Centrifugal Force |
 
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Centrifugal Force |
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Internal fluid flow through a curved pipe introduces a centrifugal force (Patrikalakis, 1986) defined as follows:
(1)
where:
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is the centrifugal force vector
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is the mass of the entrained fluid
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is the velocity of the entrained fluid
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is the curvature vector
The centrifugal force is included in the external virtual work equation and expanded to facilitate incorporation into the Flexcom equations of motion, resulting in two additional terms. The first of these is applied as an additional loading to the element ends on the right hand side of the equations of motion, and this corresponds to Equation (1) above. The second term is conjugate to effective tension and is incorporated into the stiffness matrix on the left hand side of the equations of motion – refer to Dynamic Pressure for further details.
The figure below shows a rigid spool, a type of structure where centrifugal forces play an important role. Earlier versions of the software determined curvature from the nodal rotations, but this approach is unsuitable for structures which are unstressed in a curved configuration (e.g. goosenecks). The Flexcom output for rotational degrees of freedom basically define how the instantaneous or convected axes rotate from their initial, undeformed orientation. This means that for unstressed curved structures such as rigid spools, the curvature as determined from nodal rotations is practically zero, whereas in reality this is obviously not the case.
The centrifugal force is now evaluated on an element-by-element basis, with separate computations for each of its end nodes. The curvature vector at a given node is based on the instantaneous location of the node, and two adjacent nodes, located on either side of it. Given three points in space, it is possible to compute the curvature vector using standard geometrical relationships, and the centrifugal force is assumed to act in a direction consistent with the curvature vector (i.e. normal to the maximum curvature).
As the curvature computation is based on three successive nodes, naturally any element set which is used to define internal fluid loading or slug flow is assumed to be comprised of a continuous line of connected elements. Note also that for nodes located at model extremities, there is only one “adjacent” node, so no centrifugal force is applied.
Rigid Spool
•*INTERNAL FLUID is used to define the properties of an internal fluid. Centrifugal forces are included by default, but the CENTRIFUGAL= option allows you to suppress the effects of centrifugal forces in a particular analysis, allowing the relative significance of these loads to be assessed.
•*PRINT is used to request additional printed output to the main output file. Specifically, the OUTPUT=CENTRIFUGAL option is used to request additional data pertaining to centrifugal force application.