Wave interaction with vertical cylinder

Description

This test case aims to examine the non-linear wave and breaking wave impact on a surface-piercing vertical cylinder, a typical offshore wind turbine foundation. The numerical results by OpenFOAM and PIC methods for wave interactions with a vertical surface piercing cylinder are also presented and compared with the physical experiments performed at Danish Hydraulic Institute (DHI).

Experimental Set-up

The experiments were performed at DHI, Denmark for regular waves and focused wave groups hitting a surface-piercing vertical cylinder. The DHI shallow water basin (35 m  25 m) was used for the tests with a water depth of 0.505 m. The wave field is created by a segmented piston paddle array installed at one end of the water basin. A cylinder of diameter 0.25m was suspended from a rigid frame, leaving only a 1 mm gap beneath to the bed of the basin. The cylinder was located at 7.52 m from the paddles in the centre of the tank. The total horizontal hydrodynamic force on the cylinder was measured via 4 load cells on the top of the cylinder, and 19 wave gauges were placed to monitor the wave field around the cylinder. The layout for the wave gauges can be seen in Fig. 1. All of these results of free surface elevations shown in this test case are collected at wave gauge 9 (WG9), which is 2mm in front of the cylinder and is the proposed focused point for focused wave groups.

Figure 1. The layout of wave gauges in the experiments.

Experimental Test Program

Large number of wave conditions with varying wave periods and crests were carried out in the experiments. Eight wave conditions with different wave steepness and wave periods were selected and provided here, including three regular waves (R1, R2, R3) and five focused wave groups (F1, F2, F3, F4, F5). These wave parameters are shown in Table 1. Here T is wave period, f is wave frequency, A is amplitude or the crest value of focused wave group, k is wave number, a is cylinder radius, h is water depth.

Table 1. wave parameters used in case study
Test cases Wave Period T(s) Freq f (Hz) Wave Height H (m) ka Slenderness ka Steepness ka Depth
R1/F1 1.22 0.82 0.07 0.37 0.1 1.39
R2/F2 0.14 0.2
R31/F3 1.63 0.61 0.12 0.25 0.1 0.86
F4 0.23 0.2
F5 1.22 0.82 0.22 0.37 0.3 1.39

The measured time histories of the free surface elevations at WG9 for the five focused wave cases without and with cylinder in place are shown in Figure 2. The data can be found in the attached experimental data documents.

Figure 2. Time series of the measured free surface elevations at WG9 for different focused wave groups without cylinder (left column) and with cylinder (right column) in place.

Physical Measurement Data

The free surface elevation data at each of the wave gauge positions was recorded at 1000Hz for the cases with cylinder in place and 100Hz for the cases without cylinder in place. The measured data for wave gauge 1 and wave gauge 9 can be found here. The data is arranged as follows

  • The physical free surface elevation data for the five focused wave cases are stored in 6 files; the first row tells the test case and if it is crested focused or trough focused case; the first column is the time in seconds and the proceeding columns are free surface elevation in metres at each of the probes corresponding the wave gauge positions in Table 1, or measured forces in Newtons.
  • As the total horizontal hydrodynamic force on the cylinder was measured via 4 load cells on the top of the cylinder, the measured horizontal forces for extreme wave cases may contain high frequency components due to cylinder motion. This high frequency components should be removed before comparing with numerical predictions as shown in the numerical results.

NOTE: When using this data please state that 'the physical data is from the DHI Test Cases performed by an international team led by Dr. Jun Zang at the University of Bath”, and be sure to cite Chen et al. (2018a) and Chen et al. (2014) or Chen et al. (2018b) as the source of this data (see full citation in the 'Relevant References' section below).

F1 & F3 – incoming wave data

F1 & F3 – with cylinder in place

F2 & F4 – incoming wave data

F2 & F4 - with cylinder in place

F5 - incoming wave data

F5 - with cylinder in place

Numerical Benchmarks

In order to reproduce the experiments, a 3D numerical wave tank is setup. Two CFD solvers, OpenFOAM 2.1.0 and Particle-In-Cell (PIC) solver, were used, of which the results of R1/F1, R2/F2, R3/F3, F4 were obtained by OpenFOAM 2.1.0 and the results of F5 were obtained by PIC solver. The details on these numerical methods can be found from Chen et al. (2014) and Chen et al. (2018b).

The comparisons between the numerical results and the measured data are shown in Figs. 3-5:

Figure 3. Time histories and spectra of the free surface elevations at WG9 and the horizontal forces on the cylinder for regular wave cases. (a) Case R1, (b) Case R2, (c) Case R3. The black lines: Numerical results by OpenFOAM; Dotted lines: experimental data.

Figure 4. Time histories and spectra of the free surface elevations at WG9 and the horizontal forces on the cylinder for focused wave group cases. (a) Case F1, (b) Case F2, (c) Case F3, (d) Case F4. The black lines: Numerical results by OpenFOAM; Dotted lines: experimental data.

Figure 5. Time histories and spectra of the free surface elevations at WG9 and the horizontal forces on the cylinder for Case F5. The red lines: Numerical results by PIC method; Circles: experimental data.

Relevant References

Chen, LF, Zang, J, Hillis, AJ, Morgan, GCJ & Plummer, AR 2014, 'Numerical investigation of wave-structure interaction using OpenFOAM', Ocean Engineering, vol. 88, pp. 91-109. https://doi.org/10.1016/j.oceaneng.2014.06.003

Chen, L, Zang, J, Taylor, PH, Sun, L, Morgan, G, Grice, J, Orszaghova, J & Tello, M 2018a, 'An experimental decomposition of nonlinear forces on a surface-piercing column: Stokes-type expansions of the force harmonics', Journal of Fluid Mechanics, vol. 848, pp. 42-77. https://doi.org/10.1017/jfm.2018.339

Chen, Q, Zang, J, Kelly, DM & Dimakopoulos, A 2018b, 'A 3D parallel Particle-In-Cell solver for wave interaction with vertical cylinders', Ocean Engineering, vol. 147, pp. 165-180. https://doi.org/10.1016/j.oceaneng.2017.10.023

Zang, J., Taylor, P.H., Morgan, G.C.J., Stringer, R., Orszaghova, J., Grice, J. and Tello, M. 2010. Steep wave and breaking wave impact on offshore wind turbine foundations – ringing revisited. The 25th International Workshop on Water Waves and Floating Bodies.
http://www.iwwwfb.org/Abstracts/iwwwfb25/iwwwfb25_52.pdf

Zang, J., Taylor, P.H., Morgan, G.C.J., Tello, M., Grice, J. and Orszaghova, J. 2010. Experimental study of non-linear wave impact on offshore wind turbine foundations. Coastlab10 – the 3rd International Conference on the Application of Physical Modelling to Port and Coastal Protection.

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