an introduction to finite area method (fam)
TRANSCRIPT
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Sam Fredriksson 1
buoyantBoussinesqSurfactantFoam
an introduction to
finite area method (fam)
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Sam Fredriksson 2
Gas exchange at air-water interface
Carbon Cycle – IPCC (2007)
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Sam Fredriksson 3
How are CO2 fluxes determined?Typically:
1.CO2 concentration in surface water(pCO2)
2.Flux model: F = k (Caq – Ceq)
3.Piston velocity/gas transfer koefficient (k) calculated from average wind speed at 10 m height.
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Sam Fredriksson 4
D. Bade 2009, Encycl. of Inland Waters
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Sam Fredriksson 5
Surfactant influence of flow field and gas transfer
McKenna 2000
Surface vorticity
Surface velocity
Surface divergence
Clean Oley alcohol II
k as a funct. of time(surfactant concentrationcholesterol)
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Sam Fredriksson 6
Computational domainEvaporation
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Sam Fredriksson 7
Boussinesq formulationMomentum and Continuity
U ∙ U1
ν
1 ,
∙ U 0Linear approximation of density
Temperature field is governed by a convection-diffusion equation given by
U ∙ T T S
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Sam Fredriksson 8
Temperature field, Raq ≈ 5x106
0.076 m
Played 10 times real time
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Sam Fredriksson 9
IR-measurements at Bornö
Magnus Gålfalk
≈ 1 m
Lz = 0.122 (0.08267) m
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Sam Fredriksson 10
Introduction to finite area method
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Sam Fredriksson 11
Computational space is curved substrate surface which is splited into a finite number of flat polygonal control areas (CA) bounded by arbitrary number of straight edges.
zy
x
Volume Elements
Control Areas
Tukovic, Jasak 2011
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Sam Fredriksson 12
Discretization to capture the surface integral transport equations on arbitrary polygonal unstructured meshes
Tukovic, Jasak 2011
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Sam Fredriksson 13
surfactantFoam - sphereTransport
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Sam Fredriksson 14
buoyantBoussinesqSurfactantFoam -convectiveSurfactantTransport
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Sam Fredriksson 15
Surfactant transport under convective flow 1(3)
Merge buoyantBoussinesqPisoFoam
and surfactantFoam
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Sam Fredriksson 16
Surfactant transport under convective flow 2(3)
enabling coupling coupling between fvm and fam
Us is taken from fvm where “surface” is the surface boundary (patch)
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Sam Fredriksson 17
Surfactant transport under convective flow 3(3)
And put it all together
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Sam Fredriksson 18
buoyantBoussinesqPisoSurfactantFoam 1(6)
Copy and rename the solver and edit Make/files and compile
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Sam Fredriksson 19
buoyantBoussinesqPisoSurfactantFoam 2(6)
Make/options has to be edited to include the path to buoyantBoussinesqSimpleFoam as well since the readTransportProperties.H is used in the buoyantBoussinesqPisoFoam.
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Sam Fredriksson 20
buoyantBoussinesqPisoSurfactantFoam 3(6)
In order to make it work for the solver where the finite area method is included we need to add a few lines to the Make/options as well.
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Sam Fredriksson 21
buoyantBoussinesqPisoSurfactantFoam 4(6)
Then we continue our merge of surfactantFoam and buoyantBoussinesqPisoFoamby copying surfactantFoam.C, createFaFields.H ../surfactantFoam into our ../buoyantBoussinesqPisoSurfactantFoam directory.
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Sam Fredriksson 22
buoyantBoussinesqPisoSurfactantFoam 5(6)
Now we enter buoyantBoussinesqPisoSurfactantFoam.C.
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Sam Fredriksson 23
buoyantBoussinesqPisoSurfactantFoam 6(6)
Include appropriate *.H files buoyantBoussinesqPisoSurfactantFoam.C.
save and compile
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Sam Fredriksson 24
Pre processing in tutorial
Creation of area mesh – ../constant/faMesh/–faMeshDefinition
–faLabel
–faBoundary
No turbulence model (Direct numerical simulation)
Boundary and initial condition - ../0/–Cs
–…
Solve and control - ../system–faSchemes
–faSolutions
–controlDict
–..
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Sam Fredriksson 25
faMeshDefinition and ../0/Cs
zy
x
Volume Elements
sideside
frontAndBack
frontAndBack
surface
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Sam Fredriksson 26
Running the tutorial
The case can be run by using the typing ./Allrun. If we look into Allrun we can see
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Sam Fredriksson 27
Post processing
Type paraFoam & and then open the results in VTK-format in order to have the same timing of the fam and the fvm results.