Simulation of a single bubble with a VOF-method
 

Hellow there,

I'm dealing with the topic of air bubbles ascending in stagnant water. When i was trying to simulate a bubble with 4 mm in diameter in a
rectangular 2D column of 40 mm width and 100 mm height with a grid size
of 0.125 mm (as recommended in a paper called "Simulating the motion of gas bubbles in a liquid" by Krishna, you can find it here http://ct-cr4.chem.uva.nl/ ), the results first looked pretty
well, but after a timestep of 10500 ( time steps = 10e-05 s ) the bubble abruptly breaks up. And I have the problem that the inner pressure field inside of the bubble is not developing. There is always the same pressure as in the surrounding water.

I used a uniform cartesian-coordinate grid. The front and rear faces of the column are modelled as symmetry planes and at the two walls the no-slip boundary condition is imposed. I used the homogenous model and the free surface model. I initialized the interface by using a step-function-expression that defines a circle near the lower bound of the domain. Then i smeared the interface by using a User Function so that CFX can handle the interface numerically in a better way. I used double precision to solve it....to make it short here the ccl-file:



# State file created: 2009/04/28 11:42:47
# CFX-11.0 build 2006.11.17-22.59

FLOW:
DOMAIN:Fluids
Coord Frame = Coord 0
Domain Type = Fluid
Fluids List = Air at 25 C,Water
Location = Assembly
BOUNDARY:Opening
Boundary Type = OPENING
Location = TOP
BOUNDARY CONDITIONS:
FLOW DIRECTION:
Option = Normal to Boundary Condition
END
FLOW REGIME:
Option = Subsonic
END
MASS AND MOMENTUM:
Option = Opening Pressure and Direction
Relative Pressure = 0 [Pa]
END
END
FLUID:Air at 25 C
BOUNDARY CONDITIONS:
VOLUME FRACTION:
Option = Value
Volume Fraction = 0
END
END
END
FLUID:Water
BOUNDARY CONDITIONS:
VOLUME FRACTION:
Option = Value
Volume Fraction = 1
END
END
END
END
BOUNDARY:Symmetry
Boundary Type = SYMMETRY
Location = BACK,FRONT
END
BOUNDARY:Walls
Boundary Type = WALL
Location = BOTTOM,LEFT,RIGHT
BOUNDARY CONDITIONS:
WALL INFLUENCE ON FLOW:
Option = No Slip
END
END
FLUID PAIR:Air at 25 C | Water
BOUNDARY CONDITIONS:
WALL ADHESION:
Option = None
END
END
END
END
DOMAIN MODELS:
BUOYANCY MODEL:
Buoyancy Reference Density = 1.185 [kg m^-3]
Gravity X Component = 0 [m s^-2]
Gravity Y Component = -9.81 [m s^-2]
Gravity Z Component = 0 [m s^-2]
Option = Buoyant
BUOYANCY REFERENCE LOCATION:
Option = Automatic
END
END
DOMAIN MOTION:
Option = Stationary
END
MESH DEFORMATION:
Option = None
END
REFERENCE PRESSURE:
Reference Pressure = 1 [atm]
END
END
FLUID:Air at 25 C
FLUID MODELS:
FLUID BUOYANCY MODEL:
Option = Density Difference
END
MORPHOLOGY:
Minimum Volume Fraction = 10e-15
Option = Continuous Fluid
END
END
END
FLUID:Water
FLUID MODELS:
FLUID BUOYANCY MODEL:
Option = Density Difference
END
MORPHOLOGY:
Option = Continuous Fluid
END
END
END
FLUID MODELS:
COMBUSTION MODEL:
Option = None
END
HEAT TRANSFER MODEL:
Fluid Temperature = 300 [K]
Homogeneous Model = True
Option = Isothermal
END
THERMAL RADIATION MODEL:
Option = None
END
TURBULENCE MODEL:
Option = Laminar
END
END
FLUID PAIR:Air at 25 C | Water
Surface Tension Coefficient = 0.073 [N m^-1]
INTERPHASE TRANSFER MODEL:
Option = None
END
MASS TRANSFER:
Option = None
END
SURFACE TENSION MODEL:
Curvature Under Relaxation Factor = 0.5
Option = Continuum Surface Force
Primary Fluid = Water
Volume Fraction Smoothing Type = Volume-Weighted
END
END
INITIALISATION:
Option = Automatic
FLUID:Air at 25 C
INITIAL CONDITIONS:
VOLUME FRACTION:
Option = Automatic with Value
Volume Fraction = VF Init
END
END
END
FLUID:Water
INITIAL CONDITIONS:
VOLUME FRACTION:
Option = Automatic with Value
Volume Fraction = 1-VF Init
END
END
END
INITIAL CONDITIONS:
Velocity Type = Cartesian
CARTESIAN VELOCITY COMPONENTS:
Option = Automatic with Value
U = 0 [m s^-1]
V = 0 [m s^-1]
W = 0 [m s^-1]
END
STATIC PRESSURE:
Option = Automatic with Value
Relative Pressure = 0 [Pa]
END
END
END
MULTIPHASE MODELS:
Homogeneous Model = On
FREE SURFACE MODEL:
Interface Compression Level = 2
Option = Standard
END
END
SOURCE POINT:Source Point 1
Cartesian Coordinates = 0.02 [m], 0.005 [m], 0 [m]
Option = Cartesian Coordinates
END
END
EXPERT PARAMETERS:
ggi permit no intersection = t
old surface tension numerics = t
END
OUTPUT CONTROL:
RESULTS:
File Compression Level = Default
Option = Standard
END
TRANSIENT RESULTS:Transient Results 1
File Compression Level = Default
Option = Standard
OUTPUT FREQUENCY:
Option = Timestep Interval
Timestep Interval = 50
END
END
END
SIMULATION TYPE:
Option = Transient
EXTERNAL SOLVER COUPLING:
Option = None
END
INITIAL TIME:
Option = Automatic with Value
Time = 0 [s]
END
TIME DURATION:
Option = Total Time
Total Time = 2 [s]
END
TIME STEPS:
Option = Timesteps
Timesteps = 1e-05 [s]
END
END
SOLUTION UNITS:
Angle Units = [rad]
Length Units = [m]
Mass Units = [kg]
Solid Angle Units = [sr]
Temperature Units = [K]
Time Units = [s]
END
SOLVER CONTROL:
ADVECTION SCHEME:
Option = High Resolution
END
BODY FORCES:
Body Force Averaging Type = Harmonic
END
CONVERGENCE CONTROL:
Maximum Number of Coefficient Loops = 10
Timescale Control = Coefficient Loops
END
CONVERGENCE CRITERIA:
Residual Target = 1.E-4
Residual Type = RMS
END
MULTIPHASE CONTROL:
Volume Fraction Coupling = Coupled
END
PRESSURE LEVEL INFORMATION:
Option = Automatic
Pressure Level = 1 [atm]
END
TRANSIENT SCHEME:
Option = Second Order Backward Euler
TIMESTEP INITIALISATION:
Option = Automatic
END
END
END
END

LIBRARY:
CEL:
EXPRESSIONS:
VF Init = Verschmierung((2[mm]-sqrt((x-20[mm] )^2+(y-5[mm] )^2)))
END
FUNCTION:Verschmierung
Argument Units = mm
Option = Interpolation
Result Units = m/m
INTERPOLATION DATA:
Data Pairs = -0.2,0,0.2,1
Extend Max = On
Extend Min = On
Option = One Dimensional
END
END
END
MATERIAL:Air Ideal Gas
Material Description = Air Ideal Gas (constant Cp)
Material Group = Air Data, Calorically Perfect Ideal Gases
Option = Pure Substance
Thermodynamic State = Gas
PROPERTIES:
Option = General Material
ABSORPTION COEFFICIENT:
Absorption Coefficient = 0.01 [m^-1]
Option = Value
END
DYNAMIC VISCOSITY:
Dynamic Viscosity = 1.831E-05 [kg m^-1 s^-1]
Option = Value
END
EQUATION OF STATE:
Molar Mass = 28.96 [kg kmol^-1]
Option = Ideal Gas
END
REFERENCE STATE:
Option = Specified Point
Reference Pressure = 1 [atm]
Reference Specific Enthalpy = 0. [J/kg]
Reference Specific Entropy = 0. [J/kg/K]
Reference Temperature = 25 [C]
END
REFRACTIVE INDEX:
Option = Value
Refractive Index = 1.0 [m m^-1]
END
SCATTERING COEFFICIENT:
Option = Value
Scattering Coefficient = 0.0 [m^-1]
END
SPECIFIC HEAT CAPACITY:
Option = Value
Specific Heat Capacity = 1.0044E+03 [J kg^-1 K^-1]
Specific Heat Type = Constant Pressure
END
THERMAL CONDUCTIVITY:
Option = Value
Thermal Conductivity = 2.61E-2 [W m^-1 K^-1]
END
END
END
MATERIAL:Water Ideal Gas
Material Description = Water Vapour Ideal Gas (100 C and 1 atm)
Material Group = Calorically Perfect Ideal Gases, Water Data
Option = Pure Substance
Thermodynamic State = Gas
PROPERTIES:
Option = General Material
ABSORPTION COEFFICIENT:
Absorption Coefficient = 1.0 [m^-1]
Option = Value
END
DYNAMIC VISCOSITY:
Dynamic Viscosity = 9.4E-06 [kg m^-1 s^-1]
Option = Value
END
EQUATION OF STATE:
Molar Mass = 18.02 [kg kmol^-1]
Option = Ideal Gas
END
REFERENCE STATE:
Option = Specified Point
Reference Pressure = 1.014 [bar]
Reference Specific Enthalpy = 0. [J/kg]
Reference Specific Entropy = 0. [J/kg/K]
Reference Temperature = 100 [C]
END
REFRACTIVE INDEX:
Option = Value
Refractive Index = 1.0 [m m^-1]
END
SCATTERING COEFFICIENT:
Option = Value
Scattering Coefficient = 0.0 [m^-1]
END
SPECIFIC HEAT CAPACITY:
Option = Value
Specific Heat Capacity = 2080.1 [J kg^-1 K^-1]
Specific Heat Type = Constant Pressure
END
THERMAL CONDUCTIVITY:
Option = Value
Thermal Conductivity = 193E-04 [W m^-1 K^-1]
END
END
END
MATERIAL:Aluminium
Material Group = CHT Solids, Particle Solids
Option = Pure Substance
Thermodynamic State = Solid
PROPERTIES:
Option = General Material
EQUATION OF STATE:
Density = 2702 [kg m^-3]
Molar Mass = 26.98 [kg kmol^-1]
Option = Value
END
REFERENCE STATE:
Option = Specified Point
Reference Specific Enthalpy = 0 [J/kg]
Reference Specific Entropy = 0 [J/kg/K]
Reference Temperature = 25 [C]
END
SPECIFIC HEAT CAPACITY:
Option = Value
Specific Heat Capacity = 9.03E+02 [J kg^-1 K^-1]
END
THERMAL CONDUCTIVITY:
Option = Value
Thermal Conductivity = 237 [W m^-1 K^-1]
END
END
END
MATERIAL:Steel
Material Group = CHT Solids, Particle Solids
Option = Pure Substance
Thermodynamic State = Solid
PROPERTIES:
Option = General Material
EQUATION OF STATE:
Density = 7854 [kg m^-3]
Molar Mass = 55.85 [kg kmol^-1]
Option = Value
END
REFERENCE STATE:
Option = Specified Point
Reference Specific Enthalpy = 0 [J/kg]
Reference Specific Entropy = 0 [J/kg/K]
Reference Temperature = 25 [C]
END
SPECIFIC HEAT CAPACITY:
Option = Value
Specific Heat Capacity = 4.34E+02 [J kg^-1 K^-1]
END
THERMAL CONDUCTIVITY:
Option = Value
Thermal Conductivity = 60.5 [W m^-1 K^-1]
END
END
END
MATERIAL:Copper
Material Group = CHT Solids, Particle Solids
Option = Pure Substance
Thermodynamic State = Solid
PROPERTIES:
Option = General Material
EQUATION OF STATE:
Density = 8933 [kg m^-3]
Molar Mass = 63.55 [kg kmol^-1]
Option = Value
END
REFERENCE STATE:
Option = Specified Point
Reference Specific Enthalpy = 0 [J/kg]
Reference Specific Entropy = 0 [J/kg/K]
Reference Temperature = 25 [C]
END
SPECIFIC HEAT CAPACITY:
Option = Value
Specific Heat Capacity = 3.85E+02 [J kg^-1 K^-1]
END
THERMAL CONDUCTIVITY:
Option = Value
Thermal Conductivity = 401.0 [W m^-1 K^-1]
END
END
END
MATERIAL:Soot
Material Group = Soot
Option = Pure Substance
Thermodynamic State = Solid
PROPERTIES:
Option = General Material
ABSORPTION COEFFICIENT:
Absorption Coefficient = 0 [m^-1]
Option = Value
END
EQUATION OF STATE:
Density = 2000 [kg m^-3]
Molar Mass = 12 [kg kmol^-1]
Option = Value
END
REFERENCE STATE:
Option = Automatic
END
END
END
MATERIAL:Air at 25 C
Material Description = Air at 25 C and 1 atm (dry)
Material Group = Air Data, Constant Property Gases
Option = Pure Substance
Thermodynamic State = Gas
PROPERTIES:
Option = General Material
Thermal Expansivity = 0.003356 [K^-1]
ABSORPTION COEFFICIENT:
Absorption Coefficient = 0.01 [m^-1]
Option = Value
END
DYNAMIC VISCOSITY:
Dynamic Viscosity = 1.831E-05 [kg m^-1 s^-1]
Option = Value
END
EQUATION OF STATE:
Density = 1.185 [kg m^-3]
Molar Mass = 28.96 [kg kmol^-1]
Option = Value
END
REFERENCE STATE:
Option = Specified Point
Reference Pressure = 1 [atm]
Reference Specific Enthalpy = 0. [J/kg]
Reference Specific Entropy = 0. [J/kg/K]
Reference Temperature = 25 [C]
END
REFRACTIVE INDEX:
Option = Value
Refractive Index = 1.0 [m m^-1]
END
SCATTERING COEFFICIENT:
Option = Value
Scattering Coefficient = 0.0 [m^-1]
END
SPECIFIC HEAT CAPACITY:
Option = Value
Specific Heat Capacity = 1.0044E+03 [J kg^-1 K^-1]
Specific Heat Type = Constant Pressure
END
THERMAL CONDUCTIVITY:
Option = Value
Thermal Conductivity = 2.61E-02 [W m^-1 K^-1]
END
END
END
MATERIAL:Water
Material Description = Water (liquid)
Material Group = Water Data, Constant Property Liquids
Option = Pure Substance
Thermodynamic State = Liquid
PROPERTIES:
Option = General Material
Thermal Expansivity = 2.57E-04 [K^-1]
ABSORPTION COEFFICIENT:
Absorption Coefficient = 1.0 [m^-1]
Option = Value
END
DYNAMIC VISCOSITY:
Dynamic Viscosity = 8.899E-4 [kg m^-1 s^-1]
Option = Value
END
EQUATION OF STATE:
Density = 997.0 [kg m^-3]
Molar Mass = 18.02 [kg kmol^-1]
Option = Value
END
REFERENCE STATE:
Option = Specified Point
Reference Pressure = 1 [atm]
Reference Specific Enthalpy = 0.0 [J/kg]
Reference Specific Entropy = 0.0 [J/kg/K]
Reference Temperature = 25 [C]
END
REFRACTIVE INDEX:
Option = Value
Refractive Index = 1.0 [m m^-1]
END
SCATTERING COEFFICIENT:
Option = Value
Scattering Coefficient = 0.0 [m^-1]
END
SPECIFIC HEAT CAPACITY:
Option = Value
Specific Heat Capacity = 4181.7 [J kg^-1 K^-1]
Specific Heat Type = Constant Pressure
END
THERMAL CONDUCTIVITY:
Option = Value
Thermal Conductivity = 0.6069 [W m^-1 K^-1]
END
END
END

I hope there is anybody out there who tried the bubble simulation a bit more successfully than i did......i would be very thankful about some help and hints.....blubb

Hi:

Some comments:

Why have you set "ggi permit no intersection = t" and "old surface tension numerics = t". Unless you have a specific reason to set them I would return to the defaults.

Turn volume fraction smoothing to "none"

Use adaptive timestepping, adapting to give 3-6 iterations per timestep.

With surface tension modelling you have to use MUCH smaller timesteps than otherwise (and much smaller than you probably expect).

Glenn Horrocks

Thanks ghorrocks,

i set the old surface tension numerics=t because this option reduces the so called spurious currents. That are little eddies that develop near the interface by using a VOF-method. The ggi permit no intersection=t should have no effect on my simulation as no ggi interface is used for my model. But I returned it to default and now i'm giving the adaptive timestepping a try....the timestep should be fine enough as i found papers about bubble simulations in cfx with the same timestepsize! I'll let u know what happened...:rolleyes:

Bad news...adaptive timestepping leads to an even faster breakup. It happens after timestep 3950. I`m really desperate...isn`t there anybody who succeeded in simulating a little single bubble?:confused:

Hi,

Have you tried "Volume Fraction Smoothing = None"? I suggested it because it has caused weird surface behaviour for me before and as long as your mesh is fine enough to resolve the surface nicely you don't need any smoothing (in my experience).

Also if you could post some images of the initial condition and bubble breakup that would help.

Glenn Horrocks

That are pics from the results of my first settings i've posted...
a ....after 0 timesteps
b.... after 4000 timesteps
c....after 8000 timesteps
d....after 1200 timesteps

And that are pics from the results of adaptive timestepping...the number behind the name of the file shows the timestep...now i`ll try to set the volume fraction smoothing type to none and hope that will work...thanks for your help :)

Hi,

A finer mesh will definitely help and tighter convergence might also help. You need to establish mesh, timestep and convergence sensitivity for your simulation before it will be accurate.

Glenn Horrocks

Which mesh size can you recommend? Until now i`ve worked with a mesh size of 0.125 mm in all directories, so that there are 32 grid cells per bubble-diameter and 804 grid cells per bubble-cross section...thought this might me fine enough...

Hi,

A quote from my last post - "You need to establish mesh, timestep and convergence sensitivity for your simulation before it will be accurate." These parameters are all problem dependent so you have to establish it for each case. With a bit of experience you should be able to make a pretty good guess as to the required mesh, timestep and convergence levels required for your work, but if you have not done it yet then you must do it if you want accurate simulations.

Glenn Horrocks

Hellowww....me again:rolleyes:

Thank u Glenn. Here are the first results with the volume fraction smoothing type set to none...i`m still wondering why the pressure inside the bubble is not developing, there should be a higher pressure than in the surrounding fluid. And additionally there should develop a higher pressure at the front side of the bubble than at the bottom side...
Has anybody an idea why it looks that way? Has it something to do with the homogeneous model i`m using?

Kind regards
Susann

and the rest of the pics...

hi,

is it possible to get a higher inner bubble pressure with the homogeneous transport?
Homogeneous model means shared velocityfield, so there it could only be the surface tension increasing the inner pressure?
Or am i missing smth?

neewbie

Hi,

I will quote it for the third time. "You need to establish mesh, timestep and convergence sensitivity for your simulation before it will be accurate." If you are having problems with accuracy have you checked that your mesh is fine enough to be accurate, your timestep is OK and you are converging tight enough? I can see from your volume fraction plot you have a relatively coarse mesh so you will be heaps more accurate with a finer mesh.

Also surface tension models often require double precision to run well. I would turn double precision on anyway just to be sure.

Also to see the pressure effects you will have to zoom into the pressure range near the bubble rather than the full range. Or even better look at the pressure without the hydrostatic head component. The pressure effects are likely to be small compared to the hydrostatic head so you will have to be careful to see it.

Glenn Horrocks

please help me
 

hi suzzn
I modeled a bubble of gas in a tube with rectungular cross section at cfx 10.
But can you briefly tell me how to apply VOF and multiphase flow in this model?
thanks

Do the tutorials, and have a look at the CCL you quoted. Also upgrade to V12, it has much improved free surface modelling capbilities.

hi
thanks for your help
but,I do all of the tutorials, and apply vof and multiphase to my model.
my model: a bubble of air modeled by a sphere,and the tube by a box.
but i want to move sphere through a tube?
what do I do?:confused:
thanks

If the tutorials and descriptions here aren't enough to get you started then I think you need to do a CFX multiphase training course. Talk to your CFX support people about what training courses they offer.

If you have done ALL the tutorials:
- Do again the relevant tutorials for your problem (and try to understand what you're doing)
- Try to implement your problem. Start by the simplest possible case.
- When asking questions here, you have to give more information about what you have done and what you cannot do (do really think someone is going to understand what you're asking by "I want to move sphere. What do I do?" ? ... and don't say your English is bad, because the your English is perfectly understandable)

hi
i just try to simulate this ccl file
everything goes fine except timestep interval option that i don't have it in my cfx 18 ?
what should i do to use that option in output frequency?
and in general how should i use that? i search all over net but didn't get much info. look for it in cfx help but it isn't useful.
if you have tutorial or any comment i will be thank for that.

If you load the def file and CCL you want into CFX-Pre it will put it into your version's format. Keywords it does not recognise will be missing, so you can add those using the GUI.

I dont load that CCL file ! just add all options and setting by GUI.
i found all of it except "timestep interval" that missing from option.