Blade Element Momentum Theory for Tidal Turbine Simulation with Wave Effects: A Validation Study *...
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Transcript of 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
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)
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
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
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
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