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Drag coefficient of sphere & spherical bubble at Re = 1 

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October 27, 2023, 04:52 
Drag coefficient of sphere & spherical bubble at Re = 1

#1 
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Na
Join Date: Feb 2022
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Hello, CFDers & OpenFOAMers
Recently, i am trying to validate the drag coefficient of sphere & spherical bubble at Re=1 with OpenFoam In my opinion, i think the difference between flow around sphere(fixed position) and spherical bubble(fixed position) is only depends on the boundary condition of the interface. In a word, if the boundary is noslip, it's a sphere, otherwise, a spherical bubble has slip interface. this topic is derived from professor Duineveld's publication: Bel Fdhila, R., Duineveld, P.C., 1996. The effect of surfactant on the rise of a spherical bubble at high Reynolds and Peclet numbers. Phys. Fluids 8, 310–321. The result of pimpleFoam simulated the sphere show me an perfect result, when Re is 1, the drag coefficient is 27.6, it is consistent with SchillerNewman equation(Cd=24/Re*(1+0.15*Re^0.687)). But, when I change the boundary condition from noslip to slip, the result is not consistent with HR equation(Cd=16/Re), my Cd result of spherical bubble is approximately equal to 13. that shoud be 16! Here are my case code: constant/transportProperties Code:
FoamFile { version 2.0; format ascii; class dictionary; location "constant"; object transportProperties; } // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * // transportModel Newtonian; nu [0 2 1 0 0 0 0] 2; Code:
/** C++ **\  =========    \\ / F ield  OpenFOAM: The Open Source CFD Toolbox   \\ / O peration  Version: v1812   \\ / A nd  Web: www.OpenFOAM.com   \\/ M anipulation   \**/ FoamFile { version 2.0; format ascii; class volScalarField; object p; } // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * // dimensions [0 2 2 0 0 0 0]; internalField uniform 0; boundaryField { inlet { type zeroGradient; } outlet { type fixedValue; value uniform 0; } bubbleInterface { type slip; //type fixedFluxPressure; //value $internalField; } symmetry { type symmetry; } front { type wedge; } back { type wedge; } } Code:
/** C++ **\  =========    \\ / F ield  OpenFOAM: The Open Source CFD Toolbox   \\ / O peration  Version: v1812   \\ / A nd  Web: www.OpenFOAM.com   \\/ M anipulation   \**/ FoamFile { version 2.0; format ascii; class volVectorField; location "0"; object U; } // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * // dimensions [0 1 1 0 0 0 0]; internalField uniform (1 0 0); boundaryField { inlet { type fixedValue; value uniform (1 0 0); } outlet { type zeroGradient; } bubbleInterface { type slip; } symmetry { type symmetry; } front { type wedge; } back { type wedge; } } Code:
FoamFile { version 2.0; format ascii; class dictionary; object fvSchemes; } // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * // ddtSchemes { default backward; } gradSchemes { default cellLimited leastSquares 1; } divSchemes { default none; div(phi,U) Gauss upwind; div((nuEff*dev2(T(grad(U))))) Gauss linear; } laplacianSchemes { default Gauss linear limited 1; } interpolationSchemes { default linear; } snGradSchemes { default limited 1; } system/fvSolution Code:
FoamFile { version 2.0; format ascii; class dictionary; object fvSolution; } // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * // solvers { p { solver GAMG; tolerance 1e6; relTol 0; smoother GaussSeidel; nPreSweeps 0; nPostSweeps 2; cacheAgglomeration on; agglomerator faceAreaPair; nCellsInCoarsestLevel 100; mergeLevels 1; minIter 2; } pFinal { $p; relTol 0; minIter 2; } "(UUFinal)" { solver PBiCGStab; preconditioner DILU; tolerance 1e08; relTol 0; } } PIMPLE { momentumPredictor yes; consistent yes; nOuterCorrectors 2; nCorrectors 2; nNonOrthogonalCorrectors 1; //pRefCell 0; //pRefValue 0; } relaxationFactors { fields { ".*" 0.9; } equations { ".*" 0.9; } } system/controlDict Code:
/** C++ **\  =========    \\ / F ield  OpenFOAM: The Open Source CFD Toolbox   \\ / O peration  Version: v1812   \\ / A nd  Web: www.OpenFOAM.com   \\/ M anipulation   \**/ FoamFile { version 2.0; format ascii; class dictionary; location "system"; object controlDict; } // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * // application pimpleFoam; startFrom latestTime; startTime 0; stopAt endTime; endTime 50; deltaT 1; writeControl adjustableRunTime; writeInterval 1; purgeWrite 0; writeFormat ascii; writePrecision 8; writeCompression off; timeFormat general; timePrecision 6; runTimeModifiable yes; adjustTimeStep yes; maxCo 1; maxDeltaT 0.01; functions { Forces { type forces; libs ("libforces.so"); patches (bubbleNoSlipWall bubbleSlipWall); log false; rho rhoInf; rhoInf 1; CofR (0 0 0); liftDir (0 1 0); dragDir (1 0 0); writeControl adjustableRunTime; writeInterval 1; } forceCoeffs { type forceCoeffs; libs ("libforces.so"); patches (bubbleNoSlipWall bubbleSlipWall); log true; rho rhoInf; rhoInf 1; CofR (0 0 0); liftDir (0 1 0); dragDir (1 0 0); pitchAxis (0 0 1); magUInf 1; // the velocity of flow at far field is 1/ms, then, Re=U*D/nu=1*2/2=1; lRef 2; //Diameter is 2, radiu is 1 Aref 0.04363323129985824; //5°Wedge Mesh, the project area is PI*1*1*5/360; writeControl adjustableRunTime; writeInterval 1; } }; Thanks! All Best, Na 

December 8, 2023, 15:04 

#2 
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Join Date: Dec 2019
Location: Cologne, Germany
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that is a cool project!
first of all, a bubble has lower drag bc of internal circulation, if you model it like a solid sphere and just apply a slip BC, that is not enough. you do not resolve the inner circulation! the Hadamard–Rybczynski correction has viscosity terms! if you do not resolve the bubble, where is your viscosity then? the better approach to validate this would be VoF simulation (interFoam) 

January 30, 2024, 14:44 
Unable to validate Cd for rigid sphere

#3 
New Member
Jayabrata Dhar
Join Date: Nov 2018
Posts: 17
Rep Power: 7 
Hi Foamers,
I am new to pimpleFoam and was trying to validate the overall drag on a sphere due to a flow past it. I used the entries as stated above with the given geometry, I am not getting the drag coefficient of 27.6, I am getting something around 40. I have attached my case, it would be helpful if anyone could spot where I am going wrong or share any comment that would help me validate the same. Also, is there a 3D version for such validation in OF? PS: To run the case, one has to convert the .geo file in constant to .msh using GMSH and then use the two following commands: Code:
gmshToFoam constant/sphere.msh pimpleFoam Thanks in anticipation, JD 

February 1, 2024, 21:01 

#4  
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Maoqiang Jiang
Join Date: Jun 2021
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Quote:


February 2, 2024, 13:03 

#5  
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Join Date: Feb 2023
Location: Lyon, France
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Hello Foamers,
So I'm also investigating a similar problem with an implementation of the Navier slip for the modeling of flow around bubbles with different "surface contamination" level. While trying to validate an implementation of the Navier Slip BC, I Noticed that the solution (for the case where the slip length tends to infinity, which means the free slip condition) doesn't fit the analytical one. And I have similar results to MontelukastNa. i.e for Re = 1, for the noslip condition (case of a solid sphere) and for the slip (case of a clean bubble). Looking at the tangential velocity at the bubble's surface, it reaches a maximum of instead of the analytical solution of Some investigation. I found this bug report dating from 2016 where the author claims that he has a better solution when using the symmetry (geometry) condition on the surface of the sphere. I tried it, and it does work and provides the correct value for the drag coefficient, i.e for . Looking at the code, both the the slip condition and the symmetry patch type are implemented by inheriting basicSymmetryFvPatch so the two are equivalent. (reference) The symmetry condition is a geometrical one, and the only difference is that the symmetry condition ensures that the basicSymmetry condition is applied to ALL the fields. As Mr Henry Weller put it in his response. Quote:
I haven't had an opportunity to investigate this further yet, and would be interested if you have any idea on why we have such a discrepancy? I would be posting here some simple test cases when possible. Note : this seems to be happening only with curved patches. AFAIK this discrepancy between the slip and symmetry conditions doesn't show for planar problems. TLDR: Use the symmetry geometrical condition for curved patches. The slip boundary condition (although sharing the same implementation) seems to underpredict the drag force (and overpredict the max tangential slip velocity) for curved patches. Kamel O. 

February 4, 2024, 00:11 

#6 
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Jayabrata Dhar
Join Date: Nov 2018
Posts: 17
Rep Power: 7 
Hi,
I have attempted to solve for Re=1 but cannot get the 24.7 value for Cd. I have attached my files two replies before in this thread, can you help me with the issue and where I am doing wrong, it would be of great help, thanks. Jay 

February 5, 2024, 05:12 

#7  
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Quote:
I have no problem for the case of the solid sphere. Are you sure you're setting the noSlip condition on the velocity and zeroGradient on the pressure ? can you provide the mesh for your case as I dont have Gmsh available. Kamel 

February 6, 2024, 02:52 

#8  
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Jayabrata Dhar
Join Date: Nov 2018
Posts: 17
Rep Power: 7 
Quote:
Hi, Yes, I have essentially used noSlip, I have used a zero velocity boundary condition, you may view that in my zip file previously attached. For pressure, I am also using zeroGradient, I don't know where I am missing something. You can find my constant folder with the .msh file as well as the compiled mesh in this link: https://drive.google.com/file/d/1TPD...ew?usp=sharing You can also email me at jayabratadhar03@gmail.com in case if you wish to share some files.Thanks a lot for your kind reply. Best Regards, Jay 

February 9, 2024, 10:58 
Cd found to be 40 instead of 27.6

#9 
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Nipin L
Join Date: Nov 2012
Location: India
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Hi,
I too get Cd ~40 for sphere, with Re=1 in axisymmetric case. Could you sort out the issue? 

February 9, 2024, 23:54 

#10 
New Member
Jayabrata Dhar
Join Date: Nov 2018
Posts: 17
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Hi,
Let me know if you have solved the issue with Cd~40 and not ~27 (which is right) for Re=1. Thanks, 

February 10, 2024, 10:31 
Solved. Got the value 27.538

#11 
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Nipin L
Join Date: Nov 2012
Location: India
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Finer mesh (specially near to boundary)solved the problem. For those who are interested, please find the attached case file and gmsh script.


February 11, 2024, 12:03 

#12 
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Jayabrata Dhar
Join Date: Nov 2018
Posts: 17
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Thanks a lot, Nipin L for the files. I have made some changes in the run.sh and controlDict file since it was not running properly (maybe due to compatible issues) and reattaching the files for further help to new Foamers. The present file is checked to run with OpenFOAM v8 and v10.
Preferably, install Gmsh v2.16 (a later version would work, then export the mesh in version 2 format). hope it helps! Thanks. 

February 19, 2024, 02:05 

#13  
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Maoqiang Jiang
Join Date: Jun 2021
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Quote:
Could you share the case files for the flow past a bubble? I used symmetry boundary conditions on bubble's surface, but still did not get satisfactory drag force. Thanks in advance 

Tags 
bubble velocity, drag coefficient, stokes flow 
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