Specialization in Ocean Energy MODELLING OF WAVE ENERGY CONVERSION António F.O. Falcão Instituto Superior Técnico, Universidade de Lisboa 2017

PART 6 MODEL TESTING

Model testing of 3-unit array in the wave tank of Plymouth University, UK, July 2014. Scale 1:32.

Dimensional analysis applied to wave energy conversion We may apply dimensional analysis techniques to model testing of wave energy converters in wave tank or wave flume.

This will ensure the equality of all the other dimensioless variables. Assuming the device to be an exact geometric representation of the full-sized device Applying Buckingham theorem, we may replace this equation by another one with only three independent (dimensionless) variables If dynamical symilarity is to be ensured, the three dimensionless variables on the rhs must take the same values in model and full size. This will ensure the equality of all the other dimensioless variables. Note that viscosity effects and Reynolds number were ignored. However, this analysis is valid even if wave amplitude and body motion amplitude are not small.

In the case of model tests of an oscillating-water- column converter, there are special issues concerning how to model: Volume of the air chamber Size of the air turbine Rotational speed of the turbine

Frequency domain analysis The system is linear Decompose Note: radiation conductance G cannot be negative

From frequency domain analysis Model testing of OWCs and air turbines

Model testing: similarity laws for air chamber and air turbine Correct dynamic similarity requires all terms in equation to take equal values in similar conditions at model size 1 and full size 2 . 1 air chamber 2

Turbine rotational speed The two turbines are geometrically similar Turbine dimensionless parameters (representing the turbine aerodynamic performance) take equal values for similar conditions of the air pressure cycle in the chamber of the model and the full-sized converter. We take such conditions as those of maximum air pressure . Turbine size Turbine rotational speed

Model testing of a cylindrical fixed-structure OWC in a wave flume (Instituto Superior Técnico, 2013). To appropriately reproduce the air compressibility effect in the chamber, the top of the tube is connected by a pipe to an air reservoir placed above.

Model at 1:16th scale of a spar-buoy OWC developed at Instituto Superior Técnico being tested at the large wave tank of the National Renewable Energy Centre (NAREC), Blyth, England, in 2012. The turbine was simulated by an orifice. The tank was filled with sea water.

Backward Bent Duct Buoy (1:4th of full scale) equipped with a Wells turbine being tested in Galway Bay, Ireland, about 2008.

Exercise Consider the OWCs integrated into the breakwater of Mutriku (northern Spain). Each OWC is equipped with a Wells turbine with rotor diameter D = 0.75 m and rated power 18.5 kW. The dimensions of the OWC structure are given in the figure below. The chamber width in the direction perpendicular to the drawing is 4 m. The plant is to be model tested at scale 1:5 in a large wave tank filled with fresh water. The turbine with be simulated in the tests by a geometrically similar turbine. Assume that the aerodynamic efficiency of the turbine is not affected by the scale (in reality this is not true, since Reynolds numbers are quite different). a) Determine the incident wave power (W/m) in the laboratory that simulates 30 kW/m at full size. b) Determine the air volume of the model chamber if air compressibility effects are to be adequately simulated. Divide it by the area of the model inner free-surface and compare with the height of the prototype air chamber. c) Determine the diameter of the model turbine rotor. d) Determine the rotational speed ratio between model and prototype under similar performance conditions. e) Determine the model turbine rated power corresponding to 18.5 kW for the prototype.

TURBINE

OWC breakwater, Mutriku, northern Spain, 2008-12, 16 x 18.5 kW OWCs

END OF PART 6 MODEL TESTING

Sinusoidal waves in water of arbitrary, but uniform, depth h

irregular waves