Blade Element Momentum Theory for Tidal Turbine Simulation with Wave Effects: A Validation Study * H. C. Buckland, I. Masters and J. A. C. Orme

Introduction Fast and robust turbine computer simulation: Performance, periodic stall Survivability, extreme wave climate Fatigue Fluid flow conditions

Outline Turbine Performance simulation BEMT Tidal flow boundary layer Stream function wave theory Wave acceleration Tidal flow + Wave disturbance Validation study

Blade element theory dF a1 (a,b) dT 1 (a,b) Inflow profile Waves Tidal stream Numerical aim: dF a1 (a,b) = dF a2 (a,b) dT 1 (a,b) = dT 2 (a,b) Minimise g: g=[ dF a1 (a,b) - dF a2 (a,b) ] 2 + [ dT 1 (a,b) - dT 2 (a,b) ] 2 Momentum theory dF a2 (a,b) dT 2 (a,b)

Blade Element Momentum Theory BEMT Momentum Theory

Closed System: Unknowns: a, b, T Fa Two pairs of equations: dT_{1}, dFa_{1}, dT_{2}, dFa_{2} Cavitation Blade Element Theory Blade Element Momentum Theory BEMT

Optimiser ‘fmincon’ for a closed BEMT system b

BEMT steady state example

Blade element theory dF a1 (a,b) dT 1 (a,b) Inflow profile Waves Tidal stream Numerical aim: dF a1 (a,b) = dF a2 (a,b) dT 1 (a,b) = dT 2 (a,b) Minimise g: g=[ dF a1 (a,b) - dF a2 (a,b) ] 2 + [ dT 1 (a,b) - dT 2 (a,b) ] 2 Momentum theory dF a2 (a,b) dT 2 (a,b)

Tidal boundary layer Bed friction -> boundary layer Permeates the whole water column Power law approximation for boundary layers Assume a constant mean free surface height h x

Chaplin’s stream function wave theory C u v Finite depth, 2D irrotational wave of permanent form Frame of reference moves with the wave Finite depth wave theory: Incompressible flow Boundary condition Kinematic free surface condition: Bernoulli equation on the free surface: Mean stream flow Wave Disturbance

Tidal flow +wave forces Problems: Depth dependent tide velocity Steady state BEMT Coupling: Doppler effect Alter moving frame of reference

Accelerative forces: The Morison equation c Axial oscillatory inflow: Tangential oscillatory inflow:

The Barltrop Experiments 350mm turbine diameter 200 rpm 0.3m/s 1m/s Wave height 150mm Long waves 0.5Hz Steep waves 1Hz Bending Moments Mx My Towed to simulate tidal flow! Barltrop, N. Et al. (2006) Wave-Current Interactions in Marine Current Turbines. Tidal turbine in a wave tank 2 seperate investigations

Self Weight bending moment

Mx My results: 1m/s current

The Barltrop Experiments Barltrop, N. Et al. (2007) Investigation into Wave- Current Interactions in Marine Current Turbines. 350mm turbine diameter 200 rpm 0.3m/s 1m/s Wave height 150mm Long waves 0.5Hz Steep waves 1Hz Bending Moments Mx My Barltrop, N. Et al. (2006) Wave-Current Interactions in Marine Current Turbines. 400mm turbine diameter 90rpm 0.7m/s 0.833Hz Varying wave heights 00mm 35mm 84mm 126mm Torque T Axial force Fa Towed to simulate tidal flow! Tidal turbine in a wave tank 2 seperate investigations

Axial force and torque

TSR vs Ct, Cp and Cfa

Conclusion Validation of wave theory Compatibility of dynamic inflow with BEMT Validation of self weight torque Wave effect on performance is dependent on TSR curve profiles

Further work Wave superposition Sea spectra, random phase sampling Storm event simulation Two way wave and current coupling