CFD Online Discussion Forums - Added mass from potentialFoam

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?