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Numerical study of the duct shape effect on the performance of a ducted vertical axis tidal turbine Nabavi, Yasser 2008

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Numerical Study of the Duct Shape Effect on the Performanceof a Ducted Vertical AxisTidal TurbinebyYasser NabaviBASc., Amirkabir University of Technology (TehranPolytechnic), 2004A thesis submitted in partial fulfillment of the requirements forthe degree ofMaster of Applied ScienceinThe Faculty of Graduate Studies(Mechanical Engineering)THE UNIVERSITY OF BRITISH COLUMBIAApril 2008© Yasser Nabavi, 2008AB STRACTThe current research focused on the numerical modeling of a three-bladed vertical-axis tidal currentturbine using the commercial RANS code, FLUENT. A two-dimensional, incompressible, unsteady solverwas used for the simulations in conjunction with a Spalart-Ailmaras turbulence model. This approachproved to have satisfactory accuracy at a reasonable computational cost. The first phase of the researchfocused on simulating of a free-stream turbine for a range of current velocities and tip speed ratios. Thetorque and power generated by each blade was recorded as a function of azimuth angle and comparedto experimentally measured torque and power. The experiments were conducted in parallel to thenumerical work by the research group in the Naval Architecture Laboratory at the University of BritishColumbia.In the second phase of the research, a simple venturi-shape duct was placed around the turbine toaccelerate the flow and consequently increase the torque and power generated. Similar to the firstphase of the research, the results were validated against experimental values to obtain sufficientconfidence in the accuracy of the numerical model predictions.The last phase of the project focused on the optimization of the duct shape with the goal of increasingthe power generated by the turbine’s blades over a cycle. The strategy chosen to improve the ductshape was to keep a constant contraction ratio for the duct and to redirect the flow to achieve a properangle of attack for the airfoil, especially at the azimuth angles where the torque generated by the bladeswas low.TABLE OF CONTENTSABSTRACT iiTABLE OF CONTENTS iiiLISTOFTABLES vLIST OF FIGURES viLIST OF SYMBOLS, NOMENCLATURES, AND ABBREVIATIONS xivACKNOWLEDGEMENT xviii1. Introduction 11.1 Energy Crisisin the215tCentury 11.2 Renewable Energies 31.3 History and Forms of Tidal Energy 61.4 Modeling Approaches 91.4.1 Potential Flow Modeling 101.4.2 RANS Modeling 181.4.3 Experimental Approach 192. CFD Simulation of a Free-Stream Vertical Axis Tidal Turbine 212.1 Geometry definition 222.2 Grid Generation and Boundary Conditions 242.3 Domain Size Study 292.3.1 Domain Width Effect 312.3.2 Upstream Distance 322.3.3 Downstream Distance 332.4 Solver Specifications 332.5 Turbulence Modeling 373. CFD Simulation of a Ducted Vertical Axis Tidal Turbine 433.1 Grid Generation, Boundary Conditions and the Domain Size 443.2 Solver Specifications 463.3 Turbulence Modeling 474. Experimental Design and Analysis of BERT Turbine 48III4.1 Experimental Model .484.2 Testing Procedure and Methodology 515. Numerical Results and Post Processing Procedure 535.1 Free-stream Turbine Results and Analyses 565.2 Ducted Turbine Results and Analyses 686. Discussion 766.1 Arms Effect 776.2 Validation of Numerical Results 796.3 Sources of Discrepancy 857. Duct Shape Optimization 917.1 Preliminary Approach 917.2 Steady-State Study of Different Ducts 997.2.1 Methodology 997.2.2 Grid and Solver Specifications 1027.2.3 Examined Duct Configurations 1027.3 Unsteady Simulations of Various Duct Configurations 1258. Conclusion, Recommendations, and Future Work 1318.1 Conclusion 1318.2 Recommendations 1328.3 Future Work 134References 135ivLIST OF TABLESTable 1-1: Reports on experiments conducted by Barry Davis from Nova Energy in 1980’s 20Table 2-1: Simulation Plan for a free-stream three-bladed turbine 21Table 2-2: Geometric specifications of the turbine’s model 22Table 2-3: Grid densities used for grid refinement study 28Table 2-4: Results of the grid refinement study 29Table 2-5: Domain size study results 31Table 2-6: Under Relaxation Factors used for the simulations 34Table 3-1: Gird Refinement Study for a Ducted Turbine 45Table 5-1: Reynolds number changes as TSR and inlet velocity change 64Table 7-1: Duct with guiding vane configuration results 104Table 7-2: UBC duct modifications results 105Table 7-3: Bump configurations results 109Table 7-4: Double-Duct configuration results 117Table 7-5: Guiding vane concept results 120Table 8-1: Summary of the simulation results for different duct shapes 133VLIST OF FIGURESFigure 1-1: Global Carbon emission increase [1] 1Figure 1-2: Increasing demand for energy by region [2] 2Figure 1-3: Comparison of US renewable energy consumption and other sources of energy [5] 4Figure 1-4: Predicted electricity price by solar energy [6] 5Figure 1-5: NASDAQ stock price trend for SunPower Corporation [7] 5Figure 1-6: Wave energy devices (Courtesy of Pelamis Wave Power Ltd.) 6Figure 1-7: Rance 240 MW tidal power plant in France [9] 6Figure 1-8: Horizontal axis tidal turbine (Courtesy of Marine Current Turbine Ltd.) 7Figure 1-9: Vertical axis tidal turbine (Courtesy of Blue Energy Canada)7Figure 1-10: Tidal sites of Canada [12]9Figure 1-11: Aerodynamic model of a free-stream vertical axis turbine 10Figure 1-12: Single stream tube model [14] 12Figure 1-13: Multiple stream tube model [14] 12Figure 1-14: Double multiple stream tube model [14]12Figure 1-15: Blades are replaced with vortex filaments in vortex methods [14] 16Figure 1-16: Cascade Model approach [10] 17Figure 1-17: Upstream and downstream velocities in Cascade Model [10] 17Figure 2-1: Tow tank model 22Figure 2-2: Geometry of the physical domain including inlet, outlet, tow tank walls, blades, shaft, andinterfaces23Figure 2-3: Geometry of the blades, shaft, and interfaces23Figure 2-4: NACA 634-021 profile and coordinates 23Figure 2-5: Structured fine grid used around the blades25Figure 2-6: Turbulent boundary layer profile [37]26Figure 2-7: Structured fine grid around the shaft 27Figure 2-8: Unstructured grid of the domain 28Figure 2-9: Unstructured grid around the blades and the shaft 28Figure 2-10: Grid convergence results for a free-stream turbine at TSR=2.75 29Figure 2-11: Definition of 2D blockage ratio 30Figure 2-12: Definition of 3D blockage ratio 30viFigure 2-13: Domain width effect on the torque generated by the turbine 32Figure 2-14: The upstream distance effect on the torque generated by the turbine 33Figure 2-15: Sliding mesh scheme used for modeling the moving mesh 36Figure 2-16: Sliding mesh scheme concept 37Figure 2-17: Approaches to turbulent modeling [37] 38Figure 2-18: Comparison of the results obtained for different turbulence models 41Figure 2-19: Comparison of two available approaches to the near wall modeling [37] 42Figure 3-1: UBC duct dimensions (all dimensions are in metric) 43Figure 3-2: Interfaces in the ducted turbine configuration 44Figure 3-3: Duct and blade grid in ducted turbine configuration 44Figure 3-4: Grid convergence results for a ducted turbine at TSR=2.75 46Figure 4-1: Experimental model of the turbine tested at UBCtowtank 48Figure 4-2: Force balance assembly and data acquisition devices 49Figure 4-3: Testing carriage setup 50Figure 4-4: Experimental model of a ducted turbine 50Figure 4-5: Torque curve versus the azimuth angle for a typical run 52Figure 4-6: Averaging technique 52Figure 4-7: Averaged torque curve over a 360 degrees cycle 52Figure 5-1: Wake development as the turbine rotates 54Figure 5-2: Repeating torque curves at steady conditions 54Figure 5-3: Torque curve (3 blades);V=1.0 rn/s , TSR=2.00 56Figure 5-4: Torque curve (single blade);V=1.0 rn/s , TSR=2.00 56Figure 5-5: Torque curve (3 blades);V=1.0 rn/s , TSR=2.25 56Figure 5-6: Torque curve (single blade);V=1.0 rn/s , TSR=2.25 56Figure 5-7: Torque curve (3 blades);V=1.0 rn/s, TSR=2.50 57Figure 5-8: Torque curve (single blade);V=1.0 rn/s , TSR=2.50 57Figure 5-9: Torque curve (3 blades);V=1.0 rn/s , TSR=2.75 57Figure 5-10: Torque curve (single blade);V=1.0 rn/s , TSR=2.75 57Figure 5-11: Torque curve (3 blades);V=1.0 rn/s, TSR=3.00 57Figure 5-12: Torque curve (single blade);V=1.0 rn/s , TSR=3.00 57Figure 5-13: Velocity contours at V=1 m/s and TSR=2.00 59Figure 5-14: Velocity contours at V=1 rn/s and TSR=3.O0 59viiFigure 5-15: Efficiency curve for a free-stream turbine at V=1.0 rn/s 60Figure 5-16: Torque curve (3 blades);V=1.5 mis, TSR=2.00 61Figure 5-17: Torque curve (single blade);V=1.5 mis, TSR=2.00 61Figure 5-18: Torque curve (3 blades);V=1.5 mis, TSR=2.25 61Figure 5-19: Torque curve (single blade);V=1.5 rn/s , TSR=2.25 61Figure 5-20: Torque curve (3 blades);V=1.5 rn/s, TSR=2.50 61Figure 5-21: Torque curve (single blade);V=1.5 rn/s. TSR=2.50 61Figure 5-22: Torque curve (3 blades);V=1.5 rn/s, TSR=2.75 62Figure 5-23: Torque curve (single blade);V=1.5 rn/s , TSR=2.75 62Figure 5-24: Torque curve (3 blades);V=1.5 mis, TSR=3.00 62Figure 5-25: Torque curve (single blade);V=1.5 rn/s, TSR=3.00 62Figure 5-26: Efficiency curve for a free-stream turbine at V=1.5 rn/s 64• Figure 5-27: Torque curve (3 blades);V=2.0 rn/s, TSR=2.00 65Figure 5-28: Torque curve (single blade);V=2.0 mis, TSR=2.00 65Figure 5-29: Torque curve (3 blades);V=2.0 rn/s , TSR=2.25 65Figure 5-30: Torque curve (single blade);V=2.0 mis, TSR=2.25 65Figure 5-31: Torque curve (3 blades);V=2.0 rn/s , TSR=2.50 66Figure 5-32: Torque curve (single blade);V=2.0 mis, TSR=2.50 66Figure 5-33: Torque curve (3 blades);V=2.0 rn/s , TSR=2.75 66Figure 5-34: Torque curve (single blade);V=2.0 rn/s , TSR=2.75 66Figure 5-35: Torque curve (3 blades); V=2.0 rn/s , TSR=3.00 66Figure 5-36: Torque curve (single blade);V=2.0 mis, TSR=3.00 66Figure 5-37: Efficiency curve for inlet velocity of 2.0 m/s 67Figure 5-38: Cornparison of efficiency for free-stream turbine at different current velocities67Figure 5-39: Torque curve (3 blades); V=1.5 mis, TSR=2.00 68Figure 5-40: Torque curve (single blade);V=1.5 rn/s. TSR=2.00 68Figure 5-41: Torque curve (3 blades);V=1.5 mis, TSR=2.25 68Figure 5-42: Torque curve (single blade);V=1.5 m/s , TSR=2.25 68Figure 5-43: Torque curve (3 blades);V=1.5 rn/s , TSR=2.50 69Figure 5-44: Torque curve (single blade);V=1.5 rn/s , TSR=250 69Figure 5-45: Torque curve (3 blades); V=1.5 rn/s, TSR=2.75 69Figure 5-46: Torque curve (single blade);V=1.5 rn/s , TSR=2.75 69viiiFigure 5-47: Torque curve (3 blades);V=1.5 mis, TSR=3.00 69Figure 5-48: Torque curve (single blade);V=1.5 mis, TSR=3.00 69Figure 5-49: Efficiency curve for a ducted turbine at V=1.5 rn/s 70Figure 5-50: Velocity contours at TSR=2.00 71Figure 5-51: Velocity contours at TSR=3.00 72Figure 5-52: Blade’s angle of attack calculation for a free-stream turbine 72Figure 5-53: Blade’s angle of attack calculation for a ducted turbine 72Figure 5-54: Torque curve (3 blades);V=2.0 mis, TSR=2.00 73Figure 5-55: Torque curve (single blade);V=2.0 mis, TSR=2.00 73Figure 5-56: Torque curve (3 blades);V=2.0 mis, TSR=2.25 74Figure 5-57: Torque curve (single blade);V=2.0 m/s , TSR=2.25 74Figure 5-58: Torque curve (3 blades);V=2.0 mis, TSR=2.50 74Figure 5-59: Torque curve (single blade);V=2.0 rn/s , TSR=2.50 74Figure 5-60: Torque curve (3 blades);V=2.0 mis, TSR=2.75 74Figure 5-61: Torque curve (single blade);V=2.0 m/s , TSR=2.75 74Figure 5-62: Torque curve (3 blades); V=2.0 mis, TSR=3.00 75Figure 5-63: Torque curve (single blade);V=2.0 rn/s , TSR=3.00 75Figure 5-64: Efficiency curve for a ducted turbine at V=2.0 m/s 75Figure 6-1: Arms-Shaft connections 76Figure 6-2: Arm-Blade connection 76Figure 6-3: Arms’ parasitic drag experimental model 78Figure 6-4: Comparison of the efficiency curve with and without the arms effect (V=1.5 mis) 79Figure 6-5: Comparison of numerical and experimental efficiencies for a free stream turbine at V=1.5mis 80Figure 6-6: Comparison of numerical and experimental efficiencies for a free stream turbine at V=2.0mis 80Figure 6-7: 3-Arm configuration 81Figure 6-8: Arm-blade connection at the blade’s tip 81Figure 6-9: Comparison of numerical and experimental efficiencies for a ducted turbine at V=1.5 m/s..82Figure 6-10: Comparison of numerical and experimental efficiencies for a ducted turbine at V=2.0 rn/s 83Figure 6-11: Comparison of experimental and numerical free-stream turbine torque at V=1.5 TSR=2.0084Figure 6-12: Comparison of experimental and numerical free-stream turbine torque at V=2.0 TSR=2.7584ixFigure 6-13: Comparison of experimental and numerical ducted turbine torque at V=1.5 TSR=2.75 84Figure 6-14: Comparison of experinental and numerical ducted turbine torque at V=2.0 TSR=2.00 84Figure 6-15: Comparison of 3-blade torque obtained from FLUENT, DVM, and Experiments (V=1.5,TSR=2.50) 85Figure 6-16: Comparison of single-blade torque obtained from FLUENT, DVM, and Experiments (V=1.5,TSR=2.50) 85Figure 6-17: RPM fluctuations in experiments 88Figure 6-18: Free surface disturbance at lower velocities 89Figure 6-19: Free surface disturbance at higher velocities 89Figure 6-20: Experimental torque variations 89Figure 6-21: Comparison of free-stream results from FLUENT and experiments including the error bars9oFigure 7-1: Single-blade torque curve over a cycle in the presence of the other two blades 91Figure 7-2: UBC duct with a hollow in the middle (mod 1) 93Figure 7-3: A duct with straight line connecting edges (mod 2) 94Figure 7-4: A duct with concave connecting edges (mod 3) 94Figure 7-5: Efficiency comparison of different modifications of UBC duct 95Figure 7-6: 3-Blade torque comparison of three UBC duct modifications (V=1.5 m/s; TSR=2.00) 96Figure 7-7: Single-Blade torque comparison of three UBC duct modifications (V=1.5 rn/s;TSR=2.00) ....96Figure 7-8: 3-Blade torque cornparison of three UBC duct modifications (V=1.5 rn/s;TSR=2.25) 97Figure 7-9: Single-Blade torque comparison of three UBC duct modifications (V=1.5 rn/s;TSR=2.25) ....97Figure 7-10: 3-Blade torque comparison of three UBC duct rnodifications (V=1.5 rn/s;TSR=2.50) 97Figure 7-11: Single-Blade torque comparison of three UBC duct modifications (V=1.5 rn/s;TSR=2.50) .. 97Figure 7-12: 3-Blade torque comparison of three UBC duct modifications (V=1.5 rn/s;TSR=2.75) 97Figure 7-13: Single-Blade torque comparison of three UBC duct modifications (V=1.5rn/s;TSR=2.75) .. 97Figure 7-14: 3-Blade torque comparison of three UBC duct modifications (V=1.5 rn/s;TSR=3.00) 98Figure 7-15: Single-Blade torque comparison of three UBC duct modifications (V=1.5 rn/s; TSR=3.00) .. 98Figure 7-16: Typical single-blade torque comparison for UBC duct and it s modifications (V=1.5 rn/s;TSR=2.50) 99Figure 7-17: Design box concept 100Figure 7-18: Measured flow pararneters for comparison of different ducts 101Figure 7-19: Velocity contours for the UBC duct as the reference 103Figure 7-20: YV1 (Guiding vanes at 15 degrees AOA) 104xFigure 7-21: YV2 (Guidingvanes at 5 degrees AQA) 104Figure 7-22: YV3 (Guiding vanes at 5 degrees angle of attack and with a rounded trailing edge) 104Figure 7-23: Velocity angle distribution for guiding vane configurations 105Figure 7-24: YV4 velocity contours 107Figure 7-25: YV5 velocity contours 107Figure 7-26: YV6 velocity contours 107Figure 7-27: YV7 velocity contours 107Figure 7-28: YV8 velocity contours 107Figure 7-29: Velocity angle distribution for UBC duct modifications 108Figure 7-30: Comparison of velocity magnitude distribution over the blades’ path for UBC and YV1Oducts 110Figure 7-31: Comparison of velocity angle distribution over the bladesT path for UBC and YV1O ducts .110Figure 7-32: Comparison of velocity magnitude distribution over the blades’ path for YV1O and YV11ducts 110Figure 7-33:Comparison of velocity angle distribution over the blades’ path for YV1O and YV11 ducts. 110Figure 7-34: Comparison of velocity magnitude distribution over the blades’ path for YV11 and YV12ducts 111Figure 7-35: Comparison of velocity angle distribution over the blades’ path for YV11 and YV12 ducts 111Figure 7-36: Comparison of velocity magnitude distribution over the blades’ path for YV11 and YV13ducts 112Figure 7-37 Comparison of velocity angle distribution over the blades’ path for YV11 and YV13 ducts 112Figure 7-38: Velocity angles contours for the four-bump configuration (Duct YV13) 112Figure 7-39: Comparison of velocity magnitude distribution over the blades’ path for YV14, YV15, andYV16 ducts 113Figure 7-40: Comparison of velocity angle distribution over the blades’ path for YV14, YV1S, and YV16ducts 113Figure 7-41: Comparison of velocity magnitude distribution over the blades’ path for YV17 and W18ducts 113Figure 7-42: Comparison of velocity angle distribution over the blades’ path for YV17 and YV18 ducts 113Figure 7-43: Comparison of velocity magnitude distribution over the blades’ path for YV19 and YV2Oducts 114Figure 7-44: Comparison of velocity angle distribution over the blades’ path for YV19 and W20 ducts 114xiFigure 7-45: YV9 velocity contours.115Figure 7-46: YV1O velocity contours 115Figure 7-47: YV11 velocity contours 115Figure 7-48: YV12 velocity contours 115Figure 7-49: YV13 velocity contours 115Figure 7-50: YV14 velocity contours 115Figure 7-51: YV15 velocity contours 115Figure 7-52: YV16 velocity contours 115Figure 7-53: YV17 velocity contours 116Figure 7-54: YV18 velocity contours 116Figure 7-55: YV19 velocity contours 116Figure 7-56: YV2O velocity contours 116Figure 7-57: Comparison of velocity magnitude distribution over the blades’ path for YV21, YV22,YV23,andYV24ducts 118Figure 7-58: Comparison of velocity angle distribution over the blades’ path for YV21, YV22,YV23, andYV24 ducts 118Figure 7-59: Comparison of velocity magnitude distribution over the blades’ path for YV25, YV26,YV27,and YV28 ducts 119Figure 7-60: Comparison of velocity angle distribution over the blades’ path for YV25, YV26,YV27, andYV28 ducts 119Figure 7-61: YV21 velocity contours 119Figure 7-62: YV22 velocity contours 119Figure 7-63: YV23 velocity contours 119Figure 7-64: YV24 velocity contours 119Figure 7-65: YV25 velocity contours 120Figure 7-66: YV26 velocity contours 120Figure 7-67: YV27 velocity contours 120Figure 7-68: YV28 velocity contours 120Figure 7-69: Comparison of velocity magnitude distribution over the blades’ path for YV29 and YV3Oducts 122Figure 7-70: Comparison of velocity angle distribution over the blades’ path for YV29 and YV3O ducts 122XIIFigure 7-71: Comparison of velocity magnitude distribution over the blades’ path for YV31, YV32, YV33,YV34, and YV35 ducts 123Figure 7-72: Comparison of velocity angle distribution over the blades’ path for YV31, YV32, YV33, YV34,and YV35 ducts 123Figure 7-73: YV29 velocity contours 123Figure 7-74: YV3O velocity contours 123Figure 7-75: YV31 velocity contours 124Figure 7-76: YV31 velocity vectors 124Figure 7-77: YV32 velocity contours 124Figure 7-78: YV32 velocity vectors 124Figure 7-79: YV33 velocity contours 124Figure 7-80: YV33 velocity vectors 124Figure 7-81: YV34 velocity contours 124Figure 7-82: YV34 velocity vectors 124Figure 7-83: YV35 velocity contours 125Figure 7-84: YV35 velocity vectors 125Figure 7-85: Efficiency comparison for different duct shapes 126Figure 7-86: 3-Blade torque curve for YV3 at different TSR’s 127Figure 7-87: Single-blade torque curve for YV3 at different TSR’s 127Figure 7-88: 3-Blade torque curve for YV11 at different TSR’s 127Figure 7-89: Single-blade torque curve for YV11 at different TSR’s 127Figure 7-90: 3-Blade torque curve for YV13 at different TSR’s 127Figure 7-91: Single-blade torque curve for YV13 at different TSR’s 127Figure 7-92: 3-Blade torque curve for YV28 at different TSR’s 128Figure 7-93: Single-blade torque curve for YV28 at different TSR’s 128Figure 7-94: 3-Blade torque curve for YV34 at different TSR’s 128Figure 7-95: Single-blade torque curve for YV34 at different TSR’s 128Figure 7-96: Velocity contours of YV34 show the flow separation from the upper side the guide vanes atV=1.5 rn/sand TSR=3.00 129Figure 7-97: Velocity vectors of YV34 show the flow separation from the upper side of the guide vanes atV=1.5 rn/s and TSR=3.00 129Figure 7-98: Summary of the performance of studied ducts 130XIIILIST OF SYMBOLS, NOMENCLATURES, AND ABBREVIATIONS2D Two-dimensional3D Three-dimensionalAmin Minimum area of the duct (throat area)Amax Maximum area of the ductAtfa Projected frontal area of the turbineAtsa Cross section area of the tow tankBERT Blue Energy Research TurbineC Blades chordCd Blade drag coefficientCk Turbine efficiencyCkarms Efficiency reduction due to the parasitic drag of the connecting armsC1 Blade lift coefficientNormal force coefficientC, Power coefficientC Tangential force coefficientCDD Rotor drag coefficientCAD Computer Aided Manufacturing (or Canadian Dollar)CFD Computational Fluid DynamicsCPU Central Processing UnitCR Contraction RatioD Drag force per unit spanDNS Direct Numerical SimulationDVM Discrete Vortex MethodForce vector on the bladeF0 Stream-wise drag forceTangential force exerted on the bladeGBP Great Britain PoundUnit vector in X directionIPO Initial Public OfferingxivT5,b. Torque generated by a single bladeTRF Torque Ripple FactorTSR Tip Speed Ratiou Local velocityuFriction velocityU, Interference factor for the upstream half-cycleUd Interferencefactor for the downstream half-cycleU, Velocity vectorUBC University of British ColumbiaUDF User Defined FunctionUNFCCC United Nations Framework Committee on Climate ChangeUSD United-States DollarV Inlet velocity (upstream velocity)Va Induced velocityVacjInduced velocity in downstreamVau Induced velocity in upstreamVe Wake velocity in upstream sideof the turbineV, Normal velocity component seen by the bladeVR Resultant velocity seen by the bladeV Tangential velocity component seen by the bladeV Wake velocity downstream of the turbineV, Current velocityV Sectional upstream velocityW Duct widthx Position vectorX Horizontal axis in the stationary planey Distance from wallNon-Jimensional wall distanceY Vertical axis in the stationary planeAngle of attack seen by the bladeDissipation rate of turbulence kinetic energyxviLbBlockage ratio8 Azimuth angle (phase angle)Dynamic viscosityTurbulent eddy viscosityu Kinematic Viscosityp Density of fluid (water)u Solidity ratior Shear stressw Angular velocityF Circulation around the blade’s profileCirculation of shed vorticesFBInstantaneous circulation of blade’s profileA typical scalar quantity of the flow fieldEnsemble average of a scalar quantityFluctuations of a scalar quantity in a turbulent flow fieldxviiBlockage ratioe Azimuth angle (phase angle)Dynamic viscosityTurbulent eddy viscosityv Kinematic Viscosityp Density of fluid (water)0 Solidity ratio‘V Shear stressw Angular velocityF Circulation around the blade’s profileFsvCirculation of shed vorticesInstantaneous circulation of blade’s profileA typical scalar quantity of the flow fieldEnsemble average of a scalar quantityFluctuations of a scalar quantity in a turbulent flow fieldxviiACKNOWLEDGEMENTFirst of all, I would like to thank my supervisor, Dr. Causal for his continuoushelp and support during myMaster’s program. It was Dr. Calisal’s trust and support that provided me with a wonderfulopportunityto start my research at UBC with very friendly and high calibre peopleat Naval Architecture Lab. I amalso grateful to Jon Mikkelsen, whose reliable support was available to all team membersin every aspectof the project. I would also like to thank Dr. Farrokh Sassani, the former graduate advisorof MechanicalEngineering Department, for his kind guidance throughout my studies.Also, I would like to thank my colleagues at the Naval Lab who helped mein every aspect of this project.I am so indebted to my good friend Voytek Klaptocz for his generoushelp in every aspect of the projectfrom mesh generation to editing this thesis. My uncle, Soheil, madea great contribution to the revisionof this document as well. I would also like to thank my close friend MahmoudAlidadi for sharing hisknowledge and concerns in the design and modeling parts of theproject. I am also grateful to BillRawlings for his extraordinary help in providing us with unique, high quality experimentaldata. WithoutBill’s input, this numerical modeling project would have been useless. I should alsothank the co-opstudents in our lab, Cameron Fraser, John Axerio, Florent Cultot, Pierre Leplatois, BoZulonas, andThomas Chabut. Cam especially provided a great deal of helpin the set-up and monitoring process ofthe simulations.I should also thank Blue Energy Canada, specially our good friend, Jon Ellison, for theirfinancial supportof the project and their generous help during the experiments.A warm appreciation is deserved for my father-in-law who opened new horizons inmy ambitions andmade a significant impact on my vision. I am also extremely grateful to Nana, thebest mother-in-law inthe world, whose kindness helped me and my wife overcome any challenges. I wouldalso like to thankmy parents for being my there for me. I am grateful to my dad who showed me how tothink and how tolive; although, I have not been a good learner. I should thank my mom as well for her sincerelove andsupport during every stage of my life. Moreover, I would like to express my warmest appreciationstomy dear wife, whose presence in my life is the cause of my motivation and hope for the future.At the end, I would like to thank all my professors at UBC and Tehran Polytechnic for their teachings andsupport during my Master’s and undergraduate studies.xviii1. Introduction1.1 Energy Crisis in the21stCenturyWith origins dating back to the industrial revolution that took place over a century ago, continueddevelopment and technological progress has had a tremendous impact on the all aspects of human life.One of the main factors that determine industrial and technological wealth of a country is its access tonatural resources such as minerals and energy resources. Needless to say that energy has played a keyrole in the in international relations and economy in the recent century. Although industrialisation hascaused thousands of improvements to our lives, its side effects are becoming the main challenge of21stcentury. The challenges include a vast category of environmental, social, political, and economicalproblems. Global warming, greenhouse gasses, pollution, political and military conflicts to access energyresources such as oil and gas, and shortage of energy resources are a few examples of the challengesindustrialisation has caused. According to many reports by governmental and non-governmentalorganizations, the catastrophic impact of excessive use of fossil fuels is among the imminent threats tohumanity and needs urgent considerations by governments, businesses, and individuals. The KyotoProtocol as an amendment to the United Nations Framework Convention on Climate Change (UNFCCC)was enforced to urge the governments to reduce the greenhouse gas emissions. As of December 2006,169 countries signed the protocol. Figure 1-1 shows the global increase of Carbon emission in the pasttwo centuries.1800Figure 1-1: Global Carbon emission increase [1]I10007000Global Fossil Carbon Emissions— TotalL— Petroleum— Coal— Natural Gas— Cement Production1850 1900 >01The increasing demand for energy, especially in developing countries and energy-hungry Chinaand Indiaworsen the situation. Figure 1-2 shows the global increasing demand for energy.Africa • Middle East Europe and EurasiaSouth and Central America North America h World100 —908070 —__-—.50 -g403020 I11965 1970 1975 1980 1985 1990 19952000 2005YearFigure 1-2: Increasing demand for energy by region E21The current oil price has reached a record high by topping 98 USD per barrelin November 2007substantiating the world’s thirst for energy. The decreasing fossil fuel reserves, thereducing oilproduction rates predicted by Hubert’s Peak Law [3] as well as the increasing problems due toglobalclimate change have motivated governments, corporations, and small size industrialsectors toencourage pursuing research and development in the field of alternative energies. Nuclearenergy,currently under considerations by many nations as a “clean” alternative to fossil fuels hasits ownenvironmental and political problems. The focus of research and development in therecent years hasbeen on new sustainable methods to produce energy often referred to as renewableenergies.21.2 Renewable EnergiesThere are many types of methods for extracting energy with minimal environmental impact that areknown as Renewable Energies. Renewables have gained popularity in the recent decades and billions ofdollars are being invested in research and development in these fields. The main known sources ofrenewable energy include:• Geothermal Energy• Bio-fuel and Biomass• Hydropower• Fuel Cells• Solar Energy• Wind Energy• Ocean Energyo Wave Energyo Tidal Energyo Thermal EnergyFigure 1-3 shows the renewable energy consumption in the United-States in 2006. As shown,hydropower and biomass are widely used to generate electricity. On the other hand, solar, wind andgeothermal energies are still in the preliminary stages of development and the power generated bythem is not economically competitive with other forms of energy. The investment in these fields,however, is significantly increasing. According to United Nations Environment Programme, the globalinvestment in clean energies has double from 2004 to 2006, to $70.9 billion [4]. Also, the venturecapital and private equity invested in sustainable energy increased by 69% in 2006, to $8.6 billion [4].3Total 100.942 Qua drillion BtuTotal 6588 QuadrillIon OtuNatural GasGoal 23%23%-Biomass 50%- Geothermal 5%rHydroelectric 41%Figure 1-3: Comparison of US renewable energyconsumption and other sources of energy [5]Among the renewables, geothermal energy, biomass, andhydroelectricity are widely used and havereached technological maturity. Solar power is currentlybecoming a profitable sector of sustainableenergy. The technology is well developed and is applicableespecially in the regions with low latitudes(close to the equator). This type of energyis extracted using solar panels and the price ofenergyobtained from solar panels is about 28-30 cents perkW-hr. Figure 1-4 shows the predictionsfor solarpower in the next decade. As shown in Figure 1-4, the priceof solar power is predicted to exceed thecost of production by 2014. The market value of theglobal publicly traded solar companies stood atabout $1 billion in 2004, while currently,after a myriad of lPOs, they are worth about $71billion[6}.Figure 1-5 shows a sample of revolutionary changesin the market situation for solarpower. Thisfigure shows the share price of SunPowerCorporation, a California based company in designandmanufacturing of Photovoltaic solar panels. It is seen,the stock price has almost quadrupledfromJanuary 2007 to November 2007.Petroleum 40%Lwj3%4Projected Electrlcfty Prices I30 cti’Is per kiIawtI- *aurg25Ord1”0::10_,/“A-’4Ce a gaecc2005 ‘05 10 12 14 iS ‘16 20 Jan’07 Feb07 Mar07 Apr’07 May’07 Ju&07 Ju”07 Aug’07 Sep07 Oct’CFigure 1-4: Predicted electricity Figure 1-5: NASDAQ stock price trend for SunPowerCorporation [7]price by solar energy [6]Wind energy is another alternative which is still under developmentand a large number of companiesare still trying to produce economically efficient devices in theform of wind farms or for individualbuildings. Wind energy devices (wind turbines) work by harnessing thekinetic energy of the wind. Oneof the problems with this form of energy is that wind is usually not preciselypredictable. Statistical data,however, allows designers and engineers to find suitable sites forconstruction of wind power plants.There are two major types of turbines developed to extract windenergy: horizontal axis tidal turbinesand vertical axis tidal turbines. While the majority of wind turbines today arehorizontal axis, anincreasing number of technology developers are re-examining thevertical axis concept.Ocean energy is also one of the most popular and reliable formsof renewable energies. This type ofenergy is divided into two main subsections: wave energy andtidal energy (Figure 1-6 and Figure 1-7).Wave energy is concentrated on absorbing the kinetic energy of theocean waves while tidal energy isfocused on capturing either potential or kineticenergy of tidal currents. It is estimated that marineenergy could create a global business opportunityworth 600 billion GBP (more than $1.2 trillion USD)[8].51.3 History and Forms of Tidal EnergyTidal energy has the potential to be one of the major sources of clean energy. A large number ofresearches sponsored by government and private sectors have embarked on design, development, andmanufacturing of proper devices to capture the energy of the tides in the past decades. Tides which arecreated by the gravitational forces of moon and sun on the oceans are repeated in cycles of 19 years. Asthe orbital motions of earth, sun, and moon are known, the tides are easily predicted during their cycleat any location on earth. This predictability of tides and tidal currents is one of the most importantadvantages of tidal energy compared to other forms of sustainable energy such as wave and windenergy. Tidal energy is usually harnessed in two ways. The first method of harnessing tidal power is tocapture the potential energy of the tides by building a tidal barrage. A turbine is usually mounted on thebarrage body to produce electricity as high tide occurs and water passes through the turbine channeland rotates the turbine’s blades. On the other hand, when the water level is lowered because of thetide, the water captured behind the barrage tends to drain off due to the head difference between thewater behind the tidal barrage and ocean water level. When the water is discharged from the barrage, itonce again passes through the turbine’s passages, rotates the turbine’s blades and produces electricity.The largest plant built to work based on this concept is the Rance tidal barrage. It was built in 1967 andis rated at 240 MW. The main problem with the tidal barrage is that the creation of a massiveobstruction in part of the ocean leads to a number of environmental issues. The second method ofcapturing tidal energy is to use special low-head turbines designed to capture the kinetic energy of tidalcurrents. Tidal currents are generated due to the head difference between two locations in the ocean.These currents can carry a significant amount of kinetic energy and their velocity can reach up to 20Power Ltd.)tidal power plant in I6knots in certain locations. There are two main types of tidal turbines designed to capture the kineticenergy of tidal currents, horizontal axis turbines and vertical axis turbines (Figure 1-8 and Figure 1-9).A horizontal axis turbine appears similar to a wind turbine with a number of blades rotating about ahorizontal shaft. On the other hand, a vertical axis turbine consists of a few straight or helical bladesdistributed evenly about a vertical axis. The main benefit of the horizontal axis turbine design is as it isvery similar to the wind turbines, its technology is sufficiently mature and well developed while thevertical axis turbine technology is not as far along in the design cycle. Also, the horizontal axis turbinehas larger annual output power compare to the vertical axis ones due to its higher efficiency. Inaddition, both methods have a few negative environmental effects such as noise generation that canaffect the sea life. However, large scale turbines with a low rotational speed reduce the noise level andenvironmental impact of the device.However, the horizontal axis turbine is sensitive to the direction of the current while vertical axisturbines can work independently of the current direction. Also, the horizontal axis turbine needs ahigher capital cost (1200-1400 GBP/KWh) compared to the vertical axis turbine with acapital cost of400-900 GBP/KWh [10]. The operating cost is also higher for a horizontal axis turbine (20-50 GBP/KWh)while for a vertical axis turbine, the operating cost is estimated to be 14-20 GBP/KWh [10].A large number of tidal sites have been assessed to be appropriate for mounting tidal turbines. Theestimates show that if only 10% of the tidal current power were utilized, the country could haveFigure 1-8: Horizontal axis tidal turbine (Courtesy of Marine Figure 1-9: Vertical axis tidal turbine (Courtesy of BlueCurrent Turbine Ltd.) Energy Canada)7generated about 1.5 GW of electricity which is about 6% of its current need [11]. Also, tidal currents inFlorida have the potential to produce 25GW of electricity [11].Tidal energy research in Canada dates back to 1919 when strong tidal currents in New Brunswicktriggered thoughts about harnessing tidal energy to produce electricity. There are many potential siteson both eastern and western coasts of Canada such as Ungava Bay in Quebec, the Bay of Fundy in NewBrunswick, and Queen Charlotte Islands in British Columbia. Figure 1-10 shows the potential sites inCanada. To date, thirteen potential sites have been identified along the coast of British Columbia.Among these sites, Portland Canal, Jervis and Sechelt Inlet, and the Observatory Inlet have the largestoutput with tide amplitudes of 5 m, 3.5 m, and 4.7 m respectively. A study conducted at ObservatoryInlet, close to Prince Rupert showed that the capital cost required for a 2.03 MWh output is $2,498,000CAD and for a 167 KWh plant is $243,000 CAD. This study shows that the tidal power is not economicallybeneficial in British Columbia, especially because of the relatively low power price in British Columbiawhich is about one-seventh of tidal power [11].The main problem with vertical axis turbines is their low efficiency as well as large torque ripple that cancause mechanical design problems and affect the durability of the design. The focus of the currentresearch is to increase the power generated by the turbine by placing a few of the ducts around theturbine. The shape of these ducts and their effect on the performance of the turbine is studied in thecurrent research. Duct shape optimization is obviously one of the approaches to increase the powergenerated by the turbine. Rotor optimization is another key aspect of the project which is also understudy at Naval Architecture Lab at the University of BritishColumbia.8TidI Blergy Reso,c.sMWPoiiiW Mea Poternial Powei• <2• 2...4• 4...7• 7... 140 14.27o 27.53953... 102102.198198... 383383.741741.143601436.27802780... 5384 ,•5384Figure 1-10: Tidal sites of Canada [12]1.4 Modeling ApproachesDevelopment and optimization of tidal turbines require accurate and time-efficientmathematicalmodels. Based on the computational tools available, different models with differentcomputational costswere developed and applied for optimizationand analysis purposes. These models range fromcomputationally inexpensive but low in accuracy momentummodels, to three-dimensional RANSmodels of the turbine with all the physical details taken intoaccount. It can be concluded from acomprehensive literature review that there are two families of potentialflow codes and RANS codes tonumerically model a tidal turbine. Some of these methods wereapplied to wind turbines sharing asimilar concept for operation. The RANS modeling is the subject ofthe current research and will beextensively discussed in the next chapters. In this section, differentpotential flow codes used fornumerical modeling of a vertical axis turbine arebriefly reviewed and the advantages and disadvantagesof each model are discussed. More detailed information aboutdifferent aerodynamic models used forprediction of a straight-bladed Darrieus turbine can be foundin [13, 14]. There are three maincategories of modeling approaches to numerically simulate and predictthe performance of a verticalaxis tidal turbine (also known as Darrieus turbine) as describedbelow._w•LF,1000km9• Potential flow modelso Momentum Models• Single stream tube• Multiple stream tube• Double-Multiple stream tubeo Discrete Vortex Method• Fixed Vortex Method• Free Vortex Methodo Cascade Model• RANS model• Experimental model1.4.1 Potential Flow ModelingAs shown in Figure 1-11, the incoming flow is from the left hand side of the turbine plane. When thefree-stream flow reaches the blade, it has a velocity of Va. The resultant velocity is obtained using theangular velocity of the blade and the upstream velocity. Also, the normal velocity (Va), tangentialvelocity (Vi), and angle of attack can be calculated as follows:9o27OFigure 1-11: Aerodynamic model of a free-stream vertical axis turbineI180.110= Rw +Vacos(8) Equation 1-1V,= Vasin (0) Equation 1-2I Equation 1-3VR=4(Vt2+V)Equation 1-4a = atan —All different potential flow models developed for the analysis of the turbine apply a method to estimatethe direction and magnitude of the induced velocity (Va). When induced velocity is obtained, the normaland tangential forces can usually be calculated using the experimental values of lift and dragcoefficients. The tangential force can then be used to calculate the torque generated at each orbitalposition by a single blade.C = C1 sin(8)— Ccos(8) Equation 1-5C = C1 cos(8) +Cdsin (0) Equation 1-612Equation 1-7FtPAtfaVRCTb(O) = F(8).R Equation 1-8The instantaneous torque can be calculated by adding up the effect of all N blades of the turbine.T(8)=Equation 1-9The average power can be obtained by integrating the instantaneous torque over the blades path.Thepower generated by the turbine is obtained using the average torque and angular velocity of rotation.11Tavg= JT(8)d6 Equation 1-100P= TavgCv Equation 1-11In the following section, different approaches on modeling a vertical axis turbine will be brieflydescribed, and the advantages and disadvantages of each approach will be discussed. Momentum ModelsMomentum models are based on the Glaurt’s actuator disc theory and blade element theory. Theconcept used in these models is that the total change in axial momentum across the actuator disc isequal to the aerodynamic forces exerted on the blades in the axial direction. This force is also equal tothe average pressure difference across the disc. Bernoulli’s equation is then used in each stream tube toobtain the wake velocity. The main momentum models developed are single stream tube model,multiple stream tube model, and double-multiple stream tube model as shown in Figure 1-12 throughFigure 1-14.V,(l) \ç(2) V,(3)Figure 1-13: Multiple stream Figure 1-14: Double multiple stream tube model [141tube model [1411. Single Stream TubePresented by Templin in 1974 [15], this model is the simplest approach to calculate and predict theperformance of a vertical axis turbine. In this model, it is assumed that the turbine is enclosed in onesingle tube of stream lines and the velocity across the disc is assumed to be constant. It is also assumedin this model that a single blade exists and the chord length of this blade is equal to the sum of all the%(1) V,(2) V,(3)\V,(1)SIreanitue— Blade F119111 PathI II SlaeamtubeV• I\I” /1VvwFigure 1-12: Single streamtube model [14J12chord lengths of the real turbine. Using Glaurt’s actuator disc theory, one can calculate the uniformvelocity across the rotor.(V+V)Va= 2Equation 1-12By equating the stream-wise drag force (FD) with change in axial momentum, one can obtain the velocityacross the rotor as a function of non-dimensional rotor drag coefficient.Vaui\—= I IEquation 1-13Vca\it..QQ\4CDD is therotor drag coefficient and can be calculated using Equation 1-14. The rotor drag force (FD) canbe also calculated by integrating the axial force using experimental aerodynamic characteristics of theblades. Va obtained from Equation 1-13 can be used to calculate the resultant velocity and angle ofattack at each location. The average power can be calculated by using Equation 1-1 and Equation 1-2.FDCDD— 1Equation 1-14A Ti2P ‘tfaVa1. Multiple-Stream TubeThis model was developed in 1974 by Wilson and Lissaman [16]. As shown in Figure 1-13, a single streamtube is replaced by multiple adjacent stream tubes which are aerodynamically independent. Similar tothe single stream tube model, the momentum theory and the blade element theory are used togetherfor each stream tube and different induced velocities (Va) are obtained for each stream tube. Theinduced velocity can be obtained using Equation 1-15 where k is a parameter determined iteratively.VaKNCR&)= 1—(-.-— .-j-—.sin (0))Equation 1-1513In 1975, Strickland developed a more complicated model for multiple stream tube, which accounts forthe effect of drag and momentum change along each stream tube as well [17]. Although Strickland’smodel is more accurate, Wilson’s model gives a faster convergence due to simpler physics of the model.Later in 1975, Muraca presented a model [18], which included the effect of airfoil geometry, struts,blade aspect ratio, solidity, and also flow curvature around the blade on the performance. The studyshowed that the flow curvature effect is not significant at low chord to radius ratios. Sharpe presentedanother model in 1977 [19] which took the Reynolds number effect into account. In 1980, anothermodel was developed by Sharpe and Read for a lightly loaded, high aspect ratio bladed turbine [20]. Theexpansion of stream tubes are incorporated in this model, thus improving the calculation ofinstantaneous aerodynamic forces and the induced velocities compared to other multiple stream tubemodels. Double-Multiple-Stream-TubeThe original idea of the Double Multiple Stream Tube concept was introduced by Lapin [21] in 1975. In1981, Paraschivoiu developed it as a mathematical model for prediction of the performance of Darrieuswind turbines [22, 23]. Similar to Multiple Stream tube model, the surrounding stream tube of theturbine is divided into several small strips. As shown in Figure 1-14, the improvement to the multiplestream tube model was made by introducing the upstream induced velocity and downstream inducedvelocity at the front and rear part of the turbine respectively. The upstream and downstream inducedvelocities can be calculated using Equation 1-16 and Equation 1-17.= — i) =V(2u— 1) Equation 1-16Vad = UaV=u(2u— 1)Vc,j Equation 1-17In the above equations, u and Ud are interference factors for upstream and downstream half-cyclesrespectively and can be defined as follows:14/ Vau”u=Equation 1-18V00j/Vaä\ua=Equation 1-19yeVau and Vad areinduced velocity at upstream and downstream half-cyclesand V1 is the upstreamvelocity and can be different at different heights toinclude the effect of wind shear in wind turbines.This model predicts the generated power moreaccurately than single and multiple stream tube models.However, the power is over-predicted for high solidities andconvergence problems occur in some cases. Discrete Vortex ModelsThis model was first introduced by Larsen [24]in 1975 to predict the two-dimensional performance of acyclogiro windmill. Fanucci and Walters [25]applied the model to a straight-bladed vertical axis turbine.In 1979, Strickland developed the three-dimensional modelusing the vortex method and incorporatedaerodynamic stall in his model. Research was conducted atUBC [26] to apply the model to a vertical axistidal turbine. The results presented werein good agreement with experimental results especially athighTSR’s. It is usually said that the vortex modelpredicts the performance of the turbine more accuratelycompared to the stream tube models athigher computational cost. However, with the recentimprovements in computational power, the method is fairlyreliable and economical.There are two subdivisions of vortexmodel: fixed vortex and free vortex. The vortexmethod is apotential flow solution of the flow fieldwhich takes the effect of vorticity shed from the bladesintoaccount. Fixed Vortex MethodAs shown in Figure 1-15, the blade isreplaced with a bound vortex filament. The strength of thevortexfilament is calculated using the Kutta-ioukowskilaw and experimental value of lift per unit span.L = pVFEquation 1-2015r1Figure 1-15: Blades are replaced with vortex filaments in vortex methods [14]The trailing and wake vortices can be obtained using Helmholtz and Kelvin’s theorems. The inducedvelocity by a vortex filament at any location in the flow field can be calculated using the strength of thevortex sheet. The change in the axial flow can be calculated using the strength of the vortex sheets.Therefore, the velocity field can be obtained by superimposing the upstream velocity and the inducedvelocity by the blades. Knowing the velocity at each location the angle of attack seen by the blades canbe determined. The experimental blade data can then be used to calculate the torque at each azimuthangle and consequently the generated power. Free Vortex MethodThe fixed vortex method suffers from the fact that vortex sheets are fixed and independent of time. Thisalso results in the inability of this method to predict the velocity components normal to the free stream.In the free vortex method, proposed by Strickland [27], the blade is again replaced by a vortex and thevortex strength is calculated using Kutta-Joukowski formulation for lift. The stream-wise and normalcomponent of velocity can be obtained using Biot-Savart law. Using Kelvin’s theorem, the change incirculation of the blades will result in the change of the strength of the vorticity shed from the blades(Equation 1-21)r— Ipnn—lSV — i. B — BI Equation 1-21Strickland also proposed a method to replace the vortex core strength with a linear function to solve thesingularity problem. As mentioned above, the free vortex method is capable of including the change inthe direction of velocity vector upstream and downstream of the blades resulting in a more accuratecalculation of angle of attack. Knowing the angle of attack and experimental values of lift and drag, the16tangential force, the torque generated by the blades can becalculated. There are a few problemsassociated with the discrete vortex method. These modelsare not able to model the drag inducedvortices such as vortex shedding from the shaft. They also lack areliable dynamic stall model which ismore crucial for low tip speed ratios. In addition, the experimental dataof the blade’s profile is notalways available. Their main capability is in rotor optimization andoptimization of configurations withsimple geometries and mild separation. Cascade ModelA cascade is defined as a series of identical, parallel, and equally spaced blades. Thecascade concept iswidely used in turbomachinery analysis and modeling. The cascade concept was firstapplied to avertical axis wind turbine by Hirsch and Mandal in 1987 [28]. In the proposed method,the aerodynamiccharacteristic of each blade is calculated independently for upstream and downstreamblades (similar tothe double multiple stream tube). The effect of localangle of attack and Reynolds number is alsoincluded in this model. After calculation oflocal angle of attack and velocity, the blades are placedlinearly and in tandem (like a linear cascade) as shown in Figure 1-16.[•• 2Figure 1-16: Cascade Model approach [101Figure 1-17: Upstream and downstream velocities inCascade Model [10]The cascade plan is assumed to be normal to the blades’axis of rotation. In the cascade configuration,the upstream and downstream inducedvelocities are expressed using Equation 1-22 and Equation 1-23.17=(V\”Equation 1-22Vco \Vc,J11 11Vad (VW\— 1\Ve)Equation 1-23Ve and V are the wakevelocities in the upstream and downstream sides of the turbine respectively asshown in Figure 1-17. The value of k is determined using empirical relations obtained from experiments.Hirsch and Mandal proposed Equation 1-24 for determination of the exponent (k1). In this equation, a issolidity ratio.k1 = (0.425 + 0.332a) Equation 1-24Mandal and Burton later incorporated dynamic stall and flow curvature effects into account [29]. Thismodel found to be more accurate than the stream tube models. Although it is not as accurate as freevortex models, it is computationally cheaper and has no convergence problems. It works properly forhigh tip speed ratios and high solidities as well.1.4.2 RANS ModelingWith the revolutionary improvements in the computer technology in the past two decades, conductingCPU-intensive tasks has presently become much more feasible. At the time of the vortex methodinvention, the high computational cost of the model had been described as the main problem. Today,with modern computational tools, running a vortex method code takes no longer than a few minutes.With the use of powerful computers and parallel processing technology these days, RANS simulationsare becoming more popular in industrial and academic sectors. Wind and tidal turbine optimizationtasks using RANS simulations are extensively used these days [30]. Conducting RANS simulations canprovide the user with a valuable insight into the flow field and can facilitate the decision making processfor optimization. In spite of the potential flow codes, RANS simulations do not need any external data(such as experimental lift and drag). They can include separation from the foils and drag inducedvortices from the turbine’s shaft. Also, they are able to simulate dynamicstall phenomenon (although itis not perfect due to the imperfection of turbulence models). RANS modeling is also apowerful tool forcomplex geometries in which case vortex methods cannot be used. Onthe other hand, RANSsimulations for tidal turbines still suffer from high computational cost and time.Three-dimensionalsimulations cannot be conducted on single computers and can only be done using a network of several18nodes. The other problem with RANS simulations is turbulenceand separation modeling which will beaddressed in the turbulence modeling section in Chapter2.1.4.3 Experimental ApproachExperimental modeling is still the most reliable source fordata. Most of the physics of the problem canbe modeled and measured accurately.However, it suffers from high cost and design time. Also, thetechnical problems concerned with experiments alwaysexist and should be addressed properly. Theother problem of experimental work is thatflow visualization and access to different quantities in theflow field is not easy.A series of experimental tests were conducted at the Universityof British Columbia towing tank during2006-2007. The results and the problems associatedwith those experiments will be discussed later inChapter 4 and Chapter 6. The current research at theUniversity of British Columbia is a continuation ofthe work started by the Vancouverbased company, Blue Energy Canada. This company,formerlyregistered as Nova Energy started its research and developmentin early 80’s in the field of applicationof Darrieus concept to extract tidal energy. The researchwas supervised by the veteran aerospaceengineer, Barry Davis. A Series of experimental tests wasconducted at NRC flume tank and the resultswere documented in a number of reports as presentedin Table 1-1.19Table 1-1: Reports on experiments conducted by Barry Davis from Nova Energy in 1980’sReport Title SynopsisFlume tank tests of vertical andNEL-002: Water Turbine Model Trials [31]horizontal axis water turbines.NEL-021: Ultra Low Head Hydroelectric Power Vertical axis water turbine flume tankGeneration Using Ducted Vertical Axis Water tests with caissons, walls, and vane ductTurbines [32] configurations.NEL-022: Ultra Low Head Hydroelectric Power Continuation of NEL-021 with a moreGeneration Using Ducted Vertical Axis Water robust model.Turbines [33]NEL-038: Research and Development of a 50kW toInstallation of 70 kW turbine within a100kw Vertical Axis Hydro Turbine for a Restricteddam in Nova Scotia.Flow Installation [34]NEL-070: The Ducted Vertical Axis Hydro Turbine for Investigates application of vertical axisLarge Scale Tidal Energy Applications [35] turbine in a 474 turbine tidal fence.NEL-081: Commissioning and Testing of a 100kW Examined repaired and enhancedVertical Axis Hydraulic Turbine [36] version of model in NEL-038.202. CFD Simulation of a Free-Stream VerticalAxis Tidal TurbineIn the first phase of the project, a three-bladed free-streamturbine was simulated for a range of currentvelocities and tip speed ratios presented inTable 2-1. The tip speed ratio (TSR) is a non-dimensional number representing theratio of the tangentialvelocity of the turbine’s blades to the current velocity as defined in Equation2-1.R.cüTSR= i7Equation 2-1Table 2-1: Simulation Plan for a free-stream three-bladed turbineCurrent Velocity (m/s) TSR RPM1 2.25 47.01 3.5 73.11.5 2 62.71.5 2.25 70.51.5 2.5 78.31.5 2.75 86.11.5 3 94.02 1.75 73.12 2.25 94.02 2.75 114.92 3.25 135.82 3.75 156.6212.1 Geometry definitionThe dimensions of the turbine, summarized in Table 2-2,were chosen to reflect the model tested in thetow tank shown in Figure 2-1.Table 2-2: Geometric specifications of the turbines modelBlade’s profile NACA 634-02 1Diameter 0.9144 mBlade’s Height 0.6858 mNumber of Blades 3Arms connection Quarter chordShaft diameter 0.0482 mThe geometry used for the simulations,shown in Figure 2-2 and Figure 2-3, was a 2D version of thetested turbine; therefore, the arms and. arm connectionswere not included. The boundaries on thecomputational domain represented in the 2D model consistof a velocity inlet on the left, an outlet onthe right, and two slip walls at the top and thebottom of the domain representing the tow tank walls.Figure 2-3 shows the blades, the circular shaft in the center,and two concentric circles used an interfacebetween the moving mesh section and the stationarysections.Figure 2-1: Tow tank model22Figure 2-2: Geometry of the physical domain including inlet, outlet,Figure 2-3: Geometry of the blades, shaft, andtow tank walls, blades, shaft, and interfacesinterfacesThe airfoil used for the blades is a five-digit NACA Series, NACA 634-021 (Figure 2-4).This airfoil waschosen based on previous NRC reports [3 1-36].(WFigure 2-4: NACA 634-021 profile and coordinates(pie 4 ç)I (p.r ete)(WIP0 0 0 j 02.4350.5 1.505 0.2750.821 2.2500.75 1.997 0.904 0.751USO1.25 2.827 0.728 0.8511.0842.8 3.871 (.010 (.0050.81350 0.068 1.5+20(.122 0,6537.5 6.182 1.2982.261 0.58010 7.000 1.4871.210 0.48415 0.441 2.6221.599 0.30220 *410 1.055 1.25+50.53528 10.053 1.0% 1.8050.22120 10.412 2.722 1.112(1.25550 10.500 1.7001.507 (923540 0.248 I 1,54 1,5980.12+845 9851 L878 1,154917330 0.506 2.479 1.5100.13085 8.390 1.8801.175 (1.130+10 7.441 1.241 1.132(1.112225 6.596 1.200 1,0800.00070 5.580 1.084 2.0420.08275 1.180 0.494 0.997 (906880 3.084 0,9210.954 0.05785 2.021 (9859 0.9280.0(690 1.113 (9774 0.8990.03895 0342 0.121 0.8490.823100 0j0670 0.8221..(9. edi,i 0.080 per cr08©232.2 Grid Generation and Boundary ConditionsIn order to conduct a CFD simulation, the domain needs to be descretized into very small sections calledcells or elements. Descretization of the domain allows for the conversion of the Partial DifferentialEquations (PDE’s) to algebraic equations which can be solved numerically through an iterative process.The PDE’s that need to be descretized are continuity, momentum equation (in X and V direction), energyequation (when using of a coupled solver), and the turbulence equation(s).To calculate the turbine performance, the torque generated by the blades was recorded for eachsimulation as a function of azimuth angle. The average power was then calculated based on the averagetorque over a cycle and the angular velocity of rotation of the turbine’s blades using Equation 2-2.P= f(Tavg,cu)= Tavg.w Equation 2-2The torque itself is a function of lift and drag forces generated by the blades (Equation 2-3). Since thevariation of pressure in the boundary layer along the normal axis to the surface is negligible, thepressure distribution and hence the lift force can be predicted accurately even using a potential flowcode. The complicated task in calculating the forces exerted on the blade is to accurately predict thedrag force. This requires an accurate solution of the boundary layer developed over the blades.T = f(L, D, a) = LSin(a) — DCos(a) Equation 2-3An accurate prediction of drag on the blades, especially for unsteady separated flow requires a highquality fine grid around the airfoils. Thus, a very fine C-shape structured grid was used to resolve theflow around the airfoil and the wake structure as shown in Figure 2-5. The number of nodes used on theairfoil surface and the wake was 240 and 120 respectively and the number of layers used to form the Cshape mesh was 80 with a growth ratio of 1.05. The node distribution was dense at the leading edge andtrailing edge of the airfoil where high velocity and pressure gradients exist.24The size of the grid required adjacent to the blades is dependent on the thickness of the turbulentboundary layer. The boundary layer profile shown in Figure 2-5, can be divided into three differentregions: the viscous sublayer, buffer layer and fully-turbulent layer. The viscous sublayer is theinnermost layer in which the viscous forces are dominant and the value of the non-dimensional cellheight, y (defined by Equation 2-4 and Equation 2-5) is below 5.+ PUrYyEquation 2-4u =— Equation 2-5In the buffer layer, the effect of viscosity and turbulence is of the same order and the y value isbetween 5 and 60. Fully-turbulent layer, also called the log-law region, is where the effects ofturbulence are dominant and the velocity profile can be approximated using Equation 2-6.U fUrY\—= 2.5 InI—)+ 5.45 Equation 2-6UtFigure 2-5: Structured fine grid used around the blades25UitJ 2.5 hUr/i +- 5.45inUy/vFigure 2-6: Turbulent boundary layer profile [37]It is important to note that y value is not only a function of the cell height adjacent to the wall, but alsois a function of the Reynolds number. Since the Reynolds number over a blade is dependent on itsorbital position, it changes as a function of the azimuth angle. Thus, the y value can only beapproximated based on the maximum Reynolds number seen by the blade and using the correlations forknown flows such as the turbulent flow over a flat plate given by Equation 2-7.y = 0.172()Re°9Equation 2-7The required cell height adjacent to the turbine blade was therefore computed using Equation2-7 byimposing a required y value of 2 to ensure that there is adequate number of cells to resolve the viscoussublayer. Since the method of determining the cell height is based on an approximation,the y+ valuewas monitored during the simulations to ensure that it was constantly kept in an acceptable range.Based on Equation 2-7, the height of the cells adjacent to thewall was determined and set to5.08*106m. This cell height yields a y=2.16 which is still below 5 with a safety factor of 2.Y=6OOpp.r&pth .aaZevtolds no26Also, as shown in Figure 2-7, the same type of grid was used for the flow field around the shaft toproperly solve the vorticity shed from the shaft. Because the flow velocity over the shaft is lower thanthe velocity over the blades and hence the shaft Reynolds number is lower, a larger cell height is allowedadjacent to the shaft wall. The cell height used for the shaft was12.7*106m which yielded a y value of1.56.Figure 2-7: Structured fine grid around the shaftFor the rest of the domain, a triangular unstructured grid was used as can be seen in Figure 2-8 andFigure 2-9. As shown in these figures, the mesh density is high around the turbine region and becomeslower far from the turbine zone. Because of the complexity of the flow in the wake of the turbine, themesh density is higher downstream than upstream of the turbine. Also, the grid was refined in the areasat which the pressure gradient was high.27shaftFor a CFD problem, the solution needs to be independent of the grid.Hence, a grid refinement study is anecessary component of every CFD simulation. A grid refinement study can be easily done for asteady-state problem. However, for an unsteady problem, a targetparameter should be selected and comparedfor different grid densities. In the current research, the average power generated by theturbine overeach cycle was chosen as the target parameter and was compared for threedifferent mesh densities.The mesh densities generated for the free-stream turbine model are presented in Table2-3. It should benoted that the refinement factor chosen for both free-stream and ducted turbinemodels was 1.5.Although the industry standard refinement factor is V2, a factor of 1.5enables the study of a largerrange of cell numbers. This could result in finding a smallernumber of cells with acceptable accuracy.Table 2-3: Grid densities used for grid refinement studyGrid Density Number of CellsCoarse 144,641Medium 220,803Fine 328,947The simulations were conducted for different mesh densitiesat the same inlet velocity of 1.5 rn/s and aTSR of 2.75. This TSR was selected because a relatively severeseparation occurs as the angle of attackFigure 2-8: Unstructured grid of the domain Figure 2-9: Unstructured grid around the bladesand the28seen by the blades is relatively high. Also, at this TSR the blade velocities arehigh and a finer grid isrequired. The results obtained for different grids are presented in Table2-4 and Figure 2-10.Table 2-4: Results of the grid refinement studyGrid Average Power Per Cycle (Watts)Coarse 318.3Medium 390.7Fine 389.7—Coarse —Medium Fine1008060Ez40=20-20Figure 2-10: Grid convergence results for a free-stream turbine at TSR=2.752.3 Domain Size StudyAs the final product would be installed in the free stream of theocean currents, it is necessary toconduct the simulations in a large domain in which the boundarieshave minimal effect on the solution.This was the same strategy that was tried to be achieved in the experiments. Inorder to quantify theeffect of tow tank walls on the performance of the turbine, a parameteris defined in Equation 2-8 whichis called blockage ratio.Theta (Deg)29— Atfa—tltsaFigure 2-11: Definition of 2D blockage ratio Figure 2-12: Definition of 3D blockage ratioFor the conducted experiments as a part of the current research in the Naval Architecture Lab, theblockage ratio was about 7% which implies that the test conditions can be considered as free streamconditions. Thus, the same blockage ratio was also used for the simulations. However, to ensure that thedomain size is large enough to simulate a free stream condition, a domain size study was conducted fordifferent domain sizes and the results obtained from those simulations approved that the domain size islarge enough to represent the free stream conditions. The main concern in adjusting each factor is tominimize the domain boundaries effect on the turbine performance. On the other hand the number ofcells in the domain is another concern about the computational cost of the simulations. These concernsresulted in choosing different upstream, downstream and side distances as presented in Table 2-5, andthe simulations were conducted to ensure the solution independency on the domain size.Equation 2-8Blockage Ratio is basically the ratio of the projected turbine area to the cross sectional area of the towtank. The Blockage Ratio concept is shown in Figure 2-11 and Figure 2-12 for 2D and 3D modelsrespectively.2-DIAtfa3-DAtsa30Table 2-5: Domain size study resultsCase Domain Distance From Distance FromName Width (m) Upstream (m) Downstream (m)A 2.54 1.27 2.54B 7.62 2.54 10.16C 7.62 3.81 10.16D 7.62 5.08 10.16E 10.16 5.08 10.16F 10.16 6.35 10.16G 12.7 5.08 Domain Width EffectThe small width of the domain (2.54 m which corresponds to a blockage ratio of 35%) has a large effecton turbine performance due to blockage and flow restriction. These tests do not accurately model free-stream results, but may be consistent with the flume tank testing results. The trend is such that smallerwidth domains, naturally, reduce the Betz effect and channel more flow energy through the turbineblades, thus increasing their power. Once the domain is on the order of 10 m wide, there are negligibleeffects on the flow from the tank walls and free-stream flow can be assumed to be accurately modeled.From 7.5 m to 10 m, the steady state average torque drops by approximately 0.5 N.m, and from 10 m to12.5 m, the drop appears much lower and the flow conditions can be assumed as free streamconditions. The results of the domain width study for cases A, D, E, and G are shown in Figure 2-13.3120zU1510 H-5CaseName: —A —D —E -G-5 — -——-— ———---------—--------______-—-----—----—-Theta (Deg)Figure 2-13: Domain width effect on the torque generated by the turbine2.3.2 Upstream DistanceIt appears that, on larger domains where flow eddies and vortices can beresolved, the upstreamdistance between the turbine and inlet has as adramatic effect on the flow characteristics as thedomain width. If insufficient space is provided, watercannot flow around the turbine as it would in free-stream conditions as the flow enters the domain perpendicular to theinlet boundary. It can also cause areverse flow at the inlet if the inlet is too close to the turbine. It appearsthat lengths larger than 3.81 m(more than 4 times of the turbine diameter) are required for adequateflow pattern formation prior toreaching the turbine, while smaller values lead to numerical errorsand an artificially increased turbineperformance. As can be seen in Figure 2-13, the torque variation is around 0.3N.m between 2.54 m and3.81 m, and less than 0.05 N.m between 3.81 and 5.08 m andbetween 5.08 m and 6.35 m. Theseresults are still quite accurate as the flow is largely establishedbefore the turbine early in the simulationas compared to the flow behind the turbine where turbulent eddiesmust be resolved prior to accuratemodeling. The results of the tests for upstream distanceare shown in Figure 2-14.0 200 400 600 800 1000 12O0140032Case Name: —B —C —D —F2015110za;a.0-5 .Theta (Deg)Figure 2-14: The upstream distance effect on the torque generated by the turbine2.3.3 Downstream DistanceFor an accurate depiction of vortex shedding phenomenon, a properly sized trailing distanceis requiredto allow for the formation and dissipation of eddies shed from the bladesand the shaft. The resultssuggest that a downstream spacing of around 10.16 m should sufficefor adequate realization of theshed vortices. This size is approximately 10 times larger than the turbinediameter and is recommendedin different sources such as [30].2.4 Solver SpecificationsIn the following section the solver specification used for the simulationsare described. As the workingfluid in the simulations is water which is an incompressible fluid, asegregated solver can be applied. A2’ order, implicit, and unsteady solver was used toincrease the accuracy of the solution. Theadvantageof using an implicit solver is accelerated convergence andalso the solution is stable regardless of thetime step value. On the other hand, an implicit solver requires morememory and is recommended whensufficient amount of memory is available.The flow was also a turbulent flow and the one-equation Spalart-Allmarasturbulence model was used tomodel the turbulence in the flow. The details of the procedureof selecting a proper turbulence modelare extensively described in the turbulence modeling section.0 200 400 600 8001000 1600 180033The under relaxation factors for the flow parameters were set aspresented in Table 2-6. Theseparameters can be manipulated during the solution to control the convergence andconvergence speedof the solution. In the current simulations, the only parameters which were changedduring the solutionprocess were pressure and momentum, changing gradually to the values of 0.7 and 0.3 respectively toaccelerate the convergence.Table 2-6: Under Relaxation Factors used for the simulationsParameter Under Relaxation FactorPressure 0.3Momentum 0.7Density 1Body Forces 1Modified Turbulent Viscosity 0.8Turbulent Viscosity 0.8PISO algorithm was also used for the pressure-velocity coupling. PISO which stands for Pressure Implicitwith Splitting Operators, uses one predictor step and two corrector steps and can be consideredas anextension to the SIMPLE (Semi-Implicit Method for Pressure-LinkedEquations) algorithm with one morecorrector step to improve it. The details of this method can be found in many CFD books [38].AlthoughP150 algorithm increases the computations, it shows an acceleratedconvergence compared to SIMPLE,SIMPLEC, and SIMPLER algorithm in unsteady problems.An under relaxation factor is involved in thismethod to stabilize the calculation process.The convergence criteria used for the continuity, momentum andturbulence equations were set to atleast i0. It was, however, observed that while continuity converges ata lower rate, momentum andturbulence equations were converged to a value of i0 or lower in mostcases.Selection of the time step is one of the important parts of the simulations.Choosing an improperly largetime step does not only affect the convergence of the solution,but also results in significant errors inthe results of the simulations. On the other hand, choosing anextremely small time step cansignificantly increase the simulation time. Thus, settingan optimum time step for the simulations isrequired to obtain accurate and quick results. The strategyused for the simulations was to start with arelatively large time step and allowing the turbine to gothrough a few cycles. After the solution was34periodically repeated, the time step should be decreased to a value at which the maximum cell courantnumber in the important regions of the flow field such as the blades surfaces and wakes are lower than20-40. Therefore, the contours of courant number were monitored in several steps during the solutionto ensure that the maximum courant number does not exceed the limits. This value for the courantnumber usually results in proper convergence in 10-20 iterations per time step. It should be noted thatany increase or decrease in the time step should be done gradually to prevent numerical instabilities. Inorder to make sure that the time step is sufficiently small, the time step was reduced during a typicalsimulation and the changes in the torque curve were monitored. The time step at which the differencebetween the average torque values was less than 1% was chosen as the time step for all the simulations.There are two options available to simulate an unsteady moving mesh problem: sliding mesh schemeand dynamic mesh scheme. Dynamic mesh scheme basically changes the cells shape as the objectmoves in the medium, and after a few time steps the grid for a part of or for the whole domain needs tobe regenerated to prevent the cells to be highly skewed. The disadvantages corresponding to thismethod are increased computational time and cost due to the necessity of grid generation at every fewtime steps. Moreover, the stability, convergence speed, and accuracy will be decreased because of theexistence of low quality highly skewed cells in the domain especially in the regions around the bladeswhere the flow needs to be predicted accurately.Conversely, in the 2D sliding mesh scheme, two surfaces with a relative motion to each other slide on aninterface edge and form a conformal grid at the interface. In spite of the dynamic mesh schemes, thegrid is not regenerated or dragged during the solution and hence, there is not any chance of formationof highly skewed cells in this scheme. Therefore, a more accurate and accelerated solution can beobtained by applying this method to the current simulations. The application of sliding mesh schemeforthe current turbine modeling is depicted in Figure 2-15.35Figure 2-15: Sliding mesh scheme used for modeling the moving meshAs it is shown in this figure, the domain is split into three different zones; two stationary zones insideand outside of the blades rotation area and a moving part in the middle which rotates around the centerof the shaft. As the blades are placed in this zone, the angular velocity of the moving mesh zone shouldbe the same as the turbine’s RPM. The shaft in the center is also defined as a moving wall with the sameangular velocity as the blades and the moving mesh zone.The stationary zones and the moving mesh zone are separated by two interface edges as indicated inFigure 2-15.The methodology that the sliding mesh scheme uses is based on the fact that at the intersection of theinterface zones at each time step the fluxes across the sliding interfaces can be calculated by ignoringthe interface zone faces and using the faces created by the intersection of interfaces instead. In otherwords, instead of calculating the flux from face AB, the interface area is split into two faces, AC and CBand the flux across the AB face can be calculated by adding the flux from the AC and CB faces as shownin Figure 2-16.36It might be asked that it was possible to use an external stationary zone and an internal moving meshzone in which the blades and shaft can rotate about the center of the shaft. There are two reasons thatthree zones were used instead of two because firstly, the three zone grid can allow for placing differentdesigns such using an airfoil as the shaft cover or a few number of guide vanes as flow straightenersinside the turbine area to minimize the upstream blades’ wake and shaft’s wake effect on the rear partof the turbine. Secondly, a finer grid could be used in the middle ring in which the wake of the bladesare dominant and a fine grid is needed to resolve the flow field accurately. In other words, having amiddle region can help to control the grid distribution inside the turbine area while savingcomputational time and cost.2.5 Turbulence ModelingTurbulence modeling is one the three main fields in computational fluid dynamics along with solverdevelopment and mesh generation. In the recent years, with improvements in computational toolsdifferent approaches to the turbulence problem were introduced and developed. There are threedifferent categories in numerical modeling of turbulence as follows:Figure 2-16: Sliding mesh scheme concept37• DNS (Direct Numerical Simulation)• LES (Large Eddy Simulation)• RANS (Reynolds Averaged Navier-Stokes)In order to understand the advantages and disadvantages of each approach, the turbulence mechanismshould be clarified. Briefly, turbulence is an unsteady, irregular, three dimensional, highly non-linearand, anisotropic motion of the flow in which transported quantities such as mass, momentum, andscalar quantities fluctuate in time and space. Turbulence contains different scales of eddies. Largeeddies are carried in the flow field by the free stream flow and smaller eddies are carried by largereddies. Larger eddies have size and velocity in the order of the mean flow. Their energy is transferred tothe smaller eddies through a mechanism which is called vortex stretching. This transfer of energy fromlarger eddies to smaller eddies is called Energy Cascade. When the energy is transferred to small eddies,it dissipates in the form of thermal energy via viscous dissipation. This phenomenon happens in thesmallest scales which are referred to as the Kolmogorov scale. The rate at which viscous dissipationoccurs is the same as the rate of energy transfer from larger eddies to smaller ones.Different approaches to turbulence modeling in CFD are based on the structure of turbulence and size ofeddies as shown in Figure 2-17.\o(eIwrgy— paIliZfl ofi)isipat1ngLwge-sçak I4ux of eery. edthevII. Ti=Resolved1DNSNResolved . Modeled-..———...—...—.....,“.-.-.LESResolvedModeled___RANSFigure 2-17: Approaches to turbulent modeling [37J38In DNS, full Navier-Stokes equations are solved for all scales of eddies and hence, there is no need tomodel the turbulence which results in increased accuracy and reliability. On the other hand, as thisapproach requires eddies to be solved to the Kolmogorov scale, it needs vast computational resourcesand is not practical for industrial CFD problems and is only applicable to research purposes with very lowReynolds numbers. Predictions show that with improvements in the computer technology, the flowaround a full airplane can be solved using DNS not earlier than 2080.The second approach to the turbulence modeling which was developed inrecent years is Large EddySimulations. The method that LES uses is to resolve Navier-Stokes equations for largescale eddies and tomodel small scale eddies. The small scale eddies are in fact filtered in this method.It is computationallycheaper than DNS method but less accurate. Another disadvantage of LES is that it hasto be done in 3Dand is not suitable for engineering applications that can be conducted in 2D with significantly lowercomputational cost.Another approach to solve the turbulence problem is the RANS method. RANS modeling introduces eachquantity in the form of a mean value (which is obtained by ensemble averaging) plus a fluctuating term(Equation 2-9).0 = + 0’Equation 2-9Writing the flow parameters such as pressure and velocities in this form and plugging them into theNavier-Stokes equations results in an equation identical to original Navier-Stokes equation with oneadditional term as in Equation 2-10.aul U, op aiou, ___\(--+Uk_) =Equation2-10The new term appeared in Equation 2-10 is —puu’ and is called the Reynolds stresses. This term isadded to the strain term and has the form of viscosity. The task of a turbulence model is to calculate theReynolds stresses and close the equation. Hence, the problem of obtaining turbulent shear stresses issometimes called the closure problem. A simple approach to the closure problem was introduced byJoseph Valentin Boussinesq. The Boussinesq approximation is based on dimensional analysis andassumes that the turbulence is isotropic. This approach relates the turbulence stresses to the mean flow39by introducing a turbulent eddy viscosity term This approach led to a new family of zero equations(algebraic models), one-equation and two-equation turbulence models called eddy viscosity models.Baidwin-Lomax, Baidwin-Bart, Spalart-Ailmaras, k-€ (with several modifications), Menter’s k-w and k-wSST are some examples of eddy viscosity model with different number of transport equations.Another approach that does not use the Boussinesq assumptions is Reynolds Stress Transport Models.There is no isotropy assumption in RSM models and they contain more physics of the problem but theyare more complicated than eddy viscosity models and are computationally expensive.For the current research several turbulence models were studied and applied to simulate the turbulentflow inside and outside of the turbine area. The options available for a 2D simulation were as follows:• Spalart-Ailmaras (one-equation model)• k-€ (two-equation model)o Standard k-€o RNG k-€o Realizable k-E• k-.o (two-equation model)o Standard k-wo k-wSST• Reynolds Stress ModelAfter a detailed investigation for an appropriate turbulence model and running a few number ofsimulations to compare their performance (Figure 2-18), Spalart-Allmaras was chosen as the turbulencemodel for the simulations. The main advantages of this turbulence model are its low computational cost,stability and acceptable accuracy. This model was first developed for aerospace applications but isgaining popularity in the turbomachinery fields as well. However, like many other turbulence models, itis incapable of modeling severe separations perfectly.40—SA —ke-RNG —kw-std kw-SST —rke-neq —rke-ewtI‘:‘200 400 600 800 1000 1200r\__J\/ j \/ / / \ / \ /\/\/\) \i \! \/ \/ / ‘/ \/‘ \} ‘I \ \/ \_1Theta (Deg)Figure 2-18: Comparison of the results obtained for different turbulence modelsAnother important characteristic of Spalart-Allmaras model is that it is not sensitive to the near wallmodeling approach. In other words, it is modified in a way that if the y value is in order of one, itresolves the boundary layer; otherwise, it uses the wall functions. Wall functions are empiricalcorrelations to approximate the flow field in the viscous sublayer and buffer layer. In fact, they act as abridge to relate the near wall flow field to the fully turbulent regions. For the wall functions to beengaged in the simulations, the y value should be above 5. If the value is under 5, another approachfor the near wall modeling will be engaged to resolve the boundary layer. The concepts of these twonear wall modeling approaches are depicted in Figure 2-19. The second approach is noticeably moreaccurate than the wall functions but is computationally more expensive as 10 or more cells are neededin the viscous sublayer and buffer layer. In the current research, the second approach was taken sincethe boundary layer growth and separation would largely affect the turbine performanceand needed tobe accurately predicted.One of the problems with all modification of k-€ and RSM models is that the near wallmodelingapproach has to be specified for the simulations and is applied to all the walls. However, inthesimulations conducted, especially for the ducted turbine models, the y value can change betweenvalues lower than one and 6. Also, y value on the blades changes as the turbine rotates. This is becausethat y value is not only a function of the near wall grid but also a function of Reynolds numbers. Hence,41/252015105Ezoci)D1o-15-20-25it is not possible to switch between different near wall modeling methods, the simulations, can beinstable and inaccurate. Thus, a flexible approach is essential to adapt itself to the local Reynoldsnumber and the near wall grid. Another problem with these models, especially with RSM is their stabilityproblems and high computational cost as it is a five-equation model.IWàli Functi,n Aprcacha ftc4uponzeIwd,* bi*4d bywa Icoa• Ud-b t*I*Iecce ac4eI an betii aiii a miuNoAoach• iii. ar-waU r.pc. i i.cLv.daUdntoI.•Thdeoigbtobeaha.Figure 2-19: Comparison of two available approaches to the near wall modeling[371Also, standard k-w and k-w SST did not show a superior performance in this application. They alsosometimes showed instability and convergence problems as well. Another problem these models sharewith k-€ and RSM models is their higher computational cost in comparison with Spalart-Allmarasturbulence model. In the next phase of the project in which 3D simulations will be conducted (based onthe availability of computational resources) it is recommended to study LES and DES (Detached EddySimulation) models as some unsteady phenomena may not be modeled properly in RANS modelsespecially at higher angles of attack where severe separations occur.423. CFD Simulation of a Ducted Vertical Axis Tidal TurbineThe previous research [31-36] showed that confining the turbine within a parabolic duct can result in anincrease in the power generated by the turbine. When using a venturi-shape duct, the flow acceleratesinside the duct and the kinetic energy delivered to the blades is increased. However, placing a ductaround the turbine can increase the complexity and cost of design and installation of the device. Thus, adetailed study of the mechanical design, mooring, maintenance, financial, and other aspects of theproject must be undertaken before a decision is made regarding the use of a duct.In this chapter, the simulation process of a ducted turbine will be described. After conductingsimulations for a free-stream turbine and understanding the optimum method of setting the solutionparameters, a pair of symmetrically placed parabolic shaped ducts were modeled around the turbine tosimultaneously accelerate the flow and guide the flow in a proper direction. The same duct geometrywas used in the experiments conducted at UBC tow tank. The duct shape and dimensions are shown inFigure 3-1.Figure 3-1: LJBC duct dimensions (all dimensions are in metric)43The duct was positioned in such a way as to have a wall clearanceof approximately one cord betweenthe blade and the wall at the narrowest point. The rotor geometry was identicalto the free-streamturbine. The same range of TSR’s was used along with velocities of 1.5 and 2 rn/sfor the simulations. Asit will be explained in Chapter 5, the experimental results obtained for the ductedturbine model at aspeed of 2 rn/s are of lesser quality due to significant free surface effects.3.1 Grid Generation, Boundary Conditions and the Domain SizeAs in the case of the grid generated for the free-stream turbine, a combinationof structured andunstructured triangular elements was used to discretize the domain fora ducted turbine. The same typeof 80-layer, C-Shape structured mesh was used around the blades with 240 nodeson the surface and120 on the wake. Also, a structured grid around the shaft with 60 nodes on the shaftsurface and 50layers of cells with a growth ratio of 1.1 was used to model the shaft. The remainderof the domain wasmodelled using triangular cells. The only difference between the free-stream turbine mesh and that ofthe ducted turbine was that the outer interface that defines the moving wall boundary was placed closerto the blades to allow the walls to be only a chord away from the blades (Figure 2-3 and Figure 3-2).Moreover, a structured quadrilateral grid was used to mesh the ducts (Figure3-3). The first cell height,the growth ratio, and number of layers were set to1.27*104m, 1.15, and 20 respectively. This cellheight yields a y value about 30. This grid density is sufficient for the ducts as the flow separates mildlyat the rear part of the duct compared to the sever separations on the blades. Also, the fine grid ontheblades is used to properly solve for the drag force. Since an accurate drag force of the duct is not ofinterest at this stage, a coarse grid may be used to decrease the computational time and cost.Figure 3-2: Interfaces in the ducted turbine configuration Figure 3-3: Duct and blade grid in ducted turbine configuration44To avoid large cell size gradients in the limited space between the blades and the interfaces, the numberof nodes on each interface needed to be increased. This leads to an increased number of cells in theducted turbine model in comparison to the free-stream model. The total number of nodes used for thesimulations is approximately 235,000 cells.As in the case of the free-stream simulation, grid refinement study was conducted to ensure a gridindependent simulation. Three different mesh densities were used to study the grid convergence aspresented in Table 3-1. The TSR used for the grid convergence study was 2.75 which was the same asthat used for grid refinement study of the free-stream turbine.Table 3-1: Gird Refinement Study for a Ducted TurbineGrid Number of Cells Average Power Per Cycle (Watts)Coarse 159,094 911.4Medium 235,170 587.1Fine 358,223 586.4The torque curve per cycle was also plotted for each mesh density to ensure the convergence of theresults as shown in Figure 3-4. It should be noted that the grid adjacent to the wall was not madecoarser and was kept constant for all three grids. The reason for that was to keep a consistent methodof solving the boundary layer in coarse, medium and fine grids. Had the near wall mesh been madecoarser, the y value would have exceeded 30 and hence a wall function would have to be used tocalculate the boundary layer which is different than the near wall approach used for fine and mediumgrid densities described in the previous chapter.In addition, as the grid becomes finer, a smaller time step is required to keep the cell Courant Numberin the same order for different mesh densities. In order to accelerate the solution process, a relativelylarger time step may be used at the beginning of the simulations which can be decreased gradually tosolve for a few more cycles to obtain the final results. The final time step used for the simulations in thisstudy was set to 0.2 milliseconds.45—Coarse —Medium Fine160 ——-------—-——-—_____—_______140120100Ez8060402000 90 180 270 360Theta (Deg)Figure 34: Grid convergence results for a ducted turbine at TSR=2.75The same domain size as the free-stream turbine was used for the simulationsof the ducted turbine tokeep a constant blockage ratio with the tow tank experiments. The blockage ratio for the ducted case isless than 13% and the results can still be considered as free stream conditions.Alternatively, [39]recommends an analytical approach based on the actuator disc theory to estimate theeffect of thedomain walls effect on the solution. Those recommendations can also be used to verify if thedomainwalls have negligible effect on the results. Moreover, the free vortex code developedin UBC’s NavalArchitecture Lab can be used to estimate the effect of the domain size on the simulationresults as well[40].3.2 Solver SpecificationsSimilar to the free-stream turbine model, a 2D, second order, implicit, segregatedsolver was used forthe ducted turbine modeling. A PISO algorithm was also usedfor pressure-velocity coupling inconjunction with the Spalart-Almaras turbulence model. As the grid is finer in the ductedturbine modelcompared to the free-stream turbine model, a smaller time step should beused for the solutions. Thesame strategy for under relaxation factors were used for the ducted simulationsas well. It was alsonoticed that increasing the pressure under relaxation factor beyond this thresholdleads to thedivergence of the solution. An upwind first order discretization scheme was used formomentum,pressure and turbulence equations at the beginning of the simulations becauseof the acceptable46accuracy and proper convergence behaviour. After the turbine reached quasi steady state conditions, asecond order upwind scheme was used to increase the accuracy and reliability of the solutions. At thatpoint the convergence criteria for residuals were decreased to iO for all the equations. The momentumin X and V direction as well as the turbulence equation converged beyond 1O. The continuity equation,however, converged at a slower rate and did not reach a residual value lower than iO with areasonable number of time steps. Better convergence can be achieved for the continuity equation bysignificantly decreasing the time step size, but this will increase the computational cost and is notpractical for engineering applications. The forces on the blades were monitored during each iteration toensure that the solution was converged properly.Akin to the free-stream turbine model, a sliding mesh scheme was used to simulate the blades rotationaround the turbine’s shaft center. The shaft rotation was set at the same angular velocity as the bladesand the moving mesh zone.3.3 Turbulence ModelingThe same turbulence model (Spalart-Allmaras) was also applied to the simulations of a ducted turbinebecause of its accuracy, reasonable computational cost and reliability. The significance of using thisturbulence model was more pronounced in this set of simulations because of the different meshdensities around the blades and the ducts. In other words, as the drag of the ducts is not of particularinterest at this point, a coarser grid may be used adjacent to the ducts to decrease the computationaltime and cost. A coarser grid around the ducts needs the wall function approach to be engaged tocalculate the boundary layer. Hence, a flexible turbulence model is required to apply two different nearwall approaches simultaneously to solve the boundary layer accurately on the blades and use a wallfunction to calculate the boundary layer characteristics around the ducts. As it was described in theprevious chapter, the modified Spalart-Allmaras turbulence model can handle this situation. On thecontrary, k-€ and RSM model need a single near wall modeling approach to be selected and cannotapply to the above mentioned approaches at the same time. It was observed that using either a wallfunction or enhanced wall treatment approaches with these turbulence models will lead to numericalinstability and divergence in some cases. Strictly speaking, any turbulence model needs certainmodifications depending on the application to increase the accuracy. However, modification anddevelopment of turbulence models are beyond the scope of the current research and the reader shouldbe aware of the fact that turbulence models imperfections are among the sources of error in thesimulations, especially in the cases with larger adverse pressure gradients and severe separations.474. Experimental Design and Analysis of BERT TurbineThe following chapter is selectively quoted from an internal lab reporton the experimental researchconducted in August 2006 and November 2006 by the Naval Architecture Labat UBC. Another set ofexperiments was also conducted by the Naval Lab in September 2007.Parts of the results obtained fromthose tests are used in Chapter 6 for validation of CEO results.In order to validate the numerical models and obtain a better understandingof the performance, avertical axis tidal current turbine model was designed and built in theUBC naval lab and subsequentlytested in the UBC tow tank. This turbine is a scaled version of the Blue Energy verticalaxis turbine. Thefirst set of tests took place between Aug 17, 2006 and Aug 24, 2006 on the original un-ducted versionofthe turbine. A second set of tests was performed between the13thand26thof November, 2006 on aducted version of the turbine.4.1 Experimental ModelAs shown in Eigure 4-1, the experimental model was a 0.91m diameter 3-bladedvertical axis turbine.The foil section used for the blades was a NACA 634-021 section. The NACA section was selected inprevious NRC studies. The blades were mounted to the central shaftvia two arms connected at thequarter-span locations. Arms were fixed to the blades using a pivot joint witha clamping mechanismsuch that the angle of attack could be adjusted using precision-wedges.Figure 4-1: Experimental model of the turbine tested at UBC tow tank48As shown in Figure 4-2, the upper shaft bearing was mounted out of the water onto a force balanceconsisting of a two parallel plates capable of translating relative to each other and connected via loadcells. The load cells were used to measure the drag force exerted on the turbine as it was towedthrough the water. The turbine revolution speed was regulated using an AC motor controller. Anoptical encoder was used to measure rotational speed and angular position of the main shaft. A torquemeter was connected inline to measure the torque produced by the turbine. In addition pressure tapswere placed along the length of the duct to aid with validation of the numerical modeling.Also, an auxiliary carriage was built with the purpose of providing a stable platform spanning the widthof the tank to allow for installation and testing of ocean engineering devices. This carriage was designedin the Naval Architecture lab and built at the UBC Mechanical Engineering machine shop. The auxiliarycarriage bolts directly to the main carriage by which it is driven as shown in Figure 4-3.Pressure TransducersFigure 4-2: Force balance assembly and data acquisition devices49Turbine assemblyAuxiliary carriageA generic fiberglass Venturi type duct was mounted to the carriage and the surroundingframepositioning the lower shaft bearing. The ducting was 6 feet long by 1 foot maximum width, and wasplaced a chord length from the turbine blade at its closest central point. The turbine and duct setup areshown in Figure 4-4.Main CarriageIFigure 4-3: Testing carriage setupFigure 4-4: Experimental model of a ducted turbine504.2 Testing Procedure and MethodologyThe purpose of this testing was to test a scale model of the Blue Energy vertical axis turbine. The testingin the towing tank consisted of pulling the turbine through the water at a set carriage speed and turbineRPM to measure drag, moment, torque and pressures along the blades. The testing was repeated for arange of carriage velocities and RPM’s. In addition, runaway RPM was also recorded for each carriagespeed. The tests were first done for a blade angle of attack of zero, and subsequently repeated forangles of attack ranging between -10 and +10 degrees.Live data analysis was done following each run to record the average achieved turbine torque which wasplotted versus tip speed ratio (TSR). This method was used to guide the test program and avoidunnecessary runs, namely combination of carriage speed and RPM where the turbine did not producetorque.A final round of testing was conducted with the turbine blades removed in order to provide anapproximation of parasitic drag, namely, the added drag produced by the turbine shaft as well as thearms connecting the turbine blades to the central shaft.In the second set of tests conducted November 2006 at UBC tow tank, a number of changes were madeto the August model, such as minimizing the profile of the arms and replacing the rapid prototypesection of the blade (used for measuring pressure) with a solid aluminum blade. The initial phase oftesting in November repeated a similar testing matrix to that of August in order to establish a newbaseline for the un-ducted turbine. Subsequent testing consisted of measuring the performance of asingle bladed un-ducted turbine by removing two of the three blades. This was done to isolate thetorque fluctuations over a revolution to a single blade as well as attempt to quantify the shadowingeffect produced by the presence of blades and the shaft upstream. Following these tests, a ductedversion of the turbine was tested using the same testing matrix as the un-ducted model. A final set oftests were conducted for a bi-foil configuration of the turbine in both the ducted and un-ducteciconfiguration.Figure 4-5 shows the torque profile of a typical run versus the angle of rotation showing the accelerationof the carriage, the working range of data acquired while the carriage is at constant speed, and thedeceleration of the carriage. A MATLAB code was written to automatically select the acceptable range ofdata at which the carriage velocity is constant and the torque curve is repeated as shown in Figure 4-6.51Torque (Nm)Figure 4-5: Torque curve versusthe azimuth angle for a typical runTo obtain a smooth torque curve vs.the azimuth angle, a special averagingtechnique was implemented.The methodology used forthis task was to isolate the datainto small slices (every 2 degrees)and takethe average of the data points inthat range as shown in Figure 4-6.The torque curve was then plottedover 360 degrees of rotation cycle (Figure4-7).Figure 4-6: Averaging techniqueThe torque curves obtained efromruns at different velocitiesand TSR’s wer used to comparewith theCFD model and the free vortex modelto validate the numerical models. Theexperimental resultsobtained for a free-streamand a ducted turbine will be compared with CFDmodel results in Chapter 7.The numerical and experimental errorswill also be discussed in details asthe main sources ofdiscrepancies between the results.Theta un dearee++++±+++++100 150 200 250 300Figure 4-7: Averaged torque curve overa 360 degrees cycle525. Numerical Results and Post ProcessingProcedureThis chapter includes the numerical resultsobtained from the simulations for both a free-streamand aducted turbine. The results presented include the torquecurves for different current velocities andtipspeed ratios. Also, the non-dimensional powercurves representing the turbine efficiency are givenfordifferent configurations. Comparison of thesecurves can be used to understand the effect of theductingon the turbine performance. Moreover,the torque curve for a single blade in a3-blade configuration ispresented to facilitate the understanding ofthe locations of peaks and troughs of generatedtorque overa cycle. In other words, these curves explainwhy the generated torque is low in someregions over acycle and how to address a low-torque problem.In order to obtain the torque curve for eachconfiguration, a User Defined Function(UDF) was writtenand linked to the software. A UDF consists ofa C++ code linked to the main solution platformto conductfurther detailed calculations which are notincluded or user-customizable within thesoftware. The codefor ducted turbine geometry is identicalto the code used for free-stream turbine.The main task of thecode is to integrate the pressure and shear stressdistribution around the airfoil surface area (Equation5-1). There are two types of forces exerted on the blades:pressure forces and viscous forces. Thecodegoes through each element on the surface of the bladesand calculates the pressure and viscousforcesin X and V directions knowing the normal vectorcomponents to the airfoil surface.P = + Td Equation 5-1Knowing the forces exerted on the blade in X andV directions, the magnitude of torque about the shaftcenter can be easily calculated using Equation5-2.=i x P= (ri +ryf) x (iii + F,j) Equation 5-2In Equation 5-2,r and r are the horizontal and vertical distance of the quarter chord of the blade fromthe center of the rotation. The quarter chord of the blade is the location ofarm attachment to theblades in the experimental. Connecting the arms to the quarter chord of theblades is also structurallybeneficial as the center of pressure is approximately around that point and themoments exerted to thearm-blade joint are minimal.53At the beginning of the simulation, the torque curve shows variation over each cycle. This is because thewake is not well developed. It takes about 5 to 10 seconds of simulations (depending on the inletvelocity and TSR) for the wake to develop (Figure 5-1). At this point, the torque curve starts to repeatover each cycle and the flow field reaches quasi steady state conditions (Figure 5-2).1.0 2.0 3.01ke (5ev)Figure 5-1: Wake development as the turbine rotates4030After reaching the quasi-steady state condition, the average torque and the power generated over eachcycle can be calculated. If the torque is recorded N times in a cycle of rotation, the average torque iscalculated as Equation 5-3.NTavgEquation 5-3The power generated by the turbine blades over a cycle can then be calculated using Equation 5-4.P= Tavg. Ct) Equation 5-4There are two ways to define the efficiency of the turbine knowing the powergenerated per cycle. Thefirst way is to calculate the ratio of the power generated by the turbine to the availablekinetic energy inthe current flowing towards the frontal area of the turbine. This kinetic energy available to the frontalarea of turbine can be simply obtained using Equation 5-5.E—5Leo5tte Cycle 1 —5Ley StyLe Cyc 26010010604020H0-Ojo205026106.00 50 100 150 200 250 300 350 400Theta (Deg)Figure 5-2: Repeating torque curves at steady conditions54‘av = PV3 Equation 5-5Hence, the efficiency can be calculated as follows:— P— Tavg.OJCk —— 1 Equation 5-6av!pAfV3The other way of expressing the efficiencyis to define it as the ratio of generatedpower to the powerthat can be extracted theoretically fromthe turbine. This theoretical value is called Betz limit.The Betzlimit shows theoretically that the maximumextractable power from a wind turbine ora tidal turbine isapproximately 59% (16/27) of the kineticpower available based the frontal area of the turbine.Hence,the turbine efficiency based on Betz limit is definedas Equation 5-7.— P— Tavg.(V CkC3 —— (A v’— Equation 5-727i’2P tfa, 27)As the Betz limit is only applicable to the free-stream conditionsand is incapable of including morecomplications such as the ducted turbine, the efficiencyused in the current research is based on theratio of generated power to the available power(Ck). Hence, all the figures, tables and numberspresented for efficiency in this report use thisdefinition for the turbine’s efficiency.In the design of tidal turbines, extracting the highest possibleefficiency for a set configuration does notnecessarily mean that the design is ideal. There are manyparameters that need to be considered in thefinal design such as ease of structural design, cost, reliability, durability,etc. It is even hard to claim thatthe design is hydrodynamically optimal sincea number of hydrodynamic phenomena were notconsidered in the current study. Additional topicssuch as cavitation need to be considered to obtain anoptimum design; however, these topics are beyond thescope of this research.555.1 Free-stream Turbine Results and AnalysesIn the first set of simulations, the current velocity was assumedto be 1.0 rn/s and tip speed ratio wasranging between 2.00 and 3.00 with 0.25 increments. The results presented aretorque curve over acycle for 3 blades and single blade in a 3-blade configuration as presentedin Figure 5-3 through Figure5-12. Figure 5-16 through Figure 5-25 show the torque curves forthe same tip speed ratios with anincoming current velocity of 1.5 rn/s. Finally, the torque curvesare presented for an incoming ve’ocity of2.0 rn/s.3530252015. 102-10Figure 5-3: Torque curve (3 blades);V=1.O rn/s , TSR=2.OO353025201510........................-.O 90 180 270 360-10Th. (Dig) —Figure 5-5: Torque curve (3 blades);V=1.O rn/s , TSR=2.25.35I0 270 390Th.t (Deg)Figure 5-4: Torque curve (single blade);V=1.O rn/s , TSR=2.OO353025-8zIs2015100-10- --Theta (Deg)Figure 5-6: Torque curve (single blade);V=1.O rn/s , TSR=2.255635I_____ _________Theta (Deg)Figure 5-8: Torque curve (single blade);V=1.O mis, TSR=2.5035—• 30• 2520152 1023530252015so-10 ——.Theta (Deg)Figure 5-7: Torque curve (3 blades);V=1.0 rn/s , TSR=2.50359z•1290-00 . —- Theta (Deg)Figure 5-9: Torque curve (3 blades);V=1.0 rn/s,TSR2.75360-10 — —Theta (Deg)Figure 5-10: Torque curve (single blade);V=1.0 rn/sTSR=2.753530252015! 10203530 — -252015106z‘90 90 180 270 360-30— Theta (Dog)Figure 5-11: Torque curve (3 blades);V=1.0 rn/s , TSR=3.000180 36010Theta (Deg)Figure 5-12: Torque curve (single blade);V=1.0 rn/sTSR=3.0O57The results presented in Figure 5-3 through Figure 5-12 show the torquecurve for 3 blades and 1 bladetorque in a 3-blade configuration. It can be concluded from the3 blades torque curves that:• Torque magnitude increases with the increase in tip speed ratioup to TSR=2.50.• Torque curve for 3 blades has a sinusoidal pattern with 3 peak points overa cycle.• Torque fluctuations amplitude does not change significantlywhen TSR increases. However, thetrough points appear to be shifted up as the TSR increases.• A bump in the torque curve is observed at low TSR’s (TSR=2.0O)at about 80 degrees. However,this bump is diminished at higher TSR. This bump can be the result ofsuper-imposing the torquecurves of each individual blade. As the angle of attack seenby the blades is high at a phase angleof 80 degrees, a severe separation occurs over the inner side of the blade.This bump might bealso due to the flow reattachment to the surface of the blades as well.• At TSR=2.75 and TSR=3.00 a small torque drop is observed in the maximumtorque magnitude. Itis predicted that the torque magnitude continues to decrease significantlyfor TSR’s higher than3.00 as well.The observations from torque curve for a single blade show that:• There is one significant peak point in the torque curve ranging between160 and 180 degrees ofphase angle.• The torque value at the peak point increases slightly as TSR increases.• The phase angle where the torque reaches its maximum shifts to the right as TSR increases. Thisis because when TSR increases, the phase angle at which the blade stalls shifts to a higherazimuth angle.• The important conclusion from the single blade torque curve is that the torque value issignificantly reduced in the downstream section of the turbine (phase angles between 0 and 90degrees and also phase angles between 270 and 360). This is due to the fact that at higher TSR’sthe intense vorticity shed from the upstream blades creates a wide region of disturbed,decelerated flow downstream that lowers the torque generated downstream of the turbine. Inother words, when the blades rotate at a higher angular velocity, a virtual increase in solidityoccurs that prevents the flow with high kinetic energy to be delivered to the downstreamblades. This fact can be shown by comparing the velocity contours at a low and high TSR. Figure585-13 and Figure 5-14 show the velocity contours at the TSR2.0O and TSR=3.00respectively. Theblack zones in these figures show the regions at which the velocity is lower than 0.7 rn/s.It isseen that for TSR=2.00 the low velocity region is notably smaller thanTSR=3.00. It is alsoobserved that the vorticity shed from the shaft has a significant effect onthe downstream flow.Hence, it seems that at lower TSR’s the shaft contribution to downstreamvortices is moresignificant than at higher TSR’s where the vortices shed by downstream blade havedominanteffects on the downstream disturbance.Figure 5-14: Velocity contours at V=1 rn/s and TSR=3.OOFigure 5-13: Velocity contours at V=1 rn/s and TSR=2.OO59After the torque curves were obtained, the average torque and consequently the power generated bythe turbine and efficiency at each TSR was calculated. Figure 5-15 shows the efficiency curve for the firstset of simulations at inlet velocity of 1.0 rn/s and TSR’s ranging between 2.00 and 3.00. It is seen thatefficiency curve slope decreases as the TSR increases. In other words, the torque curve seems to follow aparabolic pattern from a relatively low value at TSR of 2.00 and peaks near a TSR value of 3.00. Thisbehaviour is typical of such devices and has been documented in literature [31-36]. A decreased torquevalue at higher TSR’s is due to low angles of attack seen by the blades. Hence, the drag force will bedominant while the lift force is small resulting in a negative torque magnitude according to Equation 2-3.It is observed that the efficiency does not exceed 32% at TSR=3.00. It should be mentionedthat thisefficiency is calculated based on the average of 2D torque. The 3D effects will be discussed in moredetails in Chapter 6 as well as other sources that cause a drop in efficiency. 2 2.25 2.5TSRFigure 5-15: Efficiency curve for a free-stream turbine at V=1.O rn/sFigure 5-16 to Figure 5-25 show the torque curves for the second set of simulations at an inlet velocityof 1.5 rn/s. Similar to the simulations for an inlet velocity of 1.0 m/s, the TSR ranges between 2.00 and3.00 with 0.25 increments. Knowing the torque curves, the average torque and power can be calculatedand the efficiency can be obtained as presented in Figure 5- 3 3.2560Figure 5-16: Torque curve (3 blades);V=1.5 rn/s , TSR=2.OO1281008060Ez• 40‘9200-20-40Theta (Deg)Figure 5-18: Torque curve (3 blades);V15 rn/s , TSR2.2510080609-z4020-20-40Figure 5-19: Torque curve (single blade);V=1.5 rn/sTSR=2.25120100 —-------806024020-28-40Theta (Deg)Figure 5-21: Torque curve (single blade);V=1.5 rn/sTSR=2.5012092100806040200-2012010080602a 40200-40-20-40 -— —---------Theta (Dc9)Figure 5-17: Torque curve (single blade);V=1.5 rn/sTSR=2.OO120100180609240220120190 180 27040-Theta (Deg)Figure 5-20: Torque curve (3 blades);V=1.5 rn/s , TSR=2.50360 180 270 36061120100 .8 90 180 27020-40Tht(D)Figure 5-22: Torque curve (3 blades);V=1.5 rn/s,TSR=2.75-20-40 ——.--.________Theta(D)Figure 5-23: Torque curve (single blade);V1.5 rn/sTSR=2.75-20Theta (Deg)Figure 5-25: Torque curve (single blade);V=1.5 rn/sTSR=3.OOThe main results for the higher velocity of 1.5 rn/s are very similar to the simulations conducted forV=1.0 rn/s. Several observations and trends emerge as outlined below:• Maximum torque magnitude decreases as TSR increases. At TSR=3.00 a drop in the averagetorque is observed.• The phase angle at peak torque location shifts to the right as TSR increases. However, it is seenthat the range is slightly larger and it covers the phase angles from 150 to 180 degrees.• Similar to the previous results, the single-blade torque curves show a second low-magnitudepeak when the blades pass downstream of the central shaft.• When the TSR increases the downstream peak torque magnitude decreases.82120 .-360 180120270 36010080688240201201008060—214020090 180 270 360-20- 40——Theta (Dc8)Figure 5-24: Torque curve (3 blades);V=1.5 rn/s ,TSR=3.OO————360180 27062• As TSR increases, the torque generated by the blade at angles between 0 and 90 degreesdecreases and reaches a negative average value at TSR’s of 2.75 and 3.00. This problem is due tothe fact that the shadowing effect of upstream blades affects the performance of downstreamblades. This problem will be addressed in Chapter 7 by applying specific duct shapes to reenergize and redirect the flow to increase the power obtained from downstream blades.After obtaining the torque curves for this set of simulations, the efficiency curve is plotted to observethe change in efficiency as the inlet velocity increases as shown in Figure 5-26. A comparison betweenthe efficiency curves at the two speeds shows that the maximum torque achieved at the higher currentspeed is about 2 percent greater. Since the only difference between the two simulations is the incomingspeed of the flow, it is reasonable to assume that the efficiency of the turbine is a function of currentspeed. At the scale presently used for the simulations, the Reynolds numbers seen by the blades are inthe range of 200,000 to 550,000. The turbine is therefore operating within the transition zone betweenlaminar and turbulent flow where Reynolds effects have a substantial influence on the performanceofthe turbine. This difference in Reynolds number is maximized at 90 degrees phase angle at which theblades’ tangential velocity is opposite to the direction of the incoming flow. As density, chord length,and viscosity of water are constant, the change of Reynolds number at different inlet velocities andTSR’s can be specified based on the change in the velocity. Table 5-1 presents the maximum velocitythat the blades see and the relative change in the Reynolds number for velocities of 1.0 m/s, 1.5 m/s,and 2.0 m/s. It should be mentioned that the increase in the Reynolds number is measured based on theReynolds number change compared to the minimum Reynolds number that occurs at V=1.0 rn/s and TSRof 2.00 as described by Equation 5-8.ReV,TSR — ReV1,TSR2Reincreased= DX 100%Equation 5-8neV_1TSR2It can be seen in Table 5-1 Reynolds number increases up to 167% as the velocity and TSR change. It isalso predicted that an increased TSR (where Reynolds number is usually higher) can cause the effect ofthe Reynolds number to be minimized as the Reynolds number is above the transition values.63Table 5-1: Reynolds number changes as TSR and inlet velocity changeFigure 5-26 shows the efficiency curve for velocity 1.5 rn/s. It is observed that at lowerTSR’s where theReynolds number is in transition zone, the efficiency is higher forV=1.5 m/s compared to V=1.0 m/s.This is because of the fact that at higher Reynolds numbers the separationis postponed and the stalloccurs at higher angles of attack.3442.75 5/,512_________1 3 274,679331.5 2 4.5 309,014501.5 2.25 4.875 334,765631.5 2.5 5.25 360,516751.5 2.75 5.625 386,268871.5 3 6 412,0191002 2 6 412,019 1002 2.25 6.5 446,354 1172 2.5 7 480,689 1332 2.75 7.5 515,023 1501170.40.350.;..........................1.75 2 2.25 2.5 2.75 3 3.25TSRFigure 5-26: Efficiency curve for a free-stream turbine at V=1.5 rn/s64Figure 5-27 to Figure 5-36 show the results for the lastset of simulations for the free-stream turbinemodel. The current velocity was 2.0 m/s for this seriesof simulations. It is observed that the torquemagnitude is larger than previous cases as the energyavailable to the turbine is increased (availablepower is proportional to velocity cubed). The same trend was also observedfor the number of peakpoints on both 3-blade torque curves and single blade torquecurves. The behaviour of the upstreamblades on downstream section of the turbine is similar tothe previous simulations that resulted in hightorque upstream and a lower peak point downstreamof the turbine. However, the phase angle range atwhich the maximum torque occurs is between 150 and190 degrees. Thus, the trend seen in these setsof simulations is that the peak point occurs at higherphase angles as TSR increases. This fact can beinterpreted as a result of the stall angle postponement with increasing Reynoldsnumber.•/ZI\Figure 5-27: Torque curve (3 blades) ; V=2.O rn/s,TSR=2.00160140120100180z60a.40200-20160140120100— 80Eza 6040200-20-40Figure 5-28: Torque curve (single blade) ; V=2.0 rn/sTSR=2.0016014012010080za’ 60a.4020-20Figure 5-30: Torque curve (single blade) ; V=2.0 rn/sTSR=2.251\1601401201008060Ez40/\ /IIU180 270Theta (Deg) theta (Deg)-40Theta (Dee)Figure 5-29: Torque curve (3 blades) ; V=2.0 rn/s, TSR2.25-40Theta (Deg)65140120100I604020Theta (Deg)Figure 5-33: Torque curve (3 blades);V=2.O rn/s , TSR=2.75160----.-------— ...-.---.............-:-.—140120 ....__60402:]0 90 180 270 360-20160- — —---. —.— —140 _......20Theta (Deg)Figure 5-32: Torque curve (single blade);V=2.O rn/sTSR=2.5O16014012010080za 604020160 ...140 .. ._________120Q 90 180 270 360-20-40Theta (Deg(Figure 5-31: Torque curve (3 blades);V=2.O rn/s , TSR=L50Ez4,3C90 180 360-20180-40 — — ......_ . ..... ...... . --.._.Theta (Deg)360Figure 5-34: Torque curve (single blade);V=2.O rn/sTSR=2.75-40 .Theta (Deg)Figure 5-35: Torque curve (3 blades);V=2.O rn/s , TSR=3.OO-40Theta (Deg)Figure 5-36: Torque curve (single blade);V=2.O rn/s , TSR=3.OO66Figure 5-37 shows the efficiency curve for the final set of simulations.Figure 5-38 contains the resultsfor all velocities, previously presented separately in Figure 5-15, Figure5-26 and Figure 5-37 to providean easier comparison of efficiencies at different current velocities. In otherwords, this figure shows theeffect of Reynolds number on the rotor performance. As predicted, increasingReynolds number resultsin an improvement in performance. This effect is especiallysignificant in the current simulations as theReynolds number is in the transition range (between200,000 and 550,000). It can also be concludedfrom these results that a scaled up version of the turbinecan perform at slightly higher efficiency thanthe current models since the Reynolds number increases with increasedsize of the device.04. -0.350.20.15__________________________________...0.1 —.—.——.—--—...—... —.-0.050 -1.75 2 2.25 2.5 2.75 3 3.25TSRFigure 5-37: Efficiency curve for inlet velocity of 2.0 rn/s-.—V=1.0 rn/s -.-V=1.5 rn/s —*-V=2.0 rn/s0.05 —— —--—-----—-----0 — —1.75 2 2.25 2.5 2.75 3 3.25TSRFigure 5-38: Comparison of efficiency for free-stream turbine at different currentvelocities675.2 Ducted Turbine Resultsand AnalysesAs a further validation of the numericalmodels, a set of experiments wereconducted at UBC’s tow tankin November 2006. The tested turbinehad a convex, parabolic shape as shownin Figure 3-1. The solverspecification and the simulation procedurewere described in detail inChapter 3. In this section,theresults obtained from thesimulations of the ducted turbineare presented and analyzed.Thecomparison of the results with experimentaldata and the sources of discrepancieswill be discussed inChapter 6.Figure 5-39 to Figure 5-48 showthree-blade and single-bladetorque curves for the ductedturbine withan inlet velocity of 1.5 rn/s. TSR’s testedin these simulations ranged between2.00 and 3.00 with 0.25increments.140140120120100100808068 £604020. 2000270 360-20-40Figure 5-40: Torque curve (singleblade);V=1.5 rn/sTSR=2.00r120:. -90 1801008060zE402203-20-40ZZ90 180 270360Tht (Deg)Figure 5-42: Torque curve (single blade);V=1.5 rn/sTSR=2.25-2043Theta (Deg)Figure 5-39: Torque curve (3 blades); V=1.5 mis,TSR=2.00140120100806040200-20-40-Hi273 360Theta (Deg)Figure 5-41: Torque curve (3 blades);V=1.S rn/s , TSR=2.2568140—12010090 180270 360140120E 40180140 —._-_120 —__________________.. _.._...ioo ———0 90 180270 360-20 ... ._...—-..——-...-- ._. _.__.._..140 -—120 ——---—10000 . — .-—...-.—.. . —.-—-- —.-....-.—.———-60E 40200-20-4040.Theta (Deg)Theta (Deg)Figure 5-43: Torque curve(3 blades);V=1.5 rn/s , TSR=2.50Figure 5-44: Torquecurve (single blade);V=1.5 rn/sTSR=2.5014012010080604020-20270 36090 180 270360-40 -. ...._.._._.__ —-40 -.—Theta (Deg)Theta (Deg)Figure 5-45: Torque curve(3 blades);V=1.5 rn/s , TSR=2.75Figure 5-46: Torquecurve (single blade);V=1.5 rn/sTSR=2.75140__ —120-. — ......__......10040180 270 3600/460270 360Theta (Deg).Theta (bag)Figure 5-47: Torque curve (3blades);V=1.5 rn/s , TSR=3.OOFigure 5-48: Torque curve(single blade);V=1.5 rn/sTSR=3.OO69As it is observed at high TSR’s,the torque fluctuation issignificantly smaller thanthe torque fluctuationat lower TSR’s. A wider singleblade torque curvecan explain the reasonfor such a reductionin thetorque ripple. A higher velocitydownstream of thedevice increases theangle of attack and hence,therear blades generate a largertorque than the free-streamcase.Figure 5-49 shows the efficiencycurve obtained fromthe simulations for theducted turbine at an inletvelocity of 1.5 rn/s. Theefficiency curve revealsthat there is a substantialincrease in the efficiencyinthe presence of the UBCduct around the turbine.The results show thatthe efficiency canreach 56% atTSR=3.OO with a duct which isapproximately 22% largerthan the free-streamturbine.0.7_____0.6 ...0.5 .— -.— — . .0.1 —.——...——..--.6E-161.15 2 2.252.5 2.75 3 3.25-0.1TSRFigure 5-49: Efficiency curve fora ducted turbine at V=1.5 rn/sIt should be mentioned that similarto a free-stream turbine simulation,the efficiency is calculatedbased on the frontal area ofthe turbine, not based on thefrontal area of the device.The same area wasused for consistency betweenfree-stream turbineand ducted turbine calculations.This consistencyallows for an accurate comparisonof the total power generatedby each configuration.The main reasons for the efficiencyincrease in the case ofthe ducted turbine canbe summarized asbelow:70• Flow acceleration: The presence of a converging diverging duct results in an increase in theflowvelocity guided through the turbine. As the duct sectional area decreases in the flowdirection, itcan be simply understood from the continuity equation that the velocity should increase andreach its maximum at the mid-section of the duct where the area is minimum.When thevelocity is increased, the kinetic energy of the flow will increase significantly as the kineticenergy is proportional to the velocity squared. Hence, the power available to the turbine willincrease dramatically with velocity cubed(PayOCV3). It was also observed that the flow atdownstream of the turbine is re-energized compared to the free-stream turbine cases.The flowre-energization also results in higher Reynolds numbers downstream of the deviceand hence,decreases the separation intensity on the downstream blades. Figure 5-50 and Figure 5-51showthe velocity contours for the TSR’s of 2.00 and 3.00 respectively. Comparing Figure 5-50withFigure 5-13 and Figure 5-51 with Figure 5-14 reveals the fact that the flow velocityis higherdownstream of the ducted turbine. Hence the blades at the azimuth angles between -90and 90degrees see a larger upstream velocity and can generate a larger torque magnitude. SimilartoFigure 5-13 and Figure 5-14, the black regions show the areas where the velocity magnitudeisbelow 70% of the upstream velocity magnitude.Figure 5-50: Velocity contours at TSR=2.0O71• Flow redirection: Another factor that causes the efficiency to be increased in case of the ductedturbine compared to the free-stream turbine is the change in direction of velocity vectors. Theangle of attack seen by the blade is a function of the blade’s angular velocity as well as theupstream velocity vector. In the presence of a duct, both the direction and magnitudeof theupstream velocity vectors change resulting in different angles of attack compared to thefree-stream turbine case. The effect of the change in upstream velocity vector on the angleof attackis compared in Figure 5-52 and Figure 5-53. Figure 5-52 shows the angle of attack a blade seesinthe absence of the duct while Figure 5-53 shows the angle of attack in the presenceof the duct.v’—Vr . wav- - - - - - --: - - - - -- - -- v_ - - - -- - - -Figure 5-52: Blades angle of attack calculation for a Figure 5-53: Blades angle of attack calculation fora ductedfree-stream turbine turbineFigure 5-51: Velocity contours atTSR=3.OO72In the second set of simulations for the ducted turbine model, the inlet velocity was changed to 2.0 rn/swhile the tested TSR’s were the same as the first series. Similar to the free-stream turbine, the mainresults of an increase in the current velocity is the effect of Reynolds number on hydrodynarniccoefficients. It subsequently affects the shear stress as well as pressure drag, separation and stall angle.Figure 5-54 to Figure 5-63 present the torque curves for this set of simulations. As observed from thetorque curves, the torque amplitude is very large at lower TSR’s (2.00 and 2.25) as a result of high anglesof attack as well as dynamic stall. However, at TSR of 2.50 the torque fluctuations begin to reduce and atTSR=3.00 the torque fluctuations become minimum. The single blade torque curves can explain thereason for the reduction in the torque fluctuations. As shown in the single blade torque curves, thecurve is sharp at its peak point at low TSR’s, but at higher TSR’s this curve begins to become wider andthe peak point has a lower value compared to low TSR’s. Thus, when single torque curves are superimposed, the final curve should be smoother if three flatter and wider curves are super-imposed. TheTorque Ripple Factor defined by Equation 5-9 can be defined and used to quantify the torquefluctuations magnitude for different cases.TRF= Tmax — TminEquation 5-9avgThe results suggest that at V=1.5 rn/s and TSR=2.75 the TRF is reduced from 1.92 for a free-streamturbine to 0.82 for a ducted turbine. It is also observed that at V=2.0 rn/s and TSR=2.75, the TRF isreduced from 1.72 for the free-stream turbine to 0.37 for the ducted turbine.25080 270 360250200150Eza 100C50-50Theta (Dee)200150Ezw 100a.500-50Theta (Deg)Figure 5-54: Torque curve (3 blades);V=2.O rn/s , TSR=2.OO Figure 5-55: Torque curve (single blade);V=2.O rn/sTSR=2.OO73250 —200 —- -90 180 270 360Thete (Deg)Figure 5-58: Torque curve (3 blades);V=2.O ,TSR=2.50200______________________—150___________________________ __________________0 90 180 270 360-..--— --—-Theta (Deg)Figure 5-60: Torque curve (3 blades);V=2.O rn/s , TSR=2.75250200250 —200150Ea 100 -50-50 -Theta (Deg)Figure 5-56: Torque curve (3 blades);V=2.O rn/s TSR=2.25150 -82a 10050-50Theta)D.g)Figure 5-57: Torque curve (single blade);V=2.O rn/sTSR=2.252552001508z100C50180250r0 360-50 -Theta (Deg)Figure 5-59: Torque curve (single blade);V=2.O rn/sTSR=2.50250200 -150——— —Theta (Deg)Figure 5-61: Torque curve (single blade);V=2.O rn/sTSR=2.7574250r.250200 200............................ .•100.270 360-50Theta (Deg)________JFigure 5-63: Torque curve (single blade);V=2.O rn/sTSR=3.OOThe torque curves show that the torque amplitude decreases significantly as TSR increases withoutreducing the efficiency. The TRF for TSR=2.00 was 2.69 while for TSR=3.00 TRF decreased to 0.29. Figure5-64 present the efficiency curve for the ducted turbine at V=2.00 rn/s.‘I0.3 . . . 2 2.25 2.5 275TSRFigure 5-64: Efficiency curve for a ducted turbine at V=2.O rn/s3.25150100500 90150 .____________________1805050Thata (Deg) ** —Figure 5-62: Torque curve (3 blades);V=2.O rn/s , TSR=3.OO180 360756. DiscussionIn Chapter 5, the simulations results obtained for a free-stream and ducted turbine models werepresented. One of the main tasks in every numerical work is to validate the results obtained from anumerical model with usually experimental data as the reference. Thus, the simulation results obtainedfor the UBC turbine were compared with the experimental data obtained at UBC’s tow tank inSeptember 2007. The experimental data includes the free-stream and ducted turbine test results.As it was described in previous chapters, the CFD model developed for the tidal turbine in the currentresearch is a two-dimensional model. A 2D model was developed because of its acceptablecomputational cost. Also, as blades’ aspect ratio were relatively high (about 10), it was predicted that a2D simulation can more or less represent the trends of a 3D model. Development of a 3D model was farbeyond the financial capabilities and computational facilities available at this stage of the productdevelopment.In order to be able to compare the experimental data with the results of the numerical model, it isnecessary to compare results of similar geometries. There are two main geometric differences betweenthe numerical model and the experimental model:• The arms and the attachment assembly connecting the blades to the central shaft (Figure 6-1and Figure 6-2)Figure 6-1: Arms-Shaft connections Figure 6-2: Arm-Blade connection76. Three-dimensional blades in experiments vs. two-dimensional airfoils in the CFD modelThere are also some other physical discrepancies between the two models such as the roughness of theblades and the blades’ profile which is cut at trailing edge in experiments.To be able to compare the performance of a turbine with connecting arms (experimental model) andthe one without the connecting arms (numerical model), the effect of arms on the performance shouldbe excluded. The next section is dedicated to the approach taken to exclude the arms effect from theexperimental data.6.1 Arms EffectThe arms and the attachment assembly (which, from now on will be called the connection assembly),have a significant effect on the performance of the turbine. Although the structural difficultiesassociated with the design of the arms are very important, the main focus in the current research is onthe hydrodynamic impact of the arms on the flow field and the turbine’s hydrodynamic performance.The most significant effect of the arms on the performance is due to the counter torque generated bythe arms when the blades are rotating. The parasitic drag caused by the rotation of the arms is thesource of the counter torque generated by the arms. Consequently, the counter torque generated bythe arms lowers the average torque generated by the system over a cycle and hence lowers the turbineefficiencies at all TSR’s. As the velocity seen by the blades at different TSR’s and inlet velocities change,the parasitic drag generated by the arms, which is proportional to velocity square, will changeconsiderably. Hence, the counter torque created by the arms drag can be described as a function of TSR.In order to quantify the counter torque generated by the arms, a set of experiments were conducted fordifferent velocities and TSR’s for turbine without blades. In other words, the turbine bladesweredetached but the arms remained on the system (Figure 6-3).The counter torque generated by the arms can be obtained using Equation 6-1. Ck can be calculatedusing an empirical formula (Equation 6-2) obtained from the test results of the turbine with no blades.Tarms = Ck (_pv3AfrQflt)Equation 6-1Ck(0.020244)TSR2+ (O.041997)TSR — 0.034278Equation 6-277Figure 6-3: Arms parasitic drag experimental modelAfter obtaining the counter torque generated by the arms using the above equation, the torque valuefor a turbine without the arms can be calculated by subtracting the arms’ torque from the total torquegenerated by the blades at the same speed and TSR (Equation 6-3).T,0arms(V, TSR)= T arms(V, TSR) — Tarms(V, TSR) Equation 6-3It is important to note that although the above equation describes the effectof the arms on the torquemagnitude, it is only a rough approximation of the arms’ effect on the performance of thecompletesystem. An important phenomenon that was neglected in this approachwill be discussed later in thischapter when the sources of discrepancies are described. A comparisonof FLUENT results with andwithout the arms effect is presented in Figure 6-4. The flatness in the efficiency curveobtained from thesimulations is mainly due to subtracting the arms counter torque from the generatedtorque by theblades. It is also important to consider the arms effect when optimum operational conditionof thedevice is specified.78-.—FLUENTwithout Arms -.-FLUENTwIth ArmsFigure 6-4: Comparison of the efficiency curve with and without the arms effect (V=1.5 mis)6.2 Validation of Numerical ResultsIn this section the numerical and experimental results for the torque and power generated at differentvelocities and TSR’s will be presented. The results presented include the comparison of the powergenerated by the free-stream turbine at TSR’s ranging between 2.00 and 3.00 at velocities of 1.5 and 2.0m/s. Also, the torque curve will be compared for a few TSR’s and the differences will be discussed.Moreover, to obtain more confidence in the validity of the simulations, the results for a ducted turbineare compared with experiments.Figure 6-5 and Figure 6-6 show the comparison of efficiencies predicted by the numerical model andexperiments for a free-stream turbine at current velocities of 1.5 m/s and 2.0 rn/s respectively.0.40.350. 2 2.25 2.5 2.75TSR3.2579—.—Experiments -.—FLU ENT-2D0.70.6— — —0.50.4LZEZ1.75 2 2.25 2.5 2.75 3 3.25TSRFigure 6-5: Comparison of numerical and experimental efficiencies for a free stream turbine at V=1.5 rn/s-+-Experiments -*-FLUENT-2D0.7--0.60.5—-0.4 ______._______0.1 ---- - -----.--- —-- --01.75 2 2.25 2.5 2.75 3 3.25TSRFigure 6-6: Comparison of numerical and experimental efficiencies for a free stream turbine at V=2.O rn/sThe results show that the power coefficient by the numerical model is properly predicted and the resultsare close to the experimental results. The experimental results presented in these figures are the mostrecent results obtained at UBC in September 2007. These results are significantly closer to the numerical80model predictions compared to the previous experimental results obtained at UBC in November 2006.The main changes in the recent experiments were the new drive-terrain with a worm-gear which wasexpected to provide a more rigid system compare to the previous drive-terrain. Another importantchange in the new experimental model was replacing two arms in the quarter-span of the blade withthree arms, one at the mid-span and two at the blades’ tips as shown in Figure 6-7 and Figure 6-8.It was observed that placing the arms at the tip of the blades affects the performance of the turbinesignificantly. The efficiency was increased up to 100% relative to the November 2006 tests due to thechange in the arms’ profile and their attachment location. This is predicted to be due to the preventionof induced flow circulation from the pressure side to the suction side. In other words, the armconnection at the tips acts as a winglet in the airplane wing design which results in a decreased induceddrag. Thus, 2D simulations better represent the recent series of experiments with three arms compareto the previous experiments with two arms in the quarter span.After validation of a free-stream turbine, the ducted simulations should be validated. The comparison ofthe experimental and numerical results for the UBC duct configuration is presented in Figure 6-9(V=1.5m/s) and Figure 6-10 (V=2.0 mis).Figure 6-7: 3-Arm configuration Figure 6-8: Arm-blade connection at the blades tip81The results show that the predicted numerical results are close to the experimental results. It isobserved that the numerical efficiencies are predicted slightly higher than the experimental results. Thereason for that is because of the 3D effects included in the experiments as well as the effect of the topand bottom walls (Plexiglass plates in Figure 6-18) confining the turbine in the duct. The boundary layerseparation from these plates can increase the flow disturbance and reduce the torque in the upstreamsection of the turbine.Also, a variable RPM creates a different flow field compared to the numerical model with an absolutelyconstant value for RPM. Variable RPM also affects the amplitude of the torque curve as well as thephase angle where the torque curve reaches its maximum value.—.-Experiments -.—FLU ENT-2D0.71.75 2 2.25 2.5 2.75 3 3.25TSRFigure 6-9: Comparison of numerical and experimental efficiencies for a ducted turbine at V=1.5 rn/s82—e-Experiments -.-FLUENT-2DFigure 6-10: Comparison of numerical and experimental efficiencies for a ducted turbine at Vz2.0 rn/sThe comparison of the torque curves for free-stream and ducted turbines (Figure 6-11 through Figure6-14) show that the torque amplitude is under-predicted in the numerical models compared to theexperiments. This discrepancy may be because of two main reasons; the drive-terrain and dynamic stallsimulation. As it was mentioned earlier in this chapter, the drive-terrain was replaced in the lastexperiments to create a more rigid system, but RPM monitoring showed that the motor response wasnot fast enough to keep a constant RPM. Thus, the variable RPM problem continued to affect theresults. Also, the coupling between the shaft and motor was slightly loose and caused a bucket shape inthe torque curve especially at lower TSR’s. Another source of discrepancy in experimental and numericaltorque is the dynamic stall phenomenon. As the blade angle of attack is high in low TSR’s, dynamic stalleffect becomes more important in simulations. An extensive research on the numerical simulation of anairfoil in high angles of attack using different turbulence models and comparison with experimentalresults showed that the stall angle is usually predicted in lower angles and the lift coefficient is slightlyless at stall angle in numerical models [41]. This could be due to the low level of accuracy in theturbulence models at high angles of attack.As seen in the torque comparison figures, variable RPM as well as dynamic stall simulation problemsalso create a phase difference in the torque curves. At lower TSR’s where the torque magnitude is notlarge, the phase difference between the numerical and experimental torque curve for the free-stream0. 2 2.25 2.5 2.75 3 3.25TSR83and ducted turbine is 43 and 42 degrees respectively. However, it is observed that at higher TSR’s thephase difference is more pronounced. In fact, the motor cannot quickly respond to the changes in thetorque magnitude when the torque generated by the blades is large. The phase difference between thenumerical and experimental phase is 55 degrees for free-stream turbine and 50 degree for the ductedturbine. However, the trends are found to be similar in the numerical model and in the experiments. Inthe case of the free-stream turbine, the phase angle is shifted by 18 degrees in numerical results while itis shifted by 24 degrees in the experiments. For the ducted turbine, the phase shift is 19 degrees innumerical results while it is 15 degrees in the experimental results. A comparison between the torquevalues obtained from FLUENT and numerical results obtained from a Free Vortex Method developed inUBC Naval Architecture Lab showed agreement for torque amplitude as well as the phasing [40].-100Figure 6-11: Comparison of experimental and numerical free-stream turbine torque at V=1.5 TSR=2.OO20100 90 180 270 360Tht(Dg)Figure 6-13: Comparison of experimental and numericalducted turbine torque at V=1.5 TSR=2.75Figure 6-12: Comparison of experimental and numerical freestream turbine torque at V=2.O TSR=2.75Figure 6-14: Comparison of experimental and numericalducted turbine torque at V=2.O TSR=2.OO200—E,W000,ent —FLUEN1-2D150100050—E,perinent —FLUENT-20250200 — -—150E10050-5090 100 270 360Th(Deg)-50Th60(D)—Epenn,ent —FLUENT-lb100 .... ....908070608504030—E0perrnt —FLUENT-lb400 -300200E100aa-100-200360-300Tht(D)84Also, a comparison of the FLUENT results with the results obtained from theDiscrete Vortex Methodcode, developed in the Naval Architecture Lab, shows agood agreement between the two numericalmodels (Figure 6-15 and Figure 6-16).—FLUENT —Experia,ent DVM140120 — -100 F-80E60z4020-20180_ 360-40 -- — --Theta (Deg)Figure 6-15: Comparison of 3-blade torque obtained from Figure 6-16: Comparisonof single-blade torque obtainedFLUENT, DVM, and Experiments (V=1.5, TSR=2.5O) from FLUENT, DVM, and Experiments (V=1.5, TSR=2.50)6.3 Sources of DiscrepancyAs it was described in the previous section, there are discrepancies between the resultsobtained fromthe numerical model and the experimental model results. In this section,the sources of thesediscrepancies will be discussed in more details. The sources ofdiscrepancies can be described in twomain categories, numerical errors, and experimental errors. Below is a summaryof the errors associatedwith the experiments and numerical models:• Numerical sources of discrepancyo 2D vs. 3D: The first reason of discrepancy betweenthe numerical simulation results andthe experimental results is due to the difference in the geometryof the simulatedmodel. As it was briefly mentioned in the previous section,the simulations wereconducted for a 2D turbine without any arms. Three-dimensional effectsincluding tipvortices are neglected in the conducted simulation.o Arms effects: The arms not only have a significanteffect on the generated torque by thesystem, but also disturb the flow field inside theturbine area and affect thedownstream blades performance. Even, subtracting the arms counter torquecan notaccurately exclude the arms effect from the experimental data because theblade-arminteraction and the blade-arm connection effects are still neglectedin this approach.140—FLUENT —Etperiment -DVM90-20-40Theta (Deg)85o Blade Shape: One of the geometric differences between the numerical model andexperimental model is the difference in the shape of the blade’s trailing edge. While thenumerical model has the blades with sharp trailing edges, the experimental modelblades’ trailing edges were cut off due to manufacturing purposes. As a matter of fact, asharper trailing edge can be manufactured; however, making the trailing edge as sharpas possible could increase the manufacturing time and cost. In addition, a very sharptrailing edge is not predicted to be a viable and durable design. It is predicted that afterthe installation of the turbine into the ocean, debris, algae, and ocean species willgradually accumulate on the surface of blades; hence, sharpening the trailing edge maynot last for a long time. In addition, a sharp trailing edge may also entail environmentalissues such as endangering fish and other ocean species that may be cut by the sharpblade edges.o Blade Roughness: Another discrepancy between the numerical and experimental modelis that the roughness of the blades was not taken into account in the simulations.Although the blades were built very smooth, they still had a physical roughness thatcould make a slight difference in the experimental results and numerical results.Although the roughness of the blades can improve the performance by postponing thestall, the negative effect of the increased frictional drag caused by the blade’s roughnessis dominant and causes the average torque to be decreased.o Turbulence modeling: Turbulence modeling is one of the most important andcomplicated problems in computational fluid dynamics. Although many turbulencemodels were developed by scientists and researchers, no turbulence model has beenrecognized as a superior one. The inaccuracy of turbulence models are morepronounced at higher angles of attack with significant separation of the flow. In thecurrent research, the direct effect of this shortage of accuracy at higher TSR’s at whichangle of attack is significantly larger than the stall angle. This inaccuracy affects theturbulent viscosity calculations and consequently results in inaccuracies in prediction ofthe lift and drag forces on the blade.o Truncation error: As it was discussed earlier in this report, a computational solution tothe fluid dynamics problem should be conducted by converting Partial DifferentialEquations (PDE’s) to algebraic equations. This conversion should be done by writing theflow parameters in the form of a truncated Taylor expansion series. Dropping of higher86order terms (higher than two in the current simulations), results in a numerical errorwhich is called truncation error. Truncation error is a general part of every CFD solutionand can be reduced by using higher order solvers.o Round-off error: Round —off error is another general error contained in computationalsolutions to the physical problems. This error is basically the difference between thecalculated approximation of a number, stored in the memory of computer and the realmathematical value of that number. There are two types of solvers available in FLUENT,single-precision and double-precision solver. Although single-precision solvers aresufficiently accurate for most of the problems, a double-precision solver was used in thecurrent work to reduce the error imposed to the solution due to the round-off error.Needless to say that double-precision solver needs a larger capacity of the computer’smemory.Experimental sources of discrepancyo Arm-blade connection: It was mentioned in the previous section that a series of testswere conducted with the blades detached to measure the counter torque generated bythe arms. Although this approximation helps to exclude the arms effect on the averagetorque and efficiency, it still neglects an important part of the physics of the problem. Infact, the flow disturbance generated by the rotation of the arms inside the turbine canaffect turbine’s performance significantly. Vorticity shed from the arms results inchanges in the magnitude and direction of velocity vector observed by downstreamblades. Thus, it can change the torque generated by the downstream blades. Thisphenomenon was neglected in the numerical simulations and can be an importantsource of discrepancy between the experimental and numerical results. For the mostrecent series of experiments at UBC Naval Architecture Lab, the arms profile waschanged to a NACA 0012 profile to reduce the counter torque generated by the arms aswell as to reduce the flow disturbance and vortex shedding on downstream blades.o Drive-terrain response time: As it was observed in the validation section, there is aphase difference between the numerical results and experimental results. Part of thisdifference is due to the inability of turbulence models to predict the separationaccurately. Another important source of this phase shift is caused by the slow responseof the motor to the changes in the torque in the experiments resulting in a fluctuating in87RPM. These fluctuations were more pronounced for the cases with higher currentvelocity and TSR at which the torque magnitude imposed to the motor is relatively large.Figure 6-17 shows the RPM fluctuations for a current velocity of 2 m/s and a TSR of 3.Figure 6-17: RPM fluctuations in experimentsAs it can be observed, the RPM ripple is about ±10% of the mean value. This problemaffects not only the instantaneous power generated but also can change the physics ofthe flow field around the blade and consequently the hydrodynamic forces. To addressthis problem, the drive-terrain was changed in the most recent experiments. The mainchange was to use a worm-gear instead of the regular gear box to convert the torsionimposed to the motor to an axial force. This change was predicted to minimize the RPMripple in the experiments.o Free surface effects: As the turbine is dragged in the tow tank, the free surface of tank isdisturbed significantly as shown in Figure 6-18 and Figure 6-19. The free surfaceboundary can affect the experimental results. The free surface effect can be reduced bymounting the turbine deeper in the tank. However, there is a limit for the turbine depthas it gets close to the towing tank bed. Also a design with a lower system overall drag(such as more stream-lined blades and arms and less 3D effects) can results in reducedfree-surface effect on the solution.115110105100959085800 50 100 150 200 250 300 350 400Theta (Deg)88o Averaging Technique: If the torque generated by the turbine is plotted vs. time oraccumulative azimuth angle, it will be observed that the torque curve is not beingrepeated identically (Figure 6-20). In other words, the peaks and troughs should betheoretically close but is seen that these values are fluctuating about ±10%. In thecurrent work, the average power is calculated based on the torque generated over thewhole run as opposed to a single cycle.Figure 6-18: Free surface disturbance at lower Figure 6-19: Free surface disturbance at highervelocities velocitiesr,.i1I1•i•.iviIvTt77Figure 6-20: Experimental torque variations89o Instrumentation uncertainties and mechanical losses: Similar to every experimentalwork, there are a few uncertainties and losses in the experimental setup. The moreabout these issues will be addressed in the Naval Architecture Lab reports onexperiments. As a source of discrepancy between the numerical and experimentalresults, it should be mentioned that some losses such as mechanical losses in the drive-terrain (gear box and motor) and the bearings as well as signal losses exist in theexperiments which are not included in the CFD simulation of the turbine. However, it ispredicted that these losses are insignificant and do not substantially affect the resultsaccuracy.All the uncertainties involved with the experiments can be included in the presentation of the results byusing error bars for the experimental result. The methodology used for obtaining the range of error forthe experiments is beyond the scope of the current work. However, in order to ensure that theexperimental and numerical results are in an acceptable level of agreement, a comparison was alsomade between the numerical results and experimental results with error bars as shown in Figure 6-21.I——Experimental 1.5 m/s-a—Fluent 1.5 mIs-0— Experimental 2 m/s-St-Fluent 2 m/s0.500.450.400.350.30- 025C.) 1.75 2 2.25 2.5 2.75 3 3.25TSRFigure 6-21: Comparison of free-stream results from FLUENT and experiments including the error bars907. Duct Shape OptimizationThe preceding chapters focused on validation of free-stream and ducted turbine simulationsusingexperimentally obtained data in a towing tank. The accuracy of the simulations showed tobe adequateto justify proceeding onto the next phase of the project. This phase focuses onmodifying the ductgeometry to increase the performance of the turbine.7.1 Preliminary ApproachNumerous duct shapes were examined to understand the physics of theflow inside a duct and tounderstand whether they can be used to improve the power generated by the turbine.The torque curveover a cycle of rotation was used as a guideline to improve the performancein the regions where thetorque generated by the turbine was relatively low.Figure 7-1 shows a typical torque curve for one blade in a 3-blade configuration.A closer look at this curve reveals that the torque curve can bedivided into three main regions: greyregions, orange regions, and green region. The grey regions areexpanded through azimuth anglesbetween 0 to 90 degrees and 270 to 360 degrees. This region corresponds to thedownstream portion ofthe blade rotation. The orange regions are the regions at whichtransition between positive torque andnegative torque occurs. In these regions, the angle of attack changesfrom a positive value to a negativeFigure 7-1: Single-blade torque curve over a cycle in the presence of the other two blades91value and vice versa. Hence, the angle of attack would be zero at some point duringthis transition. Inthese transition regions, there exists a point at which the torque is negative. This occurs when the bladepasses through an ang!e of attack of zero and the only torque generated by the turbinewould be acounter torque according to Equation 2-3. The green region is where the torque magnitude reaches itsmaximum. At this point, the angle of attack is large and close to the stall angle. It should be mentionedthat at low TSR’s (TSR’s below 2), the maximum angle of attack exceeds the stall angle.The strategy chosen to increase the power generated by the turbine was to increase the torquemagnitude in the grey and orange regions while keeping the high torque of green region.As it can be seen in Figure 3-1, the narrowest part of the duct is exactly at the mid-section. Thus, inorder to satisfy the continuity equation for an incompressible flow, the maximum velocity would occurat mid-section of the duct. As it was shown in Figure 7-1, the mid-sectionof the duct is where themaximum negative torque is produced. Hence, by accelerating the flow in the middle part of the duct,the drag force (which is proportional to the velocity square) and the counter torque would increasesignificantly. Also, the grey regions can be improved by reenergizing the flow in the rear part of turbine.To be able to compare different ducts performances, a number of geometric limitations should beconsidered as the design constraints. For example, if the duct size is increased, the flowvelocity insidethe duct is increased as a result of larger inlet area. Consequently, the availableenergy to the turbinewould be different from that of the UBC duct and the comparison would not be valid. Thus, acontraction ratio is defined by Equation 7-1. For all the ducts tested, the contraction ratio was assumedto be constant (except for double-duct cases) to enable a valid comparisonbetween different cases.mmCR= AEquation 7-1maxIn order to tackle the above problems, a set of simulations were conductedfor a duct shape shown inFigure 7-2. This duct shape is similar to the UBC duct with aconcave hollow shape in the mid-section.The modified duct is referred to as UBC’s 1 modification (mod 1 to bebrief).923OQe+OO2 85e,002 70ec002 55e+OO2 40e.OO225e+OO2 10e+OO1 95e*OO1 80e+OO1 65e.OO1 50e.OO1 35e.OOI 20e.OO1 05e*OO9 OOe-O17 50e-O16 OOe-O1450,01300e-0II 50e-010 OOe+00Figure 7-2: UBC duct with a hollow in the middle (mod 1)As observed from the velocity magnitude contours (Figure 7-2), the throat is transferredto the hightorque region at the front to keep or increase the flow velocity hitting theupstream blades. Also, asecondary throat at the rear part of turbine reenergizes the flow to increasethe torque generated bydownstream blades. Also, an attempt was made to widen the duct sectional areain the mid section todecelerate the flow in the counter torque zones.In addition to the above duct, two other ducts (2 and3Idmodifications of the UBC duct, referred to asmod 2 and mod 3) with the same contraction ratio and throat locations butwith different inner edgeswere examined to understand the effect of the flow redirectionon the torque curve. Also, it waspredicted that these geometric changes slightly affect the mass flow rateinside the duct. This would bedue to the change of location of the stagnation point at themouth of the duct.Figure 7-3 shows the second duct geometry examined with straight line edgesconnecting the duct tipsto the concave hollow in the middle. This duct shapeprovides different angles for the upstream bladesclose to the duct. Figure 7-4 shows the mod 3 duct with a concaveconnecting edge. The same conceptwas pursued for this duct as well.93It can be understood from the velocity contour figures that the duct with convex connecting edges(Figure 7-2) has the widest high velocity region while the third duct with concave connecting edges(Figure 7-4) has a limited high velocity region. It is seen that for the latter, the separation zone is widelyexpanded at the downstream of the duct resulting in deceleration of the central parts of the flow.Figure 7-3: A duct with straight line connecting edges (mod 2)300e.OO2 85eOO270e,002 55e+OO2 40e*OO25e+OO2 10e.OO1 95e+OOI 8O.OO1 65e-.OO1 5Oe-OO1 35eOO1 20e-f 00I 05e+009 OOe-017 500-016000-014 5De-013 000-011500-010 OOe+00Figure 7-4: A duct with concave connecting edges (mod 3)94In order to understand the effect of the flow redirection on the torque curve it is necessary to run theunsteady simulations and observe the wake development when the blades are rotating. The simulationswere conducted for a constant velocity of 1.5 rn/s and TSR’s ranging between 2.00 and 3.00. The torquecurves and the efficiency curves were then compared to understand the effect of the duct geometry onthe turbine’s performance. All the grid specifications and solver properties used for these simulationsare identical to UBC’s duct simulations. The comparison of efficiencies obtained from different ductshapes and also the UBC duct is presented in Figure 7- -.-mod2 -*-mod3 —UBCTSRFigure 7-5: Efficiency comparison of different modifications of UBC ductThe following conclusions can be extracted from the above figure:• 3rdmodification of the UBC duct performs even worse than a free-stream turbine. Its efficiencyis lower than the UBC duct or any other modifications at all TSR’s. However, the power curve isflat which means that the turbine can work in the design conditions over a vast range of RPM’sand current velocities.1.75 2 2.25 2.5 2.75 3 3.2595• 15tand2ndmodifications’ efficiencies are higher than the UBC duct at low TSR’swhile theefficiency reaches its maximum at TSR of 2.5. At higher TSR’s they bothhave a lower efficiencycompare to the UBC duct. Also, both1stand 2’’ modifications have a flatter efficiency curve thanthe UBC duct. That means that their performance isless sensitive to the changes in RPM andcurrent velocities which results in changes in TSR.• It is observed that2ndmodification has a higher efficiency than the1stmodification at lowerTSR’s (2.00 and 2.25). On the other hand, 1 modification has a slightlyhigher efficiency athigher TSR’s.The selection of each duct depends on the design conditions andrestrictions. For example, theturbine needs to work at low TSR’s as higher TSR’s produce relativelyhigh levels of noise havingnegative environmental effects. The structural and mechanical designrestrictions are anotherconstraint to the duct design process. The cost of the ductmanufacturing is another importantparameter that should be considered in the duct selection process. Theserestrictions will bediscussed further in Chapter 8. The comparison of the three-blade and single-bladetorque curves atdifferent TSR’s is presented in Figure 7-6 to Figure 7-15.—,od1 mod2 ,,od310080 80IThet, (Deg)Figure 7-6: 3-Blade torque comparison of three UBC duct Figure 7-7: Single-Blade torquecomparison of three UBCmodifications (V=1.5 rn/s ; TSR=2.OO) duct modifications(V=1.5 rn/s;TSRZ.OO)—nod1 ---,eed2 modt10060Theta (Deg)9660z,40200 180 240\\ 300 36020Thta(Deg)Figure 7-9: Single-Blade torque comparison of three UBCduct modifications (V=1.5 rn/s ; TSR=2.25)—modi ——— ,ood2 mod3100608z40-20Thet(Dg)Figure 7-10: 3-Blade torque comparison of three UBC ductmodifications (V=1.5 m/s;TSR=Z.50)—modi --—,ood2 ood3800 60 120 180 240 300 360 0-20 -Theta (Deg)Figure 7-12: 3-Blade torque comparison of three UBC ductmodifications (V=1.5 rn/s;TSR=2.75)—rnodl --- o,od2 ood310080608z;40—nod1 --- ood2 mod3100 —-80 F200 60 120 180 240 300 360-20 --Th60 (Deg)Figure 7-8: 3-Blade torque comparison of three UBC ductmodifications (V=1.5 m/s; TSR=2.25)—modl --- n,od2 mod310080 8020 —--.------—— —--——.-0 60 120 180 240 300 360 . 20 180 240 300 360-20.-Tht (Deg)Figure 7-11: single-Blade torque comparison of three UBCduct modifications (V=1.5 rn/s ; TSR=2.50)—modl —-— madl mod3-.- 10010080 F60Ez;4020180 240 - 300 360-20Th(Deg)Figure 7-13: Single-Blade torque comparison of three UBCduct modifications (V=1.5 rn/s ; TSR=2.75)97—nod1 ----mod2 mod3 —e,o41 ---mod2 mod3100 -- - 100-— - —- ——80 80z _, ‘40 - - -2:1 -6 20 180 240 - 300 360-20 -- --Theta (Deg)Figure 7-16 shows the typical single-blade torque curve for the UBC duct and its three modifications.It is shown that the UBC duct curve is sharper at its maximum while from mod 1 to mod 3, themaximum torque decreases and the positive torque curve region widens.According to Figure 7-16, the torque generated downstream is slightly increased which can be theeffect of flow-reenergization due to the transfer of the duct throat to the rear part. Yet, it isobserved that throat designed near the mouth of the duct, adds to the blockage of the duct andprevents the flow velocity to increase upstream. As a results, the flow velocity and consequently,the maximum torque is lower in the presence of the throat in the front.Another noticeable phenomenon in the results is the widened torque curve as a result of flowredirection. Changing the place of the throat results in changes in the angle of attack in the regionsthat the torque generated is low due to low local angle of attack. However, it is observed that theeffect of flow redirection is not very significant. Also, it seems that the 2 modification has thewidest torque curve as a result of the flow redirection. Thelotand3rdmodifications however, have anarrower peak and their width is about the same as the UBC duct.60L-0 60 120 160 240 300 360-20Theta (Deg)Figure 7-14: 3-Blade torque comparison of three UBC ductmodifications (V=1.5 rn/s;TSR=3.OO)Figure 7-15: Single-Blade torque comparison of three UBCduct modifications (V=1.5 rn/s ; TSR=3.OO)987.2 Steady-State Study of Different Ducts7.2.1 MethodologyIn order to better understand the effect of blockage on the torque curve and to maximizethe mass flowrate inside the duct, a set of steady-state simulations were conducted for different duct shapes.Themethodology used for this phase of study was to examine different duct shapes with the samecontraction ratio and inlet area as the UBC duct. This means that a design box with constant boundarieswas defined and the duct shape could change inside that box as long as the duct edges touchthe boxboundaries (to meet the constant contraction ratio requirements). The box concept with constantcontraction ratio (Amin/Amax) is shownin Figure 7-7.As it will be described later in this chapter, in some cases the constant contraction ratio assumption andthe design box approach were not considered as the design constraints. This was the case to studytheconcept of a double-duct design.EzU0•—modi -——mod2 mod3 —UBC100 ——----______-— ________806040200-20Theta (Deg)360Figure 7-16: Typical single-blade torque comparison for UBC duct and it s modifications (V=1.5 rn/s ; TSR=2.50)99wr.A-.‘miniL — — — — — —AaI II II IL- I2Figure 7-17: Design box conceptThe ducts can be categorized into two main types:• Single-compartment ducts• Multiple-compartment ductsFor the first category of the ducts, similar to the UBC duct, the duct consists of two large scale parts withno add-ons. In other words, like the first three modifications of the UBC duct, the UBC duct was furthermodified to achieve the desired flow field inside the duct. For multiple-compartment ducts, however, anattempt was made to obtain the desired conditions by using some additional components inside theduct such as vanes and secondary ducts. The scale of the add-ons is usually significantly smaller than themain duct and in some cases they are used for fine-tuning of the design.The ducts were named by number and the initials of the researchers who proposed the design (YasserNabavi and Voytek Klaptocz). A few parameters where considered for the duct selection process asshown in Figure 7-18. These parameters include the mass flow rate inside the duct, the velocity at theduct entrance (mouth), velocity at maximum torque location (that corresponds to an azimuth angle of100180), and the velocity at the minimum duct area (throat). Also, the average velocity over the blade’scircular path was recorded as well as the distribution of the velocity angle over the blade’s path.Mass flow rate and average velocity at the duct entrance are parameters that represent the effect ofblockage on the upstream flow. These two parameters also quantify the level of kinetic energyentrained into the duct. As the available kinetic energy is proportional to the velocity cubed, a smallincrease in velocity inside the duct can result in significant changes in the power generated by theturbine. Theoretically, in order to increase the mass entrained into the duct area it is necessary to movethe frontal stagnation point on the duct towards the outside of the duct. In fact, the distance betweenthe stagnation point on the upper duct and the stagnation point on the lower duct determines the areathrough which the current fluxes.Moreover, average velocity at the maximum torque area (the area at which the maximum torque ispredicted to occur) shows that kinetic energy available to the upstream blades at highest torquegeneration condition. The higher velocity at maximum torque area shows a higher maximum torquepeak. However, there might be some restrictions for increasing the velocity in this region as increasedvelocity in this area can result in larger torque ripple and mechanical design problems. The flow at the0Figure 7-18: Measured flow parameters for comparison of different ducts101throat also shows the highest velocity inside the duct and can be used as a parameter for comparison ofdifferent duct configurations.In order to simplify the comparison, the velocity contours for each duct shape will be displayed and theabove-mentioned flow parameters will be compared.7.2.2 Grid and Solver SpecificationsA few changes were made to the modeling procedure compared to what was explained in Chapters 2and 3. For the simulations in this phase of the project, a two-dimensional, segregated steady-statesolver was used with a2ndorder upwind discretization scheme for momentum and turbulenceequations. As in the case of transient simulations, a Spalart-Allmaras turbulence model was used inconjunction with the SIMPLE algorithm for pressure-velocity coupling. Under relaxation factors wererearranged to accelerate the convergence. Similar to the previous cases, a combination of structuredand untreated grid was used to discretize the domain. A structured grid was used in near-wall regionssuch as duct walls and vanes, where an accurate solution of the boundary layer is needed. All thesimulations in this section were conducted in the absence of the blades in order to better understandthe effect of the duct geometry on the behaviour of the flow field inside the duct.In order to precisely calculate the average velocities at different duct cross sections (such as the mouthand the throat), a rake with 100 nodes was defined across that specific cross sectional area. The velocitywas measured on each node and the average was calculated accordingly. It should be mentioned thatthe same boundary conditions are used for this set of simulations and the inlet velocity was set to 1.5rn/s for all the ducts examined.7.2.3 Examined Duct ConfigurationsIn this section, the velocity contours for the examined ducts will be presented. The velocity contoursshow the flow field inside and outside of the duct and facilitate the prediction of the turbineperformance in the presence of any duct shape. For the ducts that show an acceptable performance, thevelocity vectors were displayed to further study the flow redirection and its effect on the torquegenerated by the blades.Figure 7-19 shows the velocity contours for the UBC duct as a reference for comparison to the variousduct studies included in this research. The contour levels were identically plotted for all ducts so as tosimplify the comparison.102Figure 7-19: Velocity contours for the UBC duct as the referenceBelow, different categories of duct shape simulated will be presented and the specification of each ductwill be analyzed.Category 1: Guiding Vane conceptDuct names: Wi, YV2, and W3Goal: To redirect the flow without any reduction in the kinetic energy available to the turbineType: Multiple-compartment ductIn the first set of simulated ducts, an attempt was made to maintain the flow kinetic energy and redirectthe flow in the regions where an increased angle of attack could generate a larger torque. Figure 7-20 toFigure 7-22 show a guide vane configuration that was used for flow redirection. A NACA 4409 airfoil witha chord length of 25 cm was used at different angles of attack and the maximum flow deflection wasrecorded. Also, the average velocity magnitude on the blades’ path was measured to understand theeffect of vorticity shed from the vanes on the kinetic energy delivered to the blades.Table 7-1 summarises the results obtained for this set of ducts and the comparison with the default UBCduct. As it is presented in the table, YV1 has guide vanes with 15 degrees angle of attack, YV2 has thesame vane geometry but set at an angle of attack of 5 degrees. W3 is identical to W2 but the trailingedge of the vanes was rounded to reduce flow separation for the rear vanes.As it is observed in Figure 7-20 and Table 7-1, in duct Wi an effort was made to deflect the upstreamflow, but the angle of attack was found to be large as the separation is intense and the blades will beplaced in the wake of the vanes. Also, excessive angle of attack increases the blockage and causes areduction in the mass flow entrained into the turbine area. As the vane angle of attack is decreased in3 00,.002 85,.0O270e+002 -002 40o.002 25e.002 10.001 95,*00I 85o*00I 50e.O0001 20e.001 05e.009 OOo 01750,016 00,014 50,01300,011 OOe-010 00,+00103W2 and W3, it is seen that the mass flow rate and velocity average on the blades’ path increase, but thedeflection mechanism is not effective as YV1. Also, it was understood that rounding the vanes’ trailingedges has no significant effect on the average velocity and deflection angle. It will be described later inthis chapter that a set of unsteady simulation was conducted for W3 to investigate the effectiveness ofthis configuration.Table 7-1: Duct with guiding vane configuration resultsVane Angle Mass flow Maximum Deflection Average Velocity onDuct Name(Deg) rate (kg/s) Angle (Deg) blades path (m/s)UBC No vane23925.30 2.189Wi 15 2177 8.51 1.973W2 5 2258 5.75 2.085W3 5 2261 5.75 2.090Figure 7-20: Wi (Guiding vanes at 15 degrees AOA) Figure 7-21: YV2 (Guiding vanes at 5 degrees AOA)Figure 7-22: YV3 (Guiding vanes at 5 degrees angle of attack and with a rounded trailing edge)Figure 7-23 also shows the comparison of velocity angle distribution over the blades’ path for Wi, W2and W3 and the UBC duct. This figure shows that although Wi is more effective than any other104configuration upstream, its performance downstream is unacceptable. Also, it appears thatW2 and W3do not significantly change the angle of attack upstream but perform slightly better than theUBC duct inthe downstream region.Category 2: Modified UBC DuctDuct names: YV4, YV5, YV6, YV7, and YV8Goal: To increase the mass flow rate and the kinetic energy available to the turbineType: Single-compartment ductIn this set of simulations, the UBC duct configuration was modified while keeping aconstant contractionratio (limited to box concept). The results obtained for this set of ducts arepresented in Table 7-2 andcompared to the UBC duct.Table 7-2: UBC duct modifications resultsMass flow Maximum Deflection Average Velocity onDuct Namerate (kg/s) Angle (Deg) blades path (mis)UBC23925.30 2.189YV4 2173 3.05 2.062W5 2366 10.35 2.165YV6 2236 5.26 2.082W7 1873 5.21 1.732W8 1773 3.60 1.690Figure 7-23: Velocity angle distribution for guiding vane configurations105As shown in Table 7-2, the only duct with acceptable performance is YV5. It appears that the incomingflow is properly redirected in this case and the kinetic energy delivered to the turbine’s blades isapproximately the same as the UBC duct.W4 was supposed to keep the same kinetic energy as UBC delivered to the upstream blades whiledecreasing the mid-section velocity where counter torque is generated. It is observed that due to aslightly larger area compared to the UBC duct, as well as sudden changes in the duct curvature in the flatregions, the velocity magnitude is significantly decreased.Duct YV5 was successful in keeping the same velocity as UBC and flow redirection. However, theseparation at the rear part of the duct prevents the flow acceleration and an increase in the mass flowrate entrained inside of the turbine area.Duct YV6 was designed to investigate the outer side of the duct on the mass flow rate and velocity fieldinside the turbine area. This configuration does not work properly as the duct acts as a deformed, lowquality airfoil.A new concept was attempted for duct YV7. The purpose of placing an injection port inside the duct wasto deliver more mass flow to the blades and hence increase the available kinetic energy. As shown inFigure 7-27, the current configuration did not work properly. This concept was investigated further andis described later in this chapter.As duct W6 did not function properly, a new geometry was designed in order to understand the effectof having a pair of large airfoils in place of the ducts. Two NACA 4409 airfoils were selected with a chordlength equal to the length of the UBC duct. However, the contraction ratio could not be kept constantand was lowered by more than 5%. The velocity contours shown in Figure 7-28 show that the concepthas a number of major problems. One of the main problems with this concept is that it is not asymmetric design. Thus, when the tidal currents change direction, the duct does not perform properlyanymore. Also, these geometries are very difficult to build, can result in increased cost and cannot leadto a viable design. In addition, the hydrodynamic performance is lower than the UBC duct due to a lowercontraction ratio and expansion of shear layer in the wake of the duct. However, using properoptimization tools and a more detailed study on the airfoil that should be selected for this purpose,more research is still needed to be conducted on this concept.106Figure 7-24: W4 velocity contours Figure 7-25: W5 velocity contours—Figure 7-27: W7 velocity contours,Figure 7-26: W6 velocity contoursFigure 7-28: YV8 velocity contoursAs shown in Figure 7-29, YV5 is the only duct with a potential to change the angle of attack seen by theblades. The deflection angle of the flow in other designs is not appropriate and is lower than the UBCduct. According to Figure 7-29, YV7 and YV8 have a decreased angle of attack in the downstream regionand the torque generated in this region is predicted to be smaller than the UBC duct.107Category 3: Bump ConceptDuct names: YV9, YV1O, YV11, YV12, YV13, YV14, YV15, YV16, YV17, YV1B, YV19, and YV2OGoal: To shift the location of maximum velocity and reenergize the flow at downstreamType: Single-compartment and Multiple-compartment ductsAs previously shown in Figure 7-1, a counter torque is generated for a blade at azimuth angles of 90 and270 degrees where the angle of attack is theoretically zero. Also, at these angles, the velocity magnitudeis at a maximum when the UBC duct is used since the throat is placed in the mid section of the duct. Anattempt was made to maximize the torque generated by the blades through transferring the throat to asection where a positive torque is generated. That was the main intention for implementing1st, 2ndand3rdmodifications on the UBC duct. It was observed, however, that the flow separation at the throat andthe vorticity shed from the duct throat decelerates the flow and reduces the kinetic energy available tothe turbine. The bump concept was originally developed to address the separation problem of the UBCduct modifications while keeping the throat transferred to a torque-generating region at angles of about0 and 180 degrees. Figure 7-45 to Figure 7-56 show the concepts designed to achieve these goals.Allexamined configurations are multiple-compartment ducts except for W9. Table 7-3 presents the resultsobtained for this category of ducts.Figure 7-29: Velocity angle distribution for UBC duct modifications108Table 7-3: Bump configurations resultsMass flow Maximum Deflection Average Velocity onDuct Namerate (kg/s) Angle (Deg) blades’ path (mis)UBC23925.30 2.189YV9 2227 4.53 2.123W102503 9.702.217YV1J.2332 9.402.207W122369 8.092.273YV132184 7.972.148YV142268 10.642.176YV152170 15.352.153YV162118 13.442.096YV172241 9.362.177YV182311 11.092.291wig2318 6.512.185YV2O2387 17.192.300Comparing the velocity contours of duct YV9 with the UBC duct shows that the local maximum velocityis shifted desirably but the average velocity magnitude, the entrained mass flow rate, and hence thepower available are decreased due to the separation at the throat and the increased blockage due tothe existence of the bump. It was observed, however, that separation is considerably less severe thanthe UBC duct modifications because the flow is expanded with a smaller positive pressure gradientdownstream of the bumps. Also, it was seen that this duct was not effective in deflecting the upstreamflow and the maximum deflection angle was lower than the UBC duct.Duct YV1O is basically the UBC duct with added bumps at the mid-section. The bumps were designed tobe positioned 1 inch away from the main duct for all the simulations except duct YV21.The simulationswere conducted to observe the effect of the bumps on the entrained mass flow rate and the velocityangle distribution. The results show that the mass flow rate is increased approximately 5% due to theexistence of the bumps. Figure 7-30 and Figure 7-31 show a comparison of the velocity magnitude andvelocity angle distribution over the blades’ path. As shown in these figures, the velocity distributioncurve is sharper for W10 compared to the UBC duct and the peak point is located at the mid-section109where counter-torque is produced. On the other hand, it is seen thatthe flow is properly redirected andextra power can be extracted due to an increased angle of attack, especially between azimuthangles of10 and 50 degrees where the difference in the velocity angle betweenthe two ducts is noticeable. Itshould be noted that an excessive flow redirection can cause the blades tostall and decrease thegenerated power. Further fine-tuning might be necessary to obtain the ideal conditions.Duct Wil has the same dimensions for the bumps as YV1O.The W10 was modified in order to shift themaximum velocity location towards the areas upstream and downstream of the turbinewhere thegenerated torque is positive. Shifting the maximum velocity location also reducesthe counter-torquegenerated at the mid-section of the turbine. Figure 7-32 and Figure 7-33 show the comparisonof thevelocity magnitude and velocity angle distribution over the blades’ pathrespectively.As shown in Figure 7-32, the maximum velocity location was properly shifted, but due to the blockageeffects at the duct entrance, the maximum velocity is lower compared to the configuration withbumpsin the center. It is also observed that the velocity vector is deflected a few degrees at the center,hence,Figure 7-30: Comparison of velocity magnitude distribution Figure 7-31:Comparison of velocity angle distribution overover the blades path for UBC and W10 ducts the bladespath for UBC and YV1O ductsFigure 7-32: Comparison of velocity magnitude distribution Figure 7-33:Comparisonof velocity angle distribution overover the blades path for W1O and YV11 ducts the blades path for YV1O and Wil ducts110allowing for a positive torque generation by a potential blade. However, since the velocity angle is lowerthan velocity angle in YV1O, the angle of attack will not be changed properly for this duct. Therefore, itwas decided to study the effect of bump shape on the velocity magnitude and angle over the blades’circular path. Duct YV12 was modeled to understand the effect of the bump length on the flow fieldwhile duct YV13 studied the effect of having four bumps instead of a diagonal pair. Ducts W14, YV15,and YV16 were designed to investigate the effect of bump thickness and camber on the flow field insidethe duct.Figure 7-34 and Figure 7-35 show the effect of the bump length on the velocity field over the blades’path. It is seen that having a longer bump slightly increases the average velocity but dampens thevelocity peaks in the upstream and downstream and increases the velocity magnitude at the center.Also, the velocity angle does not change significantly except at azimuth angles of about 60 and 120degrees where the velocity angle and thus the angle of attack seen by the blades are reduced.Figure 7-36 and Figure 7-37 show the effect of using four bumps instead of two diagonally-configuredbumps. The average velocity is lower and the velocity angle is not redirected properly. As shown inFigure 7-38, the velocity angle suddenly changes from negative to positive and vice versa in the vicinityof the bumps. That phenomenon is due to the Coanda effect - the tendency of the fluid to adhere to aconvex surface rather than following a straight path in its original direction. Hence, it can be concludedthat using four bumps with the current size and shape as in YV13, results in increased blockage andinappropriate redirection of the upstream flow. However, changing the location of the bumps and thedistance from the ducts may improve the duct performance.Figure 7-34: Comparison of velocity magnitude distribution Figure 7-35: Comparison of velocity angle distribution overover the blades’ path for YV11 and YV12 ducts the blades’ path for YV11 and YV12 ducts111-‘= 2.50e*O1225e*O12 OOe*O11 75e+O11 50e-l-011 25e+OlI OOe+O17 50e+OO5 OOe+OO2 50e+OOo OOe-OO-2 50e+OO-5 OOe+OO-7 50e-f 00-1 OOe-f01-1 2501-1 50e-01-1 75e.01— -2 OOe+01-225e+01-2 50e01Figure 7-38: Velocity angles contours for the four-bump configuration (Duct YV13)Ducts YV14, YV15, and YV16 were built to investigate the effect of the thickness and camber of thebumps on the velocity field over the blades’ path. A comparison of velocity magnitude and angle forthese ducts is presented in Figure 7-39 and Figure 7-40. The thickness of YV14 was set to be 0.10 inchwhile YV15 and YV16 have thicknesses of 0.13 and 0.14 inch. Also, in YV16, the camber location of thebump was moved towards the bump leading edge. The results show that the average velocity isdecreased with an increased bump thickness as a result of increased blockage at the duct inlet. It is alsoseen that the flow reenergization property of the bump becomes less effective as the thickness isincreased. Comparing the velocity magnitude and angle of ducts W15 and W16 also reveals thatcambering the bump has a negative effect on duct performance. The fine-tuning process of the bumpshape can be conducted using appropriate optimization tools.Figure 7-36: Comparison of velocity magnitude distribution Figure 7-37: Comparison of velocity angle distribution overover the blades path for YV11 and W13 ducts the blades path for YV11 and YV13 ducts112In order to study the effect of the duct’s length on the performance ducts W17 and YV18 weresimulated. Duct W17 has a longer bump compared to YV15 but the bump thickness was kept constant.YV18 has the same proportions but is stretched in the X-axis direction. W18 was set to be 50 percentlonger than YV17. Although this study is beyond the box concept, it is still beneficial to understand theduct length effect on the turbine’s performance.It can be observed from the results and Figure 7-41 and Figure 7-42 that a longer duct yields an averagevelocity which is approximately 5% more than the basic duct length. Also, the flow deflection seems tobe more effective when using a longer duct. In order to make a decision regarding the viability of thedesign, the increased generated power should be monitored against manufacturing, installation,mooring, and maintenance costs. However, this topic is beyond the scope of the current research.A set of simulations were also conducted to study the effect of the bump placement relative to the mainduct. Hence, YV19 which has an identical bump shape as YV14 was manufactured and simulated. Thehorizontal distance of the bump from the mouth in this configuration was 27 cm compared to 39 cm ofFigure 7-39: Comparison of velocity magnitude distribution Figure 7-40: Comparison of velocity angle distribution overover the blades’ path for YV14, YV15, and W16 ducts the blades’ path for YV14, W15, and W16 ductsFigure 7-41: Comparison of velocity magnitude distribution Figure 7-42: Comparison of velocity angle distribution overover the blades’ path for YV17 and YV18 ducts the blades path for YV17 and YV18 ducts113YV14. The simulation results showed that a slight increase in the average velocity can be achieved usingthis configuration. However, the effectiveness of the bumps seems to be reduced by placing the bumpsfurther from the blades’ path. The velocity magnitude and velocity angle distribution of YV19 ispresented in Figure 7-43 and Figure 7-44 along with the results for duct YV2O.The last study in this category of ducts was to investigate the effect of the bump distance from the mainduct. In other words, the width of the small channel between the bump and the duct was changed from2.54 cm (1 inch) to 5.08 cm (2 inches) and the results were compared. The bump configuration for thisstudy is identical to YV19 but with a larger gap of about 2 inches between bump and duct. The resultsshow that increasing the gap width has a significant effect on the velocity magnitude and velocity angleover the blades’ path. The velocity increases by more than 5 percent which can result in more than 17percent increase in the available kinetic energy to the turbine. Also, the deflection angle reaches 17degrees, a value larger than any other bump configuration studied. A comparison of velocity distributionfor this duct and YV19 is presented in Figure 7-43 and Figure 7-44.Unsteady simulations were also conducted for YV11 and W13 to investigate the effectiveness of bumpmechanism in the presence of the turbine’s blade. The results will be discussed later in this chapteralong with other duct configuration simulated in unsteady conditions.Figure 7-43: Comparison of velocity magnitude distribution Figure 7-44: Comparison of velocity angle distribution overover the blades’ path for YV19 and YV2O ducts the blades’ path for YV19 and YV2O ducts114—Figure 7-49: YV13 velocity contours Figure 7-50: YV14 velocity contoursIFigure 7-45: W9 velocity contoursFigure 7-47: YV11 velocity contoursFigure 7-46: YV1O velocity contoursFigure 7-48: W12 velocity contours‘IFigure 7-51: W15 velocity contours Figure 7-52: YV16 velocity contours115Category 4: Double-Duct ConceptDuct names: YV21, W22, YV23, YV24, YV25, YV26, YV27, and YV28Goal: To maximize the velocity magnitude inside the ductType: Multiple-compartment ductsThe double-duct concept is similar to the bump concept, but the objective of this approach is to increasethe velocity magnitude inside the duct as much as possible. Needless to say that an increased velocityinside the duct has a direct effect on the resultant velocity vector and hence the angle of attack theblades see. A larger velocity magnitude results in an increased angle of attack. Figure 7-61 to Figure 7-68show the velocity contours obtained from the simulations for this category of ducts. The results arepresented in Table 7-4 and compared to the UBC duct.Figure 7-53: YV17 velocity contours Figure 7-54: YV18 velocity contoursFigure 7-55: YV19 velocity contours Figure 7-56: YV2O velocity contours116Table 7-4: Double-Duct configuration resultsMass flow Maximum Deflection Average Velocity onDuct Namerate (kg/s) Angle (Deg) blades’ path (m/s)UBC23925.30 2.189YV2 13061 4.25 2.873YV223260 5.40 3.011YV233168 2.938YV243362 3.131 5.42YV252907 5.36 2.709YV262679 5.36 2.477YV272785 6.83 2.547YV2827719.212.643Ducts YV21, YV22, YV23, and YV24 were designed to study the double-duct concept. This concept aimsto reduce the blockage of the duct by splitting it into two sections. In this design, the fluid can flowthrough a gap between two ducts, thus preventing the severe separation downstream of the duct.Hence, the shear layer effect would be minimal and the flow expansion can occur smoothly. There aresome additional benefits from mechanical design point of view by using these type of ducts as well.These benefits include smaller duct sizes, reduced costs, and less mooring problems (due to the smallerdrag force that these ducts produce). YV21 and YV22 basically compare the performance of a single anddouble duct concept. The inner duct in YV22 was the UBC duct and the outer duct was a scaled model ofthe same duct with a scaling factor of 2. YV22 is a single duct with the same contraction ratio as YV21(approximately 30%). YV23 and YV24 were also modeled to capture the effect of the inner duct shapeon the flow field inside the turbine area. The results show that using a double-duct concept canconsiderably improve the duct performance.117As it is seen in Figure 7-57 and Figure 7-58, using the double duct concept with the same contractionratio can increase the average velocity magnitude by approximately 10 percent. Also, the velocity angledistribution improves compared to the single duct case. However, the velocity deflection is in the sameorder as the UBC duct and other methods such as guide vanes or bumps can be used to manipulate thevelocity angle and consequently the angle of attack the blades see.As the duct size is very crucial from a mechanical design point of view and has a direct effect onmanufacturing, installation, mooring, and cost, a study was conducted to investigate the effect of theouter duct size on the flow field. YV25 is a double-ducted configuration with a contraction ratio of 0.45and the outer-duct length of 3.812 m. The length of the outer-duct for W26 and YV27 was set to 2.303m in order to capture the effect of the outer-duct length on the average velocity and velocity angle.YV26 and YV27 have identical outer-duct geometries. The inner-ducts of these two ducts have the sameaspect ratio but with different curvatures. In addition to these ducts, YV28 was designed to understandhow effective a bump configuration would be in a double-duct design. The comparison of the results ofduct YV25 and YV26 reveal that using a shorter duct (approximately 40% shorter) can result in anaverage velocity drop of about 8 percent. Thus, using a longer duct with the same contraction ratio canimprove the performance at the cost of increased manufacturing, installation, and maintenance cost.Duct YV27 results show that by cambering the inner duct, it is possible to increase the average velocityand the mass flow rate inside the duct. Also, duct YV28, which is identical to YV27 with an added bumphas a larger velocity deflection and a higher average velocity but a lower mass flow rate due to theincreased blockage caused by placing a bump close to the duct’s mouth. Figure 7-59 and Figure 7-60show the velocity magnitude and angle over the blades’ path. The results show that the bumps are stilleffective in shifting the location of maximum velocity and reenergization of the flow downstream of theFigure 7-57: Comparison of velocity magnitude distribution Figure 7-58: Comparison of velocity angle distribution overover the blades’ path for YV21, YV22,YV23, and W24 ducts the blades’ path for YV21, YV22,YV23, and YV24 ducts118turbine. The angle, however, seems to be similar to the regular UBC duct and bumps configuration, andno significant change is observed.Figure 7-64: W24 velocity contoursFigure 7-59: Comparison of velocity magnitude distribution Figure 7-60: Comparison of velocity angle distribution overover the blades path for W25, YV26,YV27, and W28 ducts the blades path for W25, YV26,YV27, and YV28 ductsFigure 7-61: YV21 velocity contours Figure 7-62: W22 velocity contoursFigure 7-63: YV23 velocity contours119Figure 7-67: YV27 velocity contours Figure 7-68: W28 velocity contoursCategory 5: Guiding-Vane ConceptDuct names: YV28, YV29, YV3O, YV31, YV32, YV33, and YV34Goal: To maximize the entrained mass flow rate inside the turbine especially at downstreamType: Multiple-compartment ductsThe last set of simulations was dedicated to study a concept to entrain more fluid into the downstreamregion of the turbine in order to provide the downstream blades with a larger and more energized massflow rate. Seven different configurations were simulated as shown in Figure 7-73 to Figure 7-84. Also,the summary of the results is presented in Table 7-5.Table 7-5: Guiding vane concept resultsMass flow Maximum Deflection Average Velocity onDuct Namerate (kg/s) Angle (Deg) blades’ path (mis)YV291373 38.56 1.502YV3O1489 5.23 1.414W3 12131 6.06 1.945YV321795 6.02 1.516YV331902 6.82 1.527YV342121 9.67 1.722YV352206 10.27 1.782-66: W26 velocity contoursF120The first configuration simulated for this concept was W29. The configuration consists of 16 guidingvanes, 8 in front and 8 in the back. The front side and the backside have four vanes at the top and fourvanes at the bottom. NACA 4409 airfoil was used for the vanes’ profile. The chord length of the vaneswas 20 cm, 22.5 cm, 25 cm and 30 cm from front to the back. Also, the angle of attack of the vanes wasset to 10, 15, 20, and 30 degrees. The trailing edges of the vanes are placed on a straight horizontal line.The vane angle of attack was increased in order to capture the flow separated from the upstream vanesand to guide it into the turbine area. The upstream and downstream vanes have different directions inorder to conform to the symmetry assumption about the Y axis. This assumption explains that becausethe tidal flow changes direction by approximately 180 degrees, the duct should perform independent ofthe flow direction. The velocity contours of YV29 show that there is not a great amount of flowentrained into the downstream of the turbine because of the opposite direction of the downstreamvanes. However, it is observed that the velocity downstream is increased as the entrained flowupstream cannot pass through the space between the downstream vanes. The mass flow rate andaverage velocity obtained using this configuration does not show any improvement compared to theUBC duct. The angle of attack, however, changes significantly, especially at the azimuth angles of about90 degrees.Duct W30 uses a similar concept as YV29, but it is designed to examine whether any improvement canbe achieved using flow injection to the downstream blades. The symmetry assumption was notconsidered in this design. The first, second, third and fourth vanes are identical to W29, but the fifthand sixth vanes are identical to the fourth vane. The results showed that this configuration was notsuccessful in achieving its goals. The velocity was reduced and the deflection was not as effective asYV29. The reason for poor performance of this duct can be the massive separation of the flow from theupstream vanes and the inability of downstream vanes to guide the separated flow inside the turbinearea. Figure 7-69 and Figure 7-70 show the velocity magnitude and velocity angle distribution for YV29and YV3O. These figures show that YV3O has a minimal effect on the flow field and it does not affecteither the velocity magnitude or velocity angle. On the other hand, although upstream velocity is lowwhen YV29 is used, the downstream flow is properly re-energized as described before.121YV31 is similar to the UBC duct with a channel going through the top surface of the duct all the waydown to the inside area of the duct. This channel is basically used to increase the entrained mass flowinside the duct. However, the velocity vectors of this duct show that this mechanism does not performproperly as the flow is separated from the leading edge of the front part of the duct. W32 is a modified,asymmetric version of W31. The rear duct was designed to be more streamlined. However, this duct didnot perform appropriately, especially due to the severe separation from the sharp leading edge of thefront part of the duct. In order to address this problem, the front part was replaced with an airfoil shape(NACA 4409) in YV33 to reduce the separation from the leading edge. Also, the rear part of the duct wasslightly moved in the positive y direction. This was done to transfer the stagnation point of the rear ductto a higher point in space, thus allowing a larger mass flow to be streamed into the channel between thefront and rear parts of the duct. The results show that the performance is improved in this designcompared to YV32. YV34 has an identical front part as YV33 but a longer, more streamlined rear part.The results showed that the mass flow rate was increased more than 13 percent in this case comparedto YV33. This duct does not consider the symmetry assumption yet. YV35 is a symmetric model of YV34.Although it is observed that the velocity and mass flow rate could be kept high, the boundary layerseparation from downstream vanes is severe and affects the shear layer and flow expansiondownstream of the turbine. However, it seems that this separation cannot be avoided if the symmetryassumption is to be considered. The velocity magnitude and velocity angle distributions of YV31 to W35are compared in Figure 7-71 and Figure 7-72.Figure 7-69: Comparison of velocity magnitude distribution Figure 7-70: Comparison of velocity angle distribution overover the blades path for W29 and YV3O ducts the blades’ path for W29 and YV3O ducts122The above figures show that YV32 and YV33 do not have an acceptable average velocity and velocityangle. YV31 has a high average velocity but the flow deflection is not significant. YV34 and YV35haverelatively larger velocities and velocity deflection angles. Noneof these ducts is effective in theredirection of the flow downstream. Therefore, it can be concludedthat no superior performance ispredicted to be produced by any of the ducts modeled in thiscategory. However, in order to understandthe duct-blade interactions, duct W34 was simulated in unsteady conditions.This duct was chosenbecause of its relatively better performance (high average velocity and large velocity angles upstream)compared to the other ducts in this category. The results will be presented and discussed later in thischapter.Figure 7-73: YVZ9 velocity contours Figure 7-74: YV3O velocity contoursFigure 7-71: Comparison of velocity magnitude distribution Figure 7-72: Comparison ofvelocity angle distribution overover the blades’ path for YV31, W32, YV33, YV34, and YV35 the blades’ path forW31, YV32, YV33, YV34, and W35 ductsducts123—Figure 7-75: YV31 velocity contoursFigure 7-79: YV33 velocity contoursFigure 7-81: YV34 velocity contoursFigure 7-76: YV31 velocity vectorsFigure 7-77: YV32 velocity contours Figure 7-78: W32 velocity vectorsFigure 7-80: YV33 velocity vectorsFigure 7-82: YV34 velocity vectors124Figure 7-83: YV35 velocity contours7.3 Unsteady Simulations of Various Duct ConfigurationsSteady state simulations in the previous sections provided an idea of how each duct performs inreenergizing or redirecting the flow. The benefit of steady-state simulations was in saving computationaltime and cost. However, as steady-state models do not completely represent the flow field in thepresence of the blades, it is necessary to run unsteady simulations to study the behaviour of the ductsand turbine’s blades simultaneously. Ducts YV3, YV11, YV13, YV28, and YV34 were chosen to besimulated in unsteady conditions for this phase of the project. YV3 was chosen to capture the effect ofthe guide vanes while YV11 and YV13 were selected to show the effect of bumps. W28 was simulated toshow the effect of having bumps and double-duct concept together. Finally, YV34 was simulated toshow the effectiveness of mass flow entrainment concept. The simulations were conducted for an inletvelocity of 1.5 rn/s and TSR’s of 2.00 to 4.00 with 0.25 increments. The comparison of the efficiencycurve for the simulated ducts is presented in Figure 7-85. Finally, the torque curve for each duct iscompared at each TSR to give a clearer understanding of the duct behaviour at different workingconditions. The results show that there is no superior duct between the simulated cases. It seems thatthe flow entrainment concept (YV34) improves the performance slightly at lower TSR’s while theefficiency is lower than the UBC duct for higher TSR’s. The bump concept (YV11 and YV13) was observedto be ineffective as the increased blockage at the duct inlet reduces the mass flow rate inside theturbine in addition to reducing the average velocity magnitude and hence the kinetic energy inside theturbine area. It is also seen that the double-duct concept (YV28) increases the efficiency at TSR’s over2.75 and the maximum efficiency reaches approximately 68% at TSR of 3.00. The low efficiency of thisdesign in lower TSR’s can be explained as the increased local velocity causes a larger angle of attack andthe blade stall at lower TSR’s. At high TSR’s where the blade does not stall, the increased kinetic energyentrained into the turbine area causes an increased generated power and efficiency. The results alsoshow that the guiding vane concept (YV3) does not improve the efficiency, It is observed that theFigure 7-84: W35 velocity vectors125rotation of blades downstream of the guiding vanes affect the flow over the vanes and causes flowseparation which lowers the upstream blades’ torque. However, the size and the distance of thevanesfrom the blades’ path can be investigated in more details in future.-.-YV3 —.-W11 YV13 -w—YV28 -a W34 U BCO7-___0.1— - — —-— ------0—— -——-—- --1.5 1.75 2 2.25 2.5 2.75 3 3.25 3.5 3.75 4 4.25TSRFigure 7-85: Efficiency comparison for different duct shapesFigure 7-86 to Figure 7-95 show the torque curves over a cycle for the unsteady duct simulations. Thesingle blade torque curves are also presented to assist in evaluating the effectiveness of each conceptand to give guidelines for future improvements.—-TSR=2.00 —TSR=2.25 TSR=2.50 —TSR=2.75 —TSR=3 00 155=3.50 155=4.00 —155=2.00 -—TSR=2.25 135=2.50 —TSR=2 75 —TSR=3.00 155=3.50 -155=4.00120 120100 100220WVTheta (Sag) Theta(D.g)Figure 7-86: 3-Blade torque curve for YV3 at different TSRs Figure 7-87: Single-blade torque curve for YV3 at differentTSR’s—755=2.00 —TSR=2.25 --TSR=2.50 —TSR=2.75 —TSR=3.00 TSR=3 50 155=4.00 —755=2.00 —TSR=2.25 ----TSR=2.50 —TSR=2.75 —TSR3.00 155=3.50 - ISR=4.00120 120 - — —-OW70360JEJ\\Theta (Deg) Theta (Deg)Figure 7-88: 3-Blade torque curve for YV11 at different TSR’s Figure 7-89: Single-blade torque curve for Wil at differentTSR’s—TSR=2.00 =—TSR=2.25 TSR=2.50 —TSR=2.75 —155=3.00 —158=2.00 —758=2.25 —TSR=2.50 —TSR=2.75 —178=3.00140 140120 120080270 360O700Theta (Deg) Theta (Deg)Figure 7-90: 3-Blade torque curve for YV13 at different TSRs Figure 7-91: Single-blade torque curve for W13 at differentTSRs127—158=2.00 —TSR=2.25 TSR=2.50 —158=2.75 —158=3.00 TSR=3.50 TSR=4.00 —TSR=2.00 —TSR=2.25 158=2.50 —158=2.75 —TSR=3.00 TSR=3.50 TSR4.00160140120100:40200-20-40160Figure 7-92: 3-Blade torque curve for YV28 at different TSRs Figure 7-93: Single-blade torque curve for YV28 at differentTSRs605040z30205040z- 3020Figure 7-94: 3-Blade torque curve for YV34 at different TSR’s Figure 7-95: Single-blade torque curve for W34 at differentTSR’sThe guide vane torque curves (W3) show a trend similar to the UBC duct, and thus, the role of the guidevanes in flow redirection is not significant. It is observed that the torque amplitude decreases with anincreased TSR as a result of a smaller range of angle of attack seen by the blade. The efficiency was alsofound to be very close to the UBC duct due to the insignificant effect of the vanes. The torque curve atvery high TSR’s (3.50 and 4.00) shows that the torque ripple is minimized due to the same reason. It isalso seen that for all cases, the single-blade torque curve expands as TSR’s increase.Comparison of the torque curves obtained for YV11 and YV13 with the UBC duct shows that the torqueamplitude is smaller. Also, the maximum torque value is lower in these cases as the result of theincreased blockage due to the presence of the bumps at the inlet.14012010080z60402000-20-40Theta (Deg) Theta (Dag)8070—TSR=2.00 —TSR=2.25 TSR=2.50 —TSR=2.75 —TSR=3.00807060—TSR=2.00 —TSR=2.25 TSR=2.50 —TSR=2.75 —158=3.00100-10-2090 180 270 360Theta (Deg)100-10-20180Theta (Deg)360128W28 results show that the torque amplitude is increased as a result of increased velocity inside theturbine area. However, due to the high angle of attack at low TSR’s and high velocity, the blades stalland the dynamic stall phenomenon causes the torque curve to be sharp with a large amplitude andnegative torque. It is seen that the effect of dynamic stall decreases as the TSR increases. Hence, at highTSR’s (such as 3.00 or more) where the average torque value drops for other cases, the average torquefor this case is still high and the efficiency is the highest among the examined cases. However, there canbe two major problems with this duct. The first problem is the difficult mooring of the duct as the size ofthis duct is larger than the UBC duct and other ducts with the same contraction ratio. The other problemwith this duct is that its performance is satisfactory at high TSR’s only.The last simulated duct (YV34) proved that the flow injection can be effective at low TSR’s (2.00 and2.25). The other advantage of using this duct is the reduced torque ripple as a result of a uniformdistribution of angle of attack over the cycle. A widened single-blade torque curve for this duct (Figure 7-95) supports the fact that the flow redirection concept works properly for this configuration. However,the low torque amplitude over the downstream blade rotation shows that the flow entrainment effect isnot significant. This is due to a significantly smaller momentum of the injected secondary flow comparedto the main stream flow. As shown in Figure 7-96 and Figure 7-97, the flow separates from the suctionsides of the vanes at high TSR’s. This is the direct effect of the changes occurring downstream of thevanes. The blades rotate with a higher angular velocity thus increasing the blockage in the downstreamregions.4,Figure 7-96: Velocity contours of W34 show the flow Figure 7-97: Velocity vectors of YV34 show theflowseparation from the upper side the guide vanes at V=1.5 rn/s separation from the upper side of the guide vanes at V=1.5and TSR=3.OO rn/s and TSR=3.OOYV34 can be useful in case the turbine needs to work at very low TSR’s. Also, it can be structurallybeneficial as the torque ripple is decreased. The type, size, angle, and position of the blades should beoptimized in order to maximize the performance of the duct. The disadvantages of these ducts can be129summarized as difficult manufacturing and mooring and the high chance of blockage of the channelbetween the vanes and the main duct due to bio-fouling.Figure 7-98 presents a summary of the duct study results conducted in this chapter. This bar chartconsists of two series of bars for efficiency and the Torque Ripple Factor (TRF). This chart can facilitatethe duct selection process as a desirable duct is the one with a highCk and low TRF.Figure 7-98: Summary of the performance of studied ducts1308. Conclusion, Recommendations, and Future Work8.1 ConclusionThe current research focused on the numerical simulation of a ducted vertical axis tidal turbine using thecommercial CFD package, FLUENT. The geometric parameters of the rotor such as the radius of theturbine, the blades’ profile, and solidity ratio were assumed to be constant. Previous studies at the NRCsuggested that if the turbine were confined within a duct, the generated power could increasesignificantly. The concentration of this research was to find a duct shape that could improve theperformance of the turbine.The first stage of the research was dedicated to the validation of the numerical model. A free-streamturbine as well as a parabolic duct shape with an identical duct tested experimentally at University ofBritish Columbia, were simulated at different tip speed ratios, and the results were comparedwithexperimental results. There were several discrepancies between the two-dimensional numerical modelsand the three-dimensional experimental model. A comparison of the results, however, shows that thenumerical models have an acceptable level of accuracy and are capable of capturing important trendsaffecting turbine performance, and can thus be used as a reliable tool for optimization purposes.After gaining sufficient confidence in the accuracy and validity of the numerical models, the secondstage of the project was dedicated to the investigation of the duct shape effect on the performance ofthe turbine. Different concepts such as flow redirection, flow entrainment, and the double-duct conceptwere examined to improve the performance of the turbine relative to the case of the UBC duct. As theunsteady simulations are computationally expensive, each duct shape was simulated in the steady-stateconditions, and only when performance was promising, the unsteady simulations were conducted forthe duct shape. All the examined duct shapes were assumed to have the same contraction ratio as theUBC duct in order to standardize the performance comparison, except for the case of the double-ductconcept.The unsteady simulation results show that no superior solution was found for the ducting problem. Afew duct shapes had a higher efficiency at low TSR’s while a number of other ducts performed better athigh TSR’s. It was also observed that although certain ducts reduce the efficiency relative to the UBCduct, they can be useful in addressing the torque ripple problem. The summary of the results will bepresented in the Recommendations section.1318.2 RecommendationsThe approach taken in studying the turbine in the current research can be used as a guideline for futureresearches. This research showed that although RANS simulations are more accurate than potential flowcodes, they are efficient tools for certain applications only. It was found that RANS simulations are notvery efficient for optimization of the rotor. The RANS simulation of a free-stream turbine can take up tofour days and up to a week for a ducted turbine. Although the simulations’ run-time is very long, the setup time is significantly shorter than that of potential flow codes. Thus, RANS simulations using thecommercial packages are recommended when a quick solution is required and when there are timeconstraints in developing potential flow codes.It is also recommended that RANS simulations be used for applications with significant flow separation.Although RANS simulations suffer from lack of accurate turbulence models, they allow for the inclusionof separation which is not possible in potential flow codes. The potential flow codes can therefore beused for the free-stream turbine as well as in the UBC duct case; however, they cannot be used in theguide vane applications, bumps applications, and probably in double-duct applications. In addition,potential flow codes could not be used for the majority of the ducts studied in Chapter 7 because manyof these ducts showed significant flow separation inside the turbine operational area. Also, the shafteffect cannot be captured in the potential flow codes while it can be properly modeled in the RANSsimulations.Also, most of the potential flow codes are incapable of properly modelling the dynamic stallphenomenon. They also require experimental data of the blade profile. In such cases, CFD simulationswould be an alternative to the experiments.RANS simulations using a commercial package such as Fluent give a detailed insight to the physics of theproblem by allowing the user to examine various parameters such as vorticity levels or velocity vectormagnitude and direction. This significantly facilitates the analysis process and can help with thedevelopment of new concepts.In addition to the general recommendations mentioned above, the engineering recommendationsobtained from the current research for the duct shape are summarized in Table 8-1. The advantages anddisadvantages of each duct are also presented to give engineering guidelines for future designs.132Table 8-1: Summary of the simulation results for different duct shapesDuct Name Advantages DisadvantagesSimple and easy to manufacture, efficiency upUBC to 56%, low torque ripple at high TSR’sMedium-high efficiency, large torque(TRF=O.82)ripple at low TSR’s, high-level noiseHigh efficiency at lowTSR?s*,lower torqueripple at all TSR’s (TRF=O.65), efficiency up to7% lower efficiency, torque rippleUBC mod 149% at TSR=2.50, low-level noise, flatsignificant for low TSR’s, harder toefficiency curvemanufactureHigh efficiency at low TSR’s, lower torqueripple (TRF=O.37), efficiency up to 47% at9% lower efficiency, torque rippleUBC mod 2TSR=2.50, low-level noise, flatter efficiencyrelatively large at the lowest TSR,curve, not very sensitive to TSR changesharder to manufactureSignificantly lower torque ripple (TRF=O.56),efficiency up to 29% at TSR=2.50, low-level 27% lower efficiency (significant loss),UBC mod 3noise, very flat efficiency curve, not very harder to manufacturesensitive to TSR changesLower efficiency at all TSR’s, efficiency up to2% lower efficiency, guide vane conceptW354%, low torque ripple at high TSR’s (1RF=o.7)not effective, harder to manufacture,high-level noise4% lower efficiency, bump concept notLower efficiency at all TSR’s, efficiency up to effective in increasing the efficiency,Wil 52%, bump concept causes a slightly smaller harder to manufacture, chance oftorque ripple (TRF=O.74) blockage of the channel between bumpand duct, high-level noiseLower efficiency at all TSR’s, efficiency up to11% lower efficiency, four-bumpW13 45%, torque in the same order of magnitudeconcept not effective in increasingas the UBC duct (TRF=O.81)efficiency, larger torque ripple, harderto manufacture, high-level noiseHigher efficiency at high TSR’s, efficiency up toLarge size duct, hard to manufactureW28 67% at TSR=3.50, small torque ripple at veryand moor, lower efficiency and largerhigh TSR’s (TRF=O.29)torque ripple at low TSR’s, high levelnoiseHigher efficiency at low TSR’s, efficiency up to10% lower efficiency, very difficult toW34 46%, significantly lower torque ripplemanufacture, chance of blockage of the(TRF=0.30)channel between vane and duct, nonsym metric*All comparisons are made to the UBC duct1338.3 Future WorkThe current research should be pursued in two different paths. The first path is to improve and fine-tunethe promising concepts that emerged from the analysis of various geometries. For example, the guidingvane concept was introduced and examined for one particular vane geometry and the results obtainedfrom the simulations showed no significant improvement. However, the size, the incident angle, theprofile, and the location of the vanes are parameters that if modified, may result in significantimprovements in the performance of the turbine. In order to optimize any duct geometry, it is necessaryto use optimization packages for CFD applications such as Sculptor, developed by Optimal Solutions,which uses an ASD (Arbitrary Shape Deformation) algorithm to achieve this purpose.The second path that is vital for future development of the device is to address other engineeringaspects of the project. Cavitation is among the factors that must be investigated. The factors affectingcavitation are the current velocity as well as the angle of attack, separation, and TSR. Although it waspartially addressed in the current work, the torque ripple problem requires further study. A helical bladeshape should be considered as an option and weighed against potential drawbacks such as ease ofmanufacturing when compared to the straight blade. The mechanical design side of the project is alsovery important and Finite Element Analysis is necessary, especially for large scale models. Fatigueproblem is one of the issues that need to be addressed to ensure the reliability of the design. Also, thesensitivity of the design to different ocean conditions and the chance of blockage of the small channelsin the ducts, such as the gap between the bumps and the main duct, are among the considerations forocean applications. 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