Experimental Validation of Numerical Models for Wave Energy Absorbers

Transcription

1 Experimental Validation of Numerical Models for Wave Energy Absorbers Morten Kramer, Francesco Ferri, Andrew Zurkinden, Enrique Vidal, Jens P. Kofoed 2 nd SDWED Advances in Modelling of Wave Energy Devices Thursday April 26,

2 Laboratory test set up of pivoting absorber Laser to measure position Electrical actuator to apply any specified motion or force Force sensor Float Bearing around which the motion takes place Fixed support Moving rigid body M c M g M d Pivoting motions are described by rotations. Newton s second law: J: Mass inertia moment of the moving body M d : Hydrodynamic moment (from water pressure on hull) M g : Gravitational moment M c : Control moment from Power Take Off

3 Control sketch Laptop Simulink model. Model is compiled to C/C++ code and transferred to xpc before tests are executed. PC with xpc Online execution of control model and data acquisition. The control model specifies the target force or position based on measured inputs from the NI DAQ. NI DAQ Data logger with inputs and outputs. One output for the Linmot controller is the target force or position. Linmot controller Hardware controller. Takes care of achieving the specified target position or force using position feedback from actuator or force feedback from external force sensor. 3 Actuator Linear motor (electrical cylinder). The linear motor consists of two parts: The fixed stator (tube) and the moveable slider (piston). An internal position encoder is included and used for position control.

4 Overview of tests Test period Test description Number of tests Jan 12 1) No absorber in basin. Wave measurements with old wave gauge type. 21 regular sea states, 10 Irregular sea states ( W = +90 ) 2) Wave heading +90. Regular waves and linear PTO damping *1) 75 3) Wave heading +90. Irregular waves and linear PTO damping *1) 51 4) Wave heading +90.Wave excitation force, fixed float 31 (all sea states) 5) Radiation force tests with position control. No incoming waves. 50 (sinusoidal), 16 (gaussian) 6) Motion in air. 12 (sinusoidal) Mar 12 1) No absorber in basin. Wave measurements with new wave gauge type. 20 regular sea states, 10 Irregular sea states ( W = 0 ) 2) Wave heading 0. IRB1 tests with linear PTO damping *1) 20 3) Radiation force tests with force control. No incoming waves. 51 (sinusoidal), 24 (step) 4) Wave heading 0. IRB1 tests with PTO stiffness and damping *2) 24 5) Wave heading 0. IRB2 tests with PTO stiffness and damping *2) 24 6) Wave heading 0. IRA1 tests with PTO stiffness and damping *2) 21 7) Wave heading 0. IRA2 tests with PTO stiffness and damping *2) 17 8) Wave heading 0. IRA3 tests with PTO stiffness and damping *2) 14 Wave heading definition: Wave with W = +90 *1) Controller setup 1 ( gentle control settings) *2) Controller setup 2 (more aggressive control settings)

5 Wave conditions Red dots: Regular waves for March 2012 tests Blue dots: Irregular waves using H = H m0 and T = T p. Wave heights are target values (input to wave generator). d = 0.65 m is the water depth. Test T P (s) H m0 (m) L P (m) s P = H m0 /L P IRA IRA IRA IRA IRA IRB IRB IRB IRB IRB Test T (s) H (m) Comments RA RA RA RA Waves close to breaking RB RB RB RB Waves are rather non linear RB Waves close to breaking RC RC RC RC RC Waves are slightly non linear RC Waves close to breaking RD Wave generator does not move precisely RD RD RD Waves are rather non linear RD Waves are breaking (white capping)

6 Waves in basin Waves are measured with 6 wave gauges (WG s) with 1.0 m between each (no absorber in basin). WG 4 is located at the centre of the float position, WG3 and 5 in-line with WG4 (along the wave crest), WG1 and WG2 in front of absorber with WG1 closest to wave generator. WG6 is behind the absorber closest to beach. Measured waves are considered as incoming waves (reflections from the beach and side walls are not taken into account). IRB1 H m0,wg4 = m, T P = 1.0 s. WG1 WG2 WG3 WG5 1m 1m 1m WG4 1m 1m IRB5 H m0,wg4 = m, T P = 3.0 s. WG6

7 Moment due to gravity 0 0, 0 Slow motion in air with sinus (period 30 s, angle amplitude 0.35 rad ~20 ). Position (rad) Moment due to gravity M g (Nm) Time (s) Moment due to gravity M g (Nm) Measurements Fit M g = [Nm], in [rad] Position (rad) 7

8 Mass inertia moment Sinusoidal motion in air 0, 0 12 sinusoidal tests performed: Six periods: 0.5 s, 0.7 s, 1.0 s, 1.4 s, 2.0 s, 30 s Two angle amplitudes: 0.10 rad, 0.35 rad Example figures below are for 0.7 s and 0.35 rad. Angular acceleration (rad/s 2 ) Moment -M c -M g (Nm) Time (s)

9 Hydrostatic stiffness Slow sinusoidal motion in still water (period 30 s, angle amplitude 0.35 rad ~20 ) , 0 Hydrostatic moment: Radiation moment: Wave excitation moment: Control moment: Position (rad) Control moment -M c (Nm) Time (s) Control moment -M c (Nm) Measurements Linear fit in range of angles [ ] -M c = k h, k h = Nm/rad Position (rad) 9

10 Radiation force Example figures with sinusoidal motion (T = 1.0 s, motion amplitude = 0.1 rad) 0, 0 Completed radiation tests: Position control: 50 sinusoidal and 16 gaussian Force control: 51 sinusoidal and 25 step 10

11 Wave excitation force 0 0 0, 0 IRA4 H m0,wg4 = m, T P = 2.0 s IRB5 H m0,wg4 = m, T P = 3.0 s Completed wave excitation force tests: 31 tests (all sea states) for wave heading +90. Figures are from Non linear numerical modeling and experimental testing of a point absorber wave energy converter by A.S. Zurkinden, M.M. Kramer, J.P. Kofoed, P. Frigaard. To be submitted to Ocean Engineering Journal.

12 Float in operation Example with sea state IRB1 (H m0,wg4 = m, T P = 1.0 s) 12

13 Conclusion Basic experimental tests on a point absorber WEC has been completed. Good agreement between a traditional linear numerical model and experimental tests has been found for mild waves when the motions of the absorber is small. For steep and overtopping waves, as well as for large motions of the absorber, the linear model overestimates the forces and thereby the response of the device hereby overestimating the achievable power output. The results from the tests and the further development on non-linear numerical models are expected to enable predictions of the power performance of point absorbers operating in high seas. Hereby more suitable control strategies can be applied permitting higher power output.

14 The plan for the further testing is on: 1) Power absorption, PTO forces and motions when using advanced control strategies, online wave force predictions, and constraints e.g. on PTO efficiency and limits on force, stroke and power. 2) Estimations of viscous effects in waves 3) Measurements of extreme forces due to high and breaking waves (forces to be used for Ultimate Limit State structural design) 4) Interaction effects between several absorbers 5) Power optimization by changing physical quantities (geometry and weights, float size & shape, )

15 Funded by The International Research Alliance