View
220
Download
5
Category
Tags:
Preview:
Citation preview
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)
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
Recommended