Non-newtonian fluid flow around a cylinder

Update: June 1, 2017
OpenFOAM 4.x

Case directory

$FOAM_TUTORIALS/incompressible/nonNewtonianIcoFoam/offsetCylinder

Summary

We calculate the flow of a non-Newtonian fluid in a channel with an obstacle on one side, up to 2 seconds later.

The fluid flows in from the region "left" (white part) at a velocity of 1 m/s and flows out from the region "right" (red part). No-slip conditions are set for the cylinder and channel walls, and the flow is solved as 2-dimensional with a single mesh in the Z direction.

Model geometry Model geometry

The meshes are as follows.

Mesh Meshes

The strain rate \dot{\gamma} and the viscosity coefficient ν of the non-Newtonian fluid have the relationship as follows.

\nu = \nu_\infty + \frac{\nu_0 - \nu_\infty}{1 + (m\dot{\gamma})^n}

The value of each parameter is defined in the file "constant/transportProperties" as follows.

transportModel  CrossPowerLaw;

CrossPowerLawCoeffs
{
    nu0         [0 2 -1 0 0 0 0]  0.01;
    nuInf       [0 2 -1 0 0 0 0]  10;
    m           [0 0 1 0 0 0 0]   0.4;
    n           [0 0 0 0 0 0 0]   3;
}

The calculation result is as follows.

Flow velocity (U) Flow velocity (U)
Pressure (p) Pressure (p)

If it is a Newtonian fluid, the flow velocity will be higher in the narrower channel, but since it is a non-Newtonian fluid, the flow velocity will be higher in the wider channel.

Commands

cp -r $FOAM_TUTORIALS/incompressible/nonNewtonianIcoFoam/offsetCylinder offsetCylinder
cd offsetCylinder

blockMesh
nonNewtonianIcoFoam

paraFoam

Calculation time

--- *Single, Core(TM) i7-2600 CPU @ 3.40GHz 3.40GHz

Reference