Proceedings of the ASME th International Conference on Ocean, Offshore and Arctic Engineering OMAE2011

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1 Proceedings of the ASME 211 3th International Conference on Ocean, Offshore and Arctic Engineering OMAE211 Proceedings of Proceedings of the ASME 211 June 3th19-24, International 211, Rotterdam, Conference The onnetherlands Ocean, Offshore and Arctic Engineering OMAE 211 June 19-24, 211, Rotterdam, The Netherlands OMAE OMAE BREAKING WAVE IMPACT ON A PLATFORM COLUMN: AN INTRODUCTORY CFD STUDY Csaba Pakozdi MARINTEK, P.O.Box 4125 Valentinlyst N-745 Trondheim, Norway Phone: , Fax: csaba.pakozdi@marintek.sintef.no Timothy E. Kendon Carl-Trygve Stansberg MARINTEK Trondheim, Norway ABSTRACT The slamming of breaking waves on the legs of large volume offshore platforms has received increased attention over recent years. To investigate this problem, MARINTEK s Wave Impact Loads JIP has, in one of its sub-tasks, focused towards an idealised model test setup of a rectangular cylinder in breaking waves. The model consists of a vertical column with a fragment of a horizontal deck attached. The model is fixed at a distance L ahead of the wave maker. Physical scale model test experiments of the block in regular waves and in wave groups have been carried out in Phase 1 of the JIP (28). The objective of this study is the CFD simulation of a long crested breaking wave and its impact on the aforementioned cylinder and deck structure in order to find out the feasibility of the numerical reconstruction of such events. The commercial CFD tool Star-CCM+ V ( is used in this study. This paper considers results from the test setup, and compares the measured wave elevation against results from the CFD code. The position of the cylinder in relation to the breaking wave front is investigated in the numerical simulation in order to analyze its effect on the slamming force. Use of an unsteady wave boundary condition, matching the exact motion history of the wave-maker with the measured free surface elevation at the wave maker gives an almost exact matching between the computed wave profile and the measured wave profile. The improvement in the numerical tool of Star-CCM+ which makes it possible to use higher order time integration scheme for VOF significantly decreases the numerical Address all correspondence to this author. diffusion of the wave propagation. This new scheme also enables the use of a time step 1 times larger than the first order scheme which reduces the computational time. Because a large time step can be chosen it is important that the time step is small enough to capture the correct time evolution of the physical phenomena of interest. Capturing the pressure evolution at a slamming event demands very high spatial resolution. Spatially averaged slamming pressures look fairly similar to the model test observations, while further work is needed for a more detailed comparison. INTRODUCTION Due to its importance for the design and limit-state analysis of column-based offshore platforms such as semisubmersibles and gravity-based structures, the prediction of extreme wave impact loads on the columns of offshore structures has been a high priority field of research for many years, e.g. confer [1] and [2] In deep water, historically this research was focused towards non-breaking waves. However it is known that breaking waves (resulting from a crest height exceeding a limiting steepness) exert far larger wave induced forces on the columns of offshore structures than non-breaking waves. Perhaps one of the earliest studies on this topic was that by [3]. Their experiments on the impact loads of breaking waves on a vertical circular cylinder showed that the impact pressure at the wave crest was proportional to the square of the impact velocity (defined as the particle velocity of the breaking waves). They also showed that, for the same wave celerity, a wave-crest break- 1 Copyright c 211 by ASME

2 ing (overturning) at impact yielded significantly higher impact pressure than a so-called broken-wave whose crest overturned before impact. In line with that study, we define a breaking-wave impact event as the former of these two events and it is this more extreme impact event that this paper is focused towards. Although a significant body of experimental and theoretical work exists on breaking waves ( [4], [5], [6]), which has led to a good understanding of this phenomenon, the complex physics of breaking-wave impact in deep water is less well understood. Given the physical complexity of this phenomenon (which in addition to the complex kinematics of wave breaking involves wave-diffraction, wave run-up along the column and wave amplification) experimental validation is essential. Therefore as one of the subtasks of MARINTEK s Wave Impact Loads JIP (26-21), model test experiments of breakingwave impact on a vertical rectangular cylinder (shown in Fig. 4) were carried out; for more description about the model tests confer [7]. Although the horizontal loads on the cylinder were the focus for these experiments, a simplified horizontal deck structure was attached on top of the column to both obtain a more representative structure for fluid-structure interaction, and also to facilitate wave-in-deck measurements, which is another important area of interest with regard design loads; although not the focus of this paper, for a related paper on wave-in-deck loads confer e.g. [8] Whilst, with the advent of Particle Image Velocimetry, model tests are increasingly able to provide a spatial picture of the flow field during wave impact events, the procedure is nontrivial and so model test results are still largely restricted to time histories at specific locations, global integral loads and video snapshots. In this respect, numerical modeling using CFD is a valuable tool to provide qualitative insight into the wave impact physics simultaneously in space and time. The objective of this study is the CFD simulation of a long crested breaking-wave impact on a rectangular cylinder with simplified deck structure in order to find out the possibility of the numerical reconstruction of such events and to gain greater insight into the phenomenon to facilitate simpler engineering procedures as are applied in say coastal engineering (e.g. [9]). The commercial CFD tool Star-CCM+ v ( has been used in this study. The version used was a beta-version which includes an improved second order implicit time integration scheme for the VOF calculation. The degree of the similarity of the numerically simulated breaking wave to the measured wave is crucial for the usefulness of the comparisons. Small differences between the two can generate completely different slamming load time histories as observed and described by [8]. To this end, generation of the wave in the CFD simulation has been a focus for this study. There are two natural options which are typically available within VOFbased CFD tools with regard wave generation: FIG. 1. MARINTEK s Towing Tank III Analytically The inlet and the outlet conditions are defined by unsteady velocity profiles and the free surface displacement is defined by the VOF parameters for each cell face at the inlet boundary and at the outlet boundary according to a wave theory. The wave-field is initialized according to the chosen wavetheory. This way the assumption of periodicity of the wave theories is satisfied. The commercial CFD solver used in this study offers in-built functionality for generation of numerical waves using regular waves up to Stokes 5 th or linear irregular waves. The benefit of this technique is that it is fast, simple to implement, and not CPU hungry. The main disadvantage is that (inherently) the resulting waves will only ever approximate the physics of the waves-generated in the model tank which will worsen as the wave becomes more nonlinear (e.g. [8], [1]). Simulation of the wave flap The exact description of the kinematics of a wave maker can be applied at the inlet using a moving mesh technology. This promises the possibility of a real wave generation which could model the wave-maker used in the experiments. The advantage of this approach is that different types of wave-maker can be simulated. The unknown water level can be calculated if the wave maker is modeled explicitly using a moving mesh; however this can give a significant increase of the calculation time (according to CD-adapco). In this paper, an alternative approach was applied as a compromise to the aforementioned. This is outlined later and involves the combination of a potential flow solver to provide the unknown free-surface elevation at the wave-maker. The approach is similar to that applied in [11], although domain decomposition is not applied in this study. MODEL TEST SETUP The experiments were carried out in MARINTEK s Towing tank III (See Fig. 1). This towing tank is 85 m long and 1.5m wide. It is designed for a water depth of 1. m. A hydraulically 2 Copyright c 211 by ASME

3 +.83 m. m m m FIG. 2. MARINTEK s wave maker BM1 operated, computer controlled, two flaps wave-maker is installed in the tank (See Fig. 2). At the downstream end of the flume a parabolic beach is installed. An idealized deck structure of an offshore platform was used. A sketch of the test setup without and with the platform is shown in Fig. 3. The position of the wave probes, which are compared with the numerical simulations, are defined in Tab. 1. FIG. 3. Test setup, without and with plattform Wave probe nr. x [m] y [m] Comm. WP WP WP WP WP without platform with FIG. 4. Picture of the rectangular cylinder model with deck a transient velocity inlet condition was defined in order to sim- TAB. 1. Position of the wave probe.2 The model consists of a vertical column and a fragment of a horizontal deck attached. The model was fabricated of aluminum alloy and the vertical column has the dimensions mm 3 (length breadth height). The airgap was 5 mm above the still water line (SWL). The models are presented in Fig. 4. For consistency of reference with the CFD setup, we now define a right handed coordinate system Oxyz with the xy-plane on the still water line, the z-axis vertically upwards, and with the origin at the wave-maker s still position. The wave propagates along the length of the tank in the positive x-direction. NUMERICAL SIMULATION OF CALIBRATION WAVE Using the measured time series of the position of the flaps and using the calculated angular velocity of the flaps (Fig. 5), β(t) [rad] ω β (t) [rad/s] γ(t) [rad] ω γ (t) [rad/s] time [s] FIG. 5. The measured angles of the flaps (β(t) and γ(t)) and the calculated angular velocities (ω β (t) and ω γ (t)) 3 Copyright c 211 by ASME

4 z [m] z [m] t = 2.59 s x [m] Velocity vector (a) Explicit wave maker model t = 2.59 s x [m] Hinges (b) Simplified wave maker model FIG. 6. Wave maker models ulate the wave making device. This definition of the velocity, in combination with a zero free surface elevation at the wave maker, can work sufficiently well if the wave height and the wave steepness are small enough at the wave maker device (confer e.g. [12]). This assumption can yield large errors with steep and high waves. The unknown water level can be calculated if the wavemaker is modeled explicitly using a moving mesh. This can give a significant increase of the calculation time according to CDadapco. Using a fully-nonlinear potential flow model based on the paper of [13] it was possible to simulate the calibration wave up to the breaking event and so estimate the free surface elevation time series at the wave maker. The model solves the potential flow equations with a fully non-linear free surface condition using the linear finite element method (FEM) and a mixed Eulerian-Lagrangian time updating, based on a fourth-order explicit Runge-Kutta time integration scheme. The potential solver is quicker than the VOF solver by at least an order of magnitude. The FEM solver models explicitly the wave maker as shown in Fig. 6 (a). Fig. 7 shows the kinematic model which was implemented for the FEM solver while Fig. 6 (b) shows the simplified model used in STAR-CCM+ to define the velocity field at the inlet as a user defined field functions. Using these field functions and the numerically estimated free surface elevation time series gives similar inlet conditions to those of the analytical approach referenced earlier. CFD DOMAIN SETUP The computational domain uses a right handed coordinate system Oxyz as used in the model test; with the xy-plane on the still water level (SWL), the z-axis positive upwards, and with the origin at the mean position of the wave-maker. A three dimensional trimmed mesh with several cell layer in the y-direction was generated for the simulation cases. The simulation domain was divided into four sub-domains, upstream, model, downstream and beach, due to mesh generating and post-processing issues. When the simulation contains a platform the model sub-domain volume mesh is only replaced in the simulation setup. Extents of the domain The extents of the computational domain are defined in Tab. 2. In order to avoid reflected waves from the far field boundaries corrupting the computational solution, the inlet and outlet boundaries were set far away from the FIG. 7. Kinematical model of a two flaps wave maker Direction start [m] end [m] x y z TAB. 2. Extents of domain 4 Copyright c 211 by ASME

5 (a) (a) (b) (b) FIG. 8. Mesh topology FIG. 9. Mesh topology platform. The water depth was set to 1 m in accordance with the model test, and the top boundary was set at z = 5 m above the SWL. A wall boundary with slip condition was set to y = 5.25 m in accordance with the model test and a symmetry boundary was set to y =. m. Boundary and initial conditions Fig. 8 (a) shows the three dimensional computational sub-domains with the boundary conditions defined and without platform and Fig. 8 (b) with platform. In-place interfaces are defined (grey color) between the sub-domains. At the upstream boundary of the upstream subdomain a velocity inlet (red color) condition and a wall condition with slip (grey color) were specified. The velocity field was defined by an external data file which contained time-histories of the measured flap positions and angular velocity components. The water height was defined by another external data file which contained the calculated free surface elevation at x = m. At the downstream boundary of the beach sub-domain a pressure outlet condition (orange color) and a wall slip condition (grey color) were specified. The pressure field was defined by the hydrostatic pressure (using a user defined field function) and the water level by the neighboring cell s VOF value. The bottom and the top of the domain, and the platform, are defined as solid walls with slip (grey color). A symmetry boundary in the middle of the model tank is defined (blue color). The computational domain was initialized with a prescribed hydrostatic pressure, with a free surface height equal to zero and with a zero velocity field. Mesh topology In accordance with a recommendation provided by CD-adapco, the mesh domain was divided into several parts with different levels of mesh refinement. Where the parts are overlayed the mesh with the finest cell size is selected in the overlapping regions. Tab. 3 shows the cell size of the different parts of the mesh. When the platform is included a fine mesh zone is defined close to the cylinder (Impact zone (see Tab. 3)). The mesh is created by the STAR-CCM+ in-built mesh generator. The number of the cells is about 24 mesh cells. Fig. 9 (a) shows the three dimensional mesh structure without platform and Fig. 9 (b) with platform. Model of the physics Based on the recommendation of CDadapco, the incompressible laminar viscous model was used during the analysis. The standard VOF model was applied in the simulation with the default water and air properties defined by Star-CCM+. The standard solver with its default settings was used during the analysis with a second order implicit time integrator, with a time step.1 s which was possible due to the improved scheme (STAR-CCM ). Using a different solver setting during the project led to non-physical results. 5 Copyright c 211 by ASME

6 ζ [m].5 Potential FEM STAR CCM+ WAVE 6 x = 5.99 m 1 8 P modelscale = kpa Slamming forces P modelscale = kpa x = m x = 19.5 m ζ [m] 1.5 test Potential FEM STAR CCM+ WAVE 4 x = m F x (t) [N] 6 4 ζ [m] test Potential FEM STAR CCM+ WAVE 1 x = m time [s] FIG. 1. Calibration wave for test FIG. 11. Slamming force Measurement All the key properties (global force / VOF etc...) were monitored for each time step and exported as CSV (common separated file) files. After a simulation it is not possible to generate new monitors, therefore careful consideration has to be given as to which properties to monitor before the start of the simulation. Measuring the free surface elevation The free surface elevation is measured by monitoring the wetted length (VOF) along a vertically set numerical wave probe (line) placed according to the model tests. The numerical wave probe (line) contained 21 vertices and 2 elements with 1 mm length. The first vertex is 1 m under SWL of the numerical wave tank. The summation of the product of the VOF value at vertex and the element length gives the wetted length. The wetted length is saved at each time step. Measuring of the impact force The impact force is calculated using the Star-CCM+ Force report function. The fluid stress tensor (only pressure because of the slip condition) was integrated over the surfaces of a separated patch area of the cylinder to compute the impact load. The horizontal force was calculated and saved for each time step. NUMERICAL RESULTS The wave impact simulations are setup as described above. The input tables for the simulation are the extrapolated time series of the free surface elevation at x = m, the measured flaps position and the calculated angle velocity. Calibration wave Fig. 1 shows the comparison between the measured, potential flow simulated and STAR-CCM+ defined time series of the free surface elevation. The time series predicted by the Navier- Stokes-VOF method (NS-VOF) shows a much better agreement with the test experiment than the potential flow simulation. This indicates that the NS-VOF method is able to model the physics of local small wave breaking, which cannot be predicted by the potential flow description. Fig. 13 shows the magnitude of the velocity during the wave breaking. The maximum velocity on the jet is about two times larger than the speed of the wave propagation close to the free surface before the overturning. Fig. 12 shows the history of the free surface. The dotted black and red line show the contour of the cylinder at different positions. Two positions are chosen to see the change of the impact forces due to the movement. Breaking wave with platform Fig. 14 shows the free surface at different time points during the impact when the platform is placed at x = m. It is only close to the platform that we see three dimensional variation in the wave front. Fig. 15 displays the magnitude of the velocity during the impact. Building of air bubbles can be observed during the impact close to the patch (Fig. 15 (c)-(f)) where the slamming force is calculated. The air bubble occupied different positions, far from the patch (Fig. 16 (c)-(d)) and disappeared earlier during the impact when the platform was positioned at x = 19.5m. The effect of the air bubble can be immediately observed on the time history of the slamming forces through several peaks in Fig. 11 in the curve for x = m. For both curves shown in Fig. 11, the spatially averaged peak pressure over the force monitor patch is annotated at the maximum forces. Fig. 17 shows the pressure distribution on the half part of the patch 6 Copyright c 211 by ASME

7 where the slamming force is calculated in model scale at various time instances. The peak pressure value on the patch is about 25 kpa in model scale which equates to 1285 kpa in full scale. This peak pressure is one and half times larger than the spatially averaged peak pressure over the patch annotated in Fig. 11. CONCLUSION In general, comparing the calculated wave elevations with the data from the model test measurements shows that the computed wave profile matches better, almost exactly, the measured wave profile than was observed using the in-built analytical inlet/outlet wave conditions in Kendon et al. This can be explained by use of an unsteady wave boundary condition, matching the exact motion history of the wave-maker with the simulated free surface elevation at the wave maker. This setup gives an almost exact simulation of the model test without using the computationally costly moving mesh technique. Use of an unsteady velocity inlet boundary condition, matching the exact motion history of the wave-maker without correct description of the free surface elevation at the wavemaker gives a large deviation between the measured and simulated waves when the free-surface elevation is large at the wave maker. Further, the improvement in the numerical code which makes it possible to use higher order time integration scheme for VOF significantly decreases the numerical diffusion of the wave propagation compared to results from Kendon et al. This new scheme also enables the use of a time step ten times larger than the first order scheme which reduces the computational time. Because a large time step can be chosen it is important that the time step is small enough to capture the correct time evolution of the physical phenomena of interest (such as the slamming force or the pressure evolution during the slamming event). Capturing the pressure evolution at a slamming event demands very high spatial resolution. Spatially averaged slamming pressures look fairly similar to the model test observations, while further work is needed for a more detailed comparison. This project shows that the nonlinear wave propagation over long distance can be simulated accurately and efficiently by solvers based on potential flow theory. Use of potential flow theory for initializing the NS-VOF simulation (domain decomposition in time) can reduce the computational time and improve the accuracy of the numerical simulation. ACKNOWLEDGMENT This work has been carried out as a part of the MARIN- TEK Wave Impact Loads JIP - Phase 2 ( 29-21). Participants include: ABS; Aker Solutions; ConocoPhillips; MARIN- TEK; Petrobras; and StatoilHydro. The sponsors are gratefully acknowledged for the permission to publish this paper. Model test data were obtained from the previous MARINTEKWave Impact Loads JIP - Phase 1, where also Chevron, DNV, OIS-LLC and SEVAN participated in addition to those in Phase 2. Thanks go to Sven Enger and Jasmin Röper from Cd-adapco for their fantastic support. REFERENCES [1] Faltinsen, O. M., Kjærland, O., and Nøttveit, A., Wave impact loads and dynamic response of horizontal cylinders in offshore structures. In Proc. of 9th Offshore Technology Conference, pp [2] Sarpkaya, T., Wave impact loads on cylinders. In Proc. of 1th Offshore Technology Conference, pp [3] Ochi, M. K., and Tsau, C.-H., Prediction of impact pressure induced by breaking waves on vertical cylinder in random waves. Applied Ocean Research, 6(3). [4] Stokes, G. G., 188. Appendices and supplement to a paper on the theory of oscillatory waves. Stokes , 1, pp , [5] Longuet-Higgins, M. S., Integral properties of periodic gravity waves of finite amplitude. In Proc. R. Soc. Lond. A, Vol. 342, pp [6] Cokelet, E. D., Steep gravity waves in water of arbitrary uniform depth. In Phil, Trans. R. Soc. Lond. A, Vol. 286, pp [7] Stansberg, C. T., Baarholm, R., Berget, K., and Phadke, A. C., 21. Prediction of wave impact in extreme weather. In Proc. of Offshore Technology Conference. [8] Kendon, T., Pákozdi, C., Baarholm, R., Berthelsen, P., Stansberg, C.-T., Enger, S., and Peric, M., 21. Wave-indeck impact: Comparing CFD, simple methods, and model tests. In Proc. 29th OMAE Conf., Shanghai, China, June 6 11, ASME. [9] Sarpkaya, T., New wave pressure formulae for composite breakwater. In Proc. of 14th Conf. on Coastal Engineering. [1] Shellin, T., Peric, M., and Moctar, O., 29. Wave-deckload analysis for a jack-up structure. In Proc. 28th OMAE Conf., Honolulu, Hawaii, USA, May 3 - June 4, ASME. [11] Clauss, G. F., Stück, R., Stempinski, F., and Schmittner, C. E. Computational and experimental simulation of nonbreaking and breaking waves for the investigation of structural loads and motions. In Proc. 25th OMAE Conf. [12] Clauss, G., Habel, R., and Pákozdi, C., 21. Non-linear wave-structure interactions at artificial reefs. In Proc. 11th ISOPE Conf. [13] Wu, G. X.,, and Taylor, R. E., Finite element analysis of two-dimensional non-linear transient water waves. Applied Ocean Research, 16, pp Copyright c 211 by ASME

8 Name Absolute size m Relative size % Ratio Extends of volume shape m dx dy dz dx dy dz dz/dx dy/dx x start x end y start y end z start z end Base Beach air Free surface Wave zone Wmaker zone Simulation with platform Impact zone Impact zone farfield Impact zone nearfield Impact zone press. p TAB. 3. Cell size of the different part of the mesh Calibration wave time [s] x=19.5 m x=19.35 m 22.4 s s s s s s s s s s s s s s s s s s s s s s 21.3 s x [m] FIG. 12. History of the free surface elevation along the wave tank without platform; test nr Copyright c 211 by ASME

9 (a) (b) (c) FIG. 13. Magnitude of the velocity; calibration wave (a) (b) (c) FIG. 14. Free surface history; breaking wave with platform at x = m (a) (b) (c) FIG. 15. Magnitude of the velocity; breaking wave with platform at x = m 9 Copyright c 211 by ASME

10 (a) (b) (c) FIG. 16. Magnitude of the velocity; breaking wave with platform at x = 19.5 m (a) (b) (c) (d) (e) (f) FIG. 17. Pressure distribution on the patch in Pascals; breaking wave with platform at x = m 1 Copyright c 211 by ASME