Dissertations and Theses 5-2019 Low-Tip-Speed High-Torque Proprotor Noise Approximation for Design Cycle Analysis Xavier G. Santacruz Follow this and additional works at: https://commons.erau.edu/edt Part of the Aerospace Engineering Commons Scholarly Commons Citation Santacruz, Xavier G., "Low-Tip-Speed High-Torque Proprotor Noise Approximation for Design Cycle Analysis" (2019). Dissertations and Theses. 451. https://commons.erau.edu/edt/451 This Thesis - Open Access is brought to you for free and open access by Scholarly Commons. It has been accepted for inclusion in Dissertations and Theses by an authorized administrator of Scholarly Commons. For more information, please contact [email protected]. LOW-TIP-SPEED HIGH-TORQUE PROPROTOR NOISE APPROXIMATION FOR DESIGN CYCLE ANALYSIS A Thesis Submitted to the Faculty of Embry-Riddle Aeronautical University by Xavier G. Santacruz In Partial Fulfillment of the Requirements for the Degree of Master of Science in Aerospace Engineering May 2019 Embry-Riddle Aeronautical University Daytona Beach, Florida iii ACKNOWLEDGMENTS I would like to take this opportunity to write words of appreciation to all of those who made this endeavour possible. First and foremost is to my loving wife, Karen, who endured this research as if it had been her own. Not only by tolerating long nights and reduced attention, but also by providing selfless support and encouragement throughout these years. To my advisor, Dr. Richard Anderson, for enabling me to pursue research ac- tivities at the Eagle Flight Research Center, granting me the graduate research as- sistanceship, and providing valuable counsel. To the members of my committee, Dr. J. Gordon Leishman and Dr. Anastasios Lyrintzis, for providing invaluable guidance and support through the learning process of subject areas which I was not familiar with at the beginning. To Dr. Kenneth Brentner, from Pennsylvania State Univer- sity, for providing an executable version of his famous noise approximation algorithm PSU-WOPWOPv3, as well as aid and insight when available. To all of my new friends who endured this process with me and without whom my time spent at the university would not have been enjoyable. To old friends who provided not only encouragement but word of advice. Lastly but most importantly, to my parents, as this degree and subsequent work would not have been possible without their constant support and stimulation. iv TABLE OF CONTENTS Page LIST OF TABLES :::::::::::::::::::::::::::::::: vi LIST OF FIGURES ::::::::::::::::::::::::::::::: vii SYMBOLS :::::::::::::::::::::::::::::::::::: x ABBREVIATIONS :::::::::::::::::::::::::::::::: xii ABSTRACT ::::::::::::::::::::::::::::::::::: xiii 1 Introduction :::::::::::::::::::::::::::::::::: 1 1.1 Motivation :::::::::::::::::::::::::::::::: 1 1.2 Literature Review :::::::::::::::::::::::::::: 2 1.2.1 Rotating Blade Noise :::::::::::::::::::::: 2 1.2.2 Propeller Theory :::::::::::::::::::::::: 5 1.2.3 Rotating Blade Aerodynamics ::::::::::::::::: 6 1.3 Problem Statement ::::::::::::::::::::::::::: 8 1.4 Objectives :::::::::::::::::::::::::::::::: 9 1.5 Presented Work Outline :::::::::::::::::::::::: 10 2 Methodology :::::::::::::::::::::::::::::::::: 12 2.1 Theory :::::::::::::::::::::::::::::::::: 12 2.1.1 Rotor Aeroacoustics :::::::::::::::::::::: 12 2.1.2 Blade Element Momentum Theory :::::::::::::: 16 2.2 Implementation Overview ::::::::::::::::::::::: 24 2.2.1 PSU-WOPWOP :::::::::::::::::::::::: 25 2.2.2 Xfoil :::::::::::::::::::::::::::::: 25 2.2.3 Interface ::::::::::::::::::::::::::::: 26 2.2.4 Flow Diagrams ::::::::::::::::::::::::: 27 2.3 Parameter Sensitivity :::::::::::::::::::::::::: 30 2.3.1 Grid Resolution ::::::::::::::::::::::::: 30 2.3.2 Data Points Sensitivity ::::::::::::::::::::: 36 2.3.3 Time step Sensitivity :::::::::::::::::::::: 38 2.4 Validation :::::::::::::::::::::::::::::::: 39 2.4.1 Blade Aerodynamics :::::::::::::::::::::: 39 2.4.2 Noise ::::::::::::::::::::::::::::::: 44 3 Results and Discussion :::::::::::::::::::::::::::: 48 3.1 Low RPM :::::::::::::::::::::::::::::::: 51 3.2 Medium RPM :::::::::::::::::::::::::::::: 53 3.3 High RPM :::::::::::::::::::::::::::::::: 55 4 Conclusion ::::::::::::::::::::::::::::::::::: 60 v Page 4.1 Limitations ::::::::::::::::::::::::::::::: 61 4.2 Future Work ::::::::::::::::::::::::::::::: 63 REFERENCES :::::::::::::::::::::::::::::::::: 64 A Appendix - Sensitivity Analysis Tables ::::::::::::::::::: 68 B Appendix - Algorithm Structure and Details :::::::::::::::: 74 B.1 Structure and Details :::::::::::::::::::::::::: 74 B.2 Running Script ::::::::::::::::::::::::::::: 75 B.3 Geometry Input Scripts :::::::::::::::::::::::: 77 B.3.1 Environmental and Flight Properties ::::::::::::: 78 B.3.2 Rotor Properties :::::::::::::::::::::::: 78 B.3.3 Blade Properties :::::::::::::::::::::::: 79 B.3.4 Custom Aeroacoustic Options ::::::::::::::::: 80 B.3.5 Pre-defined Blade Geometries ::::::::::::::::: 81 B.4 Main Script ::::::::::::::::::::::::::::::: 85 B.5 Blade Element Theory Function :::::::::::::::::::: 87 B.6 Xfoil Function ::::::::::::::::::::::::::::: 90 B.6.1 Execute Xfoil ::::::::::::::::::::::::: 91 B.6.2 Interpolation of Aerodynamic Coefficients :::::::::: 93 B.7 Blade Plotting and Data Processing Function :::::::::::: 95 B.7.1 Interpolation of CP ::::::::::::::::::::::: 97 B.8 WOPWOP Function :::::::::::::::::::::::::: 98 B.8.1 Case Files :::::::::::::::::::::::::::: 99 B.8.2 Geometry Input File :::::::::::::::::::::: 99 B.8.3 Loading Input File ::::::::::::::::::::::: 104 B.8.4 Running WOPWOP :::::::::::::::::::::: 104 B.8.5 Reading WOPWOP results :::::::::::::::::: 105 C Appendix - Source Code Listings :::::::::::::::::::::: 106 C.1 runProp.m script :::::::::::::::::::::::::::: 106 C.2 geometry.m script :::::::::::::::::::::::::::: 107 C.3 blade calculations.m script ::::::::::::::::::::::: 108 C.4 BEMT v0b.m script :::::::::::::::::::::::::: 111 C.5 xfoil.m script :::::::::::::::::::::::::::::: 115 C.6 aerocalcs.m script :::::::::::::::::::::::::::: 122 C.7 wopwop.m script :::::::::::::::::::::::::::: 126 C.8 readBinPatch.m script ::::::::::::::::::::::::: 142 C.9 blade plotting.m script ::::::::::::::::::::::::: 146 vi LIST OF TABLES Table Page 2.1 Grid Sensitivity Test Matrix :::::::::::::::::::::::: 31 2.2 Time Step and Data Points Sensitivity Test Matrix ::::::::::: 37 3.1 Result Analysis Matrix ::::::::::::::::::::::::::: 51 3.2 Perceived Noise Level - Location 1, Low RPM :::::::::::::: 52 3.3 Perceived Noise Level - Location 2, Low RPM :::::::::::::: 52 3.4 Perceived Noise Level - Location 1, Medium RPM :::::::::::: 53 3.5 Perceived Noise Level - Location 2, Medium RPM :::::::::::: 54 3.6 Perceived Noise Level - Location 1, High RPM :::::::::::::: 55 3.7 Perceived Noise Level - Location 2, High RPM :::::::::::::: 57 3.8 Perceived Noise Level - Location 3, High RPM :::::::::::::: 58 A.1 Grid Sensitivity Total Run Time, No Weighting ::::::::::::: 68 A.2 Grid Sensitivity Total Run Time, Tip Weighted ::::::::::::: 68 A.3 Grid Sensitivity Total Run Time, No Bias vs. Tip Bias ::::::::: 69 A.4 ∆τ and Data Point Sensitivity Total Run Time ::::::::::::: 69 A.5 Observer time and ∆τ Sensitivity Total Run Time ::::::::::: 69 A.6 Grid Sensitivity Peak Loading Pressure, No Weighting ::::::::: 70 A.7 Grid Sensitivity Peak Loading Pressure, No Weighting ::::::::: 70 A.8 Grid Sensitivity Peak Loading Pressure, No Bias vs. Tip Bias ::::: 70 A.9 ∆τ and Data Point Sensitivity Peak Loading Pressure ::::::::: 71 A.10 Grid Sensitivity Peak Total Pressure, No Weighting ::::::::::: 71 A.11 Grid Sensitivity Peak Total Pressure, No Weighting ::::::::::: 71 A.12 Grid Sensitivity Peak Total Pressure, No Bias vs. Tip Bias ::::::: 72 A.13 ∆τ and Data Point Sensitivity Peak Total Pressure ::::::::::: 72 A.14 ∆τ and Data Point Sensitivity - PNL ::::::::::::::::::: 72 A.15 Observer time and ∆τ Sensitivity - PNL ::::::::::::::::: 73 vii LIST OF FIGURES Figure Page 1.1 Modified aircraft for quiet flight based mainly on propeller changes (Vogeley, 1949) ::::::::::::::::::::::::::::::::::::: 3 2.1 Velocities and aerodynamic forces acting on the blade element (Leishman, 2006) ::::::::::::::::::::::::::::::::::::: 17 2.2 Annulus of rotor disk as used for the local momentum analysis of a hovering rotor / static propeller (Leishman, 2006) ::::::::::::::::: 21 2.3 Top Level Script Flow Diagram :::::::::::::::::::::: 28 2.4 Blade Element Analysis Script Flow Diagram :::::::::::::: 29 2.5 Aeroacoustic Analysis Script Flow Diagram ::::::::::::::: 30 2.6 Grid resolution sensitivity analysis for the same blade, same operating conditions, with different spanwise (S) and fixed chordwise (P) elements, with constant element width (no bias) :::::::::::::::::: 33 2.7 Grid resolution sensitivity analysis for the same blade, same operating conditions, same spanwise elements (100), with varying chordwise (P) el- ements :::::::::::::::::::::::::::::::::::: 34 2.8 Linear span-wise element distribution versus tip-biased element spacing. Sample image with 10 elements (spanwise) and 20 chordwise panels. :: 34 2.9 Grid resolution sensitivity analysis to element distribution weighting for the same blade, same operating conditions, same spanwise (100) and chordwise (200) elements :::::::::::::::::::::::::: 35 2.10 Grid resolution sensitivity analysis for the same blade, same operating conditions, same spanwise elements (100), with varying chordwise (P) el- ements and tip-biased element width distribution :::::::::::: 35 2.11 SPL frequency distribution sensitivity test to variable ∆τ and nT :::