of the Maritime University of Szczecin
Akademii Morskiej w Szczecinie
2017, 51 (123), 101–108
ISSN 1733-8670 (Printed) Received: 26.07.2017
ISSN 2392-0378 (Online) Accepted: 11.09.2017
DOI: 10.17402/237 Published: 15.09.2017
Numerical simulations of water flow
around ocean mining piping
Tadeusz Szelangiewicz, Katarzyna Żelazny
Maritime University of Szczecin, Faculty of Navigation 1-2 Wały Chrobrego St., 70-500 Szczecin, Poland e-mail: t.szelangiewicz@am.szczecin.pl
corresponding author
Key words: nodules, vertical pipe, hydrodynamic resistance forces, CFD simulations, water flow, mining Abstract
Ocean mining systems that incorporate a single or double lift pipe are two methods used to obtain polimetallic nodules from the seabed. The pipe must be equipped with main cables and flexible pipe attached to the mining vehicle collecting nodules. While mining, the pipes in the vertical configuration are moving along with the ship above. They are subjected to currents in the water column. Such current-induced hydrodynamic drag results in a vertical deflection, which is dependent – among other factors such as varying current velocity at points along the length of the pipe. The present paper presents results of computer simulations using commercial CFD soft-ware to model the hydrodynamic forces acting on the vertical pipe of ocean mining systems. The results present the influence of the water flow direction in relation to the lift pipe on the hydrodynamic force and torsional moment acting upon the pipe.
Introduction
Among the mining methods considered by the IOM for collection of polimetallic nodules from the Pacific ocean floor there are two hydraulic methods: single pipeline with subsea pumps (located on dif-ferent levels in the feeding pipeline – Figure 1a) and double suction pipeline with pumps located on the mining support vessel. Design and operating prin-ciples of such suction system are similar and have been known for years. Between the mining vessel on the ocean surface and the collection point on the sea-floor, there is a single or double pipeline hydraulic suction system (riser). The lower end of the vertical pipe (buffer) is joined to a mining vehicle collecting nodules with a horizontal elastic pipeline – the length of the pipe system must be adjusted in such a way as not to exceed the length of the horizontal elastic line both while collecting and transporting nodules (Fig-ure 1). One of the tasks of the horizontal pipeline is to compensate for the distance variation between the
seafloor mining vehicle collecting nodules and the lower end of the vertical pipe in order to prevent any contact between the two. The mining vessel and riser will move along a trajectory resulting from both the mining vehicle movement and changing contour of the pipeline suspended in the sea water. The mining support vessel will also be subject to wave action resulting in swaying of the surface vessel. A com-plex, dynamic vessel movement will be a kinematic action on the upper end of the riser. Shape deforma-tions as well as tension along the pipeline are the biggest threats and, as such, play a decisive role in efficiency and reliability of ocean mining pipe.
Deformations of the mining pipeline are mainly caused by the hydrodynamic effects of water – the influence depends on the relative velocity of water flow resulting from the speed of movement of the pipeline and the velocity of the deep currents. The literature indicates that there are many examples of hydrodynamic calculations for a single pipe, Figure 2a, (Ferziger & Perić, 2002; Hong, Choi & Kim,
a) 1 7 2 5 3 4 b) 1 6 2 5 3 4 Vertical deflection Distance between a seafloor
collector and a buffer
Figure 1. Examples of hydraulic suction systems; a) double pipeline system with pumps on board of a mining support vessel, b) single pipeline system; 1 – mining support vessel, 2 – riser, 3 – horizontal, elastic pipe, 4 – a seafloor collector, 5 – buffer, 6 – deep sea pumps, 7 – pumps on board of a vessel
Figure 2. Hydraulics ocean mining systems. a) single pipe-line, b) single pipeline with mains cables c) double pipelines
2003; Yoon et al., 2003; Rahman, Karim & Alim, 2007; Sato & Kobayashi, 2012) because a single hydrodynamic drag coefficient is known for a single pipe. In contrast, no calculation results for a single pipe with cables, Figure 2b or two mining pipes, Fig-ure 2c. The purpose of the study was to determine
the drag coefficients and hydrodynamic moment depending on the direction of movement of the min-ing pipe. Since there are no experimental results of the drag coefficients for the pipes shown in Figures 2b and 2c, they were determined using Fluent.
Hydrodynamic action on the vertical pipe
Mining support vessels with an ocean mining sys-tem attached will follow the movement and location of the mining vehicle. The motions of the mining support vessel will trigger movement in the pipeline water of a pipe system. At the same time the hydrau-lic suction system will be subject to deep water cur-rents whose velocity and direction change in relation to water depth resulting in net flow of water (relative in direction and velocity) around vertical pipe.
Local components of hydrodynamic force on the vertical pipe equal (Figure 2):
) ( 5 . 0 2 V x x R w x V S C R ) ( 5 . 0 2 V y y R w y V S C R (1) ) ( 5 . 0 2 V m y R w z V S L C M where:
Rx, Ry – hydrodynamic force components;
Mz – hydrodynamic moment against the vertical axis z;
ρw – seawater density;
VR – relative velocity around the pipeline, Figure 2.
) ( ) (H V H V VR P C (2) ) (H VP
– local velocity pipe displacement vector (from kinematic enforcement of mining sup-port vessel) in the depth function H;
– local velocity vector of a deep sea current in the depth function H;
Sx, Sy – projections of the pipeline lateral surface on
relevant axes (for a single pipe Sx = Sy); L – pipeline length;
Cx(βV), Cy(βV), Cm(βV) – hydrodynamic resistance
coefficients in the VR direction function (for
a smooth and single pipe Cx = Cy= CD),
(Breb-bia & Walker, 1979; Ferziger & Perić, 2002);
βV – VR velocity direction in relation to pipeline/s. Preliminary calculation of drag coefficient – test method of CFD
Before calculating the correct calculation for the pipes in Figures 2b and 2c, calculations were made for a single pipe (Figure 2a) and the obtained results were compared with the published experimental results.
) (H
VC
present calculations
Figure 4. Residuals continuity, x-velocity, y-velocity conver-gence history (a) and drag coefficient CD convergence history
(b) for Re = 100 (present calculations)
5500 6000 6500 7000 7500 8000 8500 9000 9500 10000 1e-04 1e-05 1e-06 Iterations Residuals — continuity — x-velocity — y-velocity 0 2000 4000 6000 8000 10000 Iterations 10.0 9.0 8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0 CD [–] a) b)
Figure 5. Numerical grid for a single pipeline with mains cables, water flow direction βV = 90°
Computer-based CFD single pipe tests were per-formed using:
• 2-D finite volume method;
• unsteady flow model with RANS equations; • laminar flow (Re = 100);
• turbulence flow (Re = 0.235·106; 0.538·106) with
realizable k-ε turbulence model;
• unstructured numerical mesh with 30 500 pris-matic cells.
Reynolds number equals:
D V
Re (3)
where: ν is water kinematic viscosity (sea water vis-cosity ν = 1.19·10–6 m2/s), V – flow velocity, D –
pipe diameter).
Computational CFD calculations of the CD
drag coefficient for a single pipe (Figure 2a) were compared with experimental studies – Figure 3 and Table 1.
Figure 3. Resistance coefficient for a cylinder: experiment (Brebbia & Walker, 1979) and present calculations
Table 1. Drag coefficient for different Reynolds numbers with experimental numerical results
Re 100 0.235·106 0.538·106
Experimental CD 1.24–1.26
(Tritton, 1959)(Brebbia & Walker, 1979)Figure 3 Numerical CD
(present calculation) 1.2258 0.242 0.223
Percentage of error 2% 3% 2.5%
Residuals and drag coefficient CD convergence
history for a single pipe (Figure 2a) for Re = 100 are shown in Figure 4.
While calculating the drag force, the surface effects and an drag coefficient play a crucial role. If it is smooth and there is only a single pipeline pres-ent then drag coefficipres-ents are known. If there are two pipelines or a single pipeline with mains cables along, Figure 2b, reliable drag coefficient datais dif-ficult to find. Moreover, the Reynolds number can vary within a significant range, and it impacts the drag coefficient too (Figure 3). In order to determine
drag forces of water flow around hydraulic suction systems, computer simulations have been performed using Fluent.
Computer simulations of water flow around hydraulic lifting system
Single Pipeline with Mains Cables (Figure 2b)
Numerical grid for a single pipeline with mains cables, water flow direction βV = 90° has been shown
in Figure 5. Computer simulation results in the
1.67e+00 1.59e+00 1.51e+00 1.42e+00 1.34e+00 1.25e+00 1.17e+00 1.09e+00 1.00e+00 9.20e-01 8.36e-01 7.53e-01 6.69e-01 5.85e-01 5.02e-01 4.18e-01 3.35e-01 2.51e-01 1.67e-01 8.36e-02 0.00e+00 βV = 0° βV = 30° βV = 90° βV = 60°
Figure 6. Current lines [m/s] for a single pipeline with mains cables for water velocity V = 1 m/s and direction βV = 0°, 30°, 60°,
90°; Re = 0.387·106 (present calculations) 5.15e+02 4.76e+02 4.37e+02 3.96e+02 3.59e+02 3.20e+02 2.81e+02 2.42e+02 2.03e+02 1.64e+02 1.25e+02 8.63e+01 4.73e+01 8.31e+00 –3.07e+01 –6.97e+01 –1.09e+02 –1.48e+02 –1.87e+02 –2.26e+02 –2.65e+02 βV = 0° βV = 30° βV = 90° βV = 60°
Figure 7. Pressure distribution [Pa] for a single pipeline (Figure 2b) for water velocity V = 1 m/s and directions βV = 0°, 30°, 60°,
90°; Re = 0.387·106 (present calculations) 0 50 100 150 200 250 300 0 30 60 90 Rx [N] βV [°] -60 -40 -20 0 20 40 60 0 30 60 90 Ry [N] βV [°] -7 -6 -5 -4 -3 -2 -1 0 1 0 20 40 60 80 Mz [N m] βV [°]
form of current lines for various directions βV have
been presented in Figure 6, while Figure 7 gives the dynamic pressure distribution. Calculations of hydrodynamic force components Rx and Ry as well
as moment Mz (Figure 2) have been performed in Figure 8. Mean component values Rx, Ry and Mz in the
func-tion of βV angle for a single pipeline with mains (Figure 2b).
The values for unit length of the pipe equal to 1 m (present calculations)
βV = 0° 40 42 44 46 48 50 52 54 56 58 60 502.5 507.5 512.5 517.5 522.5 527.5 Rx [N] Time [s] -20 -15 -10 -5 0 5 10 15 502.5 507.5 512.5 517.5 522.5 527.5 Ry [N] Time [s] -0.4 -0.2 0 0.2 0.4 0.6 0.8 502.5 507.5 512.5 517.5 522.5 527.5 Time [s] Mz [Nm] βV = 60° 91.8 91.85 91.9 91.95 92 92.05 92.1 527.5 532.5 537.5 542.5 547.5 552.5 Rx [N] Time [s] 15.2 15.4 15.6 15.8 16 16.2 16.4 16.6 16.8 17 17.2 527.5 532.5 537.5 542.5 547.5 552.5 Ry [N] Time [s] -5.825 -5.820 -5.815 -5.810 -5.805 -5.800 -5.795 527.5 532.5 537.5 542.5 547.5 552.5 Time [s] Mz [Nm] βV = 90° 262 264 266 268 270 272 274 276 278 280 282 284 502.5 507.5 512.5 517.5 522.5 527.5 Rx [N] Time [s] 0 10 20 30 40 50 60 70 502.5 507.5 512.5 517.5 522.5 527.5 Ry [N] Time [s] -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 502.5 507.5 512.5 517.5 522.5 527.5 Time [s] Mz [Nm] 56 57 58 59 60 61 1061 1066 1071 1076 1081 1086 Rx [N] Time [s] βV = 30° -55.2 -55 -54.8 -54.6 -54.4 -54.2 -54 -53.8 -53.6 1 061 1 066 1 071 1 076 1 081 1 086 Ry [N] Time [s] -5.670 -5.665 -5.660 -5.655 -5.650 -5.645 -5.640 -5.635 -5.630 -5.625 -5.620 -5.615 1061 1066 1071 1076 1081 1086 Time [s] Mz [Nm]
Figure 9. Component Rx and Ry value distribution of
hydro-dynamic force and Mz moment in single pipeline with mains
(Figure 2b) in the time function for different βV angles. The
values are given for unit length of the pipe equal to 1 m (present calculations)
time domain and various directions βV.
Calcula-tion results of mean Rx, Ry and Mz values have been
shown in Figure 8, and on Figure 9 the distribution of these values in time function (Szelangiewicz,
1.74e+00 1.65e+00 1.56e+00 1.48e+00 1.39e+00 1.30e+00 1.22e+00 1.13e+00 1.04e+00 9.55e-01 8.68e-01 7.81e-01 6.94e-01 6.08e-01 5.21e-01 4.34e-01 3.47e-01 2.60e-01 1.74e-01 8.68e-02 0.00e+00 βV = 0° βV = 30° βV = 90° βV = 60°
Figure 11. Current lines [m/s] for double pipelines (Figure 2c) and water velocity V = 1 m/s; Re = 0.504·106 (present calculations)
5.99e+02 5.63e+02 5.28e+02 4.93e+02 4.58e+02 4.23e+02 3.88e+02 3.53e+02 3.18e+02 2.83e+02 2.48e+02 2.12e+02 1.77e+02 1.42e+02 1.07e+02 7.20e+01 3.68e+01 1.73e+00 –3.34e+01 –6.85e+01 –1.04e+02 βV = 0° βV = 30° βV = 90° βV = 60°
Figure 12. Pressure distribution [Pa] for double pipelines (Figure 2c) and water velocity V = 1 m/s; Re = 0.504·106 (present calculations) 0 50 100 150 200 250 0 20 40 60 80 Rx [N] βV [°] -20 0 20 40 60 80 100 0 20 40 60 80 Ry [N] βV [°] -80 -70 -60 -50 -40 -30 -20 -10 0 10 0 20 40 60 80 Mz [N m] βV [°]
Figure 14. Mean component Rx, Ry and Mz values in double
pipeline (Figure 2c) in the βV function. The values for unit
Figure 13. Component Rx and Ryvalue distribution of hydrodynamic force and Mz moment in double pipeline (Figure 2c) in the
time function for different βV angles. The values for unit length of the pipe equal to 1 m (present calculations) βV = 0° 0 20 40 60 80 100 120 140 614.5 619.5 624.5 629.5 634.5 639.5 Rx [N] Time [s] -400 -300 -200 -100 0 100 200 300 614.5 619.5 624.5 629.5 634.5 639.5 Ry [N] Time [s] -10 -5 0 5 10 15 614.5 619.5 624.5 629.5 634.5 639.5 Time [s] Mz [Nm] βV = 30° 150 160 170 180 190 200 210 220 230 240 250 1372 1377 1382 1387 1392 1397 Rx [N] Time [s] 62 64 66 68 70 72 74 76 1372 1377 1382 1387 1392 1397 Ry [N] Time [s] -71 -70.5 -70 -69.5 -69 -68.5 -68 1372 1377 1382 1387 1392 Time [s] Mz [Nm] βV = 60° 150 170 190 210 230 250 270 290 697 702 707 712 717 722 Rx [N] Time [s] 60 70 80 90 100 110 120 697 702 707 712 717 722 Ry [N] Time [s] -52 -51.95 -51.9 -51.85 -51.8 -51.75 -51.7 -51.65 -51.6 697 702 707 712 717 722 Time [s] Mz [Nm] βV = 90° 140.3198 140.3199 140.3200 140.3201 140.3202 140.3203 140.3204 140.3205 140.3206 140.3207 509 510 511 512 513 514 Rx [N] Time [s] 3.1658 3.1659 3.1659 3.1660 3.1660 3.1661 3.1661 3.1662 3.1662 3.1663 509 510 511 512 513 514 Ry [N] Time [s] 1.040135 1.040140 1.040145 1.040150 1.040155 1.040160 1.040165 1.040170 1.040175 1.040180 509 510 511 512 513 514 Time [s] Mz [Nm]
Double Pipelines (Figure 2c)
Numerical grid for double lift pipeline with water direction βV = 0° has been shown in Figure
10. The range of computer simulations for double pipeline is the same as the one for the pipeline
with mains. Calculation results are presented as follows: Figure 11 – current lines, Figure 12 – dynamic pressure distribution, Figure 13 – Rx, Ry
and Mz distribution in time domain, and finally on
Figure 14 – mean Rx, Ry and Mz values
Conclusions
1. Calculations of the hydrodynamic forces and resistance coefficient for a single, smooth pipe-line show close agreement with experimental measurements.
2. Even for a single, smooth pipeline at certain flow velocities there are noticeable vortexes locat-ed behind the pipeline, which induce oscillatory movement in the pipeline.
3. Significant variability of hydrodynamic force components in the function of water velocity vector is observed for a single pipeline with mains cables This effect is more pronounced for double pipelines. As the velocity increases, shedding vortices form and result in pipeline oscillations.
4. Moreover, in the case of double pipeline sys-tem, a hydrodynamic moment appears which results in twisting the pipelines about the verti-cal axis.
5. In order to avoid large variability of both hydro-dynamic force components and hydrohydro-dynamic moment for a pipeline with mains cable or double pipelines, cylindrical buoyancy modules can be used.
6. The results of the present work will be used for future calculations deformations and tensions of the mining pipes.
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