Experimental and numerical investigation of slamming of an Oscillating Wave Surge Converter in two dimensions

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1 Experimental and numerical investigation of slamming of an Oscillating Wave Surge Converter in two dimensions T. Abadie, Y. Wei, V. Lebrun, F. Dias (UCD) Collaborating work with: A. Henry, J. Nicholson, A. McKinley (Aquamarine Power) O. Kimmoun, G. Dupont (Ecole Centrale Marseille) University College Dublin, School of Mathematical Sciences 2015 Maynooth University Wave Energy Workshop 15 January 2015

2 Outline 2 1 Introduction 2 Wave impact : experimental observations 3 Comparison with water entry problem - Wagner theory 4 Numerical simulations 5 Conclusion

3 Oscillating Wave Surge Converter (OWSC) - Oyster Oyster wave surge energy converter, developed by Aquamarine Power. Bottom hinged large buoyant flap Wave motion back and forth oscillations of the flap High pressure water pumped to shore to drive a turbine Location in sea : distance from shoreline 500m water depth 10 15m prototype Oyster 800 (26 m wide, 15 m high)

4 Observations in real sea Prototype Oyster 800 in Oarkney Islands (significant wave height 5m) https :// 4

5 Motivations and objectives 5 Small scale experiments revealed high magnitude, short duration, "impulsive" load! slamming event Objectives Develop understanding of the slam loading process and its characteristics This knowledge feeds into the extreme load case for Oyster design, i.e. pressure scaling methodology

6 Previous work 6 Previous work is difficult to relate to wave energy converters Oyster is not a static structure as most in coastal engineering Strong coupling between Oyster and wave motion Wave impact on a fixed structure Water entry of a ship in water

7 2D tests in wave flume at Ecole Centrale Marseille 7 Experiments performed at Ecole Centrale Marseille (2013 & 2014) 40 th scale model of generic Oyster (scaled by Froude U/ gh) Flap height 31cm High speed camera visualisations Sensors Flap rotation Wave gauges Single pressure transducer

8 2D tests in wave flume at Ecole Centrale Marseille Experiments performed at Ecole Centrale Marseille (2013 & 2014) 40th scale model of generic p Oyster (scaled by Froude U/ gh) Flap height 31cm High speed camera visualisations Sensors I I I Flap rotation Wave gauges Single pressure transducer Experiments repeated recently with an array of pressure sensors

9 First observations 8

10 Slamming event 9 1 : Wave crest pushes flap landward

11 Slamming event 9 2 : Flap remerges due to its buoyancy after crest passes

12 Slamming event 9 3 : Flap accelerates seaward, water drops down the face

13 Slamming event 9 4 : Water rushing down the face creates dip in water level

14 Slamming event 9 5 : Start of slamming phase, as flap re-enters the water

15 Slamming event 9 6 : Water jet travels up the flap face

16 Slamming event 9 7 : Jet continues to move up

17 Slamming event 9 8 : Water jet is ejected in front of the flap

18 Impact pressure 10 1 : Beginning of slam event

19 Impact pressure 10 2 : Pressure increase as jet builds

20 Impact pressure 10 3 : Peak pressure under jet root

21 Pressure characteristics - Building jet A water level immersion probe jet root image processing 0.3 A B B C Flap water level (m) C D D E water level immersion probe jet root images start of pressure rise t (P = Pmax) Time (s) Pressure starts rising as the extremity of the jet approaches E Maximal pressure under the jet root Slamming duration : 200ms ( T /10)

22 Pressure characteristics Contour plot of the pressure as a function of the distance from the hinge and time : Impact pressure rises along the flap with a nearly constant velocity Longer impacts close to the hinge of the flap 12

23 Wagner s slamming theory Similarities between oyster slamming and water entry problems. Wagner theory (1932) : Impact of a wedge in water at rest Constant entry velocity V Potential flow theory Uprise of the free surface elevation Sketch of the problem

24 Wagner s slamming theory Similarities between oyster slamming and water entry problems. Wagner theory (1932) : Impact of a wedge in water at rest Constant entry velocity V Potential flow theory Uprise of the free surface elevation Maximal impact pressure Sketch of the problem p max = 1 2 ρv 2 C pmax with C pmax = π 2 4tan 2 (β)

25 Pressure results (experiments and model) P = 0.5ρu 2 jr P = Pmax Pressure (kpa) Time (s) Good agreement between measured and predicted pressures from the jet root velocity!

26 Pressure results (experiments and model) P = 0.5ρu 2 jr P = Pmax Pressure (kpa) Time (s) Good agreement between measured and predicted pressures from the jet root velocity! Maximal pressure is expected to be close to the hinge of the flap

27 Pressure results (experiments and model) P = 0.5ρu 2 jr P = Pmax Pressure (kpa) Time (s) Good agreement between measured and predicted pressures from the jet root velocity! Maximal pressure is expected to be close to the hinge of the flap Rough estimation : hinge height u jr slamming time 1.5m/s P max 1.125kPa

28 Numerical methods 15 Available tools : Smoothed Particle Hydrodynamics (SPH) code : lagrangian meshless method (Ashkan Rafiee, postdoc at UCD until 2013) ongoing work Fluent : VOF finite volume code, moving mesh around the flaps 2D and 3D simulations (Yanji Wei, PhD student at UCD) JADIM finite volume research code, VOF or LS, moving boundaries on a fixed cartesian mesh wide range of geometries available at a moderate computational cost (developed at the Institute of Fluid Mechanics, Toulouse, France)

29 Numerical method - one fluid formulation 16 JADIM : finite volume IMFT in-house code One fluid formulation of the incompressible Navier-Stokes equations Continuity : U = 0 ( ) U Momentum : ρ + (U )U = P + Σ + ρg t VOF (volume fraction C of one fluid 0 C 1) Volume fraction : C t + U C = 0 ρ = Cρ 1 + (1 C)ρ 2 µ = Cµ 1 + (1 C)µ 2

30 Numerical method - IBM 17 Immersed Boundary Method (IBM) in JADIM : volume fraction α of solid in each cell (same idea as in VOF) source term in the momentum equation fp Momentum : ρ ( U t + (U )U) = P + Σ + ρg + f p

31 Numerical method - IBM 17 Immersed Boundary Method (IBM) in JADIM : volume fraction α of solid in each cell (same idea as in VOF) source term in the momentum equation fp Summary Momentum : ρ ( U t + (U )U) = P + Σ + ρg + f p 1 Prediction step, fluid velocity in the whole domain : u f = u n + t ρ Pn + viscous terms + advective terms + gravity 2 Calculation of IBM forcing term and second prediction step thanks to the known desired particle velocity u p : u = u f + tf p with f p = α u p u f t 3 Correction step to satisfy the divergence free condition Pressure P n+1 and velocity u n+1

32 Numerical set-up 18 Loading... Waves generation with a piston-type wavemaker (linear theory : Ursell 1960, Dean & Dalrymple 1984,...) IBM method to model moving boundaries Damping beach at the end to avoid reflection

33 First observations : close-up view 19 Global behavior is well reproduced : 1 - Flap is pushed landward

34 First observations : close-up view 19 Global behavior is well reproduced : 2 - Water level drops down

35 First observations : close-up view 19 Global behavior is well reproduced : 3 - Jet builds

36 First observations : close-up view 19 Global behavior is well reproduced : 4 - Water jets out

37 Comparison exp/num (i) 20 Wave profile (close to the wavemaker) 15 Surface elevation (/H) exp num Time (s)

38 Comparison exp/num (i) 15 Wave profile (close to the wavemaker) Wave profile (close to the oscillating flap) 15 Surface elevation (/H) exp num Time (s) Surface elevation (/H) exp num Time (s) Wave height is in good agreement despite a slight underestimation in numerical simulations both : close to the wavemaker and, in the middle of the tank.

39 Comparison exp/num (ii) Rotation of the flap (angle) Flap angle (degree) exp num Time (s) Good agreement for the rotation frequency despite underestimation of the maxima

40 Comparison exp/num (ii) Rotation of the flap (angle) Angular velocity Flap angle (degree) exp num Ang. velocity (deg/s) exp. num Time (s) Time (s) Good agreement for the rotation frequency despite underestimation of the maxima Maximal velocities of the flap which lead to the stronger impacts are not captured

41 Comparison exp/num (iii) P = 0.5ρu 2 jr P = Pmax P = P max (num.) Pressure (kpa) Time (s) The impact pressure is underestimated. mesh convergence study is under way...

42 Conclusion Conclusion Recent 2D experiments allow a better description of pressure distribution on the OWSC (Henry et al., submitted to OMAE 2015) Slamming of Oyster found to be akin to the water entry problem with the formation of a building jet CFD model can describe global behaviour but underestimate amplitude of incoming waves and thus, rotation and pressure

43 Conclusion Conclusion Recent 2D experiments allow a better description of pressure distribution on the OWSC (Henry et al., submitted to OMAE 2015) Slamming of Oyster found to be akin to the water entry problem with the formation of a building jet CFD model can describe global behaviour but underestimate amplitude of incoming waves and thus, rotation and pressure Further work Further development of the numerical model and comparison with a SPH code and Fluent to gain insight in local velocity and pressure fields wide range of geometry and wave conditions available Adaptation of Wagner theory (link between rise-up velocity / rotational velocity / wave characteristics) Compressible effects? 3D effects on slamming

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