Fluid Flow Forces
In addition to the pressure expanding the pipe, there can be loads caused by momentum transfer. These loads are of several types:
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Drag forces due to friction between the fluid and the pipe wall
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Centrifugal forces due to redirection of the flow in pipe bends
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Pressure forces in pipe bends
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Point forces caused by for example pressure drops in valves and changes in pipe cross section
Drag Force
The drag force, Fd, always acts along the tangent of the pipe in the direction of the flow, t. Its contribution to the edge load per unit length is
where the subscript 'f' stands for fluid properties. The Darcy friction factor fD is a dimensionless coefficient that is specified on the Fluid Properties feature under Pipe Flow interface. For most friction models, it is effectively proportional to 1/Re, where is the local Reynolds number in the flow. Thus, the resulting magnitude of the drag force becomes proportional to the velocity.
In the Pipe Flow interface, Fd is computed and is made available for the Pipe Mechanics interface.
Centrifugal Force
The centrifugal force contribution to the edge load per unit length is
where the curvature vector is computed as a derivative of the edge tangent with respect to the length parameter
This vector is perpendicular to the tangent, and it points toward the local center of curvature. The centrifugal force acts in the direction opposite to the vector.
In the Pipe Flow interface, Fc is computed and is made available for the Pipe Mechanics interface.
Pressure Force
In curved pipes, the pressure force contribution to the edge load per unit length is
where po is the exterior pressure on the outside of the pipe.
In the Pipe Flow interface, Fp is computed and is made available for the Pipe Mechanics interface.
Junction Point Forces
Point loads are related to the momentum change due to the flow alteration at junction points. For each junction, the force can be computed as a jump in the quantity . Thus, the resulting point load can be written as
where the summation is performed over all pipe-ends at the junction point, and sn stands for either plus or minus sign depending on the flow direction.
One needs to use the functionality available on the Fluid-Pipe Interaction coupling node to apply the junction forces.