Date 2012 . Author Rene H.M. Huijsmans, Steven Schmied e.a ^ j T
Address Delft University of Technology
i h i ' r
Ship Hydromechanics and Structures Laboratory % ^ L ^ w l l I . Mekelweg 2, 2628 CD Delft
Delft University of Technology
The formation of surfable w a v e s in a circular w a v e
pool - Comparison of numerical and experimental
approaches
by
R.H.M. Huijsmans, S. Schmied, G. Thomas, J . Binns,
M.R. Renilson and M. Javanmardi
Report No. 1 8 4 8 - P 2012
Proceedings of the ASME 2 0 1 2 3 1 " I n t e r n a t i o n a l C o n f e r e n c eon O c e a n , Offshore and Arctic E n g i n e e r i n g , O M A E 2 0 1 2 , J u l y 1¬ 6, 2 0 1 2 , Rio de J a n e i r o , B r a z i l , Paper O M A E 2 0 1 2 - 8 3 2 6 7
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Proceedings ofthe ASIVIE 2012 31st International Conference on Ocean, Offshore and Arctic Engineering OMAE2012 July 1-6, 2012, Rio de Janeiro, Brazil
OMAE2012-83267
THE FORMATION OF SURFABLE WAVES I N A CIRCULAR WAVE POOL
COMPARISON OF NUMERICAL AND EXPERIMENTAL APPROACHES
Mohammadreza Javanmardi
Australian Maritime College, University o f Tasmania
Launceston, TAS, Australia
Martin R . Renilson
Australian Maritime College, University o f Tasmania
Launceston, TAS, Australia
Steven Schmied
Liquid Time P t y L t d Hampton, V I C , Australia
Jonathan Binns
Australian Maritime College, University o f Tasmania
Launceston, TAS, Australia
Giles Thomas
Australian Maritime College, University o f Tasmania
Launceston, TAS, Australia
Rene Huijsmans
Technical University o f Delft Delft, The Nethedands
ABSTRACT
This paper investigates the capability o f a numerical approach to address the problem o f designing a wave pool. The numerical approach developed has the potential to reduce the number o f design alternatives which require testing by eliminating poor performing designs early in the design cycle. For the three dimensional computations in the present study, the CFD software F L U E N T (which solves the RANS equations with finite-volume approach and uses the volume o f fluid technique to simulate the fi-ee-surface motion) was utilized. Pressure source models i n straight and round tracks were simulated. Predicted results agreed closely with experiment data.
Keywords: CFD, wave pool, free surface, F L U E N T
INTRODUCTION
The interest in water sports has been increasing. Beaches with good quality surfable waves and shore conditions are used as resorts for escape and exercise. Surfing as an
exercise is popular in many beaches around the world. Although it simply needs only a surf board and an appropriate beach, locations with a suitable environment are limited. I n addition, weather conditions are not appropriate for surfing all the time. Indeed surfing breaks that consistently produce world class surfing conditions are rare [ I ] . The growth o f surfing has led to a new concept, a surf pool. A surf pool is a basin o f water in which waves are generated to permit someone to surf. Therefore, it won't be necessary anymore to struggle to find a perfect match o f weather and location. A surf pool provides a great surfing opportunity every day, even at locations without any sea. Different approaches have been implicated so far to create surfing conditions. Many surf pools have been built around the world so far. The Wembley swimming pool in London in 1934 contained the first artificial wave maker used for surfing. In 1966, the first indoor surfing was made possible in a wave pool in Tokyo, Japan[2]. In 2003 a new surf pool concept was invented by Greg Webber. This invention is to build a circular pool in which the surfing waves are created continuously by towing ship-like hulls along the banks o f the pool[3]. According to Webber, circular wave pool is capable o f providing a theoretically infinitely long ride around a central
island which is not possible in the conventional style o f surfing pool. The pool w i l l be capable o f creating waves from beginner to expert level. Figure 1 shows the Webber wave pool concept. No surf pool has been built using this approach yet and there is insufficient knowledge to design them with confidence
Figure 1: Webber wave pool concept |4]
Two TtJDelft masters students, De Schipper[5] and De Vries[6], conducted an initial Computation Fluid Dynamics (CFD) analysis and a scale model testing o f a series o f pressure sources (hulls) traveling in a linear track. Then Schmied started
his PhD project and has been continuing the experimental research at the Australian Maridme College ( A M C ) since 2009. He has tested several different pressure sources in a straight line [7] and a circular track [8]. He also conducted investigations to determine the effect o f beach shape on wave breaking parameters. Doyle also conducted numerical investigation o f predicting a curved path wave pattern[9]. Van Essen used a non-linear potential flow code (RAPID) which was developed in T U D e l f University to predict the wave height for a wavedozer[10].
Experimental approaches such as the use o f scaled models in hydrodynamics are common practice. A scaled model o f the pool was built in the Model Test Basin at A M C and the research is ongoing. Cameras and wave probes have been used to record and examine the shape and development o f the waves. Extensive tests with various pressure source shapes have been conducted in both straight and circular tracks. Pressure source speed, draft and pressure source forms were the main parameters varied to investigate the best surfable waves.
Ahhough there are many beneflts in the experimental approach, the limitations make it desirable to develop a numerical tool to assist. Taking into account the advances in computer abilities, the use o f Computational Fluid Dynamics (CFD) is becoming a common choice in many cases. Computational analyses in the eariy stages o f design are desirable and can reduce the number o f design alternatives. In addition, operating cost can become cheaper than experimental tests once computational domain and parameters have been set up properly. For instance, for changing any part o f model, physical models must be completely reconstructed, whereas i n a numerical approach computer models can be easily reconfigured. Due to insufficient knowledge about ship induced waves in such an enclosed environment, many parameters should be considered. Beach shape, wave breakmg point, wave shape, vessel speed, vessel draft, number o f the waves generated, and size o f the pool are some o f these parameters.
To use CFD to investigate the effect o f various parameters, it is necessary to validate the code first, to insure the code's ability to accurately simulate the flow around pressure sources. It should also be capable o f predicting the free surface for a wide range o f speed. I n the next step, i f benchmark simulations results are accurate, then the CFD method can be used to simulate new cases.
In this paper, the use o f CFD to optimise the design parameters for circular wave pool parameters is discussed. The CFD is shown to be applicable for use i n circular wave pool parameters optimisation.
In this current study, flow simulations are conducted with the CFD code, FLUENT. F L U E N T can be used to solve the equations for consei-vation o f mass, momentum, energy and other relevant fluid variables using a cell-centred finite-volume method and can calculate both steady and unsteady solutions. A t first, the fluid domain is divided into a large number o f
discrete control volumes (also known as cells) by using a pre-processor code which creates a computational mesh on which the equations can be solved.
Then the governing equations (in integral form) are applied to each discrete control volume and used to construct a set o f non-linear algebraic equations for the discrete dependent variables. F L U E N T then offers the user a number o f choices for the algorithm used to solve these equations.
FLLIENT stores discrete values o f the variables at the cell centres. Where values o f the variables are required at the cell faces (the convection terms in the equations), they must be interpolated from the cell centred values. Different schemes such as first-order upwind, second-order upwind, power law, and Q U I C K are available.
In FLUENT, three different multiphase models are available: the volume o f fluid (VOF) model, the mixture model, and the Eulerian model. The V O F model is a surface-tracking technique applied to a fixed Eulerian mesh. It is designed for two or more immiscible fluids where the position o f the interface between the fluids is o f interest. In the V O F model, a single set o f momentum equations is shared by the fluids, and the volume fi-action o f each o f the fluids in each computational cell is tracked throughout the domain. Applications o f the VOF model include free-surface flows, filling, sloshing, the motion o f large bubbles in a liquid, the motion o f liquid after a dam break, the prediction o f jet breakup (surface tension), and the steady or transient tracking o f any liquid-gas interface.
The commercial CFD software F L U E N T version 12.1 is utilized for the computations in the present study. Mainly hexahedral cells are used for obtaining a good resolution o f the generated waves by pressure source. The volume o f fluid technique is employed to simulate the free-surface motion. The second order upwind scheme is used for discretizing the momentum term. A special high resolution interface capturing (HRIC) scheme is used for the convection term o f the volume o f fluid transport equation i n order to avoid excessive smearing o f the interface due to numerical difflision [ I I ] . Since the motion o f fi-ee-surface flow is governed by gravitational and inertial forces, the open channel computational domain is used, which is also consistent with the experimental setup.
MODELING AND RESULTS
S T R A I G H T T R A C K
To investigate the accuracy o f the CFD approach to predict waves' parameters, two different shapes o f pressure sources. Parabolic and wedge (wavedozer) shapes, which previously have been tested in the Australian Maritime College ( A M C ) were modeled. The A M C towing tank model has a length o f 100m and a width o f 3.5m. For numerical investigation, a domain comprising 3m i n front o f the shape model and 8m behind it was considered. Table 1 shows the parabolic pressure source parameters and Table 2 shows the wavedozer pressure
source. For the simulations, the heave and trim were flxed at the same value as used in the experimental tests. To decrease the processing time, half o f the domain was simulated, Figure 2.
Tabic 1: Parabolic pressure source charactristics
Length of model (mm) 700
Beam of model (mm) 300
Height of model (ram) 500
Drought (mm) 100
Channel width (mm) 3500
Depth of water (mm) 500
Table 2: Wavedozer and towing tank parameters
Length of model (ram) 1500
Beam of model (mm) 300
Angle of attack (deg) 14
Draught (mm) 100
Channel width (mm) 3500
Depth of water (mm) 500
During the experimental tests, several wave probes were installed at different lateral distances relative to the centreline o f the model to capture the wave profile. Figure 3 shows the free surface which was captured by simulation and experimental test. A wave time series at 750 mm lateral distance o f the centreline is presented in Figure 4. According to experimental tests, first and second waves behind the pressure sources are considered as surfable waves. Comparing the numerical results with experimental data in Figure 4, it is clear that the simulation results are in good agreement with the experimental data with respect to wave height and frequency.
Figure 2: Mesh domain
Conloi»»olZ-C<«»dnaK(mi.lu/el |m) ( T m s - I OOOOsrfl) Nov 14,2011 A N S Y S FLUENT 1S.1 ( M . pbos, vol, taosisol)
Figure 3: Free surface at Frh = 0.9
15.5 16.5 17.5 18.5 19.5
Tiine(s)
Figure 4: Wave probe results at 7S0mm (WPl) lateral distance at Fr,, = 0.9
In the towing tank tests, it was concluded that although the waves generated by the parabolic pressure source were higher than those generated by the wavedozer, they were always broken across the entire width o f the channel for Froude depth numbers (7vv,)>0.75. This breaking bow wave generated by parabolic pressure sources led to the conclusion that they are
less efficient for generating the waves. The breaking bow was seen in numerical results later. Minimal or no breaking can be seen i n wavedozer waves generated for Vi\ <0.95. Therefore, the wavedozer was selected to use as pressure source for future investigations.
In the second step, a wavedozer simulation at different speeds was undertaken. The wave pattern generated by the wavedozer was simulated at Fr,, o f 0.5, 0.75, 0.9 and 1.2. Figure 5 shows the simulated fi-ee surface and Figure 6 compares the numerical wave height results to experimental data. I 2K>!I! rSii-DI rct-01 1 ïii-oi i.iet-ST fêC)-S2 a K H Z 6CCS-S2 -ita«-cï . ! -aëia-oï I J cc» c? •itit-cz -7C1S-CJ 1 •iVJt-'iZ
Figure 5: Wavedozer free surface 0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 Experimental • Original Mesh 0.4 0.6 1.2 Fr,
Figure 6; Wave height at different Froude depth number at 750mm lateral distance
In Figure 6, wave height {H) was defined as the trough to crest height o f the first significant waves and h is equal to water depth (500 mm).
In addition, mesh independency for a wavedozer pressure source has been considered. I n this study, a simulation was repeated at the same speed by coarser and finer meshes. Finally, Results are compared and the effect o f cells size has been considered.
In this context, "grid-independent" results means results which are sufficiently independent from grid size such that the truncation error can be ignored in numerical simulation. For this study, the Richardson Extrapolation approach is used [12].
Richardson Extrapolation was used to quantify the results of a numerical method in terms o f their grid-independence. The idea is to use low order formula for which the expression o f the truncation error is well known. Then higher order accuracy can be derived from the low order formula.
Richardson Extrapolation Formula:
I f it is assumed that discretization o f the transport equations is o f second order then the grid-independent solution
{GIS) is approximately equal to the calculated value {(ji) plus a
value proportional to (Eq. ( I ) ) , where (3 is step size (grid size). Expressed mathematically:
Table 3: The number of cells for different meshes
GIS = (0)^ + c((32) (1) By refining the grid size, for instance to half o f original size, the true value can be calculated based on Eq. (2):
GIS =
((P)H + )
2 *(2)
By finding the difference o f Eq. ( I ) and Eq. (2), the Richardson extrapolation formula can be calculated:
ma -
(0)
JGIS =
(0)ft +
(3)
2 3
The common formula (for second order discretization) is:
n - f 2 (4) GIS = ƒ 1 +
Domain name number of ceils ratio
fine 23243760 8
original 2905470 1
Coarse (1) 376800 0.129686
Coarse (2) 46288 0.015931
The number o f cells i n the fine mesh is 8 times greater than the original mesh. It means the number o f nodes i n each direction is two times more than the original. Also the number of cells in Coarse(I) is almost one-eighth o f the original which means the number o f node in each direction is half o f the original and so on. Figure 7 shows the simulation results. It is clear that the original mesh domain is the ideal, because by increasing the number o f cells to the finer mesh domain, the result changed insignificandy. In addition, the domain with Coarse(2) mesh is not appropriate as a decrease in wave height is evident for a shift in Froude number where the finer meshes and the experiments all indicate that the opposite is true.
0.18 0.16 0.14 0.12 ^ 0.1 0.08 0.06 0.04 0.02 0 • Experimental
T
• Original Mesht
A coarse mesh (1)1
•
X Coarse mesh (2) T A X Fine mesh U X X . • \ X m 0.3 0.5 0.7 0.9 1.1 1.3 Fr„Figure 7: Wave height predicted by different number of cells at
750 mm lateral distance
Where, f l is result for finer mesh, ƒ 2 is result for coarse mesh and r is grid refinement ratio.
For grid independency four mesh domains with different number o f cells were simulated. Table 3 shows the number o f cells i n different meshes.
C U R V E D T R A C K
To determine the effect o f a curved track on the wave heights generated by the wavedozer and the ability o f the numerical approach to predict the wave parameters, the towing tank cross-section was modeled at half scale as a curved track. This also replicated the circular experimental tests which were undertaken previously in the A M C Model Test Basin. The outer wall radius was 5m and the width o f the channel was 888mm; Figure 8. For the simulation, 110 degrees o f this circle were modeled.Table 4 gives the wavedozer parameters f o r this curved track.
Figure 8: Scale model with wall at 88ram from outer perimeter Table 4: Wavedozer characteristics in cui-ved track
Length (mm) 602
Beam (mm) 275
Height (mm) 500
Draught (mm) 50
Depth (mm) 250
The wave height comparison based on numerical predictions and the experimental results is shown in Figure 9. As can be seen, the numerical predictions agree very well with experimental tests data.
120
0 I 1 0.5 0.6 0.7 0.8 0.9 1
Figure 9: Wave height as a function of Froude depth number for experimental results and numerical predictions at 365mm lateral
distance
In particular, it can be seen that numerical method can predict the drop in wave height for Fr/P>Q.9 as shown i n the experimental data. Some free surface pictures captured i n experimental tests and simulation results are given i n Figure 11 and 11.
Corrtoui6o(Z-CQordnate(mi.tufo) (m) (Tme*l.E237e*01) H o v i a . M l l ANSYS FLUENT 12-1 {Zó, ptns vof, ü m , transifnl)
Figure 10: Free surface (back view)
ConloufiolZ-CQOfdinale{rnb.Uie) (m) (Tme-1.5237e*01) N o v l B . S O M A N S Y S F L U E r f T I Z . I (3d. pbns, vol. lam, liandeol)
Figure 11: Free suiface (front view)
C O N C L U D I N G R E M A R K S
The results o f a preliminary investigation into RANS simulation o f free-surface f l o w around different pressure sources in straight and curved tracks have been presented. The commercial CFD software F L U E N T version 12.1 was utilised for the computations. The VOF technique was used to capture the free-surface. I n addition, since mesh quality has proven to be an important issue in the computations, several grids with different resolutions are employed and tried to find a grid independent soludons.
The comparison o f the predictions with the experimental data confirmed that the numerical approach can be used to predict the waves' shapes generated by the pressure surface travelling in both straight and curved tracks.
The above results are encouraging and indicate that the F L U E N T code is a viable tool in an extreme fiow condition, which could be considered for use i n the proposed next stage, which is an investigation into the effect o f bathymetry on wave breaking.
[10] S. V. Essen, "RAPID Non-linear Potential Flow Wave Height Prediction," Australian Maritime College, 2011.
[11] G. I . I Senocak, "progress towards RANS simulation o f free-surface flow around modern ships," in center
for turbulence research annual research briefs, 2005,
pp. 151-156.
[12] 1. F. Richardson and J. A . Gaunt, "The Deferred Approach to the limit, part I . single Lattice. Part I I . Interpenetrating lattices," in Philosophical
Transactions of the royal society of London, series A, conatining papers of a Matliematical or Physical charatcter. vol. 226, ed: the Royal society, 1927, pp.
299-361.
R E F E R E N C E S
[1] S. Mead and K . Black, "Field Studies Leading to the Bathymetric Classiflcation o f World-Class Surfing Breaks," Journal of Coastal Research, pp. 5-20, 2001. [2] J. B. Steven Schmied, Martin Renilson, Giles Thomas,
Gregor Macfarlane, Rene Huijsmans, " A Novel method For Generating Continuously Surfable Waves-Comparison o f Predictions with experimental Results," 2011.
[3] Webber, history. Available:
http://webberwavepools.com/webber-wave-pools-history
[4] W. W. R Liquid Time Pty Ltd. Available:
www.webberwavepools.com
[5] M . A . Schipper, "On the generation o f surfable ship waves in a circular pool: Part I . Physical background and wave pool design," Master, Delf University o f Technology, 2007.
[6] Vries, "On the Generation o f Surfable Ship Waves in a Circular Pool: part I I , " Master, Delft University o f Technology, 2007.
[7] S. Schmied, "test plan-Tow Tank testing," Doctorate, Australian Maritime College, 2009.
[8] S. Schmied, "Test Plan- Scale Model- Second Test Session," Doctorate, Australian Maritime College, 2011.
[9] N . Doyle, "The Circular Wave Pool- Predicting Curved Path Wave Patterns," Bachelor, Australian Maritime College, University ofTasmania, 2010.
