an introduction to finite area method (fam)

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buoyantBoussinesqSurfactantFoam

an introduction to

finite area method (fam)

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Gas exchange at air-water interface

Carbon Cycle – IPCC (2007)

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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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D. Bade 2009, Encycl. of Inland Waters

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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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Computational domainEvaporation

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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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Temperature field, Raq ≈ 5x106

0.076 m

Played 10 times real time

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IR-measurements at Bornö

Magnus Gålfalk

≈ 1 m

Lz = 0.122 (0.08267) m

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Introduction to finite area method

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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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Discretization to capture the surface integral transport equations on arbitrary polygonal unstructured meshes

Tukovic, Jasak 2011

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surfactantFoam - sphereTransport

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buoyantBoussinesqSurfactantFoam -convectiveSurfactantTransport

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Surfactant transport under convective flow 1(3)

Merge buoyantBoussinesqPisoFoam

and surfactantFoam

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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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Surfactant transport under convective flow 3(3)

And put it all together

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buoyantBoussinesqPisoSurfactantFoam 1(6)

Copy and rename the solver and edit Make/files and compile

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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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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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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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buoyantBoussinesqPisoSurfactantFoam 5(6)

Now we enter buoyantBoussinesqPisoSurfactantFoam.C.

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buoyantBoussinesqPisoSurfactantFoam 6(6)

Include appropriate *.H files buoyantBoussinesqPisoSurfactantFoam.C.

save and compile

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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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faMeshDefinition and ../0/Cs

zy

x

Volume Elements

sideside

frontAndBack

frontAndBack

surface

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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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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.