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An investigation into the effects of ducted tips on a marine propeller tested in an aerodynamic facility Li, Hsing Hui Isabella 2006

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AN INVESTIGATION INTO THE EFFECTS OF DUCTED TIPS ON A MARINE PROPELLER TESTED IN AN AERODYNAMIC FACILITY By Hsing Hui Isabella Li B.A.Sc., University of British Columbia, 2003 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in The Faculty of Graduate Studies (Mechanical Engineering) THE UNIVERSITY OF BRITISH COLUMBIA April 2006 © Hsing Hui Isabella Li, 2006 Abstract Earlier ducted tip marine propeller designs had shown reduced tip vortex intensities, which delayed cavitation inception; however, there existed discrepancy between the tip's effects on the efficiency of the propeller. The objective of this project was to confirm the findings in a more controlled environment and gain a direction for optimizing the tip geometry. A dynamometer designed to test full size marine propellers developed in 2004 for the UBC Boundary Layer Wind Tunnel was updated and used for the experiments conducted. Although cavitation cannot be observed in a wind tunnel, changes in the propeller performance will be evident with the use of the dynamometer. The dynamometer is capable of measuring torque and thrust loads up to 20Nm ±0.1% full scale and 196N ±0.03% applied load, respectively. Static and dynamic calibrations indicated that the linearity of the sensors is of a R2 value of 1.000 or higher, except for that of the dynamic torque, which had a R value of 0.998. The calibration constants were accurate to the error of the setup: ±1.5%. Two 24"x24" Dyna-Quad propellers were selected for the experiment. One of the propellers was used as a reference propeller; the other was fitted with 0.75" and 1" ducted tips. The propellers were tested at 1000, 1500, 2000, and 2500 rpm. Measurements were sampled at 100 Hz for 15 seconds at advance ratio increments of 0.05. The efficiencies measured decreased with increasing duct size. The peak efficiencies determined for the reference, 0.75" ducted tip, 1" ducted tip, and faired 1" ducted tip propellers were 61.8%, 58.7%, 56.7%, and 58.5%, respectively. Installation of the ducted tips removed lifting area and added wetted area but did not improve the overall propeller performance. Fairing of the 1" ducted tip improved the aerodynamics of the tip, but the performance remains lower than that of the reference. Although the current ducted tips did not show favourable results in the wind tunnel, with the appropriate fairing of the ducts, the design may still be effective in delaying cavitation without the expense of efficiency. ii Table of Contents Abstract u Table of Contents iii List of Tables v List of Figures y i Nomenclature viii Acknowledgements x 1 Introduction 1 1.1 Propeller Theory 1 1.2 Tip Modifiers 4 1.3 Test Facilities 7 1.4 Research Objectives 12 2 Experimental Set Up and Methodology 13 2.1 Dynamometer 13 2.1.1 Torque Sensor Calibration - 18 2.1.2 Thrust Sensor Calibration 24 2.2 The Propeller 28 2.2.1 Geometric Similarity Between Propellers 28 2.2.2 Propeller Dynamic Performance Comparison 32 2.3 The Ducted Tip Propeller 33 2.3.1 Manufacturing Process 36 3 Experimental Results •, 39 3.1 Ducted Tip Propellers 41 3.2 Faired 1" Ducted Tips 45 4 Discussion 49 4.1 Effect of the Installation of the Ducted Tips 49 4.2 The Faired 1" Ducted Tips 52 4.3 Pressure Change Due to the Ducted Tips 55 4.4 Comparison to Other Studies of Ducted Tip Propellers 57 4.5 Error Analysis • 58 iii 5 Conclusion bU 6 Recommendations 63 References 64 Appendix A: Prony Brake Specifications 67 Appendix B: Torque Calibration Data from the Prony Brake 68 Appendix C: Propeller Measurement Error Analysis 69 Appendix D: Blade Profile Measurement Transformation 70 Appendix E: Camber Comparison 71 Appendix F: Performance Comparisons of Propeller A and B 74 Appendix G: Tip Load Calculations 76 Appendix H: The Inherent Thrust and Torque of the Dynamometer 77 Appendix I: Reynolds Number Dependence 81 iv List of Tables Table 1.1: Re range of the different advance ratios tested 11 Table 2.1: Tip geometry 34 Table 3.1: Thrust and torque loads present at the peak efficiency of the reference propeller for different rotational speeds 44 Table 3.2: Summary of the peak efficiencies for the propellers at different rotational speeds 45 Table 4.1: Changes in the propeller characteristics at the peak efficiency for the propellers with the different tip geometry 50 List of Figures Figure 1.1: Division of a propeller blade into radial sections 2 Figure 1.2: Velocity and force relations relative to the blade section geometry 3 Figure 1.3: Tip rollup 4 Figure 1.4: Summary of efficiency curves for the reference propeller indicating Reynolds number independence beginning at 2000 rpm 11 Figure 2.1: Dynamometer setup, a) Dynamometer, b) Schematic of Dynamometer c) Instrumentation 15 Figure 2.2: Dynamometer with a shroud over the driveline and fairings 17 Figure 2.3: The effect of a shroud and fairings on the measured reference propeller efficiency 18 Figure 2.4: Static torque calibration curve 19 Figure 2.5: Prony brake, a) Prony brake schematic. b) Prony brake assembly 21 Figure 2.6: Static Prony brake calibration curve 22 Figure 2.7: Torque values at different dynamic test settings 23 Figure 2.8: Dynamic calibration results 24 Figure 2.9: Static thrust calibration 25 Figure 2.10: Dynamic thrust calibration results, a) Thrust measurement with increasing rotational speed, b) Measured thrust versus applied thrust 26 Figure 2.11: Dynamic thrust response with increasing torque. The shaft rotation rate was varied from 500 to 1500 rpm for these tests 27 Figure 2.12: Dynamic Torque response with an applied thrust load 28 Figure 2.13: Propeller measurement setup 29 Figure 2.14: Blade profile comparison of the three propellers at 0.5R 30 Figure 2.15: Blade profile comparison of the three propellers at 0.7R 31 Figure 2.16: Blade profile comparison of the three propellers at 0.S5R 31 Figure 2.17: Camber comparison of the different propellers at 0.7R 32 Figure 2.18: Performance comparison of Propeller A and B at 2000 rpm 33 Figure 2.19: Geometry of the ducted tip 35 Figure 2.20: Sample piece for testing the braze strength 36 Figure 2.21: Tensile loading of the braze sample 36 vi Figure 2.22: The ducted tip propeller 37 Figure 2.23: Faired ducted tips, a) The leading edge, b) Side view of the tip 39 Figure 3.1: Repeatability of the performance curves calculated for the 0.75" ducted tip propeller test data at 2000 rpm 40 Figure 3.2: Repeatability of the performance curves calculated for the 1" ducted tip propeller test data at 2000 rpm 41 Figure 3.3: Performance of the ducted tip propellers at 1000 rpm 42 Figure 3.4: Performance of the ducted tip propellers at 1500 rpm 43 Figure 3.5: Performance of the ducted tip propellers at 2000 rpm 43 Figure 3.6: Performance of the ducted tip propellers at 2500 rpm 44 Figure 3.7: Faired 1" duct 46 Figure 3.8: Performance curves of the faired 1" ducts at lOOOrpm 47 Figure 3.9: Performance curves of the faired 1" ducts at 1500rpm 47 Figure 3.10: Performance curves of the faired 1" ducts at 2000rpm 48 Figure 3.11: Performance curves of the faired 1" ducts at 2500rpm 48 Figure 4.1: Geometry of the annular airfoil tested by Fletcher 53 Figure 4.2: Performance curves of the faired 1" ducted tip propeller with the effects of the ducted tips removed at 2000 rpm 54 Figure 4.3: Changes in the reference propeller performance curves with pressure variations at 2000 rpm 56 Figure 4.4: Comparison of the reference propeller performance curves with free stream pressure with that of the faired 1" ducted tip propeller at 2000 rpm 56 vii Nomenclature (Equat ion 1.3) (Equat ion 1.4) (Equat ion 1.5) (Equat ion 4.1) Co D r a g Coeff ic ient (Equat ion 4.3) Ci L i f t Coeff ic ient c C h o r d Cf F r i c t i o n coefficient d D u c t diameter D D r a g (Equa t ion 4.2) Dp Propel le r diameter e E lement o f error G Ca lcu la ted result determined f rom independent variables (Equat ion 4.4) / Index representing the L different variables J A d v a n c e ratio Ko Torque coefficient KT Thrust Coeff ic ient k number o f element o f error L L i f t LI E n c l o s e d length o f the duct L2 O v e r a l l length o f the duct / Spi ra l length n Rota t ional speed P P i t c h Pv V a p o u r pressure Q Torque R N o m i n a l radius o f the propeller Re Reyno lds number r A fraction o f the propel ler radius T Thrust U V e l o c i t y o f the ax ia l f l o w UR Resultant ve loc i ty at a radial section o f the propeller blade UT Tangent ia l ve loc i ty at a radial section o f the propeller blade UG Uncer ta inty o f G (Equat ion 1.2) (Equat ion 1.7) (Equat ion 1.1) (Equat ion 4.5) vin uxi uncertainty of the dependent variable, x, (Equation 4.7) x, Dependent variables of G a Angle of attack (3 Angle of incoming flow r/ Efficiency (Equation 1.6) /u Absolute viscosity of air <fi Blade angle p Air density cr Cavitation Index (Equation 1.8) Gj Sensitivity index of G to x, (Equation 4.6) ix Acknowledgements I was blessed with two wonderful supervisors who are extremely knowledgeable and patient. Their guidance and encouragement helped me win the battle against Murphy. Thank you very much, Dr. Sheldon Green and Dr. Martin Davy! I would also like to express my gratitude towards Osborne Propellers for their generosity and interest in the project. Without their help with the propeller tip modifications, the experiments performed would not have been possible. In addition, much appreciation goes to Dr. Yusuf Altintas and his students in the Automation lab for providing me with access to the coordinate measurement machine as well as their help with positioning the propeller. I would like to extend my thanks to all of the technicians who have helped me troubleshoot my apparatus: Glenn Jolly, Dan Miner, and Markus Fengler. On a more personal note, I would not have been able to complete this degree with my current level of sanity (or lack of) without the endless support and patience of my family and friends. A special thanks goes to Cheryl So and Galen Wong for always being there for me, through thick and thin. Karl Davis, despite being on the other side of the world, has also provided me with much technical and moral support on this project. Last but not least, I would like to thank Larry Li and Dan Dressier for providing me with the incentive to graduate as soon as possible and for the memorable office bonding sessions. 1 Introduction Propellers, which have existed for more than a century, are still one of the most widely used marine propulsion devices. Unfortunately, the formation of cavitation at higher cruise speeds is still a major problem for propellers. Cavitation is the formation of vapour bubbles due to extreme local pressure drops in a flow. When the fluid pressure increases beyond the vapourization pressure, the bubbles will collapse, releasing energy great enough to cause erosion in hulls and propellers. The major problems that cavitation create are vibration, noise, reduction of propeller efficiency, and component erosion. The types of cavitation found on a marine propeller include sheet, bubble, cloud, tip and hub. Tip cavitation, however, has been observed to be the dominating type at inception as observed by Latorre (1981) as well as Lodha and Arakeri (1984). In order to delay the inception of cavitation, the focus is placed on reducing the intensity of the blade tip vortices. A method of reducing the cavitation due to the propeller tip is through the use of tip modifiers. One such method, using ducted tips on the end of the propeller blades, is examined. Due to the complexity of the flow dynamics, predicting a propeller's performance accurately is still a challenging task. Computational models are available, but the accuracy of the results is questionable. Experimental methods are the most reliable methods of determining a propeller's behaviour; however, it is not always possible due to facility accessibility and cost limitations. In order to perform a well-controlled study of a ducted tip propeller design in an easily accessible facility and with low cost, an aerodynamic facility has been developed. This chapter will discuss the motivation for the project, different test facilities available, design criteria for the new test facility, previous work performed on propeller tip modifiers, and the scope of this research project. 1.1 Propeller Theory To be able to effectively modify the tip flow, it is important to understand the basic flow dynamics of a propeller. There are three basic theories used to study propeller flow dynamics: momentum theory, blade element theory, and circulation theory. Of the three theories, momentum theory is the most basic. The propeller is analyzed as an actuator 1 disk that creates a sudden pressure differential to accelerate the fluid flow. The flow is assumed to be inviscid flow with no rotational effects. Solving the equations of conservation of mass and momentum, the propeller system can be vastly simplified to calculate the upper limit of the ideal efficiency. Although this information is useful, it does not account for any details, such as the number of blades and the geometry of the blade section. Blade element theory, a much more developed theory, divides a propeller blade into sections as shown in Figure 1.1. Each cross section of a blade resembles an airfoil, which generates lift and drag upon encountering relative fluid motion. The added complication with the analysis of a propeller blade is with the rotational velocity that must be considered. Since the rotational velocity can be resolved into a tangential velocity at a given radial distance, the effective velocity vector at a given radius can be determined by summing the local tangential and axial velocities as shown in Figure 1.2. The resultant velocity vector will allow for airfoil analysis on a section of propeller blade. For propeller analysis, the relevant outputs are thrust and torque, which can be resolved from the lift and drag forces calculated with airfoil theory. Thrust Figure 1.1: Division of a propeller blade into radial sections. 2 In the plane of rotation. Figure 1.2: Velocity and force relations relative to the blade section geometry. Figure 1.2 demonstrates that by knowing the lift and drag produced by a section of a blade, the resultant thrust and torque can be calculated using Equations 1 and 2. dT = dL • cos + dD-sin/3 (1.1) dQ = (dL • sin j3 + dD-cos fi)-r (1.2) By applying blade-element theory, multiple radial sections of a propeller blade are analyzed and integrated to estimate the thrust and torque generated by the whole blade. The thrust and torque is then multiplied by the number of blades to determine the performance of the whole propeller. Although blade element theory provides a good approximation of the propeller performance, it does not account for the rollup effect at the tip of the blades. It also does not directly consider the local axial velocity enhancement produced by the propeller blade rotation. As for any lifting body, such as an airplane wing, there exists a pressure difference between the two surfaces. Where the barrier between the two surfaces terminate, the 3 fluid on the high pressure side will rollup towards the lower pressure side, forming a vortex structure. This is illustrated in Figure 1.3. Although similar to the tip vortices shed from an airplane wing, propeller blades have an added rotational velocity producing a helical shedding pattern. Blade tip vortices change the local effective angle of attack creating a downwash effect, which reduces the efficiency of the propeller. In the case of a marine propeller, the drop from the free stream pressure to the core pressure of the vortex can be enough to reach vapourization pressure, at which cavitation occurs. THRUST I Figure 1.3: T ip rollup. 1.2 Tip Modifiers The intensity of tip vortices is proportional to the loading at the tip. As Kuiper (2001) discussed, when the tip loading is low, flow separation may occur, but when the tip load is high, strong vortices are formed. Although reducing the load at the tips can reduce the tip vortex strength, efficiency is often penalized. Platzer and Souders (1979) indicated that by reducing the pitch at the tip of a propeller by 10°, the cavitation index was reduced by 25%; however, the efficiency was also reduced by 5%. From studying the cavitation of vortex trailing different planform configurations, McCormick (1962) noticed that the size of the vortex core was dependent on the boundary layer thickness of 4 the tip. Other researchers have also noticed that the rollup process is very sensitive to the tip geometry; hence tip thickness, roughness, and other modifiers have all been studied. Kuiper (2001) observed that increasing the tip thickness can help suppress separation and local tip cavitation; however, the increased tip thickness also decreased the local pressure, which promotes cavitation inception. A similar concern arises with increasing blade tip roughness as well. Katz and Galdo (1988) studied the effects of roughness on the tips of a hyrdrofoil by using different flow visualizations and monitoring the surface pressure variations near the tip. Their results indicated that the surface pressure near the tip of the hydrofoil was increased with the application of roughness, implying that the vortex strength was reduced. Stinebring et al. (1991) confirmed that adding blade tip roughness increased the vortex core pressure with minimal effect on lift. Despite the benefits of applying roughness to the tips, there are concerns such as inducing local cavitation as discussed by Kuiper (1978) in regards to adding roughness to the leading edge of a blade. The objective is to reduce the tip vortex's propensity to cavitate with minimal negative effect on the propeller performance. Platzer and Souders (1979) performed a thorough review on the different tip modifiers that had been studied before 1979. Although the review was performed in 1979, much of the research performed between then and now has been further explorations of the designs they discussed. Examples of tip modifiers mentioned in Platzer and Souders which have been studied on marine propellers in more recent years include porous tips by Mani et al. (1988), tip-fins by Anderson (1997), polymer-injection by Fruman and Aflalo (1989), as well as the ducted tip by Green and Hordnes (1998). Of the large number of tip modifiers that had been studied, polymer injection, ducted tips, and bulbous tips appear to hold good potential for suppressing cavitation on a marine propeller. Mass injection into a flow surface was initially studied on wing tip vortices in the 1970's. The idea was later applied on marine propellers. Of all the different tip modifiers, mass injection is one that has been quite thoroughly studied. Fruman and Aflalo (1989) observed that upon injecting a polymer solution into the blade tip, developed cavities disappeared. Observations made during monitoring of the axial and tangential velocity of the vortex structure with a laser Doppler anemometer indicated that the tangential 5 velocity of the vortex was greatly reduced. Fruman and Aflalo's results showed that the core radius of the vortex increased upon the injection of the polymer. Chahine et al. (1993) studied the effectiveness of polymer injection on the inception of cavitation as opposed to the desinence of cavitation. Chahine et al.'s results agree with Fruman and Aflalo's, confirming that injecting a polymer solution at the blade tip can reduce the tip vortex intensity. As well, both groups illustrated that injecting either water or a water and glycerine solution are not effective. It was assumed that the swelling of the non-Newtonian fluid exiting from a jet flow diffused the vortex core, which in turn delayed cavitation inception. Chahine et al. also investigated the effects of different injection locations and found that it is most effective when it is at the very tip of the blade. The results from the polymer injection indicated a maximum of 35% decrease in the inception cavitation index. Bulbous tips, which were studied by Crump (1948), appeared to be a viable solution to delaying cavitation inception on a marine propeller with negligible detrimental effects on the propeller performance. However, Johnson and Rutgersson (1991) observed that although the bulbs increased the cavitation-free vessel speed by about 10-15%, the propeller efficiency was decreased by roughly 2%. Another design, which had been shown to reduce tip vortex intensity, is ducted tips. Ducted tips were discussed only briefly by Platzer and Souders, as it did not seem suitable for marine propellers at the time. The investigation into ducted tips was sparked again after seeing Duan and Green (1995) present promising water tunnel test results obtained from a ducted tip hydrofoil. Duan and Green observed a substantial reduction, 50 ± 15%, of the cavitation index at normal operating angles of attack. In addition, at angles of attacks greater than 8°, induced drag was reduced and the lift to drag, L/D, ratio became 6 ± 1 % better than that of the conventional tip. The success of the ducted tip was attributed to the alteration of the vorticity being shed in the Trefftz plane. Hordnes and Green (1998) performed sea trials comparing a stock 36" diameter propeller with a 36" ducted tip propeller. The duct-diameter to span ratio was 0.5 and the duct length to chord ratio was 0.65. The copper tube used for the ducts were bent into an arc to 6 match the radius at which they were to be brazed on. The outer diameter of the propeller was maintained by trimming the propeller down by the diameter of the duct prior to brazing. The results from the sea trials provided further evidence that a ducted tip propeller holds much promise for the marine industry. The ducted tip propeller was able to increase the shaft speed by almost 50%, without penalizing efficiency, before cavitation inception. At higher advance ratios, it was found that the ducted tip propeller even increased efficiency by 6%. Despite the efforts put into running sea trials with the stock and modified propeller under the same sea conditions, it is inevitable that there will be differences in the operating conditions. Due to the challenge of controlling the experimental conditions at open sea, it is difficult to have full confidence that the performance improvement observed with the ducted tip propeller was attributed solely to the effects of the tips. Building upon the promising sea trials, Ingvarsdottir (2001) investigated the tip vortex shedding characteristics of a ducted tip hydrofoil by using a finite-volume solver, CFD-ACE(U). The numerical results showed that the vortex shed from the ducted tip was in the shape of the duct as opposed to the tight circular vortex shed by a rounded tip. Such results support the benefits of the ducted tips. To study the ducted tips in a more repeatable manner, Straver (2002) tested a scaled down ducted tip propeller in a towing tank and cavitation tunnel. Although the ducted tip propeller's performance in the towing tank indicated a decrease in efficiency, observations in the cavitation tunnel indicated that ducts were able to greatly weaken the tip vortex strength, which successfully delayed cavitation inception. 1.3 Test Facilities From the work performed by the researchers discussed in the previous section, it is evident that a propeller's performance is extremely sensitive to even minor changes to the propeller. In order to acquire reliable propeller performance data, it is essential that a test facility provides sensitive and accurate instrumentation. Marine propeller testing can be performed at sea, in a cavitation tunnel, or in a towing tank. Sea trials most accurately reflect real world performance but must overcome a number of challenges, such as 7 minimizing variations in operating conditions and protecting the instrumentation. Waiting for proper testing conditions can be prohibitively time consuming and expensive. Towing tanks are commonly used for testing propellers at lower advance ratios, where the disrupt the measurements being acquired. Some of the main concerns with using towing tanks and cavitation tunnels include time, cost, and the difficulties associated with having electronics in a wet environment. A s well , few publicly accessible facilities are capable o f testing full size propellers. Davis (2004) designed and commissioned an aerodynamic test facility, which has now been updated and improved upon, for marine propellers at the University o f British Columbia (UBC) . The intent of the facility is to allow for more cost-effective and convenient marine propeller testing. The dynamometer developed for the U B C test facility can measure up to 100N of thrust and 20Nm of torque with an accuracy of 0.1% full scale and a repeatability of 0.3% (at 2000+rpm). The facility was improved during the course of this project to produce the level of accuracy stated. Incidentally, a similar test facility was designed and constructed by Molland and Turnock (2002) at the University of Southampton during approximately the same time period. Although both facilities can measure marine propeller torque and thrust, the design of the dynamometers, their accuracies, and their measurement ranges are quite different. The maximum design loads of the dynamometer at the University of Southampton are 750N of thrust and 1 lONm of torque, with an accuracy of 1% full scale. In order to obtain relevant data from an aerodynamic facility, it is essential that the relevant appropriate non-dimensional groups be properly matched. The non-dimensional groups that are important for modeling propeller flow include the following: pressure range is higher. A t higher advance ratios cavitation can form prematurely and J = U Advance Ratio ( 1 . 3 ) n-Dp Torque Coefficient (1.4) 8 Kj — p-n2-D; ( J ^ 2-n \Z. • JL J R e a 7 -p - c 0 1 - n - D p - p 2 +(0J-7TY P - P v Thrust Coefficient (1.5) Efficiency (1.6) Reynolds Number (1.7) Cavitation Index (1.8) where u = Linear forward velocity [m/s] n = Rotational speed (RPS) [rev/s] DP = Propeller diameter [m] C0.7 = Propeller chord at 70% radius [m] P = Fluid density [kg/m3] M = Fluid viscosity [kg/m-s] T = Propeller thrust [N] Q = Propeller torque [N-m] Pv = Liquid vapour pressure [Pa] p = Fluid static pressure [Pa] The advance ratio, J, relates the propeller's rotational speed to the boat speed. The characteristics of a propeller are defined by the advance ratio and the non-dimensional form of torque and thrust, KQ and K T , respectively. By combining the three groups, the propeller efficiency can be calculated to summarize its performance. The Reynolds number, Re, for a propeller is defined based on the chord length at 70% radius, since that is approximately where the most thrust is generated. The velocity term used in defining the Reynolds number is the effective velocity vector, which accounts for the rotational and axial velocity components, at 0.7R. Although the Reynolds number is one of the most pertinent dimensionless groups for fluid flow modeling, it is unrealistic to 9 match the Reynolds number of a marine propeller operating in water to one operating in air. Typical hydrodynamic Reynolds number for a propeller is on the order of 1 x 10 , where as the maximum Reynolds number of the propeller to be tested in the wind tunnel will be just under 1 x 106. To ensure that the results acquired from an aerodynamic facility were applicable to practical conditions, research was carried out on the dependence of propeller performance on Reynolds number. It was found that in scaled airplane propeller tests performed by the North Atlantic Treaty Organization's (NATO) Advisory Group for Aerospace and Development (AGARD) that Reynolds number effects become reasonably small when Re > 0.5 x 106 (Haines 1994). Airplane propeller performance becomes completely Reynolds number independent at a Re just under 1.0 x 106. The Reynolds number dependence of marine propeller hydrodynamics was studied by Bazilevski (2001) and it has been showed that propeller performance is Reynolds number independent for Re greater than approximately 1.0 x 106. With literature supporting that propeller performance is nearly independent of Reynolds number for Re > 0.5 x 106, it is reasonable to trust that the UBC facility will produce reliable propeller evaluations. To investigate the Reynolds number dependence of propeller performance and to confirm the ability of the UBC aerodynamic test facility to provide reliable propeller performance data over a range of operating conditions, a bronze, right hand propeller was tested. The efficiency curves calculated from measurement for the different rotational speeds are summarized in Figure 1.4. The corresponding Re range to the advance ratio range tested at each rotational speed is indicated in Table 1-1. The results illustrated in Figure 1.4 shows that the peak efficiency of the propeller appears to converge with increasing rotational speed. Unfortunately the efficiency curve for 2500 rpm is incomplete due to the wind speed limitations of the wind tunnel. Although complete Reynolds number independence is not observed; the behaviour illustrated in Figure 1.4 strongly suggests that the results acquired at 2000 rpm will be a good representation of the propeller's performance. 10 Table 1.1: Re range of the different advance ratios tested. Rotational speed [rpm] Re Range 1000 3.314 x 10 5-3.705 x 105 1500 4.971 x 10 5-5.557 x 105 2000 6.628 x 105 - 7.160 x 105 2500 8.285 x 105 - 8.693 x 10s 0.70 0.00 -I r- , , , , , , , , , , 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 Advance Ratio, J — A — 1 0 0 0 rpm o 1500 rpm o 2000 rpm x 2 5 0 0 rpm Figure 1.4: Summary of efficiency curves for the reference propeller indicating Reynolds number independence beginning at 2000 rpm. It is obvious that cavitation cannot be modeled in a wind tunnel but the performance of a propeller can be closely monitored for changes caused by geometric modifications. Changes in thrust and torque characteristics can then be allocated to the modifications performed. 11 1.4 Research Objectives Because of the detrimental effects that cavitation has on a propeller and its vessel, much research effort has been invested into finding ways to delay the inception of cavitation. As discussed in Section 1.1.2, ducted tips show high potential for a practical means of cavitation suppression. The main research objectives of this project is to verify the effects of ducted tips on a marine propeller's efficiency and to investigate the influence of different duct diameters on the performance of a marine propeller tested in an aerodynamic facility. As the experimental results from Hordnes and Green as well as Straver both demonstrated a delay in cavitation inception with the installation of the ducted tips, the information now required is whether it penalizes the efficiency of the propeller. With the test facility available, although cavitation cannot be observed directly, the effects of the ducted tips on a marine propeller can be determined from high precision results. 12 2 Experimental Set Up and Methodology The UBC aerodynamic marine propeller test facility was designed and commissioned by Davis in 2004. The propeller dynamometer allows full-sized marine propellers to be tested in the Boundary Layer Wind Tunnel at UBC. Although the apparatus, as completed by Davis, was shown to provide good results, improvements on the instrumentation and calibration process were made to ensure higher precision measurement results. 2.1 Dynamometer The dynamometer setup is illustrated in Figure 2.1. Two design guidelines influenced the overall design of the dynamometer; the torque and thrust of the system must be completely decoupled and independent, and highly accurate sensors must be used in order to keep overall measurement error to within 2%. Adherence to the first principle allowed for the measurement of very small thrusts even in the presence of large torque loads. The conventional method of measuring torque and thrust is by adhering strain gauges to the shaft; however, as the torsional strain from driving the propeller is typically 20 times or greater than that from the thrust created, it is difficult to resolve the thrust component without influence from the torque applied. The second guiding design principle for the system led to selecting and implementing only transducers that were accurate to better than 0.1% throughout their full-scale range, in order to keep the overall measurement error to less than or equal to 2%, even when operating under low-load conditions. Since the forces generated by a marine propeller can vary by a factor of 20 or more with changes in the rotational speed and advance ratio, transducers with a wide dynamic range were required. Apart from the sensors, the selection of the supporting equipment for the driveline was also very important. A total of five air bearings were used for constraining the propeller shaft and minimizing the effects of bearing friction on the torque and thrust measurements. Three 3" diameter air bearings were used to support the 3" propeller shaft and the propeller while two V" diameter air bearings were used to support the drive shaft. 13 14 Figure 2.1: Dynamometer setup, a) Dynamometer, b) Schematic of Dynamometer c) Instrumentation. A W E G 15HP (W21 T E F C (IP55)) electric motor, capable o f a m a x i m u m rotational speed o f 3500rpm, drove the propeller at an adjustable speed. A photo-emitter/detector pair directed at b lack tape on the propeller shaft was used as a tachometer to conf i rm and log the rotational speed o f the propeller shaft. A be l lows coup l ing was instal led between the thrust bearings and the electric motor as w e l l as between the torque sensor and the propeller shaft. Such a coup l ing was able to transmit the comparat ively large torque required to drive the propeller, but was f lexible and very compl iant i n thrust. The be l lows coupl ings m i n i m i z e d the thrust transmitted to the motor as w e l l as a l l o w e d for minor misal ignments i n the dr ivel ine , reducing the stress on the components o f the dr ivel ine. A torque l imiter , w h i c h was set to disengage at torques o f 20 N m or greater, had also been instal led a long the dr ivel ine to prevent the be l lows coupl ings and torque sensor f rom exceeding their specified torque load. In compl iance w i t h the design guidelines previous ly mentioned, a P r e c i s i o n Transducers shear beam load ce l l (model P T 2 0 0 0 ) and a Sensor Techno logy non-contact surface acoustic wave ( S A W ) torque sensor (model E 3 0 0 R W T 1 ) were selected for the thrust and torque sensors, respectively. The shear beam load ce l l was rated for 1 9 6 N w i t h a total 15 error of ±0.03% the applied load. The thrust was transmitted to the load cell through a set of thrust bearings mounted on a floating plate and a flexure rod. This load cell absorbed the vast majority of the axial load generated by the propeller. The bellows couplings supported 0.3% of the thrust but this component deviated less than 0.05% and was accounted for during calibration. The maximum torque expected from the test propeller was approximately 10 Nm, hence, a 20 Nm SAW torque transducer calibrated to provide an accuracy of 0.1% F.S. was selected. The entire propeller shaft between the propeller and the torque sensor was supported only by air bearings, and therefore, except for the minimal torque variation caused by the air bearings, the torque generated by the propeller was the same as that in the shaft at the location of the torque sensor. After preliminary testing of the dynamometer, a shroud over the driveline and fairings on the test stand were added to streamline the airflow around the apparatus. The addition of the shroud and fairings, which substantially improved the propeller performance, is illustrated in Figure 2.2. The peak efficiency measured after the installation of the shroud and fairings increased by 5%, as illustrated in Figure 2.3. The impact of such geometrical changes to the setup indicates the sensitivity of the instrumentation of the system as well as the flow around the propeller. To ensure the precision and accuracy of the dynamometer's performance, the calibration processes were carefully designed and executed. The thrust and torque transducers were calibrated under both static and dynamic conditions. Given that both the torque and thrust transducers were calibrated to be accurate to 0.1% F.S. or better by the manufacturers, no attempt was made to verify their accuracy. Rather, calibration checks were used to ensure that the signal outputs behaved in a physically sensible manner. In all cases, the calibration curves measured were within 3% of the manufacturer's calibration constant. This was the approximate error of the calibration procedures, and thus, the manufacturer's calibration was used in subsequent analysis. 16 Figure 2.2: Dynamometer with a shroud over the driveline and fairings. 17 0.70 0.00 -I , , , , , 1 1 , , , — , 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 Advance Ratio, J -••A--- Bare — • — W i t h Shroud and Fairings Figure 2.3: The effect of a shroud and fairings on the measured reference propeller efficiency. 2.1.1 Torque Sensor Calibration Two separate methodologies were developed for calibrating the torque transducer. The static calibration setup allowed for verification of the torque signal when a propeller was mounted onto the drive shaft. The dynamic calibration procedure was slightly more complex, yet more accurate, although, the setup could only be installed without a propeller mounted. To check the calibration of the torque sensor under static conditions, a 0.75 m long aluminum arm was secured on the propeller shaft directly in front of the propeller. A stop was placed at the solid coupling near the electric motor to prevent any rotational movement of the shaft. A cable, attached perpendicular to the arm, was run over a pulley and from it was hung a carriage. Weights in 1.4 N increments were placed in the carriage to create varying torque loads of up to 10.5 Nm on the driveline. 18 Figure 2.4 shows the voltage output by the torque sensor under different propeller shaft torque levels. The curve shows a highly linear relationship between the applied torque load and the senor output, with a linear fit R2 value of 1.0 to four significant figures. Calibration was performed with both increasing and decreasing applied torques. No discernible difference was observed in the results proving that the torque sensor's hysteresis was negligible. -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 Output Signal [V] Figure 2.4: Static torque calibration curve. A Prony brake was developed for calibrating the propeller test rig dynamically. The Prony brake was used to determine whether the torque response of the SAW torque transducer changed with rotational speed. A schematic diagram of the Prony brake used is shown in Figure 2.5. During dynamic calibration, the brake rotor took the place of the propeller. A friction band placed around the brake rotor was used for applying a torque load. The torque load 19 was controlled by adjusting the tension of the band around the rotor via adjustment nuts. The Prony brake was designed to be able to provide a torque load of more than 10 Nm, as that was the maximum torque previously measured with the current reference propeller. To test the torque range of interest without generating excessive heat flux at the brake pad, a brake rotor of 17.8 cm diameter was selected. A go-kart brake band from Great Lake Friction Products was used around the 3.2 cm thick, mild steel brake rotor. The friction material on the brake band was rated to a maximum of 1637 rpm providing an effective limit to the rotational speed of the device. Please refer to Appendix A for the brake band friction material specifications. The brake band was connected to a tension arm, which was inline with an S-type load cell, at a distance of 14 cm from the axis of rotation. With the known torque arm distance and the force measured by the load cell, the torque being applied could be calculated. The torque measured by the inline torque sensor was then compared to the calculated torque applied by the Prony brake for verification. Initially, the brake band was connected to the load cell with a solid tension arm. It was later realized that the rotation of the brake rotor introduces a large enough of a lateral load to result in erroneous force measurements on the S-type load cell. A section of the tension arm was replaced with a cable connection to provide lateral flexibility to allow for angular displacement and relieve the sensor from parasitic lateral loads. The substitution made with the tension cable greatly improved the accuracy of tension measurements. Prior to running the dynamic tests, a load was applied to the tension arm of the Prony brake to perform a static calibration of the setup. The applied torque was calculated from the load cell readings and measured by the torque sensor to ensure that both values agreed with each other. Figure 2.6 illustrates the good agreement between the torque applied and the torque measured by the torque sensor. Refer to Appendix B for the calibration data. 20 f = fin BRAKE TENSION ARM a) b) Figure 2.5: Prony brake, a) Prony brake schematic, b) Prony brake assembly. 21 5 10 15 Torque App l ied [Nrn] Figure 2.6: Static Prony brake calibration curve. 20 The dynamic calibration process consisted of running the dynamometer at various rotational speeds and tension band settings. The rotational speeds tested were 500, 750, 1000, 1250, and 1500 rpm. Each rotational speed was tested with three tension levels of the brake band: low, medium, and high. The tension level was set by adjusting the gap distance, x, between the adjustment blocks. When x = 3.8 cm, the tension level was considered zero. Increments of the tension level were gauged by the number of revolutions advanced by the adjustment nut. At the maximum tension level tested, the adjustment nut had advanced five revolutions from the reference point. The results from the dynamic tests, shown in Figure 2.7, illustrate that the torque applied, Qa, to the system varied with the tension setting of the brake band as well as the rotational speed of the rotor. The heat generated by the brake band on the rotor was expected to change the friction coefficient, which would change the applied torque on the rotor. Despite these variations in applied torque at different test settings, the measured 22 torque value , Qs, agreed very c lose ly w i t h the calculated appl ied torque. A s il lustrated i n F igure 2.8, measurement values taken at a l l three tension levels a l l fa l l approximate ly on the 1:1 l ine . The best-fit l inear curve through the data points gave a slope o f 1.0034 and an R 2 value o f 0.9981. The close agreement o f the torque measured by the torque sensor to that appl ied torque calculated clear ly indicates that the accuracy o f the torque sensor was indeed independent o f rotational speed. Concerns over the heat generated from the Prony brake affecting the sensi t ivi ty o f the load ce l l and the torque sensor were considered, but after testing the method, it was found that the instruments were distant enough f rom the brake rotor that they remained at r o o m temperature dur ing the cal ibrat ion process. E z 3 cr 300 600 900 1200 Rotational Speed [rpm] 1500 Qs-Low Qs-High Qa-Low Qa-High Qs-Mid • - x - • Qa-Mid 1800 Figure 2.7: Torque values at different dynamic test settings. 23 15 Torque A p p l i e d [Nm] Figure 2.8: Dynamic calibration results. 2.1.2 Thrust Sensor Calibration The thrust transducer was also calibrated under static and dynamic condi t ions . F o r static cal ibrat ion, an end cap w i t h a s w i v e l was mounted on the end o f the propel ler shaft. One end o f the cable was connected to the s w i v e l and the other end was connected to a carriage. The cable rested on a l o w fr ic t ion pul ley w h i l e weights o f 6.8 N increments were p laced o n a carriage for static thrust cal ibrat ion. A s i l lustrated i n F igure 2.9, the results show very good l ineari ty, w i t h a R2 o f 1.0 to four significant figures. Ca l ib ra t ion was performed w i t h both increasing and decreasing appl ied loads. The independence o f measured thrust w i t h load history was evidence that thrust sensor hysteresis is negl ig ib le . 24 0.0 0.5 1.0 1.5 2.0 2.5 Output signal [V] Figure 2.9: Static thrust calibration. The setup for dynamic cal ibra t ion o f the thrust transducer was the same as that o f the static ca l ibra t ion w i t h the except ion that the shaft rotated at a set speed. A propel ler nut w i t h a s w i v e l end was used to connect the tension cable to the propeller shaft. The thrust sensor was tested at the same six rotational speeds used dur ing the dynamic torque cal ibrat ion: 500, 750, 1000, 1250, 1500, and 2000 rpm. A t each rotational speed, four different thrust loads were applied: 20.4, 40.9, 61.3, and 95.4 N . A l inear trend l ine fitted to a plot (Figure 2.10) o f the measured thrust against the appl ied thrust had a slope o f 1.004 and a R2 o f 1.000. The plot shows no signs o f hysteresis or rotational speed dependence. 25 a) 1000 1500 Rotational Speed [rpm] o 2 0 N m 4 1 N A 6 1 N x 9 5 N b) 20 40 60 Thrust Applied [N] 80 Figure 2.10: Dynamic thrust calibration results, a) Thrust measurement with increasing rotational speed, b) Measured thrust versus applied thrust. The 1:1 line is shown. 26 To ensure that the torque and thrust measurements were independent of each other, a dynamic test was performed to check for cross-talk. The test was performed with the Prony brake set at a medium tension level and an applied thrust load of 61.3 N. Tests were performed at 500, 750, 1000, 1250, and 1500 rpm. The results, shown in Figures 2.11 and 2.12, remained accurate and linear, indicating that there was no significant cross-talk between the two measurement signals. 70 60 50 (0 3 \-£ 40 y--a o t— 30 3 ID ro O S 20 10 0 3.5 3.6 3.7 3.8 3.9 4.0 Measured Torque [Nm] 4.1 4.2 Figure 2.11: Dynamic thrust response with increasing torque. The shaft rotation rate was varied from 500 to 1500 rpm for these tests. 27 A p p l i e d T o r q u e [Nm] Figure 2.12: Dynamic Torque response with an applied thrust load. 2.2 The Propeller The propeller chosen as a reference and for modification was the Dyna-Quad propeller manufactured by Michigan Wheel. It is a 24" diameter by 24" pitch right hand manganese bronze propeller, mainly used on fishing boats. Three Dyna-Quad propellers were purchased: one was used as a reference, one was modified, and one was a spare. 2.2.1 Geometric Similarity Between Propellers Prior to performing any modifications, all of the propellers were measured to ensure geometric similarity. A coordinate measurement machine (CMM) in the UBC Manufacturing Automation Laboratory was used for measuring the blade profiles of the four blades on each propeller. In order to measure the effective cross sections at a given radial distance, a rotary indexer was modified with a dummy key mounting for the propeller. Figure 2.13 illustrates the propeller measurement setup. 28 Figure 2.13: Propeller measurement setup. The suct ion and pressure sides o f the propeller were measured to provide the cross sectional profi les at three rad i i : 0.5R, 0.77?, and 0.857?, where 7? is the radius o f the propeller. The accuracy o f the C M M was ± 5 u m . The error o f the measurements is calculated and shown i n A p p e n d i x C . The plane o f rotation was taken to be the x - y plane w i t h the suct ion side facing the posi t ive z-axis . The total error i n the z-measurements, resulting f rom the tilt o f the propeller, the accuracy o f the machine and the run out o f the rotary indexer, for the 0.57?, 0.77?, and 0.857? were 0 .418mm, 0 .550mm, and 0 . 6 7 7 m m respectively. The probe f rom the C M M machine traveled o n l y f rom the top d o w n , i m p l y i n g that the propeller must be f l ipped to measure the second side. A l l o f the measurements taken for the pressure side must then be transformed pr ior to matching up w i t h the measurements f rom the suct ion side to fo rm the section prof i le . The transformation procedure is described i n A p p e n d i x D. 29 The four blades of each propeller were measured. The profiles of the four blades were averaged to provide a representative contour for each propeller at the three radii. The results, illustrated in Figures 2.14 to 2.16, indicate that there are some minor differences between the blade profiles of the different propellers. The camber line for the sections were also determined and compared. The results indicate that the camber of a given radial section for the three propellers were similar, with propellers A and B being the most alike. The process for determining the camber of the profiles is discussed in Appendix E. As most of the thrust from a propeller is generated near the tips, the propellers that were most geometrically similar near the tips, propellers A and B, were selected for the experiments. The camber difference between propeller A and propeller B was 1.3% at 0.7R. This is illustrated in Figure 2.17. 140 120 4 Degree of Rotation [deg] Prop A Prop B Prop c| Figure 2.14: Blade profde comparison of the three propellers at 0.5R. 30 120 0 -I , , , 1 — . > ' 0 10 20 30 40 50 60 70 Degree of Rotation [deg] Prop A Prop B Prop C Figure 2.15: Blade profile comparison of the three propellers at 0.7/?. 100 0 4 - , . . 1 • ' ' ' ' 0 5 10 15 20 25 30 35 40 45 50 Degree of Rotation [deg] - -» • Prop A Prop B • Prop C Figure 2.16: Blade profile comparison of the three propellers at 0.85/?. 3 1 E E N -90- .=40—-•KG-U-O- BO- 440- 2--to— x [mm] Prop A Prop B Prop C Figure 2.17: Camber comparison of the different propellers at 0.1R. 2.2.2 Propeller Dynamic Performance Comparison Once it was confirmed that the selected propellers were geometrically identical to within measurement error, they were tested to ensure that they performed in an identical manner as well. The propellers were run at 1000, 1500, 2000, and 2500 rpm on the dynamometer. As mentioned in Chapter 1, the lowest Reynolds number at which scaling effects become small is 0.5 x 106. Table 1-1 indicates that the Reynolds number range for tests performed at 1000 rpm was too low for the results to be credible. Although the Re range for 1500 rpm approached the magnitude at which the performance become independent of Reynolds number, the measurements acquired at 1500 rpm contain greater signal variations due to the vibration present as 1500rpm was near the resonant frequency of the apparatus. At 2000 rpm, the Reynolds number range was above 0.5 x 106 and the results are much more consistent as the vibration was greatly reduced at the higher rotational speed. Although the Reynolds number range for 2500 rpm was higher and would provide more confidence in the validity of the results, the complete efficiency curve could not be acquired for 2500 rpm due to the limitations of the wind tunnel's maximum wind speed. 32 Since the best representation of the propeller's performance was obtained at 2000 rpm, it will be the rotational speed for which the results will be presented. The performance curves acquired at 2000 rpm for propeller A and B were essentially identical (Figure 2.18). The maximum differences in KQ, K T , and 77 were within 1.4%, 2.9%>, and 0.7% respectively. This confirmed that one of the pair could be modified while the other was used as a reliable reference. The performance curves for the two propellers at 1000, 1500, and 2500 rpm are illustrated in Appendix F. 0.00 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 Advance Ratio, J Propeller A Propeller B Figure 2.18: Performance comparison of Propeller A and B at 2000 rpm. 2.3 The Ducted Tip Propeller As the pair of propellers had been confirmed to be highly similar, the ducted tip modification was carried forward with one while the other propeller was kept as a reference. As mentioned in Chapter 1, there have been previous studies on ducted tip propellers, but they drew contradictory conclusions. By testing the ducted tip design in 33 the wind tunnel, the effects of ducted tips on a marine propeller could be confirmed, and a direction for optimization of the geometry of the tips would be observable. The tips were made from commercially available copper tubes. Two different sizes of tips were tested. The geometry of a tip is illustrated in Figure 2.19. The dimensions of the tips tested are indicated in Table 2-1. LI, c, d, /, and L2 are the length of the enclosed tube, chord of the propeller blade at the section of union, diameter of the ducted tip, length of the spiral, and the overall length of the tube, respectively. The first set were smaller in diameter, which was use to test the effect of tip diameter on the performance. The second set, which was the base case, will maintain the scale of Ll/c and d that was tested by Green and Hordnes (1998). The spiral leading edge on the ducted tips used on the propeller tested by Green and Hordnes was replicated as well. The overall radius of the propeller was maintained at 0.610 m regardless of the tip configuration being tested with the outer radius of curvature of the tip, Ro, was always 0.305m. It was thus necessary to remove portions of the end of the propeller blades to accommodate the addition of the ducted tip. The copper tubes were attached to the propeller blade by brazing. To ensure that the brazed joint would be able to withstand the centripetal forces (calculated in Appendix G) generated by the added tips, a sample tip was brazed onto a dummy propeller blade. The centripetal force generated by a 38.1mm diameter tip, the largest potential tip size, rotating at 2500 rpm was calculated to be 5102 N. This test specimen is shown in Figure 2.20. The sample was loaded on a tensile machine, as shown in Figure 2.21, until mechanical failure was observed. The applied tensile load upon failure was 13096N, at which the cable connectors failed. Cracks at the braze joints were visible, but was not the cause of failure. These testing results imply that the welds had a factor of safety of greater than 2. Table 2.1: Tip geometry. Tip Geometry L1/c c [mm] L1 [mm] d [%R] d [in] / [mm] L2 [mm] Set1 0.65 155.6 101.1 6.3% 0.75 18.3 119.3 Set 2 0.65 181.0 117.6 8.3% 1 21.1 135.8 34 35 Figure 2.20: Sample piece for testing the braze strength. Figure 2.21: Tensile loading of the braze sample. 2.3.1 Manufacturing Process The first step to manufacturing the ducted tips was to bend them to the correct curvature for fitt ing onto the t r immed propeller blade. The first set o f tips was soft enough that it was bent manua l ly w i t h a conduit bender. The larger set was too st i ff to be bent manua l ly wh i l e mainta in ing a consistent curvature; hence, it was commerc i a l l y ro l l ed into the correct curvature pr ior to part i t ioning. 36 The propeller was fitted w i t h the smallest set o f ducted tips first, as less blade material had to be removed to accommodate the modi f ica t ion . The tips were s i lver brazed onto the propeller. The ducted tip modi f ica t ion is illustrated i n Figures 2.22. Figure 2.22: The ducted tip propeller. U p o n the comple t ion o f a set o f tip instal lat ion, the angle o f the tips was checked on the C M M . The blade angles o f the 0.75" diameter tips were a l l w i t h i n 1° o f the specif ied blade angle o f 18.19°. The implementat ion o f the 1" set o f t ips was less accurate. One o f the tips deviated more than 2° f rom the nomina l 18.37° at on o f the tips. T o reduce the potential force imbalance that w o u l d be generated, the tips were adjusted to b r ing the t ip angles to w i t h i n 1 ° o f each other. T h i s was performed by insert ing a steel bar, w h i c h was formed to the correct curvature, through the tips and app ly ing pressure where adjustment was necessary. Af te r the tips were adjusted, a l l o f the brazed joints were faired w i t h auto 37 body f i l ler to create smooth and consistent transitions between the tips and the blade. The tips are as i l lustrated i n Figure 2.23. Figure 2.23: Faired ducted tips, a) The leading edge, b) Side view of the tip. 3 E x p e r i m e n t a l R e s u l t s As previously demonstrated with the addition of the shroud and fairings on the apparatus, the airflow over the propeller is sensitive to the geometry of the dynamometer. To investigate the torque and thrust characteristics of the bare dynamometer, a series of tests were conducted without a propeller. The thrust and torque generated by the pure operation of the dynamometer both decrease with increasing wind speed. The overall decrease from peak efficiency of the dynamometer at 2000 rpm was about 3%. To account for the dynamometer's effects, results of the tests with the propellers were offset by a thrust and torque function derived from the measurements of the dynamometer without the propeller. The thrust and torque offset functions are described in Appendix H. To ensure the accuracy of the test results, static calibration of the torque and thrust sensors were performed at the beginning of each day prior to testing. Pressure and temperature values were recorded before and after each test to account for changes in the air density between runs. Dynamic zeros, taken with a wind speed of 1 m/s and rotational speed of 100 rpm, were also recorded at the beginning and end of each test. The dynamic zeros were used to account for signal offsets caused by the electrical noise generated by the operation of the electric motor. For data acquisition of the zeros and test measurements, the torque, thrust, wind speed, and rotational speed were sampled at 100 Hz for 15 seconds. Each curve presented for a specified rotational speed was attained by averaging the results of three runs performed on the same day. Averaging over three runs help minimize the error of the results as well as ensure that the repeatability of the system was maintained. Shown in Figures 3.1 and 3.2 are the efficiency curves acquired for the 0.75" and 1" ducted tip propellers from 3 tests. The peak efficiencies measured for the 0.75" and 1" ducted tip propellers were 58.7% ± 0.14% and 56.7 ± 0.06%, respectively. The results provide evidence of that the apparatus provides the precision for which it was designed. 39 0.00 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 Advance Ratio, J -A—Trial 1 x Trial 2 « Trial 3 Figure 3.1: Repeatability of the performance curves calculated for the 0.75" ducted tip propeller test data at 2000 rpm. 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 Advance Ratio, J 1.00 1.10 -Trial 1 x Trial 2 •» Trial 3 40 Figure 3.2: Repeatability of the performance curves calculated for the 1" ducted tip propeller test data at 2000 rpm. 3.1 Ducted Tip Propellers The 0.75" ducts were attached and tested first as it required less material to be removed from the blade tip. Once the performance of the 0.75" ducted tip propeller was thoroughly tested, the 0.75" tips were removed and the 1" ducts were brazed on. The ducted tip propellers were tested at 1000, 1500, 2000, and 2500 rpm. As mentioned in Section 2.2.2, results acquired at 2000 rpm gives the best representation of the propeller's performance due to the lower resonance limit of the dynamometer apparatus and the upper limit of the wind speed in the wind tunnel. However, the results acquired at the other rotational speeds are presented to demonstrate the consistency of the effects of the different tip geometries on the propeller's characteristics. The torque and thrust values acquired from the tests were used for calculating the torque coefficient, KQ, and thrust coefficient, KT, respectively. The coefficients, along with the resultant efficiencies, t], were plotted against the advance ratio, J, to give the performance curves for the propellers, as shown in Figures 3.3 to 3.6. The graphs summarize the KT, IOKQ, and 77 for each propeller tested. The series of curves indicate a clear trend of decreasing efficiency with increasing ducted tip size. The test results indicate that the efficiency reduction is a result of both an increase in the amount of torque required to drive the propeller and a decrease in thrust output. It should be noted that the torque coefficient curves have been scaled by a factor of 10, so that the curves can be plotted on one graph as per convention. Equation 6 indicates that the efficiency of the propeller is a function of the ratio of KT to KQ. This implies that even minor changes in either value will have a significant effect on the efficiency calculated. This is evident in the performance curves illustrated in the following figures, especially in the case of the 0.75" ducts at lower rotational speeds. At 1000 and 1500 rpm, the deviation of the KQ and KT curves for the 0.75" ducted tip propeller from those of the reference propeller appears to be insignificant at higher 41 advance ratios, but the resultant efficiency curve shows a clear reduction in the peak efficiency achieved. The differences between the reference KQ and Kj curves and those of the 0.75" ducted tip propeller appear small at higher advance ratios is because the thrust and torque load present at 1000 and 1500 rpm are quite low. As the rotational speed increases, the loads present also increase to provide more evident changes in KQ and KT. Table 3-1 indicates the thrust and torque ranges as well as the thrust and torque at peak efficiency generated by the reference propeller at different rotational speeds. 42 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 1 0 % ^ —-™-~**/^X.. \ - \ w \ \ X : ^ j i p 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 Advance Ratio, J — Reference 0.75" Ducts —x— 1" Ducts 1.00 1.10 Figure 3.4: Performance of the ducted tip propellers at 1500 rpm. 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 Advance Ratio, J - « — Reference - - -a- - - 0.75" Ducts —x— 1" Ducts Figure 3.5: Performance of the ducted tip propellers at 2000 rpm. 43 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 1 0 K Q ' 1 ^ K T a t 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 Advance Ratio, J -•—Reference a - - 0.75" Ducts —x — 1 " Ducts Figure 3.6: Performance of the ducted tip propellers at 2500 rpm. Table 3.1: Thrust and torque loads present at the peak efficiency of the reference propeller for different rotational speeds. Rotational Speed Thrust Range Tpkr| Torque Range Qpkri [RPM] [N] INI [Nm] [Nm] 1000 0.98-22.21 7.20 0.37-1.96 0.86 1500 0.95-59.60 14.00 1.07-4.72 1.93 2000 22.43 -91.82 27.5 3.17-8.38 3.6 In the case of the 1" ducted tip propeller, the increase in KQ is evident even at lower rotation speeds. Kj, however, seems to remain the same as that of the 0.75" ducted tip propeller regardless of rotational speed. Although KT remains the same, due to the significant increase in KQ, the resulting efficiency is penalized. Table 3-2 summarizes the peak efficiencies acquired from the ducted tip propellers compared to that of the reference. 44 Table 3.2: Summary of the peak efficiencies for the propellers at different rotational speeds. Rotational Speed [RPM] Peak Efficiency [%] Reference 0.75" Ducts 1" Ducts 1000 60.9 58.9 58.0 1500 59.4 56.9 55.9 2000 61.8 58.7 56.7 3.2 Faired 1" Ducted Tips The results presented in the previous section indicated that the addition of ducts increase the torque required for driving the propeller; hence, decreasing the efficiency of the propeller. The ducts tested in the previous section had square leading and trailing edges, which were created during the tip manufacturing process. As the faired ducted tips tested by Hordnes and Green in sea trials showed beneficial outcomes, the leading and trailing edges of the 1" tips were faired and tested again. Figure 3.7 shows a modified 1" duct tip for which a smooth leading edge was formed with automotive body filler while the trailing edge was filed down to a taper. The thickness of the leading edge of the tip was increased from 0.0625" to 0.130" and was tapered along 0.75". The results for the faired 1" ducted tip propeller are compared with that of the original 1" ducts and the reference in Figures 3.8 and 3.9. Except at 1000 rpm, for which the performance curves are comparable, fairing the 1" tips improved the performance of the propeller. The fairing of the tips appears to have a greater influence on KQ than Kr, except at 2500rpm. At 2000 rpm, the faired 1" tip propeller achieved a higher efficiency than the original 1" tips by 2%. At 2500 rpm, the fairing of the tips evidently reduced the KQ of the propeller, in turn, increased the efficiency of the 1" ducted tip propeller by 3%. The fairing of the tips improved the performance of the propeller, but was not enough to surpass the performance of the reference propeller. 45 T o ensure that the results presented are applicable to practical operating condi t ions , the eff iciency curves calcula ted for the 0 .75" and 1" ducted tip propellers were checked for Reyno lds number dependence. A s illustrated i n A p p e n d i x I, R e y n o l d s number dependence was not observed for results acquired at 2000 rpm and higher. T h i s provides confidence that the results illustrate a fair compar ison o f the different tip geometries. 46 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 1 0 K 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 Advance Ratio, J - * — 1" Ducts o Faired 1" Ducts » Reference Figure 3.8: Performance curves of the faired 1" ducts at lOOOrpm. 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 Advance Ratio, J • 1" Ducts — © — Faired 1" Ducts —«—Reference Figure 3.9: Performance curves of the faired 1" ducts at 1500rpm. 47 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 ^ ^ 1 0 K Q / O f ^"""H y/^ ^^^^^^ 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 Advance Ratio, J -x— 1" Ducts o Faired 1" Ducts * Reference Figure 3.10: Performance curves of the faired 1" ducts at 2000rpm. 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 1 ^ 1 0 K Q * , * * . . . . KT ,.y y -** 1 1 1 1 i i i i i i i 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 Advance Ratio, J -x—V'Ducts o Faired 1" Ducts • Reference Figure 3.11: Performance curves of the faired 1" ducts at 2500rpm. 48 4 Discussion The results shown in Chapter 3 demonstrate that the aerodynamic marine propeller test facility is able to produce precise results for propeller performance evaluation. Although the effectiveness of the ducted tips on the cavitation characteristics of the propeller cannot be determined directly using this facility, three key observations concerning the effects of ducted tips on propeller efficiency were obtained from the tests performed: 1) installation of the ducted tips reduced the efficiency of the propeller, 2) increasing the duct diameter reduced the peak efficiency further, and 3) fairing the ducts reduced the performance loss caused by the ducted tips. 4.1 Effect of the Installation of the Ducted Tips One of the major concerns of implementing the ducted tips was the effect on the balancing of the propeller. However, the system vibrations did not increase during operation with the 0.75" and the 1" ducted tips. The resonant frequency of the dynamometer was shifted down by approximately 100 rpm, from the 1400 rpm with the reference propeller to 1300 rpm with the ducted tip propellers. Changes in vibration intensity near resonance were not discernable. The results presented in Chapter 3 clearly indicate that the installation of ducted tips on the marine propeller does not benefit its aerodynamic performance. The results were consistent for both the 0.75" and 1" diameter tips at the four rotational speeds tested. The installation of the ducts changed the slopes as well as the offset of the KQ and Kj curves. The decrease in the thrust coefficient and the increase in the torque coefficient both contributed to reducing the efficiency. Table 4.1 illustrates the changes in the advance ratio and efficiency of the different tip geometries at the point of peak efficiency with respect to the reference propeller. The differences in KQ and KT at the J = 0.83, the advance ratio of the reference propeller's peak efficiency, are also indicated to gauge the influence of the tips. The table shows that the ducted tips not only decreased the efficiency of the propeller, but also moved the optimum operating point to a lower advance ratio. The smaller set of ducted tips had minimal effects on KQ, but reduced Kr 49 the most out of all the geometries. One interesting point to be noted is that though the fairing of the ducted tips increased the leading edge thickness by a factor of two, KQ was still reduced with respect to the unfaired ducted tips, while the loss in Kj observed was recovered. Table 4.1: Changes in the propeller characteristics at the peak efficiency for the propellers with the different tip geometry. Tip Configuration Anpk AKQ (at J = 0.83) AKT (at J=0.83) 0.75" Ducts -6.13% -5.00% 0.04% -5.22% 1" Ducts -6.19% -7.94% 4.37% -4.74% Faired 1" Ducts -6.81% -4.60% 3.96% -0.78% Having fit a ducted tip to the propeller, a portion of the lifting surface was removed and frictional drag was added. Considering the lift and drag of an airfoil in greater detail than discussed in Chapter 1, a better understanding can be gained on the effects of the tip modifications. Equations 4.1 and 4.2 show that the change in lift, L, and drag, D, of an airfoil is determined by the air density, free stream velocity, lift coefficient, drag coefficient, and projected lifting area, which correspond to p, U, Ci, Q> and A, respectively. L=l--p-U2-CL-A (4.1) D=l--p-U2-CD-A (4.2) As most of the lift of a propeller blade is produced near the outer radius, due to the increase in tangential velocity with radius, removing blade tip area will have a significant effect on the propeller's performance. In the case of the ducted tips, the projected lifting area is 5% greater than the original blade tip. In theory, the increase in lifting area should increase the lift generated, but observations showed otherwise. The original cross section of the blade tip resembles an ogival airfoil, whereas the cross-section of the ducted tip resembles two flat sections with zero camber, which will have a lower lift coefficient 50 than any positively cambered airfoil; hence, the increase in lifting surface doesn't necessarily increase the overall lift generated. Installation of the ducted tips greatly increased the wetted area, which consequently increased the drag created by the tips. The wetted surface areas of the 0.75" and 1" ducted tips were calculated to be 3.73 and 3.58 times that of the reference propeller. Friction drag coefficients for a duct can be crudely approximated by using the drag of a flat plate with the same wetted area and friction coefficient, c/. The drag of a turbulent flow over a flat plate is indicated by Equation 4.3. It shows that the drag coefficient over a flat plate is a function of Reynolds number, which is dependent on a characteristic length. Applying this relationship to the ducted tips is reasonable, since drag coefficients are generally dependent on Reynolds number. C D = M 1 (4.3) Re The characteristic length of the ducted tip is taken to be the chord average between the enclosed portion of the duct and the full length that includes the spiral extension. The characteristic length is calculated to be 70% of the chord of the blade at the point of attachment. Due to the sweep of the propeller blade, 70% of the chord length at the tip interface seems to be a reasonable characteristic length to be used for the removed blade tip. Assuming that the air density, velocity, and the skin friction coefficient are the same for the reference and the ducted tip propeller, the only difference in D is due to the added wetted area. By considering only the additional wetted area, the drag from the ducted tips was found to be more than three and a half times that of the original tips. The torque and thrust characteristics of a propeller is dependent on the lift and drag of the blades. Equations 1.1 and 1.2 show that decreasing the lift of the blade element will decrease the thrust and the torque generated; increasing the drag will increase both the thrust and torque. The trigonometric functions paired with the lift and drag parameters dictate the extent of the effect lift and drag has on the torque and thrust values. For fj values of less than 45°, the cosine component will be greater than the sine component. It is unrealistic for blade tip angles to exceed 45° as it will exceed the angle of attack of the 51 maximum lift coefficient. Equations 1.1 and 1.2 indicate that changes in lift will affect torque to a greater extent. The same argument applies to the effect of drag on torque. As reasoned previously, the installation of the ducted tips will likely decrease lift and increase drag; hence, they will decrease the thrust produced and increase the torque required to drive the propeller. Both effects were observed in the results for the 0.75" and 1" ducted tips. The detrimental effects of an increase in drag were more evident with the 1" ducted tips as more skin friction was added. 4.2 The Faired 1" Ducted Tips As the results from the unfaired ducted tips were not favourable as had expected, the aerodynamics of the tips was modified to help improve the lift and drag properties of the ducted tips. The minor change in the leading and trailing edge geometries greatly reduced Kg at higher rotational speeds. At 2500 rpm, the fairing of the tip reduced KQ significantly to achieve an efficiency that was essentially identical to that of the reference propeller. The immense change in performance due to the slight modification to the 1" ducted tips demonstrate how sensitive the performance of the propeller is to the tip geometry. The ducted tips tested by Hordnes and Green were faired as well, but to a much lesser extent. The leading edges of the ducted tips used in the sea trial were coated in epoxy to provide a smooth leading edge, but the thickness was not significantly increased. A more in-depth investigation into the effects of the faired ducted tips can be performed by analyzing the tips as annular airfoils, as shown in Figure 4.1. The aerodynamic properties of an annular airfoil with a Clark Y airfoil section were used to approximate the lift and drag coefficients of the faired 1" ducted tips. The aspect ratio defined for an annular airfoil is the ratio of the inner diameter to the chord of the airfoil section, d/c. The aspect ratio of all of the ducted tips is 0.23. Pertaining to the 2000 rpm tests, the Reynolds number ranges from 0.663 x 106 to 0.722 x 106. The experimental results from Fletcher (1957) provided data for Clark Y annular airfoils with an aspect ratio of 1/3, 2/3, 1.0, 1.5, and 3.0 for a Reynolds number range of 0.704 x 106 to 2.11 x 106. The aspect ratio and Reynolds number range of the annular airfoils tested were slightly higher than 52 that of the faired 1" ducted tip, but the Q, and CD data available will provide a close approximation of the aerodynamic behaviour of the ducted tips. Lift Figure 4.1: Geometry of the annular airfoil tested by Fletcher. (Fletcher, 1957) The aerodynamic information for the annular airfoil with an aspect ratio of 1/3 was chosen for the following analysis. The angle of attack of the ducted tip, as illustrated in Figure 1.2, was calculated for 2000 rpm at a wind speed of 16.26 m/s, where the peak efficiency was achieved. The Ci and Co of the annular airfoil corresponding to the calculated angle of attack of 16° were 0.2 and 0.09, respectively. Using blade element theory, the torque and thrust values were determined from the lift and drag forces generated by the ducted tips. The calculated torque and thrust loads of the annular airfoil tips were then subtracted from the faired 1" ducted tip propeller data to observe how close the calculated load offset would bring the performance curves to that of the reference propeller. 53 The results of this exercise are shown in Figure 4.2. The figure indicates that reducing the approximated lift and drag components of the duct improved the performance but did not exceed that of the reference propeller. This demonstrates that the Q, and Co values used were good estimates for the true values of the faired 1" ducted tips. The figures show that by theoretically removing the ducted tips from the propeller, Kj will be slightly lowered as lifting area is reduced. However, the decrease in KQ appears to be greater, which results in improved efficiency. This implies that a 22" diameter propeller of the same blade geometry will be more efficient than the 24" diameter ducted tip propeller due to the increased drag introduced by the ducted tips. An attempt was made to account for the lift and drag contribution of the original blade tips removed, but the C\ and Co values of the airfoil chosen to resemble the tip sections were very similar to that of the annular airfoils used. The result was performance curves that coincided with the original curves of the faired 1" ducted tip propeller, as the effects of removing the ducted tips and adding the blade tips essentially cancelled out. 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 X : •:: - 10K Q 8* to. jr. 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 Advance Ratio, J - o— Faired 1" • Duct effects — • — Reference Figure 4.2: Performance curves of the faired 1" ducted tip propeller with the effects of the ducted tips removed at 2000 rpm. 54 4.3 Pressure Change Due to the Ducted Tips The change in lift and drag forces discussed explains the offset of KQ and KT evident between the performance curves of the 0.75" and 1" ducted tips, but does not explain the change in gradient of the curves. The ducted tips were meant to reduce the pressure difference between the surrounding flow and the vortex core to delay cavitation inception. As the current experiments were conducted in a wind tunnel, cavitation could not have been observed. However, to reveal any pressure changes the ducted tips introduced, a set of data acquired with the reference propeller at 2000 rpm was modified with free stream pressure variations. Figure 4.3 shows that by decreasing the free stream pressure, the performance of the reference propeller behaves in a very similar manner as that of a ducted tip propeller. The performance curves with a decreased pressure measurement are plotted against the performance curves of the 1" ducted tip propeller for comparison. Surprisingly, with a pressure reduction of 5.2 Pa, the two sets of performance curves, illustrated in Figure 4.4, behave almost identically. The gradients of the Ko and Kj curves decreased and the peak efficiency was lowered and shifted to a lower advance ratio. The KQ curve of the adjusted set of data has an offset from that of the ducted tip propeller, but the changes in the behaviour of the KQ, KT, and rj parameters of the ducted tip propeller are the same as if the free stream pressure was reduced with the reference propeller. This trend is possibly due to potential stalling of the ducted tips, which will cause flow separation and decrease the local pressure at the ducted tips. 55 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 o 10KQ -Q. ~x^ s x 0 2"'» K T x""> P 0.. t°-. x^ 5><^  •io... 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 Advance Ratio, J -Reference --x--Pressure reduced —o—Pressure increased Figure 4.3: Changes in the reference propeller performance curves with pressure variations at 2000 rpm. 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 10KQ a ->o.. Tl .- B - - n - - 'Rf f - " ° o a--. K t ~ " Q B . X.. 8 -n tt'XO^ B mr ~ ~ B © . . o. ' B : ~;-o, " E£ % , ° B 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 Advance Ratio, J a Reference with pressure reduction © Faired 1" ducted tip propeller Figure 4.4: Comparison of the reference propeller performance curves with free stream pressure with that of the faired 1" ducted tip propeller at 2000 rpm. 56 4.4 Comparison to Other Studies of Ducted Tip Propellers The aerodynamic results for a ducted tip hydrofoil tested at a Reynolds number of 0.6 x 106by Duan and Green (1995) demonstrated that the ducted tips enhanced the L/D ratio of the hydrofoil at angles of attack greater than 8°. The benefits of the ducted tips was shown to have increased with incidence angle until about 14°, when the improvements lessened. The effective angle of attack of the ducted tip on the propeller at the point of peak efficiency at 2000 rpm is 16°. According to the results of the ducted tip hydrofoil, the L/D ratio of a ducted tip was still greater than that of a rounded tip at 16°. The relationship of the L/D of an airfoil is dependent on Reynolds number as well as the airfoil. Since the Reynolds number of the tested hydrofoil match that of the 1" ducted tips at 2000 rpm and the 1" ducted tips were modeled to the same geometric scale as those tested by Duan and Green, the benefits of the ducted tips should be observed in the current results. At lower advance ratios, the effective angle of attack of a blade section is higher and the effects of the ducted tips were expected to be evident, though favourable changes were not observed in the results. Not only was there a lack of improvement in the efficiency of the propeller, but K T decreased significantly at lower advance ratios. The results of the current experiments consistently demonstrate a penalty on the efficiency with the installation of the ducted tips. Cavitation tunnel tests conducted by Straver (2002) as well as sea trials performed by Hordnes and Green (1996) with ducted tip propellers indicated that the tips successfully delayed cavitation inception. However, there was discrepancy between the two studies. Straver's results indicated that the delay in cavitation inception was at the cost of efficiency. Sea trial results, on the contrary, indicated that the ducted tips decreased the cavitation index as well as enhanced the performance of the propeller. One interesting observation made by both studies is the drop in KQ and Kj at low advance ratios. Studying their results in greater detail, it was noticed that the drop in KQ and Kj at low advance ratios was due to a reduction in the gradient of the curves at the introduction of the ducted tips. Such evidence confirms that the ducted tips reduce the rate of change of the Ko and Kj with advance ratio, as was observed in the current results. Computational results from Ingvarsdottir (2001) on the flow over a ducted tip hydrofoil indicated that 57 leading edge separation occurred at an angle of attack of 12°. As mentioned at the beginning of this section, the effective angle of attack at the faired 1" ducted tips at 2000 rpm is 16°. Assuming that the faired 1" ducted tips installed on the current test propeller experiences leading edge separation at 12° as well, then the assumption of stall occurring at the tips resulting in reduced gradients of the KQ and Kj curves and decreased efficiency is plausible. The variation of the performance of the ducted tip geometry on a lifting body confirms the sensitivity of the thrust and torque behaviours to the tip geometry. The discrepancy between the test subjects may be mainly due to the variation in the extent of fairing created for the ducted tips. The lift data provided by Fletcher for the annular airfoils show that the C\ decreases with decreasing aspect ratio, but the stall angle also increases. For an annular airfoil with a Clark Y section and aspect ratio of 1/3, the stall angle is approximately 33°. If tip stall was the main cause for the change in propeller performance then it may be corrected by changing the cross-sectional properties and aspect ratio. 4.5 Error Analysis The error analysis for the experimental results consisted of two parts: error of the measured data and error of the non-dimensional values calculated. The advance ratio, torque coefficient, thrust coefficient, and efficiency of a propeller are functions, G, of multiple variables, x,; hence, their uncertainties are functions of the error of their dependent variables as indicated in Equation 4.5. The uncertainties of the dependent variables are calculated using Equation 4.7 to account for all of their error sources. Each dependent variable consists of instrumental error, which is the uncertainty specified by the manufacturer, as well as experimental error, which is calculated with the standard deviations of the measured values using the student t-distribution. C — f\ {Xl > X2 '••••>XL } (4.4) (4.5) 58 (4.6) (4.7) where G = result determined from independent variables, UG = uncertainty of G 6j = sensitivity index of G to x„ Xj = dependent variables of G, i = index representing the L different variables, uxi = uncertainty of the dependent variable, x, e = element of error k = number of element of error Applying the error analysis for multivariable functions, the uncertainty for J, KQ, K T , and rj, are listed as uj, UKQ, UKT, and ut] as shown as in Equations 4.8 to 4.11. The total error at peak efficiency calculated for the reference and ducted tip propellers tested at 2000 rpm are identical. The uj, UKQ, UKT, and un calculated are 0.2%, 0.5%, 0.1%, and 1%, respectively. + - u V " -DP J (4.8) Ut, - . 2 n 5 e p-n • D + •2-Q (4.9) 2 n 4 7 p-n -Dp + -2-T p-n -D (4.10) T 2-npn-D-Q A 2 ( •U-T 2-nn1 DpQ \ 2 uT 2-K-n-D-Q -U-T 2-K-n-Dp-Q 2 "Q (4.11) 59 5 Conclusion The preparation procedure fo l lowed for the ducted tip propeller experiments p rov ided confidence i n the qual i ty o f the results acquired. The repeatability o f the results f rom the series o f tests performed illustrated a prec is ion level o f ± 0 . 1 5 % o f the eff ic iency measured at 2000rpm. D y n a m i c and static cal ibrat ion methods developed for ve r i fy ing the operation o f the dynamometer demonstrated that the torque and thrust sensors were accurate, to w i t h i n the error o f the cal ibrat ion set up, and p rov ided good l inear responses. The propel ler test results strongly suggest Reyno lds number independence at R e = 0.66 x 10 6 , w h i c h corresponds to 2000 rpm. P r io r to the instal lat ion o f the ducted tips, the second stock propeller was checked to be ident ical , geometr ical ly and i n performance, to the reference. The al ignment o f the ducted tips was ver i f ied to be correct w i t h the use o f a C M M before proceeding w i t h testing. U p o n ver i fy ing the re l iab i l i ty o f the aerodynamic test apparatus, experiments were conducted w i t h the 0.75", 1" and faired 1" ducted tip propellers. Tests were performed at 1000, 1500, 2000, and 2500 rpm. The outcome o f the tests ran at 2000 r p m best represent the performance o f the propeller , as it is reaches Reyno lds number independence as w e l l as provide complete eff iciency curves. The efficiencies measured at 2000 r p m for the 0.75", 1", and faired 1" ducted tip propeller are 58 .7%, 56.7%, and 58 .5%, respectively. Such efficiencies are a l l lower than the 61 .8% achieved by the reference propeller . The results acquired for the three different t ip configurations indicate the f o l l o w i n g : ducted tips reduce the performance o f the propeller; a larger duct size is more detrimental to the performance; and fairings on the 1" duct reduces the loss i n eff iciency caused by the addi t ion o f the ducted tips. The results for the different tip geometries were consistent i n showing that the addi t ion o f the ducted tips shifts and decreases the gradient o f the torque coefficient and thrust coefficient curves. A s a consequence, the peak eff iciency achieved was decreased and shifted to a lower advance ratio. F r o m inspection, the changes i n the torque and thrust 60 behaviours are likely caused by a combination of a decrease in lift, an increase in drag, and tip stall. The installation of the ducted tips replaced the original cambered sections with a duct having zero camber, which decreases the lift generation at the same operating conditions. The tips also increased the drag by more than two and a half times due to skin friction alone. The lift and drag characteristics of the 1" ducted tips were improved by fairing the leading edges and streamlining the trailing edges. The modifications greatly reduced the negative effects of the ducted tips illustrating the sensitivity of the propeller's performance to the tip geometry; however, the propeller's performance still did not surpass that of the reference. The lift and drag effects were evident with the shifting of the KQ and Kj curves. The change in the gradient of the KQ and Kr curves were found to behave in the same manner as decreasing the free stream pressure. This change was allotted to potential stalling of the ducted tips. Computational results from Ingvarsdottir showed that leading edge separation was observed at the ducted tip of a modified hydrofoil at an incident angle of 12°. The incidence angle of the ducted tip was 18°, implying that tip stall may have occurred. Tip stalling would result in flow separation at the ducted tips. Flow separation would decrease the pressure of the local flow field, which agrees with the trends observed in the results obtained with the ducted tips. The discrepancies between the influence of ducted tips on a propeller shown in experiments performed by different researchers demonstrate the high dependence of the propeller performance on tip geometry. The improvement in the KQ and Kr curves caused by the fairing of the 1" propeller suggests that the variation in the outcomes of the ducted tip propeller experiments may be caused by different adaptations of the ducted tip. Although the results from the ducted tip geometry demonstrated that the tip modifications have a detrimental effect on a propeller's aerodynamic performance, no conclusions can be drawn on the cavitation characteristics of the propeller. It is possible that the current ducted tips are effective in delaying cavitation, but at the expense of efficiency. Despite the fact that cavitation cannot be observed in the aerodynamic test facility the 61 dynamometer is a valuable and reliable piece of equipment for evaluating and comparing propeller performances prior to cavitation inception. 62 6 Recommendations Despite the reduction in the performance of the ducted tip propeller design, the idea still bears potential for a commercial product. The experimental results indicate that the performance of the ducted tip propeller is sensitive to tip geometry. Witnessing the significance a minor change to the tip geometry has on the propellers characteristics, it wi l l be wise to perform future preliminary tip designs through computational means. Modeling propeller f low may be challenging and computationally expensive; an alternative would be to model a single blade as a hydrofoil as was performed by Ingvarsdottir. Using computational methods, a larger variety of geometric changes can be performed to gauge their influence on the propeller's performance. Duct geometries recommended for testing computationally are an unfaired duct with an aspect ratio of 0.23, an annular airfoil with an aspect ratio of 1/3, and variations of the latter with changes in airfoil thickness and aspect ratio. The unfaired duct case would be the base case used for comparison, as experimental data already exists. Once a favourable ducted tip geometry has been found, then experimental work can be performed to confirm its effectiveness. Due to the precision, cost effectiveness, and availability of the aerodynamic test facility, it can be used for preliminary testing to confirm the thrust and torque behaviours of the design. If the propeller performs in a similar manner as predicted by computational fluid dynamics then it should proceed to being tested in a cavitation tunnel or at sea to confirm the improved inception characteristics of the propeller. 63 References Andersen, P. 1997. A comparative study of conventional and tip-fin propeller performance. Proceedings form the Twenty-First Symposium on Naval Hydrodynamics, Trondheim, 930-945, June. Anderson, J.D. Jr., 2001. Fundamentals of aerodynamics. 3 r d ed. New York: McGraw-H i l l . Atlar M , Takinaci A . C . , Korkut E . , Sasaki N . , Aono T. Cavitation tunnel tests for propeller noise of F R V and comparisons with full-scale measurements. Proceedings of the 4th International Symposium on Cavitation, sessionB8.007, Pasadena, Jun 20-23. Available at http://cav2001.library.caltech.edu/277/ [10 October 2005]. Bazilevski, Y . S . 2001. On the propeller blade turbulization in model test. Proceedings from the International Symposium on Ship Propulsion,S?200\ Lavrentiev Lectures, St. Petersburg, June 19-21. Chahine G . L . , Frederick, F.F. , & Bateman, R . D . 1993. Propeller tip vortex cavitation suppression using selective polymer injection. ASME Journal of Fluids Engineering, 115:497-503 Crump. S.F. 1948. The effects of bulbous blade tips on the development of tip vortex cavitation on model marine propellers. Report C-99, David Taylor Naval Ship Research and Development Centre. Davis, K . R . 2004. Development and testing of an aerodynamic marine propeller test facility: an investigation into making boats fly. British Columbia, Canada: University of British Columbia. M . A . S c . thesis. Figliola, R.S. , & Beasley, D . E . 1995. Theory and design for mechanical measurements. 2" y ed. N e w York: John Wiley & Sons. Fletcher, H.S . 1957. Experimental investigation of lift, drag, and pitching moment of five annular airfoils. Technical Note 4117, National Advisory Committee for Aeronautics. Fruman, D . H . , Aflalo , S.S. 1989. Tip vortex cavitation inhibition by drag-reducing polymer solutions. ASME Journal of Fluids Engineering, 111:211-216. Green, S.I., & Duan, S.Z. 1995. The ducted tip - a hydrofoil tip geometry with superior cavitation performance. ASME Journal of Fluids Engineering, 117:665-672. Haines A . B . 1994. Scale Effects n Aircraft and Weapon Aerodynamics. AGARDograph 323. Loughton, United Kingdom: North Atlantic Treaty Organization 64 Hordnes, I., & Green, S.I. 1998. Sea trials of the ducted tip propeller. ASME Journal of Fluids Engineering, 120:808-817, December. Hordnes, I. 1996. Sea trials of a ducted tip propeller designed for improved cavitation performance. British Columbia, Canada: University of British Columbia. M.A.Sc. thesis. Ingvarsdottir, H . 2001. Computational studies of the flow around rounded and ducted tip hydrofoils. British Columbia, Canada: University of British Columbia. M.A.Sc. thesis. Johnsson, C.A., & Rutgersson, O. 1991. Leading edge roughness- a way to improve propeller tip cavitation. Proceedings from the Propellers and Shaftering '91 Symposium, Virginia Beach, September 17-18, paper no. 12. Katz, J., & Galdo, J.B. 1989. Effect of roughness on rollup of tip vortices on a rectangular hydrofoil. Journal of Aircraft, 26(3): 247-253, March. Kuiper, G. 2001. New developments around sheet and tip vortex cavitation on ships propellers. Proceedings of CAV2001: Fourth International Symposium on Cavitation,. lecture 007, Pasadena, June 10-23 Available: http://cav2001 .library.caltech.edu/418/00/kuiper.pdf [ 10 October 2005] Kuiper, G. 1978. Scale effects on propeller cavitation inception. Proceedings from the 12th Symposium on Naval Hydrodynamic, Washington, D.C. 12:400-429. Latorre, R. 1981. Propeller tip vortex cavitation noise inception. Proceedings of the Propellers '81 Symposium, Virginia Beach, Virginia, May 26-21, 319-334, New York: The Society of Naval Architects and Marine Engineers Lodha, R.K., & Arakeri, V . H . 1984. Observations of tip vortex cavitation inception from a model marine propeller. Journal of the Indian Institute of Science, 65(A): 11-20, January. Mani, K. , Sharma, S.D. & Arakeri, V . H . 1988, "Effect on propeller blade modification on caviation induced noise. ASME FED, 64:64-67. Molland, A.F. , & Turnock, S.R. 2002. A propeller thrust and torque dynamometer for wind tunnel models. Strain, 38:3-10. Platzer, G.T., & Souders, W.G. 1979. Tip vortex cavitation delay with application to marine lifting surfaces. A literature review. Report 79/051, David Taylor Naval Ship Research and Development Centre. Stinebring, D.R., Farrell, K.J . , Billet, M.L . 1991. The structure of a three-dimensional tip vortex at high Reynolds numbers. ASME Journal of Fluids Engineering, 113:496-503, September. 65 Straver, M.C. 2000. Experimental and computational studies of a ducted tip propeller. British Columbia, Canada: University of British Columbia. M.A.Sc. thesis. White, F.M. , 1999. Fluid mechanics. 4 th ed. United States of America: McGraw-Hill. Selig M . 2005. UIUC Airfoil Wind Tunnel Data on the Web [Online]. Available: http://www.ae.uiuc.edU/m-selig/pub/LSATs/vol4/4 txt/ [25 March 2006] 66 Appendix A: Prony Brake Specifications A light duty brake band from Great Lake Friction Products was used on the Prony brake for the dynamic torque sensor calibration. Included below are the properties of the friction material used on the brake lining. Table A . 1: Properties of band brake liner. GL121-110 Mechanical Properties Tensile Strength 400 PSI Flexural Strength 900 PSI Max. Compressive Strength 2500 PSI Max. Operating Pressure 150 PSI Max. Rubbing Speed 3000 F P M Friction Properties Avg. Coefficient of Friction 0.43 Normal 0.41 Hot Static Coefficient 0.53 Wear Rate / HP Hour 0.009 in 3 Thermal Properties Max. Operating Temp. 500° F Physical Properties Specific Gravity 2.15 g/cm3 Shore D Hardness 38-42 This document is a guideline. Each intended application of this material needs to be adequately evaluated using good engineering principles. 67 Appendix B: Torque Calibration Data from the Prony Brake The tension level applied, Qap, is determined by the number of revolutions advanced by the adjustment nut from the reference gap size. The corresponding torque measured, Qm, by the inline torque sensor, TorqSense, is shown in Table B . l . The referenced gap size used was 3.8cm. Table B. 1: Data from the dynamic torque calibration. Tension Measured Applied [Rev] TorqSense Qm Load Cell Qap [V] [Nm] [V] [Nm] 1 0.076 0.304 0.064 0.301 2 0.216 0.864 0.183 0.861 3 0.302 1.208 0.254 1.195 4 0.408 1.632 0.342 1.609 5 0.534 2.136 0.449 2.113 6 0.671 2.684 0.565 2.658 7 0.87 3.480 0.726 3.416 8 1.08 4.320 0.908 4.272 9 1.327 5.308 1.119 5.265 10 1.623 6.492 1.372 6.455 11 2.037 8.148 1.72 8.092 12 2.51 10.040 2.124 9.993 13 3.033 12.132 2.568 12.082 14 3.611 14.444 3.06 14.397 15 3.863 15.452 3.29 15.479 16 4.213 16.852 3.584 16.862 15 3.518 14.072 3.01 14.162 14 2.595 10.380 2.22 10.445 13 2.054 8.216 1.754 8.252 12 1.536 6.144 1.311 6.168 11 1.14 4.560 0.929 4.371 10 0.871 3.484 0.739 3.477 9 0.656 2.624 0.561 2.639 8 0.485 1.940 0.415 1.953 7 0.354 1.416 0.302 1.421 6 0.254 1.016 0.217 1.021 5 0.161 0.644 0.137 0.645 68 A p p e n d i x C : P r o p e l l e r M e a s u r e m e n t E r r o r A n a l y s i s F o r the error analysis o f the profi le measurements o f a propeller blade the t i l t and run out o f the rotary table were measured. A s the rotary indexer 's center o f rotation had to be determined manua l ly , there was a slight run out that resulted. T o determine the magnitude o f the run out, a c i rc le was scribed o n the mount ing plate as a guide. The indexer was then rotating around to determine what the run out was. The error result ing from the unparal le l hub surfaces that created a til t affect o f the propel ler pos i t ion ing was also considered. A c c o u n t i n g for the errors previous ly ment ioned and the accuracy error o f the C M M , the resultant error i n the height measurement, z, was determined. Table C . 1: E r r o r in the z-value from different causes. Error Source Error Run out: 0.318 m m C M M accuracy : 0.005 m m Tilt: 0.141° z offset at 0 .5R 0.376 m m 0.7R 0.526 m m 0 . 8 5 R 0.639 m m Angu lar , ^ ( i ndexer ) 0.5' (0.008°) The total x-error i n result o f the error sources explored above w o r k e d out to be 0 .323mm. Heigh t measurements were taken at the nomina l x,x± 0 .323mm, nomina l <f>, and to determine the error i n the z measurement that might result. The total error result ing f rom the different sources is summarized be low. Table C . 2: Total error in the z-value at different radial distances. Error Type z - Error at different radial distances [mm] r = 0 . 5 R r = 0 . 7 R r= 0 . 8 5 R Tilt 0.376 0.526 0.639 Angu la r 0.000 0.015 0.028 X 0.042 0 . 0 0 9 ^ 0.010 Total 0.418 0.550 0.677 69 Appendix D: Blade Profile Measurement Transformation As the propeller was mounted on a rotary indexer, the angles of rotation were translated into arc length, which was used as the x-value for the transformation. To be able to match the profile of the pressure side with that of the suction properly, the measurement points are transformed 180°. The equation used for the transformation is as indicated below: z, = x • sin 6 + z • cos 6 + zhuh where z, = transformed height, x = arc length, from the trailing edge of the pressure side, z = height of the of the blade when the pressure side is facing up, 6= angle of transformation, and Zhub= the height of the hub. 5.0 10.0 x [in] Pressure side raw — • — Pressure side transformed Table D . 1: Elevation measurements of pressure side before and after a 1 8 0 ° transformation. 70 Appendix E: Camber Comparison To determine the camber line of a given cross section, the sections were first transformed to an angle of attack of 0° then the mid points between the pressure side and the suction side contours were calculated. The initial transformation is as illustrated in Figure E. 1. The pressure side of the hydrofoil was flat; hence the angle of transformation was determined by calculating the angle of the pressure surface at the section of interest. The angles of transformation for the sections at 0.5R, 0.77?, and 0.857? are 32.4°, 24.6°, and 20.6° respectively. The x-values from the pressure side taken from the CMM measurements did not correspond to those on the suction side after the profiles were transformed; hence the camber line could not be determined by taking the average of the two z-values at an x-value measured. In this case, the profiles of the pressure and suction side were fitted with polynomials of an 7?2 value of 0.99 or higher. Using the polynomial equations for the fitted contours, z-values for the pressure and suction sides were determined for 0.1 chord increments. The two values were then averaged to acquire the camber line for the section. The camber lines calculated for the three propellers at the different radial sections are indicated in the figures below. 71 -16070--42070--807©--4070-_ o _ 0 --100.0 -50.0 0.0 50.0 100.0 150.0 200.0 x [mm] • Original Transformed Figure E. 1: Blade profile transformation to 0C Figure E. 2: Camber line comparison at 0.5R. 72 -1-1-0-8r0 E E -Sr0-/ — 2 . 0 / Y 90 ' l •40 -1 0 -4-0 60 I 1-10 1-60 2TC> x [mm] • Prop A Prop B Prop C Figure E. 3: Camber line comparison at 0JR. -1-1.0 8T0 4 r 0 -x [mm] • Prop A - • • Prop B Prop C Figure E. 4: Camber line comparison at 0.85/?. 73 Appendix F: Performance Comparisons of Propeller A and B Illustrated below are the performance curves acquired for propeller A and propeller B at different rotational speeds. 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 10K r KT 4r: 1 0.00 0.20 0.40 0.60 0.80 1.00 -0.10 Advance Ratio, J Propeller B Propeller A 1.20 Figure F. 1: Performance curves for propeller A and propeller B at 1000 rpm. 74 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 " - ^ 1 0 K Q i i Tf IF-0.0 0.2 0.4 0.6 0.8 Advance Ratio, J 1.0 1.2 Propeller A Propeller B Figure F. 2: Performance curves for propeller A and propeller B at 1500 rpm. Efficiency at 2500 RPM 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0 .00 _ - 1 0 K Q ... = -JET**' x ^ 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0 .70 0.80 Advance Ratio, J Propeller A Propeller B Figure F. 3: Performance curves for propeller A and propeller B at 1500 rpm. 75 Appendix G: Tip Load Calculations The centripetal forces generated from the ducted tips were calculated for the different rotational speeds using F = mofr, where F, m, co, and r correspond to the centripetal force, mass of the tips, rotational velocity, and radial distance from the axis of rotation to the center line of the ducted tips. The forces calculated are summarized below. The d listed in the table is the diameter of the ducted tip used for the calculations Table G. 1: Summary of the centripetal forces generated by the different tips. Rotational Speed, co [rpm] 1500 2000 2500 3000 [rad/s] 157.1 209.4 261.8 314.2 Set1 d=0.75" [19.1 mm] m = 93.44g Force [N] 680.8 1210.3 1891.0 2723.1 Set 2 d=1" [25.4 mm] m = 130.9g Force [N] 943.4 1677.2 2620.6 3773.7 76 Appendix H: The Inherent Thrust and Torque of the Dynamometer Without the installation of the propeller, the dynamometer still experiences minute forces due to aerodynamic effects. The bare dynamometer was tested to acquire information for accounting for the inherent torque and thrust effects of the apparatus. The movement of the shaft alone creates skin friction drag. Skin friction resists the rotational motion resulting in an applied torque. An estimate of the induced torque cannot be simply modeled due to the sensitivity of the friction coefficient between the interaction between the shaft and the flow; however, the relationship between the induced torque and free stream velocity can be observed from the results acquired experimentally. Aside from skin friction, the dynamometer also experiences a negative applied thrust force caused by the frontal drag of exposed the 3" shaft when exposed to airflow. A nose cone is mounted on the exposed end of the propeller shaft to reduce the drag of the shaft end. Using a reasonable drag coefficient approximation for the shaft end, the frontal drag of the propeller shaft can be approximated by Equation H. 1. The equation indicates that the drag is a function of U2. D^-'p-U1 -CD-A (H.l) where p = air density [kg/m ] U = free stream velocity [m/s] Co = drag coefficient of the body [-] A = frontal area of the shaft [mz] The propeller shaft was set to rotate at 2000 rpm, while the wind speed was increased up to the full capability of the wind tunnel. The thrust and torque values generated by the operation of the dynamometer are plotted against that of the reference propeller for comparison in Figures H.l and H.2. By fitting a trend line to the data, as shown in Figures H.3 and H.4, the inherent torque and thrust generated by the dynamometer is described by polynomial functions of the free stream velocity. Considering the torque 77 and thrust generated by the apparatus are relatively small, the lowest order polynomial function to give an IT of 0.95 or better was sufficient to characterize their behaviour. 5.0 4.0 E z 3.0 a a>~ a- 2.0 o H 1.0 0.0 At & & & r 4 & jfi^ * & _ p . & & A it A is it | 4 6 8 10 12 14 16 Freestream Velocity [m/s] • Reference Propeller A Dynamometer Figure H . 1: Magnitude of the inherent torque compared to that produced by the reference propeller. 78 50 40 30 *• 20 3 10 -10 &—A it—rif-10 12 14 16 Free stream Velocity [m/s] • Reference Propeller A Dynamometer Figure H . 2: Magnitude of the inherent thrust compared to that produced by the reference propeller. 0.12 0.10 ^ 0.08 z 3 0.06 4 0.04 0.02 0.00 6 8 10 12 Freestream Velocity, U [m/s] 14 16 18 Figure H . 3: A trend line fitted onto the torque values generated by the bare dynamometer. 79 0.0 c -0.2 -0.4 -0.6 z r -08 in S -1.0 I--1.2 -1.4 -1.6 -1.8 2.0 4.0& 10.0 12.0 14.0 16.0 18.0 Freestream Velocity, U [m/s] Figure H. 4: A trend line fitted onto the thrust values generated by the bare dynamometer. Figure H.3 shows that the torque varies approximately linear with free stream velocity. Figure H.4 shows that the thrust varies approximately in a parabolic manner with free stream velocity, as expected. Equations H.2 and H.3, used for removing the dynamometer's effect from the test data, fitted to the data with R2 values of 0.97 and 1.00, respectively. Qdyno = -0.0080U + 0.1480 Tdyno = -0.0007U2 +0.017 5U (H.2) (H.3) 80 Appendix I: Reynolds Number Dependence To ensure that the results are valid for full scale applications, the efficiencies calculated from the measurements are checked for signs of Reynolds number dependence. The efficiency curves for the range of tested rotational speeds, with which Reynolds number varies, are plotted on a single graph for each propeller. Figures 1.1 and 1.2 illustrates that there is no Reynolds number dependence observable. If Reynolds number dependence was observed, the peak efficiency for higher rotational speeds would be expected to increase and to occur at a higher advance ratio. 0.70 0.00 -I , , , , , 1 0.00 0.20 0.40 0.60 0.80 1.00 1.20 Advance Ratio, J — A — 1 0 0 0 rpm — o — 1 5 0 0 rpm - - o - - 2000 rpm — * — 2 5 0 0 rpm Figure 1.1: A summary of efficiency curves for the 0.75" ducted tip propeller tested at the different rotational speeds illustrating Re independence beginning at 2000 rpm. 81 >» u c o> 'o E LU 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 0.00 -0.10 0.20 0.40 0.60 0.80 Advance Ratio, J 1 1.00* 1.20 - A — 1000 rpm o 1500 rpm * 2000 rpm x 2500 rpm Figure 1.2: A summary of efficiency curves for the 1" ducted tip propeller tested at the different rotational speeds illustrating Re independence beginning at 2000 rpm. 82 

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