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Unformatted text preview: 11/9/2010 Wind Turbine Aerodynamics and Aeroacoustics Roger E. A. Arndt Professor Emeritus Saint Anthony Falls Laboratory 6126252883 arndt001@umn.edu Outline
• • • • • • • • Brief Historical Review Basic Concepts Betz Theory Rotor Aerodynamics Principles of Aerodynamic Lift Rotor Design Elements of Acoustics A Brief Primer on Rotor Noise 1 11/9/2010 Types of Turbines
Many types have been tried over the years. These are probably the two most important. This type of turbine will be installed at U of M Umore Park Our emphasis will be on HAWTs
Source: Sandia National Laboratory and Clipper: VAWT or Darrieus HAWT How Much Power Can We Generate? Betz Momentum Theory
• The power available per unit area is ½ ρ V3. The cross sectional area of a rotor is πR2 P • We can define a power coefficient as Cp = 1 3
2 ρV πR 2 • Cp can be thought of as an efficiency. Can this value approach unity? • The answer lies in the analyses of Betz (1919) and Glauert (1935) 2 11/9/2010 Betz Actuator Disk Theory
Define U – V’ = aU V′ = (1 − a )U
Cp = P
1 ρV 3 πR 2 2 U V’ V2 Using conservation of momentum,Betz (1919) showed that Cp = 4(1 – a)2a Maximum power is obtained when a = 1/3 Ideal Cp = 16/27 = 0.593 Glauert Improved the Betz Theory The Glauert analysis added conservation of angular momentum 3 11/9/2010 Aerodynamic Lift The inplane component of the lift provides torque φ Rotation Blade Element Theory
By integrating the applied torque over the entire rotor an expression for the power output can be found:
2 T = ∫ 1 ρVR CLcB cos φrdr 2 R 0 B = number of blades CL = lift coefficient c = chord length P = TΩ
2 VR = [(1 − a )V ]2 + Ω 2R 2 Note that there are several parameters, some interrelated, that dictate the design of a rotor. 4 11/9/2010 Blade Element Theory
Twist is defined as β (r) Pitch is defined as β (R). Many machines can vary this parameter as wind velocity increases or decreases (1 − a )U (this is approximate since rotation in the wake tan φ ≅ has not been considered) Ωr φ = α + β, where α depends on the lift coefficient of the blade element CL The number of blades, B, and the planform shape, c(r), depends on issues more complex than can be discussed here. An important parameter that prescribes some of the geometry is the tip speed ratio, λ = ΩR/U Rotor Solidity
The trend is towards fewer, slender blades with increasing tip speed ratio
20 σ=
C'L =
CL = BA b πR 2
L' 1 ρV 2 c 2R 15 10 5 L
1 ρV 2 A Rb 2 0 0 5 10 15 Tip Speed Ratio λ = Ωr/U CL ≅ C' L 5 11/9/2010 Airfoil Theory
CL is defined by α and blade cross section A Variety of Blade Shapes Have Been Considered
Blade Thickness Increases from tip to hub Some Considerations:
•Stable Clmax •High L/D •Limited Clmax at Outboard Sections •Minimal effects of roughness
Sources: Spera (1994), Timmer and van Rooij (2003) 6 11/9/2010 DU 96180 Wind Tunnel Tests
Currently undergoing research in the SAFL wind tunnel
Excellent L/D = CL/Cd Stall α0 CL ≅ 2π(α − α 0 ) Source: Timmer van Rooij (2003) Variable Pitch Versus Stall Control
1000 800 600 400 200 0
Note: With increasing wind speed β must increase for constant α or α must increase for β constant 0 5 10 15 Wind Speed, U, m/s 20 25
Adapted from Spera (1994) 7 11/9/2010 Tip Vortex Effects Rotational effects in the rotor wake complicate the analysis Propeller Tip Vortices What’s Different? 8 11/9/2010 Detailed Considerations: Tip Vortex Effects Wind Turbine Propeller Wind Tunnel Modeling St Anthony Falls Laboratory Atmospheric Wind Tunnel
Source: Chamorro (2011) 9 11/9/2010 Atmospheric Boundary Layer Effects Boundary layer implies symmetry is lost ∆Ux = UoUwake Nondimensional distributions of mean velocity and velocity deficit downwind of the turbine Source: Chamorro, PorteAgel (2009) Turbulence intensity distribution downwind of the turbine. Wind Farm Optimization Turbulence intensity: staggered v/s aligned configuration. Turbine layout has strong implications on power and turbulence loads.
Source: Chamorro, Arndt and Sotiropoulos (2011) Relative angular velocity: staggered v/s aligned configuration 10 11/9/2010 Aerodynamic Control
Riblet film (h < 100µ) being considered to reduced drag
Experimental data Bechert et al 1997
s+ =
τ0 s ρ ν Vortex Generators
Vortex generators are used improve flow over thicker sections of blades
Vortices provide mixing of highspeed flow with low speed flow in the vicinity of the blade close to stall 11 11/9/2010 Active Control Active flow control technology is being considered for improvements in power output A synthetic jet to be used in our active flow control work Fundamentals of Acoustics
• • • • Increasing emphasis on noise because of proximity to builtup areas Much of what we know is based on the aeroacoustics of flight vehicles such as helicopters Only a few essentials can be discussed here due to time constraints Some issues: – Wide range of amplitude, Power output of a whisper is about 109 watt, while a rocket engine produces about 107 W atts – Tiny output: A 75 piece orchestra produces about 10 Watts, a 10 MW jet engine produces only about 104 Watts or about 0.1 % of the power available – Several different noise sources are competing for our attention 12 11/9/2010 Fundamentals
p − po = A sin( 2πx − 2πft ) λ p − po u= ρo a o fλ = a o
__ __ p2 I = pu = ρ oa o ao = kRT W = ∫∫ IdA Sound Power Level = 10 log W/Wref, dB Sound Pressure Level = 10 log p2/p2ref = 20 log p/pref Typical Levels
SPL (dB) 140 120 100 80 60 40 20 0
Source
Pain Threshold, Pneumatic Chipper Rock Group, Auto Horn Subway Conversation Bedroom Threshold of Hearing 13 11/9/2010 Perceived Loudness Allowable Exposure Times Frequency, Hz 14 11/9/2010 Sound Sources
Many of these sources of sound will become more important with locations closer to residential areas A Little Aeroacoustics
The most important noise source is a dipole due to aerodynamic loading The pressure field at x due to a dipole at y moving relative to the observer with velocity aoMr is Unsteady lift contribution Steady lift contribution 15 11/9/2010 Blade Noise Two contributors to the noise field: unsteady loads on the blade acceleration of a steady load A sketch of aeroacoustics Is provided in the course notes Helicopter Noise Spectrum 16 11/9/2010 Wind Turbine Noise Spectrum Note the lower frequency content Source of Noise From a Wind Turbine Note the dominant noise source from downward moving blade Broadband trailing edge noise is the dominant noise source for this wind turbine Source: Oerlemansa et al (2007) 17 11/9/2010 Noise Comparison
Helicopter: Much louder, Higher frequency Low noise levels Much lower frequency Blade passing harmonics not audible What’s the problem? References
Arndt, REA (1998) Wind Turbines in Handbook of Fluid Dynamics, Chapt. 41.3, RW Johnson, Ed. Arndt, REA (1978) “A Sketch of Aeroacoustics” The Shock and Vibration Digest Vol 10, #12, Dec. Arndt, REA (1975) Wind PowerAn Ancient Answer to Modern Needs? AIAA Student Journal Betz, A and Prandtl, L (1919) “Schraubenpropeller mit geringsten Energieverlust”, Nacht. Ges. Wiss. Gottingen Math Phys., K1, 193217 De Vries, O (1983) On the theory of the horizontalaxis wind turbine Ann. Rev. Fluid Mechanics, 15, 7796 Glauert, H (1935) Airplane Propellers in Aerodynamic Theory, vol 4, Div J, WF Durand, Ed., Julius Springer, Berlin, Reprinted by Dover 1963 Hansen, AC and Butterfield, CP (1993) Aerodynamics of horizontalaxis wind turbines Ann. Rev. Fluid Mechanics 25: 11549 18 11/9/2010 References
Hau, E (2006) Wind Turbines 2nd Edition, Springer Hutter, U (1977) Optimum windenergy conversion systems, Ann. Rev. Fluid Mechanics, 9, 399419 Oerlemansa, S, Sijtsmaa, P, Mendez Lopez, B (2007) Location and quantification of noise sources on a wind turbine Journal of Sound and Vibration 299 869–883 Spera, DA Ed. (1994) Wind Turbine Technology ASME Press
(See Chapter 5: Aerodynamic Behavior Of Wind Turbines, Chapter 6: Wind Turbine Airfoils and Rotor Wakes, Chapter 7: Wind Turbine Acoustics) Sorenson, JN (2011) Aerodynamic aspects of wind energy conversion, Ann. Rev. Fluid Mechanics In Press Betz Analysis
Replace rotor with actuator disk p1 U V p2 V2 T = (p1 − p 2 ) A = ρAV[U − V2 ]
2 1 ρU 2 + p 1 atm = 2 ρV + p1 2 2 1 ρV 2 + p 1 atm = 2 ρV + p 2 2 2 A ≡ πR 2
2 T = 1 ρ U 2 − V2 2 19 11/9/2010 Betz Analysis (cont)
T = ρAV[U − V2 ] 2 T = 1 ρ U 2 − V2 2 Momentum Bernoulli V= U + V2 2 Let U – V = a, Then it follows that U – V2 = 2a
2 P = TV = 1 ρA U 2 − V2 V 2 CP = P
1 ρAU 3 2 CP = 4a(1 − a )2 20 ...
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This note was uploaded on 02/26/2011 for the course EE 523 taught by Professor Dr.hopkins during the Spring '11 term at SUNY Buffalo.
 Spring '11
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