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RotatingWallVelocity Boundary Condition: mathematical and physical explanation?

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Old   June 19, 2015, 07:27
Default RotatingWallVelocity Boundary Condition: mathematical and physical explanation?
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Dear All Foamers,

I am using the 'rotatingWallVelocity' boundary condition for a rotating device. The description of the boundary condition available in OpenFOAM is; "Replaces the normal of the patch value so the flux across the patch is zero"

I would appreciate if someone could explain how this type of boundary condition actually takes place, both from a mathematical point of view and from a physical point of view. In particular, I am curious on how the effect of the boundary condition is reflected on the flow field around the patch.

Many thanks in advance!
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Old   November 11, 2015, 23:29
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methma Rajamuni
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Quote:
Originally Posted by MrScience View Post
Dear All Foamers,

I am using the 'rotatingWallVelocity' boundary condition for a rotating device. The description of the boundary condition available in OpenFOAM is; "Replaces the normal of the patch value so the flux across the patch is zero"

I would appreciate if someone could explain how this type of boundary condition actually takes place, both from a mathematical point of view and from a physical point of view. In particular, I am curious on how the effect of the boundary condition is reflected on the flow field around the patch.

Many thanks in advance!
Hi,

If you look at the rotatingWallVelocityFvPatchVectorField.C file you will see how they have done it mathematically. Usually a boundary condition is updated in the member function updateCoeffs().

Code:
void Foam::rotatingWallVelocityFvPatchVectorField::updateCoeffs()
{
    if (updated())
    {
        return;
    }

    const scalar t = this->db().time().timeOutputValue();
    scalar om = omega_->value(t);

    // Calculate the rotating wall velocity from the specification of the motion
    const vectorField Up
    (
        (-om)*((patch().Cf() - origin_) ^ (axis_/mag(axis_)))
    );

    // Remove the component of Up normal to the wall
    // just in case it is not exactly circular
    const vectorField n(patch().nf());
    vectorField::operator=(Up - n*(n & Up));

    fixedValueFvPatchVectorField::updateCoeffs();
}
according to the angular velocity, omega and the axis of rotation they calculate the surface velocities on the patch.
Surface velocity of a cell face, Up = omega * (radius x axis), where radius = (patch().Cf() - origin_). radius x axis, '(patch().Cf() - origin_) ^ (axis_/mag(axis_))' give the direction of the velocity.

The they corrected Up if it is not tangential to the surface, by removing the component of Up along the normal direction to the surface. where n.Up (n & Up) give the magnitude along the normal direction.

In the physical point of view this is a no-slip boundary condition which assume the velocity on the surface of the patch is same as the velocity on the wall. This boundary condition is a no-penetration boundary condition as well since fluid particle do not penetrate to the wall because no flow velocity on the surface normal direction.

Best,

Methma
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