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Numerical benchmark studies on drag and lift coefficients of a marine riser at high Reynolds numbers
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ARTICLE IN PRESS Applied Ocean Research xxx (2017) xxx–xxx
Contents lists available at ScienceDirect
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Numerical benchmark studies on drag and lift coefficients of a marine riser at high Reynolds numbers Wei Qiu a,∗ , Dong-Yeon Lee b , Halvor Lie c , Jean-Marc Rousset d , Takashi Mikami e , Sergio Sphaier f , Longbin Tao g , Xuefeng Wang h , Viacheslav Magarovskii i a
Memorial University, Canada Samsung Ship Model Basin, Republic of Korea c Marintek, Norway d Ecole Centrale de Nantes, France e Akishima Laboratory (MITSUI ZOSEN) Inc., Japan f Universidade Federal do Rio de Janeiro, Brazil g University of Newcastle, United Kingdom h Shanghai Jiao Tong University, China i Krylov Shipbuilding Research Institute, Russia b
a r t i c l e
i n f o
Article history: Available online xxx Keywords: Vortex induced vibration RANS DES LES Drag crisis phenomenon
a b s t r a c t Numerical benchmark studies on drag and lift coefficients of a marine riser have been organized by the 27th ITTC Ocean Engineering Committee. The purpose of the studies was to benchmark the capabilities of CFD methods through quantitative comparisons and validation studies against the model test results of a circular cylinder by MARIN. Studies were focused on the drag crisis phenomenon for the stationary smooth cylinder in the critical Reynolds number regime. Eight organizations have participated in the studies by using RANS, DES and LES methods. An overview of the model test results, test cases, submissions and comparison results are presented in this paper. Conclusions and recommendations are made for future studies. © 2017 Elsevier Ltd. All rights reserved.
1. Introduction Vortex Induced Vibration (VIV) of marine risers poses a significant challenge as the offshore oil and gas industry moves into deep water. Due to the asymmetric nature of the vortex shedding, risers vibrate in both in-line and cross-flow directions. The in-line motion can be a major contributor to the fatigue damage due to its higher frequencies and response modes although the in-line displacement is normally less than the cross-flow one. It also triggers higherorder harmonic responses in both in-line and cross-flow directions which further increase the fatigue damage. Marine risers have very large length-to-diameter ratios, especially for deepwater risers. The length of risers cannot be scaled due to the depth limitation of existing wave basins and therefore experimental methods cannot be reliably employed for design verification. To predict the VIV response of a riser system, practical numerical methods have been developed by making use of
∗ Corresponding author. E-mail address: [email protected] (W. Qiu).
databases with experimental hydrodynamic coefficients at various Reynolds numbers, for example, those by Oakley and Spencer [1]. Most experiments have been carried out to measure the hydrodynamic forces on a segment of a riser. The experimental databases, however, cover a limited range of Reynolds numbers for a segment of rigid or flexible riser. It is desirable to use computational fluid dynamics (CFD) methods to compute the hydrodynamic forces on marine risers, complementing the experimental databases for VIV prediction, and to simulate the responses of long risers. CFD simulations of VIV have been focused on flow around circular cylinders and their induced forces. While the cylinder geometry is simple, it remains challenging for CFD methods to resolve the flow instability and separation in the boundary layer and in the wake. Since 2009, the ITTC Ocean Engineering Committee has carried out studies to benchmark the capabilities of CFD methods for the prediction of hydrodynamic forces on a stationary smooth cylinder at high Reynolds numbers. In the benchmark studies organized by the 26th ITTC Ocean Engineering Committee, all participants used the two-dimensional unsteady Reynolds Averaged Navier-Stokes (URANS) method. Various turbulence models were employed with the assumption that the flow is fully tur-
https://doi.org/10.1016/j.apor.2017.10.010 0141-1187/© 2017 Elsevier Ltd. All rights reserved.
Please cite this article in press as: W. Qiu, et al., Numerical benchmark studies on drag and lift coefficients of a marine riser at high Reynolds numbers, Applied Ocean Research (2017), https://doi.org/10.1016/j.apor.2017.10.010
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2
Nomenclature Abbreviations AR Aspect ratio of the cylinder, L/D CD Drag coefficient, FD /( 12 U 2 DL) Lift coefficient, FL /( 12 U 2 DL) CL D Cylinder diameter FL Lift FD Drag Shedding frequency fs L Length of the cylinder Reynolds number, UD/ Re Strouhal number, fs D/U St U Inflow velocity Density of water Kinematic viscosity ITTC International towing tank conference Computational fluid dynamics CFD DES Detached eddy simulation LES Large eddy simulation URANS Unsteady Reynolds averaged Navier-Stokes equations VIV Vortex induced vibration
Fig. 2. High Reynolds Number VIV Test Apparatus by MARIN.
Fig. 3. Drag Coefficient for the Smooth Cylinder.
Fig. 1. The Smooth Stationary Cylinder.
bulent. It was concluded from the studies that the drag crisis phenomenon on the stationary smooth cylinder was not captured by the URANS methods (ITTC Ocean Engineering Committee Report [2]). It is well known that the drag crisis is caused by the instability of separated shear layer in the critical Reynolds number regime (2 × 105 < Re < 5 × 105 ). At the critical Reynolds numbers, the transition points are very close to the points of flow separation. As a result, the shear layer eddies cause the mixture of flow in the boundary layer and the flow separation is delayed. The delay of flow separation leads to the reduction of the drag coefficient. Since numerical methods based on two-dimensional URANS solvers are inadequate to simulate this physical phenomenon, it is necessary to extend the benchmark studies by including other CFD methods. The 27th ITTC Ocean Engineering Committee extended the VIV benchmark studies by including the detached eddy simulation (DES) and the large eddy simulation (LES) methods. The CFD solutions were compared with the model test results for a circular cylinder. An overview of the model tests carried out by MARIN, test cases, the comparison of experimental and numerical results, as well as conclusions and recommendations, are presented in the paper.
Table 1 Participants of the Benchmark Studies.
1 2 3 4 5 6 7 8
Organization
Country
China Ship Scientific Research Centre Seoul National University Samsung Ship Model Basin Memorial University Inha University University of Iowa University of Southampton Shanghai Jiao Tong University
China Korea Korea Canada Korea USA UK China
2. Experimental data As reported in the ITTC Ocean Engineering Committee Report [2], the benchmark experimental data for the VIV of a stationary circular cylinder was provided by MARIN. The rigid cylinder is 200 mm in diameter and 3.52 m in length (Fig. 1). The cylinder was suspended from the carriage about 1.7 m below the calm water surface. The VIV test apparatus is shown in Fig. 2. The towing tank of MARIN is 4 m deep, 4 m wide and 210 m long. The cylinder was towed horizontally by the carriage at various speeds. Details of the tests can found in the work of de Wilde and Huijsmans [3], de Wilde and Huijsmans [4], de Wilde et al. [5] and de Wilde et al. [6]. As an example, the measured drag coefficient for the smooth stationary cylinder is presented in Fig. 3.
Please cite this article in press as: W. Qiu, et al., Numerical benchmark studies on drag and lift coefficients of a marine riser at high Reynolds numbers, Applied Ocean Research (2017), https://doi.org/10.1016/j.apor.2017.10.010
2D/3D
Steady/Unsteady
Method
FLUENT (Commercial Code) SNUFOAM (In-house Code) FLUENT CFDShip-IOWA (In-house Code) Code-S (In-house Code) OpenFOAM (Open Source Code) Naoe-FOAM-SJTU (In-house Code) STAR-CCM+ (Commercial Code) STAR-CCM+ STAR-CCM+ STAR-CCM+ STAR-CCM+ STAR-CCM+
2D 2D 2D 3D 3D 3D 2D 2D 2D 3D 3D 3D 2D
Unsteady Unsteady Unsteady Unsteady Unsteady Unsteady Unsteady Unsteady Unsteady Unsteady Unsteady Unsteady Transient
RANS RANS RANS LES LES LES RANS RANS RANS DES LES RANS RANS
Table 3 Computational Details. y+
Number of Grids
Type of Grids
Wall Function (Used/Not Used)
Turbulence Model
Transition Model (Used/Not Used)
Convection Term
t (s)
Aspect Ratio (AR)
A B C D E
59 2 10 0.03–0.15 –
87,223 32,280 43,820 67,000,000 11,300,000
U N N N N
SST k-ω SST k-ω SST k-ω Dynamic model Dynamic model
N N N N N
Upwind Upwind Upwind QUICK/WENO Upwind
0.001/0.0005 0.001/0.0002/0.0001 0.001 0.00008/0.0001 CFL = 0.5
– – – 2 and 8
F G H1 H2 H3 H4 H5 H6
1 1.0–4.9 0.06–0.56 0.06–0.56 0.06–0.56 0.06–0.56 0.06–0.56 0.06–0.56
Max 4,000,000 100,000 592,478 592,478 21,215,000 12,400,000 10,517,000 592,478
Structured Structured Structured Structured Unstructured (Cartesian) Unstructured Chimera Hybrid Hybrid Structured Structured Structured Hybrid
N U N N N N N N
Dynamic model SST k-ω SST k-ω k-ε (Standard) – – SST k-ω LCMT
N N N N N N N Y
Hybrid (Central + Upwind) Upwind Upwind Upwind Upwind Upwind Upwind Upwind
0.005 0.00017–0.0015 0.0001–0.002 0.0001–0.002 0.002–0.02 0.002–0.02 0.002–0.02 0.0001–0.002
1.7, , 2 – – – 3.0 12.0 6.0 –
ARTICLE IN PRESS
Program Name
G Model
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A B C D E F G H1 H2 H3 H4 H5 H6
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Table 2 Numerical Methods Used by Participants.
3
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Fig. 4. Mean Drag Coefficient. (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)
For numerical computations, the following six (6) Reynolds numbers were selected to cover the critical Reynolds number regime: 6.31E + 04, 1.26E + 05, 2.52E + 05 3.15E + 05, 5.06E + 05, 7.57E + 05
3. Participants and numerical methods A number of organizations and individuals have been invited to participate in the benchmark studies. A list of participants is given in Table 1, which include those participated in the studies organized by the 26th and the 27th ITTC Ocean Engineering Committee. In general, three CFD methods were employed in the studies, including 2-D/3-D URANS, DES and LES methods. Commercial software packages, such as FLUENT and Star-CCM+, in-house codes and open-source based codes (OpenFOAM) were used by the participants. The numerical methods are summarized in Table 2 and the computational details are presented in Table 3. 4. Numerical methods and results 4.1. Numerical methods used and key findings by participants In the benchmark studies, each participant submitted the computed mean CD , mean CL , RMS of CL , and the Strouhal number at selected Reynolds numbers. Note that the frequency of vortex shedding was determined from the spectrum of the lift force. Numerical methods and key findings by some participants are summarized as follows. Yeon et al. [7] used an in-house program, CFDShip-IOWA, a highfidelity orthogonal curvilinear grid solver based on the LES method. In their program, the dissipative eddies are modelled by the Lagrangian dynamic subgrid-scale (SGS) model. The Navier-Stokes equations are discretized on a non-uniform staggered orthogonal curvilinear grid. A four-step fractional step approach is used for
velocity and pressure coupling. The convective terms are approximated by QUICK and WENO schemes. Some sensitivity studies were carried out on aspect ratio, grid resolution and convection scheme. It was found that the small aspect ratio, AR = 2, along with a conservative scheme led to the best results at super-critical Reynolds numbers while AR = 8 produced the best solutions at sub-critical Reynolds numbers. The mean drag coefficients were compared to experimental data and other solutions. The general trend of the drag crisis was captured by the LES-based program. The work of Lloyd and James [8] used OpenFOAM libraries based on the LES method. It was found that unstructured grids provided better resolution of key flow features than a structured grid when similar grid number and boundary layer resolution were used. A blended upwind-central scheme was employed to avoid unnecessarily high numerical dissipation and to remove artificial wiggles observed in the fully central scheme. In their studies, the dynamic mixed Smagorinsky model was employed, which allowed the model coefficient to be adjusted dynamically according to the local flow and grid size. The dynamic model gives better solutions than the original Smagorinsky model does. AR = 1.7, and 2 were used to investigate the effect of aspect ratio on the solution at the Reynolds number of 6.31 × 104 . It was concluded that the use of relatively large aspect ratios can improve the results at low Reynolds numbers. Extensive studies were carried out by Wen and Qiu [9] by using 2D and 3D URANS, DES and LES methods based on the commercial software package, Star-CCM+. In the simulations by URANS, the effects of various turbulence models, including the SST k-ω model, the k-ε model, the SST with the local correlation transition model (LCTM), were examined. In the LES method, the wall-adapting local eddy-viscosity (WALE) SGS model was adopted. In their DES simulations, the improved delayed detached eddy simulation (IDDES) model, which combines the DDES and an enhanced RANS-LES hybrid model, was employed. Extensive studies were performed to examine the effects of grid size, time step, the first grid size and aspect ratio (for 3D solutions) on the results. Uncertainties due to spatial and temporal discretizations were also quantified. It was indicated that turbulence models have significant effects on the
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Fig. 5. RMS of Lift Coefficient. (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)
Fig. 6. Strouhal Number. (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)
solutions. Various aspect ratios (between 1.0 and 12) were used to investigate their impacts on solutions by DES and LES at various Reynolds numbers. The DES method improved the prediction; however; it was inadequate to capture the sudden drag reduction at the critical Reynolds regime. The predictions by the LES method are better than others in predicting the drag crisis, however, with an earlier drop. Ye and Wang [10] used a URANS solver, pimpleFoam in OpenFOAM, coupled with an overset grid technique. The SST k-ω turbulence model and a set of wall functions were employed. Their studies indicated that the combination of the overset grid and the RANS solver improved the numerical stability.
4.2. Benchmark results The computed mean CD , RMS of CL , and Strouhal numbers at selected Reynolds numbers by participants are compared with the experimental data in Figs. 4–6, respectively. Note that the Strouhal number in the experimental data at Re = 5.06E + 05, presented in Fig. 6, may be peculiar. Attempts have been made to investigate the experimental data at this particular Reynolds number, however, no conclusion has been drawn. In the figures, blue symbols for A, B, C, G, H1, H2, H5 and H6 represent the numerical solutions by URANS methods, red ones for D, E, F and H4 represent the LES results, and the DES solutions are denoted by the green symbol H3. The relative
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Fig. 7. Relative errors for CD . (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)
errors for CD by each method at various Reynolds numbers are also presented in Fig. 7. In terms of the overall trend, results obtained by LES are generally in better agreement with the experimental data than those by URANS and DES. There is no indication that DES leads to improved predictions in comparison with URANS. The steep drop of mean CD was captured by LES. In addition, the LES results agree better with the experimental data at most points than those by URANS. Some URANS methods gave reasonably good results at high Reynolds numbers.
5. Conclusions and recommendations A reasonably large number of organizations have participated in the benchmark studies organized by the ITTC Ocean Engineering Committee. CFD methods, including URANS (2-D and 3-D), DES and LES, were used by participants. In terms of overall trend, numerical predictions by LES are generally in better agreement with the experimental data than those by URANS and DES at most Reynolds numbers. It can be concluded that the LES method in general cap-
tures the drag crisis phenomenon. In the LES simulations, most participants have studied the effect of aspect ratio on the solution. As indicated by Norberg [11], the spanwise correlation lengths are larger for lower Reynolds numbers. Large aspect ratios are therefore required for LES simulations at low Reynold numbers than those at high Reynold numbers. One should be cautious when comparing 2-D RANS solutions with 3-D experimental data since the correlation length is not considered in 2-D solutions. The time averaging models in URANS solutions tend to smooth out the turbulent flow and lead to narrow banded force spectra. In addition, it was found that uncertainties in URANS simulations are mainly due to modelling rather than discretization. The errors due to spatial and temporal discretization are relatively small. Although the overset grid technique seems to improve the 2-D URANS prediction, it can be concluded that 2-D or 3-D URANS without a transient turbulence model is inadequate to capture the drag phenomenon. Only one participant used DES for the simulations. It was concluded from the limited studies that the DES model, utilizing the
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RANS model in the near wall region, is not able to capture the drag crisis either. LES shows promises in predicting drag crisis. However, the discretization errors of LES simulations are significant. The aspect ratio has a great impact on the solution. The following recommendations are made to further address the drag crisis phenomenon: • More experiments need to be carried out and uncertainties in model tests should be examined. • Transient turbulence models may be further studied in URANS simulations. • More studies on LES should be performed, while the uncertainties due to spatial and temporal discretization and particularly aspect ratio need to be further investigated. • Further benchmark studies based on DES are recommended. References
7
[2] ITTC, Final Report of Ocean Engineering Committee, 2011. [3] J.J. de Wilde, R.H.M. Huijsmans, Experiments for high Reynolds numbers VIV on risers, in: Proceedings of ISOPE, Stavanger, Norway, 2001. [4] J.J. de Wilde, R.H.M. Huijsmans, Laboratory investigation of long riser VIV response, in: Proceedings of ISOPE, Toulon, 2004. [5] J.J. de Wilde, R.H.M. Huijsmans, M.S. Triantafyllou, Experimental investigation of the sensitivity to in-line on vortex-induced vibrations, in: Proceedings of ISOPE, Hawaii, USA, 2003. [6] J.J. de Wilde, R.H.M. Huijsmans, J. Tukker, Experimental investigation into the vortex formation in the wake of an oscillating cylinder using particle image velocimetry, in: Proceedings of ISOPE, San Francisco, USA, 2006. [7] S.M. Yeon, J. Yang, F. Stern, Large-eddy simulation of the flow past a circular cylinder at sub- to super-critical Reynolds numbers, Appl. Ocean Res. 59 (2016) 663–675. [8] T.P. Lloyd, M. James, Large eddy simulations of a circular cylinders at Reynolds numbers surrounding the drag crisis, Appl. Ocean Res. 59 (2016) 676–686. [9] P. Wen, W. Qiu, Investigation of drag crisis phenomenon using CFD methods, Appl. Ocean Res. 67 (2017) 306–321. [10] H. Ye, D. Wan, Benchmark computations for flows around a stationary cylinder with high Reynolds number by RANS-overset grid approach, Appl. Ocean Res. 65 (2017) 315–326. [11] C. Norberg, Flow around a circular cylinder: aspects of fluctuating lift, J. Fluids Struct. 15 (2001) 459–469.
[1] O.H. Oakley, D. Spencer, Deepstar high Reynolds number cylinder test program, in: Proceedings of Deep Offshore Technology Conference, New Orleans, USA, 2004.
Please cite this article in press as: W. Qiu, et al., Numerical benchmark studies on drag and lift coefficients of a marine riser at high Reynolds numbers, Applied Ocean Research (2017), https://doi.org/10.1016/j.apor.2017.10.010
ARTICLE IN PRESS Applied Ocean Research xxx (2017) xxx–xxx
Contents lists available at ScienceDirect
Applied Ocean Research journal homepage: www.elsevier.com/locate/apor
Numerical benchmark studies on drag and lift coefficients of a marine riser at high Reynolds numbers Wei Qiu a,∗ , Dong-Yeon Lee b , Halvor Lie c , Jean-Marc Rousset d , Takashi Mikami e , Sergio Sphaier f , Longbin Tao g , Xuefeng Wang h , Viacheslav Magarovskii i a
Memorial University, Canada Samsung Ship Model Basin, Republic of Korea c Marintek, Norway d Ecole Centrale de Nantes, France e Akishima Laboratory (MITSUI ZOSEN) Inc., Japan f Universidade Federal do Rio de Janeiro, Brazil g University of Newcastle, United Kingdom h Shanghai Jiao Tong University, China i Krylov Shipbuilding Research Institute, Russia b
a r t i c l e
i n f o
Article history: Available online xxx Keywords: Vortex induced vibration RANS DES LES Drag crisis phenomenon
a b s t r a c t Numerical benchmark studies on drag and lift coefficients of a marine riser have been organized by the 27th ITTC Ocean Engineering Committee. The purpose of the studies was to benchmark the capabilities of CFD methods through quantitative comparisons and validation studies against the model test results of a circular cylinder by MARIN. Studies were focused on the drag crisis phenomenon for the stationary smooth cylinder in the critical Reynolds number regime. Eight organizations have participated in the studies by using RANS, DES and LES methods. An overview of the model test results, test cases, submissions and comparison results are presented in this paper. Conclusions and recommendations are made for future studies. © 2017 Elsevier Ltd. All rights reserved.
1. Introduction Vortex Induced Vibration (VIV) of marine risers poses a significant challenge as the offshore oil and gas industry moves into deep water. Due to the asymmetric nature of the vortex shedding, risers vibrate in both in-line and cross-flow directions. The in-line motion can be a major contributor to the fatigue damage due to its higher frequencies and response modes although the in-line displacement is normally less than the cross-flow one. It also triggers higherorder harmonic responses in both in-line and cross-flow directions which further increase the fatigue damage. Marine risers have very large length-to-diameter ratios, especially for deepwater risers. The length of risers cannot be scaled due to the depth limitation of existing wave basins and therefore experimental methods cannot be reliably employed for design verification. To predict the VIV response of a riser system, practical numerical methods have been developed by making use of
∗ Corresponding author. E-mail address: [email protected] (W. Qiu).
databases with experimental hydrodynamic coefficients at various Reynolds numbers, for example, those by Oakley and Spencer [1]. Most experiments have been carried out to measure the hydrodynamic forces on a segment of a riser. The experimental databases, however, cover a limited range of Reynolds numbers for a segment of rigid or flexible riser. It is desirable to use computational fluid dynamics (CFD) methods to compute the hydrodynamic forces on marine risers, complementing the experimental databases for VIV prediction, and to simulate the responses of long risers. CFD simulations of VIV have been focused on flow around circular cylinders and their induced forces. While the cylinder geometry is simple, it remains challenging for CFD methods to resolve the flow instability and separation in the boundary layer and in the wake. Since 2009, the ITTC Ocean Engineering Committee has carried out studies to benchmark the capabilities of CFD methods for the prediction of hydrodynamic forces on a stationary smooth cylinder at high Reynolds numbers. In the benchmark studies organized by the 26th ITTC Ocean Engineering Committee, all participants used the two-dimensional unsteady Reynolds Averaged Navier-Stokes (URANS) method. Various turbulence models were employed with the assumption that the flow is fully tur-
https://doi.org/10.1016/j.apor.2017.10.010 0141-1187/© 2017 Elsevier Ltd. All rights reserved.
Please cite this article in press as: W. Qiu, et al., Numerical benchmark studies on drag and lift coefficients of a marine riser at high Reynolds numbers, Applied Ocean Research (2017), https://doi.org/10.1016/j.apor.2017.10.010
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Nomenclature Abbreviations AR Aspect ratio of the cylinder, L/D CD Drag coefficient, FD /( 12 U 2 DL) Lift coefficient, FL /( 12 U 2 DL) CL D Cylinder diameter FL Lift FD Drag Shedding frequency fs L Length of the cylinder Reynolds number, UD/ Re Strouhal number, fs D/U St U Inflow velocity Density of water Kinematic viscosity ITTC International towing tank conference Computational fluid dynamics CFD DES Detached eddy simulation LES Large eddy simulation URANS Unsteady Reynolds averaged Navier-Stokes equations VIV Vortex induced vibration
Fig. 2. High Reynolds Number VIV Test Apparatus by MARIN.
Fig. 3. Drag Coefficient for the Smooth Cylinder.
Fig. 1. The Smooth Stationary Cylinder.
bulent. It was concluded from the studies that the drag crisis phenomenon on the stationary smooth cylinder was not captured by the URANS methods (ITTC Ocean Engineering Committee Report [2]). It is well known that the drag crisis is caused by the instability of separated shear layer in the critical Reynolds number regime (2 × 105 < Re < 5 × 105 ). At the critical Reynolds numbers, the transition points are very close to the points of flow separation. As a result, the shear layer eddies cause the mixture of flow in the boundary layer and the flow separation is delayed. The delay of flow separation leads to the reduction of the drag coefficient. Since numerical methods based on two-dimensional URANS solvers are inadequate to simulate this physical phenomenon, it is necessary to extend the benchmark studies by including other CFD methods. The 27th ITTC Ocean Engineering Committee extended the VIV benchmark studies by including the detached eddy simulation (DES) and the large eddy simulation (LES) methods. The CFD solutions were compared with the model test results for a circular cylinder. An overview of the model tests carried out by MARIN, test cases, the comparison of experimental and numerical results, as well as conclusions and recommendations, are presented in the paper.
Table 1 Participants of the Benchmark Studies.
1 2 3 4 5 6 7 8
Organization
Country
China Ship Scientific Research Centre Seoul National University Samsung Ship Model Basin Memorial University Inha University University of Iowa University of Southampton Shanghai Jiao Tong University
China Korea Korea Canada Korea USA UK China
2. Experimental data As reported in the ITTC Ocean Engineering Committee Report [2], the benchmark experimental data for the VIV of a stationary circular cylinder was provided by MARIN. The rigid cylinder is 200 mm in diameter and 3.52 m in length (Fig. 1). The cylinder was suspended from the carriage about 1.7 m below the calm water surface. The VIV test apparatus is shown in Fig. 2. The towing tank of MARIN is 4 m deep, 4 m wide and 210 m long. The cylinder was towed horizontally by the carriage at various speeds. Details of the tests can found in the work of de Wilde and Huijsmans [3], de Wilde and Huijsmans [4], de Wilde et al. [5] and de Wilde et al. [6]. As an example, the measured drag coefficient for the smooth stationary cylinder is presented in Fig. 3.
Please cite this article in press as: W. Qiu, et al., Numerical benchmark studies on drag and lift coefficients of a marine riser at high Reynolds numbers, Applied Ocean Research (2017), https://doi.org/10.1016/j.apor.2017.10.010
2D/3D
Steady/Unsteady
Method
FLUENT (Commercial Code) SNUFOAM (In-house Code) FLUENT CFDShip-IOWA (In-house Code) Code-S (In-house Code) OpenFOAM (Open Source Code) Naoe-FOAM-SJTU (In-house Code) STAR-CCM+ (Commercial Code) STAR-CCM+ STAR-CCM+ STAR-CCM+ STAR-CCM+ STAR-CCM+
2D 2D 2D 3D 3D 3D 2D 2D 2D 3D 3D 3D 2D
Unsteady Unsteady Unsteady Unsteady Unsteady Unsteady Unsteady Unsteady Unsteady Unsteady Unsteady Unsteady Transient
RANS RANS RANS LES LES LES RANS RANS RANS DES LES RANS RANS
Table 3 Computational Details. y+
Number of Grids
Type of Grids
Wall Function (Used/Not Used)
Turbulence Model
Transition Model (Used/Not Used)
Convection Term
t (s)
Aspect Ratio (AR)
A B C D E
59 2 10 0.03–0.15 –
87,223 32,280 43,820 67,000,000 11,300,000
U N N N N
SST k-ω SST k-ω SST k-ω Dynamic model Dynamic model
N N N N N
Upwind Upwind Upwind QUICK/WENO Upwind
0.001/0.0005 0.001/0.0002/0.0001 0.001 0.00008/0.0001 CFL = 0.5
– – – 2 and 8
F G H1 H2 H3 H4 H5 H6
1 1.0–4.9 0.06–0.56 0.06–0.56 0.06–0.56 0.06–0.56 0.06–0.56 0.06–0.56
Max 4,000,000 100,000 592,478 592,478 21,215,000 12,400,000 10,517,000 592,478
Structured Structured Structured Structured Unstructured (Cartesian) Unstructured Chimera Hybrid Hybrid Structured Structured Structured Hybrid
N U N N N N N N
Dynamic model SST k-ω SST k-ω k-ε (Standard) – – SST k-ω LCMT
N N N N N N N Y
Hybrid (Central + Upwind) Upwind Upwind Upwind Upwind Upwind Upwind Upwind
0.005 0.00017–0.0015 0.0001–0.002 0.0001–0.002 0.002–0.02 0.002–0.02 0.002–0.02 0.0001–0.002
1.7, , 2 – – – 3.0 12.0 6.0 –
ARTICLE IN PRESS
Program Name
G Model
APOR-1451; No. of Pages 7
A B C D E F G H1 H2 H3 H4 H5 H6
W. Qiu et al. / Applied Ocean Research xxx (2017) xxx–xxx
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Table 2 Numerical Methods Used by Participants.
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Fig. 4. Mean Drag Coefficient. (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)
For numerical computations, the following six (6) Reynolds numbers were selected to cover the critical Reynolds number regime: 6.31E + 04, 1.26E + 05, 2.52E + 05 3.15E + 05, 5.06E + 05, 7.57E + 05
3. Participants and numerical methods A number of organizations and individuals have been invited to participate in the benchmark studies. A list of participants is given in Table 1, which include those participated in the studies organized by the 26th and the 27th ITTC Ocean Engineering Committee. In general, three CFD methods were employed in the studies, including 2-D/3-D URANS, DES and LES methods. Commercial software packages, such as FLUENT and Star-CCM+, in-house codes and open-source based codes (OpenFOAM) were used by the participants. The numerical methods are summarized in Table 2 and the computational details are presented in Table 3. 4. Numerical methods and results 4.1. Numerical methods used and key findings by participants In the benchmark studies, each participant submitted the computed mean CD , mean CL , RMS of CL , and the Strouhal number at selected Reynolds numbers. Note that the frequency of vortex shedding was determined from the spectrum of the lift force. Numerical methods and key findings by some participants are summarized as follows. Yeon et al. [7] used an in-house program, CFDShip-IOWA, a highfidelity orthogonal curvilinear grid solver based on the LES method. In their program, the dissipative eddies are modelled by the Lagrangian dynamic subgrid-scale (SGS) model. The Navier-Stokes equations are discretized on a non-uniform staggered orthogonal curvilinear grid. A four-step fractional step approach is used for
velocity and pressure coupling. The convective terms are approximated by QUICK and WENO schemes. Some sensitivity studies were carried out on aspect ratio, grid resolution and convection scheme. It was found that the small aspect ratio, AR = 2, along with a conservative scheme led to the best results at super-critical Reynolds numbers while AR = 8 produced the best solutions at sub-critical Reynolds numbers. The mean drag coefficients were compared to experimental data and other solutions. The general trend of the drag crisis was captured by the LES-based program. The work of Lloyd and James [8] used OpenFOAM libraries based on the LES method. It was found that unstructured grids provided better resolution of key flow features than a structured grid when similar grid number and boundary layer resolution were used. A blended upwind-central scheme was employed to avoid unnecessarily high numerical dissipation and to remove artificial wiggles observed in the fully central scheme. In their studies, the dynamic mixed Smagorinsky model was employed, which allowed the model coefficient to be adjusted dynamically according to the local flow and grid size. The dynamic model gives better solutions than the original Smagorinsky model does. AR = 1.7, and 2 were used to investigate the effect of aspect ratio on the solution at the Reynolds number of 6.31 × 104 . It was concluded that the use of relatively large aspect ratios can improve the results at low Reynolds numbers. Extensive studies were carried out by Wen and Qiu [9] by using 2D and 3D URANS, DES and LES methods based on the commercial software package, Star-CCM+. In the simulations by URANS, the effects of various turbulence models, including the SST k-ω model, the k-ε model, the SST with the local correlation transition model (LCTM), were examined. In the LES method, the wall-adapting local eddy-viscosity (WALE) SGS model was adopted. In their DES simulations, the improved delayed detached eddy simulation (IDDES) model, which combines the DDES and an enhanced RANS-LES hybrid model, was employed. Extensive studies were performed to examine the effects of grid size, time step, the first grid size and aspect ratio (for 3D solutions) on the results. Uncertainties due to spatial and temporal discretizations were also quantified. It was indicated that turbulence models have significant effects on the
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Fig. 5. RMS of Lift Coefficient. (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)
Fig. 6. Strouhal Number. (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)
solutions. Various aspect ratios (between 1.0 and 12) were used to investigate their impacts on solutions by DES and LES at various Reynolds numbers. The DES method improved the prediction; however; it was inadequate to capture the sudden drag reduction at the critical Reynolds regime. The predictions by the LES method are better than others in predicting the drag crisis, however, with an earlier drop. Ye and Wang [10] used a URANS solver, pimpleFoam in OpenFOAM, coupled with an overset grid technique. The SST k-ω turbulence model and a set of wall functions were employed. Their studies indicated that the combination of the overset grid and the RANS solver improved the numerical stability.
4.2. Benchmark results The computed mean CD , RMS of CL , and Strouhal numbers at selected Reynolds numbers by participants are compared with the experimental data in Figs. 4–6, respectively. Note that the Strouhal number in the experimental data at Re = 5.06E + 05, presented in Fig. 6, may be peculiar. Attempts have been made to investigate the experimental data at this particular Reynolds number, however, no conclusion has been drawn. In the figures, blue symbols for A, B, C, G, H1, H2, H5 and H6 represent the numerical solutions by URANS methods, red ones for D, E, F and H4 represent the LES results, and the DES solutions are denoted by the green symbol H3. The relative
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Fig. 7. Relative errors for CD . (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)
errors for CD by each method at various Reynolds numbers are also presented in Fig. 7. In terms of the overall trend, results obtained by LES are generally in better agreement with the experimental data than those by URANS and DES. There is no indication that DES leads to improved predictions in comparison with URANS. The steep drop of mean CD was captured by LES. In addition, the LES results agree better with the experimental data at most points than those by URANS. Some URANS methods gave reasonably good results at high Reynolds numbers.
5. Conclusions and recommendations A reasonably large number of organizations have participated in the benchmark studies organized by the ITTC Ocean Engineering Committee. CFD methods, including URANS (2-D and 3-D), DES and LES, were used by participants. In terms of overall trend, numerical predictions by LES are generally in better agreement with the experimental data than those by URANS and DES at most Reynolds numbers. It can be concluded that the LES method in general cap-
tures the drag crisis phenomenon. In the LES simulations, most participants have studied the effect of aspect ratio on the solution. As indicated by Norberg [11], the spanwise correlation lengths are larger for lower Reynolds numbers. Large aspect ratios are therefore required for LES simulations at low Reynold numbers than those at high Reynold numbers. One should be cautious when comparing 2-D RANS solutions with 3-D experimental data since the correlation length is not considered in 2-D solutions. The time averaging models in URANS solutions tend to smooth out the turbulent flow and lead to narrow banded force spectra. In addition, it was found that uncertainties in URANS simulations are mainly due to modelling rather than discretization. The errors due to spatial and temporal discretization are relatively small. Although the overset grid technique seems to improve the 2-D URANS prediction, it can be concluded that 2-D or 3-D URANS without a transient turbulence model is inadequate to capture the drag phenomenon. Only one participant used DES for the simulations. It was concluded from the limited studies that the DES model, utilizing the
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RANS model in the near wall region, is not able to capture the drag crisis either. LES shows promises in predicting drag crisis. However, the discretization errors of LES simulations are significant. The aspect ratio has a great impact on the solution. The following recommendations are made to further address the drag crisis phenomenon: • More experiments need to be carried out and uncertainties in model tests should be examined. • Transient turbulence models may be further studied in URANS simulations. • More studies on LES should be performed, while the uncertainties due to spatial and temporal discretization and particularly aspect ratio need to be further investigated. • Further benchmark studies based on DES are recommended. References
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[2] ITTC, Final Report of Ocean Engineering Committee, 2011. [3] J.J. de Wilde, R.H.M. Huijsmans, Experiments for high Reynolds numbers VIV on risers, in: Proceedings of ISOPE, Stavanger, Norway, 2001. [4] J.J. de Wilde, R.H.M. Huijsmans, Laboratory investigation of long riser VIV response, in: Proceedings of ISOPE, Toulon, 2004. [5] J.J. de Wilde, R.H.M. Huijsmans, M.S. Triantafyllou, Experimental investigation of the sensitivity to in-line on vortex-induced vibrations, in: Proceedings of ISOPE, Hawaii, USA, 2003. [6] J.J. de Wilde, R.H.M. Huijsmans, J. Tukker, Experimental investigation into the vortex formation in the wake of an oscillating cylinder using particle image velocimetry, in: Proceedings of ISOPE, San Francisco, USA, 2006. [7] S.M. Yeon, J. Yang, F. Stern, Large-eddy simulation of the flow past a circular cylinder at sub- to super-critical Reynolds numbers, Appl. Ocean Res. 59 (2016) 663–675. [8] T.P. Lloyd, M. James, Large eddy simulations of a circular cylinders at Reynolds numbers surrounding the drag crisis, Appl. Ocean Res. 59 (2016) 676–686. [9] P. Wen, W. Qiu, Investigation of drag crisis phenomenon using CFD methods, Appl. Ocean Res. 67 (2017) 306–321. [10] H. Ye, D. Wan, Benchmark computations for flows around a stationary cylinder with high Reynolds number by RANS-overset grid approach, Appl. Ocean Res. 65 (2017) 315–326. [11] C. Norberg, Flow around a circular cylinder: aspects of fluctuating lift, J. Fluids Struct. 15 (2001) 459–469.
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Please cite this article in press as: W. Qiu, et al., Numerical benchmark studies on drag and lift coefficients of a marine riser at high Reynolds numbers, Applied Ocean Research (2017), https://doi.org/10.1016/j.apor.2017.10.010