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Snap#1.png (113,841 bytes) Snap#2.png (43,263 bytes) |
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I agree that the dimensions are incorrect but by a factor of sqr(kappai) rather than 1/d (I am not sure what "d" is in the code snippet). Also according to eq. 11-163 in Mamoru Ishii, Takashi Hibiki Thermo-Fluid Dynamics of Two-Phase Flow Second Edition the expression should be divided by 18 rather than 3 so I think the correct expression is: R[celli] = (Cti/18)*Ut[celli]*sqr(kappai[celli]) *sqrt(1 - WeCr/We[celli])*exp(-WeCr/We[celli]); |
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Dear Henry, I am not sure how the unit sqr(kappai) missing since the local R (dimensionedScalar(kappai.dimensions()/dimTime, 0)) is 1/ms and the returned R (fvm::Su(R, kappai)) is in m/s*1/m = 1/s. kappai has the unit of 1/m. What am I missing here? All the literature of IATE is combined in Ishii's book, however the details of the derivations are usually missing. Although it is the same in one-group IATE, the equation you are referring to is for two-group IATE. I'd recommend checking Wu et. al, 1998 (One-group interfacial area transport in vertical bubbly flow) or Dr. Kim's thesis in 1999 (Interfacial Area Transport Equation and Measurement of Local Interfacial Characteristics) for more details. Back to the expression you provided, the 1/18 comes from how the sphericity (shape factor) is defined for assuming the bubbles to be in spherical shape, i.e. 1/36*PI(). However, please remember that the expression is for IATE not ICTE which is implemented in OpenFOAM. The "d" in the snippet refers to the Sauter mean diameter (shown below) which is updated after the kappaiEqn is solved in IATE.C. Foam::tmp<Foam::volScalarField> Foam::diameterModels::IATE::d() const { return d_; } If you want to calculate R[celli] in terms of kappai but not d then the you can replace d with 6/k which ensures both the units and the constant. Please see the equations 4 and 19 through 22 in the following link (https://snip.mathpix.com/nucerl/notes/11e456fc-17f4-427c-ab48-b927c863844a) for detailed explanation. Thank you, Erol. |
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fvm::Su(R, kappai) returns R as an explicit source which should and does have the units of kappai/time according to R[celli] = (Cti/18)*Ut[celli]*sqr(kappai[celli]) *sqrt(1 - WeCr/We[celli])*exp(-WeCr/We[celli]); From the references I have the term would be divided by 18. eq. 11-163 in Mamoru Ishii, Takashi Hibiki Thermo-Fluid Dynamics of Two-Phase Flow Second Edition I cannot work out the correspondence between your notes and the references I have. |
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Resolved in OpenFOAM-dev by commit 3aea199ebebd440e0032ad40e61e6c968b248ba5 |
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It's still not correct. Regardless of the explicit/implicit treatment, the IATE source must return 1/ms. The partial differential equation (dk/dt) has a unit of 1/ms. As I already mentioned, the term having a factor of 1/18 does not mean we can directly use it. OpenFOAM does not solve for interfacial are concentration (ai), it solves for interfacial curvature (kappai). You can see this in the implementation of the sink terms as well; Random Collision (Rrc) and Wake Entrainment (Rwe). The sources in the uploaded image are the same as your reference but the implementation is different. For the Turbulent Breakup, there are 2 ways: 1) Using kappai: R[celli] = (Cti/18)*Ut[celli]*kappai[celli] *sqrt(1 - WeCr/We[celli])*exp(-WeCr/We[celli]); 2) Using d_: const volScalarField& d(iate_.d()()); R[celli] = (Cti/3)*Ut[celli]/d[celli] *sqrt(1 - WeCr/We[celli])*exp(-WeCr/We[celli]); IATE General Form.png (161,601 bytes) |
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The dimensions of (Cti/18)*Ut[celli]*kappai[celli] *sqrt(1 - WeCr/We[celli])*exp(-WeCr/We[celli]); are 1/s, but R has dimensions of 1/ms so your proposed expression is incorrect. |
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I don't agree with your assessment of the 1/18. |
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From my understanding the internal R should have the unit of 1/s and once it’s multiplied by kappai through Su() then source R will have the unit of 1/ms. This is how it is done for the Rrc source as well. Though it uses implicit source treatment, Sp(). So, unless Su() somehow multiplies R with kappai in a way that I don’t understand, then I don’t know why the defined unit of R[celli] should be 1/ms instead of 1/s. |
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Where in Su() is R multiplied by kappai? |
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I guess I have a misunderstanding of what return fvm::Su(R, kappai); does. I think that’s where my confusion comes from. |
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Resolved by commit 3aea199ebebd440e0032ad40e61e6c968b248ba5 |
- Anonymous
