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Added mass from potentialFoam

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Old   December 18, 2018, 04:15
Default Added mass from potentialFoam
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Even Lund
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I want to use potentialFoam to find added mass of a cylinder. It is well known this geometry has an added mass equal to the displaced fluid (rho*pi*r^2*L).

Frank White, Fluid Mechanics, writes: "According to potential theory, mh depends only on the shape and direction of motion and can be computed by summing the total kinetic energy of the fluid relative to the body and setting this equal to an equivalent body energy: KEfluid=integral(0.5*dm*Vrel^2)=0.5*mh*U^2)", where mh is the added mass. I interpret this for a numeric solver so that mh=sum(dm*Vrel^2)/U^2=sum(dVolume*rho*Vrel^2)/U^2.

I have set up a model in OpenFOAM similarily to the example "Flow around a cylinder". The biggest difference being that the uppper and lower boundaries are set to walls with slip boundary condition, to enable uniform flow over the geometry. I have used 10 non-orthogonal corrector steps, to get correct results. I use a fluid volume that is about 4 diameters in the flow direction and 3 diameters across, use snappyHexMesh and extrudeMesh to get a nice mesh with boundary layers around the cylinder.

After solving with potentialFoam I extract the cell volume of each cell with "postProcess -func writeCellVolumes" and use an octave script to extract the cellvolume and velocity vectors from the OpenFOAM U and V files and calculate the added mass through a loop:

Code:
for i=1:L
  Urel=U(i,:)-Uinit;
  Urelsq=Urel.^2;
  dm=rho*V(i);
  mVsqtot=mVsqtot+dm*Urelsq;
end
madd=mVsqtot./Uinit.^2;
where Uinit is the input flow, a vector with 1 m/s in the X direction, rho is hardcoded to 1000 kg/m^3 (water) and mVsqtot is an accumulator for the sum of dm*Vrel^2.

Unfortunately this does not give me correct result of 2.86 kg for a cylinder with radius of 30.165 mm, length 1 m, but rather close to half of that, 1.4361 kg. What am I doing wrong? Is it correct that the viscosity set is neglected with potentialFoam, but what density is used?
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Old   May 8, 2022, 03:41
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ozi
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Ph.D.(c) Oğuzhan KIRIKBAŞ
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@ evenlund I encountered the same problem with DARPA Suboff geometry. Did you find any solution.
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Old   June 8, 2024, 19:59
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Joćo LeitÕ
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i believe what you calculated was the hydrodynamic mass which is added mass + displaced mass.

2.86 kg is 1.43*2 kg

so just subtract the displaced mass, and you get the added mass coefficient
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Old   June 11, 2024, 04:56
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Joćo, no I don't think that's it, my friend. He has calculated the kinetic energy of the fluid in the domain, and that is equal to the added mass times half the velocity squared - see the snippet below, from White's book.

Instead, I think it's much simpler - I think that he used the cylinder tutorial for potentialFoam. However, this case only models half the domain, and uses a symmetry plane on the centreline, so the KE sum will be only half the full value. He needs to double the sum, to get the full value, and then he'll get the proper added mass.


EDIT. Hmm ... maybe not - reading his post again, he talks about using snappyHexMesh, so presumably he has modelled the full domain.
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Old   June 11, 2024, 09:20
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Okay - I have it. There's a mistake in his calculation of the relative velocity magnitude. I initially did the same when I ran a quick test, and got the same (wrong) answer. He has calculated the velocity magnitude at a point in the flow, then subtracted the cylinder velocity.
U_{rel} = \sqrt{U_x^2 + U_y^2} - U_{cyl}

Instead, you should subtract the cylinder velocity just from the relevant component. E.g. with a cylinder moving in the x direction:
U_{rel} = \sqrt{(U_x - U_{cyl})^2 + U_y^2}

With the correct relative velocity formulation, you get an added mass coefficient of almost exactly 1 for the cylinder, even with a fairly crude mesh.
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