The Proceedings Fifth International Conference on Numerical Ship Hydrodynamics (1990) / Chapter Skim
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Simulation of Hydrodynamic Loading and Structural Response of a Marine Riser
Simulation of Hydrodynamic Loading and Structural Response of a Marine Riser
Pages 617-628
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From page 617... ...
On the contrary, very advanced numerical schemes exist for solving the instationary viscous Navier Stokes equations. These methods certainly take into account the flow field, but even with present day computing power such complex simulations will impose an economical limit on their use for practical problems.
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From page 618... ...
The equations governing the evolution of a vorticity field A, defined as the curl of the velocity field A, in a viscous incompressible fluid in a Eulerian reference frame are commonly known as the viscous vorticity transport equations. They can be summarized as: D~-=~-Vu+Z'V2w (1)
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From page 619... ...
The main result of Van der Vegt t9; states that, provided the inviscid flow map exists and is unique, the expectation of the viscous evolution operator converges to the evolution operator of the viscous vorticity transport equations. Analogously, the expectation of the particle paths, converge to the real particle paths.
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From page 620... ...
The vorticity field obtained by this discretization, however, does not satisfy the inviscid transport equations. Convergence criteria for the two-dimensional vortex blob methods are given by Hald et al.
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Van der Vegt t9] developed a special purpose spectral model to calculate the flow map.
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From page 622... ...
The region which is of practical importance is the lock-in region, where the vortex shedding frequency is near the natural frequency of the mass-spring system. The added mass and damping are incorporated in the calculation of the forces from the vorticity field.
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7. Discussion of Vortex Blob Calculations Calculations using the vortex blob method, were performed for values of the reduced velocity ranging from 5.0 to 7.0.
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From page 624... ...
Table 2 Vertical riser properties Quantity Unit Value Length m 100 Diameter m 2 Mass kg/m 3220 Natural frequency rad/sec 0.71 Flow velocity m/& 1.0 Tension N 1.6 x 106 Response parameter _ _ _ 0.15 Comparison between calculated results for vertical riser Quantity Unit Calculated Hansen .
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From page 625... ...
3. In-line displacements of vertical riser Relatively large displacements are shown which are not unusual for lightly damped structures.
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From page 626... ...
9. Conclusions The results presented in this paper support the authors' view that complex flow simulations based on the Navier Stokes equations are invaluable for understanding flow phenomena.
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From page 627... ...
Vegt, J.J.W. van der, A variationally optimized vortex tracing algorithm for three dimensional pow around solid bodies, PhD thesis, Techni cal University Delft, The Netherlands (1988~.
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