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Blade Element Momentum Theory for Tidal Turbine Simulation with Wave Effects: A Validation Study

Blade Element Momentum Theory for Tidal Turbine Simulation with Wave Effects: A Validation Study . * H. C. Buckland, I. Masters and J. A. C. Orme *513924@swansea.ac.uk. Introduction. Fast and robust turbine computer simulation: Performance, periodic stall

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Blade Element Momentum Theory for Tidal Turbine Simulation with Wave Effects: A Validation Study

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  1. Blade Element Momentum Theory for Tidal Turbine Simulation with Wave Effects: A Validation Study * H. C. Buckland, I. Masters and J. A. C. Orme *513924@swansea.ac.uk

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

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

  4. Inflow profile • Waves • Tidal stream Blade element theory dFa1(a,b) dT1(a,b) Momentum theory dFa2(a,b) dT2(a,b) • Numerical aim: • dFa1(a,b) = dFa2(a,b) dT1(a,b) =dT2(a,b) • Minimise g: • g=[ dFa1(a,b) - dFa2(a,b) ] 2 + [ dT1(a,b) - dT2(a,b) ] 2

  5. Blade Element Momentum Theory BEMT Momentum Theory

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

  7. Optimiser ‘fmincon’ for a closed BEMT system b

  8. BEMT steady state example

  9. Inflow profile • Waves • Tidal stream Blade element theory dFa1(a,b) dT1(a,b) Momentum theory dFa2(a,b) dT2(a,b) • Numerical aim: • dFa1(a,b) = dFa2(a,b) dT1(a,b) =dT2(a,b) • Minimise g: • g=[ dFa1(a,b) - dFa2(a,b) ] 2 + [ dT1(a,b) - dT2(a,b) ] 2

  10. 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

  11. Chaplin’s stream function wave theory • 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: v C u Bernoulli equation on the free surface: Mean stream flow Wave Disturbance

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

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

  14. The Barltrop Experiments Tidal turbine in a wave tank 2 seperate investigations Barltrop, N. Et al. (2006) 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 Towed to simulate tidal flow!

  15. Self Weight bending moment

  16. Mx My results: 1m/s current

  17. The Barltrop Experiments Tidal turbine in a wave tank 2 seperate investigations Barltrop, N. Et al. (2006) 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. (2007) Investigation into 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!

  18. Axial force and torque

  19. TSR vs Ct, Cp and Cfa

  20. 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

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

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