2006Harmonization

sect 2 5 e
06. 11. 2007
0 views

sect 2 5 e

grovemtns
02. 10. 2007
0 views

grovemtns

canterm presentation en
12. 11. 2007
0 views

canterm presentation en

HIROSHIMA
13. 11. 2007
0 views

HIROSHIMA

Geocaching NDSU Ext
19. 11. 2007
0 views

Geocaching NDSU Ext

chelsom2
19. 11. 2007
0 views

chelsom2

productbasics
20. 11. 2007
0 views

productbasics

Phenologyperennials
07. 12. 2007
0 views

Phenologyperennials

camusintro
14. 12. 2007
0 views

camusintro

2006summernmmtutorial
12. 12. 2007
0 views

2006summernmmtutorial

Kugler 3 Mar22
24. 12. 2007
0 views

Kugler 3 Mar22

Discipline
29. 12. 2007
0 views

Discipline

protect skin
02. 01. 2008
0 views

protect skin

Rome 09 04copy
29. 10. 2007
0 views

Rome 09 04copy

ch12
05. 01. 2008
0 views

ch12

johns
07. 01. 2008
0 views

johns

bakalar
06. 11. 2007
0 views

bakalar

sea tac presentation
07. 11. 2007
0 views

sea tac presentation

Brand
23. 11. 2007
0 views

Brand

bas2003 3870
04. 01. 2008
0 views

bas2003 3870

power generation in singapore
20. 02. 2008
0 views

power generation in singapore

prez0301
24. 02. 2008
0 views

prez0301

MULTIMED
27. 02. 2008
0 views

MULTIMED

FastingforWomen
05. 03. 2008
0 views

FastingforWomen

carruthers2
30. 12. 2007
0 views

carruthers2

200701 PCC Manahilov
14. 03. 2008
0 views

200701 PCC Manahilov

mln 1
19. 12. 2007
0 views

mln 1

Travel Lit Slide SHow
27. 03. 2008
0 views

Travel Lit Slide SHow

InfoASEAN
30. 03. 2008
0 views

InfoASEAN

Blogging jbp bristol seminar
03. 12. 2007
0 views

Blogging jbp bristol seminar

Week 8 Managerial learning
14. 11. 2007
0 views

Week 8 Managerial learning

aggdem
13. 04. 2008
0 views

aggdem

FAO5
31. 10. 2007
0 views

FAO5

RSP2004 Varsamou
26. 11. 2007
0 views

RSP2004 Varsamou

11 climber
31. 12. 2007
0 views

11 climber

preliminary proposal
25. 12. 2007
0 views

preliminary proposal

T3 lexer
28. 11. 2007
0 views

T3 lexer

THirano PPTWin noAnimations
27. 09. 2007
0 views

THirano PPTWin noAnimations

Final prj12
04. 01. 2008
0 views

Final prj12

405 Green
21. 11. 2007
0 views

405 Green

2b RolfSedlmayr
15. 11. 2007
0 views

2b RolfSedlmayr

Albany CC Hazmat Forum Aug 15
28. 09. 2007
0 views

Albany CC Hazmat Forum Aug 15

haynes rmspg
14. 11. 2007
0 views

haynes rmspg

jmw0
30. 10. 2007
0 views

jmw0

linfaalargada
28. 12. 2007
0 views

linfaalargada