A MORE COMPREHENSIVE DATABASE FOR PROPELLER PERFORMANCE VALIDATIONS AT LOW REYNOLDS NUMBERS. A Dissertation by. Armin Ghoddoussi

Transcription

1 A MORE COMPREHENSIVE DATABASE FOR PROPELLER PERFORMANCE VALIDATIONS AT LOW REYNOLDS NUMBERS A Dissertation by Armin Ghoddoussi Master of Science, Wichita State University, 211 Bachelor of Science, Sojo University, 1998 Submitted to the Department of Aerospace Engineering and the faculty of the Graduate School of Wichita State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy May 216

2 Copyright 216 by Armin Ghoddoussi All Rights Reserved

3 A MORE COMPREHENSIVE DATABASE FOR PROPELLER PERFORMANCE VALIDATIONS AT LOW REYNOLDS NUMBERS The following faculty members have examined the final copy of this dissertation for form and content, and recommend that it be accepted in partial fulfillment of the requirement for the degree of Doctor of Philosophy with a major in Aerospace Engineering. L. Scott Miller, Committee Chair Klaus Hoffmann, Committee Member Kamran Rokhsaz, Committee Member Charles Yang, Committee Member Hamid Lankarani, Committee Member Accepted for the College of Engineering Royce Bowden, Dean Accepted for the Graduate School Dennis Livesay, Dean iii

4 ACKNOWLEDGEMENTS I would like to express my deepest gratitude to my advisor and mentor, Professor L. Scott Miller for his guidance throughout this project. Also, I am sincerely grateful for the opportunity and help that the department of Aerospace Engineering, NIAR W. H. Beech Wind Tunnel, NIAR Research Machine Shop, NIAR CAD/CAM Lab, Cessna Manufacturing Lab and their generous staff provided. Above all, none of this would be possible without the love and care of my parents, brother and friends. This is dedicated to my family members, Akhtar, Ali and Elcid Ghoddoussi. Thank you for your constant support and patience. iv

5 ABSTRACT Validation is the essential process of evaluating the precision and reliability of analytical or computational solutions. In this dissertation, a series of comprehensive propeller wind tunnel tests were designed for validation of propeller design and analysis techniques. This work focused primarily on small propellers operating at lower Reynolds numbers in the range of 9, to 12,, which is particularly helpful for unmanned aerial vehicle applications. Extensive propeller and experimental apparatus geometries along with test section spatial dimensionality are described. An open-source computer-aided design (CAD) method was used to create the propeller blades, nacelle, and spinner surface outlines, aiming for easy reproduction. Two different propeller designs were tested: a simple propeller with a constant pitch-to-diameter ratio, chord length, and thickness; and a complex propeller with a pitch-to-diameter ratio and chord length as a function of blade radius. Both propellers with a variable pitch of five degrees increment were tested at several angle settings. Critical test section flow field and geometry information that can be used as boundary conditions are also presented in this study. In addition to classical propeller performance plots of thrust and torque coefficients and efficiency against the advance ratio, nacelle surface pressure distribution in terms of coefficients and propeller wake survey results are provided. Two different wind tunnels were utilized to evaluate the experimental and facility bias. Known errors, uncertainties, and instrumental accuracies are quantified and presented here. v

6 TABLE OF CONTENTS Chapter Page 1. INTRODUCTION Propulsive Efficiency in Propeller Design Challenges in Propeller Design and Analysis Development in Analysis and Design Methods MODERN PROPELLER ANALYSIS AND DESIGN Momentum-Blade Element Theory JavaProp Vortex Theory Computational Fluid Dynamics CFD Example CFD Example PROBLEMS AND GOALS Problems in Propeller Validation Statement of Objective Methods of Approach EXPERIMENTAL APPARATUS Geometry Descriptions Wind Tunnels and Model Installations Model Propellers Model Nacelle-Spinner Model Setup Assessment System Performance Prediction Data Measurement and Process System Calibration Data Corrections and Tares Test Procedure System Evaluations RESULTS Propeller Performance PD1 Results of Propeller Performance COMP Results of Propeller Performance Nacelle Pressure Distribution PD1 Results of Nacelle Pressure Distribution...89 vi

7 TABLE OF CONTENTS (continued) Chapter Page COMP Results of Nacelle Pressure Distribution Wake Survey Nacelle-Spinner Effect Dynamic Tare CONCLUSIONS REFERENCES APPENDIXES Appendix A.153 Appendix B.157 vii

8 LIST OF TABLES Table Page 1. Summary of System Accuracy, Precision, and Errors.. 67 viii

9 LIST OF FIGURES Figure Page 1. Rotating propeller: (a) front view, (b) velocities and forces on blade element looking toward hub BART data vs. M-BE analysis of APC Thin-E propellers [24] Synthetic drag polar of Clark Y airfoil at different Reynolds numbers [22] JavaProp validation results compared with NACA TR-594, designated blade angle at.75r [22] Vortex theory, JavaProp, and propeller experimental results [39] comparison, with designated blade angle at.75r Combined propeller/nacelle/wing grid domain [28] Propeller/nacelle pressure distribution at Mach.15, 665 rpm: (a) α =, (b) α = 1, data digitized from [26] Propeller/nacelle/wing slipstream dynamic pressure survey behind the propeller [28] Propeller wind tunnel model and grid domain [3] Sensitivity analysis of pitch angle using JavaProp Sensitivity analysis of chord length using JavaProp Sensitivity analysis of propeller section airfoil using JavaProp Sensitivity analysis of airfoil aerodynamics for ClarkY using JavaProp Photo (top) and description (bottom) of 3 4 LSWT at Wichita State University Model installation (top) and side view (bottom) in 3 4 LSWT Description of Beech wind tunnel and C-mount assembly in 7 1 NIAR Model installation and side view in 7 1 NIAR PD1 propeller in OpenSCAD interface PD1 Propeller blade assembly D scan of PD1 propeller blade, within ±.2 inch accuracy ix

10 LIST OF FIGURES (continued) Figure Page 21. COMP propeller blade design and assembly without nacelle and spinner D scan results of COMP blade within -.7 inch accuracy Nacelle assembly CAD design (dimensions in inches) Nacelle bottom side modification for 7 1 NIAR setup Top and bottom of PD1 blade 3D scan set at β.75 = 23, within +.15 inch accuracy Top and bottom of COMP blade 3D scan at β.75 = 15, within ±.2 inch accuracy Both sides 3D scan of the nacelle-spinner assembly, within +.7 inch accuracy PD1 propeller performance analysis COMP propeller performance analysis PD1 blade radial distribution of angle of attack, lift and drag coefficients at J =.2 and β.75 = COMP blade radial distribution of angle of attack, lift and drag coefficients at J =.2 and β.75 = PD1 and COMP blades local Reynolds number distributions at J = Data measurement and processing block diagram Load cell calibration for thrust Test section velocity and temperature variations of 7 1 NIAR (courtesy of NIAR) Five-hole probe wake survey at 7 1 NIAR wind tunnel Inside the nacelle in each tunnel: 7 1 NIAR (left) and 3 4 LSWT (right) Thrust coefficient repeatability test of APC Thin-E propeller in 3 4 LSWT Power coefficient repeatability test and efficiency of APC Thin-E tests in 3 4 LSWT Reynolds number (Re.75) repeatability test of APC Thin-E in 3 4 LSWT Tunnel data comparison of 3 4 LSWT and 7 1 NIAR for APC Thin-E x

11 LIST OF FIGURES (continued) Figure Page 42. Tunnel data comparison from WSU, BART [24], and UIUC [58] for 1 7 APC Thin- E propeller Tunnel data comparison from WSU, BART [24] and UIUC [58] for and 8 8 APC Thin-E Coefficients CT, CP, and η against J for PD1 at 5, rpm, where β.75 = Coefficients CT, CP, and η against J for PD1 at 5, rpm, where β.75 = Coefficients CT, CP, and η against J for PD1 at 5, rpm, where β.75 = Coefficients CT, CP, and η against J for PD1 at 4, ~ 6, rpm, where β.75 = Eppler 387 airfoil wind tunnel results comparison at two Reynolds numbers, data digitized from [47] Coefficients CT, CP, and η against J for COMP at 6, rpm, where β.75 = Coefficients CT, CP, and η against J for COMP at 6, rpm, where β.75 = Coefficients CT, CP, and η against J for COMP at 6, rpm, where β.75 = Coefficients CT, CP, and η against J for COMP at 6, rpm, where β.75 = Coefficients CT, CP, and η against J for COMP at 4, ~ 6, rpm, where β.75 = Nacelle coordinate system Nacelle surface pressure distribution for PD1 at 3 4 LSWT for different Φ, where β.75 = 23 (continued) Nacelle surface pressure distribution at 7 1 NIAR for different Φ, where β.75 = 23 (continued) Test section side wall pressure distribution at 7 1 NIAR, where β.75 = Nacelle surface pressure distribution at 3 4 LSWT for different Φ, where β.75 = 28 (continued) Nacelle surface pressure distribution at 7 1 NIAR for different Φ, where β.75 = 28 (continued) xi

12 LIST OF FIGURES (continued) Figure Page 6. Test section side wall pressure distribution at 7 1 NIAR, where β.75 = Nacelle surface pressure distribution at 3 4 LSWT for different Φ, where β.75 = 33 (continued) Nacelle surface pressure distribution at 7 1 NIAR for different Φ, where β.75 = Test section side wall pressure distribution at 7 1 NIAR, where β.75 = Nacelle surface pressure distribution at 7 1 NIAR for different Φ without propeller (continued) Test section side wall pressure distribution at 7 1 NIAR without propeller Nacelle surface pressure distribution at 3 4 LSWT for different Φ, where β.75 = 15 (continued) Nacelle surface pressure distribution at 7 1 NIAR for different Φ, where β.75 = 15 (continued) Test section side wall pressure distribution at 7 1 NIAR, where β.75 = Nacelle surface pressure distribution at 3 4 LSWT for different Φ, where β.75 = 2 (continued) Nacelle surface pressure distribution at 7 1 NIAR for different Φ, where β.75 = Test section side wall pressure distribution at 7 1 NIAR, where β.75 = Nacelle surface pressure distribution at 3 4 LSWT for different Φ, where β.75 = 25 (continued) Nacelle surface pressure distribution at 7 1 NIAR for different Φ, where β.75 = 25 (continued) Test section side wall pressure distribution at 7 1 NIAR, where β.75 = Nacelle surface pressure distribution at 3 4 LSWT for different Φ, where β.75 = 3 (continued) Nacelle surface pressure distribution at 7 1 NIAR for different Φ, where β.75 = xii

13 LIST OF FIGURES (continued) Figure Page 77. Test section side wall pressure distribution at 7 1 NIAR, where β.75 = Nacelle surface pressure distribution at 7 1 NIAR without propeller (continued) Test section side wall pressure distribution at 7 1 NIAR without propeller Slipstream velocity components for PD1 at Φ =, x/l =.2, where β.75 = 23, U = 67 ft/s, 5, rpm (7 1 NIAR) Slipstream velocity components for PD1 at Φ = 9, x/l =.2, where β.75 = 23, U = 67 ft/s, 5, rpm (7 1 NIAR) Slipstream velocity components for PD1 at Φ = 27, x/l =.2, where β.75 = 23, U = 67 ft/s, 5, rpm (7 1 NIAR) Slipstream velocity components for PD1 at Φ =, x/l =.49 where β.75 = 23, U = 67 ft/s, 5, rpm (7 1 NIAR) Slipstream velocity components for PD1 at Φ = 9, x/l =.49 where β.75 = 23, U = 67 ft/s, 5, rpm (7 1 NIAR) Slipstream velocity components for PD1 at Φ = 27, x/l =.49, where β.75 = 23, U = 67 ft/s, 5, rpm (7 1 NIAR) Slipstream velocity components for PD1 at Φ =, x/l =.843 where β.75 = 23, U = 67 ft/s, 5, rpm (7 1 NIAR) Slipstream velocity components for PD1 at Φ = 9, x/l =.843, where β.75 = 23, U = 67 ft/s, 5, rpm (7 1 NIAR) Slipstream velocity components for PD1 at Φ = 27, x/l =.843, where β.75 = 23, U = 67 ft/s, 5, rpm (7 1 NIAR) Swirl angle at different longitudinal locations and azimuth angles for PD1, where β.75 = 23, U = 67 ft/s, 5, rpm (7 1 NIAR) Slipstream velocity components for COMP at Φ =, x/l =.2, where β.75 = 2, U = 67 ft/s, 6, rpm (7 1 NIAR) Slipstream velocity components for COMP at Φ = 9, x/l =.2, where β.75 = 2, U = 67 ft/s, 6, rpm (7 1 NIAR) xiii

14 LIST OF FIGURES (continued) Figure Page 92. Slipstream velocity components for COMP at Φ = 27, x/l =.2, where β.75 = 2, U = 67 ft/s, 6, rpm (7 1 NIAR) Slipstream velocity components for COMP at Φ =, x/l =.49, where β.75 = 2, U = 67 ft/s, 6, rpm (7 1 NIAR) Slipstream velocity components for COMP at Φ = 9, x/l =.49, where β.75 = 2, U = 67 ft/s, 6, rpm (7 1 NIAR) Slipstream velocity components for COMP at Φ = 27, x/l =.49, where β.75 = 2, U = 67 ft/s, 6, rpm (7 1 NIAR) Slipstream velocity components for COMP at Φ =, x/l =.843, where β.75 = 2, U = 67 ft/s, 6, rpm (7 1 NIAR) Slipstream velocity components for COMP at Φ = 9, x/l =.843, where β.75 = 2, U = 67 ft/s, 6, rpm (7 1 NIAR) Slipstream velocity components for COMP at Φ = 27, x/l =.843, where β.75 = 2, U = 67 ft/s, 6, rpm (7 1 NIAR) Swirl angle at different longitudinal locations and azimuth angles for COMP, where β.75 = 2, U = 67 ft/s, 6, rpm (7 1 NIAR) Nacelle-spinner effect on PD1 β.75 = 23 performance tested at 3 4 LSWT Nacelle-spinner effect on PD1 β.75 = 28 performance tested at 3 4 LSWT Nacelle-spinner effect on PD1 β.75 = 33 performance tested at 3 4 LSWT Nacelle-spinner effect on PD1 β.75 = 23 performance tested at 7 1 NIAR Nacelle-spinner effect on PD1 β.75 = 28 performance tested at 7 1 NIAR Nacelle-spinner effect on PD1 β.75 = 33 performance tested at 7 1 LSWT Nacelle-spinner effect on COMP β.75 = 15 performance tested at 7 1 NIAR Nacelle-spinner effect on COMP β.75 = 2 performance tested at 7 1 NIAR Nacelle-spinner effect on COMP β.75 = 25 performance tested at 7 1 NIAR Nacelle-spinner effect on COMP β.75 = 3 performance tested at 7 1 NIAR xiv

15 LIST OF FIGURES (continued) Figure Page 11. Dynamic tare for spinner-nacelle configurations in loads and coefficient forms and corresponding trend line equations Dynamic tare for no-spinner no-nacelle (nsnn) configurations in loads and coefficient forms, and corresponding trend line equations Dynamic tare results ( D ) for configurations with and without spinner-nacelle for PD1 β.75 = 23 at 3 4 LSWT compared with vortex theory analysis results Dynamic tare results ( D ) for configurations with and without spinner-nacelle for PD1 β.75 = 28 at 3 4 LSWT compared with vortex theory analysis results Dynamic tare results ( D ) for configurations with and without spinner-nacelle for PD1 β.75 = 33 at 3 4 LSWT compared with vortex theory analysis results Dynamic tare results ( D ) for configurations with and without spinner-nacelle for COMP β.75 = 15 at 7 1 NIAR compared with vortex theory analysis results Dynamic tared results ( D ) for configurations with and without spinner-nacelle for COMP β.75 = 2 at 7 1 NIAR compared with vortex theory analysis results Dynamic tared results ( D ) for configurations with and without spinner nacelle for COMP β.75 = 25 at 7 1 NIAR compared with vortex theory analysis results Dynamic tared results ( D ) for configurations with and without spinner-nacelle for COMP β.75 = 3 at 7 1 NIAR compared with vortex theory analysis results xv

16 LIST OF ABBREVIATIONS 2D 3D Two-Dimensional Three-Dimensional AGARD Advisory Group for Aerospace Research and Development BART CAD CFD CMM CNC COMP CPU FFA FS LSWT LTPT mv NACA nsnn NIAR PLA psf psid RD Basic Aerodynamics Research Tunnel Computer-Aided Design Computational Fluid Dynamics Coordinate Measuring Machine Computer Numerical Control Complex Propeller Central Processing Unit Flygtekniska Försöksanstalten (Aeronautical Research Institute of Sweden) Full Scale Low-Speed Wind Tunnel Low-Turbulence Pressure Tunnel (at Langley Research Center) Millivolts National Advisory Committee for Aeronautics No-Spinner No-Nacelle (Configurations) National Institute for Aviation Research PolyLactic Acid Pounds per Square Foot Pounds per Square Inch Differential Readings xvi

17 LIST OF ABBREVIATIONS (continued) RO rpm UAVs UTRC VWT WSU WOZ Rated Output Revolutions per Minute Unmanned Aerial Vehicles United Technologies Research Center Vertical Wind Tunnel (at Air Force Research Laboratory) Wichita State University Wind-Off-Zero xvii

18 LIST OF SYMBOLS Degree α αi αl β Angle of attack Induced angle of attack Zero-lift line angle of attack relative to the chord line Geometric pitch angle β.75 Pitch angle at 75% of radius 1 ut ε Swirl angle, tan ux ϕ Angle of resultant flow CJ T η Efficiency, C U λ Tip speed ratio, V μ Viscosity P T ρ σ ω Γ Φ a Density Propeller solidity for rectangular blades, Angular velocity Bound circulation around any blade station Azimuth angle Lift-curve slope Bc R c Local chord length cpr Pressure coefficient, cpr p p q d 2D drag or differential dl, dd Differential lift and drag, respectively xviii

19 LIST OF SYMBOLS (continued) l 2D lift l Non-dimensional axial location of wall pressure port to 7 1 test section length where l = at entrance and l = 1 at exit n Revolutions per second p Pitch, distance p Local pressure p Freestream static pressure q Dynamic pressure q Freestream dynamic pressure, q 1 U 2 2 r Radial location t Blade thickness ux, ut, ur v Flow velocity components (axial, radial, and tangential, respectively) Velocity vector and/or magnitude v Vortex displacement velocity w Induced velocity wa Axial component of induced velocity wt Tangential component of induced velocity x Non-dimensional radial location, x r R x, y, z Nacelle/tunnel fixed coordinate system or distances xix

20 LIST OF SYMBOLS (continued) A B CL Disk area Number of blades 3D lift coefficient (lower case subscript: 2D design lift coefficient) CD 3D drag coefficient (lower case subscript: 2D design drag coefficient) CP P Power coefficient, CP 3 5 n D CQ Q Torque coefficient, CQ 2 5 n D CT T Thrust coefficient, CT 2 4 n D D Propeller diameter Dhub DC F Propeller hub diameter Direct Current Prandtl s tip loss factor HP Horsepower J Advance ratio, J U nd L Nacelle length M Mach number P Shaft power Q Propeller shaft torque R Propeller radius Re Uc Reynolds number, Re Re.75 VR c Reynolds number at 75% of radius, Re.75 2, where V U R R xx

21 LIST OF SYMBOLS (continued) T U V VE VR VT Thrust Freestream velocity Voltage (mv = millivolts) Effective freestream velocity Resultant freestream velocity Tip velocity, VT = ωr xxi

22 CHAPTER 1 INTRODUCTION 1.1 Propulsive Efficiency in Propeller Design A propeller is a device that generates thrust or force in a fluid medium such as water or air. A mass of fluid medium driven by the propeller causes a reaction in the opposite direction, that is, the craft s forward thrust. An airscrew propeller, commonly used on aircraft, screws or twists its way through the air, pushing or pulling the aircraft forward as it turns. The rotational kinetic energy increment added by the shaft power in the air moving backward, also called the slipstream, cannot be regained and is considered a power loss [1, 2]. Another type of energy loss may be the friction between the air and propeller blades. Therefore, the thrust available or power produced by the propeller is less than the power provided by the engine. A propeller designer aims to increase the ratio of useful power to engine power in order to obtain greater propulsive efficiency. During World War II, propeller propulsion achieved a standard that was quite high. With the debut of jet engines, the progress in propeller propulsion struggled for a period of a time. But with the increase in the price of oil, there has been great demand for optimally improving the efficiency of propeller propulsion, hence making it the most economical means of propulsion [3]. Most aircraft propellers are run by internal combustion engines, and the best propeller performance is at a certain speed of revolutions whereby the engine is designed to operate at its highest efficiency. With recent improvement in lithium-ion battery technology, the use of electrical motors with innovative propeller designs has increased rapidly, especially in small unmanned aerial vehicles (UAVs). This requires a large shift in design from traditional propellers to a new propeller design and analysis method for different environments. In addition to its aerodynamic efficiency, 1

23 a propeller must also show its structural trustworthiness with sufficient strength, that is, longer fatigue life [4]. A variety of elements are considered in propeller selection. Interestingly, propeller performance is not always the only priority in choosing propellers. For instance, it may be necessary to have wide blades with a low tip speed to lower the noise level of a propeller. Also, the propeller diameter can be limited based on of ground clearance or the distance from the nacelle to the fuselage. Propeller and motor dynamics also need to be in compliance. Furthermore, the impulse response of the engine should not match the natural frequency of the first bending mode or harmonics of the blade. This will lead to excessive vibration and ultimately fatigue failure [5]. From an aircraft performance and designer point of view, it might be important to choose a propeller with a high static thrust for takeoff and a high efficiency at cruise. With an appropriate propeller mechanism, these are relatively easy to achieve if the propeller pitch is variable. A fixedpitch propeller requires settling for something between these two extremes. The pitch of the propeller defines the distance it translates through the air in one revolution without slipping. The rotation of the whole blade about its long axis determines if the blade has a fixed or variable pitch. A constant-pitch propeller has the same twist throughout the radius of the entire blade and refers to the propeller geometry. The design procedure of a propeller is not well defined [5]. Generally, one must first decide on the number of blades, which may be based on experience or could be an arbitrary number, for starting its design and the analysis iteration process. Similarly, pitch distribution contributes essentially to the efficiency and performance of the propeller. The results of stress calculations determine whether the thickness distribution needs to be changed or not. Finally, a radial distribution of pitch and blade thickness may be prescribed. 2

24 The propeller analysis and design process and its historical development will be discussed in detail in sections to follow. As explained, each method has its advantages and disadvantages. An attempt has been made to provide additional detailed information, especially for low Reynolds numbers that will eventually improve the methods of both analysis and design. 1.2 Challenges in Propeller Design and Analysis As discussed briefly in this section, three main concerns are involved in the propeller design process. These issues, in order of their importance and difficulty level, are introduced here. The first issue in this process is to design a propeller according to the rotational speed desired by the engine or motor. A rotating propeller causes resistance as it turns around the shaft axis. This resistance, also known as torque, Q, increases as the rotational speed increases. Therefore, the speed of revolution is decided by the power available to spin the propeller. In contrast, engines and motors operate most efficiently at their designated rate of revolution. Designing a propeller for a certain rate of revolutions that are suitable for a motor is a relatively easier task, but the speed of the aircraft for which it is designed to perform must also be considered, and this has considerable impact on the torque or power settings. Consequently, it is difficult to design a propeller based only on its engine performance without knowing the aircraft operating speed. In other words, an individual propeller must be designed for each combination of aircraft and engine, which makes the effort challenging. Therefore, it is essential to develop a reliable theory on which to base the design. The second issue in the design process is to create an efficient propeller. Only a portion of power, P, generated by the engine is converted into thrust, T, and the remainder primarily disperses into the slipstream. Efficiency (η) is the ratio of the useful power delivered by the propeller and power provided by the motor (shaft power): 3

25 TU (1.1) P where U is the velocity of the aircraft. Typically, the efficiency of the propeller is shown by a percentage, and a designer aims to maximize this value by applying a reliable and accurate analysis method. The final issue in the design process is to develop a dependable and safe propeller. A series of forces and bending moments act on a rotating propeller due to centrifugal forces and thrust. Also, vibration and torque of the engine or motor cause severe wear and tear on the blades, shifting the blade into thicker and heavier designs. In the meantime, it may be challenging to increase the efficiency and reliability of a propeller because they are mutually opposing matters, but achievable. However, the toughest obstacle for a designer is the first problem to design a propeller for a particular engine and aircraft operating speed combination [4]. 1.3 Development in Analysis and Design Methods Early propeller studies conducted by Rankine [6] and Froude [7] in the 19 th century established the fundamentals of momentum theory for a propeller in a fluid medium, such as air or water. In this theory, an actuator disk replaces the propeller geometry, thus neglecting the geometric features and the slipstream rotation. In 19, Drzewiecki [8] introduced the blade element method, including section lifting surfaces set to an optimum angle of attack. Although Drzewiecki was the first to introduce the blade element theory, this work failed to account for the induced velocity at each element. It seems that Wilbur and Orville Wright were the first who combined the momentum and blade element theories and successfully introduced highly efficient propellers [9]. In 1925, Weick [1] published the empirical method, a simple system for small airplane designers and builders derived from wind tunnel models and in-flight full-scale tests. Here, design 4

26 steps are made through easy calculations and charts for a baseline propeller with an average fuselage. To increase accuracy, it is necessary to provide precise horsepower, revolutions per minute (rpm), and velocity of the operating condition, otherwise performance diminishes. This method is sufficient only for low-power engines, that is, engines that have a little less than one horsepower to about fifty horsepower. With the application of Prandtl s lifting line theory [11] to propellers, a new era of propeller development began. Circulation over a finite wing was shown, which is applicable to the propeller blade as a lifting surface incorporated by the bound vorticity and a vortex sheet shed from the trailing edge of the blade. Betz [12] showed that a propeller with optimum-induced velocity distribution causes undeformed or rigid helical vortex sheets to move downstream of the propeller. This occurs where each point of the radius in a helical wake has the same velocity in axial distance from the propeller, that is, parallel to the rotation axis, so that the induced loss is minimal. Betz assumed that the propeller would be lightly loaded, or the slipstream would roll up as wake contraction occurred. The helicoidal vortex sheet is assumed to move as a rigid body, but that is not the case in reality. The averaged axial and swirl velocity components between the vortex sheets of the slipstream are less than the sheet velocities by a factor F. Also, the swirl component of the velocity varies throughout slipstream radius. Prandtl provided an approximation method, also called Prandtl s tip loss factor F, using a series of semi-infinite plates. This factor becomes more exact as the number of blades increases or the advance ratio becomes smaller. Goldstein [13] found the exact solution to the ideal Betz wake problem. His vortex theory resulted in the geometry of a propeller rather than predicting its performance. Lock et al. [8] applied Goldstein solutions to a design and conducted high-speed aircraft propeller performance analyses from 1941 to 1945; this work is published in an Aeronautical Research Council report 5

27 [14]. Throughout a series of National Advisory Committee for Aeronautics (NACA) reports [15-18], Theodorsen showed that the same light-loading assumption made by Betz, Prandtl, and Goldstein was not necessary and could be removed. Due to contraction, instead of Goldstein s solution concentrating right behind the propeller, Theodorsen proved that this solution was effective even far downstream. Theodorsen s theory, like Goldstein s solution, resulted in the geometry of the propeller but with an ideal wake far downstream. In 1949, Crigler [19] applied Theodorsen s theory to propeller design. The optimum propeller efficiency can be described from a number of graphs for any design condition. In a more recent work in 1994, Adkins and Liebeck [2] modified Larrabee s [21] method by removing the light-loading assumption and small-angle approximation. They presented an iterative design procedure to calculate the axial velocity of the vortex filament and flow-angle distribution. Parameters required for analysis and design are the number of blade elements, number of blades, propeller diameter, hub diameter, revolution speed, freestream velocity, and particularly lift and drag coefficients of the section design. Accurate airfoil geometry specifications and its aerodynamic characteristics lead to better propeller performance predictions. In addition, for design, thrust or power inputs must be provided in order to obtain chord length and pitch distribution along the radial direction for an optimum wake or inverting the process for propeller performance analysis. An open-source program called JavaProp [22], written by Hepperle using a Java application, is available using Adkins, Liebeck, and Larrabee s blade element methods, which is discussed in Chapter 2. Despite the evolution of the lifting line theory and its robustness, the limitations of this theory must be considered. First, it is only applied to conventional blades with a large aspect ratio, not wide-chord propfan blades, for instance. Next, and importantly, high Mach numbers and low 6

28 Reynolds number effects are not incorporated into basic theories that require corrections to section airfoil data [23, 24]. Furthermore, the theory does not account for three-dimensional effects, such as sweep angle or cross flow, since the bound vorticity is assumed to be straight. Progress in computational capabilities makes complex numerical analyses, such as solving Euler or Navier-Stokes equations, more affordable and accurate. Although still computationally more expensive than traditional momentum-blade element theory, these methods can implement viscous phenomena like turbulence and flow separation. Unprecedented details of the propeller flow field and its interaction with a wing or fuselage are some of the greatest advantages of computational fluid dynamics (CFD) [23, 25-33]. It appears that the future of CFD methods is promising; however, some issues need to be addressed. As mentioned above, computational costs are significant. But with advancement in computer technologies, this problem should be solved eventually. Another important concern is the lack of validated code to prove that the method is authentic with a certain level of confidence. When accuracy and limitations of experimental measurements and CFD codes, grid-density effects, and physical basics are equally known, they can be compared over a range of specified parameters. A detailed surface and flow-field comparison with experimental data justifies the code s ability to accurately model the critical physics of the flow. Precision in geometric measurements of the actual model is imperative, especially when operating at low Reynolds numbers. This is because any small defect in fabrication or change in geometry affects aerodynamic characteristics at lower Reynolds numbers, thus making the propeller performance even more unpredictable. Previous discussions have suggested procedures for assessing the accuracy and credibility of CFD techniques [34-36]. The scope of this study is to provide comprehensive propeller experimental data designed for validating analysis and design tools at low Reynolds numbers. 7

29 Without a doubt, this is the first step in improving tools and processes of modern propeller analysis and design, in hopes of ultimately enhancing propeller efficiency. The goal here is to provide extensive measurements of the performance, geometries, flow field, and boundary conditions required for validation and development of analysis and design tools, particularly for UAV applications operating at lower Reynolds numbers. Prediction and eventually agreement in analysis results with experimental data capturing Reynolds number effects potentially lead to establishment of the code s ability. In Chapter 2, we will further discuss the recent analysis methods and design process with corresponding problems and inquiries. 8

30 CHAPTER 2 MODERN PROPELLER ANALYSIS AND DESIGN Aerodynamically, a designer struggles to deliver a propeller with maximum efficiency in order to satisfy all performance expectations. Hence, an accurate analytical method is required to achieve this goal. Modern analysis and design processes have evolved over the years, as previously reviewed in the historical development section of Chapter 1. The different propeller analysis and design tools that are dominantly used in the field will be examined in this chapter. Any prediction method must be validated, typically using existing experimental results, in order to endorse its credibility. The detailed experimental data can verify the tool s ability and accuracy. 2.1 Momentum-Blade Element Theory The momentum-blade element theory is a relatively simple means to approximate the induced angle of attack αi by combining two different methods. This approach allows the prediction of propeller performance more accurately by examining the aerodynamics of the blade section. This theory does not particularly account for the flow rotation and tip loss factor, unless it has been imposed. Approximation of the induced effects gives only a rough estimate for the analysis. Although this is one of the original blade element methods that accounts for the induced velocity, with the improvement in computers, the use of this method has diminished [5]. Yet, it is useful to be familiar with this theory because of its applications to other models, which can be found in numerous literature reviews. In general, if the propeller with radius r screws itself through the air without slipping, then the distance it would travel in one revolution is the pitch, p: p 2 rtan (2.1) 9

31 assuming the pitch is constant throughout the blade radius, where the pitch angle β is the angle between the plane of rotation and the section chord line. However, for the following analysis, it is more convenient to define it relative to the zero-lift line instead of the chord line. Figure 1(a) shows the front view of a rotating propeller with two blades and an angular velocity ω rad/s with incoming freestream velocity U. The notation on this figure is similar to that of McCormick [5]. Note that the induced velocity w, shown in Figure 1(b), is much smaller in scale than indicated here. (a) (b) Figure 1. Rotating propeller: (a) front view, (b) velocities and forces on blade element looking toward hub. Each blade is divided into several radial elements, dr, which contribute to thrust T and torque Q resulting from section lift and drag. From Figure 1, these values can be calculated as dt dlcos ddsin( ) (2.2) i dq r dlsin i dd cos( i) (2.3) where the differential lift dl and the section lift coefficient Cl will be, respectively, 1 2 dl VEcCldr (2.4) 2 i C a( ) (2.5) l i 1

32 Similarly the differential drag dd can be found as 1 2 dd VEcCddr (2.6) 2 To find the induced angle of attack αi in equations (2.2) and (2.3) for the following analysis, assume that αi and the drag-to-lift ratio are small. This assumption is not valid at high disc loadings or when flow separation occurs, thus causing a deviation in results. Now, the resultant velocity VR and the effective velocity VE in Figure 1(b) are almost equal, that is, VR VE. As a result, for B blades, equation (2.2) can be rewritten as B 2 dt VR ca( i)cos dr (2.7) 2 Note that blade section lift-curve slope a, has a direct impact on the thrust obtained in this equation. At this point, linear lift with angle of attack (i.e., ) is assumed. From the momentum principle, thrust is i T 2 A U w w (2.8) For small αi, the induced velocity can be approximated as w VR αi, and equation (2.8) can be written for dt as dt 2 rdr U V cos 2V cos (2.9) R i R i By equating equations (2.7) and (2.9), the induced angle of attack can be determined as where 2 1 av R av R av R i x 8x V T x 8x VT 8x VT U R 2 2 V V x R T 1/2 (2.1) Bc R tan 1 x 11

33 VT R x r R The dimensionless characteristics of propellers are defined by thrust coefficient CT and power coefficient CP obtained from experiment results as C C T P T (2.11) 2 4 n D P 3 5 (2.12) n D In momentum-blade element theory, these are functions of the advance ratio J and expressed as CT J x [ Cl cos i Cd sin( i )] dx 8 (2.13) xh where CP x J x [ Cl sin i Cd cos( i )] dx (2.14) 8 xh U J (2.15) nd Hence, the propeller efficiency in equation (1.1) can be written in terms of CT, CP, and J as CJ C T (2.16) Inevitably, the efficiency increases as the advance ratio increases until the windmill condition approaches. This is because of how the term is defined in equation (2.16). Note that section lift and drag coefficients directly affect CT and CP, as shown in equations (2.13) and (2.14). Hence, it is critical to provide precise section airfoil aerodynamic characteristics in order to obtain accurate thrust and power predictions. Torque coefficient CQ and power coefficient CP result in a relationship of C P P 2 C (2.17) Q 12

34 Assumptions made in this theory of a small induced angle of attack and drag-to-lift ratio are not necessarily true but convenient for the sake of simple calculations. Ol et al. [24] presented an analytical-experimental comparison for a range of small propellers using the momentum-blade element theory for the analysis. The XFOIL interactive program was applied to predict the section airfoil characteristics and low Reynolds number effects. Sectional coefficient analysis results for Re 6, vary significantly and hence are unpredictable. High sensitivity to twist, chord length distribution, and Reynolds number effects is predicted. Especially, low Reynolds numbers highly affect the results when the propeller rpm varies throughout advance ratio sweeps. The variation in rpm causes scattered thrust and torque measurements in the wind tunnel test data. However, Reynolds number effects cannot be demonstrated well in traditional coefficient plots [24]. Analysis results for uniform compared to non-uniform induced velocity for the entire blade show a small difference in thrust coefficients, except at low advance ratios. Uniform induced velocity is preferred for the analytical method to avoid calculation complexity. Thrust and torque coefficients as well as efficiency against a series of advance ratio are shown in Figure 2. Wind tunnel tests were performed in the Basic Aerodynamics Research Tunnel at the NASA Langley Aerospace Research Center in Virginia and the Vertical Wind Tunnel at the U.S. Air Force Research Laboratory in Ohio. Six Thin-Electric propellers, APC series, were considered by Ol et al. [24] for widerange selections of the pitch-to-diameter ratio including square propellers (pitch = diameter). Some wind tunnel results were compared with the experimental data of Brandt and Selig [37], showing significantly higher efficiency due to discrepancies in twist measurements. In Ol s study, each blade segment was sliced with a band saw or digitally scanned to render the airfoil, and then input to the XFOIL program to analyze the section s aerodynamic performance. A significant uncertainty in twist angle was observed with an estimate of +/ 1 degree. As a result, an inconsistency in twist 13

35 distribution was detected in comparison with Brandt s [37] cross section measurements for the same propeller. An offset of ±2 in analytical predictions shows a substantial shift in thrust and torque coefficients and efficiency in Ol s report. Lack of information on propeller geometry is a common issue when approaching analytical predictions, since the manufacturer does not provide any information on geometric characteristics [26, 36]. The momentum-blade element analysis results mostly under-predict the experimental data, as shown in Figure 2. Figure 2. BART data vs. M-BE analysis of APC Thin-E propellers [24]. Uncertainty remains on the selection of the correct twist angle for blade sections in the analytical attempts. Nevertheless, it can be argued that the other reason for such a discrepancy is possibly the 14

36 Reynolds number effects as the result of not choosing the appropriate rpm used in the analytical method. Small propellers operating at such low Reynolds numbers may produce a massive separation bubble, thus altering entire section aerodyanmic characteristics, hence occasionally unpredictable. 2.2 JavaProp JavaProp is a new version of the SimProp program written by Hepperle in Java on an open source domain [22]. It is a simple, user-friendly code incorporating blade element theory introduced by Adkins and Liebeck in designing an optimum propeller [2]. Ignoring the threedimensional effects of the blade, it has the additional ability of finding circumferential and axial velocities added to the incoming flow of each blade element. This simplified method agrees relatively well with experimental data when disk loading is small but is not accurate under static conditions, as mentioned in Chapter 1. The blade element theory with additional Prandtl s tip loss factor is integrated into JavaProp to account for the effect of number of blades and tip loss. Yet, this approximation loses accuracy with fewer blade numbers or at high advance ratios. A series of off-design analyses for a full range of propeller operating conditions and a detailed analysis for a specific advance ratio can be executed by the program. These analysis modes predict the propeller performance, if the local twist and chord distribution as well as the number of blades, propeller diameter, and rpm are known. Furthermore, the design lift-to-drag ratios of four radial segments must be specified. The Multi Analysis mode in JavaProp computes a full range of thrust and power coefficients against the advance ratio from static to windmill conditions. Here, the only detailed description shown is the stalled percentage of the airfoil. For a fixed-pitch propeller operating at lower freestream velocities, the blade section is mostly stalled since it performs at high angles of 15

37 attack or beyond the maximum lift. As the advance ratio increases, which is a function of the freestream velocity, efficiency also increases. However, it is not very clear if the designer intentionally reached the target efficiency or it may be only because of how the term is defined, as shown in equation (1.1). The Single Analysis mode in JavaProp performs an analysis based on a given advance ratio or velocity in addition to previous given values. This mode allows for studying aerodynamic characteristics along the radius. In addition to lift and drag coefficient radial distributions, the locally induced velocity by the propeller wake is presented as an interference factor. This factor, in terms of axial and swirl components, is coupled to the incoming flow velocity. Force and bending moment coefficients are also included for structural stress calculations. The Flow-Field Card in JavaProp offers a convenient study of the slipstream for a specific advance ratio. The color spectrum describes the axial acceleration of the flow field before and after the propeller in the form of the axial velocity-to-freestream velocity ratio [22]. On the other hand, the propeller design process results in the chord length distribution and geometric pitch angle β along the radius r. The design lift coefficient Cl or lift-to-drag ratio L/D, which affects the local chord length c, needs to be specified in advance. It is important to emphasize that the aerodynamic characteristics of an airfoil depend on its chord and thickness. The geometry of a blade section or an airfoil consists of the airfoil profile, thickness, and chord length, and all contribute to its performance, although the contribution of each may vary. It is critical that all necessary geometry details are provided in advance. The Airfoil Card in JavaProp offers a limited airfoil selection along with synthetic airfoil data which are reproduced considering parameters such as zero lift, maximum lift and minimum drag coefficients. Randomly choosing the highest L/D airfoil consequently means sacrificing the off-design performance as well as overall accuracy of the prediction. Smaller design lift coefficient 16

38 values result in wider blades. Decreasing the L/D at the tip widens only the tip chord length. For off-design performance at a lower speed or high disk loadings, it is necessary to reduce the lift coefficient for inboard sections to delay the stall when the blade sections are wider and set at lower angles. The engine/motor and propeller combination may influence system performance, which can be derived from the power coefficient and rpm curve. To satisfy the optimum propeller theory originally presented by Betz and Prandtl, the following design parameters [22] need to be prescribed: Number of Blades A propeller with more blades increases the uniform distribution of thrust and power in the wake of the propeller but with a small improvement in efficiency. For a constant power or thrust, an increase in the number of blades causes shortening of the chord length. Reducing the propeller diameter is the tradeoff for maintaining the chord length, although this will usually decrease efficiency if the tip speed is less than Mach one. The number of blades B also contributes to the propeller solidity σ, which represents the ratio of blade area to disk area as defined, and directly contributes to the thrust and power coefficients see equations (2.13) and (2.14). Velocity Freestream velocity along with rotational speed defines the pitch distribution of the propeller. The desired efficiency might be obtained by increasing the pitch of the propeller but causes the blade to stall at certain incoming flow speeds or rotational speeds. Diameter The diameter of the hub determines the effective propeller diameter. The effect of the propeller diameter on performance is significant: the larger the propeller diameter, or consequently the propeller area, from the continuity equation, the more thrust that can be obtained for a constant 17

39 velocity along the control volume. On the other hand, the same effect can be observed on highaspect-ratio wings on sailplanes that produce more lift with less drag or L/D. In general, the best performance is attained when the pitch-to-diameter ratio is one. Lift and Drag Distributions The prescription of drag polar and design angle of attack at each radial location is more convenient than section design lift and drag coefficients. Figure 3 shows an example of a canned or artificial airfoil drag polar used in JavaProp, which characterizes essentially zero lift, maximum lift coefficient, and minimum drag coefficient. Usually, a propeller maximum efficiency can be obtained when the section lift-to- drag ratio is at its peak. Lower angle of attack settings work better for the overall design aspects that include off-design conditions since the stall occurs gently. Regardless of how one delays stall by controlling the lift-to-drag ratio, analysis results are unreliable at very low advance ratios. Figure 3. Synthetic drag polar of Clark Y airfoil at different Reynolds numbers [22]. Desired Thrust or Power Available Based on the total drag or the available motor, either the desired thrust of the propeller or a given useful shaft power can be specified. Density 18

40 Fluid density does not have any influence on the power or thrust coefficients as well as efficiency, but it greatly impacts the propeller size and shape. For example, hydro-propellers have smaller dimensions compared to airscrews. Moreover, the air density determines whether the tip has reached supersonic speed. Values for power and thrust are calculated directly from the fluid density. The Adkins and Liebeck design method used in JavaProp is intended to correct Larrabee s difficulties and find the exact solution. With specifications of the previous terms, the following iterative design procedure is used to find the pitch and chord-length distribution. a. Select an initial estimate for the ratio of vortex displacement velocity to the freestream velocity v /U, or select v /U = to start. b. Find Prandtl s momentum loss factor and flow angle at each element. c. Calculate the product of the local total velocity and blade section chord along with the local Reynolds number. d. Determine the airfoil section drag-to-lift ratio and angle of attack from the airfoil data. e. For the minimum drag-to-lift ratio, revise Cl, and repeat step c. f. Calculate the axial and rotational interference factors as well as local total velocity. g. Determine the blade chord length using step c results, and twist β. h. Find the four derivatives as defined, and integrate them over the blade region. i. Find v /U and either the non-dimensional power or thrust coefficients. j. If the new value for v /U is different from the old value (e.g.,.1%), then return to step b. k. Determine the propeller efficiency and other parameters, such as propeller solidity. These steps usually take more than a few iteration cycles to converge. Also, the viscous loss term can be added for more accurate results. 19

41 Although JavaProp is a fast and user-friendly code, it has its limitations, as discussed previously. Predictions where flow separation occurs are poor, e.g., at high disk loadings or low advance ratios. Furthermore, restrictions limit the section blade aerodynamic characteristics that can be implemented. Finally, boundary layer interactions with complex phenomena in cases such as three-dimensional effects, Mach number effects, etc., are ignored in JavaProp. Users must agree on whether to sacrifice accuracy in order to obtain a quick and fairly reasonable estimate. Hepperle presented validation results of his code in comparison with Theodorsen s experimental data [38]. The geometry was imported by the JavaProp Geometry Card feature using a three-bladed propeller and Clark Y section airfoil at Re = 5,. However, it is not clear if the airfoil data used appropriately represented the exact tested propeller blade characteristics. Figure 4 shows all validation results obtained in coefficient forms and efficiency against advance ratio J. Angles settings show the pitch angle at 75% radius, or.75r. The thrust coefficient (shown in the upper left portion of Figure 4) only agrees with the trend of the linear region of the curve with a systematic shift, but not as much where the flow is mostly separated. Here, a similar trend is apparent, as the analysis results underpredict the experimental data, as was shown in momentumblade element theory validations. The power coefficient curves (right side of Figure 4) show an identical trend to the thrust coefficient graph, with large deviations at the lower advance ratios. Note that the experimental data has some discontinuities as well, depending on each test condition. Generally, a propeller operates at the linear region of this regime, except for takeoff and landing. The efficiency curve may cancel out practical errors since it depends on both the thrust and power coefficients. It may not be wise to validate a method with the efficiency plot. 2

42 Nonetheless, the more accurate it becomes, the better its assessment on overall aircraft performance. Figure 4. JavaProp validation results compared with NACA TR-594, designated blade angle at.75r [22]. 2.3 Vortex Theory Unlike the previous momentum-blade element theory, vortex theory incorporates the induced effect. A complex iterative process and, therefore, an increase in calculation time is inevitable for obtaining considerably more accurate results. The vortex theory starts with consideration of the ultimate wake of the optimum propeller, or Betz s condition, as discussed previously in Chapter 1. 21

43 Studies have been conducted to justify the assumption that the normality condition holds between the effective velocity VE and the induced velocity w (see Figure 1). Prandtl s tip loss factor F is an approximation for Goldstein s kappa factor, which becomes more exact as J decreases or the number of blades increases, and can be expressed as 2 B(1 x) 2sin T 1 F cos exp (2.18) where ϕt is the tip helix angle of the blade. For a lightly loaded propeller, 1 T tan (2.19) With Prandtl s tip-loss approximation of Goldstein s vortex theory, the bound circulation Γ and the tangential velocity component wt of the induced velocity can be related in BГ 4π rfwt (2.2) From the Kutta-Joukowski theorem, 1 cclve (2.21) 2 Substituting equation (2.21) into equation (2.2) yields Now VE /VT can be shown in terms of wt /VT as V w E t Cl 8xF V T V (2.22) T V E 2 w t 2 wt wt x x 4 x VT VT 2 VT VT 1 2 (2.23) Solving for wt /VT will determine the induced angle of attack αi as tan i 1 U w a r wt (2.24) 22

44 The axial component of induced velocity wa can also be found as a function of wt. From the geometry above, V V cos (2.25) E R i Hence, it is possible to derive 2 V ( J x )cos 2 E i VT (2.26) which shows the vortex theory and momentum-blade theory differences in CP and CT equations (2.13) and (2.14). The left-hand side of equation (2.26) is used in vortex theory, and the right-hand side of the equation is used in the momentum-blade element, where cos 2 αi 1, since αi is assumed to be a small angle. Other refinements to the angle of attack and the lift coefficient in vortex theory may increase the accuracy. Validation of vortex theory was attempted by Moffitt et al. [36] for UAV-scale propellers using similar method to measure blade-section geometry, as described in section 2.1. A given fullscale propeller was also designated by McCormick [5] to exercise vortex theory applications and compare with wind tunnel data for validations. This three-blade propeller has a Clark Y section with chord, twist, and thickness distribution, as provided by previous researchers [38-4]. Although details on other geometric features and test conditions are not specified, results are used in different validation examples, such as JavaProp. McCormick s vortex theory approach is relatively easy to utilize since the computer programming procedure is provided to predict the performance of this specific propeller. Software Maple 16 was used for developing this program. Results for thrust and torque coefficients in addition to efficiency are shown in Figure 5. Most airfoil characteristics, except post-stall lift coefficient behavior, are estimated with a no-detail description of the approximation process. The Cl range is limited between.8 and

45 for this calculation. As discussed, a major portion of the propeller blade stalls at a lower advance ratio. Evidently results for the thrust coefficient in this region are poor; however, it becomes astonishingly accurate in the linear region (see Figure 5). As discussed previously, the blade twist angle β needs to be adjusted to the zero-lift line instead of the chord line. McCormick estimates the zero-lift line angle αl to the chord line for this particular airfoil as t l 46 (2.27) c The slope of the section lift coefficient a for the Clark Y airfoil is taken to be a.1 1. t c (2.28) Cl can be determined from equation (2.5), and Cd is also expected to be where d dmin l 2 C C.1 C.15 (2.29) C dmin t.4.17 (2.3) c Note that parameters αl, a, and Cdmin are a function of the thickness-to-chord length ratio t/c. It is convenient to use t/c in these equations, since the blade s radial distribution is presented in the report. To find both Cl and Cd as a function of angle of attack, an iterative process needs to be implanted to simultaneously calculate all the unknown parameters, primarily wt /VT and the induced angle of attack αi in equations (2.22) and (2.24). 24

46 C T JP-15 JP-25 JP-35 VT-15 VT-25 VT-35 Exp-15 Exp-25 Exp-35 C P J J η J Figure 5. Vortex theory, JavaProp, and propeller experimental results [39] comparison, with designated blade angle at.75r. Close agreement of vortex theory predictions is clear when the blade is at lower angles or not stalled. This is because the airfoil characteristics are fairly known in this region. As the advance ratio decreases, the section angle of attack increases, and the blade starts to stall from the inboard section of the blade. The results of vortex theory prediction show linear behavior for the thrust coefficient throughout the advance ratio (shown in left top of Figure 5). No post-stall treatment is 25

47 applied for the airfoil lift coefficient. The power coefficient and efficiency curves coincide rather well with the test data. However, JavaProp analysis has a systematic under-prediction for most regions. This deviation possibly indicates that the zero-lift line of the airfoil might be off and not well prescribed in JavaProp validations, according to Hepperle [22]. Despite the offset of the results, it appears that the overall outcome of JavaProp is acceptable for the initial design for such a simple and fast tool. One can argue whether the time and effort used in the programming of vortex theory is worth the sacrifice of obtaining a more reasonable overall result. 2.4 Computational Fluid Dynamics Without a doubt, the most sophisticated and potentially accurate analysis and design tool is computational fluid dynamics. Solving Euler and Navier-Stokes equations also requires extensive calculation and central processing unit (CPU) time when compared with previous analytical methods. This is not the only concern; CFD codes also need to be verified. CFD validation is a principle that must be coordinated between computational and experimental constraints. Lack of knowledge in physical modeling, limited computer resources, and mathematical approximation increase the uncertainties in the CFD application [34]. As a result, the extension of CFD into the design process depends on the credibility of how the code is validated through experiments, that is, how the code is an essential part of its evolutionary progress. Two examples are introduced here to show the extent of CFD applications in propeller analysis and in the existing validation problems CFD Example 1 An analysis of propeller wake interference effect was conducted by Strash et al. [26]. Their results are compared with wind tunnel test data obtained by the Flygtekniska Försöksanstalten (FFA) or Aeronautical Research Institute of Sweden [41, 42] in the late 198s. The extensive 26

48 experimental data consist of four nacelle/wing combinations where axisymmetric nacelle and axisymmetric nacelle/wing combinations were used for validations (see Figure 6). Time-averaged pressure distribution over the nacelle and wing, a velocity components survey on the propeller slipstream, and typical thrust and torque measurements for a single advance ratio of.7 were investigated. The propeller used was a one-fifth scale model of a Dowty Rotol R243 propeller on a SAAB 34 powered nacelle. Figure 6. Combined propeller/nacelle/wing grid domain [28]. It seems that the vast amount of experimental data is best suited for CFD validations as used in other studies [28, 33]. Nonetheless, despite specifications of nacelle/wing geometry and wind tunnel model installation, no information on the propeller geometry is available except for the diameter of.64 m. Reluctantly, Strash et al. [26] compromised the R243 propeller to a similar one but with a different section chord and twist distribution than the Dowty Rotol R212 propeller that was apparently available. Therefore, credibility of the validation of this study is questionable since the exact propeller geometry is unknown. It seems like this is a common issue in most 27

49 validation processes, as explained in previous examples, before examining the credibility of the code. The calculated thrust coefficient was 12% off from the test data. The surface pressure coefficient distribution along the x-axis of nacelle is presented in Figure 7 at an advance ratio of.7. Figure 7 (a) represents the propeller/nacelle combination with no wing interaction at a -degree angle of attack, and Figure 7 (b) shows this for a 1-degree angle of attack. Strash et al. concluded that with the qualitatively quite good comparison results, the numerical simulation is feasible for preliminary design applications Test Data Upper Surface.4 Test Data Upper Surface Lower Surface c pr c pr x (a) x (b) Figure 7. Propeller/nacelle pressure distribution at Mach.15, 665 rpm: (a) α =, (b) α = 1, data digitized from [26]. The same FFA wind tunnel data was applied for validation purposes in numerical simulations [28], although there was no indication of whether the exact propeller geometry was used or not. A wake survey in terms of non-dimensionalized dynamic pressure immediately behind the propeller where x/r =.14 is shown in Figure 8. Time-averaged data match well in comparison with two other time-accurate pressure profiles. 28

50 Figure 8. Propeller/nacelle/wing slipstream dynamic pressure survey behind the propeller [28] CFD Example 2 Another dilemma in CFD validation is when the code developer only holds details of the propeller model geometry and tunnel boundary conditions, which have not been disclosed to the public. Moffitt et al. [3] compared the experimental data of a sub-scale six-bladed propeller designed by Aero Composites Inc. to the solution of a Reynolds-averaged Navier-Stokes CFD flow solver. Geometry descriptions of this investigation exclusively belong to the United Technologies Research Center (UTRC). Generally, readers are not able to verify and compare a code s ability to any other published test data for this reason. Eventually, analysts must run a series of wind tunnel tests for the purpose of individual validation. In addition to feasibility of the facility and cost of the wind tunnel testing, the experiment needs to be designed and scaled for a validation goal. The results of propeller testing and CFD analysis were compared by Moffitt using the prescribed traditional vortex theory [36]. Figure 9 shows the UTRC wind tunnel settings and computational domain for the tunnel boundaries and propeller geometry. To assess the fabricated blade geometry, a white light scan was used on three of the six propeller blades made with 29

51 maximum variations of a few thousandths of an inch. Moffitt et al. concluded that the CFD codes agreed better than the classical vortex theory, especially in predicting thrust and torque as a function of blade pitch angle. Also, they argued that the code has the ability to overcome the effects of a low Reynolds number, wall blockage, and other measurement difficulties in the predictions. Figure 9. Propeller wind tunnel model and grid domain [3]. Another CFD propeller analysis problem is using an inadequate validation method. The experiment chosen by Westmoreland et al. [29] for code validations consisted of two untwisted symmetric rotor blades at hover [43]. Although this test was comprised of a pair of rotating blades set at a five-degree angle of attack, the helicopter rotor model did not fully replicate the complex propeller geometry. Moreover, the pressure coefficients of the rotor blade surfaces were compared, not the expected propeller thrust and torque coefficients. Recognizing the existing problems in CFD propeller analysis, especially in its validation methods, the urgency to solve these issues and build confidence in CFD results is high. Chapter 3 presents a summary of the problems and goals, including the approach taken to obtain these objectives. 3

52 CHAPTER 3 PROBLEMS AND GOAL Validation is the primary means to examine the precision and reliability in analytical and computational solutions [35]. The basic method of validation is to quantify error and uncertainty of prediction in simulation and compare this with experimental data. As the examples in Chapter 2 describe, propeller analysis and prediction methods suffer from lack of extensive experimental data designed specifically for validation purposes. This chapter provides a summary of the problems and difficulties in existing propeller analysis. Furthermore, the objectives of this project and considerations made to approach the challenge are explained. 3.1 Problems in Propeller Validation Geometry Details For most validation experiments, few details on propeller, spinner, nacelle, and tunnel test section geometry are available. The absence of any of these geometric features or even accurate confirmation of the constructed model dimensions causes a severe failure in the essential physics of modeling. Especially, the complex geometry of the propeller blade requires a comprehensive instruction of reproduction or modeling procedure. Accessibility of wind tunnel data for section aerodynamic characteristics at various Reynolds numbers is also very important. A series of analysis was executed to evaluate the influence of each critical factor in design, fabrication, and testing environment. JavaProp was utilized for its convenience and its broad setup flexibility in model selections to compare results APC Thin-Electric propeller twist and chord distribution was used as the baseline. Factors found to have the most impact on the propeller performance are, in order, the following: pitch angle, chord length, section airfoil, and airfoil aerodynamics characteristics used based on its operating Reynolds number. Figure 1 to Figure 13 31

53 show sensitivity comparisons of individual variable as indicated for a generic propeller. An additional measurement of the blade deformation or calculated load of deformed components can also be helpful. Spatial dimensionality of the wind tunnel test section, as well as geometric specifications of the nacelle, spinner, and model mount, etc., must be fully documented..2.2 Δβ = Δβ =.16 Δβ = 1 Δβ = 2.16 Δβ = 1 Δβ = C T C P J J Figure 1. Sensitivity analysis of pitch angle using JavaProp c/r c/r c/r c/r c/r c/r C T.8 C P J J Figure 11. Sensitivity analysis of chord length using JavaProp. 32

54 Clark Y Flat Plate.16 Clark Y Flat Plate Eppler 193 Eppler C T C P J J Figure 12. Sensitivity analysis of propeller section airfoil using JavaProp..2.2 Re=25, Re=25,.16 Re=1, Re=5,.16 Re=1, Re=5, C T C P J J Figure 13. Sensitivity analysis of airfoil aerodynamics for ClarkY using JavaProp. 33

55 Test Conditions Boundary conditions of the experiment are also critical parameters for computational simulations that are frequently missed in validation reports. Typically, these consist of average quantities of test section freestream velocity, dynamic pressure or total pressure with static pressure, and total temperature. Essentially, all measurements are required to be calibrated for wind tunnel testing. Turbulence intensity, boundary layer thickness, and boundary layer transition are also supplemental quantities. Although it is important for CFD turbulence codes to reference these data as accurately as possible, some wind tunnel facilities are reluctant to measure or disclose detailed flow quality. Furthermore, the position of all instrumentation needs to be specified for CFD boundary condition settings. Results Lack of collective global and local measurements is evident in previous work. These are fundamental requirements in CFD validation experiments. Global quantities may be classical propeller thrust and torque coefficients, and efficiency as a function of the advance ratio. Local measurements may include nacelle surface pressure coefficients, slipstream local velocity distribution and its components, and wing surface pressure distribution. Also valuable are revolution speed, local Reynolds numbers, and freestream velocity, since they can identify the effects of coupled parameters against each other. Similarly, accuracy and limitations of individual instruments are recommended to be introduced. In addition, methods of dynamic and/or static tare and blockage corrections applied in the results must be recognized. Measurement Repeatability and Error Experimental errors, such as random and bias uncertainties in measurements, are suggested to be evaluated. An Advisory Group for Aerospace Research and Development (AGARD) 34

56 document [44] on standard wind tunnel testing has procedures for error estimation; however, they are not widely used in validation experiments. Finally, repeatability tests on the model and facility are advised, for example, duplicating the test on a different day with the same test conditions. Also, repeatability on a reconstructed model can be beneficial if cost and time allow. Exercising another wind tunnel facility with the equivalent test conditions proves that the results are independent from instrumentation bias. 3.2 Statement of Objective The objectives of this dissertation are as follows: To provide a universal geometric description as well as comprehensive experimental data on two propellers, primarily for low Reynolds number propeller performance validations. To capture critical elements of the experiment in the results. 3.3 Methods of Approach The primary purpose of this effort is to provide a database for analysts to assess the validity and accuracy of a computational analysis by providing crucial information. Considering the existing problems discussed above, the following steps were taken to achieve the objectives above: Geometry Primarily, a simple blade propeller with a constant pitch-to-diameter ratio, chord length, and thickness was tested. Then, a practical blade propeller with a varying pitch-to-diameter ratio and chord length as functions of the propeller radius was evaluated. The applied blade section airfoil profile and experimental data is well documented for a range of Reynolds numbers, particularly lower Reynolds numbers by different sources. All critical geometries are reproducible via simple programming or an accessible computer-aided design (CAD) file. The test section 35

57 geometry, nacelle, spinner, and model mount geometries are presented. The coordinate measuring machine (CMM) or 3D scan (point cloud) measured accuracy of the blades actual fabrication. Test Conditions The freestream flow was calibrated at the test section by measuring the average freestream velocity, total and static pressures, and tunnel temperature. The experimental procedure and apparatus descriptions were provided from the work of Merchant and Miller [45]. The test section inlet and outlet pressures, test section pressure gradient, and instrumentation positions were determined. Known wind tunnel flow quality, such as turbulence intensity and flow angularity, are provided. Collective Results Thrust coefficient, power or torque coefficients, and revolutions per minute for an adjustable pitch propeller with five degrees increment were obtained as global quantities. In addition, nacelle surface pressure distribution and propeller wake velocity components were measured as local quantities. Some crucial low Reynolds number effects on results were captured using a variety of rpm and freestream velocity tests. Corrected and uncorrected wind tunnel blockage data and the method of dynamic and static tares are provided. Experimental Errors Repeatability tests on the propeller model, test condition, test facility (wind tunnel), and testing procedure were implemented. Known instrumentation bias and error as well as uncertainties in measurements are quantified and documented in the report. 36

58 CHAPTER 4 EXPERIMENTAL APPARATUS As previously explained, the initial objectives and considerations were implemented in model selections and wind tunnel testing methods. Accordingly, apparatus geometries and specifications are described in detail in this chapter. The measurement system and experimental procedures are also documented in detail by Merchant and Miller [45]. 4.1 Geometry Descriptions This section provides all the geometry details necessary for modeling and reproduction purposes. This includes the wind tunnel, model installation apparatus, and all critical components such as nacelle, spinner, and propeller blade specifications Wind Tunnels and Model Installations 3 4 LSWT at Wichita State University Tests were carried out in two separate low-speed wind tunnel facilities with different test section geometries. Initially, all tests were conducted in the 3-foot by 4-foot low-speed wind tunnel (3 4 LSWT) at Wichita State University (WSU). This open-return tunnel has a rectangular eightfoot-long test section that can reach a maximum dynamic pressure of 38 pounds per square foot (psf). However, results are obtained at a dynamic pressure of no higher than 2 psf. The total pressure ring is located at the tunnel pre-section inlet, which is 2 feet long and has a cross section of 7 feet by 1 feet. The static pressure ring is at the test section entrance, and the difference of the two pressure measurements gives the tunnel dynamic pressure reading that is calibrated to the center of the test section. However, the indicated dynamic pressure is neither compensated nor corrected for the presence of the C-strut mount (also referred to as C-mount) since its blockage is 37

59 estimated to be less than.4% increase in the tunnel dynamic pressure readings. A picture of the tunnel and its geometry details including the C-mount are presented in Figure 14. Figure 14. Photo (top) and description (bottom) of 3 4 LSWT at Wichita State University. 38

60 The model was mounted on a sensor/motor platform attached to the C-mount and described in Figure 15 along with a full-model assembly photograph. The model nacelle front edge was set at ±.3 inches from the tunnel C-mount tip, the geometry of which is shown in Figure 14. The rotation axis coincides with the nacelle center line, and the distances to the plane of rotation presented here. All tests were conducted at a zero-degree angle of attack and yaw angle within accuracy of ±.2 degree. Figure 15. Model installation (top) and side view (bottom) in 3 4 LSWT. 39

61 7 1 Wind Tunnel at the National Institute for Aviation Research To minimize the tunnel blockage effect and assess facility bias error in results, more tests were performed in the Walter Beech Memorial 7-foot by 1-foot low-speed wind tunnel at the National Institute for Aviation Research (7 1 NIAR). This unique facility has a rectangular test section that is 7 feet high, 1 feet wide, and 12 feet long, with a contraction area ratio of 6 to 1 from a circular pre-section. A 2,5 horsepower (HP) fan can generate a test speed up to 24 mph and a maximum dynamic pressure of 125 psf. The closed-loop tunnel has an active heat exchanger temperature control that allows continuous full-speed operation all day long. Flow conditioning tools were implemented to reduce the turbulence intensity of the tunnel as low as.7% at 3.8 psf tunnel q in core flow regions, that is, at least a foot from any wall. The tunnel total pressure ring is located at the pre-section where the static pressure ring is at the inlet of the test section. The tunnel dynamic pressure was calibrated to the center of the test section and corrected for the presence of the C-mount. In addition to uncorrected and corrected tunnel q for blockage, two pitotstatic tubes located at the entrance and exit of the test section provide the total and static pressures for boundary condition settings. Moreover, pressure gradients along the test section are measured via pressure transducers connected to both test-section side walls. All pressure ports measured the pressure differential to the tunnel barometric pressure. The geometry details of the 7 1 NIAR wind tunnel and the model installation on the C- mount are provided in Figure 16. The model was installed far ahead of the mount so that the flow affected by its existence was minimal, as shown in Figure 17. For easy reproduction and modeling purposes, considerations were made not to expose any wiring or tubing at the vicinity of the model or the test section in both wind tunnels. 4

62 Figure 16. Description of Beech wind tunnel and C-mount assembly in 7 1 NIAR. 41

63 Figure 17. Model installation and side view in 7 1 NIAR Model Propellers PD1 Propeller Two different propeller blade geometries were designed and tested. Initially, a basic propeller geometry was considered for wind tunnel testing, which was expected to simplify the modeling and analysis effort for validations. Propeller blade PD1 was selected to have a constant pitch-to-diameter ratio (p = 12 inches, D = 12 inches, or p/d = 1), chord length, and thickness. Hence, the geometric twist angle β at 75% blade radius, β.75, was 23 calculated from equation (2.1). For the blade profile, an Eppler 387 (E387) airfoil was utilized for its high lift-todrag aerodynamic characteristics in addition to the extensive experimental data available, especially at low Reynolds numbers [46-51]. This airfoil is designed for model gliders operating at Re = where theoretical predictions and empirical drag polar agree surprisingly well [51]. The maximum thickness of this airfoil is 9.6% of the chord length and the maximum camber of 3.2%. The XFOIL program was used to extrapolate 2 profile coordinates from the original 61 42

64 points, as presented by Somers and Maughmer [46], which are tabulated in Appendix A. For its manufacturing feasibility, 5% of an inch chord length trailing edge was omitted, as presented in the coordinates. This was necessary to ensure a reasonable trailing-edge thickness. An open source CAD software written in C++ language, OpenSCAD, was used for the initial design and outline drawings [52]. Figure 18 shows the software interface. The left-hand side describes the script file that generates an object, or in this case, the propeller. Initial designs of critical geometries were rendered by OpenSCAD, the program files of which are provided in Appendix A. The advantage of this program is that it is capable of producing complex-defined shapes. The profile coordinates were imported into OpenSCAD s propeller file, and then Figure 18. PD1 propeller in OpenSCAD interface. 43

65 extruded and twisted to build the blade shape using simple scripted functions. Note that the blade was twisted at its profile s centroid, that is, x/c = 4.4% and y/c = 2.95% of an inch chord length NOT.95 inch. A detailed design was performed using SolidWorks software. The blade file exported in STL format by OpenSCAD in a metric unit system was imported into SolidWorks. Sixteen profile segments were extracted, and loft function was used to recreate the geometry for the fabrication purposes. Figure 19 shows the CAD design of the propeller blade assembly and final computer numerical control (CNC) machined products. The assembly consisted of the blade, blade root, pitch angle control plate, and pin for blade pitch angle adjustments with five degrees increment at three different β.75 settings: 23, 28, and 33. The blade was connected to the root through two stainless pins perpendicular to the longitudinal blade axis. The blade was machined from an aluminum alloy 775-T6 block. Stress analysis results show that the blade deflection under maximum loads at β.75 = 33 is.5 inch at the tip in the thrust direction. For the analysis, centrifugal force, thrust, and torque were simultaneously applied. Figure 19. PD1 Propeller blade assembly. 44

66 A 3D scan on both sides of each blade was performed to verify the accuracy of the constructed models. Figure 2 shows a very good match when comparing the final fabricated blade to the design CAD geometry, indicating that the variation is within ±.2 inch, where the accuracy of the scan system is ±.1 ~.2 inch. Figure 2. 3D scan of PD1 propeller blade, within ±.2 inch accuracy. COMP Propeller Likewise, for practical and advanced analysis efforts in validations, a complex propeller geometry COMP was considered. This propeller blade has a twist and chord length as functions of the blade radius with a constant thickness. Similar to the previous PD1 blade, the E387 airfoil was utilized. However, contrary to the 5% reduction in the PD1 s trailing edge, 1% was omitted. The coordinates of this propeller blade are presented in Appendix A. This reduction was necessary 45

67 to ensure a reasonable trailing-edge thickness of the blade since it has shorter chord length at the tip of the blade. Since OpenSCAD operates in a metric system, equations are written accordingly. However, the U.S. unit system is adopted in this document. The blade design was inspired by Hartman s 5868-R6 blade form curves, though simplified to fit equivalent polynomial functions [39]. The twist distribution β is a function of the local blade radius r as β = /r (4.1) where the propeller radius R = 6. inches or mm for equation (4.1) and β is calculated in degrees, where the reference β.75 = 15. The chord length c (mm) is also described as c = -.33r 2 +.6r (4.2) where the blade thickness remains constant relative to the chord length of 9.6% to avoid unnecessary complexity. Figure 21 shows the OpenSCAD blade design, detailed design, and fully assembled COMP aluminum blades. Twenty-four profile sections were exported as an STL file and used for the detailed design in SolidWorks. This propeller also has a variable five-degree increment pitch with four angle settings that can be manually set at the hub. The blade pitch angles can be adjusted at β.75 = 15, 2, 25, and 3. Structural analysis shows each blade can withstand a maximum centrifugal force of 77.1 lbf, 1.5 lbf thrust, and 3.1 in-lbf torque loads applied simultaneously with less than.1 inch of deflection at the tip in the thrust direction (at β.75 = 3 ). Figure 22 shows the 3D scan results for one of the blades. The CNC machining accuracy is satisfactory for such a small and thin blade and kept mostly under -.7 inches variation showed in dark purple color. 46

68 Figure 21. COMP propeller blade design and assembly without nacelle and spinner. Figure 22. 3D scan results of COMP blade within -.7 inch accuracy. 47

69 4.1.3 Model Nacelle-Spinner Similar steps were taken for the nacelle and spinner designs using OpenSCAD. The geometry script files are available in Appendix A. These components were constructed using a 3D printer using polylactic acid (PLA) filaments. The nacelle was divided into halves for easy accessibility and strapped to the sensor/motor platform. The nacelle surface had a total of 62 orifices eight around the perimeter and eight in the longitudinal direction which were connected to a pressure transducer to measure static pressure. Figure 23 shows the full CAD model assembly including important dimensions. Two pressure ports are omitted as a slot was made on the rear bottom of the nacelle for 3 4 LSWT C-mount, as shown in Figure 23. This slot was sealed for the 7 1 NIAR testing with the original design curvature part shown in Figure 24. Hub components were also constructed using the 3D printer enclosing the blade root and the angle control plate, which was installed on the motor shaft. The hub consisted of two parts top and bottom and a U-hold to tighten the propeller blades and hold the hub parts together on the motor shaft. A magnetic pickup tab was located between the hub and the nacelle. The spinner enclosed the hub assembly. The spinner was aligned carefully with the nacelle to replicate the design geometry. The gap between the spinner and the nacelle was.5 inch. Two screws were used to attach the spinner to the hub, and screw caps were designed to fill the holes and render the geometry. Considerations were made to increase the stiffness of the spinner, in order for it to withstand high rpm centrifugal forces without deflection. The blades were balanced where the center of gravity deviated within ±1.% of the blade length in order to decrease system vibration. The motor shaft and nacelle alignment were also important to reduce vibration. The gap between the motor shaft, magnetic pickup, and nacelle were sealed with brushes and tapes. The nacelle and spinner surfaces were painted and polished several times to achieve a smooth finish. 48

70 Figure 23. Nacelle assembly CAD design (dimensions in inches). Figure 24. Nacelle bottom side modification for 7 1 NIAR setup. 49

71 4.1.4 Model Setup Assessment Sensitivity analysis in the previous chapter showed that the pitch angle setting significantly influences performance. Here, a 3D scan was performed to evaluate the hub setup accuracy for a pitch that is true to the design criteria. The PD1 pitch angle set to β.75 = 23 is shown in Figure 25 for one blade s top and bottom sides. Both sides have nominal differences of less than a fifteen thousandth of an inch when compared to the CAD models. The same results are shown for the COMP blade in Figure 26. Note that the spinner and nacelle are excluded from the picture to focus on the pitch setting accuracy. In addition, Figure 27 shows the 3D scan image of the nacelle-spinner assembly when compared with the CAD design. The overall setup and manufacturing accuracy were satisfactory for such a large-scale and complex model. Maximum offset appeared in the nacelle mid-section at approximately +.7 inch that is less than 1.% of the nacelle diameter. It also shows that alignment of the spinner/hub with the nacelle was excellent, which requires an extensive setting effort. Figure 25. Top and bottom of PD1 blade 3D scan set at β.75 = 23, within +.15 inch accuracy. 5

72 Figure 26. Top and bottom of COMP blade 3D scan at β.75 = 15, within ±.2 inch accuracy. Figure 27. Both sides 3D scan of the nacelle-spinner assembly, within +.7 inch accuracy. 51

73 4.1.5 System Performance Prediction Numerical analyses were performed for the designed propellers to predict the performances, integrating JavaProp and vortex theory, as discussed in previous chapters. This also helped to set an appropriate test matrix. The results are shown in Figure 28 and Figure 29 for the two models PD1 and COMP, respectively. Since JavaProp does not have the E387 airfoil in its database, the drag polar of the E193 profile was selected with section L/D set at 3. E193 was slightly thicker with 1.2% thickness and the maximum camber of 3.% compared to the E % and 3.2% respectively. However, XFOIL aerodynamics analysis showed identical results for both airfoils. Geometry descriptions of the chord length and blade twist distribution as a function of the radius were imported into JavaProp for both propellers. The spinner area covered 3% of the propeller diameter. In addition, vortex theory was utilized based on self-written program with E387 aerodynamics data obtained from the low-turbulence pressure tunnel (LTPT) at the Langley Aerospace Research Center [47]. A linear curve estimated the Cl as a function of angle of attack α and a fourth-order polynomial curve for Cd as a function of Cl obtained from a range of α = -3 ~ 8. Hence, poststall treatment on the Cl curve was not implemented. The Cl -α and Cl -Cd relations are, respectively, Cl (4.3) C C C C C (4.4) d l l l l.3413 However, JavaProp airfoil database had a drag polar with several key parameters implemented, such as maximum lift, minimum drag coefficients in addition to post stall trend which is similar to Figure 3. 52

74 As shown, performance analysis results between the two methods vary for the PD1 model as opposed to the COMP propeller. Both thrust and torque predictions have large differences between the two analysis methods for the PD1 model. This may suggest a large flow separation, especially when the propeller is highly loaded or at lower advance ratios. On the other hand, surprisingly, both methods match very well for the COMP model for a range of advance ratios for thrust and power coefficients as well as efficiency curves. Regardless of the conclusion, analysis results provide a good estimation of the expected values. A detailed analysis at a certain test condition was also performed using same methods to study the aerodynamics characteristics along the radius for both propellers as shown in Figure 3 to Figure 31. The angle of attack, lift and drag coefficients at local radius locations were presented for one advance ratio where J =.2, and the PD1 was set to β.75 = 23, and β.75 = 2 for the COMP. Although the angle of attack curves had a similar trend for both propellers, the difference between the two methods was significant for the PD1 propeller. A substantial portion of the blade was at stall where α > 12 for the PD1, according to the E387 wind tunnel results showed in Chapter 5. Thus, the difference in post-stall treatment between the two methods was clear in lift and drag coefficient plots which also explains the PD1 performance plots disagreements. Finally, Figure 32 shows the local Reynolds number along the radius for the same advance ratio calculated by JavaProp. The Reynolds number of a significant portion of the blade was under 1, (i.e., r/r.75) which can be considered as low Reynolds number. Furthermore, this was less than 6, where r/r was.45 or less. Hence, low Reynolds number effect could cause discrepancy in the wind tunnel results as shown in Chapter 5. 53

75 JavaP Vortex.2 JavaP Vortex C P C T β = β = J J η.4 β = 23.2 JavaP Vortex Figure 28. PD1 propeller performance analysis. J 54

76 .2.2 JavaP JavaP.16 Vortex.16 Vortex C T C P β = β = J J 1 JavaP Vortex.8 η.6.4 β = J Figure 29. COMP propeller performance analysis. 55

77 JavaP Vortex 2.4 Cl JavaP Cl Vortex Cd JavaP Cd Vortex α (deg) 16 C l, C d r/r r/r Figure 3. PD1 blade radial distribution of angle of attack, lift and drag coefficients at J =.2 and β.75 = JavaP Vortex Cl JavaP Cl Vortex Cd JavaP Cd Vortex α (deg) 16 C l, C d r/r r/r Figure 31. COMP blade radial distribution of angle of attack, lift and drag coefficients at J =.2 and β.75 = 2. 56

78 2 PD1 1.6 COMP Re ( 1 5 ) r/r Figure 32. PD1 and COMP blades local Reynolds number distributions at J = Data Measurement and Process As documented by Merchant and Miller [45], the measurement system consisted of three divisions: the sensor/motor platform, instrument and power unit, and data processing devices as shown in Figure 33. The sensor/motor platform was mounted directly on the C-mount in the 3 4 LSWT and fixed at the nacelle s center line, concentric with the motor shaft. In the 7 1 NIAR, it was connected to the C-mount via an adaptor steel pipe, as shown previously in Figure 16. The sensor or balance measured two components tension/compression and torque and had a combined nonlinearity and hysteresis of ±.5% for a rated output of 2 mv/v. The capacity of the balance was 5 lb for thrust and 5 in-lb for torque directions. Two 1,2-watt DC brushed electric motors with identical specifications were randomly switched between tests to include motor performance bias in results. The motor was set on a rigid adaptor specifically designed to connect the motor to the load cell. The motor holder also encased a 1-VDC magnetic-pickup to measure and record the propeller rpms in proximity of a spinning metallic 57

79 Figure 33. Data measurement and processing block diagram. tab measuring a maximum of 2, targets/s. The motor temperature was monitored by a thermocouple attached to the surface of the motor. An insulated adaptor isolated the balance from the motor s thermal effects. However, minor heat transfer to the balance may have been picked up as loads when a high shaft power was required. Although these thermal effects on measurements are insignificant, they are quantified as thermal error in the following section. Signals from the balance were sent to a conditioner/amplifier located outside the test section and then to an array of optical isolators. Finally, the signal processing and reduction was implemented in the computer and Microsoft Excel software sheet via a 16-bit analog-to-digital card. The data acquisition and reduction system, or DAQ, established by Merchant and Miller [45] in 26, was written in Visual Basic language. The reduction process incorporated the tunnel blockage correction for a given propeller diameter and tunnel cross section as described by Glauert 58

80 [53]. In addition to the load calculations, the DAQ generated non-dimensionalized propeller performance properties, such as propeller efficiency, coefficients of thrust and torque, etc. Based on sensitivity studies performed by Merchant, the sample rate was set to 5, Hz per channel with a sample period of 8 seconds. Details of the DAQ are discussed in Merchant s master s thesis [54]. The tunnel dynamic pressures were measured and recorded differently for the two tunnels. At the 3 4 LSWT, the tunnel dynamic pressure recording was integrated into the DAQ and readouts were obtained directly from a high precision ±1 psid pressure transducer into the data reduction system. The tunnel dynamic pressure from the DAQ was compared with the test section pitot-static probe for a range of dynamic pressure and found to be within ±5.% of the readings. For the nacelle pressure port measurements, a 16-channel Scanivalve with a full scale of ±1 in H2O differential was used. The Scanivalve was set to a different DAQ with a sample rate of 4 Hz and sample period of 5 seconds, which measured the differential of the local pressure and tunnel static ring pressure. Data were synchronized with tunnel dynamic pressure measurements after the test was completed to obtain the pressure coefficients. In the case of the 7 1 NIAR, the tunnel dynamic pressure was recorded through the tunnel system separately but collected simultaneously with the load measurements. Data were added into the DAQ once the testing ended. All pressure transducers read the differential to the tunnel barometric pressure including tunnel dynamic pressure, nacelle pressure, test section wall pressure, test section inlet, and outlet pitot tubes. The nacelle pressure ports were connected to a 32-channel electronic pressure scanner embedded inside the nacelle with a full scale of ±2.5 psid at a 15 Hz sample rate. The same rate was used for the wall measurements. Entrance and exit probes as well as a five-hole probe used for the wake survey were sampled at 5 Hz via a ±1. psid Scanivalve. 59

81 The sample period for all tests was 5 seconds, except for the wake survey five-hole probe, which was 1 second. The cone head five-hole probe had a 6 flow angle receptivity System Calibration The load cell was calibrated for thrust and torque using known weights, as shown in Figure 34 for the thrust direction. The balance had a linear trend when loads were applied or removed from the apparatus. Interactions between the load readings were accounted for in the final balance behavior matrix. The calibration procedure frequently was performed to ensure the accuracy of the load cell and DAQ. When a 5 lb load was applied in the thrust direction, the accuracy of the system was +1.5% of thrust readings, and for a 1 lb load, this was +1.% of thrust readings. Based on balance specifications, the total error for hysterisis, nonlinearity, and nonrepeatability was +.55% of rated output. Similar results were observed in the torque measurements. The rpm sensor measurements were also cross-checked with a calibrated strobe light. The DAQ rpm readouts had an accuracy of ±.3%. Figure 34. Load cell calibration for thrust. 6

82 The two tunnel dynamic pressures are also calibrated to the one measured at the center of the test sections. For the tunnel total pressure and temperature in the 3 4 LSWT, the ambient readouts were input into the DAQ to calculate air density where the deviation was ±1.% of readings in a standard day similar test conditions. The indicated dynamic pressure was not corrected for the blockage of the C-mount, which is estimated to be less than.4% increase in the tunnel dynamic pressure readings. The angle of attack offset was within ±.2 from zero. At the 7 1 NIAR wind tunnel, an instant tunnel barometric pressure and ambient temperature was measured internally for each tunnel dynamic pressure. All pressure measurements are the differential to the barometric pressure, and system transducers and gauges were calibrated frequently. The accuracy of the 7 1 tunnel dynamic pressure was.1 psf or better when q > 2.5 psf. The tunnel dynamic pressure can be cross-checked with the readouts of two pitot-static probes located at the entrance and the exit of the test section, especially for q < 2.5 psf. Flow uniformity and temperature variation across the 7 1 test section is plotted in Figure 35. The highest investigated tunnel dynamic pressure at 1 psf is where the temperature variation is at peak because of the wall friction. The tunnel cross section velocity distribution varies the most at the lowest tunnel dynamic pressure. However, results show an excellent flow quality at q = 3.8 psf with variation less than ±1.% of the velocity readings. Corrected tunnel dynamic pressure due to existence of the C-mount is used for the 7 1 tunnel data comparisons. Although the difference between uncorrected and corrected data for the presence of the C-mount was very small, both data are available in Appendix B. The angle of attack α was measured by a calibrated inclinometer prior to each test and a zerodegree offset was expected to be within ±.2. The five-hole probe was also calibrated at two flow speeds of 16 ft/s and 328 ft/s or Mach = 3. by the Aeroprobe Corporation. The measurement 61

83 accuracy for the flow angles was up to.4, and.8% of the total flow velocity readings. The fivehole probe calibration details and manual were accessible through the Aeroprobe website [55]. Measurement errors and accuracy are also summarized and tabulated in the following data analysis section. Figure 35. Test section velocity and temperature variations of 7 1 NIAR (courtesy of NIAR). 62

84 4.2.2 Data Corrections and Tares As explained, corrections due to the propeller blockage were incorporated into the results for the presented global quantities and tunnel data comparisons. Although an increase in the velocity increment due to propeller blockage of the tunnel test section should be less than a few percent except for the static runs, corrections due to the effect are considered. Nevertheless, uncorrected data for the blockage are provided for the reader s discretion for validation purposes. Since the propeller diameter was the same for both propellers, the only variable for the blockage correction in DAQ was the tunnel cross section. According to the study by Merchant [54], other tunnel corrections such as solid blockage are negligible, since the total uncertainty is less than.3%. The effect of instruments or support or even parts of a wind tunnel model on measurements is called tare or interference. Two different types of tare were considered here: static tare and dynamic tare. Static tare, which was integrated into the DAQ Wind-Off-Zero (WOZ) module, was considered for the weight of the system attached to the sensor and also for the minor temperature effects. The average of two WOZ readings, the beginning and the end of each run with ten measurements, was subtracted from each collected data. The difference of these two readings in terms of load was treated as thermal effect error since weight distribution variation before and after runs is zero. On the other hand, dynamic tare was investigated to mainly exclude the drag effect of the spinner and study the actual loads generated by the propeller, mainly thrust. A similar method as that of Ol et al. [24] was used here. Sweeps of tunnel dynamic pressure with all models except the propeller were tested at certain rpms. Drag was measured and curve-fitted as a function of the tunnel dynamic pressure, and then added to the specified propeller s thrust data. This approach 63

85 makes it applicable to a wide range of tunnel speeds. The results were also calculated and presented in coefficient forms. Dynamic tare for torque measurements, which is caused by spinner/hub and shaft power only, was neglected, since it was less than 1% of the readings at maximum with the propeller on. The same method was taken for the no-spinner no-nacelle models for comparison. Note that dynamic tare is only applied to the data in the Dynamic Tare section in Chapter 5. The intrusive effect of the five-hole probe on the flow was not considered here (see Figure 36). These effects are believed to be most severe in the vicinity of the slipstream boundaries and quite difficult to estimate, according to Samuelsson [42]. Nonetheless, pressure values in other regions, that is, between the blade tip and the root, are considered true. Figure 36. Five-hole probe wake survey at 7 1 NIAR wind tunnel Test Procedure A sweep of tunnel dynamic pressure at each run, which consists of ten data collections, was set to cover the propeller performance curves for a range of advance ratio. The rpm was pre-set by a fixed voltage on the power supply to the motor, and variation of the amperage was logged in order to monitor the shaft power delivered for the operator s reference. Shaft power varied, 64

86 depending on the individual system wiring setup and motor electrical efficiency. The maximum voltage and amperage delivered were set to the motor specifications in order to avoid extreme motor heat or damage. Note that the rpm increases slightly as the tunnel q increases for the constant voltage delivered, although the effect was nominal for the non-dimensionalized propeller performance parameters. The tunnel q step size was predetermined by Merchant; nonetheless, supplementary data may comply to fill the voids in the performance curves. In those cases, repeated runs were performed with a shift in the tunnel q set. For the static thrust measurements, the initial tunnel dynamic pressure was set to < q.1 psf, in order to create a gentle airflow so the propeller was not rotating in its own wake. The spinner and nacelle must be disassembled in order to obtain access to the hub and propeller pitch angle setting. The spinner has two screw caps to maintain the designated curvature. All exposed small gaps such as ones between the blade and spinner or nacelle screw holes were covered with Scotch tape to avoid any flow disturbances. Scotch tape is a convenient and inexpensive tool and found to be almost as effective as clay for small hole treatments in laminar regions [56]. Model gaps must be re-taped prior to the next run. Meanwhile, an air tube was ducted into the nacelle; this tube can inject compressed air towards the motor, in order for it to cool down as the following test preparations are made. Note that the cooling system was shut off and did not operate while testing was in progress. For pressure measurements in the 3 4 LSWT, a total of 62 nacelle pressure ports were divided into four test runs for each pitch angle setting since the Scanivalve has only 16 channels. The Scanivalve is located right outside and underneath the test section to increase the system sensitivity in pressure perturbation measurements. In the 7 1 NIAR, a smaller 32-channel pressure scanner was enclosed inside the nacelle, thus allowing twice as much data acquired per 65

87 run. For test time constraints, only half of the nacelle pressure survey was performed. In both tunnels, the reference pressure port was connected to the tunnel static ring to measure freestream static pressure, p, and each channel to the local nacelle pressure ports, p, to obtain the differential pressures. The final results are presented in the form of pressure coefficients. All wiring and tubing were run internally through the C-mount to maintain the overall simplicity in geometry (see Figure 37). Figure 37. Inside the nacelle in each tunnel: 7 1 NIAR (left) and 3 4 LSWT (right). 4.3 System Evaluations System evaluations were performed prior to the model experimentation in order to quantify and qualify the reliability of the data presented in the following chapter. It was critical to analyze the total amount of experimental error in the system especially for this study. The aim of this section is to identify all the known errors and reveal them to the readers. By using the 3D-scanning method, the model fabrication quality was also demonstrated and compared to the design geometry. Additionally, predictions for the designated propellers performance were made utilizing JavaProp and vortex theory analysis. Instrument accuracy is addressed in the system calibration section. Other uncertainties in measurements can also affect results, thus increasing the overall experimental error. Bias in the 66

88 facility or system measurement or test procedure can cause systematic or fixed error, which is typically proportional to the true value and can be eliminated by identifying the accuracy of the system. On the other hand, random error is usually unpredictable and depends on repeatability of the system measurement. Typically, a large number of repeated tests may quantify random error, providing a normal distribution and standard deviation. Table 1 provides a summary of the accuracy and error that is known. The statistical measurements shown are the maximum value in each data set. Therefore, typically the system is more accurate than listed here. A commonsense analysis of the data suggests that error in the final results equal the combined maximum error of all parameters in the most detrimental way [57]. Accuracy, standard deviation, and thermal errors for thrust and torque measurements are based on observed readouts or readings (RD). Other parameters refer to the model specifications from the manufacturer based on the rated output (RO) or the full scale (FS). TABLE 1 SUMMARY OF SYSTEM ACCURACY, PRECISION, AND ERROR Unit Accuracy RD STDV RD Thermal Error Instrument Errors Thrust lb +1.5% ±.15% ±1.5% RD ±.55% RO Torque in-lb +1.% ±.1% ±1.% RD ±.55% RO rpm rpm ±.3% ±1.% - ±.5% 3 4 LSWT Tunnel q 3 4 LSWT Scanivalve 7 1 NIAR Tunnel q 7 1 NIAR Scanner Five-Hole Probe lb/ft 2 ±5.% where q > 5. psf ±9.% ±1 C (at sensing element) lb/ft 2 - ±5.% ±.1% FS lb/ft 2 ±4.% where q > 2.5 psf ±.1% FS (1. psid) ±.2% FS (±1 in H2O) N/A - - lb/ft 2 - N/A ±.4% FS/ C ft/s <.4 angles, <.8% total velocity N/A ±.1% FS/ C ±.6% FS (±2.5 psid) ±.12% FS (±1. psid) 67

89 Note that the standard deviation of the 3 4 LSWT Scanivalve is high. This is due to the rapid pressure fluctuations of the nacelle surface that is located behind the propeller caused by the presence of the propeller wake. The 7 1 wind tunnel DAQ is not set to output standard deviation for the pressure systems. Initial tests demonstrate the quality and repeatability of data obtained at the 3 4 LSWT to assess the random error in the system. Tests were executed by different operators on separate days. Figure 38 to Figure 4 show four test performances of the same off-the-shelf APC Thin- Electric propeller. The first number in the APC propeller specification indicates its diameter in inches and the second number is its pitch in inches. The efficiency η, along with CT and CP, are plotted against J at approximately 7,5 ~ 8,5 rpm, and each compares well, showing system repeatability. The Reynolds number at 75% of the radius (Re.75) is also plotted as a function of J to show the test conditions of each run. By default, all data shown are corrected only for tunnel blockage WSU Run 324 WSU Run 368 WSU Run 371 WSU Run C T Figure 38. Thrust coefficient repeatability test of APC Thin-E propeller in 3 4 LSWT. J 68

90 .2.16 WSU Run 324 WSU Run 368 WSU Run 371 WSU Run C P J 1.8 WSU Run 324 WSU Run 368 WSU Run 371 WSU Run η J Figure 39. Power coefficient repeatability test and efficiency of APC Thin-E tests in 3 4 LSWT. 69

91 2 1.6 WSU Run 324 WSU Run 368 WSU Run 371 WSU Run 418 Re.75 ( 1 5 ) J Figure 4. Reynolds number (Re.75) repeatability test of APC Thin-E in 3 4 LSWT. The WSU 3 4 LSWT and 7 1 NIAR data are compared for the same APC Thin- E propeller in Figure 41. Results show a good comparison indicating nominal bias error from the two facilities and partially different DAQ systems, as explained previously. Figure 42 compares the 3 4 LSWT results with two other wind tunnel test data for a 1 7 APC thin-e propeller at 6,5 rpm. Data from the Basic Aerodynamics Research Tunnel (BART) at Langley Aerospace Research Center, which is digitized from the Ol et al. study [24], did not specify the rpm. Although the results seem scattered, the authors state that no drastic variation resulted between 6, and 8, rpm. WSU s data agrees with BART data and also data from the University of Illinois at Urbana-Champaign (UIUC), which are plotted in Figure 42 and Figure 43 for APCs 1 7, 8 8, and Thin-E. It is shown that the integrated DAQ is repeatable and comparable with other wind tunnel measurements throughout a series of testing. 7

92 .2 3x4 LSWT Run x1 NIAR Run C T J 1 3x4 LSWT Run x1 NIAR Run η J Figure 41. Tunnel data comparison of 3 4 LSWT and 7 1 NIAR for APC Thin-E. 71

93 .2 WSU 6,5 rpm.16 UIUC 6,5 rpm BART.12 C T J 1 WSU 6,5 rpm.8 UIUC 6,5 rpm BART.6 η J Figure 42. Tunnel data comparison from WSU, BART [24], and UIUC [58] for 1 7 APC Thin-E propeller. 72

94 .2 12x12 WSU 12x12 BART.16 8x8 BART 8x8 UIUC.12 C T J 1 12x12 WSU 12x12 BART.8 8x8 BART 8x8 UIUC.6 η J Figure 43. Tunnel data comparison from WSU, BART [24] and UIUC [58] for and 8 8 APC Thin-E. 73

95 CHAPTER 5 RESULTS Test results for the model propellers are presented in this chapter. The plotted results are reduced data, which account for the blockage corrections and thermal-static tares, as discussed in the previous chapter for tunnel comparisons. Load measurements, nacelle pressure distributions, and a wake survey were performed on two propeller blades in two different wind tunnels. Application of the dynamic tare (spinner drag effect) and nacelle-spinner effects on performance will be discussed later in this chapter. Finally, the performance results are compared with the predicted values. 5.1 Propeller Performance This section shows traditional performance plots such as thrust and torque coefficients with efficiency curves against a range of advance ratios. Two different propeller blades were examined and results are separated into subsections. However, results for the two wind tunnels are compared in the same corresponding graphs PD1 Results of Propeller Performance As discussed earlier, a PD1 propeller blade has a constant twist, p/d = 1, as well as constant chord length and thickness throughout its six-inch radius. Hence, the design twist angle at 75% radius, β.75 is 23. Additional tests were conducted at 28 and 33 pitch angles at approximately 5, rpm (i.e., 4,8 to 5,6 rpm), which is equivalent to Re.75 = 9, to 12, for a range of advance ratios. Thrust and power coefficients as well as efficiency results are shown for the 3 4 LSWT and 7 1 NIAR wind tunnels in Figure 44 to Figure 46. Figure 47 shows PD1 performance at three different revolution speeds, i.e., 4,, 5, and 6, rpms, in order to evaluate the Reynolds number (Re.75 = 75, ~ 13,) dependency, where β.75 = 23. Runs were repeated 74

96 on two or three different days for both tunnels, with test apparatus disassembled and reassembled, to check the system repeatability. For such a low Reynolds number range, data repeatability can be confirmed for each tunnel. Thrust coefficients for higher pitch angles agree well for both wind tunnels, that is, except for β.75 = 23, where the 7 1 NIAR results are about 4% on average higher than 3 4 LSWT (Figure 44 to Figure 47). Also, power coefficients results in the 7 1 NIAR for all pitch settings are 5 ~ 6% higher than the 3 4 LSWT on average. Several reasons may be causing this outcome. First, the total uncertainty of the system at its worst is estimated to be about 5%, which includes the accuracy, thermal error, and other instrument and random errors. However, this is unlikely the case, since COMP blade results shown in the next section are consistent for both tunnels. Next, and most likely, the tunnel systematic bias was caused by the difference in tunnel flow characteristics at certain test conditions. As presented previously, the flow quality of the 7 1 NIAR tunnel is well known, reducing the tunnel turbulence intensity. On the other hand, the 3 4 LSWT is expected to have higher turbulence intensity than the 7 1 NIAR tunnel. Blade s local Reynolds number depends on the advance ratio and the section location and chord length, nonetheless, the higher flow turbulence intensity increases the overall effective Reynolds number. Higher turbulence intensity causes earlier transition by tripping the flow, and as a result, the effective Reynolds number is higher than lower turbulence flow. Figure 48 shows E-387 airfoil data among three different wind tunnels at two Reynolds numbers [47]. The airfoil aerodynamic characteristics vary between tunnels at Re = 6, with a possible separation bubble at α 6 for LTPT and Delft results. This demonstrates the effect of the tunnel flow characteristics on the aerodynamics performance, especially at lower Reynolds numbers. Moreover, post stall behavior 75

97 varies at higher angles of attack for each tunnel (i.e., α 12 ) which is also possibly caused by the reason explained above. The vast majority of the blade section operates at Re 1, at lower advance ratios as explained in previously. For example, Re.45 6, at J =.2, that is the local Reynolds number at 45% of the blade radius. In addition, both JavaProp and vortex theory analysis results indicated that blade section angles of attack were higher than 12 at lower advance ratios (i.e., J 1.) especially for r/r =.7 or less regions. This implies that separation or stall, at least for a portion of the blade. Also shown in Figure 28 and Figure 29, vortex theory and JavaProp predictions did not match well for the PD1 as opposed to the COMP results. The reason can be explained by the post stall treatment, that is, the difference in the drag polar of the two methods which may cause a similar outcome by operating at different effective Reynolds numbers produced at individual wind tunnels. As will be discussed in the following sections, the wake survey results show a possible flow separation region in the vicinity of the root for β.75 = 23. This region can be smaller or rather different in the 3 4 LSWT based on the tunnel flow characteristics or at the higher Reynolds numbers causing a change in performance curves. Higher pitch settings thrust coefficients are more consistent between the two tunnels because the section angles of attack are dominantly at post stall. Therefore, tunnel flow characteristics have minimal impact on the results. The gap between the tunnels data diminishes at higher advance ratios also supports this argument, resulting lower section angles of attack for the same pitch settings. Nonetheless, it is fair to say that the efficiency curves are consistent for both tunnels. In contrast, propeller performances are consistent for the COMP blade in both tunnels. This is caused by significantly lower pitch setting throughout the blade sections and relatively low section angles of attack. The COMP results are shown in the following section. 76

98 x4 Run 1 3x4 Run 2 3x4 Run 3 7x1 Run 1 7x1 Run 2 7x1 Run x4 Run 1 3x4 Run 2 3x4 Run 3 7x1 Run 1 7x1 Run 2 7x1 Run 3 C P C T J J 1 3x4 Run 1.8 3x4 Run 2 3x4 Run 3 7x1 Run 1.6 7x1 Run 2 7x1 Run 3 η J Figure 44. Coefficients CT, CP, and η against J for PD1 at 5, rpm, where β.75 =

99 x4 Run 1 3x4 Run 2 3x4 Run 3 7x1 Run 1 7x1 Run x4 Run 1 3x4 Run 2 3x4 Run 3 7x1 Run 1 7x1 Run 2 C P C T J J η.4 3x4 Run 1 3x4 Run 2 3x4 Run 3.2 7x1 Run 1 7x1 Run J Figure 45. Coefficients CT, CP, and η against J for PD1 at 5, rpm, where β.75 =

100 x4 Run 1 3x4 Run 2 3x4 Run 3 7x1 Run 1 7x1 Run 2.2 3x4 Run 1.2 3x4 Run x4 Run 3 7x1 Run 1 C P.16 7x1 Run C T J J 1.8 η x4 Run 1 3x4 Run 2 3x4 Run 3 7x1 Run 1 7x1 Run J Figure 46. Coefficients CT, CP, and η against J for PD1 at 5, rpm, where β.75 =

101 x4 4 rpm 3x4 5 rpm 7x1 4 rpm 7x1 5 rpm 7x1 6 rpm x4 4 rpm 3x4 5 rpm 7x1 4 rpm 7x1 5 rpm 7x1 6 rpm C P C T J J 1 3x4 4 rpm 3x4 5 rpm.8 7x1 4 rpm 7x1 5 rpm 7x1 6 rpm.6 η J Figure 47. Coefficients CT, CP, and η against J for PD1 at 4, ~ 6, rpm, where β.75 = 23. 8

102 Re = 6, Re = 1, C l.4 C l.4 Stuttgard Stuttgard Delft Delft LTPT LTPT α (deg) α (deg) Figure 48. Eppler 387 airfoil wind tunnel results comparison at two Reynolds numbers, data digitized from [47]. 81

103 5.1.2 COMP Results of Propeller Performance This propeller blade has a varying twist distribution and chord length as a function of radius with a constant thickness ratio, which was specified previously. The design blade twist angle at 75% radius, β.75 is 15. The blade s variable pitch was set at additional three different angles: 2, 25, and 3 at.75r. Figure 49 to Figure 52 show CT, CP, and η as a function of J at approximately 6, rpm (i.e., between 5,8 and 6,4 rpm), which is also equivalent to Re.75 = 9, to 12,. All tests are repeated at the two facilities on different days. Results shown in Figure 53 verify the Reynolds number (Re.75 = 65, ~ 12,) independency for β.75 = 2 for a range of advance ratio. In contrast to the PD1 results, the COMP performance curves agree well for both wind tunnels. This is an ideal outcome for validations purposes. In general, the COMP propeller consumes significantly less power relative to the PD1. Also, a higher efficiency of 85% is obtained for β.75 = 25 and 3. Note that a few percent shift in the power coefficient is detected between the tunnel results for a blade pitch at β.75 = 3. It appears that a systematic gap between two tunnels increases as the pitch angle increases. Consequently, the torque measured has increased, as shown in Figure 52. Overall, the COMP performance curves are consistent and repeatable throughout all pitch settings. 82

104 .2 3x4 Run 1.2 3x4 Run x4 Run 2 3x4 Run x4 Run 2 3x4 Run 3 7x1 Run 2 7x1 Run x1 Run x1 Run 2 C T C P J J 1 3x4 Run 1.8 3x4 Run 2 3x4 Run 3 7x1 Run 1.6 7x1 Run 2 η J Figure 49. Coefficients CT, CP, and η against J for COMP at 6, rpm, where β.75 =

105 .2.2 3x4 Run 1 3x4 Run x4 Run 2 3x4 Run x4 Run 2 3x4 Run 3 7x1 Run 1 7x1 Run x1 Run x1 Run 2 C T C P J J 1 3x4 Run 1.8 3x4 Run 2 3x4 Run 3 7x1 Run 1.6 7x1 Run 2 η J Figure 5. Coefficients CT, CP, and η against J for COMP at 6, rpm, where β.75 = 2. 84

106 .2.2 3x4 Run 1 3x4 Run x4 Run 2 3x4 Run x4 Run 2 3x4 Run 3 7x1 Run 1 7x1 Run x1 Run x1 Run 2 C T C P J J 1 3x4 Run 1.8 3x4 Run 2 3x4 Run 3 7x1 Run 1.6 7x1 Run 2 η J Figure 51. Coefficients CT, CP, and η against J for COMP at 6, rpm, where β.75 =

107 x4 Run 1 3x4 Run 2 3x4 Run 3 7x1 Run 1 7x1 Run x4 Run 1 3x4 Run 2 3x4 Run 3 7x1 Run 1 7x1 Run 2 C T C P J J 1 3x4 Run 1.8 3x4 Run 2 3x4 Run 3 7x1 Run 1.6 7x1 Run 2 η J Figure 52. Coefficients CT, CP, and η against J for COMP at 6, rpm, where β.75 = 3. 86

108 x4 4rpm 3x4 5rpm 3x4 6rpm 7x1 4rpm 7x1 5rpm 7x1 6rpm x4 4rpm 3x4 5rpm 3x4 6rpm 7x1 4rpm 7x1 5rpm 7x1 6rpm C T C P J J 1 3x4 4rpm.8 3x4 5rpm 3x4 6rpm 7x1 4rpm.6 7x1 5rpm 7x1 6rpm η J Figure 53. Coefficients CT, CP, and η against J for COMP at 4, ~ 6, rpm, where β.75 = 2. 87

109 5.2 Nacelle Pressure Distribution This section presents the nacelle surface pressure distribution along the longitudinal axis in non-dimensional forms, i.e., pressure coefficient cpr, and x/l. The origin of the coordinate system is the nacelle upstream leading edge at x/l =, as shown in Figure 54. This coordinate system is applied to all the following results. Longitudinal stations were divided into eight segments with x/l =.118 increments, where x is the local distance from the nacelle upstream leading edge, and L is the length of the nacelle. Both side walls of the 7 1 NIAR entire test section pressure coefficients are also plotted against non-dimensional distance l from the entrance of the test section showing the test section pressure gradient at different advance ratios. The azimuth angle Φ represents the nacelle pressure port angle, where 12 o clock is at Φ =, and has an increment of 45 in the clockwise direction about the longitudinal axis or the axis of rotation when looking downstream. Note that both propellers also rotate clockwise when looking downstream. All static pressure ports are perpendicular to the nacelle surface. Figure 54. Nacelle coordinate system. 88