Postgraduate, School of Naval Architecture and Maritime, Zhejiang Ocean University

Postgraduate, School of Naval Architecture and Maritime, Zhejiang Ocean University

Configuration of a beam element in the framework of ALE-ANCF

3.  Dynamic modelling of a flexible deep-water riser subjected to the internal slug-flow using 7-DOF ANCF combined with Arbitrary Lagrangian-Eulerian description (ALE-ANCF) (2020.11~2021.03)

  The two researches presented above is to understand the underlying principles of the finite element method and the implementation of FEM. 

  On the basis of Fortran based 6-DOF ANCF program, the 7-DOF model — ANCF combined with Arbitrary Lagrangian-Eulerian description (ALE-ANCF) is proposed to investigate the dynamic response of the flexible deep-water riser subjected to the internal slug-flow. 

  Two cases are carried out to validate the implementation of the present model. A third case is carried to study the dynamic response of the steel catenary riser considering the internal fluid moving inside the riser.

Case 1. Free-falling elastic beam in the air

  First, a free-falling elastic beam under gravity in the air is set up to validate and demonstrate the implementation of the ALE-ANCF model. The initial setting and configuration of the elastic beam are the same as “2.  Dynamic modelling of an elastic beam using 6-DOF Absolute Nodal Coordinate Formulation (2020.07~2020.10)“. Note that in this case, all the nodes’ nodal material coordinates have been fixed, which is done to ensure the results obtained from this ALE-ANCF model will keep consistent with conventional ANCF when mesh nodes don’t move in the simulation.

  Fig. 1 shows the impact of number of elements on the dynamic response of the cable. It can be viewed that the position of last node display no significant difference when the number of elements is more than 40. Thus, for the purpose of improving the computational  efficiency and the accuracy, 40 elements are used to conduct the comparison with Berzeri and Shabana (2000) whose resluts are displayed in Fig. 2. The comparison results demonstrate our code results keep consistent with the results from the conventional ANCF method.

Fig. 1 The number of element impact on the dynamic response
Fig. 2 Comparisons results between ALE-ANCF and conventional ANCF (Berzeri and Shabana, 2000)
Case 2. Motion analysis of a simple Horizontal tether submerged in the still water
  To validate the proposed ALE-ANCF model experiencing a complex external loads, the hydrodynamic drag force and buoyancy are considered. In this case, the free-falling of a rubber tether submerged in the still water is investigated. The evaluation of hydrodynamic drag force can refer to Takehara (2011) and Choo Y et al. (1971).
  Fig. 3 shows the tether configuration’s comparisons at every 0.6 s between the present numerical results and the same setup presented by Takehara (2011). Fig. 4 (a) and (b) present the comparison results of the horizontal and vertical positions of the midpoint and endpoint, respectively. Both comparison results between numerical simulation and experimental match well.
  In conclusion, the implemented model ALE-ANCF model is acceptable through these two validation cases.
Fig. 3 Comparison of the tether configurations at every 0.6 s. (a) the experimental results (b) the current model
Fig. 4 Comparisons of the positions of the mid and endpoints of the tether. (a) horizontal position (b) vertical position
Case 3. Dynamic response of SCR subjected to the internal slug-flow
  In this section, the dynamic behavior of a steel catenary riser (SCR) subjected to the internal upward slug-flow is investigated. For simplicity, only the partial riser is assumed to contain the inertial fluid — represented by the variable-length elements controlled by the moving material coordinates. The physical parameters of this scale model of SCR are taken from Morooka and Tsukada (2013). The schematic of SCR’s initial configuration is plotted in Fig. 5 using 3 elements. The time step is set to be 0.0001 s, and the simulation is set as 60.0 s.
Fig. 5 Free-falling of an elastic pendulum in the air

  The stable dynamic configuration of SCR without the movement of internal slug-flow is firstly obtained to observe the riser’s variety of configurations subjected to the internal slug-flow. In this case, the first 30.0 s is set to obtain the stable dynamic configuration. After that, the internal slug-flow begin to move upward.

  The comparisons of riser configuration are presented in Fig. 6. I can be viewed that the node 2 moves gradually to the upper left with node 3 shifts to the lower right with the movement of internal slug-flow. 

  To further reveal the impact of upward slug-flow on the structure of SCR, Fig. 7 presents the displacement time history in the y-direction and z-direction of nodes 2 and 3.

Fig. 6 Comparisons of SCR dynamic configuration subjected to different conditions at 29.9 s, 45.0 s, and 60.0 s
Fig. 7 Displacement time history in (a) horizontal direction of node 2 (b) vertical direction of node 2 (c) horizontal direction of node 3 (d) vertical direction of node 3

  Note that the average amplitude of SCR’s nodes with internal slug-flow is more significant than when there is no internal slug-flow movement inside the SCR. 

  Furthermore, node 2 gradually moves to the upper left under the influence of moving internal slug-flow in the global frame as shown in (a) and (b), at the same time, node 3 shifts to the lower right can be seen in (c) and (d)

  The reason for this phenomenon is that the movement of internal slug-flow controlled by the moving material coordinates corresponds to the introduction of external force to push the variable-length fluid element moving upward.

  This phenomenon indicates that the internal slug-flow generates a superposition of the structure deformation, which aggravates the SCR oscillates.

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