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 Survivability, extreme wave climateFatigue

Fluid flow conditions

Outline

Turbine Performance simulation BEMT

Tidal flow boundary layerStream function wave theoryWave accelerationTidal flow + Wave disturbance

Validation study

Blade element theorydFa1(a,b)dT1(a,b)

Inflow profile• Waves• Tidal stream

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

Momentum theorydFa2(a,b)dT2(a,b)

Blade Element Momentum Theory BEMT

 

 

Momentum Theory

U

0

)1( aU

)21( aU

Closed System:Unknowns: a, b, T FaTwo 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 theorydFa1(a,b)dT1(a,b)

Inflow profile• Waves• Tidal stream

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

Momentum theorydFa2(a,b)dT2(a,b)

Tidal boundary layer

Bed friction -> boundary layerPermeates the whole water column

Power law approximation for boundary layersAssume a constant mean free surface height

10/1)/( sB Hhuu

h

x

Chaplin’s stream function wave theory

C uv 02

0dy

d

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:

Cu

v

x

Bernoulli equation on the free surface:

g

CuvxQ

2

)()(

22

N

nn L

nx

L

ydnax

T

Lyx

1

2cos)(2

sinh),(

Mean stream flowWave Disturbance

Tidal flow +wave forces

Problems:

Depth dependent tide velocity

Steady state BEMT

Coupling:

Doppler effect

Alter moving frame of reference

costww uuU

costuC

Accelerative forces: The Morison equation

indrME FFF inFa inTF

dldt

dUACdF xmin

dlA

MCC

x

AAm

11

dlWM A2

cAxial oscillatory inflow:

drcM A2)sin(

Tangential oscillatory inflow:

drcM A2)cos(

indFadFadFa inTTT dFdFdF

The Barltrop Experiments

350mm turbine diameter200 rpm0.3m/s 1m/sWave height 150mmLong waves 0.5Hz Steep waves 1HzBending Moments Mx My

Towed to simulate tidal flow!

Barltrop, N. Et al. (2006) Wave-Current Interactions in Marine Current Turbines.

Rr

RhubrardFMx

Rr

RhubrT rdFMy

Tidal turbine in a wave tank2 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 diameter200 rpm0.3m/s 1m/sWave height 150mmLong waves 0.5Hz Steep waves 1HzBending Moments Mx My

Barltrop, N. Et al. (2006) Wave-Current Interactions in Marine Current Turbines.

N

n

Rr

Rhubraa dFF

1

N

n

Rr

RhubrT rdFT

1

400mm turbine diameter90rpm0.7m/s0.833HzVarying wave heights00mm 35mm 84mm 126mmTorque TAxial force Fa

Towed to simulate tidal flow!

Tidal turbine in a wave tank2 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