Numerical Investigation of Wind Turbine and Wind Farm Aerodynamics
by
Suganthi Selvaraj
A thesis submitted to the graduate faculty
in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE
Major: Aerospace Engineering
Program of Study Committee:
Anupam Sharma, Major Professor
Eugene Takle
Hui Hu
Iowa State University
Ames, Iowa
2014
Copyright Suganthi Selvaraj, 2014. All rights reserved. ii
DEDICATION
For their constant support, their unmovable devotion and loyalty to my dreams and ambi- tions, I dedicate this thesis to my parents, Dr. Selvaraj Rajendran and Dr. Eunice Selvaraj, and my brother, Dhanraj Selvaraj. I pray that this accomplishment brings you some measure of joy because it would not be possible without your example of faith, love and dedication. iii
TABLE OF CONTENTS
LIST OF FIGURES ...... v
ACKNOWLEDGEMENTS ...... ix
ABSTRACT ...... x
CHAPTER 1. Wind Turbine Aerodynamics ...... 1
1.1 Introduction ...... 1
1.2 CP Entitlement for a HAWT Operating in Isolation in Uniform Flow ...... 4 1.2.1 1-D Momentum Theory ...... 5
1.2.2 Actuator Disk With Swirl ...... 7
1.2.3 E↵ect of Finite Number of Blades ...... 8
1.2.4 E↵ect of Viscosity ...... 9
1.3 Numerical modeling of wind turbine aerodynamics ...... 11
1.3.1 Airfoil force distribution ...... 12
1.3.2 Gaussian Distribution of forces ...... 13
1.3.3 Simulation set-up ...... 16
1.3.4 Validation ...... 16
1.4 Conclusion ...... 22
CHAPTER 2. Investigation of a Novel, Dual Rotor Wind Turbine Concept . 28
2.1 Numerical Simulations using RANS CFD ...... 32
2.1.1 Simulation set-up ...... 33
2.1.2 Rotor Design ...... 34
2.1.3 Optimization Study ...... 34
2.1.4 Large Eddy Simulations ...... 37 iv
2.2 Conclusion ...... 38
CHAPTER 3. Wind Farm Aerodynamics ...... 42
3.1 Surface Flow Convergence in Wind Farms ...... 44
3.2 Numerical simulations ...... 45
3.2.1 Problem set-up ...... 45
3.2.2 Boundary conditions ...... 46
3.2.3 Atmospheric stability conditions ...... 48
3.2.4 Concept Simulation ...... 49
3.2.5 Story County Wind Farm Simulation ...... 53
3.3 Conclusion ...... 56 v
LIST OF FIGURES
1.1 Current installed wind capacity in the USA [1]...... 2
1.2 Annual and cumulative wind installations by 2030 [1]...... 3
1.3 A schematic of the proposed dual rotor wind turbine (DRWT) concept 4
1.4 An illustration of the flow convergence phenomenon. The slanted arrow
on the left refers to the incoming freestream velocity direction and the
arrow on the right refers to the turned velocity due to flow convergence 5
1.5 Illustration of 4 cross sections in the actuator disk method ...... 5
1.6 Evolution of pressure and velocity through an actuator disk ...... 6
1.7 CP and CT values as functions of induction, a from the 1-D momentum theory...... 7
1.8 Variation of (a) axial & swirl induction with r, and (b) maximum CP as a function of ...... 8
1.9 CP versus curves for varying number of blades of a HAWT. Taken from Okulov [33]...... 10
1.10 Maximum possible CP with various approximations (Selvaraj et al. [42]). 11 1.11 Airfoil ...... 13
1.12 Axisymmetric cross section of the annulus at radius rm ...... 14 1.13 Illustration of Gaussian distribution ...... 15
1.14 2-D simulation schematic ...... 16
1.15 Illustration of a wedge mesh ...... 17
1.16 Two dimensional grid for the uniformly loaded rotor ...... 18
1.17 Simulation of the uniformly loaded rotor using a =0.1...... 19
1.18 Simulation of the uniformly loaded rotor using a =0.5...... 20 vi
1.19 Validation against analytical results using 1D momentum theory for CT
and CP . Plot on the right uses the computed value of ‘a’ on the abscissa. 21 1.20 Geometric chord and twist distribution for the Ris rotor ...... 22
1.21 Cp comparison between various measured data, BEM theory and actuator disk simulation results...... 23
1.22 Pressure contours and streamlines through the Risoe Turbine (actuator
disk simulation results) for tip speed ratio, =4.0...... 24
1.23 Pressure contours and streamlines through the Risoe Turbine (actuator
disk simulation results) for tip speed ratio, =7.0...... 24
1.24 Torque force coe cient, c⌧ and thrust force coe cient, cN distributions compared between Actuator disk model predictions against BEM pre-
diction...... 25
1.25 Geometric chord and twist distribution for the NREL phase VI rotor . 25
1.26 Cp curve...... 26 1.27 Pressure contours and streamlines through the NREL-VI Turbine (ac-
tuator disk simulation results) for tip speed ratio, =4.0...... 26
1.28 Pressure contours and streamlines through the NREL-VI Turbine (ac-
tuator disk simulation results) for tip speed ratio, =7.0...... 27
1.29 Torque force coe cient, c⌧ and thrust force coe cient, cN distributions compared between Actuator disk model predictions against BEM results. 27
2.1 Maximum possible CP with various approximations (Selvaraj et al. [42]). 29 2.2 Family of airfoils for a medium NREL blade (Tangler et al. [46]). . . . 29
2.3 A schematic of the proposed dual-rotor concept...... 30
2.4 Comparison of numerically predicted and analytically evaluated (by
Newman [32]) CT and CP for a 4-disk turbine...... 33 2.5 Comparison of numerically predicted and analytically evaluated (by
Newman [32]) CT and CP for a 3-disk turbine...... 33 vii
2.6 Comparison of numerically predicted and analytically evaluated (by
Newman [32]) CT and CP for a 2-disk turbine...... 34
2.7 Radial distributions of (a) input (a and Cl) and (b) output (blade chord and twist) for the secondary rotor with the DU96 airfoil...... 35
2.8 The lift and drag coe cient polars for the DU96 airfoil ...... 36
2.9 The radial chord and twist distributions of the NREL 5MW turbine. . 37
2.10 Simulations for two di↵erent rotor sizes showing pressure contours and
streamlines ...... 38
2.11 CP (DRWT - SRWT), di↵erence in aerodynamic power coe cient, C = C C due to the addition of a secondary rotor. . 39 P P DRWT P SRWT 2.12 Simulations for two axial separation distances showing pressure contours
and streamlines ...... 39
2.13 CP (DRWT - SRWT), di↵erence in aerodynamic power coe cient, C = C C due to the addition of a secondary rotor. . 40 P P DRWT P SRWT 2.14 Radial distribution of the torque force coe cient for the main rotor,
secondary rotor and the main rotor operating in isolation...... 40
2.15 Radial distribution of the angle of attack for the main rotor, secondary
rotor and the main rotor operating in isolation...... 41
2.16 A snapshot of iso-surfaces of Q-criterion from the DRWT LES simulation. 41
3.1 The phenomenon of flow convergence in wind farms. (a) A schematic
illustrating micro-scale pressure gradient that is set up by turbines in a
wind farm, and (b) CWEX measurements of resulting flow convergence
in neutral atmospheric stability condition...... 44
3.2 The di↵erent refinement regions for a turbine ...... 46
3.3 Inlet velocity profile for inviscid and viscous simulations ...... 47
3.4 The di↵erent atmospheric stability conditions [18]...... 48
3.5 Simulation setup and mesh at turbine hub height...... 49 viii
3.6 Inviscid simulation: Kinematic pressure contours drawn (a) at hub
height and (b) on the ground...... 50
3.7 Inviscid simulation: flow angle (w.r.t. x direction) contours drawn (a)
at hub height and (b) on the ground...... 51
3.8 Average (over Y direction) pressure and flow angle on the ground versus
distance along the turbine array...... 52
3.9 Kinematic pressure contours drawn (a) at hub height and (b) on the
ground...... 53
3.10 Flow angle contours drawn (a) at hub height and (b) on the ground. . 54
3.11 Average (over Y direction) pressure and flow angle on the ground versus
distance along the turbine array...... 55
3.12 Layout of the story county farm turbines. The locations denoted by the
circles in the red box are the locations of the meteorological towers. . . 57
3.13 Relative locations of the meteorological towers and the turbines in the
Story County wind farm. The hollow rectangles denote turbine locations
and the filled circles denote meteorological tower locations...... 58
3.14 Simulation results for case A. Contours of (a) pressure and (b) flow
angle, drawn on a plane at a height of 0.27 r above the ground. . . 58 ⇥ tip 3.15 Simulation results for case A. Contours of (a) pressure and (b) flow
angle, drawn on a plane at a height of 0.27 r above the ground. . . 59 ⇥ tip 3.16 Simulation results for case B. Contours of (a) pressure and (b) flow
angle, drawn on a plane at a height of 0.27 r above the ground. . . 59 ⇥ tip 3.17 Simulation results for case B. Contours of (a) pressure and (b) flow
angle, drawn on a plane at a height of 0.27 r above the ground. . . 60 ⇥ tip 3.18 Change in flow angle (w.r.t. the value at M1) as functions of distance
from B2 turbine for (a) case A, and (b) case B...... 60 ix
ACKNOWLEDGEMENTS
For good health, the strength, the perseverance, the blessing of opportunities, first and most importantly, I thank my Father, God Almighty. Without His grace and love, I would not be who I am and where I am today.
To Dr. Anupam Sharma, my major professor, I would like to express my deepest apprecia- tion. Without his guidance, persistent encouragement and advice, this dissertation would still be a figment of my imagination. Dr. Sharma has been more than just a source of knowledge and under his mentorship, I have drawn much inspiration from his personable and patient nature.
To the members of my Program of Study(PoS) committee, Dr. Eugene Takle and Dr. Hui
Hu, I express my gratitude for their e↵orts in helping me successfully complete this work.
To Dan Rajewski, I express my gratitude for his time in providing me with the necessary experimental data.
To my colleagues who through blood, sweat and tears became friends, Karthik Reddy,
Varun Vikas, Lei Shi, Meilin Yu, Ben Zimmerman, Daniel Garrick, Bharat Agrawal, Aaron
Rosenberg and Behnam Moghadassian, I thank you for the invaluable, educational discourses.
Your support meant more to me than you will ever know.
I would also like to express my appreciation to Dr. Paul Durbin, Dr. Zhi J. Wang and Dr.
Ganesh Rajagopalan whose inspirational conversations, lectures and teaching styles stoked the ember of a passion for CFD.
To the lovely aerospace engineering o ce sta↵, Gayle Fay and Laurie Hoidfelt, for patiently holding my hand through the mountains of paperwork.
Last but certainly not least, I thank my parents and brother who have been a continuous source of encouragment and support. I would also like to thank all my family and friends for the immense emotional and mental support throughout this endeavour. x
ABSTRACT
A numerical method based on the solution of Reynolds Averaged Navier Stokes equations and actuator disk respresentation of turbine rotor is developed and implemented in the Open-
FOAM software suite for aerodynamic analysis of horizontal axis wind turbines (HAWT). The method and the implementation are validated against the 1-D momentum theory, the blade element momentum theory and against experimental data. The model is used for analyzing aerodynamics of a novel dual rotor wind turbine concept and wind farms.
Horizontal axis wind turbines su↵er from aerodynamic ine ciencies in the blade root region
(near the hub) due to several non-aerodynamic constraints (e.g., manufacturing, transportation, cost, etc.). A new dual-rotor wind turbine (DRWT) concept is proposed that aims at mitigating these losses. A DRWT is designed that uses an existing turbine rotor for the main rotor (an
NREL 5 MW rotor design), while the secondary rotor is designed using a high lift to drag ratio airfoil (the DU 96 airfoil from TU Delft). The numerical aerodynamic analyses method developed as a part of this thesis is used to optimize the design. The new DRWT design gives an improvement of about 7% in aerodynamic e ciency over the single rotor turbine.
Wind turbines are typically deployed in clusters called wind farms. HAWTs also su↵er from aerodynamic losses in a wind farm due to interactions with wind turbine wakes. An interesting mesoscale meteorological phenomenon called “surface flow convergence” believed to be caused by wind turbine arrays is investigated using the numerical method developed here. This phe- nomenon is believed to be caused by the pressure gradient set up by wind turbines operating in close proximity in a farm. A conceptual/hypothetical wind farm simulation validates the hypothesis that a pressure gradient is setup in wind farms due to turbines and that it can cause flow veering of the order of 10 degrees. Simulations of a real wind farm (Story County) are also conducted which give qualitatively correct flow direction change, however quantitative agreement with data is only moderately acceptable. 1
CHAPTER 1. Wind Turbine Aerodynamics
A basic description of the 1-D momentum theory along with e↵ects of swirl and finite number of blades is presented in this chapter. The actuator disk theory to model wind tur- bine aerodynamics is also provided with validation again experimental data and against other theories.
1.1 Introduction
Electricity is an important part of our every day lives. In this day and age, electricity is used for virtually every task, regardless of complexity. The need for energy sources is ever increasing while natural resources such as coal, petroleum and natural gas are rapidly depleting. Thus we look to sustainable energy resources such as solar, wind, etc. The most invested form of sustainable(renewable) energy source in the last few years is wind [15].
The United States Department of Energy investigated the implications if 20% of the nation’s electricity demand were to be provided by wind by the year 2030. As of November 2013, 4.16% of the nation’s electricity demand was provided by wind[11]. By the year 2030, the electricity demand in the US is predicted to increase by 39%. To meet 20% of that demand, the wind capacity would have to reach more than 300 GW. Currently, 61.108 GW are available in the
US Fig. 1.1. If we assume all the wind turbines are of 2 MW capacity, then 30000 additional such turbines need to be deployed to reach the target milestone. This is roughly equal to eight times the number of turbines currently installed in the USA.
The US DOE predicts installation of many more turbines in the upcoming years to meet the 20% target by 2030 as shown in Fig 1.2. Assuming electricity price to be 5/kWh, a 1% aerodynamic e ciency increase was tantamount to savings of USD 1.31 billion per year. 2
Hence, research on improving e ciency of wind farms and individual turbines is worthwhile.
Several investigations ([3], [29], [51])are being done to understand and eventually improve the e ciency of a turbine and wind farms. Two such investigations are performed and described in this thesis.
Figure 1.1: Current installed wind capacity in the USA [1]
The Betz-Lancaster-Zhukowski limit of aerodynamic power coe cient, CP = 16/27 is often casually referred to as the highest obtainable e ciency of a single-rotor horizontal axis wind turbine (HAWT). The realizable, practical limit of a torque-based, finite-bladed HAWT, op- erating in a viscous fluid is actually much lower [49]. A more “practical” limit on CP for a single-rotor HAWT is thus proposed. After accounting for these (almost unavoidable) physical limits, this “practical” limit on CP is found to be just a few percentage points higher than that of modern, utility-scale HAWTs.
A novel dual rotor wind turbine (DRWT) concept is proposed and analyzed for its aero- 3
Figure 1.2: Annual and cumulative wind installations by 2030 [1] dynamic performance. The motivation for this comes from the fact that wind turbine blades have high aerodynamic losses near the root of the blades (approximately bottom 25%). That particular region of the blade is primarily designed for maintaining the structural integrity of the blade. It causes high aerodynamic losses and thus reduces the overall e ciency of a turbine.
A new, dual-rotor design is proposed to mitigate these losses by introducing another rotor of a smaller size upstream of the main rotor (See Figure 1.3). Secondary rotor e ciently captures the power lost due to the aerodynamic ine ciency of the main rotor in the root region.
Most utility scale turbines are deployed in clusters and due to aerodynamic interactions between turbines in a cluster, they do not operate in isolation. Barthelmie et al. [5] shows that up to 40% losses occur in a wind farm due to wake interaction between turbines. Therefore, it is important to study aerodynamic interaction of turbines in a wind farm in order to improve the e ciency of a farm. A physical phenomenon called ‘flow convergence’ is observed from experimental measurements in wind farms where the flow coming at a certain direction tends to align itself with the direction of the turbine array as illustrated in the Figure 1.4.Itissuspected that this phenomenon is caused by the pressure jump across each turbine which leads to an overall pressure gradient in the direction of the array. This pressure gradient drives the change in direction of the freestream flow towards the direction of the array. In this thesis, a verification of this physical phenomenon is performed using computational fluid dynamics(CFD) methods.
While the exact implications of the surface flow convergence phenomenon are unclear, it is possible that some important meteorological implications exist.
For such CFD analyses, there are several ways of modelling a wind turbine. One could 4
Figure 1.3: A schematic of the proposed dual rotor wind turbine (DRWT) concept build a model of the entire turbine using a CAD package or assume and take advantage of flow symmetry and periodicity between blade passages to simulate only one blade passage (e.g., a
120 for a 3-bladed HAWT). Such methods are computationally expensive even for a single turbine. Hence, a more feasible actuator disk method that does not resolve the blade geometry in the simulation but models its e↵ect using body forces is adopted in this study. This approach gives substantial computation time savings.
1.2 CP Entitlement for a HAWT Operating in Isolation in Uniform Flow
Several theories with varying degrees of approximations are available to analyze aerody- namic e ciency of a horizontal axis wind turbine (HAWT). The simplifications in these the- ories typically neglect one or more physical phenomena that reduce the practically attainable e ciency. The simplest of these theories, for example, is the 1-D momentum theory that gives the Betz limit [7] for aerodynamic e ciency of a HAWT of C = 16/27( 0.593). The turbine P ⇠ 5
Figure 1.4: An illustration of the flow convergence phenomenon. The slanted arrow on the left refers to the incoming freestream velocity direction and the arrow on the right refers to the turned velocity due to flow convergence rotor is represented by an actuator disk that supports a pressure jump across it. Figure 1.6 shows a schematic of the actuator disk model.
1.2.1 1-D Momentum Theory
Figure 1.5: Illustration of 4 cross sections in the actuator disk method
The 1-D momentum theory makes the simplifying assumptions that the flow is (1) one- dimensional (zero swirl), and (2) inviscid. Consider Fig. 1.5 representing the cross sections of
flow through a wind turbine. Stations 1 and 4 are far upstream and downstream of the turbine respectively such that the pressure at these locations are equal to the freestream pressure
(P1 = P4 = P ). Stations 2 and 3 are cross sections just upstream and downstream of the 1 6
Figure 1.6: Evolution of pressure and velocity through an actuator disk
+ turbine rotor. A sharp pressure jump occurs across the rotor (P2 = pd and P3 = pd ). The velocity at Stations 2 and 3 are equal (U2 = U3 = Ud) from flow continuity. Mass conservation, momentum balance, and energy conservation can be expressed as
m˙ = ⇢U A = ⇢AdUd = ⇢UwAw, (mass) 1 1 + ⇢UdAd(U Uw)=(p p )Ad, (momentum) 1 d d + 1 2 1 2 p + ⇢Ud = p + ⇢U , or d 2 1 2 1 1 2 1 2 p + ⇢Ud = p + ⇢Uw (energy) (1.1) d 2 1 2
The thrust produced due to the rearward increased momentum is represented by
+ T = U m˙ Uwm˙ = Ad(p p ) (1.2) 1 d d
Axial induction factor, a is defined as the fractional decrease in wind velocity between the free stream and the energy extraction device,
U Ud a = 1 . (1.3) U 1
The above representation can be used to derive thrust (axial force) force coe cient, CT and power coe cient, CP in the forms
2 CT =T/(1/2⇢U Ad)=4a(1 a), and 1 3 2 CP =P/(1/2⇢U Ad)=4a(1 a) . (1.4) 1
HAWTs are designed to maximize CP , while propellers maximize CT . The extrema for CP (a) are obtained by solving dCP /da = 0, which gives maximum CP = 16/27 at a =1/3. This 7
maximum CP (limit) is also known as the Betz limit, or more appropriately the Betz-Lancaster-
Zhukowski limit. Figure 1.7 plots the variation of CP and CT with axial induction factor, a given by the 1-D momentum theory.
1 CT CP Uw/U∞ 0.8
0.6 0.593 T ,C P C 0.4
Betz theory invalid 0.2
0 0.333 0.5 a
Figure 1.7: CP and CT values as functions of induction, a from the 1-D momentum theory.
1.2.2 Actuator Disk With Swirl
The 1-D momentum theory ignores the fact that HAWTs are torque devices. Torque gener- ation requires a change in angular momentum of the fluid across a rotor. This is incorporated by allowing the flow to swirl behind the actuator disk. The swirl velocity, U✓ behind the disk is non-dimensionalized to get tangential induction factor, a0 = U✓/(2⌦r). To satisfy radial equilibrium (force balance in radial direction), a, a0 and other quantities have to vary radially and the flow has to be analyzed in 2-D (axial and radial); azimuthal symmetry is still assumed.
This is typically done by discretizing the actuator disk into multiple annular sections. Con- serving angular momentum at each annular strip of width r at radius r (area, Ad =2⇡r r) gives: