an investigation into blockage corrections for cross-flow hydrokinetic turbine performance robert j....
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An Investigation into Blockage Corrections for Cross-Flow
Hydrokinetic Turbine Performance
Robert J. Cavagnaro and Dr. Brian PolagyeNorthwest National Marine Renewable Energy Center
University of Washington
APS DFD MeetingPittsburgh, November 24, 2013
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Motivation Understand hydrodynamics of a full-scale vertical-axis
cross-flow turbine by testing at lab scale Explain variable turbine performance at different testing
facilities
Lab-scale – high variability of performance with velocity and faclity
Field-scale – limited variability of performance with velocity
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Micropower Rotor Parameters High-Solidity, Helical Cross-flow
turbine N: Number of blades (4)
H/D: Aspect Ratio (1.4)
φ: Blade helix angle (60o)
σ: Turbine solidity (0.3)
Lab scale
H = 23.4 cm, D = 17.2 cm
Field Scale
H = 101.3 cm, D = 72.4 cm
DNc
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Performance Characterization Experiments
Niblick, A.L., 2012, “Experimental and analytical study of helical cross-flow turbines for a tidal micropower generation system,” Masters thesis, University of Washington, Seattle, WA.
Torque control Torque measurement
Angular position measurement
Inflow velocity measurement
Upstream ADV
Thrust measurement
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Experimental Facilities
8.04.0
19.015.0
Flow speed (m/s)
Blockage Ratio
35.02.0 FrFroude number
%4U
I UTurbulence Intensity
UW Aero Flume
1.14.0
09.006.0
Flow Speed (m/s)
Blockage Ratio
4.02.0 FrFroude number
%10U
I UTurbulence Intensity
Bamfield Flume
Reynolds Number Reynolds Number43 1010 cRe
43 1010 cRe
Cross Section (m2)80.0
Cross Section (m2)35.0
Uc
Rec
Channel
RigTurbine
A
AA )(
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Blockage Corrections
Corrections rely on various experimental parameters
TU 2U
3U
WACA
TAT
h
1U
3
F
TPP U
UCC
TF
F
TTF U
U
3
F
T
P
PTF C
CUU
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Blockage Corrections: Glauert (1933)
Becomes unstable for CT ≤ -1
TU 2U
3U
WACA
TAT
h
1U
T
TTF
C
CUU
141
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Blockage Corrections: Maskell (1965)
Relies on knowledge of wake expansion or empirical constant
TU 2U
3U
WACA
TAT
h
1U
2
1
1
AA
UUW
TF
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Blockage Corrections: Pope & Harper (1966)
TU 2U
3U
WACA
TAT
h
1U
44
1 C
Tt A
A
“… for some unusual shape that needs to be tested in a tunnel, the authors suggest”
)1( tTF UU
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Blockage Corrections: Mikkelsen &Sørensen (2002)
TU 2U
3U
WACA
TAT
h
1U
Extension of Glauert’s derivation
u
CuUU T
TF 4
1
12)23(
)1( 2
u
T
W
A
A
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Blockage Corrections: Bahaj et al. (2007)
TU 2U
3U
WACA
TAT
h
1U
Iterative solution of system of equations, incrementing U3/U2
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Blockage Corrections: Werle (2010)
TU 2U
3U
WACA
TAT
h
1U
Approximate solution
2max, )1(
27/16
PC
02
0 )()1( PP CC
Also reached by Garrett & Cummins, 2007
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Case 1: Lab to Field ComparisonSame flow speed (1 m/s), different blockage
Lab0 09.0
LabcFieldc ReRe ,, 4
Field
No thrust measurements for lab test case
Case 1 RSSE
Uncorrected Werle Pope & Harprer
0.034 0.074 0.021
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Case 2: Performance at Varying SpeedSame blockage ratio and facility 15.0
Case 2 Total RSSE Uncorrected Werle Pope & Harper Bahaj
0.983 0.717 0.883 0.938
Pope & Harper
Bahaj
Werle
Indicates strong dependence on Rec at low velocity
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Case 3: Performance with Varying BlockageSame flow speed (0.7 m/s) at different facilities
Case 3 Total RSSE Uncorrected Werle Pope & Harper Bahaj
0.4618 0.2157 0.3582 0.3265
Pope & Harper
Bahaj
Werle
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Conclusions Determining full-scale, unconfined hydrodynamics
through use of a model may be challenging All evaluated corrections reduced scatter of lab scale
performance data Thrust measurements may not be needed to apply a
suitable blockage correction
Caution is needed when applying blockage corrections
Especially for cross-flow geometry
No corrections account for full physics of problem
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AcknowledgementsThis material is based upon work supported by the Department of Energy under Award
Number DE-FG36-08GO18179.
Adam Niblick developed the initial laboratory flume data.
Funding for field-scale turbine fabrication and testing provided by the University of Washington Royalty Research Fund.
Fellowship support for Adam Niblick and Robert Cavagnaro was provided by Dr. Roy Martin.
Two senior-level undergraduate Capstone Design teams fabricated the turbine blades and test rig (and a third is developing a prototype
generator).
Fiona Spencer at UW AA Department and Dr. Eric Clelland at Bamfield Marine Sciences Centre for support and use of their flumes
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Re Dependence
Lift to drag ratio for static airfoil NACA 0018 at 25˚ angle of attack
Effect of blockage raises local Reynolds number by increasing flow speed through turbine
Effect less dramatic at higher Re
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Bahaj Velocity Correction (2007)
Bahaj, a. S., Molland, a. F., Chaplin, J. R., & Batten, W. M. J. (2007). Power and thrust measurements of marine current turbines under various hydrodynamic flow conditions in a cavitation tunnel and a towing tank. Renewable Energy, 32(3), 407–426. doi:10.1016/j.renene.2006.01.012
Linear Momentum Theory, Actuator Disk Model, thrust and rpm same in flume and free-stream
Solved iteratively by incrementing ratio of bypass flow velocity to wake velocity (U3/U2)
Free-stream performance and λ derived from velocity correction
Where U1 is the water speed through the disk
Depends on inflow velocity, blockage ratio, and thrust
4/)/(
/2
1
1
TT
T
F
T
CUU
UU
U
U
)1)/((
)1)/((11
23
223
2
1
UU
UU
U
U
1
2
3
2
1
2
3
2 U
U
U
U
U
U
U
UT
1)/(
1
223
2
UUCU
U
T
T