Overtopping Wave Energy Converter

Here we have a back to back simulations of two different overtopping wave energy converter geometries, performed in 2D. The simulation includes turbines with a quadratic pressure drop to flow rate relationship, located in the outlets.  The incident regular waves have a height of 3m and period of 10s.  The geometry on the RHS has an additional ramp inside the reservoir to encourage a greater overtopping volume and to guide the flow into the turbine and recover some of the waves kinetic energy into pressure in order to force it through the turbine more effectively. One can see that with this particular design (based loosely on the wave dragon concept) the existence of  a bi-directional flow through the turbines and that some water escapes from the reservoir back over the crest after reflecting from the end wall.

Flow over a Sharp Crested Weir with Opening of Radial Gate

CFD model of the flow of water over a curved sharp crested weir and the  opening of the radial gate adjacent to it. The simulation shows the increase in  total flow rate as the gate is opened.

Breaking Wave on Beach

CFD simulation of a breaking wave on a beach.The beach has a slope of 8 degrees and is orientated 18 degrees from the wave direction. Wave period 10s wave amplitude 3m. The simulation was performed using FLOW-3D and required 27 million mesh cells.

Ricochet of a Spinning Cylinder 

CFD simulation of the ricochet of a spinning cylinder for a water surface. The case is based on the famous ” bouncing bomb” experiments made by Barnes Wallis in the 1940s. The cylinder has the same geometry and mass as that used by Barnes Wallis and was given an initial forward velocity of 100m/s and a vertical velocity equivalent velocity to that of  the actual cylinder  which was dropped from a height of 18m at a forward speed of 100 m/s.  A backspin of 52 rads/sec was also applied in line with the experiments. The cavitation model was activated to limit the low pressures which would otherwise occur and prevent the cylinder from bouncing. One can observe that the backspin applied  leads to a magnus effect which prevents the cylinder from sinking and is also crucial to the bouncing phenomena.

Multi Flap Bottom Hinged Wave Energy Converter

This is a CFD simulation of a three flap bottom hinged wave energy converter. The individual flaps are 15m wide, 10m in height and 2m wide and are operating in a 4m height, 10s regular wave in a depth of 30m.  No PTO damping has been applied in this case.

Bristol Cylinder Wave Energy Converter

Here we see a simulation of a full scale 14m diameter X 28m width Bristol Cylinder with four PTO’s (not shown) applying damping and additional stiffness designed to induce both surge and heave resonance at the incident wave period of 10 seconds. The numerical wave tank is 5 cylinder width wide and 50m deep and generates a 2m, 10s regular wave. The cylinder absorbs 1343 kW equivalent to a capture width ratio of 1.2.  Notice the occurrence of local wave refraction as the cylinder nears the free surface with then results in energy dissipation due to wave breaking and the formation of two counter rotating vorticies.

Vertical Axis Turbine

The three videos below relate to the 2D simulation of a single NACA0018 aerofoil  in cross flow as would be found in a vertical axis wind turbine (VAWT) or vertical axis  tidal turbine (VATT) . The medium used is water and the Reynolds number is 1 million. The turbine has a chord length of 1 metre. In the first two videos the blade is rotated at a tip speed ratio of 1.0 and the resulting PTO torque is output with negative values corresponding to power out. Note that the power out stroke only occurs when the rotational angle is between approximately 120 deg and 180 deg. In the 3rd video the turbine is not restricted in terms of speed and zero PTO torque is applied, hence it is allowed to rotate freely with it motion dependent upon the lift and drag forces acting on it and its own inertia. All models have used FLOW-3D’s moving bodies model which allows the aerofoil to pass through the mesh without any need for re-meshing and the associated computational cost and instability.



Sloshing in a Rectangular Liquid Damper

A rectangular tank with dimensions 1m x 0.5m x 0.1m and water depth of 0.25m,  is excited by a harmonic pitching motion with a 5 degree amplitude and 3.16s period about an axis through the centre line and floor of the tank. The non-inertial reference frame model is used to account for the  accelerations produced by the pitching motion whilst allowing the mesh to move with the tank. A damper is placed between the central partition and tank floor which allows fluid to pass under it subject to a quadratic relationship between the volumetric flow rate and pressure drop across the damper in order to extract energy from the sloshing motion. The partition effectively divides the flow into two regions which then behave with almost translational symmetry despite fluid passing between the two regions via the damper.



Sloshing in Long Narrow Liquid Damper 

As the above “Rectangular Liquid Damper” case except the tank is now 4m in length, 0.75m high and with a 0.4m water level. The flow is now more disordered but still maintains its near translational symmetry, despite fluid passing between the two regions via the damper as seen from the velocity contours.



Sloshing in Curved Liquid Damper

This tank has a curved floor with a defined radius and dimensions of 40m X 7.5m X 1m with a water depth of 4m. The harmonic pitch excitation has an amplitude of 5 deg and period of 10 secs. The flow has lost its translational symmetry due to the curved tank floor boundaries and is again more disordered. The flow rate through the damper is seen to peak close to the point where the difference in the free surface height adjacent to the partition is at its maximum. The damper extracts 35 kW on average from the sloshing motion.



Free surface flow simulation of the water exit of a buoyant rising sphere at Reynolds number 20,000

Simulation of a buoyant sphere originally constrained then allowed to rise and eventually exit the water surface. The Large Eddy Simulation model was used on a 7.5 million cell mesh. The Reynolds number is 20,000.

Free surface flow simulation of wave loading on a tall square cylinder due to a dam break event, validation study

This is the classic dam breaking validation case of water impacting on a square cylinder. The  original experiment was  performed by  Gomez-Gesteria and Dalrymple [1]  in 2004 and consist of a rectangular block of water being suddenly released  and impacting on a square cylinder.  The two plots below and in the video show the resulting X direction force on the cylinder and the X direction velocity at a location in front of the cylinder for various mesh resolutions. The experimental values, also shown, are taken from one instance of the experiment, for which the repeatability is unknown. Notice how the force peaks at 0.3 seconds and then peaks in the opposite direction at 1.5 seconds as the wave rebounds off the end wall and hits the cylinder for a second time. The experiment is representative of a tidal bore or tsunami wave impacting a static coastal structure and has been called  the “bore in a box” case. The coarse mesh solution was achieved in under 15 minutes on 12 cores.























Free surface flow simulation of wave loading on a rectangular object due to a dam break event, validation study

This is another classic validation test case for a dam breaking onto a rectangular object. The original experiment was performed at the MARIN institute [2] as was designed to representative of green water on the deck of a ship impacting a shipping container.  The plots below and in the video show the water depth and pressure on the front face of the object as the fluid impacts onto it, along with the experimental results. The coarse mesh solution was obtained in under 15 minutes on 4 cores. Full details can be found at, Dam Break Rectangular Object





















Vortex shedding past a square cylinder, validation study

Another classic validation case of  vortex shedding due to flow over an infinite square cylinder at Re = 22,400 as reported by Rodi et al [3]. The experiment has been conducted by several people over the years with some differences in the span and inlet turbulence intensity. As a result a range of values, particularly in the standard deviation of the  lift force,  have been found as shown in the table below. The most important parameters and the most stable in both experiment and simulation are the mean drag coefficient and the Stouhal number St.  Notice how the vortex shedding is not synchronized along the entire span of the cylinder but rather breaks up into local regions of vortex shedding.



Numerical Solution Experimental Results [3]
CD mean 1.97 1.9  to 2.1
CL mean 0.00 0.0
CD std 0.15 0.1 to 0.23
CL std 0.96 0.1 to 1.4
St 0.13 0.132




Vortex shedding at high Reynolds number past a circular cylinder, validation study

This is a CFD simulation of a classic experiment for the cross flow over a  circular cylinder at a Reynolds number of 106  i.e. in the critical to supercritical region using a Large Eddy Simulation model. Whilst the geometry is straightforward, predicting the pressure coefficient distribution on the cylinders surface and the integrated drag coefficient turns out to be extremely challenging and a wide range of results are reported both experimentally[4,5,6] and numerically [7,8] as shown in table along with our simulation results. The boundary layer separation point is known to be very sensitive to the surface roughness of the cylinder and the inlet turbulence intensity which then has a large effect on the size of the wake, the resulting drag coefficient and the magnitude of the fluctuation in the drag and lift coefficients and their frequency. In general we find that the later the separation point occurs the narrower the wake and consequently the smaller the drag. This narrower wake is then associated with a lower lift force fluctuation and higher fluctuation frequency due to the reduction in distance travelled during the wakes oscillation.

The flow is seen to separate at between 95 and 105  degrees, whilst the wake oscillation frequency clearly consists of more than a single frequency such that the Strouihal number cannot be defined. Both of these results are in keeping with the experimental results. The pressure coefficient plot also shows the range in the experimental results [4,9,10] despite the similar Reynolds numbers , alongside the numerical simulation. The agreement where the flow impact the cylinder and up to 80 degrees is excellent and almost identical for all experimental results. After 80 degrees the differences due to the different flow separation points become more apparent and the pressure finally plateauxs  between 120 and 180 degrees.


CD CD rms CL rms St
                                                                          Numerical Solution Results
Numerical Solution Achenbach Geometry 0.44 0.00 0.03 N/A
Numerical Solution Alternate Geometry 0.35 0.01 0.03 N/A
Catalano et al, LES [7] 0.31 0.35
Catalano et al, RANS [7] 0.39
Catalano et al, URANS [7] 0.40 0.31
Stringer et al [8] 0.15 to 0.54 0.13 to 0.19 0 to 0.3
                                                                             Experimental Results
Achenbach [4] 0.48
Zdravkovich [5] 0.17- 0.4 0.18-0.50
Shih et al [6] 0.24 0.22
















Free surface flow simulation of the pitch decay of an axisymmetric point absorber wave energy converter, validation study

Simulation of a pitch decay experiment originally performed at the MARIN institute in 2010 on behalf of Wavebob. The experiment was used to confirm the expected  natural  period of oscillation of the WEC  and to extract damping coefficients for use in further hydrodynamic simulations.















Free surface flow simulation of the extreme wave loading on a 35th Scale axi-symmetric point absorber wave energy converter

Simulation of a survival tank test experiment originally performed on a moored 35th scale axi-syymnetric WEC at the MARIN institute in 2010 on behalf of Wavebob. The incident waves represent a Jonswap spectrum with Hs = 12.25m and Tp = 13.5 s at full scale.


Free surface flow simulation of a falling sphere of water and its impact 

Impact of a 6 cm diameter sphere of  water dropped from a height of 16 cm in a solid box of side 20 cm. The simulation used 8 million 1mm cells and had a maximum time step of 1/1000th of a second shot at 1000 fps.The blue lower plot shows the impact force of the water on the floor of the box, which initially  spikes at 0.18 secs followed by a rebound where the force drops to zero and then many smaller impacts as water droplets fall for the 2nd time.The red upper plot is the total volume of the fluid, which the VOF algorithm tries to keep track of throughout the simulation. Despite its efforts there is a 25% increase in the volume of fluid which is due to the finite mesh resolution and complexity of the event, a difficult tests for any free surface simulation.




[1]          Gomez-Gesteira, M.,  and Dalrymple, R.A., ( 2004) ” Using a 3D SPH Method for Wave Impact on a  Tall  Structure, J.Waterway., Port, Coastal and Ocean Eng. 130(2) 63-6

[2]          SPH European Research Interest Community SIG, Test-Case 2 3D dambreaking, R.Issa and D. Violeau.

[3]          Rodi,w. Ferziger,J.H, Breurer,M. Pourquie,M. “ Status of large Eddy Simulation: Results of Workshop,                 Transactions of ASME, vol 119, June1997 pp 248-262.

[4]         Achenbach, E. (1971). Influence of surface roughness on the crossflow around a circular cylinder. J. Fluid Mech., 46, 321-35

[5]         Zdravkovich, M. M. 1997 Flow Around Circular Cylinders. Vol. 1: Fundamentals. Oxford University Press, Chap. 6.

[6]         Shih, W. C. L., Wang, C., Coles, D. & Roshko, A. 1993 Experiments on flow past rough circular cylinders at large Reynolds numbers. J. Wind Engg and Industrial Aerodynamics 49, 351-                368.

[7]         Numerical simulation of the flow around a circular cylinder at high Reynolds numbers, International Journal of Heat and Fluid Flow 24 (2003) 463–469

[8]         R.M Stringer, J. Zang and A.J.Hillis, Unsteady RANS simulations of the flow around a cylinder for a wide range of Reynolds numbers, Ocean Engineering, 87 (2014) 1-9

[9]         Warschauer, K. A. & Leene, J. A. 1971 Experiments on mean and fluctuating pressures of circular cylinders at cross flow at very high Reynolds numbers. Proc. Int. Conf. on Wind Effects                on Buildings and Structures, Saikon, Tokyo, 305-315.

[10]       Falchsbart as given in Zdravkovich 1997 [5]