Drag and Inertia on Inner Pipe Sections |
 
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Drag and Inertia on Inner Pipe Sections |
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Unlike elements that are exposed to the prescribed water particle motions, the drag, hydrodynamic inertia and added mass terms of the inner pipe-in-pipe elements are accommodated into the Finite Element Equation of Motion via the global damping matrix (for drag forces) and global mass matrix (for the hydrodynamic inertia and added mass). This is necessary because the fluid motion used to determine these loads depends on unknown solution variables that are not prescribed (as is the case for the ambient fluid). Further detail on the relevant implementation is outlined in the following points:
•Drag and hydrodynamic inertia loads depend on the motion of the surrounding fluid, typically the prescribed motion of the ambient sea water. The instantaneous hydrodynamic drag and inertia of a standard element surrounded by ambient seawater is therefore a known external force as it does not depend on any solution variables. In this case, the drag and hydrodynamic inertia is computed directly, and added to the global force vector on the right hand side of the finite element equations of motion.
•In the case of an inner pipe-in-pipe element, the motion of the annular fluid is assumed to be consistent with that of the outer element. Nodal velocities and accelerations in Flexcom are computed by taking derivatives of the instantaneous solution displacement variables. Therefore any terms dependent on the instantaneous motion of a finite element node are calculated as part of the finite element solution itself. For example, the added mass is computed alongside the element mass, and is included in the global mass matrix, as it depends on the instantaneous nodal acceleration which is itself a solution variable dependent term.
•While conceptually similar to added mass, incorporation of the hydrodynamic inertia load for inner elements is not quite so straightforward. Rather than the inner pipe acceleration, it is actually the acceleration of the outer pipe that is used to calculate the hydrodynamic inertia on the inner pipe.
•In a way similar to the hydrodynamic inertia above, the drag load applied to the inner elements has a dependency on the outer node velocity and modifications to the finite element connectivity for inner elements are made to capture this dependency also.
As discussed above, drag forces and hydrodynamic inertia on inner pipe-in-pipe elements are modelled as mass and damping terms on the left hand side of the equations of motion, capturing the required coupling between the outer node’s velocity/acceleration and the inner node loading. However this was not always the case, and in versions prior to Flexcom 8.6.3, drag and inertia were included directly as force terms on the right hand side of the equations of motion. This approach was theoretically incorrect, as it meant that the outer node’s velocity and acceleration at the previous time step was used to compute the drag forces and hydrodynamic inertia on the inner node at the current time step. Notwithstanding the theoretical limitation, it is conceivable that some software users may occasionally wish to invoke this modelling approach (for example, to quantify any level of inaccuracy associated with an earlier study). For this reason, it is possible to select the modelling approach (be it left hand side or right hand side) via the *PIP SECTION keyword (INNER_HYDRO option).
An inherent prerequisite for the left hand side modelling approach is that pipe-in-pipe connections must exist in the global connectivity matrix. In versions prior to Flexcom 8.10.1, such connections had to be explicitly created by the user, if there was no physical connection between all inner nodes and the outer pipe. In more recent versions of the software, token connections of zero stiffness are automatically inserted where required to ensure that hydrodynamic loading on all inner nodes is modelled. The procedure is as follows:
•Flexcom firstly identifies all potentially 'isolated inner nodes'. These are inner nodes which are not guaranteed to have a pipe-in-pipe connection to an outer node at all times during the simulation i.e. they do not form part of any standard connection, and they do not act as the primary node of any sliding connection (the latter case is highly unlikely, as recommended practice is to designate nodes on the outer pipe as primary nodes - refer to Primary and Secondary Pipes for further details).
•Secondly, a sliding connection is automatically created between each 'isolated inner node' and a suitable outer element set. A suitable element set is one which has been designated as an outer set via the *PIP SECTION keyword, and whose corresponding inner element set includes the 'isolated inner node'.
One disadvantage of this modelling procedure is that it may create a large number of additional pipe-in-pipe connections, which can have a negative impact on run-time performance. For example, let's suppose you have created a pipe-in-pipe model which has 100 nodes on the outer pipe and 100 nodes on the outer pipe. If the mesh densities are identical on both pipes, and you are expecting little or no relative axial sliding, then you would typically create 100 standard connections between the pipes. In this case, all inner nodes are guaranteed to have a pipe-in-pipe connection to an outer node at all times during the simulation, and no additional connections are created by the software.
If the mesh densities are similar on both pipes, but not identical, you might create 100 sliding connections, with each one linking an outer node with a set of inner elements. This means that the program will automatically determine the optimum configuration thereby reducing effort on your part (i.e. Flexcom figures out which nodes should be connected). As you are not anticipating any relative sliding, you would typically include the *NO PIP SLIDING keyword also for computational efficiency. This means that once the optimal configuration has been attained, the connections are effectively treated as standard rather than sliding from that point onwards. However, in order to guarantee with absolute certainty that no inner node is isolated from the outer pipe at any point during the entire simulation, Flexcom will automatically create 100 additional connections, with each one linking an inner node with a set of outer elements. So you now have 200 pipe-in-pipe connections rather than 100. This approach may be viewed as overly conservative by some software users for the following reasons:
•As the mesh densities are similar on both pipes, the majority of inner nodes will have an active connection to an outer node at all times during the simulation regardless.
•The additional connections are created and monitored purely as a fail-safe mechanism, and it is highly likely that most of them will be redundant at any given time during the simulation.
•Assuming that a small number of inner nodes do become 'isolated' at various stages during the simulation, the omission of a small proportion of the overall hydrodynamic loads is arguably unlikely to have a significant effect on the global response of an offshore structure.
In summary, some users may feel that the additional computational effort associated with the additional connections is simply not justified. So you have the option to:
•Suppress the creation of the additional connections via the *PIP SECTION keyword (AUTO_CREATE option).
•Check if any inner nodes become 'isolated' during the simulation, via the *PRINT keyword.
It should be noted that recommended practice is to accept the additional connections which guarantee correct application of hydrodynamic loading to all inner nodes at all times. If you reject the additional connections, then it is your responsibility to ensure that the model behaviour is consistent with expectations. In this case, some sensitivity studies would certainly be advisable.
•*PIP CONNECTION is used to define pipe-in-pipe connections between nodes of the finite element model.
•*NO PIP SLIDING is used to disable the interchangeable nature of sliding pipe-in-pipe connections.
•*PIP SECTION is used to define internal and external pipe sections when part of a pipe model is contained within another.
If you would like to see an example of how these keywords are used in practice, refer to A03 - Pipe-in-Pipe Production Riser (Standard Connections) and H02 - J-Tube Pull-In (Sliding Connections).