Theses - Daytona Beach Dissertations and Theses Fall 2007 Study of Contra-rotating Coaxial Rotors in Hover, A Performance Model Based on Blade Element Theory Including Swirl Velocity Florent Lucas Embry-Riddle Aeronautical University - Daytona Beach Follow this and additional works at: https://commons.erau.edu/db-theses Part of the Aerospace Engineering Commons Scholarly Commons Citation Lucas, Florent, "Study of Contra-rotating Coaxial Rotors in Hover, A Performance Model Based on Blade Element Theory Including Swirl Velocity" (2007). Theses - Daytona Beach. 127. https://commons.erau.edu/db-theses/127 This thesis is brought to you for free and open access by Embry-Riddle Aeronautical University – Daytona Beach at ERAU Scholarly Commons. It has been accepted for inclusion in the Theses - Daytona Beach collection by an authorized administrator of ERAU Scholarly Commons. For more information, please contact [email protected]. STUDY OF COUNTER-ROTATING COAXIAL ROTORS IN HOVER A PERFORMANCE MODEL BASED ON BLADE ELEMENT THEORY INCLUDING SWIRL VELOCITY by Florent Lucas A thesis submitted to the Aerospace Engineering Department In Partial Fulfilment of the Requirements for the Degree of Master of Science in Aerospace Engineering Embry-Riddle Aeronautical University Daytona Beach, Florida Fall 2007 UMI Number: EP32005 INFORMATION TO USERS The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleed-through, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. UMI® UMI Microform EP32005 Copyright 2011 by ProQuest LLC All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest LLC 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106-1346 A STUDY OF COUNTER-ROTATING COAXIAL ROTORS IN HOVER by Florent Lucas This thesis was prepared under the direction of the candidate's thesis committee chair, Professor Charles Eastlake, Department of Aerospace Engineering, and has been approved by the members of his thesis committee. It was submitted to the Aerospace Engineering Department and was accepted in partial fulfilment of the requirements for the degree of Master of Science in Aerospace Engineering. THESIS COMMITTEE Professor Charles Eastlake Chair Dr. Magdy Attia Member 1U Dr. Frederique Drullion Member ?j2 -s> ii^/n/^ooj Department Chair, Aerospace Engineering Date izjfi//) 7 Vice President for Research and Institutional Effectiveness Date ii ACKNOWLEDGMENT I wish to deeply thank the Thesis Chair, Professor Charles Eastlake, for his practical suggestions and his priceless help all along this study. It was a pleasure to share discussions as much on a professional point of view as on a personal one. My appreciation is extended to the thesis committee members, Dr. Magdy Attia and Dr. Frederique Drullion for the support and help they gave me in the redaction of this document. I would also like to express my deepest gratitude to my family and my friends for their constant encouragement and moral support. iii ABSTRACT Author: Florent Lucas Title: A Study of Contra-rotating Coaxial Rotors in Hover A Performance Model Based on Blade Element Theory Including Swirl Velocity Institution: Embry-Riddle Aeronautical University Degree: Master of Science in Aerospace Engineering Year: 2007 The purpose of this study is to create a simple model to evaluate the performance of a counter-rotating coaxial rotor system. As it is based on the blade element theory, it could be used as a design tool where the engineer can modify all parameters - rotor radius, blade pitch distribution, tip velocity, rotor spacing, number of blades, blade chord, and airfoil's shape through its lift coefficient versus angle of attack slope. Different blade pitch distributions are tried and are assessed based on the power required to hover at the same weight. Also, the impact of the swirl velocity induced by the upper rotor is included and discussed. In order to verify the credibility of the model, results are compared to what was obtained from other researches. The main result is to compare performance of the current AH-64 Apache single rotor system with the optimal coaxial rotor model. IV " When will man cease to crawl in the depths to live in the azure and quiet of the sky? " Jules Verne, Robur the Conqueror, 1886 TABLE OF CONTENTS ACKNOWLEDGMENT iii ABSTRACT iv TABLE OF CONTENTS vi List of figures vii List of tables viii 1 Introduction 1 1.1 About coaxial rotor helicopters 1 1.2 A few steps of history 2 1.3 20th century and current state 3 1.4 Literature survey 4 1.5 Scope of this thesis 5 2 Model developed ~..7 2.1 Blade element theory for a single rotor 7 2.2 Description of coaxial rotor environment 11 2.3 Induced velocity at lower rotor including swirl velocity: 14 2.4 Model function 20 3 Results 24 3.1 Comparison to existing literature 24 3.1.1 Contribution of swirl in the wake 24 3.1.2 A coaxial rotor system or two isolated rotors 24 3.1.3 Rotor spacing, pitch increment and thrust ratio 27 3.2 Effect of pitch distribution 29 3.2.1 Untwisted blade 30 3.2.2 Linearly twisted blade 31 3.2.3 Enhanced blade twist 32 3.3 Comparison to a single rotor 34 4 Special case of ducted rotor 41 4.1 Simple coaxial configuration 42 4.2 In skewed-duct coaxial configuration 42 4.3 In straight-duct coaxial configuration 43 5 Conclusion 44 5.1 Concluding remarks 44 5.2 Recommendation for future work 45 References 46 Appendices 47 vi LIST OF FIGURES Figure 1: Da Vinci rotor design 2 Figure 2: J. Verne's Albatross & first aluminum counter-rotating coaxial rotor (d'Amecourt) 2 Figure 3: Various coaxial helicopters 4 Figure 4: Description of blade element 7 Figure 5: Aerodynamics around a blade element 8 Figure 6: Example of single rotor spreadsheet 11 Figure 7: Description of vena contracta 12 Figure 8: Definition of parameters around blade 14 Figure 9: Relation between rotor spacing and air streamtube 15 Figure 10: Inputs of the model 20 Figure 11: Coaxial rotor blade element spreadsheet .21 Figure 12: Coaxial spreadsheet results 22 Figure 13: Coaxial and tandem configuration 25 Figure 14: Power required for coaxial or isolated rotors 27 Figure 15: Velocity induced by rotors with untwisted blades 30 Figure 16: Linear twist distribution 31 Figure 17: Induced velocity for rotor with linear twist 31 Figure 18: Enhanced twist 32 Figure 19: Induced velocity for enhanced twist 32 Figure 20: Mathematical approximation of enhanced twist 33 Figure 21: Power required versus rotor radius 34 Figure 22: Power required versus tip speed 35 Figure 23: Design parameters of modified Apache with linearly twisted blades 38 Figure 24: Performance of coaxial system with linear twist 38 Figure 25: Optimum performance of coaxial configuration 39 Figure 26: Power required if lower rotor influences upper one 40 Figure 27: Different design for duct tests 41 Figure 28: Simple coaxial configuration 42 Figure 29: In skewed-duct coaxial configuration 42 Figure 30: Straight-duct coaxial system 43 vii LIST OF TABLES Table 1: Importance of swirl in the wake 24 Table 2: Difference between coaxial and isolated rotors 26 Table 3: Pitch difference required to matain torque balance 28 Table 4: Relation between performance and blade pitch distribution 30 Table 5: Increase of power required for various blade twist 33 viii 1 INTRODUCTION 1.1 About coaxial rotor helicopters The most common configuration of a helicopter is to have a main single rotor to create the lift and a small tail rotor whose purpose is to balance the torque created by the main rotor. Consequently, the machine can be directionally stabilized and the pilot has control over the yaw angle of the aircraft. Having two counter-rotating rotors is another solution to directionally stabilizing a helicopter and it provides the advantage of not having a tail rotor since the torque reaction from the two rotors can cancel each other. Indeed, a tail rotor uses power without providing lift. Moreover, it is the source of many accidents which could happen because the pilot hits something when hovering close to ground, because someone walks by the tail without seeing it or also because an enemy shoots the tail itself. The loss of the tail rotor often translates to a loss of lives. 1 1,2 A few steps of history This chapter does not have the purpose of offering an exhaustive history of helicopter but offers a glimpse at important steps. Leonardo Da Vinci is very s^^ii-^ often credited for being the conceptual inventor of helicopter. Although his design never took life and apparently could not ,! work, he surely had sensed what the future would offer to . NI 'i . • *>>S f?vy."»sW'!li mankind. An opportunity to make a human dream come true, a chance to fly in the skies, hover and go rearward. »,*{«•*>»-».* v*» w? Figure 1: Da Vinci rotor design In his book "The God Machine", James R. Chiles [1] describes early inventors' work and intellectuals' contribution. The word 'helicopter' is adapted from the French hehcopiere, coined by Gustave de Ponton d'Amecourt in 1861. It is linked to the Greek words hehx/helik- (EXiKctc;) = "spiral" or "turning" and pteron (nxepov) = "wing". D'Amecourt's efforts were backed up by the famous Jules Verne through, for example, "Robur the conqueror" in which the main character, captain of the Albatross, states: "With her, I am master of the seventh part of the world".