Hydrodynamic Forces |
 
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Hydrodynamic Forces |
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The main fluid forces modelled by Flexcom include buoyancy, hydrodynamic and internal fluid.
•Buoyancy forces effectively represent the resultant of the sum of all the pressure forces acting on a particular element. Theoretically, the net buoyancy force may be shown to correspond exactly to the volume of displaced fluid, and this is the modelling approach adopted by Flexcom. Refer to Buoyancy Forces for further details.
•Hydrodynamic forces are computed based on Morison’s Equation, and include three distinct components, drag, added mass and hydrodynamic inertia. Refer to Hydrodynamic Loading for further details.
•Flexcom provides a comprehensive internal fluid modelling capability. Stationary internal fluids, uniform steady state internal fluid flow and multi-phase slug flow may all be modelled. Refer to Internal Fluid for further details.
Each of these three areas is also influenced by the presence of pipe-in-pipe data. In the absence of pipe-in-pipe, the program operates in standard fashion, as outlined in the relevant sections quoted above. Pipe-in-pipe introduces some subtle differences over the standard modelling procedures, as now documented.
For pipe-on-pipe set-ups, the primary and secondary sections are both exposed to the ambient environment. There are no ‘outer’ or ‘inner’ sections, as none have been defined using *PIP SECTION. So the program operation in terms of buoyancy, hydrodynamics and internal fluid is the same as normal, and the remainder of this page is immaterial.
For pipe-in-pipe configurations, there are clearly defined ‘outer’ or ‘inner’ sections, as defined via the *PIP SECTION keyword. This naturally leads on to the concept of outer and inner ‘element pairs’.
•Each element in the inner set is associated with a corresponding element on the outer set through pipe-in-pipe connections, if present.
•The outer element is chosen such that the physical separation between the mid-point of both inner and outer elements is as little as possible.
•Given that the pipes can move independently over the course of a simulation, the optimal inner/outer element pairs are revised at every solution time step.
•Buoyancy forces on outer elements are computed in the standard fashion based on the density of the ambient fluid (typically seawater).
•Buoyancy forces on inner elements are computed based on the density of the annular fluid.
•Hydrodynamic forces on elements that are exposed to prescribed water particle motions are computed in the standard fashion based on Morison’s Equation.
•Drag forces on inner elements are based on the density of the annular fluid, and the relative velocity between the inner element and the outer element (the annular fluid motion is assumed to correspond with that of the outer element).
•Hydrodynamic inertia terms associated with the inner elements are based on the annular fluid, and the structural acceleration of the outer element (the annular fluid motion is assumed to correspond with that of the outer element).
•Added mass terms associated with the inner elements are based on the density of the annular fluid, and the structural acceleration of the inner element.
Refer to Drag and Inertia on Inner Pipe Sections for further information on this important topic.
The presence of internal fluid induces the following load terms.
•Gravitational and Inertial Forces
The modelling of internal fluid within a particular pipe section is unaffected by any inputs pertaining to pipe-in-pipe. Each pipe is filled with internal fluid as dictated by the *INTERNAL FLUID keyword, and all computations are performed in standard fashion. Consider the mass of annular fluid for example, which contributes to static (gravitational) and dynamic (inertial) loads. The mass of annular fluid contained within an outer pipe section, is defined as the internal area (derived from internal diameter) of the outer pipe, times the pipe length, times the fluid density. So the internal volume in this case is the total internal volume, rather than the annular volume (i.e. the volume computation disregards the presence of the inner pipe). Conceptually this may sound counter intuitive, but it is theoretically consistent with the computation of the buoyancy force, which is based on pressure differentials around the inner surface of the outer pipe. The pressure exerted on the inner wall of the outer pipe section is unaffected by the presence or absence of the inner pipe. This computational methodology has also been investigated and verified using a range of unit test cases.