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Parametric characterization of an experimental vertical axis hydro turbine Rawlings, George William 2008

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PARAMETRIC CHARACTERIZATION OF AN EXPERIMENTAL VERTICAL AXIS HYDRO TURBINE by George William Rawlings BASc, University of British Columbia, 2005  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in The Faculty of Graduate Studies (Mechanical Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) April 2008 © George William Rawlings, 2008  ABSTRACT The current research focuses on the design, fabrication, and testing of an experimental vertical axis tidal current turbine model to obtain first hand experimental data for use in validating numerical codes.  In addition to obtaining repeatable experimental results  using an entirely new system developed for the UBC towing tank, a parametric study was performed examining the effects of parasitic drag, tip losses, angle of attack, cambered blades, and shaft fairing on a free-stream device. The impacts on overall efficiency of each characteristic are quantified, leading to a prediction for the maximum efficiency of a free-stream device in the absence of losses.  Upon the application of a venturi-style duct, significant gains were demonstrated in the shaft power acquired, as well as in the reduction of torque fluctuations. Application of downstream deflectors provided a further decrease in torque fluctuations with minimal decrease in efficiency, which is significant for structural considerations. A maximum Ck value of 0.473 was obtained for the ducted device compared to 0.272 for the free-stream case; however, the power produced was 12% less than what may be expected from a freestream rotor of cross-sectional area equivalent to the duct capture area. An investigation into drag characteristics of a free-stream device further quantified the drag coefficient that may be expected, as well as the fluctuations of forces in parallel with the free-stream flow.  Experimental results were then compared with a commercial RANS solver CFD model from a parallel study. This validation will enable further numerical refinement of the optimum tip-speed ratio and solidity values identified in previous research, as well as further advancements into angle of attack, airfoil profile, and ducting configurations. Lastly, a case study was presented using specif’ing a ducted 3.375m x 3.375m rotor operating in Quatsino Narrows on Vancouver Island capable of powering approximately 17 homes.  11  TABLE OF CONTENTS  ABSTRACT  ii  .  LIST OF TABLES  v  LIST OF FIGURES  vi  LIST OF SYMBOLS, NOMENCLATURES, AND ABBREVIATIONS  xi  ACKNOWLEDGEMENTS 1  2  3  INTRODUCTION  xiii 1  1.1  Turbine Operating Principles  3  1.2  Previous Work / Motivation  6  1.3  Objectives / Scope of Work  9  EXPERIMENTAL SETUP AND PROCEDURE  11  2.1  Towing Tank and Carriage Overview  11  2.2  Baseline Model Parameters  13  2.3  Instrumentation  15  2.3.1  Instrumentation Components  15  2.3.2  Drive-train / Force Balance Configuration  15  2.4  Data Acquisition System  17  2.5  Calibration  18  2.6  Experimental Procedure  18  2.7  Data Processing Methodology  19  2.7.1  Data Selection and Averaging  20  2.7.2  Data Presentation  23  EXPERIMENTAL RESULTS  25  3.1  Angle of Attack and Revolution Angle Notation  25  3.2  Test Program Overview  26  3.3  Free-stream Turbine  28  3.3.1  Velocity and Reynolds Number Effects  30  3.3.2  Drive-train Comparison  34  3.3.3  Arm Profile Reduction  38  111  3.3.4  Single-blade  3.3.5  Angle of Attack  47  3.3.6  Cambered Blades  53  3.3.7  Blade End Plates  55  3.3.8  Shaft Fairing  59  3.3.9  Summary  63  3.4  Venturi-type Ducting  66  3.4.2  Ducting with Deflectors  71  3.4.3  Summary  75  3.5.1  Drag Force Summary  DISCUSSION 4.1  Measurement Accuracy  76 83 84 84  4.1.1  Instrumentation Uncertainty and Data Point Averaging  84  4.1.2  Run Repeatability  88  4.1.3  Revolution Speed Variation  95  4.2  5  64  3.4.1  3.5  4  Ducted Turbine  .43  Comparison with Numerical Predictions  4.2.1  Numerical Model Overview  4.2.2  Comparison of Results  99 99 101  4.3  Sources of Error  108  4.4  Sample Application  109  CONCLUSIONS AND RECOMMENDATIONS  112  5.1  Conclusions  112  5.2  Recommendations for Future Work  113  REFERENCES  116  APPENDIX A: Design Calculations  119  APPENDIX B: Component Drawings  132  APPENDIX C: Instrumentation and DAQ Components  159  APPENDIXD: Run Log  161  iv  LIST OF TABLES Table 1-1: Available Davis et al. reports  7  Table 2-1: Principal model turbine parameters  14  Table 2-2: Degrees of revolution per sample for representative carriage speeds and TSR values  18  Table 3-1: Test program and corresponding parameters  26  Table 3-2: Reynolds numbers at varying velocities and TSR values for a free-stream device  31  Table 3-3: Expected and observed torque frequencies for gearbox and chains/sprockets drive-train  37  Table 3-4: Blade angle of attack at varying TSR and preset angle values at the  900  angle  of revolution  48  Table 3-5: Blade angle of attack at varying TSR and preset angle values at the 270° angle of revolution  48  Table 3-6: Maximum Ck and percent increase over free-stream baseline  64  Table 3-7: Torque fluctuation coefficient for a free-stream and ducted turbine  70  Table 3-8: Maximum Ck and corresponding  CTF  for ducted turbine configurations (1.5  mis)  75  Table 3-9: Maximum Ck, percent change, and torque fluctuation coefficient  75  Table 3-10: Expected and observed experimental drag force frequencies  83  Table 4-1: Torque sensor and encoder uncertainty (percent of rated output) and absolute error  84  Table 4-2: Gearbox drive-train repeated run percent variation in Ck  90  Table 4-3: Sample chain/sprockets drive-train repeated run percent variation in Ck  91  Table 5-1: Maximum Ck, percent change, and torque fluctuation coefficient  113  v  LIST OF FIGURES Figure 1-1: Distribution of Canada’s in-stream tidal current resource [3]  3  Figure 1-2: Vertical axis turbine schematic  []  4  Figure 1-3: Turbine driving force generation  5  Figure 2-1: Secondary carnage and turbine assembly drawing  12  Figure 2-2: Towing tank facility with main and secondary carriage  12  Figure 2-3: Turbine assembly with force balance and frame  13  Figure 2-4: Turbine rotor nomenclature (top view, inches)  14  Figure 2-5: Force balance and instrumentation configuration  16  Figure 2-6: Gearbox drive-train configuration  17  Figure 2-7: Typical run description (run duration 31.5 sec)  19  Figure 2-8: Matlab program interface  20  Figure 2-9: Range of data at steady-state for analysis  21  Figure 2-10: Torque vs. Angle of Revolution overlaid over one turbine revolution  22  Figure 2-11: Ensemble averaging  23  Figure 2-12: Example of Polar plot (counter-clockwise rotation)  24  Figure 3-1: Angle of attack notation  25  Figure 3-2: Flow direction relative to blade angular position  26  Figure 3-3: Free-stream turbine positioning (arm profiles A and B)  29  Figure 3-4: Arm profile C free-stream turbine positioning  30  Figure 3-5: Lift Coefficient vs. Angle of Attack using CFD for 634-021 at Re = 200 000, 500000  31  Figure 3-6: Cl! Cd vs. Angle of Attack for 634-021 at Re  =  200 000, 500 000  Figure 3-7: Power coefficient (Ck) vs. tip-speed ratio (TSR) at varying velocities  32 33  Figure 3-8: Ck vs. TSR illustrating power loss due to parasitic drag from arm configuration A  34  Figure 3-9: Ck vs. TSR drive-train comparison (medium profile arms)  35  Figure 3-10: Torque vs. Angle of Revolution comparing chains!sprockets with gearbox drive at TSR  2.25, 2.5, 2.75, v=l.5 rn/s  36  vi  Figure 3-11: Torque vs. Angle of Revolution comparing chains/sprockets with gearbox drive at TSR  2.25, 2.5, 2.75, v=2.0 mis  37  Figure 3-12: Torque data normalized frequency content for chains/sprockets and gearbox drive-train (free-stream, 1.5 mis, 2.5 TSR)  38  Figure 3-13: Arm profile cross-sections and connections  39  Figure 3-14: Ck vs. TSR for supporting arm comparison at 1.5 m/s  40  Figure 3-15: Ckvs. TSR of varying arm configurations (blades removed) at 1.5 mIs.... 41 Figure 3-16: Torque vs. Angle of Revolution for arm profiles B and C (ends and middle) at 1.5 mis and varying TSR  42  Figure 3-17: Torque vs. Angle of Revolution for 3 arms and end arms only at TSR=2.75, 3andv1.5mis  43  Figure 3-18: Ck vs. TSR for single and 3-bladed tests at 1.5 mis  44  Figure 3-19: Torque vs. Angle of Revolution at 1.5 rn/s for a single blade test  45  Figure 3-20: Torque vs. Angle of Revolution at 1.5 mis for a 3-blade test, single-blade test, and 3 superimposed single-blade tests  46  Figure 3-2 1: Torque vs. Angle of Revolution for a single-blade test with arm profiles B and C at TSR=3, v=l.5 rn/s Figure 3-22: Ck vs. TSR for AoA  47 =  0, 3, 5 degrees at 2 rn/s  Figure 3-23: Torque vs. Revolution Angle for AoA  49  0, 3, 5 deg at 2 mis, TSR = 2.25.50  Figure 3-24: Polar Plot of Torque vs. Revolution Angle for AoA  0, 3, 5 deg at 2 mis,  TSR=2.25 Figure 3-25: Torque vs. Revolution Angle for AoA  51 0, 3, 5 deg at 2 mIs, TSR = 2.5. 51 .  Figure 3-26: Polar Plot of Torque vs. Revolution Angle for AoA = 0, 3, 5 deg at 2 mis, TSR = 2.5 Figure 3-27: Torque vs. Revolution Angle for AoA = -3 deg at 1.75 mis, TSR  52 2.5.... 53  Figure 3-28: Ck vs. TSR for cambered (0 and 5 deg) and symmetric (0 deg) blades at 1.5 mis  54  Figure 3-29: Torque vs. Angle of Revolution for symmetric (0 deg) and cambered (0 and 5deg)atl.5mIsandTSR=2.75  55  Figure 3-30: NACA 0012 profile and circular end plates  56  Figure 3-31: Ck vs. TSR for end plate comparison at 1.5 mis  57  vii  Figure 3-32: Ck vs. TSR for end plate comparison at 2 mIs  57  Figure 3-33: Torque vs. Revolution Angle comparing end plates at 1.5 mis  58  Figure 3-34: Torque vs. Revolution Angle comparing end plates at 2 mIs  59  Figure 3-35: Shaft fairings  60  Figure 3-36: Ck vs. TSR with and without shaft fairing (1.5 and 2 mIs)  61  Figure 3-37: Torque vs. Revolution Angle with and without shaft fairing at 1.5 mis, TSR=2.75  61  Figure 3-38: Single blade with installed shaft fairing  62  Figure 3-39: Single Blade Torque vs. Revolution Angle with and without shaft fairing at 1.5 mis, TSR=2.75  63  Figure 3-40: Plan view of ducting (inches)  65  Figure 3-41: Cross-section of towing tank with ducting and turbine  66  Figure 3-42: Ck vs. TSR for the free-stream and ducted turbine at 1. 5 mIs  67  Figure 3-43: Extracted Power (W) vs. TSR for the tested ducted turbine and a freestream turbine of equivalent capture area at 1.5 m/s  68  Figure 3-44: Torque vs. Revolution Angle for free-stream turbine at 1.5 m/s  69  Figure 3-45: Torque vs. Revolution Angle for ducted turbine at 1.5 rn/s  70  Figure 3-46: Ducting with deflectors  72  Figure 3-47: Ck vs. TSR for duct and deflector configurations  73  Figure 3-48: Torque vs. Angle of Revolution for ducted and deflector configurations. 74 .  Figure 3-49: Polar plot of Torque vs. Angle of Revolution for ducted configurations.  ..  74  Figure 3-50: Side view providing location of assumed centre of drag force  77  Figure 3-51: Drag Force vs. TSR for a free-stream turbine at varying velocity  78  Figure 3-52: Drag Coefficient vs. TSR with trend line for data at v=1.5, 1.75, 2mIs  79  Figure 3-53: Drag Force vs. Revolution Angle at 1.5 mIs, AoA=0  80  Figure 3-54: Drag Force vs. Revolution Angle at 2 mIs, AoA=0  80  Figure 3-55: Drag Coefficient vs. TSR for a single and 3-bladed device at 1 .5mIs, AoA=3  81  Figure 3-56: Drag Force vs. Revolution Angle for a single blade at 2 mIs, AoA=3  82  Figure 4-1: Standard Deviation and Torque vs. Revolution Angle for a free-stream device with gearbox drive-train at 1.5 rn/s and TSR=2.5 (N  -  34)  85  viii  Figure 4-2: Standard Deviation and Torque vs. Revolution Angle for a free-stream device with gearbox drive-train at 2 m/s and TSR2.5 (N  52)  86  Figure 4-3: Standard Deviation and Torque vs. Revolution Angle for a free-stream device with chains/sprockets drive-train at 2 mIs and TSR=2.25 (N  -  33)  87  Figure 4-4: Standard Deviation and Torque vs. Revolution Angle for a ducted device with gearbox drive-train at 1.5 mIs and TSR3 (N  —  45)  88  Figure 4-5: Torque vs. Revolution Angle for repeated runs with gearbox drive-train at 1.5 mIs, TSR=2.5 (arm profile C)  92  Figure 4-6: Torque vs. Revolution Angle for repeated runs with gearbox drive-train at 2 mis, TSR=2.5 (arm profile C)  92  Figure 4-7: Polar plot of Torque vs. Revolution Angle for repeated runs with gearbox drive-train at 2 mIs, TSR=2.5 (arm profile C)  93  Figure 4-8: Torque vs. Revolution Angle for ducted repeated runs with gearbox drivetrain at 1.5 mIs, TSR=2.75  94  Figure 4-9: Torque vs. Revolution Angle for repeated runs with chains/sprockets drivetrain at 1.5 and 2 mis, TSR=2.5 (arm profile B)  94  Figure 4-10: Torque (below) and RPM (above) vs. Revolution Angle for runs with chains/sprockets drive-train at 1.5 m/s  96  Figure 4-11: Torque (below) and RPM (above) vs. Revolution Angle for runs with gearbox drive-train at 1.5 mIs  97  Figure 4-12: Torque vs. Revolution Angle for ducted device at 1.5 mis  98  Figure 4-13: RPM vs. Revolution Angle for ducted device at 1.5 mis  98  Figure 4-14: Sample grid around the blades and shaft  100  Figure 4-15: Sample velocity contours for a simulation at 1 mis with TSR=2  100  Figure 4-16: Experimental Ck vs. TSR for arm profile C at 1.5 and 2 m/s  102  Figure 4-17: Ck vs. TSR for free-stream comparison of experimental and numerical results  102  Figure 4-18: Ck vs. TSR for ducted comparison of experimental and numerical results at 1.5 rn/s  103  Figure 4-19: Torque vs. Revolution Angle comparing free-stream experiments and Fluent at 1.5 rn/s and TSR2  104  ix  Figure 4-20: Torque vs. Revolution Angle comparing free-stream experiments and Fluent at 2 rn/s and TSR=2.75  105  Figure 4-21: Torque vs. Revolution Angle for a ducted turbine at 2 ni’s and TSR=2.. 106 Figure 4-22: Torque vs. Revolution Angle for a ducted turbine at 1.5 m/s and TSR=2.75. 106 Figure 4-23: Drag Force and Torque vs. Revolution Angle for free-stream Fluent and experiments at 2 rn/s and TSR=2.75  107  Figure 4-24: Tidal current data  110  Figure 4-25: Power and torque output  111  Figure 4-26: Representative device configuration  111  x  LIST OF SYMBOLS, NOMENCLATURES, AND ABBREVIATIONS A  Turbine cross-sectional area (O.914m x O.686m)  AoA  Blade angle of attack (leading edge rotated outwards is positive)  Bk  Betz coefficient = 16/27  c  Blade chord  Cd  Drag coefficient  Ck  Power coefficient  CI  Confidence Interval  Cl  Lift coefficient  C  Power coefficient accounting for Betz limit  CTF  Torque fluctuation coefficient  CFD  Computation fluid dynamics  D  Drag force  DAQ deg,  °  Data acquisition Degrees  FFT  Fast Fourier Transform  HMCS  Her Majesty’s Canadian Ship  kWh  Kilowatt-hour  1  Length  m  Metres  MW  Mega-watt  n  Number of blades  N  Number of observations in a sample (for standard deviation calculation)  NI  National Instruments  NRC  National Research Council of Canada  r  Turbine radius (centre of shaft to ¼ chord)  p  Density  PA  Extracted power = torque* angular frequency for current experiments  xi  RPM  Revolutions per minute  s  Seconds  Tavg  Average torque  Tmax  Maximum torque  Tmin  Minimum torque  TSR  Tip-speed ratio  p  Viscosity  UBC  University of British Columbia  V, v  Free-stream velocity  VAHT  Vertical Axis Hydro Turbine Turbine angular velocity  “,  in  Inches  xii  ACKNOWLEDGEMENTS Firstly, I would like to extend a sincere thank you to Dr. Sander Calisal for providing me with the opportunity to venture into the field of ocean energy. His openness to new ideas, guidance in all aspects related to fluid dynamics, and constant push to discover more is a first-class example of how research should be conducted. Secondly, thank you to Jon Mikkelsen for his almost daily consultation, as well as his demonstrated commitment to  enhancing student experiences and providing new opportunities for every student showing an interest in marine engineering.  To those in the lab, we’ve accomplished a large amount of work and have been fortunate to do it so well as a group. Specifically, Voytek Klaptocz has been a great example by simply getting stuff done when it matters and making sure everyone’s having a good time doing it, all the while being a valuable resource for ideas and general guidance. Yasser Nabavi and Mahmoud Alidadi have demonstrated immense dedication to the project and I am grateful for the time we have spent chasing ideas, as well as their repeated patience when explaining concepts. Similarly, thank you to Ye Li for his keenness to help out whenever possible.  A large number of co-op and visiting students have also made  valuable contributions to the project through work on design drawings, instrumentation, data acquisition, and data analysis. Those include Florent Cultot, Cameron Fraser, John Axerio, Robby Chen, Pierre Leplatois, Bo Zulonas, and Thomas Chabut.  I would also like to extend my appreciation to Blue Energy, and in particular Jon Ellison, for both their financial contributions to the research as well as the good times we shared during the experiments. Additionally, thank you to Western Economic Diversification for the funding of experimental equipment and personnel to make the project possible.  Lastly, thank you to my friends for their patience and to my family for their unwavering  support in whatever I choose to do, and encouragement to do it right.  xiii  I INTRODUCTION The mounting evidence substantiating human-caused climate change [1], as well as the pending shortage of fossil fuels [2], is creating an increasing demand for clean, renewable sources of energy.  Harnessing wind and photovoltaic energy is among the more  traditional means of renewable energy capture; however, increasing attention is being turned to the world’s oceans as a resource for wave, tidal, and thermal energy extraction. Canada is fortunate to possess vast wave and tidal energy resources. The Canadian wave resource is estimated to be 146,500 MW, or more than double the current electricity demand, though it should be noted that only a fraction of this total may be extracted and converted to useful power due to power conversion, socio-economic factors, or technology limitations [3]. Similarly, Canada is endowed with abundant tidal current resources. Recent estimates put Canada’s tidal current resource at 42,240 MW based on examination of sites with over 1MW of in-stream power, again with only a fraction of that being extractable.  Figure 1-1 below provides the distribution of this resource,  equivalent to approximately 63% of Canada’s current electricity demand [3]. In addition to the significant resource available, tidal currents are advantageous in that they are highly reliable and predictable, and the extraction of this energy using low-head turbines  is expected to be environmentally benign [4]. Tidal current energy extraction differs from tidal barrage type power plants (existing in France and Nova Scotia), which function primarily as dams and release water in a controlled manner after the water level on one side of the dam has dropped. Dr. Barry Davis, former Chief Hydrodynamic Designer for the HMCS Bras D’Or Hydrofoil Ship and Aerodynamic Loads Analyst for the Avro Arrow, was one of the first people to recognize the potential of tidal current energy extraction and began focusing his research here in 1978. Building upon the National Research Council of Canada’s (NRC) development of the Darrieus vertical axis wind turbine, he applied the technology to low head hyciro applications [4]. Dr. Davis’ research led to an extensive research program during the 1980’s developing the vertical axis hydro turbine (VAHT) funded by over $1.3 million Canadian dollars. This work, completed as Nova Energy in collaboration with 1  the NRC, led to a number of demonstration projects, the publication of multiple reports, and several independent assessments validating the technology; however, due to the low cost of fossil fuels and the lack of political support for further development of tidal energy at the time, neither Nova Energy nor its successor Blue Energy could establish any major projects through the 1990s. In 2005, Blue Energy approached the University of British Columbia (UBC) to inquire about developing a computational fluid dynamics (CFD) model of the turbine to update their technology. Numerical models are a particularly useful tool in the field of tidal energy extraction as they: •  Can be linked with an optimizer tool to efficiently conduct parametric studies and determine optimum turbine parameters  •  May evaluate designs at various scales, thus minimizing unknown scaling effects when changing turbine size  •  Can calculate blade loads used for mechanical calculations or incorporated directly into Finite Element Analysis software  •  Permit two-phase simulations that can predict cavitation inception  •  May incorporate site-specific current data, accurately predicting power output including cut-in and cut-out operating regimes  •  Enable examination of turbine interaction and provide insight into productive I destructive interference  •  Allow for flow visualization enabling prediction of environmental effects  This need for numerical model development led to a collaborative research agreement and the ongoing research into the VAHT at UBC. In the meantime, since Dr. Davis’ research in the 1980’s, the market price of a barrel of oil had risen from $18 USD [5] per barrel in 1985 to over $100 USD in 2008, rendering tidal energy a feasible method of energy extraction. A number of tidal energy technology developers have also entered the market, attracted by current tidal energy cost estimates of 11  —  25 /kWh, and future  estimates in the 5 —7 /kWh range [6].  2  —  -%‘  I-  Tidal Energy Resources MW Points: Mean Potential Power  <2  4”.7 0  S  0  7... 14 14...27 27... 53 53... 102 102... 198 198... 383 383...741 741  ...  1436  1000km  1436,.. 2780  .  2780... 5384 >5384  Figure 1-1: Distribution of Canada’s in-stream tidal current resource 13].  1.1 Turbine Operating Principles The vertical axis turbine is a lift-driven device consisting of vertical foils (typically 3 or 4) mounted perpendicular to the flow, usually to a spinning central shaft as shown in Figure 1-2. This differs from a horizontal axis device, which is often similar to a wind turbine or ducted impeller or propeller mounted to the seabed.  As the foils rotate,  typically at 2-3 times the free-stream flow velocity, the free-stream flow inducess an angle of attack on the foil. The resultant of the lift and drag forces generated by the foil may be reduced to radial and tangential components, of which the tangential component drives the turbine rotation. Figure 1-3 illustrates this concept when a blade passes across the upstream side of the turbine. As the turbine continues to rotate, the relations between the vectors shift, and as a result tangential force is generated primarily in the regions upstream and downstream of the shaft. This causes torque fluctuations, or torque ripple,  3  of the turbine due to blades passing in and out of torque-generating regions. Similarly, the radial component of the force on the blades and the drag forces on the turbine fluctuate with blade position. These cyclic loads are of concern when designing for turbine reliability and longevity.  TOP VIEW  generaloc gearbox  Figure 1-2: Vertical axis turbine schematic  17].  4  Figure 1-3: Turbine driving force generation.  These torque fluctuations are much less evident in horizontal-axis designs, and the primary arguments against the vertical-axis turbine are that the torque ripple is difficult to manage both for structural integrity and generator function, and that efficiency is lost given the turbine blades are only generating torque through select regions of each revolution. Conversely, there are a number of advantages unique to the vertical axis turbine, encouraging further examination: •  Generators may be easily stored above the water surface and directly driven by the shaft  •  Only a single bearing is required underwater  •  Turbine rotates in same direction regardless of flow direction  •  The vertical design is conducive to stacking multiple turbines under bridges or other existing infrastructure  5  Until functional commercial units of both horizontal and vertical axis turbines are established and the cost per kWh is compared on a site-by-site basis, the design most suitable to tidal current applications remains unknown.  1.2 Previous Work I Motivation Prior to Davis’ work, Templin examined key parameters affecting Darrieus wind turbine operation by plotting power coefficient (Cp) as a function of tip-speed ratio (TSR) and solidity [8].  Cp  1 Bk  =  Equation 1  .—  2  TSR  =  r.co V  Equation 2  —  solidity  =  n.c r  Equation 3  —  In the Cp calculation above, it is interesting to note the extracted power (PA) is divided by the power available in the free-stream passing through the turbine cross-sectional area, which would be the equivalent of efficiency for a free-stream device. This Cp value is then divided by the Betz coefficient (Bk  =  16/27), which is the maximum theoretical  efficiency for a free-stream turbine according to idealized wind theory [9], thus yielding the efficiency of the device compared to the theoretical maximum extraction possible. Davis then adapted Templin’s work to tidal turbines and generated a number of reports in collaboration with the NRC, upon which many of the initial turbine parameters and dimensionless coefficients were based for the UBC series of tests. Davis initiated the use of the power coefficient (Ck) to quantify turbine performance. This is similar to Cp above, though it is not divided by the Betz coefficient:  6  Ck=  Equation 4  .A  It should be noted that the Ck value is often used interchangeably with efficiency, though this is only appropriate when used in free-stream applications.  This is because the  addition of ducting, or operation in a confmed flume or tank, will enhance the turbine power output; however, the power output (PA) is still only being divided by an extractable power term that is a function of the free-stream velocity and cross-sectional area of the turbine, instead of a function the effective velocity through the turbine which is altered by the duct or confmed domain, or a function of the increased area affected by the duct cross-sectional area or the domain boundaries. As per Davis, power output data discussed below is presented in terms of Ck.  The available Davis reports were as  follows:  Table 1-1: Available Davis et al. reports  Report Title  Synopsis  NEL-002: Water Turbine Model Trials [10]  Flume tank tests of vertical and horizontal axis water turbines. Vertical axis water turbine flume tank tests with caissons, walls, and vane duct configurations. Continuation of NEL-021 with a more robust model.  NEL-02 1: Ultra Low Head Hydroelectric Power Generation Using Ducted Vertical Axis Water Turbines [11] NEL-022: Ultra Low Head Hydroelectric Power Generation Using Ducted Vertical Axis Water Turbines [12] NEL-03 8: Research and Development of a 50kW to 100kW Vertical Axis Hydro Turbine for a Restricted Flow Installation [13] NEL-070: The Ducted Vertical Axis Hydro Turbine for Large Scale Tidal Energy Applications [14] NEL-08 1: Commissioning and Testing of a 100kW Vertical Axis Hydraulic Turbine [15]  Installation of 70 kW turbine within a dam in Nova Scotia. Investigates application of vertical axis turbine in a 474 turbine tidal fence. Examines repaired and enhanced version of model in NEL-038.  Numerical model validation requires both power extraction data and torque data as a function of blade angle. Torque data as a function of blade angle, also known as a torque curve, is critical to provide insight into the regions where torque generation may be  7  enhanced to improve turbine performance, or may be altered to reduce torque ripple. Unfortunately, though discussed briefly by Davis et al. [12], the reports above did not contain sufficient torque curve data for model validation. Aside from Davis et a!., Gorlov patented a vertical axis turbine using helical blades to distribute the torque loading in 1994 (U.S. Patent 5451127) and continues development work in Korea [16]. Given the commercial nature of this venture, efficiency data and torque curve data is closely guarded. Similarly, research has been undertaken in Italy by the Ponte di Archimede S.p.A. Company and the University of Napoli on a turbine with a patented passive angle of attack adjustment mechanism [17,18]; though no publicly available torque curve data has been found. The United Kingdom is a leader in tidal energy technology given the active resource in Northern Scotland and generous government incentives promoting technology development. The former Department of Trade and Industry sponsored three reports on vertical-axis tidal turbines, though only one attempted experimental trials for numerical model validation and provided no useful quantitative data due to a number of factors, including excess friction in the gearbox and a less than ideal experimental flume facility [19]. Other recent efforts include a group from the University of Buenos Aires [201 that has looked into ducting effects, and a group from the University of Edinburgh [21] that has developed a number of numerical models and a conceptual design, though both are lacking experimental data for validation. Considering torque curve data that was able to be located, Shiono et al. [22] only provided torque curve data upon turbine start-up, and Highquest [23] obtained torque curve data limited to 2 or 3 turbine revolutions on a chart recorder in 1987, providing little accuracy for validation. Secondly, the literature search outlined above revealed no investigation into the drag forces on the turbine during operation, making mechanical design (particularly bearing specification) very difficult. Apart from the apparent lack of available turbine performance, torque ripple, and drag data, a number of factors affect one’s ability to properly use another researcher’s experimental data for model validation:  8  •  Flume/towing tank blockage affects turbine performance and must be well documented  •  Drive-train losses may affect power output or dampen torque readings  •  Shaft and mounting arms affect turbine performance through interference effects and parasitic drag, and geometry and effects of each must be examined  •  Knowledge of revolution speed fluctuations is required as performance is highly dependent on TSR  This lack of data and need for comprehensive first-hand knowledge of the experimental setup and parameters provided the motivation for the experimental investigation presented in this thesis.  1.3 Objectives I Scope of Work The primary purpose of this thesis is to acquire baseline power output and torque ripple data for both a free-stream and ducted vertical axis current turbine for the purpose of validating numerical models, which are currently being developed by two other graduate students. These tests will also serve to enhance understanding of work completed by previous researchers, as well as investigate a number of turbine parameters and quantifr their corresponding effects on performance. More specifically: •  Acquire power coefficient data for both a free-stream and ducted vertical axis turbine in the UBC campus towing tank  •  Acquire torque fluctuation data for both a free-stream and ducted vertical axis turbine over the course of a turbine revolution  •  Investigate effects of TSR, blade angle of incidence, cambered blades, and various ducting configurations on turbine performance and torque fluctuations. Effects of shaft fairings, arms, and foil end plates are also examined  •  Experimentally investigate magnitude of forces parallel to the free-stream flow on the turbine for future design applications (referred to as drag forces)  9  Chapter 2 below outlines the entirely new system developed for conducting tests in the UBC towing tank.  This includes the requirement for a secondary carriage to  accommodate the turbine testing. An overview of the data acquisition (DAQ) software, instrumentation, experimental procedure, and data analysis program is also provided as well as the baseline model parameters.  Chapter 3 presents the experimental power coefficient and torque curve results from the three experimental test programs and discusses their significance. An overview of the recorded drag data is also provided.  Chapter 4 examines experimental errors and  compares select power output, torque curve, and drag curve results with theory. These results are then used to develop a case study specifying a sample unit capable of powering 17 homes in Quatsino Narrows on Vancouver Island.  Chapter 5 contains  conclusions and recommendations for future work.  10  2 EXPERIMENTAL SETUP AND PROCEDURE All instrumentation, data acquisition equipment and software, experimental equipment, and data analysis software was purchased, built, or written specifically for this research program and is described below.  2.1 Towing Tank and Carriage Overview Experimental testing was conducted in the UBC campus towing tank, which is a 200’ long by 12’ wide by 8’ (7’ of water) deep fresh water tank. The main cantilevered carriage, typically used for ship model testing, runs on rails alongside the tank. The tank is oriented in the east-west direction and runs were performed traveling both towards the wave-maker (due east) and towards the dock (due west). A secondary carriage spanning the width of the tank was constructed and attached to the main carriage and used as the testing platform for the turbine, as shown in Figure 2-1 and Figure 2-2. The use of the secondary carriage was necessary to accommodate the large turbine device:  •  Support increased weight and drag force compared to typical ship hull model tests  •  Facilitate turbine installation and removal  •  Provide easy access for adjustments  •  Serve as a platform for the large amount of instrumentation including motor and drive-train  The secondary carriage was fabricated of welded aluminum c-channel in two halves that were then bolted together. Two rubber wheels rested on both the outer rail and the side of the tank opposite the main carriage, while two v-grooved wheels ran along the rail closest to the water. The entire secondary carriage was bolted to the front of the main carriage, with a diagonal brace providing added support.  11  Turbine assembly  Secondary carriage  /  Main carriage location  /  Figure 2-1: Secondary carriage and turbine assembly drawing.  Figure 2-2: Towing tank facility with main and secondary carriage.  12  2.2 Baseline Model Parameters The three turbine blades are attached to a central shaft that is supported at both ends by ball bearings. The top bearing is mounted on the force balance, while the bottom bearing is constrained to a horizontally-mounted bottom plate supported by two vertical rectangular beams forming a u-shaped frame. These beams are bolted to the secondary carriage and stiffened using 3 guy wires each; two extending in the plane of the flow direction (one forwards and one backwards) up to the secondary carriage, and the third extending in the plane perpendicular to flow direction and out towards the side up to the secondary carriage. The turbine assembly with arms supporting the blades at the ¼ span locations is shown in Figure 2-3 below, along with the supporting frame and force balance for mounting the instrumentation.  Figure 2-3: Turbine assembly with force balance and frame.  13  Principal model parameters are provided in Table 2-1 and Figure 2-4:  Table 2-1: Principal model turbine parameters.  PARAMETER  DIMENSION / CHARACTERISTIC  Diameter (across foil chord)  36 in  Number of blades  3  Blade span  27 in  Blade profile  NACA 634-02 1 and 634-42 1  Chord length  2.70 in ideal; 2.57 in manufactured  Shaft outer diameter  1.9 in  /7  01.90 ,1  /  /  036.00  120°  —  /  /‘  //  2.57 CHORD 27 BLADE SPAN (TYP)  ,,  ‘V -  Figure 2-4: Turbine rotor nomenclature (top view, inches).  Arm profiles supporting the blades varied between test programs and therefore are not listed above. Appendix A and Appendix B contain component sizing calculations and part drawings respectively. Specific turbine and ducting position within the towing tank is discussed in Section 3 for each case presented. 14  2.3 Instrumentation 2.3.1 Instrumentation Components The components used for measuring drag force, torque, turbine angle, and for driving the  turbine were as follows: •  31W Micro Max motor 182TCZ TEFC from Marathon Electric with Parker SSD AC vector drive controller and braking resistor kit (may be used for both driving and braking turbine) (7/8” shaft; 230V, 4.6A, 5400 max. safe rpm)  •  2 of PT-Global SG-PT4000-500 lb s-type load cells  •  Futek Torque Sensor, 0  -  369 ft lb, 0.2% accuracy, aluminum, 2mV/Voutput, 7”  length (TRS300) •  Accu-Coder 776-B-S-2048-R-PP-E-P-A-N 1-7/8” through-bore encoder (2048 increments per revolution)  •  U.S. Digital encoder digital-analog converter (used with encoder)  •  CONEX gearbox B091020.LAAJU, TEXTRON fluid and power. Ratio 20:1, SHC 634 lubrication, helicoidal gear geometry  Additional specifications on the components above may be found in Appendix C. Carriage speed was monitored using a pre-existing system on the towing carriage.  2.3.2 Drive-train I Force Balance Configuration Model revolution speed was controlled using an AC motor, and for the first two test programs chains and sprockets drove the turbine shaft, as well as provided the ratios necessary to scale the revolution speeds between the turbine and motor shafts.  The  motor, chains and sprockets, and lay-shaft (consisting of the torque sensor) all mounted to the bottom plate of the force balance as shown in Figure 2-5. This lower plate was hung from the top plate using two pairs of hinged arms and was thus free to translate relative to the top plate; additionally, large holes were cut in the top plate to allow the main turbine shaft and lay-shaft to pass through without contact. Two load cells (one on each side of the force balance) were then used to ground the bottom plate relative to the top, and thus measure the forces on the bottom plate. To accelerate the turbine to the desired rotation speed, the motor drove the lay-shaft, which consisted of the torque sensor  15  and adaptive couplings mounted vertically on two bearings, at a 14:72 ratio. The layshaft then drove the main turbine shaft at a 20:3 6 ratio. Alternately, when the motor was acting as a brake to slow the turbine rotation, the system drove in the reverse direction. This chain and sprocket system was used to facilitate drag force measurement using this force balance design, as well as to allow for flexibility to change the sprocket ratios should the motor or torque sensor not performed as anticipated. Lastly, the encoder was mounted directly around the main turbine shaft above the top bearing.  Torque sensor  —I \Bottom plate Turbine shall Figure 2-5: Force balance and instrumentation configuration.  For the third test program, the chain and sprocket drive-train was replaced with a 20:1 gearbox, and the force balance plates were rigidly joined using a plate and aluminum channel (Figure 2-6).  This was an attempt to reduce revolution speed fluctuations  (discussed in Section 4.1.3 below) by using a more rigid system with the 90° worm gear drive, and thus drag measurements were no longer recorded. A second bearing was  16  added to the top plate to minimize shaft deflections, and a flexible coupling was used to couple the torque sensor and gearbox.  Flexible coupling— (torque sensor hidden)  Encoder// Turbine shaft  Shaft beaiings  Figure 2-6: Gearbox drive-train configuration.  2.4 Data Acquisition System The following National Instruments (NI) data acquisition hardware components were used for these trials: •  1 cDAQ-9 172 8-slot USB Chassis with rail mounting kit  •  1 NI 9205 32-Channel +1- 1OV 250 ks/s 16-bit analog input module used with encoder and carriage speed  •  1 NI 9237 4-Ch 50 ks/s per channel 24-bit analog input module used with torque sensor  Supplementary DAQ hardware information may be found in Appendix C.  Labview software was developed to take 100 samples on each channel (angle, torque, carriage speed, and load cell 1 and 2 where necessary). Each set of 100 samples was then averaged and written to an output file, and this sequence was performed at a frequency of  17  approximately 240 Hz, or every 0.00406 seconds. Table 2-2 below provides number of degrees of revolution per data point for representative velocity and TSR values. Table 2-2: Degrees of revolution per sample for representative carriage speeds and TSR values. Number of Degrees per Sample TSR = 1.5 Velocity (m/s) TSR = 2.5 TSR = 2 TSR = 3 1.5 1.14 1.53 1.91 2.29 2 1.53 2.04 2.54 3.05  2.5 Calibration Calibration of the instrumentation components was performed as required. The torque sensor utilized a manufacturer supplied constant that was verified in the lab. Routine checks using the shunt resistor were then performed validating the 0-500Nm range. Similarly, routine checks were used to verify that the angular encoder was accurate over 0-360°. Lastly, each load cell was connected one at a time and calibrated by applying a force (typically up to 16 lb) to the lower force balance plate using a rope and pulley system.  2.6 Experimental Procedure For each test run, a standard procedure was followed: 1. The carriage and turbine were stopped while the waves dissipated on the water surface and the vortices dissipated in the tank 2. The turbine was manually rotated such that a blade was in the 180° position and the encoder was reset to 180° (0° corresponds to when a blade is heading directly into the oncoming flow as discussed Section 2.7 below) 3. The DAQ system and motor driving the turbine were started a. If drag data was being recorded, then the DAQ system was started and allowed to run for a few seconds to record values at zero velocity before starting the turbine and allowing it to reach the desired revolution speed b. If no drag data was being recorded, the turbine was started and allowed to reach the desired revolution speed; the DAQ system then started to record 4. The carriage accelerated up to speed while the motor maintained the turbine at the desired revolution speed 18  5. The carriage ran down the tank at the desired speed for the maximum allowable  distance 6. The carriage was decelerated to a stop 7. The DAQ system was stopped and the motor driving the turbine was turned off, allowing the turbine to come to rest Figure 2-7 below illustrates this procedure (case 2.b) using a plot of torque measurement vs. cumulative angle of turbine rotation for a typical run; the duration of the recorded data period was 31.5 seconds. Torque vs. Cumulative Angle 140  ----  ---  120  .jI ill_i  t_ 11.1  100  80 -  60  I  z 4)  40  0  20  I-  0 2500  .20  5000  — ;—-;; —;  ‘I  ‘;;; 1  20000  .40  -60  Turbine rotation at arriag acceleration desired rpm  Steady state operation at desired carriage speed  Carriage deceleration  Angle (deg) Figure 2-7: TypicaL run description (run duration 31.5 sec).  2.7 Data Processing Methodology A Matlab program was developed to first read the raw data files output from the DAQ program, then format the data, and subsequently facilitate “on-the-spot” data analysis. This analysis primarily consisted of plotting loads recorded by each individual load cell,  19  the total load, the torque values, or the turbine revolution speed versus either time or revolution angle (either cumulative or reduced to over 1 revolution). The raw data files were processed such that the recorded parameters from the different test programs could be plotted on the same plots, enabling comparison.  Figure 2-8 displays the primary  Matlab program user interface.  -  —  ‘T  DataBasev2 I  ,  Please select the Its(s) that you woiid Ie to lead: C:lDocumerits end Sefti &OdlOesktop2(t)7 Experimertel Data’From Tow  Llrs:  Metric (Nm)  Abscissa (x):  Theta  O II.w 5rm  RunOl 3_vi .5_2.Stsr-M.txt  :RunO13v1 .5_2.5tsr.txt RiinOl4-v1 -2JStsr-Mlxt Ren014_vl 5_27sr-M1xt  CWiate (y)  [j  Rue0141.52.7ttsr.txt  I  SaveAs:  Legend  Save Database  -  Torque Filename  •1  c___. n. —  cnuor  L,e  ® z 0 L Q P01W Grh  E OiApiA data to excel (wi 0L*pt to screen if ftenne left blat) Er Excel lienwie to wrte to: E Pr* Black and l.Me aFils  ane (easig  Polar Zero: Crne  P:  Sort  0 Decreasing  Plow Pilezsae  RPM  Vel.  Tiae  TSP.  S  Wells  85.6  Turbulence Model S Tnt.  I  Mezh  Size  Ord.  I  Airfoil  Coexe.nt  -  i.-9so / RunOl4—vl.5—2.7Stsr—M.txt  Step  Despey FF701 ‘dirrate  Z.49  lSOe/s  2.73  ö.OO 0.004  N/A N/A  N7A N/A  N/A N/A  Ni N/A  >1 Select All  j  [Select None  lop  ci Files  Update Selected DataItes  Stsit  FftSit:  0  Figure 2-8: Matlab program interface.  2.7.1 Data Selection and Averaging The Matlab program was written to select the range of data at outside of the carriage acceleration and deceleration periods and thus suitable for analysis.  Examining the  carriage velocity data column, the beginning and end of the range of data at the desired carriage velocity was specified. 10% of the length of this specified range was further eliminated from either end, leaving the middle 80% of the data at the constant velocity to  20  be written to a new Matlab file (with a “-M” extension to the file name) for further analysis as shown in Figure 2-9. This method of selecting the steady-state range was tested during experiments and provided consistent torque profiles at either end of the range. Columns written in the “-M” file included Time, Theta, Torque, RPM, Carriage Velocity, Time-step, as well as Load Celli, Load Cell 2, and Total Load where applicable. Calculations were performed as necessary to complete the columns above: Shaft revolution speed ratios were applied to the torque values when the lay-shaft  •  experimental setup was used. Moment arm ratios were applied as needed to the drag force calculation (further  •  discussed in Section3.5). •  Instantaneous angular velocity, and subsequently RPM, for a given point was the average of the 12 closest points to minimize data spikes from the small interval (change in theta over time-step) used for calculation.  Torque vs. Cumulative Angle 140 120 100  E z  80 60  0  I.  40 20 0 8( ‘0  f 9000  10000  11000  12000  13000  14000  15000  16000  17000  -20 Angle  (deg)  Figure 2-9: Range of data at steady-state for analysis.  21  18 00  An ensemble averaging technique was then used to collapse the data onto one turbine revolution. The torque values over each revolution for a single run were plotted over 360 degrees, or overlaid on each other, as shown by the small points in Figure 2-10. The data was then isolated into 4 degree increments, as demonstrated in Figure 2-11, in which an average (cross) is obtained from the overlaid data points for each increment. Figure 2-10 also displays the resulting average torque curve over one revolution.  140  -----.-.--  120  -  A  A 11  100 80  E  I  i1  $  Overlaid Data Points —.—Averaged Data  z 0  I  60 40 20 0 50  100  150  200  250  300  350  400  -20  Angle (deg) Figure 2-10: Torque vs. Angle of Revolution overlaid over one turbine revolution.  22  + +  +  + +  ±+ +  4 ++  Figure 2-11: Ensemble averaging.  2.7.2 Data Presentation Data is typically presented in three forms.  Firstly, plots are often given as power  coefficient vs. tip-speed ratio, demonstrating the capability of the device to extract power from the free-stream current. The two other plots are used to enhance understanding of  the turbine operation, and provide the parameter of interest (typically torque) vs. angle of rotation in both Cartesian (ie. Figure 2-10) and Polar (ie. Figure 2-12) coordinates. Because Polar plots typically distort the plots and don’t easily display negative values, they are primarily used as a visualization tool for highlighting the regions of turbine revolution that could benefit from flow adjustment to enhance turbine performance as well as reduce torque fluctuations. Figure 2-12 illustrates the torque generated by a three-bladed turbine oriented such that at 0 degrees a blade is headed directly into the flow. Flow enters the turbine from the top of the image (90°) and rotation is counter clockwise. The 3 peaks are created as torque is generally produced by each blade as it passes through approximately 90°-120° in the region upstream of the shaft.  23  Torque (Nm) vs. Angle (deg) Flow direction 120  60  1W  / 33  -S  S•  S  210  240 270  Figure 2-12: Example of Polar plot (counter-clockwise rotation).  24  3 EXPERIMENTAL RESULTS The specific setup and results for each test program conducted are discussed in the Sections 3.2 through 3.4.  Experimental errors and measurement accuracy are later  discussed in Section 4.1.  3.1 Angle of Attack and Revolution Angle Notation Blade incidence angle (commonly referred to as angle of attack  —  A0A) was investigated  in a number of the experiments, and is considered positive when the leading edge of the blade was rotated outwards from the main shaft as shown in Figure 3-1 below.  Figure 3-1: Angle of attack notation.  Blade position over the course of a revolution is also of importance when reading plots and understanding turbine operation.  For the results presented below, a blade is  considered to be at 0 degrees when it is headed directly into the flow, and is at 180 degrees when it is moving in the same direction as the flow. This is illustrated in Figure 25  3-2 below, with a blade generally producing torque at approximately the 90 degree position and 270 degree position, as it passes perpendicular to the free-stream flow.  Flow into Turbine  111111 9 or-’  /—  —  ()  180°  I!’ — —  270° Figure 3-2: Flow direction relative to blade angular position.  3.2 Test Program Overview Three programs were performed in August 2006, November 2006, and Aug/Sep 2007. Table 3-1 provides details on model configuration and parameters examined during each test program.  It should be noted that for each test program the arm profiles were  subsequently reduced, while specific arm profiles, end plate specifications, and other turbine parameters may be found in Appendix B. A detailed run log may be found in Appendix D.  Table 3-1: Test program and corresponding parameters.  TEST PROGRAM August 2006  PROGRAM DETAILS •  Chain and sprocket drive-train  (approx. 575 runs)  26  TEST PROGRAM  PROGRAM DETAILS •  High-profile arms (configuration A) supporting blades at Y4 chord  •  Symmetric blade profile 634-021  •  Parameters tested: o  Blade angles of attack -5, 0, 3, 5, 10  o  Carriage velocities 1,1.25,1.5, 1.75,2 mIs  o  TSR values 1.25 —3.5 at 0.25 increments  o  Single blade  o  Arms without blades attached  November 2006  •  Chain and sprocket drive-train  (approx. 460 runs)  •  Medium-profile arms (configuration B) supporting blades at ¼ chord  •  Symmetric blade profile 634-02 1  •  Parameters tested: o  Carriage velocities 1  o  TSRvalues 1.25—3.5  o  Free-stream turbine at AoA  o  Single blade at AoA = 3 deg  o  Ducted turbine with open ends at AoA  o  Medium profile arms without blades  Aug/Sep 2007  •  Gearbox drive-train  (approx. 340 runs)  •  Parameters tested: o  TSR values 1.5 1.5  o  —  —  —  2 mIs at 0.25 increments  -3,0,3,5 deg  0,3,5 deg  3.5 at 1.5 mIs carriage speed, and  2.75 at 2 mIs carriage speed  Medium-profile arms at ¼ locations vs. low-profile (NACA 0012) arms at ends and middle of blades  o  Medium-profile arms with circular and foil end plates  o  2 vs. 3 arms (foils end supported with removable  27  TEST PROGRAM  PROGRAM DETAILS arm at centre) o  Symmetric blade 634-021 at AoA blade 634-421at AoA  =  =  0, and cambered  0, 5 deg  o  Single blade  o  Duct with end covers and deflectors at varying positions  o  Shaft fairing with single blade, 3 blades, and ducted turbine  o  Low-profile arms without blades  3.3 Free-stream Turbine Figure 3-3 below illustrates turbine positioning within the tank for both the high and medium profile arms (profiles A and B discussed in Section 3.3.3) supporting the blades at the ¼ chord locations. Figure 3-4 highlights the change in turbine position to accommodate ducting with end caps when the low-profile (NACA 0012) supporting arms were used at the ends, and usually middle, of each blade.  The following tests and  parameters are discussed in Sections 3.3.1 through 3.3.8: •  3.3.1 Velocity / Reynolds Number Effects  •  3.3.2 Drive-train Comparison  •  3.3.3 Arm Profile Reduction  •  3.3.4 Single-blade  •  3.3.5 Angle of Attack  •  3.3.6 Cambered Blades  •  3.3.7 Blade End Plates  •  3.3.8 Shaft Fainng  Lastly, Section 3.3.9 summarizes these results.  28  Tank width  =  144”  Figure 3-3: Free-stream turbine positioning (arm profiles A and B).  29  Figure 3-4: Arm profile C free-stream turbine positioning.  3.3.1 Velocity and Reynolds Number Effects Reynolds number, and as a result free-stream velocity and tip-speed ratio, affect turbine performance. Table 3-2 below illustrates the range of Reynolds numbers observed at the primary velocities and TSR values examined. As these values range between 32 600 and 522 000, the foil is in a transition region and the lift coefficient will be significantly affected as the turbine velocity is increased. Figure 3-5 and Figure 3-6 provide lift coefficient and lift/drag coefficient respectively vs. angle of attack for a NACA 634-02 1 foil at Re  =  200 000 and Re  =  500 000 [24]. These results were obtained using CFD  software, as it is very difficult to find experimental data for such coefficients at the range of angles of attack needed for turbine analysis at the Reynolds numbers of interest. At Re 500 000, Cl / Cd may be 35% larger than for Re  =  200 000, greatly affecting turbine  performance. These effects are evident in Figure 3-7, demonstrating improved turbine  30  O  CDk)k) —-C0 CDCD  -k)W WCICD -3’J  cD  C,J  0)0)0) 0)0)0)  0)0)0) 010)0)  ÷++  mmm  —C.JU) co—o 0)0)N3  N)C3 0)-N) -ü)NJ  mmm +++  0)0)0) 0)0)0)  +++  mmm 0)0)0) 0)CJIOI  +++  mmm  C 0) 0)  - l’J C)  - C) •C00)0) 0) N) -  -  ( - N)  43Ui  0)CyI0)  -  0)0)0) (310101  mmm +++  -N)N) LJbO -0)-  JU1CYI  0)0)0)  +++  mmm  .CJ1U1  +++  -  q  ;w  z  mmm +++  mmm  mmm +++  0)-” (J1CD C)0)0)  4C3iC31  -,-++  mmm  cD 31UI  0  (J—I’-3--O) 0) W C)  0 0  -  CD  -I  mmm  4.cYi  mrnm +++  0  +++  0 0  ---J CD-J -J CJi  0  CD  O)kJW CYiLJ W U’I 0)  04 0  CD  I’)  m  <  (I)  -I  , D  .  (D  D j  DD  -  (M  D  -  CI)  .  —  D  .  -  D  —  .  ••  D  -  0  II  CD  CD  .  0  0  CD  CD  CD  C)  C)  0  Cl)  -t  Q CD  Cl)  CD  .-. CD C)  CD  0  cj  I-  0  CD C)  CD  C)  CD -t  C) CD  o  C)  40  35 30 25  Re=50U 000 Re=200000  20  7/ 15  p /  /  10• 5 0  I  0  5  10  15  I  20 25 Angle of Attack (deg)  Figure 3-6: Cl! Cd vs. Angle of Attack for 634-021 at Re  =  30  35  40  45  200 000, 500 000.  32  0.1 0.08 0.06 0.04  C)  0.02 0 -0.02 -0.04 -0.06  TSR Figure 3-7: Power coefficient (Ck) vs. tip-speed ratio (TSR) at varying velocities.  Upon removing the airfoils and testing the supporting arms to investigate parasitic drag, at all velocities the power coefficient as a function of TSR is quite consistent (Figure 3-8). This indicates the Reynolds number effects are having a more significant impact on the lift characteristics of the foil than on the drag characteristics of the supporting arms (supporting arm effects are discussed in more detail in Section 3.3.3, along with connections between arm and foil). The supporting arms operate at lower Reynolds numbers, primarily due to the majority of the arm length is at a shorter radius leading to lower velocities, and thus are further from the sensitive transition region.  33  0.00 1  0.5  1.5  2  2.5  3  3.5  -0.02 004 -0.06 00  -0.08  -0.10  +  Velocity 1 .0 Velocity 1.25  .  -0.14  D  Velocity 1.5  Velocity1.75 Velocity 2.0  -0.16  o Velocity 2.25  -0.18 -0.20  TSR Figure 3-8: Ck vs. TSR illustrating power loss due to parasitic drag from arm configuration A.  3.3.2 Drive-train Comparison It is important to compare similar turbine configurations using the two different drivetrains to ensure that the data from each program was reasonably similar, given turbine operating efficiency should be the same regardless of the drive-train used to drive or break the turbine; however, one may expect minor differences in the efficiency and torque curve plots, primarily due to the fact that in the chain/sprockets drive-train the torque sensor also served as a lay shaft and was not linked directly in-line with the turbine shaft as it was with the gearbox. Figure 3-9 provides the power coefficient vs. TSR for runs using the different drive-trains at both 1.5 m/s and 2 rn/s at the optimum operating TSR values of a free-stream turbine. The higher efficiency at 2 m/s, is attributed to Reynold’s number effects, as discussed in Section 3.3.1.  34  0.160  :: 0.100  F  1 ./  .7  0.090  //  —a— Chains/sprockets_i .5m/s  0.060  -—Gearbox_1.5m/s -*-  0.040  Chains/sprockets_2m/s  —-Cearbox 2m/s  0.020 0.000 1.50  1.75  2.00  2.25  2.50  2.75  3.00  TSR  Figure 3-9: Ck vs. TSR drive-train comparison (medium profile arms).  The efficiencies above show percent differences typically on the order of 10%, though less agreement is observed at 2 m/s and with a TSR of 2. Apart from measurement accuracies, differences in the curves may result from: •  With the layshafi, power is transmitted through a chain and additional bearings before being registered by the torque sensor, so one may expect this drive system to have lower power, as is the case at higher TSR values, while flexing in the chain/sprocket system could also have an effect.  •  Fly-wheel effects of the sprockets about the torque sensor and flexing in the system may also serve to minimize the tendency of the chain/sprocket configuration to require/receive driving torque from the motor, thus artificially increasing the apparent efficiency.  Figure 3-10 and Figure 3-11 illustrate the torque curves at the optimal TSR values (2.25, 2.5, 2.75) at 1.5 rn/s and 2 rn/s respectively. It is evident that the chains/sprockets drivetrain configuration has lower, wider torque peaks observed by the torque sensor at both velocities due to flexing in the chains absorbing shock in the system, and inertial effects of the sprockets.  Alternately, the flexible coupling used with the gearbox drive-train  35  allowed for a small amount of backlash, leading to the flattening of the curve observed as torque magnitude passes through zero. This backlash likely also produced a slamming effect once the coupling re-engaged, leading to sharper, higher peaks than what may actually be observed in an ideal system.  Figure 3-10: Torque vs. Angle of Revolution comparing chains/sprockets with gearbox drive at TSR 2.25,2.5, 2.75, v=1.5 rn/s.  =  36  E  z II, 0  I-  Theta (degrees)  Figure 3-11: Torque vs. Angle of Revolution comparing chains/sprockets with gearbox drive at TSR = 2.25, 2.5, 2.75, v2.O rn/s.  Frequencies of torque input are also masked by the chains/sprockets drive-train. Table 3-3 provides the expected frequencies of torque ripple based on blade position, as well as the observed frequencies which were obtained by running a Fast Fourier Transform on the torque data for runs at 1.5 rn/s and TSR=2.5. Figure 3-12 provides the frequency content of these runs, and it is evident that the higher frequencies have a greater influence with the gearbox drive train.  Table 3-3: Expected and observed torque frequencies for gearbox and chains/sprockets drive-train. Run # Drive-train radlsec Runi 045a Chains/sprockets 8.12 RunOiG Gearbox 8.30  Expected Experimental Frequencies (radisec) Primary Observed 1 puiselblade 2 puiseslblade 3 pulses/blade 4 puiseslbiade Frequencies from FFT 24.36 48.72 73.08 97.44 24.32 48.6 72.95 49.80 24.90 74.70 99.60 24.69 49.4 74.14 98.77 —  37  1 .0 0.9  :  -e—Run 1045a  Chains  E.RunOi6Zarbox  0.61 >.  ° 05 ci,  0.4 U  0.3 0.2 0.1 0.0 -0.1  L  0  Angular Frequency (radls) Figure 3-12: Torque data normalized frequency content for chaiiis/sprockets and gearbox drivetrain (free-stream, 1.5 mIs, 2.5 TSR).  Recognizing these differences in the drive-trains, it is reasonable to have confidence in the efficiencies obtained in using either drive-train; however, one must recognize that the chains/sprockets configuration masks the peak torque values. Alternately, the play in the flexible coupling of the second configuration leads to a bucketing of the torque curve, and potentially sharper, higher peaks due to impact in the coupling when it re-engages. It is reasonable to expect that the true torque curve in an ideal system would lie between the two, likely closer to the gearbox drive-train case.  3.3.3 Arm Profile Reduction Figure 3-13 illustrates the various arm profiles examined during the test programs. It is  important to notice the clamping mechanism allowing for adjustable angle of attack used for profiles A and B. Upon removing the blades to examine the power absorbed by the arms, a large portion of the clamping mechanism was also removed, greatly reducing the  38  parasitic drag compared to when the blade was mounted.  The ends and middle  connections used for profile C are also shown.  Profile Cross-section (inches) Arm profile A  Connection Type Quarter-chord  0.1  0 Arm profile B  —1MH 0.38 A  Ends and middle Arm profile C (NACA 0012) 0.32  CZEZzE:  Figure 3-13: Arm profile cross-sections and connections.  Figure 3-14 below provides Ck vs. TSR of the turbine model using the various arms illustrated in Figure 3-13 above. Efficiency significantly increases with each subsequent decrease in arm profile. The most significant jump comes when changing from arm profile B to C, even though configuration C has a third central arm. This is primarily due to reduced drag, but also due to the end-plate effect gained from mounting the arms at the ends of the blades, as well as the increased working span of the foil compared to the ¼ chord mounted configurations. The more stream-lined design of configuration C also performs better at a higher TSR, indicating the foil provides better performance at TSR  39  closer to 2.75 or 3, but the trade-off with parasitic drag from the bulkier arms lowers the optimal TSR ratio with configuration B.  A further significant increase in performance is  gained when removing the middle arm and running with the blade mounted using arms only at the ends. The Ck value of the two arm configuration decreases much more slowly at TSR values of 3  —  3.5, indicating better performance at a larger range of TSR values,  which is beneficial for performance over a range of current speeds. The large difference in performance between 2 and 3 arms at TSR  >  2.25 may be explained by the v 2  dependency of arm drag having a larger relative impact at higher rotation speeds, and thus removal of the middle arm creates a significant drop in resistance. Additionally, the middle arm does not improve lift characteristics about the end of the foil as the end arms do, so its removal is purely reducing parasitic drag and not reducing lift generated by the foil.  0.35 0.3 0.25 0.2 0.15 C., 0.1 0.05  0 -0.05 -0.1  TSR Figure 3-14: Ck vs. TSR for supporting arm comparison at 1.5 mIs.  To facilitate comparison with theory, which typically ignores arm effects or requires an empirical formulation, the parasitic drag induced by the arms must be known. Figure 3-15 presents Ck vs. TSR of the various arm configurations when running the turbine 40  model with the blades removed. Though this plot provides insight into what Ck losses  are occurring due to the drag on the arms, simple subtraction of these Ck values from those in the plot above does not simulate an ideal case without parasitic drag for the following reasons: •  ¼ span mounting of the foils reduces span of the blade working as an airfoil  •  Positioning the arms at the ends of the foil will affect tip losses  •  Upon removing the blades for these tests, bolt heads, etc. are also removed and thus in the assembled case parasitic drag will be larger. This was particularly the case for arm configurations A and B, where their mounting configuration incorporated a clamping mechanism about the arm, which added much drag but was removed with the blade (Figure 3-13 above).  0 0.5  1.5  1 .  -0.02  2  2.5  3  3.5  -  •-.. •N  -0.04  N  •••.  N N  -0.06  N  US\  -0.08 .  -0.1  -0.12 -0.14 -0.16  —  \\  —ArmA  \  ---ArmB —.—  \  Arm C (ends and middle)  -0.18  -0.2  TSR Figure 3-15: Ck vs. TSR of varying arm configurations (blades removed) at 1.5 mIs.  41  Torque curves comparing arm profiles B and C (ends and middle) are provided in Figure 3-16 below. Arm profile C has significantly higher torque peaks transmitted to the shaft due to the reduced drag from the arms, though it is interesting to note that profile C demonstrates more negative torque readings at TSR = 2.25 and 2.5.  Figure 3-16: Torque vs. Angle of Revolution for arm profiles B and C (ends and middle) at 1.5 mIs and varying TSR.  Figure 3-17 provides the torque curves at 1.5 mIs comparing the three arms (profile C) for each blade vs. the case when just the end arms were supporting the blades at TSR  =  2.75 and 3. As one might expect, the removal of the middle arm leads to significantly higher torque peaks (hollow data points), which is reflected in the increased Ck value in Figure 3-14.  42  E  z  60 0  I-  Theta (degrees)  Figure 3-17: Torque vs. Angle of Revolution for 3 arms and end arms only at TSR2.75, 3 and v1.5 rn/s.  The plots above (primarily Figure 3-14) demonstrate an improvement in turbine performance by a factor of four simply when going from arm profile A to C; Section 3.3.7 further examines the effect of tip losses on turbine performance.  3.3.4 Single-blade Figure 3-18 below provides Ck vs. TSR for a 3-bladed test (arm configuration C), and two single-bladed tests (arm configurations B and C) at 1.5 m/s using the gearbox drivetrain.  It is apparent that interference and flow disruption play a significant role in  reducing the power output of the 3-bladed configuration. At the highest Ck value for the 3-bladed test (TSR  =  2.5), the single blade efficiency is 55.5% that of the 3-bladed  design. Beyond this TSR value, the 3-bladed efficiency drops, while the single bladed efficiency continues to climb.  43  0.300  0.250  -*— ——  1 Blade. Arm Config C 1 Blade, Arm Config B 3 Blades, Arm Config c  -  /  0200  •  ,1  0.150  /••  /  0.100 0  0.050  0.000 0. 10  I  I  0.50  1.00  I  1.50  2.00  2.50  I  3.00  3.50  4. 0  -0.050  TSR Figure 3-18: Ck vs. TSR for single and 3-bladed tests at 1.5 mIs.  Figure 3-19 illustrates the torque output of the single-blade test over a revolution at 1.5 rn/s for TSR = 2.5, 3, 3.5. The double peak at the primary torque-producing region (near 900)  is believed to be caused by flow separation on the blade. When the flow separates  due to the large angle of attack induced by the free-stream flow, the drag increases and the turbine produces less torque until the flow re-attaches. Meanwhile, near 270°, a double peak in torque creation due to a loss in lift caused by vortices shed by the shaft may be observed.  44  E z 0 0 F-  Theta (degrees) Figure 3-19: Torque vs. Angle of Revolution at 1.5 mIs for a single blade test.  Figure 3-20 superimposes three sets of torque data (TSR  =  2.5 at 1.5 m/s) from the  single-blade tests phased at 120° and compares them to the 3-bladed experimental test. The 3-bladed experimental result varies greatly from the superimposed single-blade result, and this is likely due to a combination of a number of factors: •  Interference and vortex shedding disrupts the flow at the downstream blades, reducing ability to cleanly create lift  •  The additional power being extracted by the multiple blades changes pressure distribution at the front of the turbine, affecting the amount of torque available for extraction at the 90° position  •  The phase shift observed between the peaks is believed to be caused by the fluctuating turbine revolution speed due to the larger forces involved (discussed further in Section 4.1.3)  45  Figure 3-20: Torque vs. Angle of Revolution at 1.5 mIs for a 3-blade test, single-blade test, and 3 superimposed single-blade tests.  Lastly, an interesting result was obtained when comparing tests done using arm profiles B  and C, as shown in Figure 3-21 at 1.5 m/s with a TSR  =  3 (both using the gearbox drive-  train). Similar shaft interference is obtained in the vicinity of 2700, though surprisingly the larger arm profile (B) shows higher torque values.  Meanwhile, across the 90°  position, a near opposite torque profile is created. An explanation for this is that across 900  the added drag from the arms and clamping mechanism, as well as tip losses, reduce  the torque generated, while just before 270° vortex interactions with the anns or clamping mechanism may be acting on the arms to enhance performance. Lastly, the dual peak observed in the 90° position with the lower profile arm is likely due to flow separation on the blade. With profile B, it is hypothesized that the large clamping mechanism at the ¼ chord locations, as well as tip losses, result in a much less pure observation of flow separation characteristics and instead yield a single pulse. Similar results were obtained at different TSR values.  46  Figure 3-21: Torque vs. Angle of Revolution for a single-blade test with arm profiles B and C at TSR=3, v=1.5 rn/s.  3.3.5 AngIe of Attack Blade set angles of attack of-5, -3, 0, 3, 5, and 10 degrees were tested throughout the test programs. 0, 3, 5 and -3 degrees provided the most insightful results and are discussed below. -3 degrees reduced turbine performance by almost 50%, while -5 and 10 degrees were highly ineffective. Figure 3-22 presents Ck vs. TSR at 2.0 mIs for AoA  0, 3, and  5 degrees.  It is interesting to note that at TSR < approximately 2.35, an AoA performance, while at TSR > approximately 2.35 an AoA  =  =  3 yielded the best 5 provided better  performance. In the vicinity of 90° of the turbine revolution (ie. directly upstream of the shaft), having a positive preset angle of attack decreases the angle of attack observed by the blade; meanwhile, in the vicinity of 270° (directly downstream of the shaft), a preset angle of attack on the blade increases the observed angle of attack on top of that caused by the free-stream flow. These are the most significant angles of attack experienced by  47  the blades (not accounting for vortex interactions) and are provided in Table 3-4 and Table 3-5.  Table 3-4: revolution.  Blade angle of attack at varying TSR and preset angle values at the  900  angle of  Angle of Attack (degrees) at 90° Position TSR  Flow-induced Angle  Net Angle (3° preset)  Net Angle 5° preset)  2  26.6  23.6  21.6  2.25  24.0  21.0  19.0  2.5  21.8  18.8  16.8  2.75  20.0  17.0  15.0  Table 3-5: revolution.  Blade aagle of attack at varying TSR and preset angle values at the 270° angle of  Angle of Attack (degrees) at270° Position TSR  Flow-induced Angle  Net Angle (3° preset)  Net Angle 5° preset)  2  26.6  29.6  31.6  2.25  24.0  27.0  29.0  2.5  21.8  24.8  26.8  2.75  20.0  23.0  25.0  48  018  1f 4/  0.1  A0A = 0 I—A0A=3 L..AoA=5 —*-  1/  J/ /  0.08 006. 0.04 0.02  /  0•  I  0  0.5  1  1.5  I  I  I  2  2.5  3  3.5  TSR Figure 3-22: Ck vs. TSR for AoA =0,3,5 degrees at 2 mIs.  Figure 3-23 illustrates the torque generated at a TSR peaks than at TSR  =  2.5 (Figure 3-25).  =  2.25, which is generating higher  This is because larger angles are being  experienced at 900 at the lower TSR value, generating more lift. A contributing factor to this is the dynamic stall effect, which tends to delay stall [25] that typically occurs near AoA  =  8° for the 634-02 1 airfoil at these Reynolds numbers (2.92E05 to 3.82E05 for 2  m/s). Also at TSR  =  2.25, the 5° angle of attack generates larger peaks due to reduced  stall upstream of the turbine, while it also creates similar, or slightly worse, low torque values downstream of the shaft due to an increased tendency to stall.  At TSR  =  2.5, the peak values in general are lower, though the turbine performance is  better. This is due to the fact that the low-points in the torque curve are higher than at TSR = 2.25. This is caused by less stalling around the back of the turbine since the angle induced by the free-stream flow is smaller at the higher TSR value. Comparing the 3°  and 5° preset angles of attack, 5° is creating substantially higher peaks due to reduced stall upstream of the turbine.  Downstream of the shaft, both angles create similar  49  negative torque peaks.  One should note that this is a simplified assessment of the  situation, as dynamic stall and vortex shedding onto the downstream blades play a significant role; however, flow visualization capturing these phenomena is extremely difficult. A key conclusion from this examination is that optimal angles of attack likely lie in the vicinity of 2 to 5 degrees, and are dependent on operating tip-speed ratio. Polar plots (Figure 3-24 and Figure 3-26) are also provided to aid with visualization.  70 j—.——Run1084--A0A=0 I —4——-Tun1284—AoA3 [—Run1384_AoA=5  60 50 —  E z  40  e  30  0 i—.  20 10 0 -10 I  I  I  0  50  100  I  I  150 200 Theta (degrees)  250  300  350  400  Figure 3-23: Torque vs. Revolution Angle for AoA =0,3, 5 deg at 2 mIs, TSR = 2.25.  50  90  120  T—...  ._—  .Lec  /  7  60  / N  ——RunlOS4--AOA=O Run12--AoA3 Run1384-.AoAS  /  /  /  207A’. 9’  / I--  180  A  -----“- --—---  -“-. “-. -.-. ‘---“.  ..-.  “----  210  0  339  /  /  N:  .-.1  ..__.__r  240 270  Figure 3-24: Polar Plot of Torque vs. Revolution Angle for AoA =0,3,5 deg at 2 mIs, TSR = 2.25.  ti_i  I  I  I  I  I  I  I  I  4r A  60  I  f  50  1  44  47/  E40  14  II  \:  (/,  1/  I—.-—Run1085AoA=0 —‘—Run1285--AOA=3 [z—Run1385AoAr5  1+  30  20  10  -50  it  UI  -1  -_-‘  I  I  I  0  50  100  I  150 200 Theta (degrees)  I  I  I  250  300  350  400  Figure 3-25: Torque vs. Revolution Angle for AoA =0,3, 5 deg at 2 mIs, TSR = 2.5.  51  go  180  Figure 3-26: Polar Plot of Torque vs. Revolution Angle for AoA  =  0, 3,5 deg at 2 mIs, TSR  Lastly, Figure 3-27 illustrates the torque curves generated with a preset AoA deg at 1.75 mIs.  The reduced torque peak at AoA  =  2.5.  -3 and 0  -3 indicates that this angle is  significant enough to increase the angle of attack observed by the blade past its stall point, reducing its ability to produce torque in the vicinity of 90°. The more negative lows in the torque curve indicate that this was also effective at reducing torque generated in the vicinity of 270° by reducing the observed angle of attack.  52  50  I  I  I  I  I  I  I  I  I  Run1485 A0A -3 —--—Run1065_AoA=0  —  40  —  4 30  E 20  z 4,  10  0  -10  I  I  I  I  0  50  100  150  200  I  I  I  250  300  350  400  Theta (degrees)  Figure 3-27: Torque vs. Revolution Angle for AoA = -3 deg at 1.75 mIs, TSR = 2.5.  3.3.6 Cambered Blades Investigation using cambered blades was performed using a cambered version (634-421) of the symmetric blade tested above. Power coefficient vs. TSR at 1.5 mIs is plotted in Figure 3-28 for the cambered blade at AoA blade case.  =  00  and 5°, as well as for the symmetric  It is apparent that the cambered blade offers a substantial increase in  efficiency, especially at 5°.  53  Figure 3-28: Ck vs. TSR for cambered (0 and 5 deg) and symmetric (0 deg) blades at 1.5 rn/s.  Examining the torque curves, Figure 3-29 provides torque vs. angle of revolution for the symmetric blade (AoA TSR  =  =  0) and the cambered blade (A0A  =  0 and 5) for the optimum  2.75 at 1.5 mIs. As expected, the symmetric blade produces higher peaks as a  blade passes near the 90°, because the cambered blade is effectively flying upside down. However, the cambered blade at 5° is effective in reducing this upside down angle of attack, and produces greater torque than the 0° cambered blade case. Additionally, as the cambered blade passes downstream of the turbine near 270°, the cambered blade is better suited to producing lift in this location, increasing the minimum torque values observed. This also appears to produce torque over a greater range, as indicated by the wider peaks,  leading to improved turbine performance.  54  Figure 3-29: Torque vs. Angle of Revolution for symmetric (0 deg) and cambered (0 and 5 deg) at 1.5 rn/s and TSR = 2.75.  3.3.7 Blade End Plates Proof of concept tests were performed using end plates on the blades to examine the possibility of reducing tip losses when supporting arms were mounted at the ¼ chord positions. Riley examined the use of end plates [261 and demonstrated that end plates with a foil-shaped cross-section were advantageous. Therefore, rectangular end plates with length equal to the chord and width of 1.5” with a NACA 0012 cross-section profile were applied, as suggested by Klaptocz [27]. Additionally, disc shaped end plates [0.25” thick] with a rounded edge and diameter equal to the foil chord were also tested given the circular path the turbine blade travels. Figure 3-30 displays the NACA 0012 (with flattened edge to sit flush on the foil) end plate and the circular end plate mounted to the blade.  55  Figure 3-30: NACA 0012 profile and circular end plates.  Figure 3-31 and Figure 3-32 below provide Ck vs. TSR for the end plate configurations compared to the case without end plates at 1.5 mIs and 2 m/s respectively. At both speeds the NACA 0012 end plates provided the best results, increasing the Ck value by 16% (at 1.5 mIs) and 12% (at 2 mIs). The circular end plates also demonstrated an improvement over the case without.  56  0.160 0.140 0.120  iN  7/  —n--No end plates NACA 0012 end plates  t  0.100 -*—  Circular end plates  0.080 0.060  0.040 0.020 v/i  0.000 0. 0  / I  0.50  1.00  1.50  2.00  2.50  3.00  3. ‘0  -0.020 -0.04 0  TSR Figure 3-31: Ck vs. TSR for end plate comparison at 1.5 mIs.  0.180 0.160 0.140  c  No end plates  if  NACA0012endplates 0.120 —  Circular end plates  0.100  I  /1  C) 0.080  /,/ 7/  0.060 •//  0.040  V V  0.020 0.000 0.00  0.50  1.00  1.50 2.00 TSR Figure 3-32: Ck vs. TSR for end plate comparison at 2 mIs.  2.50  3.00  57  Considering the torque curves, at 1.5 m/s (Figure 3-33) the NACA 0012 appears to produce increased torque peaks, while the circular end plates produces smaller and slightly wider torque peaks which rarely enters a negative torque region. Conversely, at 2  rn/s (Figure 3-34) the NACA 0012 end plates produce lower, wider torque curves while the circular end plates produce higher torque peaks. Lastly, it is possible to create thinner disc end plates, which would reduce associated drag and improve performance.  E  z a, 0 I-  Theta (degrees) Figure 3-33: Torque vs. Revolution Angle comparing end plates at 1.5 mIs.  58  Figure 3-34: Torque vs. Revolution Angle comparing end plates at 2 m/s.  3.3.8 Shaft Fairing Given the interference observed in the single blade tests, fairings were fabricated and placed around the shaft as an attempt to minimize the shaft vortices (Figure 3-35). Figure 3-36 below provides Ck vs. TSR for runs with and without the shaft fairing at 1.5 and 2 rn/s. Tests were conducted using arm configuration C, and a fairing was placed each between the upper/middle arms and the middle/lower arms. For both speeds, the fairings either reduced performance or had negligible effect.  59  Figure 3-35: Shaft fairings.  Figure 3-37 displays torque curves for the cases with and without shaft fairing for a TSR 2.75 at 1.5 mIs. The fairing reduces the torque peaks, as well as shifts the peaks approximately 12 degrees to the left, or earlier in the rotation. A similar effect was observed at 2 mIs. Friction is the likely cause of the reduced torque peak, while different vortex interactions, as well as the reduced torque peaks resulting in less revolution speed fluctuation, are the most reasonable explanation for the phase shift in torque curve (revolution speed fluctuations discussed below in Section 4.1.3).  60  0.300  II  0.250  -  o  0.  / /  0200  A  i5u  \\ IAoA=0(1.5s) shaft fairing (1.5 mis) AoA=0 (2 mis) I— with shaftfairing (2 m/s)  7  •  /1  0100  0.050  0.000 1.00  I  1.50  2.00  2.50  I  I  3.00  3.50  4.00  TSR Figure 3-36: Ck vs. TSR with and without shaft fairing (1.5 and 2 m/s).  I  I  I  I—Run225--withFairing Run205.1 without Fairing —  __100  I  I  80 E  z  60 0  40 20 0  50  100  150  200  250  300  350  400  Theta (degrees) Figure 3-37: Torque vs. Revolution Angle with and without shaft fairing at 1.5 mis, TSR=2.75.  61  Tests were also conducted for a single blade with the shaft fairing, as shown in Figure 3-38. Figure 3-39 provides torque vs. revolution angle with and without the shaft fairing. The fairing appears to smooth out the torque curve downstream of the turbine near 2700 as one might expect, though the general effect of the fairing was to reduce the average torque by 4 % (Ck  =  0.15 1 without the shaft fairing for a single blade vs. 0.145 for the  case with the shaft fairing).  This reduction in power is likely caused by additional  friction between the fairing and shaft, as well as an increase in frontal area of the shaft increasing the effective blockage of the turbine and causing more flow to pass around.  Figure 3-38: Single blade with installed shaft fairing.  62  2  z 0  0 0 I-  Theta (degrees)  Figure 3-39: Single Blade Torque vs. Revolution Angle with and without shaft fafring at 1.5 mIs, TSR=2.75.  3.3.9 Summary Considering the data above, it becomes possible to summarize the improvements to be gained from each parameter by comparing to its baseline configuration. NACA 0012 end plates were shown to increase the baseline Ck value by 12.2% and 16.6% at 1.5 mIs and 2  rn/s respectively, though in general the contribution of tip losses to overall device performance will reduce with increasing aspect ratio. Angle of attack provided a notable improvement over the baseline case of 0° (tested with arm profile B), as at 1.5 m/s 3° and 5° increased the Ck value by 21.1% and 14.8% respectively, while at 2 m/s 3° and 5° increased the Ck value by 17.3% and 2 1.6% respectively.  Table 3-6 below summarizes the incremental improvements achieved over the 3-armed baseline (profile C) for the following cases: 2 arms at the ends only, cambered blades at 0° and 5°, and shaft fairing application.  63  Table 3-6: Maximum Ck and percent increase over free-stream baseline.  Maximum Ck Case 3 arms (baseline) 0.272 2 arms 0.303 Cambered blade J° AoA) 0.285 Cambered blade (50 A0A) 0.319 Shaft fairing 0.255  % change --  11.4% 4.8% 17.3% -6.3%  Using this data, it is possible to hypothesize the maximum efficiency of a free-stream, 3bladed rotor. As moving from 3 to 2 arms yielded an increase in Ck of approximately 0.031, it seems reasonable that in the absence of all arms, the Ck may increase by an additional 0.062; however, one must recognize that removing end arms will also allow for tip losses (Ck  approximately 0.02 at this aspect ratio). Assuming tip losses may be  eliminated by some other hypothetical means, the maximum efficiency of this device would be approximately 0.3 65. The shift to cambered blades at 5° further increased Ck by a value of 0.047, bringing our theoretical maximum Ck value, without arms or tip losses using the cambered blade at  50,  to 0.412. Two other major components affecting  rotor design and not examined as part of this thesis are solidity and foil shape. Recognizing these, a rotor with Ck of 0.45 in the absence of all losses seems to be a reasonable theoretical maximum after using numerical codes or an extensive experimental program to pin-point optimum solidity and foil shape/angle of attack.  3.4 Ducted Turbine Figure 3-40 provides a dimensioned plan view of the venturi-type ducting installed around the turbine, while Figure 3-41 illustrates the ducting position within the tank. A top and bottom was installed as shown in Figure 3-4 1, and a large Plexiglas window was installed to allow for removal of the turbine while leaving the ducting in place, as well as to facilitate visualization. The duct shape was determined based on previous NRC trials [11] as well as what was suitable for the current experimental setup. Results for the venturi-type ducting (Section 3.4.1) and ducting with flow deflectors (Section 3.4.2) are discussed below.  64  I-  75.1  12.1  40.4 \  /  Figure 3-40: Plan view of ducting (inches).  65  ernal width4O.4” Water depth = 84”  External duct width=64.6”  ‘1  I...  Tank width  =  144”  Figure 3-41: Cross-section of towing tank with ducting and turbine.  3.4.1 Venturi-type Ducting  Figure 3-42 provides Ck vs. TSR for the free-stream and ducted turbine at 1.5 mIs. The ducted turbine greatly enhances power output from the turbine, though Ck is still calculated based on the turbine area, and not the duct frontal area affecting the flow. Secondly, TSR is calculated relative to the free-stream velocity, and not relative to the accelerated velocity through the duct, explaining why the highest Ck value is occurring at a higher TSR value for the ducted case.  66  0.50 0.45 0.40 0.35 0 30 .  o 0.25 0.20 0.15 0.10 0.05 0.00 0.0  0.5  1.0  1.5  2.0  2.5  3.0  3.5  4.0  TSR Figure 3-42: Ck vs. TSR for the free-stream and ducted turbine at 1. 5 mIs.  It is interesting to compare the power harnessed by the ducted turbine vs. the power that would be extracted by a free-stream turbine of capture area equivalent to the duct (approximately 32.5” x 63.1”) operating at the Ck values obtained in previous tests. This is provided in Figure 3-43 which indicates the ducted turbine captured a peak of 501 W, while a free-stream turbine of equivalent capture area may be expected to harness 560 W, not accounting for Reynolds’ effects. Therefore, the ducted configuration tested was approximately 12% less efficient than an equivalent-sized free-stream turbine, having a peak Ck value based on the capture area of 0.239, vs. 0.272 for the free-stream device. A free-stream device of equivalent size to the ducted device tested may be capable of generating more power due to more flow passing through the device given there is less blockage in the absence of a duct, as well as the increased diameter and blade size of the free-stream device is capable of producing larger torque forces on the shaft.  67  600  500  400  300  200  100  0 0.00  0.50  1.00  1.50  2.00 TSR  2.50  3.00  3.50  4.00  Figure 3-43: Extracted Power (W) vs. TSR for the tested ducted turbine and a free-stream turbine of equivalent capture area at 1.5 m/s.  Considering torque curves for the free-stream vs. the ducted turbine, Figure 3-44 illustrates the torque curves for the free-stream turbine at 1.5 mIs, while Figure 3-45 provides torque curves for the ducted device at 1.5 mIs.  The most significant (and  surprising) result is the decrease in amplitude of the torque curve for the ducted configuration once a TSR of 2.75 or greater is reached. A similar decrease in torque ripple was observed in the 2 m/s ducted tests beginning at TSR = 2.5. It is convenient to define a torque fluctuation coefficient calculated as follows from values of the torque curve:  CTF  = Tm  —  Tmj  Equation 6  avg  = maximum torque  where: Tmjn  minimum torque  Tavg = average torque  68  CTF  facilitates comparison of torque curve fluctuations, which are a key parameter in the  mechanical design of the device as reduced fluctuations may greatly enhance both reliability and operation life of the device.  z 0 0 0 I—  Theta (degrees)  Figure 3-44: Torque vs. Revolution Angle for free-stream turbine at 1.5 mIs.  69  E  z 0 0 I-  Figure 3-45: Torque vs. Revolution Angle for ducted turbine at 1.5 m/s.  Table 3-7 below tabulates torque fluctuation coefficient for both a free-stream and ducted turbine in the runs shown above.  Table 3-7: Torque fluctuation coefficient for a free-stream and ducted turbine. CTF  TSR Value 2.25 2.5 2.75 3 3.5  Free-stream 6.48 5.44 4.24 3.8 5.4  Ducted 9.54 5.71 1.45 1.25 1.26  Percent Change 47.2% 5.0% -65.8% -67.1% -76.7%  This decrease in CTF is primarily due to the duct constraining the flow and not allowing it to expand and slow in way of the downstream blade, thus increasing the available power; altered vortex interactions compared to the free-stream case may also be increasing performance of the downstream blade though flow visualization would be required to be certain. Lastly, tests were also conducted with the ducted configuration and the shaft fairing. As for the free-stream result, a slight decrease in performance was observed for all runs, except for TSR=2.75 at 2 mIs which showed a 6% increase in performance. This  70  point is believed to be an outlier, but may warrant future investigation should the device be re-examined.  3.4.2 Ducting with Deflectors In place of testing a large variety of duct shapes which are both expensive and laborious to construct, 4 deflectors were fabricated to be placed at various locations within the duct to adjust the flow. Figure 3-46 below illustrates deflector positioning and size, with additional details in Appendix B. The configurations tested were as follows: •  All four deflectors  •  Blades spinning towards (deflectors 1 & 3)  •  Blades spinning away (deflectors 2 & 4)  •  Downstream (deflectors 1 & 2)  •  Upstream (deflectors 1 & 2 while running in opposite direction; equivalent to 3 & 4 with flow direction as shown on diagram)  The rationale behind the use of the deflectors was to reduce the cross-sectional area, and thus increase the speed and available power, in the blade positions where the turbine is generating the most torque  (900  and 270°). Additionally, deflectors were offset from the  ducting to allow for flow to pass in-between, limiting separation that may occur behind the deflector. This design was developed by Yasser Nabavi and Voytek Klaptocz [281.  71  Blade /2 rotation Flow into turbine  /  Figure 3-46: Ducting with deflectors.  Figure 3-47 below provides Ck vs. TSR for the various deflector configurations, as well as for the plain venturi-type duct. The configuration without deflectors produced the highest Ck values, and this is likely due to the deflectors reducing the flux through the ducting assembly and thus reducing the available power to be extracted by the rotor. The 4-deflector and upstream deflector designs appear to be the least efficient, likely due to increasing resistance to the flow before the rotor, while the downstream deflectors as well as 1+3 and 2+4 yield similar peak Ck values.  72  0.500 0.450 0.400 0.350 0.300 0.250 0.200 0.150 0.100 0.050 0.000 0.00  0.50  1.00  1.50  2.00  2.50  3.00  3.50  4.00  TSR Figure 3-47: Ck vs. TSR for duct and deflector configurations.  The primary significance of the deflector designs is observed when examining the torque curves of the various configurations. Maximum Ck values were observed at TSR values of 2.75 and 3, and Figure 3-48 and Figure 3-49 provides torque curves for the various configurations at TSR  =  3. The downstream deflectors (solid dashes) greatly reduce the  torque fluctuations observed, believed to be due to higher torques at the downstream blade caused the smaller cross-sectional area and resulting higher flow velocities. Conversely, the deflectors upstream of the turbine appear to cause much greater torque fluctuations due to the increased velocity passing past the blade upstream of the turbine, which is already producing the majority of the torque.  73  E  z 0 I-  Theta (degrees)  Figure 3-48: Torque vs. Angle of Revolution for ducted and deflector configurations.  90 Run204.1 Free-stream Run 485— Ducted no deflectors Run407.1 —4 deflectors —a--— Run 445— Spinning towards Run 525— Downstream deflectors  —  —  —a——  —÷-—  180  270  Figure 3-49: Polar plot of Torque vs. Angle of Revolution for ducted configurations.  74  Table 3-8 below provides the maximum Ck values and corresponding CTF for the various ducted configurations examined, as well as for the free-stream case. The downstream deflectors offer a 62% reduction in the torque ripple experienced by the shaft over the case without deflectors. This is considered due to the reduced cross-sectional area in way of the deflectors at the downstream positions of the blades, which increases flow velocity and thus lift extracted in this position, resulting in a torque generation more comparable  to the 900 position upstream of the shaft. Lastly, in the figure above it should be noted that reduced torque fluctuations resulted in reduced revolution speed fluctuations (Section 4.1 .3)shifting the peaks back closer to their theoretical position near 90°. Table 3-8: Maximum Ck and corresponding CTF for ducted turbine configurations (1.5 mIs).  Case  -  No deflectors Downstream deflectors All four deflectors Spinning towards deflectors Spinning away from deflectors Upstream deflectors  Ck Value 0.473 0.442 0.393 0.426 0.442 0.407  % Ck Change —  -6.6% -16.9% -9.9% -6.6% -14.0%  CTF  % C Change  1.25 0.47 1.4 1.17 1 .23 2.61  -62.4% 12.0% -6.4% -1 .6% 113.6%  --  3.4.3 Summary  As for the free-stream case, it is possible to quantify the effect of the various ducting configurations compared to the baseline free-stream case. Table 3-9 below provides maximum Ck value, Ck percentage increase over the free-stream baseline, and coefficient of torque fluctuation. Table 3-9: Maximum Ck, percent change, and torque fluctuation coefficient  Case Free stream (baseline) No deflectors Downstream deflectors Al four deflectors Spinning towards deflectors Spinning away from deflectors Upstream deflectors -  Ck Value 0.272 0.473 0.442 0.393 0.426 0.442 0.407  % Ck Change --  73.9% 62.5% 44.5% 56.6% 62.5% 49.6%  C 4.24 1.25 0.47 1 .4 1.11 1.23 2.67  % CT Change --  -70.5% -88.9% -67.0% -72.4% -71.0% -37.0%  75  As expected, ducting around the rotor increases power output; however, the power obtained from the ducting design tested is less than what may be expected from a freestream turbine of equivalent cross-sectional area. Recognizing this, ducting (especially with modifications such as the downstream deflectors) is demonstrated to greatly reduce torque ripple. Additional potential benefits such as structural support for the bottom bearing and to facilitate mooring render ducting a prospective enhancement to a turbine design requiring a comprehensive cost-benefit analysis.  3.5 Drag Force No previous documentation has been found on the forces parallel to the free stream flow acting on the turbine rotor, and subsequently the shaft bearings. These forces are a combination of drag forces on the shaft and supporting arms, as well as the component of the lift and drag forces on the turbine blades acting parallel to the free-stream flow. For this thesis, the combination of forces parallel to the free-stream flow will be referred to collectively as drag forces.  A means of approximating the drag force on the turbine was devised by measuring the force at the top bearing using the force balance, estimating the centre of action of the drag forces, and balancing moments about the bottom (self-aligning) bearing to solve for the magnitude of the drag force. Figure 3-50 below illustrates the location of the assumed and measured forces. Analytical calculations demonstrated that the blades and arms may be expected to account for approximately 83-93% of the forces parallel to the free-stream flow, while the shaft and arms account for the remaining forces. Given the centre of the blades and arms is 21.5” above the bottom bearing and the centre of the shaft is 26” above the bottom bearing, this results in an assumed centre of force about 22” above the bottom bearing to within approximately +1- 15%.  The broad range is due to the  simplified analytical calculations as well as the dynamic nature of the system, but is  76  sufficient for this preliminary investigation. With the top bearing 68” above the lower bearing and the force balance measuring the load parallel to the free stream on this top bearing, it is possible to use moment calculations and determine that the drag load at the turbine is 68/22 times the in-line load measured at the force balance.  V Top shaft bearing 68”  Flow  Centre of  I  I  Figure 3-50: Side view providing location of assumed centre of drag force.  Figure 3-51 provides drag force of a free-stream turbine vs. TSR for angles of attack at 00  and  30  for TSR values between 1.5 and 3 at velocities between lmJs and 2mJs. Using this  measured drag force (D), it is possible to calculate a drag coefficient (Cd) for the turbine as follows:  Cd=  D 2 .A ).p.v  Equation 7  Drag coefficient vs. TSR for these same trials is provided in Figure 3-52. The data for velocities of 1.5, 1.75, and 2 m/s collapses reasonably close together, while the data for lmIs yields slightly higher drag coefficients. As these drag forces are a combination of  77  resistance on the shaft and arms, as well as components of lift and drag on the foil parallel to the flow, Reynolds effects will be present and it is apparent that at the lower Reynolds numbers in the lmIs tests the result is increased relative drag forces on the device. A linear trend line fit through the combined 1.5, 1.75, and 2mIs data points yields an equation with slope of 0.41 and y-intercept  =  -0.16 (R 2  0.91). This enables a rough  approximation for the drag coefficient of the tested device at varying TSR values over this range of Reynolds numbers. One must exercise caution if attempting to extrapolate these results directly to other vertical axis turbines of different solidities, or proportionally larger shaft and arm sizes, as all of these will affect the magnitude of the drag forces generated.  1800 1600 —u— 1 mIs, AoA=0  1400  1 mIs, AOA=3 1200 —-  1  1.5 mIs, AOA=0 1.5 mis, AoA=3  1000 —+-  1.75 mis, AoA=0  —.--  1.75 mis, AoA=3  I-  ci ‘:3—  —s-- 2 mis, AoA=0  600  2 mis, AoA=3 400 200 0 0  0.5  1  1.5  2  2.5  3  3.5  TSR Figure 3-51: Drag Force vs. TSR for a free-stream turbine at varying velocity.  78  1.4 y0.41x0.16 R’=O.91  1.2  C)  —--1m/s,AoA=0 0  0.8  1 mis, AOA=3  0— —.—  .  .  4  —&-  1.5 mis, AoA=0  —A—  1.5 mis, AoA=3  6  1.75 mis, AoA=0 1.75 mis, AOA=3  -— —.--  /  0.4  -8--2mis,A0A=0 2 m/s, AoA=3  0.2  0  0  0.5  I  I  I  I  I  I  1  1.5  2  2.5  3  3.5  TSR  Figure 3-52: Drag Coefficient vs. TSR with trend line for data at v=1.5, 1.75, 2mIs.  As for the torque curves, it is possible to plot drag data as a function of revolution angle. Figure 3-53 provides drag force vs. revolution angle at the TSR values for which optimal power is typically being generated. The most drag is being produced in the vicinity of 900  as one might expect, since this is where peak torque is typically being generated, and  a large component of the lift generating this torque is in the free-stream direction, resulting in drag on the device.  Of note are the smaller peaks for the TSR=2 and  TSR=2.25 cases, which occur at frequencies of approximately 57.8 rad/s and 64.1 rad/s respectively as determined by performing a Fast Fourier Transform (FFT) on the data set within the analysis software. This occurrence is discussed further after examining the single-blade case below. Figure 3-54 provides drag force vs. revolution angle at 2 mIs for TSR2, 2.25, 2.5, 2.75. It is apparent that these high frequency oscillations have disappeared, and clean drag curves are obtained with peaks near the 90° position.  79  4  •Thnn  I LIlt)  1000  snn  z uu  a, C, 0 ‘J O) CU  .  .\  in fl\. in’ aJd  a  -0  :  An  ‘1 k  —-  —e—Run 1043 2.0 TSR  —Run 1044 2.25 TSR  —h--Run 1045 2.5 TSR  ?  Run 1046 2.75 TSR  lic  50  100  150  200  250  300  30  41  -“nfl Revolution Angle (deg)  Figure 3-53: Drag Force vs. Revolution Angle at 1.5 mIs, AoA=O.  100 150 200 250 RevolutIon Angle (deg) Figure 3-54: Drag Force vs. Revolution Angle at 2 mIs, AoA=O.  80  Considering the experimental tests with only a single blade attached to the shaft, Figure 3-55 provides drag coefficient vs. TSR for both the single and 3-bladed case at 1.5 m/s with AoA=3. A single-blade device has approximately 2/3 of the drag coefficient of a 3bladed turbine.  Figure 3-55: Drag Coefficient vs. TSR for a single and 3-bladed device at 1.SmIs, AoA=3.  Examining single-blade drag vs. revolution angle (Figure 3-56), drag is again being generated in the 90° and 270° regions, as is torque. The high-frequency oscillations, however, are apparent at TSR values of 2, 2.25, and 2.5, and are less apparent at TSR=2.75.  81  iIuu  loop  nn  z 41 (3 0  U  ::  —--Run 1643 2.0 TSR  ât’’k  .  u:  50  100  150  AM” \j 200  250  300  2:5 TSR 1ERU  350  400  Revolution Angle (deg) Figure 3-56: Drag Force vs. Revolution Aiigle for a single blade at 2 mIs, AoA=3.  Table 3-10 provides expected frequencies based on the turbine revolution speed for both one primary pulse (ie. at 90°) and two primary pulses (ie. at 90° and 270°) per blade per revolution. Approximate observed frequencies obtained from a FFT on the recorded data are also provided. The observed frequencies are where one may expect based on the turbine blade frequency and the two pulses per blade; however, there is the unique frequency at about 57-63 radJs that isn’t easily explicable by blade pulsing, and that disappears at higher drag forces. Additionally, these oscillations appear with both the single-bladed and 3-bladed device at about the same frequency, making it unlikely that this is due to arm forces or flow around the foils separating and then re-attaching. If that was the case, this frequency near 57-63 Hz would appear at much different values when comparing the 3-bladed and single-blade device. Considering this, it is reasonable to conclude that the oscillation was at a natural frequency of the force balance / load cell configuration. At higher velocities and drag forces, this oscillation has disappeared, hinting to the fact that these higher loads were perhaps capable of dampening the motion at the force balance. Lastly, the vortex shedding frequency on the shaft was predicted to  82  be approximately 345 radls, while the natural frequency for the shaft was predicted to be 622 radls, both of which are too high to be responsible for the oscillations discussed here. Table 3-10: Expected and observed experimental drag force frequencies. Expected Experimental Frequencies (radls)  3 Blades  Single Blade  2.0 TSR 2.25 TSR 2.5 TSR 2.0 TSR 2.25 TSR 2.5 TSR  J J.  Radians I sec  Blade Frequency  6.54 7.21 8.11 6.91 7.64 8.37  1961 21.62 24.32 6.91 7.64 8.37  Expected Frequency (2 pulses per blade) 3923 43.25 4863 13.82 15.28 16.75  Expected Frequency (3 pulses per blade) 58.84 6487 72.95 20.73 22.92 25.12  Primary Observed Fre encles (raWs) 18.28 57.93 39.65 2130 42.60 63.90 24.32 48.63 63.84 6.47 12.88 57.99 15.77 15.58 59.31 —  —  3.5.1 Summary  The drag force measurements above provide an insightful first look into the magnitude of drag forces that may be expected on a vertical axis hydro turbine. The high frequency oscillations (57-63 Hz) appear to dampen out at higher velocities and drag loads, indicating that they are likely caused by a natural frequency in the flexibility of the load cell / force balance system. Lastly, the equation approximating Cd [Cd = O.41*tsr  —  0.161  only accounts for forces parallel to the free-stream flow, and much further work is required to understand the interaction between parasitic drag forces, lift/drag forces acting on the turbine blades, and the net forces observed by the bearings, which are likely to have a variable direction during turbine revolution.  83  4 DISCUSSION Below, measurement errors and repeatability are discussed, followed by a comparison with the numerical predictions and a general discussion on sources of error.  4=1 Measurement Accuracy Typically, when considering measurement accuracy and error, one must consider both systematic error and random error. Random error is the experimental error that occurs given no two runs will yield exactly the same result due to random variation in the experimental setup and surrounding conditions.  Systematic error results from an  erroneous method that is repeated with each test and consistently provides a similar inaccurate result.  Random errors are addressed below in the form of measurement  uncertainty, ensemble averaging for obtaining torque curve data points, and run repeatability. Revolution speed variation is a source of systematic error and is examined in Section 4.1.3.  4.1.1 Instrumentation Uncertainty and Data Point Averaging Precision of the recorded values affects measurement accuracy, and this uncertainty is typically specified with the instrumentation component being used. Error is also attributed to the DAQ component reading and amplifying the signal, as well as any other signal conversion devices. Table 4-1 below provides the uncertainty associated with the torque sensor and angular encoder. Table 4-1: Torque sensor and encoder uncertainty (percent of rated output) and absolute error. Item Torque Sensor Encoder Sensor 0.20% 0.10% Digital-Analog Converter 0.50% 0.10% 0.04% DAQ Card Sum 0.30% 0.64% Absolute Error (extreme case) 1.5 Nm 2.27 deg --  84  These maximum errors due to instrumentation are very small, and given the number of data points recorded and the averaging techniques applied, these uncertainties do not provide a good understanding of the accuracy of each data point. Considering the torque curves, it is more useful to know the standard deviation of the ensemble averaged data used to obtain the plots. Figure 4-1 and Figure 4-2 provide standard deviation of the data points used for obtaining torque curves of the free-stream device at 1.5 and 2 mIs with the gearbox drive-train at TSR=2.5.  Representative 95% CI obtained from the standard  deviations are also provided for three locations on the first peak and are circled. The magnitude of the standard deviations are similar for each plot, though one difference is that at 2 m/s the torque values do not drop significantly below zero. The play in the coupling in way of torque values about zero and the resulting steep slopes contribute to the fluctuating standard deviations observed.  Revolution Angle (Deg) Figure 4-1: Standard Deviation and Torque vs. Revolution Angle for a free-stream device with gearbox drive-train at 1.5 m/s and TSR=2.5 (N 34).  85  Revolution Angle (Deg) Figure 4-2: Standard Deviation and Torque vs. Revolution Angle for a free-stream device with gearbox drive-train at 2 mIs and TSR=25 (N 52).  Figure 4-3 provides a similar plot for the free-stream device using the chains and sprockets drive-train at 2 mIs with TSR=2.25. The combination of dampening from the chains and sprockets system, as well as lack of play in the coupling, significantly reduces the standard deviation values to be consistently less than 4, though the peak torque values have also been decreased by a factor of approximately 3 from the gear-box drive-train case.  86  —a—  70  60  120  180  FnsemLt Averaged  240  300  Torque__F  30  -10  0  Revolution Angle (Deg) Figure 4-3: Standard Deviation and Torque vs. Revolution Angle for a free-stream device with chains/sprockets drive-train at 2 rn/s and TSR=2.25 (N —33).  Lastly, for the case with ducting  and  gearbox drive-train (Figure  4-4),  the reduced torque  fluctuations also lead to reduced standard deviations. In this case, the standard deviation is consistently less than  3,  with peak torque values ranging up to approximately  The standard deviation above comparing  with theory  80 Nm.  is used to create error bars in efficiency plots when  (Section  4.2.2).  87  Torq::  60  7  :  z50  I  40  0  60  /  120 180 240 Revolution Angle (Deg)  :1  300  360  : :  Figure 4-4: Standard Deviation and Torque vs. Revolution Angle for a ducted device with gearbox drive-train at 1.5 mIs and TSR=3 (N 45).  4.1.2 Run Repeatability Given the time constraints due to working in the towing tank facility and the number of parameters requiring investigation, it was not possible to conduct a large number of repeated runs for completion of a comprehensive statistical analysis. Table 4-2 below compares Ck values for repeated runs using the gearbox drive-train for both free-stream (arm profiles B and C) and ducted tests. The percent difference between a series of runs completed at a given set of conditions and their respected mean is provided.  For free-stream runs, 18 of the 29 repeated runs have a percent difference of less than 1% in magnitude from their respective mean value. 6 of the 29 are between 1-2%, while the  remaining 5 values are between 2-4%.  This repeatability is acceptable considering  carriage speed, torque, and revolution speed are all being recorded and used for the calculation of the Ck value. Examining the ducted device, 75% of the points have a percent differences less than 2%, with the remaining points having differences of 2.74%  -  88  4.2%. A larger error for the ducted device is reasonable given the size of the duct being towed through the water resulting in large disturbances in the flow and increased forces, and thus flexing, on the mounting structure.  Runs noted as being in the opposite  direction were performed towards the wavemaker instead of the dock so as to investigate consistency between directions. This enabled runs with duct deflectors upstream of the turbine to be performed without having to move deflectors from the downstream position.  89  0  <  CM  CD  Cd  Q  z  g as  Cd  0  C  CM  ‘  e*  ,-  CM  CM  CD  -i  ‘4  CD  C  D)  CD  Cd  CD  0  CD  I—’  CD  CD  -  -ot fr4) CD  CD  CD  CD CDCD CD CD CM  a’  C  I  Q  0  ‘tad CD C fri CD  CD  t CM  BCD  CM CM t<  o o  CM  •  ‘  CD  ad  a’  °H  e2.  tjM  CD  &Q  CD  0  a  fl  a  —  -  a  -.  D  a,  (F  C  a,  a  (F  a,  -  n  .  0)  bi bi  (,‘  en  N N N N  en  Cn  F’)  bi  0)  P.)  en e  N N  en  Co  t’.’  F’.’.  -‘  P.)  r’.  -‘  F’)  p..’  F’)  r’.’  -‘  P.)  F’.’  F’.’  r)  F’) p..’  —  F’)  F’)  N N N N  r’.’  ——  -  a.  C 0  P.)  F’)  P.)  P.)  en  bi  p.)  —  F’)  F’)  P.) 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P a a  0  C.)  bi  2  C,’  C,’  r,  o  z  —  Table 4-3: Sample chain/sprockets drive-train repeated run percent variation in Ck Run # Speed (m/s) Nominal TSR Ck % Oifference*  *  1045 1.5 2.5 0.1284 1045b 1.5 0.1266 2.5 1085 2 2.5 0.1367 1085b 2 2.5 0.1395 cakulateci as (Run-Mean)/Mean for each condition  0.73% -0.73% -1.03% 1.03%  Just as Ck values should be equal for each run at the same conditions, torque curves should also match over a revolution cycle. Figure 4-5 provides torque vs. revolution angle for repeated runs at 1.5 m/s and TSR2.5, while Figure 4-6 and Figure 4-7 provide Cartesian and polar plots respectively of repeated runs at 2 mIs, TSR2.5. It is evident that the peak locations are very repeatable, providing consistent knowledge on which regions of a revolution are in need of performance enhancement. The polar plot is a nice visualization tool, accentuating that torque is generally created as a blade passes across the flow upstream of the turbine.  91  200  -.  f  —Run204.1  150 IRun204.3 Lz-Run204.4 —  100.  o  I—  V  I 1  0  ‘f ‘V  1 4  50  100  150  200  250  300  350  400  Theta (degrees) Figure 4-5: Torque vs. Revolution Angle for repeated runs with gearbox drive-train at 1.5 m/s, TSR=2.5 (arm profile C).  200  —.---Run214.1 HRun214.2 Run214.3 __e_Run2144 [-Run214.5  150  V  E 1 00 z  50  0  V  0  50  I  “  100  150 200 250 Theta (degrees)  I 300  350  400  Figure 4-6: Torque vs. Revolution Angle for repeated runs with gearbox drive-train at 2 mIs, TSR=2.5 (arm profile C).  92  180  270 Figure 4-7: Polar plot of Torque vs. Revolution Angle for repeated runs with gearbox drive-train at 2 mIs, TSR=2.5 (arm profile C).  Figure 4-8 provides torque curves for the ducted configuration, again highlighting repeatability of the system. It is particularly impressive considering tests were conducted on different days amongst configuration changes. Lastly, Figure 4-9 provides repeated runs with the chains and sprockets drive-train for TSR=2.5 at speeds of 1.5 and 2 mIs. Again, repeatability is reasonable given the flexibility in the chain and sprockets drive train, and flexing of the force balance.  93  120  100  p  80  z 4, -p  0 0  60  1 I ‘I ‘I ‘I  it  I  I-  40  Run 484 -j—e--Run 624 I—e--Run 501 [sun 502  20  0 0  50  100  150  200  250  300  350  400  Revolution Angle Figure 4-8: Torque vs. Revolution Angle for ducted repeated runs with gearbox drive-train at 1.5 mis, TSR=2.75.  E z C. 0 I—  100  150 200 250 Theta (degrees)  Figure 4-9: Torque vs. Revolution Angle for repeated runs with chains/sprockets drive-train at 1.5 and 2 mis, TSR=2.5 (arm profile B).  94  4.1.3 Revolution Speed Variation  When comparing to numerical predictions, it was observed that the peak torque locations were phased to a higher revolution angle than expected (discussed further in Section 4.2.2). Data examination revealed a fluctuating revolution speed due to the torque being generated. This is illustrated in Figure 4-10 for runs at 1.5 m/s at varying TSR values with the chains and sprockets drive-train.  The revolution speed (rpm) provided is  representative as it is a spline fit through the multiple data points based on very small sampling periods; however, it provides insight into what is occurring. Additionally, as RPM and torque are being plotted vs. revolution angle, any average taken from this plot will be artificially increased compared to the true average over time of the run. When plotted against time, less time is spent at the angles with higher torque generation and revolution speed; however, when plotting against revolution angle equal weighting is given to all points in the revolution, skewing the average. Averages displayed in the legend provide the true average revolution speed when taken over the time duration of the run. It is interesting to note that the peak revolution speed typically occurs earlier in the rotation, or closer to 90° as one may expect. As the motor controller responds to the increasing rpm, it acts as a brake and the torque continues to increase for another 25° or so as the turbine is slowed. This process is repeated for all TSR values.  95  160  200  Theta (degrees)  Figure 4-10: Torque (below) and RPM (above) vs. Revolution Angle for runs with chains/sprockets drive-train at 1.5 mIs.  Hypothesizing that the chains and sprockets drive-train, as well as the flexing in the load cells, was adding to the cause of the revolution speed fluctuation, the chain and sprockets drive-train was replaced with a gearbox and the bottom force-balance plate was fixed firmly to the carriage. Figure 4-11 provides the resulting revolution speed and torque values recorded at the same condition as in Figure 4-10 (profile B arms, 1.5 mIs). Much higher peaks were recorded with torque sensor and coupling attached directly in-line with the shaft, and though the revolution signal was much cleaner, fluctuations still occurred on the order of +1- 15-20% of the target value. Given the magnitude of these fluctuations (ie. from -60 Nm to 90 Nm at a frequency of 3 Hz for TSR=2.0), it is not surprising that these fluctuations occurred. Again, the maximum revolution speed peaks appeared closer to 90° where maximum torque was expected, and the subsequent torque peak appeared approximately 25° later.  96  — —  41)  —  —  CU  0  Runll RPM for Runl 11(62.6 avg) RunI 1 2-2.25tsr RPM for Runll2(70.5 avg) Runl 1 3-2SOtsr RPM for Runhl3(78.O avg) RunI 14-2.75tsr RPM for Runl 14  CU  41)  -o E  z 41) D  0  Figure 4-11: Torque (below) and RPM (above) vs. Revolution Angle for runs with gearbox drivetrain at 1.5 mIs.  Not surprisingly, the observed reduction in torque ripple when using ducting also corresponded to a reduction in revolution speed fluctuations.  Figure 4-12 provides  torque curves for the ducted turbine at 1.5 mIs, while Figure 4-13 provides revolution speed vs. revolution angle for the same runs. Worth noting are the way the revolution speed mimics the torque ripple at TSR=l .5, indicating that revolution and torque ripple are closely tied.  Secondly, it is interesting to note that the drop in torque ripple at  TSR=2.75 greatly reduces the revolution speed fluctuations (ie. from approximately +129% at TSR=2.5 to +1- 8% at TSR=2.75). Importantly, with the reduction in revolution speed fluctuations, the position of the peak also shifts back in revolution angle from 103° to 95°. It has been demonstrated that in the absence of external factors, an increase in TSR value shifts the torque peak to increasing angle of revolution; however, due to the reduction in torque speed fluctuations and revolution speed fluctuations, in this case the torque peak has shifted to the left with the increase in TSR. This is strong evidence that the revolution speed fluctuations are responsible for a phasing of the torque curve when comparing with numerical predictions, with the largest torque fluctuations leading to a peak phase shift of 20-25°.  97  E z 4’,  Theta (degrees) Figure 4-12: Torque vs. Revolution Angle for ducted device at 1.5 mIs.  I  Theta (degrees) Figure 4-13: RPM vs. Revolution Angle for ducted device at 1.5 mIs.  98  Additionally, with the revolution speed fluctuations, torque values observed will be less than the peak torques that would exist in a constant revolution speed system, as some of the torque will have gone into accelerating the turbine revolution speed.  4.2 Comparison with Numerical Predictions Below, an overview of the numerical model used for comparison to theory is provided. This is followed by a comparison of experimental and numerical Ck values and torque curves. 4.2.1 Numerical Model Overview The numerical model used for comparison to experimental results was developed by Nabavi [281 using the commercial RANS code FLUENT.  A two-dimensional,  incompressible, unsteady solver was used in conjunction with a Spalart-Alimaras turbulence model. An extensive examination into grid density was also conducted, and a fine structured grid around the blades contained within a sliding unstructured ring in way of the turbine blades was used (Figure 4-14). This combination of parameters provided the best compromise between accuracy, computational cost and reliability, though it still took upwards of two weeks to run a ducted turbine simulation. Lastly, domain size was also examined to ensure that the blockage ratio in the 2D simulations (same percent as 3D blockage in the experiments) was consistent with free-stream results. For the free stream device, this corresponded to 8% blockage, and for the ducted device this corresponded to 18%. Extensive discussion on the numerical model is beyond the scope of this thesis, and details may be found in the referenced document [28]. Figure 4-15 provides a sample output from a simulation highlighting velocity contours at a TSR=2 and free-stream velocity of 1 rn/s.  99  S  -.  C  S  C  C  C  S  ()  JI  4.2.2 Comparison of Results Firstly, given the 2-dimensional nature of the numerical models, arm effects were not simulated and must be extracted from the numerical results. Figure 4-16 provides the experimental Ck values obtained for tests with arm profile C without blades to examine power absorbed in the bearings and parasitic arm drag, which were subsequently added to the CFD simulation efficiencies for comparison with experimental data. Figure 4-17 and Figure 4-18 provide Ck vs. TSR comparing the numerical and experimental results for the free-stream and ducted device.  Ck values from the  experiments with only arms have been added to the numerically predicted Ck to facilitate comparison.  Error bars shown for the experimental tests are a combination of the  maximum 95% CI calculated from the standard deviations from the appropriate representative torque curve Section 4.1.1 plus the potential error due to the 1.5 Nm uncertainty from the torque sensor. It should be noted that this is likely an over-estimate of the error, as the maximum standard deviation for one location on the torque curve was assumed to be applied to the average torque for that condition. Errors on the Fluent prediction are from the 1.5 Nm uncertainty in the torque sensor when adding the experimental negative Ck due to the arms.  101  0.000 0. 0  0.50  1.00  -0.010  1.50  2.00  2.50  -  4 0.0362 —y.005x  0020  3.00  3.50  4. 0  0.086 0.091x + 0.0289 =1 2 R +  -  --0.030  .1.5mfs • 2 mIs  -0.040 C-)  -0.070  3 4 y=0.0051x + 0.1783-0.2822x÷0.1531 0.0512x 2 0.9997 R  -0.080 -0.090  TSR Figure 4-16: Experimental Ck vs. TSR for arm profile C at 1.5 and 2 ni/s.  0.50 Experimental 1 .5 rn/s —.—Fluent 1.5 mIs Experimental 2 m/s Fluent 2 rn/s  0.45  —.—  0.40 0.35 0.30  ——  .  —  .  1I  0.25  .[  I  2.75  3  0.20 ,7 0.15 0.10 0.05 0.00 1.5  1.75  2  2.25  2.5  3.25  TSR Figure 4-17: Ck vs. TSR for free-stream comparison of experimental and numerical results.  102  0.65  0.55  0.45 ZPementaI  0.35  0.25  0.15 0.05 0051 5  I  I  I  1.75  2  2.25  I  2.5  2.75  3  3.  TSR Figure 4-18: Ck vs. TSR for ducted comparison of experimental and numerical results at 1.5 mIs.  The figures above illustrate reasonable agreement between experimental performance and the numerical simulations. The discrepancies observed are likely due to a combination of both experimental and simulation errors. Experimental errors affecting the accuracy of the results are outlined in Section 4.3 below. Though a detailed discussion on potential sources of error in the simulations is beyond the scope of this report and is discussed in detail by Nabavi [28], factors to consider include: •  Turbulence modeling difficulties (including capturing dynamic stall)  •  2-dimensional simulations vs. 3-dimensional experiments  •  Inability to fully correct for lost power due to arms and bearings by subtracting results of tests without blades for Ck comparisons o Flow disturbance created by the arms reducing lift generated by the foils  103  o  Upon removing the blades, bolt heads and other attachment components creating drag also get removed  o  Lost lift on the blades in way of the arm attachments  •  Trailing edge of blades in experiments was cropped for manufacturing purposes  •  Truncation and round-off errors during simulation calculations  These same factors will also affect torque curve plots. Figure 4-19 and Figure 4-20 compare experimental torque curves (gearbox drive-train with arm profile C at ends only) with Fluent torque curves for the free-stream device.  As discussed above, the  experimental torque peaks are phased from the theoretical positions due to revolution speed variation. Fluent also predicts shorter, wider peaks, and the lashing in the coupling as the torque transitions through zero is visible in the experimental data.  200  150  1:0 [ExPerlmentl  Iso -50  100  1  200  • 300  350  4 0  1  -100  Revolution Angle Figure 4-19: Torque vs. Revolution Angle comparing free-stream experiments and Fluent at 1.5 mIs and TSR=2.  104  250  200  150 z -p  100  50  0  -50 Revolution Angle Figure 4-20: Torque vs. Revolution Angle comparing free-stream experiments and Fluent at 2 mIs and TSR=2.75  Comparing ducted experimental results to the simulations, Figure 4-21 (v=2 mis, TSR=2) again displays phasing between the expected torque peaks and experimental torque peaks, along with more extreme and narrower peaks. Figure 4-22 compares results for a TSR value of 2.75, which as demonstrated above provides a significant decrease in torque ripple and revolution speed fluctuations for the ducted case. Significantly, this decrease in torque ripple (which is also predicted numerically), and consequently revolution speed fluctuations, aligns the peaks of the two data sets very nicely. In this case, phasing is only approximately of 6° instead of the typical 200250 degrees. This confirms that the torque ripple and corresponding revolution speed fluctuations are the cause of the peak phasing.  Also interesting to note is that the predicted and experimental peaks have  similar shapes now that the torque curve does not pass through zero. This is indicative that the play in the coupling may be contributing to a backlash effect, leading to recording of higher and narrower peaks than what would be nominally occurring.  105  400  300  200  1  100  I  (I)  = aa 0  I—  1  0 150  I  I  I  100  200  0  (300  350  40  h1  k  100  ‘Expehmental’ —Fluent  -200  -300 Revolution Angle Figure 4-21: Torque vs. Revolution Angle for a ducted turbine at 2 mIs and TSR2.  100 •0%  90 80  70 j60 z 50 a. a40  I—.— Experimental I I—Fluent I I  \  1  30\j 20  /  10 0  0  50  I  I  I  I  100  150  200  250  300  350  400  Revolution Angle Figure 4-22: Torque vs. Revolution Angle for a ducted turbine at 1.5 mIs and TSR=2.75.  106  Lastly, Figure 4-23 compares drag force for the experiments and Fluent at 2mIs and TSR=2.75, with torque being displayed below. Given the number of assumptions in the procedure above for balancing moments to record drag and the assumed accuracy on the order of 20%, the results are in good agreement. The average predicted by Fluent is 1290 N, while the average from the experiments is 1325 N. Two significant factors that will raise both averages in the true application are as follows: The Fluent simulation does not include shaft drag (predicted to be approximately  •  155 N) •  When drag was being recorded, the turbine used arm configuration B at the quarter-chord positions, and hence more lift will be generated in an optimized design increasing the drag component on the turbine.  It is also significant that the drag peak position aligns well with both the theoretical torque peak, as well as the theoretical drag peak. This is correct given that at an angular position, drag reading will be independent of the torque reading, which is directly affected by the motor control and phased due to the fluctuating revolution speed.  2500  > 0  z 0  I  .2  ‘I7 500  z  j  /  0 50  100  150  200  250  300  350  4 0  -500  Revolution Angle Figure 4-23: Drag Force and Torque vs. Revolution Angle for free-stream Fluent and experiments at 2 mIs and TSR=2.75.  107  4.3 Sources of Error In addition to the revolution speed variation that appears to artificially phase the peak in the torque curves up to approximately 25°, additional sources of error include: •  Backlash in the flexible spider coupling used with the gearbox drive-train is potentially affecting the results in two ways: o When torque is transitioning through zero a “bucketing” is observed in the torque curve, which should have a much rounder profile. o When the play in the coupling re-engages, there is likely a “slamming” effect that creates a narrower torque curve than what would actually occur, with a larger maximum height.  •  Considering runs with the chains and sprockets drive train, inertial effects of the sprockets on the lay-shaft torque sensor appear to be dampening out the maximum and minimum torque values.  •  Free-surface interactions are an additional potential source of error. With the given time constraints and associated difficulty in producing a structure rigid enough to tow through the tank, the turbine was placed at a depth believed to be deep enough yet still facilitating the structural setup required.  After a few  seconds of spinning the turbine in a stationary position, disturbance was observed at the free surface; however, with the moving device the accumulation of vortices, and thus large interactions, would be minimized. Waves created by the shaft and surrounding frame as the device was being dragged may also potentially affect the results, though these small variations in pressure are expected to cause error of magnitude well below (if any at all) others identified in the system. Lastly, the comparative nature of these tests examines each parameter under equivalent conditions to observe its effect. •  Blockage of the tank must be considered when extrapolating the results to true free-stream conditions. This would most likely occur with the ducted device, given the 18% blockage of the cross-sectional area of the tank. 2-dimensional simulations revealed blockage should not have a large effect on the result [28]; however, predicted decreases in Ck of 18% and 11% for blockages of 17% and 7.5% respectively when moving to a free-stream condition were predicted by  108  Bahaj et al. [29] using actuator disk theory for a horizontal device without ducting. •  The angular encoder seemed to wander about  10  or 2° after each run. This is  believed to be due to skipping of increments, or truncation error upon digitalanalog signal conversion, but was easily managed by resetting the angular position and encoder before each run. •  The method of assuming a centre of force and balancing moments for drag force estimation could likely lead to errors on the order of +1- 20%. Additionally, initial readings on the load cells were tared out before each run; however, settling after the previous run led to variation in the initial readings, and if the force balance system settled in an odd manner this may also introduce error to the measurement. Given the large number of unknowns, one must consider a possible error as large as 25%, though 10% is likely more reasonable.  4.4 Sample Application From the findings above, it is possible to develop a sample device for the purpose of replacing diesel generators used to power remote communities.  Using dwelling and  power usage statistics from the B.C. Hydro Remote Community Electrification Program [30], a device capable of producing 257 000 kWh per year was targeted. At 15 000 kWh per year estimated usage per dwelling, this is sufficient for approximately 17 homes. Multiples of these units (ie. for 34, 51, and 68 homes) are consistent with the larger communities targeted for power generation by B.C. Hydro. A power coefficient of 0.45 was assumed using a ducted device with deflectors and is suitable for the purpose of this exercise. It is likely that a higher value may be achieved through further optimization of the duct and foil, though transmission losses must also be considered. Tidal data for Quatsino Narrows in Northern Vancouver Island was used to assess extractable power from the current. This is considered to be a moderate-high resource, and tidal data is provided in Figure 4-24. Power generation was assumed to begin at a current velocity of 1.5 mIs (minimal extraction is available below this speed),  109  and to cut off at current speeds greater than 3.84 m/s due to structural and cavitation limitations.  Generator selection has not been performed as part of this application  exercise.  8 6 4  0  a 4,  > -2 -4 .6 -8 Days Figure 4-24: Tidal current data.  The resulting rotor required was a 3.375m x 3.375m device assuming an aspect ratio of one, which is suitable for the forces anticipated.  Figure 4-25 illustrates the resulting  power output from the device as a function of current speed. Torque is also provided, and the dashed lines show maximum and minimum values due to torque fluctuations. Interestingly, maximum and minimum values are also provided for a free-stream device producing the same amount of power should ducting with deflectors not have been used. It is apparent that the resulting stress on the structure due to the large fluctuations would present a significant reliability obstacle.  Lastly, Figure 4-26 provides a sketch of a  representative configuration for the device to be moored offshore or in a river near the community. The nominal rating of the device at 2.5 m/s (a typical current speed for rating hydro current turbines) is 41 kW.  110  160000 140000 120000 100000  0  80000  0  60000 40000  I.  -20000 -40000  Current Speed (mis) Figure 4-25: Power and torque output.  Figure 4-26: Representative device configuration.  111  5 CONCLUSIONS AND RECOMMENDATIONS 5.1 Conclusions The research presented above details one of the few available experimental data sets and all associated setup information suitable for the validation of both a free-stream and ducted vertical axis hydro current turbine model. Building upon past NRC research identifying near optimum TSR and solidity ratios, an experimental turbine model (and all associated testing equipment and instrumentation) was built, commissioned, and tested in the UBC campus towing tank. In addition to obtaining repeatable experimental data for use in validating numerical codes, a parametric study was performed yielding baseline data on the effect of a number of parameters.  For a free-stream device with  span/diameter = 0.75, end plates were shown to increase the baseline Ck value by 16.6% through the reduction of tip losses for the tested aspect ratio. Additionally, changes in angles of attack between  30  and 5° were shown to increase the Ck value by over 21%.  Further testing of a 3-armed and 2-armed model allowed for the quantification of arm effects, as well as demonstrated an increase in Ck of 0.047 by applying cambered blades at  50  This yielded a theoretical maximum performance without tip losses of Ck0.412.  Accounting for further possible optimization of solidity, airfoil shape, and angle of attack, a theoretical maximum of Ck=0.45 in the absence of parasitic and tip losses is reasonable.  Application of a venturi-style duct increased power output by the rotor to a Ck value of 0.473 compared to 0.272 for the free-stream case; however, the power produced was 12% less than what may be expected from a free-stream rotor of cross-sectional area equivalent to the duct capture area. Significantly, the duct provided a decrease in peak torque values, as well as in torque fluctuation coefficient from 4.24 to 1.25, over the free stream case which is very important for cyclic loading considerations.  Subsequent duct  configuration changes, as provided in Table 5-1 below, led to an additional reduction in torque fluctuation coefficient. The optimal reduction was provided with two downstream deflectors, providing a Ck = 0.442 and a CTF = 0.47. 112  Table 5-1: Maximum Ck, percent change, and torque fluctuation coefficient.. Case Ck Value %Ck Change CTI  Free stream (basehne) No deflectors Downstream detiectors All four detlectors Spinning towards deflectors Spinning away from deflectors Upstream deflectors  0.272 0.473 0.442 0.393 0.426 0.442 0.407  --  73.9% 62.5% 44.5% 56.6% 62.5% 49.6%  4.24 1.25 0.47 1.4 1.17 1.23 2.67  A preliminary investigation into drag force on the turbine was also conducted, and an approximation for the drag coefficient (accounting only for forces parallel to the flow) was found to be [Cd = 0.41*tsr_ 0.16]. A primary source of error was the fluctuating revolution speed of the device caused by the large torque fluctuations involved; however, understanding of this error (up to 25° with the largest torque fluctuations down to only a few degrees for minimal fluctuations) renders the data presented suitable for validation of numerical models.  Such a  comparison was provided for both a free-stream and ducted numerical simulation created using a commercial RANS solver, and optimal correlation was obtained for the ducted comparison when reduced torque and revolution speed fluctuations were observed in the experimental results. Lastly, a sample case study was presented for a ducted 3 .375m diameter by 3.375m span rotor operating in Quatsino Narrows on Vancouver Island capable of powering approximately 17 homes.  5.2 Recommendations for Future Work Recommendations for tests conducted with the same or a similar setup are as follows: Application of a flywheel between the torque sensor and drive-train as a means to better regulate revolution speed control. Applying a flywheel connected by a shaft out of the top of the gearbox would allow for a variable revolution speed control by when adjusting the added weight, while still registering true torque values observed in the shaft.  113  •  Replacement of the flexible coupling with a universal joint without backlash, or an alternative coupling.  •  Use of a flume tank of suitable size and speed instead of a towing tank, as it would serve as a more reasonable facility for such turbine tests: o Allow for a more rigid, fixed structure o Permit longer run durations o Decrease testing time by not having to return to starting position o  Simplify installation and removal of turbine  In addition to recommendations for improving the experimental setup used above, general understanding of the model testing of vertical axis hyciro turbines may be greatly improved through the following: •  A study investigating how free-surface effects affect turbine performance. To do this, however, a deeper tank may be required so as to ensure interactions with the bottom of the tank are not a factor.  •  An examination into performance differences (if any) between operation in a flume tank vs. a towing tank, potentially due to differing pressure field development upstream of the turbine  •  A detailed investigation quantifying blockage effects on vertical axis turbine performance.  This may be most effectively performed in a flume tank by  reducing cross-sectional area through the addition of a series of false bottoms and walls. Alternatively, tests may also be conducted in tanks of varying dimensions. Key  factors suitable for experimental investigation and providing additional  understanding of turbine operation and quantification of loading design requirements include: •  The complex interactions between blade lift and drag, parasitic drag forces, and drag on the shaft should be investigated to resolve net force fluctuations and directions on the bearings. Given the difficulty in simulating blade arms due to the computational cost of a 3D model, this research is likely best suited to an  114  experimental study instrumented for measuring bearing forces in multiple directions. •  Detailed force data on an individual blade of a multi-blade device would be valuable for numerical model validation.  This may include the use of strain  gauges at the connection point between the arm and blade to resolve radial and tangential forces acting on the blade. The key challenge of such a study would be to get the low-signal strength data recorded using the underwater strain gauges synchronized with the revolution angle and transmitted to the stationary computer for analysis. Numerical models are an invaluable tool for optimization studies pertaining to the duct shape, foil shape, and solidity ratio, as well as for understanding cavitation inception. Such numerical optimization should be ongoing, with the current limiting factor being high computational costs coupled with the high monetary costs to meet them. Lastly, considering the device and its path towards commercial application, a number of factors require close examination and an exhaustive list is beyond the scope of this thesis; however, of primary significance from a hydrodynamics and mechanical engineering perspective are the requirement for: •  A detailed cost-benefit analysis assessing the use of ducting  •  A mooring investigation to best understand how to overcome the fluctuating loads and how to best assure device stability  •  Antifouling considerations to minimize performance reduction due to marine growth  •  A detailed examination of cavitation avoidance/management caused by the pressure fluctuations on the blades  115  REFERENCES [1]  Intergovernmental Panel on Climate Change Fourth Assessment Report, “Climate Change 2007: Synthesis Report Summary for Policy Makers.” Nov 2007. <http://www.ipcc.ch/>.  [2]  Rifkin, Jeremy. The Hydrogen Economy. Penguin Group Inc., New York, 2002.  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Jeffers “Ultra Low Head Hydroelectric Power Generation Using Ducted Vertical Axis Water Turbines.” Nova Energy Limited for NRC Hydraulics Laboratory NEL-02 1, March 1981.  [12]  Davis, B.V., D.H. Swan, and K.A. Jeffers. “Ultra Low Head Hydroelectric Power Generation Using Ducted Vertical Axis Water Turbines.” Nova Energy Limited for NRC Hydraulics Laboratory NEL-022, October 1983.  [13]  Davis, B.V., J.R. Farrell, D.H. Swan, and K.A. Jeffers. “Research and Development of a 50kW to 100kW Vertical Axis Hydro Turbine for a Restricted Flow Installation.” Nova Energy Limited for NRC Hydraulics Laboratory NEL 038, March 1984.  —  Tidal Current  116  [14]  Davis, B.V., D.H. Swan, and K.A. Jeffers. “The Ducted Vertical Axis Hydro Turbine for Large Scale Tidal Energy Applications.” Nova Energy Limited for H. A. Simmons NEL-070, March 1984.  [15]  Davis, B.V. and D.H. Swan. “Commissioning and Testing of a 100kW Vertical Axis Hydraulic Turbine.” Nova Energy Limited for NRC Hydraulics Laboratory NEL-081, December 1985.  [16]  Gorlov, A. M., “Tidal Energy.” Encyclopedia of Ocean Sciences, Academic Press, London, pp. 2955-2960, 2001.  [17]  Coiro, D.P., A. De Marco, F. Nicolosi, S. Melone, F. Montella. “Dynamic Behaviour of the Patented Kobold Tidal Current Turbine: Numerical and Experimental Aspects.” Acta Polytechnica Vol. 45 No. 3, pp. 77-84, 2005.  [18]  Guido, C., S. Francesco, L. Greco, A. Moroso, H. Eriksson. “An Experimental Investigation and a Theoretical and Computational Methodology to Study an Innovative Technology for Marine Current Exploitation: the Kobold Turbine.” Bolletino della Communita Scientifica in Australasia, December 2006.  [19]  “Cycloidal Tidal Power Generation Phase 2.” QinetiQ Ltd. for the Department of Trade and Industry Contract T/06/00229/00/REP/2, 2004.  [20]  Ponta, F. and P. Jacovkis. “Marine-Current Power Generation by DiffuserAugmented Floating Hydro-Turbines.” Renewable Energy, Elsevier, 2007, in press.  [21]  “Variable Pitch Foil Vertical Axis Tidal Turbine.” Edinburgh Designs Ltd. for the Department of Trade and Industry Contract T/06/00234/00/REP/2, March 2006.  [22]  Shiono, M, K. Suzuki, S. Kiho. “Output Characteristics of Darrieus Water Turbine with Helical Blades for Tidal Current Generation.” Proc. of the Twelfth International Offshore and Polar Engineering Conference, Kitakyushu, May 2002.  [23]  Taylor, Julian. “Crossflow Turbine Developments & Testing for Ultra-Low Head Hydro Applications.” Highquest Engineering Inc. DSS Contract File No.: 51SZ.23216-6-6156, Vancouver, Aug 1987.  [24]  Alidaadi, M. (private communication), 2007.  —  [25] McCroskey, W.J. “The Phenomenon of Dynamic Stall.” NASA Technical Memorandum B 1264, Moffett Field, Ca, March 1981.  117  [26]  Riley, Donald R. “Wind-Tunnel Investigation and Analysis of the Effects of End Plates of the Aerodynamic Characteristics of an Unswept Wing.” National Advisory Committee for Aeronautics Technical Note 2440, Aug 1951.  [27]  Klaptocz, V. (private communication), 2007.  [28]  Nabavi, Y. “Numerical Study of the Duct Shape Effect on the Perfonnance of a Ducted Vertical Axis Tidal Turbine.” MASc thesis, University of British Columbia, Vancouver, B.C., Canada, 2007.  [29]  Bahaj, A.S., A.F. Molland, J.R. Chaplin, and W.M.J. Batten. “Power and thrust measurements of marine current turbines under various hydrodynamic flow conditions in a cavitation tunnel and a towing tank.” Renewable Energy, Volume 32 Issue 3 pp. 407-426, March 2007.  [30]  B.C. Hydro (private communication), January 2008.  118  APPENDIX A: Design Calculations  119  SCALING AND CONSTANT DEFINITION The term prototype refers to the kill-scale unit. while model refers to the model being tested in the tank. Variable Scale Factor Prototype Diameter  Notation  Value  SF Up  22.214 20.32 66.66 10.16 33.33 1.52  m ft m ft m  S  ft  Prototype Radius  Rp  Prom Airfoil Chord Length  Lcp  Number of Bodes Blade ReightDlameter Prototype Span Length  Nb ltD Lap  Rhom Viscrn  0.91 3.001 0A6 1.50 0.069 2.701 0.656 2.25 8 1 .OOE-03  m Use Toos -> Goal Seek.... to sets rnodei diameter by changing SF or Up ft m ft m in m ft 3 kg!m kg/trn*a)  Am  0.63  Scp Rhop Viacp  Model Diameter  Urn Rm  Model Chord Length  Lcm  Model Span Length  Lent  Model Turtine Area Model Current Speed Model Cisrent Speed  Solidity Ratio Solidity Rato  Tip Speed Ratio lip Speed Ratio TipSpeedRatio  Scm = Scan =  (Based on value from NEL-002 p. 20)  m  Scp/agrtlSF) 2.00 6.56  SR = SR =  NbLOIR 0.45  TSR = TSR=  R*cdSc 2.25  nVaec nvseo Nseo  Prototype Tip Speed  RPMp = 6 Scp,1Rp2pi) t TSR 0 RPMp = 6.53 rev!min Omegap = 0.68 red/a TSp =  TSp = Model RPM  Model Tip Speed  RPMp 2 t ’PlQ’RpitSO 6.94 nfl  RPkti = TSRS2*pii))60 RPMm = revimin 93.97 Omega_m= 9.84 rad/a  TSm = TSm =  =Scp/SORT(SF)  where a = angus frequency ‘N:’kairLp:o3tdadeana lfeantnocebiadea.tl-ennuszciianoe. Eased on qn. p. 21 of NEL-002. Sets oplara TSR according to aodduty from NEL002  3  RPM and Tip Speed Prototype RPM  Scale factorto make Urn = 4 with Dp = 66.66 a 16.664 (To make Urn = 3.5, SF = 19.045) (To make Urn = 3, SF =22.214) (to chord line if symmetrical, else pivot point( <—  m ft knots m!aec kg& kgl(m’a)  Model Radius  Model Water Density Model Water Vacoeity  Conwnenta  3 0.75 15.24 50.0 6 3.09 1025 1 .OOE-03  Prototype Cuinent Speed Prototype Water DersJry Prototype Water ‘[racostly  Unit  rev!min  tWa  rev/mm  RPMm’2PlO’Rm/60 4.50 nfl  120  Reynolcfs Number Estimation Point in rotation Prototype Re:  Pr =  0  Rep Rep = =  Where:  Model Re:  deg  Vt’here 0 deg is ckectly into the cuirent (rotating cow).  Rliopwencp’Lqwiscp 1.567E÷07 Vencp a Vencp = Vencp=  Prototyçe encounter velocity TSp + Scpcos(Pr) ni/s 10.03 Wa  Ran, = Rem a  RhonrVencn’LcmMscm 4.460E÷0S  Where:  Vencm — Vencm = Vencrn=  Model encounter velocity iNs 6.50 iNs  TSm ÷ Scncos(Pr)  Stagnation Pressures (to aid with calculating required P range for transducers) Prototype Stagnation ft Pstsgp = o 1l2 V t encp2 p Re Pstagp= 5.16E÷04 Pa 7.6 psi Model Stagnation P:  Patagro Pstsgm  =  112*Rhon?VencnV2 2.IIE÷04 Pa  3.1  psi  121  (‘a  L’3  r-.r  -  -  -  0  c  a  I  0  0  a  0  j.j —  0  a t .. 0  000  PoP  ————oco. a cc cc cc —  —  .  —  In  a  3  C  iS a C  a  3  S  a  3  —  a  3 i1  a:= g  at  pp  a  a  .5  a  S  taa3a  *  U I  aa  a  a a a  a  5  0  m  C)  z r  5,  0  z  5,  0  0  m r  r  0  ‘1  MODEL DRAG FORCE ESTIMATION Model Chord Lrr Max ntrn Mode Arfoi Width Acojat Max Model Mrfoil W& Model Spar Length Carnage Sceet  Crag Coefficiem ororat shaft  Lcn Wan, kaam Lam  0066 210% O.044 OS.tf 0  m perert of thorO (p.72 NEL-002 for NACA 52.41-021 m rn  5cr. cc other  2000  rn’s  Cdsnat Cdshaft =  From te Wi,re 40! for Re> 10000 Assure LID vey large) 12  Drag on oensat shalt  =.SRhornscnArCsrtLaraftCceraft Lahaft 132n Dsht C.24826rn 1_9 in 152.7 N  Crag on Mounbng Ans  Cdshaft =  Drag on cenrat shalt  rag on amt  1.2  =0fRhorSert2’Camm’Larrn’Cdshaft Larrs= C0Q57n, Darn = 0.0254 n I in 07.1  Cranonairre:  Tha Drag #of tens CemtalSlsat 1 Mounting errs: 6 Net ES cireoton force (fror ‘o velocity arc MA)  N  1527 742 -1515.’  N N  six rms 1’3oorfl2igodraginfreestericondthon  2112 N 47&2tf  ITotauFvrce:  I  Alternate Dresawe-based scenato for deterninino &ao  -earl  Current Speed:  2 n*  020c3873fG8 m Turbine Area = 0.60  Fressr.re = rr,crngtHead  pressure is als V2’rho’W2)  G6 ?a Force Fvrce  P-essu-eWea  1252 N flit tf 126 kg  123  Angular Natural Frequency of Loaded Beams Reference: Saths. Peter. Wnd Fcrces in Erneerrg. Perganxri Press, Oxford. 1072. Angu ar Natural Freq.ency, o =  = =  YM  .,“scrifl1’I:M’ n;  coefildemfron reference ad1e Young’s MoöJus (Pa) 6.E+10  Shaft atr d ametr Shaft thicW’ess:  cd_shaft LShai  6.23 p. if?) E= 1.9 0.2  I= I= I=  Area rrcment ci tiertia of beam x-secocr ‘nj piC864:od_shaft’4- (co_shaft -2’t_shaft:rM: 1.63E.07 m 4  ln= ln  Length of bean, rn) 1.t2m  n  Mass perunit engthkg/m) Arex  lassurnedSiset)  Densty =  in in  &89E+10 Pa Mr Aiwniium (matweixcom) I.93E+11 Pa Mr 304 Stainless Steel 0.C4SD en 0.00508 en  ps:’:cd_shaft’2- (od_shaft -2’t_shaftr2) 14 0.000588 122 rn2 2700  Area’dersity 1.88 kgfm  For a fixed-free candlever  nocies 2 3 4  —  —  —  s  For a fixed-hinged cantilever  4 nodes 3  For a hlnged.hinged cantilever  c (ra&s) 221.4 1409.0 3881.1 76112 12580.5  Seq it-t: 35.2 224.3 617.7 1211.4 2002.3  2  a.  15.4 5 104 178  .7 3145.1 6541.9  Seq (1*) 1542 500.5 10412  2:2  11 VdO.( I (lOWS  1151.L? y’z3-I  9.87 30.5 88.9 158 247  a. 620.8 2484.7 5692.0 9038.6 15536.9  Seq (It) 98.8 3954 890.0 1581.8 2472$  3.52 22.4 61.7 121 200  4 nodes 1  —  2 3 4  5  124  Slit Exoon Due to blade pulsinw ItissafetassirethatthewahwJ eencapulseatarateoftherwinterciblaces’therpm, asanwtg a pdse occurs as a blade passes a specific port in the rotation. Pulse frequescy = = = =  model rpii • ntrtbw of blades RPf*n ‘Nb puls.esimin 281.9 4.70 It  Due to vorWx shecking on central shalt Ratio of staface 0 free stream velocty. a4tha ha = od_shatt2One_m f mha 0.119 for a stationay cylinder a be deemed ok  TIn ratio is so icw that the retadot Shaft Re)nolcfs flutter Res_n, = Resjn =  licm’Swt’c 98327  Shaft Sirotlral sitter  hat /Vscm tg(Res_m; 1.3  Sts_m =  Excitation Frequeroy = =  =  4.96  For use in table raenced below  {appr) Table p. 140 ‘Wet Forces in Enneedng by Saotrs. Peter. Vol.3 1972  San’Sts_m/ oti shaft 74.8 It  Ecitation Freouenoes: blade pulstig kiLn kline t ntex fldderg Panl Frnencies for  4.70 74.6  Hz It  flfli.LIw  4 nodes 1  2  tee ilti  35.2 224.3  Natal Frequencies for a 4Jjjp qjjj. 4 nooes tea Ha) 1542 1 500.6 2 Nafl Frequencies for a hinged-hinged oflever 4 nodes tsq lal 1 98.8 2 396.4  Slit Strength and De*ecfion od,aft L5h inc  0.0426 0S0508  m m  is? it 0.2 a  Lsthofteam{m 1.52 m Area torn of nets of beam xsecscn 4 1.63E.07m  Drag Fata  21112 N (from Drag Etnacsnwcataheetcle-caeescenaio)  125  With Bottani Locational Beaiing: CAsiaice between bangs U’S!:  iSchigley p. 071) 75 in t005 n  Cstarce from tçcerbearriglc force (AC):  55 hi 1.270 ii  Distance from krceie lower beaing (CS’.  25 hi 0.835 ‘i  A  —  Fa  SunFx0; Fa+FbF Sun Ma = 0; F’AC = Fb’AB Fb=  F’ACIAB 1408  Fa  F-Fe  Fa  IC 704.0  ShearFrjits:  F  N  FrcniA->C:  704.0  Frcn,C->B  -1407.9  Moment  Stress:  N  AtM  0  At C:  B4.O5 Nm  AtS:  0  4f’yil 0.00413 m 894.0  1.83E-O7mM  1  132E+08 Pa 132 MPa 1.62  Slress Stress = FoS =  Tensile Yield Stress is: Yield Stress for Aluminum Yield Stress for Stainless SteeL  215 MPa 276 ?4a 215 bPs  Dëeodons: E= I= Ft  1.93E÷11 Pa 1.63E47 mM 2ttE.03N  6.SSE+10 PaforAlLmilnum 1.93E+1t Pafor3o4Stalnless Steel  E  Ce’eotionfrona->a  (x hioreasflg ten B-> Candn’usibetween C and xrncter 0.554 m The = Ybc  F’AC’x O’E’ ‘AE:’(t2 + ADA2 ABA2) -0.0071 m -  Ce’aclion toniC A: (xnustbebetween 0.79 x incer -,  Yes = Yca  0.825  and  1.905  n)  m  F’BC’(I-x) I I6’E9’AS)’ (t2 + BC’2 -2’ABx) 4.0063 m  126  Cantilevered Desiwr (Schigley p 6tZ4: Cistance between berrgs (AS): siance fran lower beating to force (BCX  16  in  0.4572  ni  37 in 0.9306 in  Sun rxO: Fa+FFb Sun * = 0; Fs ?2 = FEC 3 P’BCAB  F; =  Fa  4341  N  Fb Fb  Fs4F 6453  N  1452l  PcrnA->B: FrcrnB->C: Fran C -> E’rc  Shear Force:  Mcment  A  0771bf  Pb  4341 N -2112 N 0.0  AIB: fttC:  lists 0.0  • C F  Sflsv 0.02413m 1984.8 Mi  1=  1.63E-C7ni’4  Stress = Stress = FoS =  2.04E+08 Pa 294 liPs  MacDeL E 1 SC = hr =  Tensite Yield Stress is:  0.73  215 liPs  Yield Stress for Alugnaim: Yield Stress for Stainless SteeL  276 ½)a 215 MPa  ;mnseb.ocrn)  =FBC)’2U6t9 •:BC-31n) Schçeyp.9 ¶cCE+11 Pa 6.89E+lOPaforAhminsn 1.83E-C7rtt4 6= l.93E÷11 Pafor30dStainlessSteel 00Q98 m 2111.0 N 1.52 miflthofbesnibnsbotanbeaing)’:letcniBbowid(  Max Deft.:  -0.038 in  Shaft Critical Speed  Distance beffisen berrgs (AS):  f&8 in 1.748n  Ciexcefrcnixcerbearrgiowl 1ACi  425 in  1.022  Distance fran iii  to cC  (CD)  —  in  13.5 in O.343n  Disance fran w2 to lower beai(ng (D0(:  A  wit  c  15Sf’ in 0.362  in  w2 Critical Speed (no adthtional weilt)  ongai  =  B  (pil)lerqht2 sz(E’T?n) Iengtft  1.743w  1.035+11 Pa 1.63E-0 in 4  =  m ngal oniegal  = =  1.Btce2Ooe3  420.02 radls 4011 ‘pm  127  00  [1  *  .  .•  .  1-:  —  :  J0O,,WI4—O-lt*W-&  i: 91  .  -4 0  • -.  0  -“4’4-.  G4  ‘  11  0  ‘pp.  —I  ..  *  .  ‘)--“  ii:  .  0  -4  .  0  a  -  a  i  C)  1  !.  3  h H  “  0  •  -j  n  C -l  C  0  AIRFOIL STRENGTH CALCULATIONS Mc0 8ar L-;th:  0335 rn 131311 332 b  351 0 3trjt xt 36r iJt  rtI:  Uel5ct Of .rtha: Uax’Y 0118995.:  114 93415  -.4 1.ZIE B 213  t’;  srt5 FDL:  Cisance ho— srrol ercs 10  25%  Idax Wons.nt for ;upport a lJ4 of the GØan 1ron the ends: 9ee l: CMI rre4Isls’j eIoeI 511515 r 14: Satettj Faotor:  A  J:  V/. ...-_,I  ‘1C.l  /1 ‘ -  293  —  4a  e  —.  \ *2%  —  r. r  \ 595%  Nm  6—37 5 9.92  ‘10%  1l:0  : :.: :  r0Itt 01 5(101 53511  0 3Cg 51101 0% 2% 4% 6% 5% ‘0%  5t  --  s8eofra— #oI ysfol fld ACA  348.13 11 1322 1011s  Cs rlSaJteS .ft :-‘so  312.1 ‘15 C  on 8is ste  ‘4% ‘3% 1% 20% 22% 34% 21% 23% 24% 30% 32% 34% 35% 33% 40% 42% 44% 46% 46% 50% 52% 54% 55% 55% 30% 52% 54% 31% 54% 70% 72% 74% 75% 79% 73% 50% 52% 64% 33% 95% 50% 92% 54% 94% 93% ‘00%  sIance A)0153 Fol r 0333 0.314 0227 0.341 0 333 0.359 0.252 0 385 0.112 0.323 0.13’ 0.131 0.133 0.171, 0.17S 0.132 0225 0.222 0:33 0.247 1231 0.274 0.265 0.322 0.315 0.323 0.343 OW’ 0.371 0.334 0.335 0312 0323 0435 0353 0433 0483 0.43’ 0.333 0.514 0.321 0.335 0343 0.552 0.373 C’.353 0334 0.517 0.531 0343 01.333 0.372 0.536  381111817348 14.1Y2i 003 35.37  ‘  7313 03.47 ‘21.33 ‘5-3.21 14.87 :10.94 237.31 25233 25C 33 3-1631 -325.62 -315.81 -242.35 -44.53 -237.11 -213.58 -134.37 -153.21 -131.35 -135.47 -73.12 -3174 -23.1’ 0103 2337 5274 7312 03.47 131.34 13621 33.57 210.35 237.31 25334 2!C.35 31531 -329.53 -31331 •293.05 -243.33 -237.31 -213.93 -133.37 -194.21 -131.34 -133.47 -79.12 -32.74 -23.37 0.00  MCrett N.’n1 2302 2.131 2.723 1325 2.338 £422 5.333 11.373 14.351 13.397 21.595 35.355 29.261 23.543 21.836 15.297 14.331 113’S 3.363 5.9’ 1 4.522 2-354 1.525 3.723 3.131 .3332 3.131 2.723 1.523 2.335 4.332 3.311 8.533 11.375 14.331 21 .335 23.343 25.251 24.345 21.333 11.33’ 14.351 11.376 3.363 5.311 2322 2.334 1.323 2.723 3.131 ‘3.333  129  End4apaflerl Faa: Max Mcrentlor e44 at06orted ze!m Max Mcre or cr4 onm (lax flt4tll c?Is rr’tlalfl tefl) Max SIrfS% r tar taf4 nolan  —  L4IWLSm,2I.sfl Lsm0.) 114 Nn -  1.224—35 3 225  Cicrçsfla[(%j 0% 2% 4% 4% 9%  14%  DflrcoPIan9Fo.IIcrl 0.333 0.314 o.rr 0,240 0.345 0.359 0.282 0.295  Mcmoi-t;Nri 0.033 443 17:54 24433 31213 40’344 47.753 54.432  22%  0.151  77.430  0.223 0247 0.240 0.274 0.225 022 0.318 0.329 0.333 0.357 0.373 0.354 0.395 0313 0325 0439 0353 0455 0453 0494 0.538 0.91’ 0.321 0.535 0.349 0.532 0,575 0.593 0.524 0.817 0.530 0.445 0,448 or: 0388  101 449 C4 132 ‘04.433 108.323 110.151 111.417 111321 111594 111345 111194 112321 111417 110.151 C1.523  10%  2  L//  ‘EE  .  Tt Cnt  I  34% 34% 34% 4C% 32% 44% 45% 44% 50%  54% 54% 54% 50% 52% 54% 55% 58% 70% 72% 74% 74% 75% 75% 80% 82% 84% 85% 88% 80% 52% 54% 54% 54% ‘00%  106433  04.152 101459 44494 54495 51.159 85493 94.794 81477 7741 71449 54.732 50.773 54442 47.753 40599 31253 24.433 17.154  4s53 0.032  130  VERTICAL LOWER BEARING SUPPORT CALCULATIONS Dragtoroecnrnode.  2112W 262 Sf E”sjre to ciarge wee1 on aag ‘:r ;treadnhee: rot ctezkir; :r’eert saee4s  Njntr of struts: 2 Force pernin.s dueto motel drag:  156.D N  Strtt argon: 77 In 1.956 m crorn bottom of suppcctng beam on sib-carrIage to plate with bearirgi Dstartce from bottom of st-carnage to water 19 In SLomerged length of tearng support ann: 56 In  Stppcc arm tinrerslons: rec1anguIartube’  Lergoli wIdth  —  —  Tnicsness  irerta— Speed: Reyndd Number  —  4 0.1:16 2 0.0606 0.1575 0.0046  1.473 rn ire. urtoe’water want iparailei to noel  In In In In In In  iperper4lcular to howl  1.75458E-06 n’4  2 rn/s 2.016—0!  Drag cc’ellclent otsupport arm:  9etererlce Area:  0.2 fora 2:1 eitpse ir tirtuien: tow rflrerce V4r:e p. 4.63  —urnoe’water span 0.150 n”2  length parallel to foe  Drag ne to a sngle tearmg support ann: Totat trag force on a  bearIng support arm:  Dl&ance to cewe otforce:  Maxlntrr Morrent  60 N  —Fccoe  II1C N  50.5 ir rouT appronlmallon: 1.25 m Distance to centre of’crce 1431 Mn  Maxlmur t—Myil &14EO7  MLrrinurn Yle.d Stress:  2.765—0! Pa  FoS = Yrnax — Ymax=  —F’dlstance to ftrct2 4.011601 Iii  rn;  dls1ance to force 3.IengthI :reference Sct-ley p. 960’; 5— 6.60’t-€1D PacrAlLmnun -  131  APPENDIX B: Component Drawings  132  Figure B-I: ¼ span rotor assembly.  A  Existinj hoIes—  l)  /  /  114-20 UNC -28 3 Places  -—-  ----  114-2OUNC-2B 3 Places  SECTION A-A  / / ,4_  A  MATERIAL: Stainless SteeI 440C  Typic& of all three )ocations  3.438 01.875  --  /  1.479  U  A  tlUliuliuiiAU bJlIlkutT ID Ut ii Ililliulil  IlUtitili UTCTiU.Wltli  UNLAtAL Td*Nl’tOLtAw.iHAVP*)A Ui  br 111 liLt PDWI.Oi. A11L(A  tn,thuu.LATIrW. .WUbLtliGld. Aatwr,l IC, lit  PUtUtCUL  rn  UBC  U, AarD AUUEDIDUT nil  bAT U ril tUtti U. UrCUC rib liRMeb SUDL bATK litPUXT.UCD C .‘TlU  CHt.lCtl) Ti  bArb  lAit UTFOU  iJAit fl1EI  ;RDU.l CJiWl’4ti”  002-012-ROl  c’t  UtDt SA.E  UtliUlitLU lii lti,ili  ‘•D  8  QTY: 1 Turbine Shaft  N  100  1?4-2OUNC-2B 3 Places  Add additional 9 threaded holes to existing shalt  Figure B-2: Main shaft.  I.247—  Eystiii hc4es—/  zzzzz-zzzzzzr zzzzzzzz ri [———a--  8  0  REVISIONS :1  MATERIAL: Alurninurn-6061  REVISIONS:J  A  A  1  -  T .975  or  Figure B-3: Upper bearing mount.  11151155551111115  bItASLI SflAIIPtiIZOVOIK*.V1W3.t 1W  L•1 I  114-20 UNC 2B.75 4 places  2.406 THRU 4 places  tHIthULU.0H!TV I flJtOLttIIU.  0.  -  QTY: 1  UBC  T  002-013-ROO  c  Turbine Top Bearing Support  SECTION A-A  0  MATERIAL: AIuniinurn-D61  REVISIONS:  A  OaI  n1tt4  Figure B-4: Lower bearing mount.  ZFNtt4J4 AL JHfAc;t5 ,L,tte,hW Wri  bIItA1 ..t PIAMI’ t LZV In &I*CIA. U’ hkIJ1ex,Cft4I4ttN  AI.r4rtk I)Pt INLt  75 R2.4  QTY: I  UBO  CAIt [alt  uAAVUt #t.It  cqtCKtt)$Y  002-1)14-ROD  CAre a3O,,a  o.aaht,ay rand  Turbine Bottom Bearing Support  SECTION A-A  THRU  ,rAeG8 4Aflefl IWUTVIZ pqC’dccn rc. In .rDd ,anDesr drI  • c 406 THRU $ places  80  85  MATERIAL: Aluminum-6061  REVISIONS:I  ci  U  —  lt.A  Afl.ItLJfiU. LIT[L Nit lUCII it  I-N:IIL,’4.L. :lpI,:UN  lute  N: I,WSUt1  tftItAilA$ ot4w e(Z8 tail! AI.J!*AL UI’ IIULII;ULJNCOUIUtY(  MLCt,4rtk lop:  IthPthL)L)J.MI1I  03500 THRU  Figure B-5: Lower bearing support plate.  ,rØ.4Q6THRU / 8 p’aces //‘  UNC-2B  UBC  “‘it  002-01 6-RUU  ,I:.lt  Turbine Bottom Plate  [.WAtt4tS  0n 175 —-—6.00  C)  QTY: I  C)  C) CC) ø C)  ft5” THK  0O  :1  MATERIAL: Aluniinum-6061  2  I  IlHtAtA;L StOOP tOIa.5 VattMWmoL Ut’ IlOflttt000tAUttN  *htLt,It. 012 t’tHtthItUI..AWi L I*W..LtUM. OOV 111 2.IL NTtI1Z 101St THLtI’ttI tY. 12L4l.  Ic4tN44:.t -  ED  El’)  ED  UBC  PfiCtvCDlt N. IStiOd 44n515 IdYll  lIt Its ,,.4 fl 1SStStt5 RotSsaenstLStTU NFl. 00514 11fl RI P1SI4OLI4FIM’)1OII POt 110 lOINS Ill  El  QTY: 2  El’)  MUON  SHEET  1  0 D  ‘1  LISlE ‘ICROEN  002-O’l 7ROO  UNSIN000T 111,1.10  tat  DC NOT SCH_E PRt,4 ERAWINO  Turbine Rectangular Support  ED  5-,  El’)  RECTANGULAR TUBE 4x2x01875 THK  Figure B-6: Vertical supports for lower bearing support plate.  This part formed the two large vertical suppofls position thg the lower bearing plate. The ends were faired with a pipe that was split and glued in place to create a rounded pmflle.  3.25  .75  REVISIONS  MATERIAL: Alunhinum-6061  REVISIONS:i  I  LI)  0  h  I  •  I  I  £ r  hNØlIIJI A. IJIFACIS IA 1*53 INC leA  fltAA A. I 114111 L.ZLt.A Vt In Afl*aA UI us C,IAWItN  All cenrtMlIo Is lILt IUI  TCltJC4’ltC  —  I  Q  8  UBC  1  1  002-O’19-ROO  CF  IAMC  QTY: 4 I ur1ne Angle Support  “V  .z 0.406 THRJ 4 Places  7.11 CR*lMUtdtAt MQKZIWOflJle 7513  -—----—-—  ———-—-——----———  CA  C)  C)  N-  Figure B-7: Angle bracket connecting vertical supports to bottom plate.  1.20—  .250—  .000—  2.000—  1250  .250—  .oc  8 0  ç  e  ,y)C4  L)  4  E  ç\ô  MATERIAL: Aluminuni-6061  REVISIONS:I  4)555411551.54  It.LTñ IH5VPLAt  55145555 ?LL AJITFACSS  flL*JL AL 5  TIZSMASLFTL  ‘19  .000  002-028-ROD  I  RHEET  1  ‘OTt  .1.1St  240154141  Strut Collar Top  U5SWI5PUT 145  505_F FROM OAAWI4IG  QTY3  ris 5.545.14mm. pLontTsanjrS 54.00 .01  Figure B-8: Top of shaft collar for mounting arms to main shaft.  SECTION A-A  I  I  A  -0.266 THRU \/ 531 X 82,O 0 Places FROM OTHER SIDE  /  /  r  0  E  C  ‘F 0  Z  4ANP t::aaW,rhA.,.W1A 0! ftACAtStW CACtJA  s*tAxa.  I.tNIthoatAHilV I MIMttIJ5U — III •:I. a:NTtK IOØt IHI.t LW Ca:. a: rICA  I. CIfl .anssoaw.I  1tttQQtI qv  c.  1  UU2-U)4’<UU  sOAtDuT —  Strut Collar Bottom  QTY 3  ASAa,.G4 .L.JCAI ,ra.TA..m.  219  ann  Figure B-9: Bottom of shaft collar for mounting arms to main shaft.  SECTION A-A  ½I 0  .266 V .800 _J 2.375 W .375 120 Apart  MATERIAL: Alurninum-6061  I  REVISIONS:  L’J  MATERAL Stainless SteeL 440C  REVISIONS:I  :  BOTH ENDS  KvF  =  PC9CCSK* WIfl#a*ta(r..7 AT.I  spar  !  U.3f5  1  002-041 -RaG  C  QTY: 3 FROM PROVIDED MATERIAL  .  N>  26.250—  Figure B-1O: 3/8” spar for foil assembly.  ;- 1.00  C 4 MAFtI  REV ISIONS:i  a  F —  =  —  = ———  .  -.  ftftftI- t.Ltz V. I 4ft.AL o.  PNCAuIAL. TLTMIA&.tS TACICINWI un  hfttI.A4  4L.t,4rtI’,  A-  ,: -  r..ftcsn.f,,rpIo,E.r.ru rEft  Sd1E  O.  Veil  lATe  UUt  —  L_QP2IQQ  1  UlhttLV  V.flt_KNL, ft I  Nt ft]l  DD NOT SDA..E aRDU  0.250 Spar  QTY: 3 FROM PROVIDED MATERIAL  —‘  -.—-i-.-t.  = =-=--==-==--—  Figure B-il: 1/4” spar for foil assembly.  i.  1.00  ==  BOTH ENDS  -  Figure B-12: ¼ span blade assembly as for arm profiles A and B.  a  2.28  H  Figure B-13: Arm profiles A and B with fairings.  0.38 —EEEE--H 1.00 H  Arm profile B  Arm profile A  U’  .43.8 I Iii  I  MATRLAL Aluniinum-6061  .000  REVISONS:I  II  II II  I  C)  RPHIlUM AL. S.IMI,_tS IUB&AAWALIN  UIItA k.L SflMI tLt,flT,, A*D.  II II  I I II  0Th’: 6  II II  ..cqccAr IA yfl. AGAIDJDAT A4Th1  1  C.It..AtIZ IA  0U2-03D-RUU  /  • .423  .577 • .500  4,  .438 •375 L—.000  Strut Mounting Block  I liii 11111  TO ,.,ang -..rwAtOA TOA WI MAXHA OT  I I II  Figure B-14: Arm block used for arm profiles A and B.  II  LI)  0  g  II  /,250’THRU  Figure B-15: 634-021 foil fabrication components.  .344 Countersunk to 0,313 deep  0.313 deep  —6 ends r’eqred c 2125 inches deep wiih cocinerbores  —  —Ahinun holes through unLess otherwise specified —30 ctIons qubed t 2125 Inch deep —6 secllons requh’ecl a± 0.375 Inches deep In w.y of’ rns  I 1 Is  RO 250 (TYP)  -_  4t . 0 90  i59 1*21 DRILL OR 10—22 UN (2 PLACES)  (COUNTERSUNk TO 0.0€23 OCEP) (2 P1_ACES)  ØO.251 (2 PLACES)  -1’  00-3’ #29 tRILL PU? 8—32 lIt  0938  F, -r  —s-Leiit attachMent botior’i plate —6 sections requIred at 0.1875 inches deep  I  1.125  0.302  Figure B-16: 634-021 foil fabrication clamping components for ¼ span configuration.  1.375  I I I 0,688  0363-  —1.425  1.627 Th.623  asia  —strut attachMent top plate —6 sections required at 0.1875 Inches deep  00  MATERIAL: Alumthurn-6061  0j2  N/ 0531 X 820n  c.266 THRU  REVISIONS:  2  Xr Ut  Ut  tililCUtI TUI*OIWCLUTS  51212U1 till CUOUTtN  UUtMlS.S llhLAIlItilCt V. ll!Ai’PltlL Ill,  lit trw tillS loUt lint Pus 101.  *hC1.t: lilt  Figure B-17: Circular end plates.  )  0.359 X 82.O  UBC  TO 1121111 241(1144111 P21 flIt 14044221  SHE(  1  end plate 2  litre 142._tIlS  UU3-entWlate2  QTY: 6  MATERIAL: 4Juminum-6O61  REV lSONS:  t*ItIlC)ft  UsfaJcA.a ,UUflIt UM COAWItN  •LL  U?,  HUt  “4OA.  Ut  Figure B-18: NACA 0012 profile end plates.  /  UBC  IMI.o4 NUDWS*L OCFT MC  CR$d*i S.MEI I.t If RCfXtCOC,! EL  ZI  CHt.Ktt) OH  UU3-end i-late  LAHTtUU_t.H  UAt ,U1.tUtH  DD P.T SDAI FCM CAWIN’  End Plate 1  0Th’ 6  /  ---  Figure B-19: Rotor assembly with arm profile C.  Figure B-20: Blade assembly with arm profile C.  8  0  MATERIAL: Aluniinurn-7075  188—  -43  REVISIONS:l  fl  /  QTY: 9  USC  A*%Gc. LRDV.aAE flKLPT QMPR( MG’CIorfl a thrfld I1UDtDT aStt,i  ND  ‘I  Ct  1  fitIt L”L,XtP  QO3-OO1-RO  UR4jl P14.41  L,.’t ,flI,;&W  SOA_E ROFA CRAWI4G L,ttItlKttllV ,ke  ‘4 LIlt  DO  StrLit Mounhng Block TnSm.aiM,. L fit Plotal. rurt r.,  THRU  Figure B-21: Block for attaching profile C arms to shaft collars.  tHIthLLJJ..AHIflbIfla.LEUKII. Ib’  N  &fl  0.250 2 PUces  MATERIAL: Aluniinurn-6061  REVISIONS:I  (.33)  JC,4L4tSN  Figure B-22: Profile C upper arm.  NAt  UBC  .‘I  )IAVtt)  1  Top Arm  Material Provided (NACA 0012 Extrusion)  4’/////////.2-  SECTION A-A  ///////////4  I  003-003-R02  OF  QTY: 3  .000  .425  1.050 925  MATERIAL: Aluminuni-6061  REVISIONS:  )J 33 (.  A  NAbIAAUk_,tAI4ttN  SECTION A-A  Figure B-23: Profile C central arm.  I  UBC  T.IACR*A.M!fl,tt*OttaT?  ar.  I  bAte 1  003-006-ROO  C  CIJ CRAWI4G  QTY: 3 Dt r1 5&.E  Centre Arm  Material Proic1ed (NACA 0012 Extrusioni  .00  øi5O  Ui UI  MATERIAL:  REVISIONS  :1  ,  II”  Pta,lU.MJIlI*::tpUtScI2iflt1  A.L 5tkP’ tO5 flIflAPPCS fl42LON OIAWtn  2 iIS4tIC  _z  UBC  Material Provided (NACA 0012 E:trusion)  ALLtZflttJWiIJbt IW*P(3SI IE*A  SECTION A-A  ‘<‘///////////1  Figure B-24: Profile C lower arm.  ‘0  i  Bottom Ann  • 05 • 00  1  003-004-ROD  0  QTY: 3  A  I  0.5o  II  Figure B-25: Replacement 634-021 central foil pieces for use with arm profile C.  0,750  3 tcb mounting pieces in woy oF centr1 or’m of non—ccribered foi’ shcpe’  (M  0.5679-s  0,2819  I’  0.677 0.673  0.37G 0  2.572  V \__t—  ‘—1.625  crt 25’ deep  L2’o 6.E56  Figure B-26: 634-421 cambered blade foil components.  3 mountIng pieces In way of central arm’  G  O.O454  8c i  00  C.) C  C  C C’,  C  C  -1  Ic  -<  APPENDIX C: INSTRUMENTATION AND DAQ COMPONENTS Instrumentation: • 2 of PT-Global SG-PT4000-500 lb s-type load cells  www.sensor-technik.co. ukldatasheets/pt4000. pdf •  Futek Torque Sensor, 0  -  369 ft lb, 0.2% accuracy, aluminum, 2mV/Voutput, 7”  length (TRS300)  http://www.futek. com/product.aspx?stock=FS HO I 992&acc2=acc •  Accu-Coder 776-B-S-2048-R-PP-E-P-A-N 1-7/8” through-bore encoder (2048 increments per revolution)  •  http://www.encoder.com/model776. html Extech 0 18 Volts DC, 3 Amps, 2 digital/four digit display power supply  •  BK Precision triple output 12V, 5V, and 0-30Volts DC, 5 Amp, 2 digital/three  -  digit display power supply •  BK Precision 0-18 Volts DC, 5 Amp programmable power supply with Labview RS232  •  U.S. Digital encoder digital-analog converter (used with encoder)  www.usdigital.com/products/edac/  Drive-train: • 3HP microMAX motor 182TCZ TEFC from Marathon Electric with Parker SSD AC 690+ vector drive controller and braking resistor kit (may be used for both  driving and braking turbine) (7/8” shaft; 230V, 4.6A, 5400 max. safe rpm) www.marathoneIectric.com/motors/docs/manuals/SB548. pdf www.ssddrives.com/usa/Resources/PDFs/Catalog/690%2OSeries%2OAC %2ODrives.pdf •  CONEX gearbox B091020.LAARJ, TEXTRON fluid and power. Ratio 20:1, SHC 634 lubrication, helicoidal gear geometry (used with gearbox coafiguration)  www.akrongear.com/docu ments/catalogs/textron/Series%20B%20232930503. pdf  159  Data Acquisition Hardware: •  1 cDAQ-9172 8-slot USB Chassis with rail mounting kit  •  http:Ilsine. ni .com/nips/cds/view/p/Iang/fr/nid/202545 1 NI 9205 32-Channel +1- 10V 250 ks/s 16-bit analog input module used with encoder and carriage speed  •  http://sine.ni.com/nips/cds/view/p/Iang/fr/nid/202571 1 NI 9237 4-Ch 50 ks/s per channel 24-bit analog input module used with torque sensor  http://sine. ni com/nips/cds/view/p/Iang/fr/nid/202632  160  APPENDIXD: RUN LOG  161  t%)  a a a a a a a in in in in in a o ia CO m in  a  a a a a a a a a in in in in in a in a o io Co  a a a a a N) N) N) N) a -I G% in a in a  i-  a  a a o  a a  a a a a  a a  o j o  a a  in  a a  a  a a  a  a a  a  a a  a a a o 0 0 U) a a 0 La CO -  a a  a a  a  a  0 0 0 0 0 a” in a in  a  a  0 o  a  0  0  a  L  a  a  0  it  a  a  a  a  in  in  a  in  a Lii  a  0 Lii Lii  a Lii  Lii  a  a a Lii  Lii  a  a  Lii  a  Lii  a  a  Lii  a  a  Lii  a  N)N)N)t’3  a  a  a  in in  a  in  a  in  a  N)  a  N)  a  N)  a  N)  a  a  a  a  N) N) N) N)  a  N)  a  a  M  N) a a a  a  a  a  a  a a  koóbbào boooooo oooooàb—,. 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437 100 432 2.2 5.47 2.50 235 6.01 636 !.00  1.50 1.50 150 150 130 1541 1.50 1.50 154) 1.50  v (mis)  —  —  ca  TSR  4dievtd Carditons Avg Torque otorqueM  Pawn  Cli  1.00 1.00 1.00 1.00 1.00 1.00 1.00  (rad/s) 323 1.47 51.1174 4.36 199 418 225 5.84 249 539 2.74 5.51 297  f?fraj 0.29 -016 -1.63 -2.91 -3.22 -2.16 -031  {radiaec) 5.82 636 735 8.78 9.80 10.71 1172  (W) 1.66 -5.39 -12.77 -23.58 -3137 -23.25 -3.68  -0.0053 0.0157 0.0605 0.0613 0.1003 0.0739 0.0117  4.20 1.25 4321.50 1.7 5.74 5.55 2.00 73322 5.20230 9.0223 9343.00 10.55 32 1141 330  1.50 1.50 154) 1.50 1.50 1.50 1.50 1.50 1.50 150  4.11 125 417148 5.66 3 6.54 139 7212.20 1.11 254 334273 1.14289 10.24 3.13 1132 3.51  0.21 -2.55 -457 -7.43 -913 -9.29 -630 -238 1.56 6.75  7.40 8.76 10.19 11.77 12.97 14.60 16.09 16.44 18.44 20.73  2.11 -12.58 46.63 -8738 -13434 -13559 -10137 -39.11 28.68 139.93  -0.0020 0.0212 0.0441 0.0833 0.1113 0.1214 0.0960 0.0371 -0.0272 -0.1327  1064 1065 1066 1067  1.75 1.75 1.75 1.73 1.75 1.75 1.75  5.74130 53013 1552.00 5.6122 9.57 2.50 10.53 2.7 1143 3.00  1.75 1.75 125 1.75 1.75 1.75 125  5301.49 6.55174 739199 1332.23 9.47 248 10.43 273 1138 298  -533 -7.62 -1255 -1435 -1324 -935 -4.27  10.27 1197 13.67 1536 17.05 18.77 20.48  -54.76 -91.18 -17153 -220.41 -224.07 -175.55 -87.47  1080 14111b 2*182b 1083 1084 1085 1086 1087  2.00 2.00 2.00 2.00 230 2.011 2.00 2.00  5.47 6-55 736 £75 9.34 1034 12.03 13.12  1. 2 I. 50 z; 7 2. DO I2 2.50 2. 3. DO  2.00 2.00 1.99 1.99 1.99 139 1.99 1.99  5.45 632 7.66 1.76 9.75 1034 1191 12.82  125 149 175 201 223 245 2.75 294  -1.97 -7.61 -1120 -1736 -1933 -17.36 -13.16 -1.57  9.81 11.73 13.79 15.77 17.54 19.32 21.44 23.08  1200 12.01 1202 1203 1204 1205 1206 1207  1.00 tAXI tAXI 1.00 1.00 1.00 1.00 1.00  2.73  6.55  1. 2 1. 50 1. 7 I DO 2. 2 I 50 2. 7 3.i DO  1.00 lix) 1.00 130 1.00 1.00 1.00 130  233 326 3.71 4.36 5.03 525 6.12 6.51  124 1.49 159 199 229 240 279 297  —  1.04 0.54 4.47 -1.99 -332 4.22 -2.87 -1.38  1280 1241 1242  1.50 1.50 150 1.50 130 1541 130 1.50 1.50 150  410 432 5.74 536 731 5.20 9.02 934 10.65 1143  12 1.50 1.7 100 22 250 23 100 52 3.50  1.50 1.50 1.50 130 150 1.50 1.50 130 1.50 1.50  4.09 431 5.63 632 7.07 1.11 134 9.63 10.45 1126  125 150 172 139 215 247 273 294 3.19 144  0.48 -1.34 -5.25 -7.96 -1133 -1123 -8.67 -5.01 4.93 3.77  —  -  1001 1002 1003 1004 1005 1006  :i: 1010 1042 1043 1044 1045  11 1047 1048 1049 1081  :i: 1063  :i.: 1244 1245 1245 1247 1245 1249  -  323 333 437 432 5.47  531  Or 0ta Initial load Mg 4mg  —  Cd  (t4) -6.95 -6.25 -3.56 -5.06 -5.96 -5.81 -6.60  (N) 25743 257.070.320 262.95 0.139 289.75 032 351.44 1. 36432 1164 402.41 1.284  311 -146 -4.71 -0.74 -613 -5.05 -4.56  247.lsa 351.02 0.498 459.28 0.65 461050.65 607.63036 699220.99 789.271.  0.0527 0.0545 0.1025 0.1311 0.1341 0.1051 0.0524  -710 -5.91 -631 -7.77 -627 -6.89 -612  467.72 0.487 489.9803 596360. 690.20031 76536 0.797 896.18 0334 1035.48 107  -19.31 -89.21 -153.09 -283.24 -346.03 -33911 -282.19 -3615  0.0077 00358 0t6 0.1142 0.1391 0.1367 0.1136 0.0145  4.99 -19.14 -17.45 -12.34 -15.19 434 -22.54 -22.06  68.59 690.26 758.00 808.61 928.89 931.18 1324.84 1-i 1558.44 1.  4.91 5.88 6.68 7.85 9.05 945 1101 11.72  520 3.18 -3.13 -15.60 -31.83 -39.91 -3156 -16.23  4.0162 4.0101 0.0099 0M95 0.1010 0.1266 0.1001 0.0515  -7.02 -6.80 -9.26 -7.74 -1.06 -7.94 -7.67  193.71 218.13 267.76 260.17 302.28 329.52 349.61  0.614 1 01.94 I 0.I5 0.8Y 1 0.96 1M1  7.35 834 1014 1173 12.73 14.60 16.10 17.34 16.80 20.27  333 -1.136 -5317 -93.44 -149.42 -164.05 -139.52 -8634 -17.43 7638  -0.0035 0.0112 0.0503 0.0884 01414 0.1553 0.1321 0.0823 0.0165 4.0724  -5.63 -7.00 -7.05 -732 -7.03 -6.48 -734  403.01 38353 425.77 486.53 560.49 636.23 740.01  0. 7 0.54 0. 0190 0394 0.902 1069  -  -  tILl! -  —  170  November 2006 runs Arm Profile ‘ chains and sprocket EWe-train. ninno  12160  Tirget Canditio’ is(rnhj ca TSR  v(rnh)  1.75 1.73 135 1.75 1.75 1.75 1.75 1.73  4.78 1.2 1741.50 6301. 2.00 5-6122 230 3 23 3.00  1.73 1.75 1.75  200 239 2.00 2.00 2.00 2.00 239 2.00 239’  5.47 12 8.55130 7.65 1. 5-73 2.00 9.84 2.2 10..94 2.50 120323 13.12 3.00 8.56  2.00 2.00 2.00 2.00 1.99 1.99 1.99 1.99  1348 1349  1.541 1.541 1.50 1.50 1.50’ 1.54) 1.54) 1.54) 1.50 1.50  4.10 432 5.74 6.56 738 8.20 9.02 9.84 10i65 11.48  1380 1381 1382 1383 1384 13.85 1326 1387  2.00 2.00’ 2.00 2.00 239’ 239 239 2.00  :i: 1262 ThE iii? ilil 12167 1280 1281 flfl 1283 1284 1285 1286 1288 ‘AcA 1340 1341 1342 1343 13.44 1345 1346  -ii:y  c  73W  AdiicMtd Cacidilicns AvgTarqwe otarrzeM  Pcwr  Ck  410 1.25 5191.49 6.65 1.74 199 8542.23 2.48 1138 2.59 2.98  -0.10 -2.88 -8.13 22.50 -16.93 28.80 -7.32 13.16  8.64 1023 1197  -0.14 -29.47 -9736  03905 0.0176 0.0582  15.37  -260.19  01556  20.48  -150.00  0.0698  £JAI  5.45 125 5.52149 7.66 1.75 8.19 1.88 9.83 2.23 10.64 2.44 11.232.5.8 1337 6.49 2.49  -2.14 -7.61 -12.24 -19.51 -2234 -1836 -1721 -6.14 -5-88  9.80 11.74 1178 2473 17.59 19.15 20.21 24.43 1169  -2100 -89.37 -168.62 -287.42 -405.90 -355.02 -347.82 -149.93 -80.37  03984 0.0358 0.0676 01154 0.1631 0.1459 0.1399 0.0606 0.0322  12 130 I. 2.00 22 250 2. 3.00 3.2 330  1.50 1.50 1.50 1.50 1.50 1.50 1.50 1.50 1.50 1.50  4.10 4.97 531 5-31 7.15 5-10 9.17 9.78 10.60 1144  125 152 174 192 2.18 2.47 2.80 2.99 123 149  1.10 4.66 -1.52 -5.15 -9.60 -10-66 -9.10 -163 -1.89 2.61  7.38 8.95 10.29 1135 12.87 2458 fl51 17.51 19.07 20.59  6.79 -5.93 -15.59 -58.52 -123.52 -155.51 -150.19 -99.08 -36.05 53.57  4.0085 0.0056 0.0147 0.0558 01169 0.1472 0.1423 0.0939 0.0342 4.0509  547 6.56 7.66 5-73 9.84 10.94 1203 13.12  1.2 130 17 2. 22 250 2. 3.00  2.00 2.00 2.00 2.00 2.00 1.99 1.99 139  5.45 653 710 5-74 934 1039 11.89 13.30  125 1.50 139 2.00 223 2.47 273 105  -0.54 -2.97 -7.80 -15.02 -2172 -2165 -1723 -9.43  9.81 1176 14.03 15.73 17.54 19.42 21.40 23.94  -5.30 -3433 -1.09.46 -23623 -380.97 -420.36 -558.75 -223.80  01)021 0.0140 0.0639 0.0949 01530 01689 0.1483 0.0908  1.00 139 139 1.00 1.00 139 1.00 1.00 1.00 1.00  273 3.28 3.13 437 432 5.47 6.01 6.56 7.21 7.65  12 150 1 2.00 22 250 2.7 3.00 32 3.50  1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00  2.67 109 177 4.39 4.90 544 6.01 653 7.11 7.66  In 14.1 172 200 224 248 274 298 125 150  1.37 0.46 0.40 4.63 -1.20 -0.34 032 1.75 338 628  4.81 5.56 6.79 7.89 8.82 9.79 1012 1176 12.80 1178  639 2.58 219 -4.98 -9.68 -3.32 332 2035 50.87 86.50  4.0209 4.0082 4.0085 0.0158 0.0307 0.0105 4.0112 4.0652. -0.1615 4.2746  1.75 1.75 1.75 1.75 1.75 1.75 1.75 1.75  4.78 5.74 6.70 7.66 8.51 8.61 937 10.53  1.2 1.50 1.7 2.00 22 2.23 230 2.7  1.75 1.75 1.75 1.75 1.75 1.75 1.75 1.75  4.66 3.68 6.62 7.56 730 8.44 930 1031  1.22 1.49 173 1.98 201 221 259 270  015 -3.07 -3.60 -750 -7.85 -7.75 4.29 -336  8.40 10.23 11.91 1161 1185 15.19 1712 18.56  129 -31.40 -4293 -102.07 -108.68 -117.71 -11209 -66.00  43908 0.0188 0.0257 0.0610 0.0650 0.0708 0.0571 0.0395  .  1.75 1.75  rr  Drag Data irñtiaIIcad Avg dra4  —  -14.86 -1641 -14.93 -16.95 -15.40 -15.12 -17.30  378.160.602 597370.623 639.71 0.666 7572.20.789 807.67 0141 930.94 0.969 1073.23 1.118  -7.24 -12.14 -1103 43.06 -13.57 -13.65 -1339  591.670.472 685.35 0.346 765.73 0.611 89737 .716 1004.41 0.849 1127.640199 1405.58 1121  —  0.. 1400  iIii 1402  Thi 1404 1405 1406 1407 1408 1409 1460 1461 1462 1463 1464 14Mb 1466  cii  171  August/September 2007 Tests  —  Free Stream, Gearbox Drive-train  rninnoTargetv Ccndhons w TSR (TWSI  Exp  I  nyc  .  Vt Nov20O6aems(ProfileB) IAoA=0 34-021 blades  Exp  2  End Plates NACA 0012 Nov2006atms (Profile B) AoA=0 63.4-021 blades  11  1.50  12  1.50  13 14 15 1! 17  1.50 1.50 1.50 1.50  3  Nov2006ms (Profile B) AoAO 63.4-021 blades  2.2!  2CC  9250  9.55  9.24  2.2!  924 9.24  2.2! 22! 2.52  9250 9180  9.71  2.00 2.00 2.00  iCC 2CC  931  22!  iCC 2CC 2CC  9170 12192 113.22  9.72 10.77 11.2!  40 41 42  1.50 1.50 1.50  43 44 45  1.50 1.50  4.10 4.92 5.74 6.66 7.38  1.2! 1.52 135 2.02 2.2!  1.50 1.50 1.50 1.50 1.50  1.50  8.20  2.50  1.50  429 4.92 513 6.54 7.3’ 8.14  46 47 43  1.50 1.50 1.50  9.22 9_4 10.56  2.7! 302 32!  1.50 1.50 1.50  39.10 47CC 64.70 5150 7040 77.60 25.70 93.30 101.22  go Cl @2  2.00 2.00 2.00 2.00 2.00 2.00 2.00 1.50 1.50 1.50 1.50 1.50 1.50 1.50 1.50 1.50  5.47 6.!€. 7.56 8.75 954 1034 1223 4.10 432  12! 1.5:  2.50 ICC  52.10 €2.70  1034 12.23  17!  2CC  7180  200 2CC 2CC  10.55  1.50 1.50 1.50 1.50 1.50 tSO 1.50 1.50 1.50  6150 9150 10252 1132D 3903 47,CC €4.80 5260 7030 77.90 2560 93.30 101.12  110  2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.20  5.47 6.56 7.56 8.75 9.54 10.94 12.23 5.47  125 1.50 17! 2.02 225 2.50 2.7! 12!  2CC 2CC 2CC 2CC 2CC iCC 2CC 2CC  €2.10 52.53 7250 62.70 92.50 122.70 112.9: €210  111 172 113 114  1.50 1.50 1.50 1.50  636 7.38 8.20 9.22  2.02 22! 2.52 2.7!  1.50 1.50 1.50 1.50  5260 70.50 75CC 55.50  115 110 117 118  2.00 2.00 2.00 2.00  835  2.00  9.54  22! 2.52  200 2CC 2CC 2CC  52.70 9290 10232 11310  80  81 82 83 84 85 ec 8e 100 101 102 103 10.1 106 106  Repeatwlo end plates  2.00  202 22! 2.50 2.75 12! 1.53 1.7! 202 22! 2.52 2.7! 302 325  87  Repeatwloendptaes  5.73 7.57 8.15 815 7.35 822 8.95  9.54  CC -  €470 7040 77.90 5560 7030 79.30 5560  2.00 2.00  @4 @5  End Plater Circular  2.53 23! 21! 252 2.7!  1.50 1.50 1.50 1.50 1.50 1.50 1.50  1.7!  22!  30 3 32 33 34 35  g3  Exp  1.50  (rad/s) 5.74 7.38 SiC 922 7.26 8.20 9.22  Achieved ccndi:ons v RPM w TSR I)  5.74 636  735 820 9.22  9.24  10.94 12.03  2.7!  iCC  Measured Data AvgTorque Power  273 224 253 273  1W) 3t55 113.31 131.91 102.09 114.64 127.14 106.31  0.032 0107 0125 0.10! 0.109 0.122 0102  227 222 222 222  33.95 35.10 3428 3317  322.59 34193  0.131 0.135  24!  32.45 24.32  [75 225  242  271 [2! 1.52 1.7! [33 225 245 273  331.22  0132  329.50 349.49 236.15  0 131 0.139 0.11!  -5.21 2!.14 35.24 63.59 124.82 14710 125.03 73.92  -0.02! 0024 0034 0062 0.115 0.140 0.119 0072  3.27  0.003 000! CiG4 005! 0.08! 0152 0155 0.129 -GODS 0024 0034 0.05€ 0112 2.13’ 0.113 0.052 -0031  9.77 10.59  235 3.23  -1.28 5.11 63! 9.72 1634 18.15 142! 757 0.29  5.4! 6.!€ 7.52 8.54  [2! [50 1.74 12.7 221 24! 271 [24 [50 1.74 200 224 242 273 235 3.23  2.42 15.61 19.12 2537 38.55 38.33 27.23 -uS 5.11 6.2! 9.02 16.14 17.79 13.29 5.4’ -3.22  13.20 101.79 145.59 222.50 375.13 39190 32223 -4.82 2514 3!.59  1.2! 1.50 1.74 [38 221 240 270 [2!  4.42 1135 152.2 22.76 33.53 3374 25.24 1.12  24.10 72.37 115.97 197.01 325.59 362.56 29526 6.11  230 225 242 274  6.37 152€ 16.68 12.33  54.84 113.34 13536 11173  138 222 24! 271  23.15 33.94 32.13 24.33  250.38 330.02 345.37 265.01  8.2’  9.5! 10’S II.!!  425 4.22 5.71 6.!! 735 8.1! 8.9€ 9.77 1O.!8 5.45 6.55 7.52 8.5€ 9.55 10.75 11.82 5.45 030 63!  7.35 8.15 8.92 0.20 8.5€ 9.72 10.75 11.54  Ck  ciern 5.55 15.37 1617 12.17 15.50 1531 11.56  112.76 145.25 119t7 53.42 -3170  172  0.010 0.031 0.055 0.079 0130 0.14! 0.119 0.002 !0PI10 0.052 0.107 0.128 0.10€ #DW’0 0.050 0132 0.136 0.115  August/September 2007 Tests 5” 1 WEx  4  I  :  Exp  5  NovemberArm £ On (BLADES REMOVED) Nov2006arrns(ProfiIeB) AoA=0 634-021 blades  -  A  Single Blade, B Arms  ov2006arms (Profile B) 4-021 blades  Ininnol 120 121 122 123 124 125 129 127 128 125 140 141 142 143 144 145 149 108 1’1 102 103 194 105 100 107 108 172 100 iti 182 183 184 185 las  —  Free Stream  v I w ITSRI v IRPMI w ITSRIAvciTornuelPowerI Ck 1.50 4.10 3910 128 1.50 4.09 1.25 -1146 -250 -0211 -15.75 4.92 1.50 1.50 2710 423 LEG -340 -0215 6.50 1.50 574 1.75 1.50 84.70 5.73 1.75 -4.16 -2152 -0.223 1.50 5.56 2.00 1.50 62.50 5.55 2C%Z -4.54 -30.40 -0229 1.50 7,36 7.35 225 1.50 70.50 225 -5.52 -41.47 -0:3; 1.50 5.20 5.21 2.50 1.50 75.40 2.50 -5.40 -52.52 -0.253 921 1.50 902 2.75 1.50 86.10 2.75 -719 -55.50 -0 253 1.50 9.84 320 1.50 93.90 913 3.02 -5.53 -54.52 -0.283 1.50 10.55 325 1.50 121.70 1054 124 -104.10 -9.78 -0395 1.50 3.42 1145. 3.50 1.50 18940 1145 -10.98 -125.73 -0119 200 #DPtO! 5.47 5.45 2.00 1.25 125 2.00 82.20 -4.25 -23.22 -0.209 2.00 5.36 1.50 2.00 52.50 5.54 LEG -5.15 -3319 -0.214 2.00 7.54 7.65 1.75 2.00 7330 1.75 -5.41 -4818 -0223 2.00 5.75 2.20 2.00 83.50 3.72 tOO -7.55 -56.70 -0.227 2.00 934 225 2.00 93.50 912 224 -915 -9013 -0.235 2.00 1094 242 2.50 2.00 124.20 1059 -10.5.3 -117.59 -0.247 2.00 2.78 2.00 114.50 1135. 2.74 12.33 -12.59 -150.58 -0.262 1.50 4.10 125 1.50 39.30 4.05 1.24 -2.57 -10.49 -0.213 4.92 1.50 1.50 47.30 422 LEG -0.59 -3.39 -0.203 1.50 5.74 1.50 1.75 1.50 5450 5.71 1.74 14.74 2.85 2014 1.50 6.35 2.20 1.50 6250 6.55 2.02 405 25.73 2.025 1.50 7.35 7.37 2.25 1.50 7040 225 6.25 35 75 2 037 1.50 5.20 5 15 242 2.50 1.50 75.20 6.85 69.95 2 056 1.50 902 2.78 1.50 8550 595 2.74 2.32 83.52 2279 1.50 9.84 93.50 2.79 320 1.50 298 585 85.90 2 052 1.50 1055 3.25 1.50 121.50 1052 7.64 81 15 3.24 2 077 1.50 5.15 2.42 6.47 S.20 2.50 1.50 75.20 62.33 2 056 200 #DPfl! 5.47 5.45 2.00 1.28 2.00 52.20 1.25 -2.16 -‘1.50 -0.205 2.00 5.85 1.50 2.00 52.50 5.85 150 235 2.15 2 001 2.00 7.65 1.78 2.00 72.90 7.63 1.74 42.35 585 2 017 2.00 5.70 5.75 220 2.00 8310 1.92 792 5285 2024 2.00 9.84 2.75 13.12 2.25 2.00 93.40 223 125.25 2 051 2.00 245 1014 2.50 2.00 123.70 10.55 15.32 17714 071 2.00 1225 2.75 2.00 i’SdO 11.57 2.71 1525 19229 2 077  InmnoI v NewArms: 3,OAoA= 0 7 Arns (profile C) oA = 0 1-021 blades Ifree-stream  201 202 203 284 209 287 293.1 294.1 293.2 294.2 2921 294.3 298.1 293.3 294.4  1.50 6.50 1.50 1.50 1.50 1.50 6.50 1.50 1.50 1.50 1.50 1.50 1.50 1.50 6.50  w ITSR v 4.92 1.50 1.50 5.86 220 1.50 7.35 2.25 1.50 5.20 2.50 1.50 9.84 320 1.50 11.48 3.50 1.50 7.35 2-25 1.50 5.20 2.50 1.50 735 2.25 1.50 6.20 2.50 1.50 5.35 2.20 1.50 5.20 2.50 1.50 2.78 1.50 202 7.35 225 1.50 520 2.50 1.50  IRPMI  w  2510 62.40 7050 7520 93.40 136.70 72.20 7540 7020 7730 52.40 75.50 85.50 7050 77.90  4.91 6.53 7.3€ 5.15 9.75 11.35 7.55 521 7.35 LIE 5.53 523 5.95 7.39 5.15 2.00  TSRAvgTorquePower Ck LEG 15.68 75.97 2.073 14051 1.92 21.55 2 133 2.24 30.60 225.16 2213 2.42 3375 275.78 3251 205 275.51 25.82 2 253 3.47 1720 195.59 3.158 230 29.19 220.59 3206 250 32.72 2.254 263.50 234 30.17 22118 2.209 2.42 33.01 269.1$ 2254 1.92 2129 139.25 3131 251 282.57 34.35 9.257 273 32.14 28712 2.272 29.47 217.77 225 3206 242 32.75 25727 2253 #D1V•0  173  ist /September 2007 Tests 211 212 2121 213 214 215 218 217 213.1 214.1 213.2 214.2 2143 2121 2144 215.1 213.3  214.5 215.5  Shaft Fairing 2007 Arms (profile C)  L0A =0 634-021 blades  tree-stream  txp  NewArms: 2 ONLY 2 arms only 2007 Arms (profile C) AoA = 0 634-021 blades  tree-stream  —  Free Stream  2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 200 2.00 200 2.00 200 200 2.00 2.00 2.00 2.00 200  656 6.75 6.75 84 10:34 12.03 1112 15.31 9.84 10.34 9.64 10.94 10:38 8.75 10.38 12.03 9.84 10.38 1203  1.50 200 2.00 2.25 2.50 2.75 3CC’ 3.50 2.50 2.25 2.50 2.50 200 2.50 2.75 2.25 2.50 2.75  2.00 2.00 2.00 2.00 2CC 2CC 2CC 2CC 2CC 2.00 2.00 2.00 2.00 2.00 2.00 200 2.00 2CC 2CC  62.50 82.70 82.80 92.70 102.92 11100  92CC 10320 92.90 103.20 10310 82.80 ICC.10 112.00 92.80 103.00 112.00  Irunnol  v  w  ITSRI  221 222 223 224 225 228 227 2241  1..50 ISO 1.50 1.50 1.50 1.50 1.50 1.50  4.92 5.56 7.38 8.20 9.02 9.84 11.48 8.20  1.50 2CC 225 250 2.75 ICC 3.50 2.50  1.50 1.50 1.50 1.50 1.50 1.50 1.50 10  47.10 62.50 70.30 77.90 85.80 93.30 106.70 77.90  231 232 233 234 235  2.00 2.00 200 2.00 200  5.56 815 9.84 10.34 12.03  1.50 2CC 225 2.50 2.75  2.00 200 2CC 2CC ICC  62.50 83.20 92.70 103.20 112.60  I  v IRPMI  Irunnol  v  w  ITSRI  v  241 242 243 244 245 248 247 243.1 244.1  1.50 1.50 150 1.50 150 1.50 1.50 tso ‘150  4.92 6.56 7.38 8.20 9.02 9.84 11.48 7.38 8.20  1.50 2CC 2.25 150 275 3.CC 150 225 250  1.50 1.50 1.50 1.50 1.50 1.50 1.50 1.50 1.50  46.10 6200 70.30 77.80 85.40 9320 106.50 70.20 77.80  251 252 253 254 255 253.1 2541  200 200 200 2S0 2.00 200 200  8.56 8.75 9.84 10.38 12.03 9.84 10.94  1.50 200 225 150 2.75 225 2.50  2.00 2.00 2.00 2CC 2CC 200 2.00  62.30 82.60 9290 104.00 113.30 9290 103.00  RPMI  8.54 6.66 6.67 9.70 10.77 11.72 0.00 0.00 9.89 10.80 9.72 10.80 10.80 6.67 10.79 11.82 9.71 10.78 11.72  w  1.50 1.98 1.98 222 2.46 2.88 0.50 0.00 222 247 222 247 247 1.98 2.47 270 222 246 288  56.26 8199 56.06 84.24 63.25 48.15 8417 61.49 56.09 6464 5934  184.21 367.67 399.95 54.2.29 604.79 700.31 0.00 0.00 535.59 891.19 545.30 693.89 663.20 399.95 692.47 728.62 544.81 585 700.31  ITSRlAvaTorciuelpowerl  4.93 8.54 7.36 8.15 8.98 9.77 11.38 8.15 0.00 8.54 8.71 9.70 10.80 11.81  w I 4.83 6.49 7.36 8.14 8.94 9.75 11.36 7.35 8.14 0.00 8.52 8.85 9.72 10.89 11.86 9.72 10.87  2818 44.9 46.15 66.51 64.51 59J4  1.50 1.99 224 249 274 298 3.47 249  11.44 19,11 28.55 31.08 30CC 24.8.5 14.92 30.41  56.40 125.01 210.07 253.41 289.41 24187 189.75 247.95  15) 1.99 222 247 270 TSR 1.47 1.98 224 248 272 297 3.46 224 248  28.19 41.79 5t94 63.81 57.85  171.33 383.92 503.95 689.25 683.35  1.49 1.98 222 249 271 222 249  AvgTorquePowerj 15.78 21.35 2993 33.27 35.25 3291 26.53 31.63 34.04  78.94 142.44 220.23 270.92 320.45 321.03 30128 232.40 277.19  3129 47.98 59.27 67.82 68.11 6327 69.30  294.89 414.84 578.31 73824 783.98 61521 753.63  174  0.073 0.155 0.159 0.219 0.277 0279 0.000 0.000 0214 0276 0217 0277 0272 0.159 0278 0.290 0.217 0276 0279  Ck 0.053 0.118 0.199 0239 0.255 0.229 0.180 0234 401 V0! 0.088 0.145 0201 0275 0.272  Ck 0.072 0.135 0.208 0256 ‘1303 0303 0285 0220 0282 $01 VOl 0.062 0.185 0230 0294 0.313 0245 0.300  August/September 2007 Tests runnol Cantered  Blade: MA =0  Arms (profile AoA =0 34-421 blades 2007  C)  free-stream  v  w  ITSRI  v  RPM  4.92 6.56 7.38 8.20 9.02 9.84 11.48  1.50 2.00 2.25 250 2.75 2.00 3.52  1.50  47.20  1.50  62.50  7.38  225  1.50 1.50 1.50 1.50 1.50 1.50  6.20  2.50  1.50  70.50 78.00 85.9C 93.40 !C€52 71.00 77.9C  1.50 2.00 2.25 2.50 2.75 2.25 250  301 302 303 304 305 306 307 324.1  2.00 5.56 2.00 6.75 9.84 2.00 2.00 1o34 2.00 12.03. 9.84 2.00 10.34 2.00 V j w 1.50 4.92 150 6.56 1.50 7.38 1.50 8.20 1.50 9.02 9.84 1.50 1.50 11.48 1.50 6.20  2CC 2CC 2CC 2.CC 2CC 2.CC 2CC V 1.50 1.50 1.50 1.50 1.50 1.50 1.50 1.50  311 312 313 314 315 314.1  2.00 2.00 200 2.00 2.00 2.00  341 342 343 344 345 348 347  1.50 tso 1.50 1.50 1.50 1.50 1.50  351 352 353 354 355  2.00 2.00 200 2.00 2.00  Irunnoi Bladr MA ‘  )7Arnis (profile C)  oA= 6 1-421 blades free-stream  — —  &  Free Stream  1.50  281 282 283 284 285 286 287 283.1 294.1 291 292 293 294 295 293.1 294.1  Cambered  —  1.50 1.50 1.50 1.50 1.50  1.50 iso 1.50  ITSRI 1.50 2.00 225 2.50 2.75 3CC 2.50 2.50  62.50 82.80 9210 103.00 113.10 92.70 ‘02.60  RpM 47.10 8240 70.20 77.90 85.60 93.30 108.50 77.80  w AvgTorquePower TSP 4.94 1.51 15.03 74.25 6.54 1.99 23.36 156.87 7.39 33.00 2.25 243.85 34.52 8.16 249 262.64 2.74 8.99 33.53 302.00 9.78 291.5 291.81 2.98 11.37 3.46 191 225.74 743 3201 2.27 245.31 2.49 34.72 6.15 263.09 0.00 5.54 1.52 31.50 20e06 8.87 1.98 5233 453.51 81.13 9.54 220 569.85 10.78 246 717.86 88.59 11.84 271 83.18 747.86 9.70 60.88 568.75 222 10.78 246 85.25 702.18 JJSF?J vg iorque vower 10.12 4929 4.93 1.52 1.99 24.53 11021 6.53 31.57 7.35 224 231.95 3817 8.15 318.93 249 37.84 8.96 273 337.23 34.00 9.77 298 332.02 3.46 11.3’S 2213 258.13 8.14 248 37.33 309.36  0.00  Inwno 3 New Arms Only  No blades  ice-stream  v  2CC 2.CC 2.CC 2.CC 2.00 2CC  4.92 6.56 7.38 6.20 9.02 9.84 11.48  1.50 2CC 225 250 275 2.50 ITSRI 1.50 200 225 2.50 2.75 3.00 320  1.50 1.50 1.50 1.50 1.50 1.50 1.50  60.10 84.40 9290 C3.10 “210 103.20 RPM 47.00 62.50 70.40 78.20 85.90 92.90 10920  6.66 8.76 9.84 10.94 1203  1.50 2.00 225 250 275  2CC 2CC 2CC 2CC 2CC  82.80 83.20 93.80 104.20 114.20  6.56 6.75 9.84 10.34 1203 10.34  I  w  v  I  6.29 6.83 9.72 10.79 11.79 10.80 w  4.92 6.54 7.37 8.18 6.99 9.83 11.43 0.00 6.66 8.71 9.82 10.91 11.35  I  1.44 202 222 247 269 247 TSR 1.52 1.99 225 249 274 3.00 3.48 1.50 1.99 224 249 273  I  Ck  0.070 0.148 0.230 0267 0265 0.278 0213 0232 0268 UDIV,’O! 0.062 0.181 0235 0268 0.298 0235 0260 i UK 0.047 0.151 0219 0299 0.319 0.314 0244 0.292 *0IV0! 28.50 17926 0.071 51CC 450.53 0.160 81.54 539.39 0239 891! 751.93 0.300 82.57 611.67 0.324 758.49 70.22 0.302 AvgTorquelPowerl Ck -3.40 -18.73 -0.016 4.22 -27.61 -0.026 4.39 -32.35 -0.031 -5.01 -4’ .01 -0.039 -5.55 -0.047 -49.90 -8.19 -10.84 -0.057 -7.38 -84.35 -0.080 #011/,0! 4.22 -27.85 -0.011 -5.47 47.63 -0.019 -5.49 -63.72 -0.025 -7.51 -61.91 -0.033 4.31 -93.33 -0.040  175  August/September 2007 Tests S.iflQ ‘ 5 lade arms profile C 1634-021 blade lee-stream  Free Stream  —  Irunnol  v  w  361 382 363 364 385 306  1.50 1.50  4.02 6.56 7.38  1.50 1.50 1.50  47.00 58.30 73.50  1.50 1.50  0.20 9.02 9.84  1.50 2.00 2.26 2.50 2.76 3.00  1.50 1.50 1.50  78.10 85.00 93.50  4.02 6.10 7.69 8.17 8.09 9.79  367  1.50  11.48  3.50  1.50  10883  11.39  368 369  1.50  7.38 820  2.25 2.50  1.50 1.50  70.43 78.20  371  2.00 2.00  6.56  1.50  2.00  62.50  7.37 8.18 0.00 6.54  8.76 9.84 1094  2.30 2.25 2.50 2.76 2.50  2.00 2.30 2.20  83.00 03.43 103.60 113.20 103.60  372 373 374 375 376  1.50 1.50  1.50  2.00 2.00 2.00 2.00  InnoI v Exp  F airing. One Blade  New Arms:3 A0A=0 634-021 blades free-stream  ITSRI v I RPM! w  12.03 10.94  w ITSRI  381 382  1.50 1.50  383  1.50  4.02 6.55 7.38  384  1.50  820  365 386  1.50  9.02 9.84 11.48 820  384.1  1.50 1.50 1.50  391 392 393 394 386  2.00 2.00 2.00 2.00 2.00  387  6.56 8.75 9.94 10.9k  12.03  2.00 2.00 v  RPM  1.50 2.00 225 2.50 2.75 2.30 2.50 2.50  1.50 1.50 1.50 1.50  47.00 52.50 70.40 7820 65.00 03.50 108.70 78.10  1.50 2.00 2.25 2.50 2.75  2.00 2.3C 2.30 2.30 2.30  62.60 82.00 03.42 103.63 11323  1.50 1.50 1.50 1.50  0.89 9.78 1Q54  I  11.65 10.63 w 4.02 6.54 7.37 8.18 0.99 9.80 11.38 8.17 0.00 5.55 8.80 9.78 10.64 11.88  TSR IAvgTorquelPowerl 1.50 1.66  2.34 2.49 2.74 2.98 3.47 2.25 2.49  2.86 8.56 11.97 16.38 17.82 19.17  187.50  18.09 11.02 15.01  206-DO 87.13 122.86  1.50  745  4814  1.99  15.82 24.12 27.50 29.63 27.06  135.78 235.70 298.20 351.37 302.80  2.23  2.48 2.71 2.48  Ck  14.01 62.23 91.32 125.72 180.22  0.013 0.049 0.986 0.119 0.151 0.177 0.195 0.382 0.116 #DIV:C! 0.019 0.064 0.394 0.119 0.140 0.121  TSR fAvgTorquePower 1.50 1.99  2.25 2.49  2.74 2.99  3.47 2.49 1.60 1.98  2.23 2.48 2.71  Ck  1.37 8.31 11.27 14.60 17.05 10.00 18.43 14.29  6.74 52.40 83.04 119.50  0.006 0.060 0.07-9 0.113  15320 185.16 209.58 116.81  0.145 0.175 0.198 0.113 #0MG!  3.30 14.41 22.83 2727 29.72  21.52 125.03 232.96 235.70 352.44  0.009 0.060 0.093 0.119 0.141  176  August/September 2007 Tests  —  Ducted, Gearbox drive-train Tpet  nirno  v  (mis) Ducts+4Bumns  i  Exp 16  PrafileCarms AoAO 634-021 blades  Duct 2bum ps ProflleCanns AoAO 634-021 blades Bump din. opposite turbine spinningtowards  400 401  1.60  RPM  w TSR (rads) 4.35 .91  402  1.60 1.60  ‘.7!  403  1.60  2.CC  1.52  404  1.60  2.22  1.53  6.24• 7.20  400  1.60  2.20  1.52  400 407 40*  1.60 1.60  tio  2.72 3cC 3-2!  1.52 1.52 1.13  403  1.60  230  410  1.60  3.?  431.1  1.60  *0  4n  1.60  4311 437.1  1.60 1.60  436.1  1.60  420  2.00  421 422 420  2.00  ‘.25 .W  1.24 1.53  Measured Data Power Ck  Torque (Nm)  tW  8.10 449  1712 42.77  2.C’0 2.040  70.02  2.C!  1.74  13.91  1.22  23.90  2.24  2&90  .5449  2.72  9.11  2.43  33.3€  23202  3.254  9.92 931 13.05  2.72 227 12*  4’.72 42.75 34.55  42025 41525 30045  2.443 2.253 2.341  1.50  11.31  2.49  2e.34  252.25  2.270  133  12.0-  3.63  :8.34  22713  2.2-9  *40  4.93  453  932  42.53  2.C41  230  1.53  6.54  1.32  22.20  4159  2.32  2.20  1.53  9.14  2.45  31.9C  29274  3.242  3CC 3.90  1.53  3.7C  43.30  42047  2.297  133  11.26  2.25 2.40  :6.14  294.73  2.290  ‘30 1.79 1CC  on  244  S-an  2.32  0.0-3  CCC  2.2CC  2.33 2.32 2.33  7.SC 9.72  0.03 1.74 1.29  44.73 53.25  CCC 34CC? 431 33  2.CCC 3.3€ 2.73  4  2.00 2.00 2.00  2.22  2.32  5C.  947  2.3  53.32  470.14  0.’90  425  2.00  190  233  109.7  II.’?  2.55  31.92  91205  2.304  420 429.1  2.00 2.00  172 2.72  2.33 2.33  112.7 12233  11.62 il.9C  2.73 2.73  3’.22 51.20  553.53 50413  2.250 2.290  440 441  .20 2.00  1.53 1.52  47.33 62.53  4.92 9.54  1.53 1.22  2.2.5  1.53  7043  7.37  2425 90C1 3.3C45  440  1.60  2.20  1.53  77.52  9.12  2.25 2.40  v.28 2942 I.26  2.C23 2.0  442  1.60 1.60 1.60  L4.90  20422  2.344  444  1.60  2.71  1.53  22.33  9.91  2.72  51.37  1.60  2CC  1.52  51.22  936  2.27  443  1.60  2.25  1.52  ‘CC.53  12.53  121  45.32 39.93  42227 421.12  2.434  442  405131  3.397  1.60  1.20 2.90  1.53 1.53  3*43  11.40  2.42  29.74  24007  3.322  77.53  9.11  2.4-0  46.30  270.73  2.350  1.60  72.; 23.3  2.2-9  2.425  490  2.00  .72  2.33  72.93  7.52  474  49.36  37032  2.’6C  431  zoo  2.33  23.32  9.95  1.29  57.33  49332  2.55  402  00  230 2.22  2.33  90.12  9.22  2.13  53.3  54171  2.224  2.90  2.33  12.22  13.74  2.45  50103  2.391  2.72  2.32  12.52  11.73  2.73  39.SC 93.36  ICC.74  3.433  1.0  37.1  4.91  1.53  9.54 7.24  jOtS 34.51  42.03 37.37  2.242  02.53 70.12  1.5-3 1.22 124  5.73  1.53  253.33  3.97 2.230  47.12 54.7’  27463  2.264  443.39  2.441  51.51  6CC 21  2.473  439?  401.72  zoo zoo  ‘rofile C arms AoAO 1-021 blades  Achieved conditions v mls) 1.53 t.50 1.53  443-1  Duct No Bumps  [TSR I  480  1.60  .20  431 432  ICC 2.2.2  483  1.60 1.60 1.60  2.20  1.52  72.32  7.95  142  484  1.60  2.72  1.53  5143  9.63  433  1.60  2.OC  1.53  02.33  932  1C3 2.25  1.60  1.22  1.53  l3.62  437  1.60  3.50  1.53  CC.52 -Cc522  11.33  12$ 145  1&.97  390.23  2.420 9.374  400.1  1.60  1.20  1.53  47.33  4.92  1.53  13.35  51.12  2.242  480  zoo  -.72  2.32  72.53  2.71  2CC  2.33  23.32  56.33 34.97  42703  2.00  7.05 9.73  1.74  481 402 433  2.00  233 233  1343 102.52  zoo  2.33  2.62  zoo  172  2.33  l243 112.53  723€ 37.20 96.97  2225 2.227 2.4’!  484  2.22 230 2.72  50325 609.21 1041.13 114133  2.62  59.95  1177.23  9.465  2.00  9.47 12.73 11.17 11.76  1.29 110 2.45  2.452  177  August/September 2007 Tests Ducted —  run no  v  TSR  v  RPM  w  TSR  Torque  Power  Ck  s_Direction wvemaker deck wavemaker  601  1.60  2.75  13  55.33  9.93  2.72  34.66  457.72  0.461  502  1.50  2.75  133  55.33  933  2.72  53.96  452.19  0.455  606  1.60  3.00’  1.53  22.33  9.2  49.32  454.15  0.455  504  1.80  3CC  133  52.03  9.72  2.34 2.35  47.9!  454.79  0.440  dock wavemaker  SIO  2.00  2.75  2.33  i2.53  11.72  2.73  193.25  15233  0.471  611  2.00  175  2.33  11243  11.77  2.53  99.95  116234  3.444  153  6253  654  02  21.56  .404  622  1.60  2.25  1.33  70.43  7.37  2.25  29.157  215.25  2.263  620  230  133  75.33  9.17  2.40  41765  33159  0.35  624  1.80 1.80  2.75  1.53  55.33  3.92  31.976  46233  3.435  624  140  3.00  1.53  22.33  9.72  40.12  465.13  0.442  624  1.60  3.30  1.43  0543  11.35  ‘.72 237 3.4!  :9.393  24033  3.322  537  1.60  171  133  53.23  3.33  2.72  5132  44735  0.442  604  2.00  2.50  2,33  102.53  1172  95424  9.267  2.00  2.75  2.33  112.53  11.72.  24.4 2.53  93.44  604  93.59  l0l37  0.425  544 541  130 1.60  .5C’ 2.C  1.53  0253  654  542  1.60  2.25  1.33  70.23  540  1.60  2.50  133  444  1.60  2.74  645  160  640 .547  Duct: 2 Bumps Downstream ProfileCarms oA=O 634-021 blades rur towards dock  Exp 22  Duct 2 Bwiips Upstream ProlIle C arms AoA=O 634-021 blades .....  towards wavemaker  Duct 2bwnps Profile C arms 0 4-021 blades ‘umps e diagonally app. turbine rotating away  aD  31.12  CCC’ 20401  .36  2.33 2.24  3.4.4.46  25122  0.235  77.33  B.3  2.4!  46.442  377.43  9.367  1.53  0113  9.9  2.72  41459  1252  300  1.33  02.73  97  2.34  L3 44.395  42043  0.407  1.60  330  133  C  11.24  3.45  27.734  31434  2.257  1.60  2.75  1.53  43.43  L9  2.72  4.!.51  433.23  0.404  604  2.00  2.50  233  102.33  1177  2.45  92.1!  55113  0.255  544  2.00  2.75  2.33  112.73  11.00  2.73  9197  1072.44  2.424  600  1.50 130  5C 2CC  133 1.53  47.9 42.33  4.94 655  1.01 2.34  27.92  -a:  5541 03  2.667 0.73  2.25  31.14  224.57  0.2’7  2.47  .44.6!  362.13  2.243  2.73 2.35  51.95  442.14  0.440  493  454 03  3.442  641  12.  3.52  602  1.80  2.2.5  133  70.43  604  1.60  2.54  1.53  77.53  7.37 3.12  604  1.60  2.75  1.33  24.33  936  604 644  1.80  3.00  1.53  02.53  9.65  1.60  2.50  133  1te73  11.36  3.47  31.154  25453  2.335  s,4.f  140  .75  133  4543  934  2.73  11.3!  45539  9.434  570  2.00  1.75  2.33  7233  7.62  .7S  64.052  40027  572  2.00  2.25  2.33  3743  9.15  2.03  ,53•95  652.01  ‘TO  2.00 2.00  2.30  2.33  ‘02.33  1:74  2.45  93.2!  67013  3.39.7  2.75  233  11253  II.?!  2.73  94.104  1110.33  3.443  (14  178  2.222  August/September 2007 Tests —Ducted Exp •25  Duct: Barge 1’  S C arms  =0 4-021 blades  Exp 26  Duct no bumps repeat Profile C arms AoA =0 634-021 blades  Exp 27  Duct wi shaft fairing  1 Profile C arms AoA=0 L021 blades  run no  v  TSR  600 601 602 603 604 605 606 604.1  1.50 1.50 1.50 1.50 1.50 1.50 1.50 1.50  1.50 2.00 2.25 250 2.75 3.00 3.50 2.75  v  RPM  w  TSR #0/V/OF 200 2.24 2.48 2.73 2.97 #DNiOI 2.72  1.50 1.50 1.50 1.50 1.50  62.60 70.20 77.60 85.40 92.90  1.50  85.30  0.00 6.56 7.35 8.13 834 9.73 0.00 8.93  Power  Ck  54.32  0.00 165.52 256.16 363.81 485.88 492.75 0.00 465.22  #0MG! 0.175 0.242 0.344 0.459 0.466 #DIVIO! 0.459  Toraue 28.3 34.845 44.77 54.33 50.65  620  1.50  1.50  0.00  #DIV/0!  621 622 623 624 625  1.50 1.50 1.50 1.50 1.50  2.00 2.25 2.50 2.75 3.00  1.50 1.50 1.50 1.50 1.50  62.50 70.40 77.60 85.30 92.90  6.54 7.37 8.13 8.93 9.73  1.99 2.25 248 272 2.97  29.695 33.9 47.862 53.92 50.776  194.35 249.92 368.94 481.65 493.97  0.184 0.236 0.368 0.455 0467  632 633 634  2.00 2.00 2.00  2.25 2.50 2.75  2.00 2.00 2.00  91.90 02.60 112.60  9.62 10.74 11.79  2.20 2.46 2.70  60.86 94.58 97.82  778.18 1016.19 1153.44  0.310 0.405 0.460  640 641 642 643 644 645 646 644.1  1.50 1.50 1.50 1.50 1.50 1.50 1.50 1.50  1.50 2.00 2.25 2.50 2.75 3.00 3.50 2.75  1.50 1.50 1.50 1.50 6.50  62.50 70.20 77.70 85.50 93.00  6.54 734 8.14 8.95 9.74  #0/V/OF 1.99 224 2.48 2.73 2.97  26.96 32.725 43.967 53.186 48.05  #0MG! 0.167 0.227 0.338 0450 0.442  1.50  85.40  8.94  2.73  52.752  0.00 176.58 240.23 357.75 476.20 467.96 0.00 471.76  652 653 654  2.00 2.00 2.00  2.25 2.50 2.75  2.00 2.00 2.00  90 102.2 112.5  9.42 10.70 11.79  2.15 245 270  66.472 91.06 104.24  626.48 974.56 1229.14  0.250 0.389 0.490  #0/ViOl  179  0.446  

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