Smith, Harry Redgrave (2015) Engineering models of aircraft propellers at incidence. PhD thesis. http://theses.gla.ac.uk/6799/ Copyright and moral rights for this thesis are retained by the author A copy can be downloaded for personal non-commercial research or study This thesis cannot be reproduced or quoted extensively from without first obtaining permission in writing from the Author The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the Author When referring to this work, full bibliographic details including the author, title, awarding institution and date of the thesis must be given Glasgow Theses Service http://theses.gla.ac.uk/ [email protected] ENGINEERING MODELS OF AIRCRAFT PROPELLERS AT INCIDENCE HARRY REDGRAVE SMITH Submitted in partial fulfilment of the requirements for the Degree of Doctor of Philosophy Aerospace Sciences Research Division School of Engineering College of Science and Engineering University of Glasgow January 2015 c 2015 Harry Redgrave Smith “The literature of propeller aerodynamics is scattered and in some respects is inconsistent and incomplete.” – Quentin Wald (2006) i PREFACE This dissertation presents work carried out by the author in the Aerospace Sci- ences Research Division at the University of Glasgow in the period from March 2011 to September 2014, supervised by Dr. Eric Gillies and Dr. Richard Green. The work is part of an EPSRC CASE Ph.D. studentship between the University of Glasgow, the Engineering and Physical Sciences Research Council (EPSRC), Dowty Propellers (GE Aviation) and the Aircraft Research Association (ARA). In- dustrial supervision has been provided by Dr. Josef Trchalík and Dr. Angela Knepper (GE Aviation) and Mr. Peter Wong (ARA). The content is original except where otherwise stated. ii ACKNOWLEDGEMENTS I would like to extend my deepest gratitude to my academic supervisor, Dr. Eric Gillies, for his continued hard work and patience throughout my doctoral studies. He’s taught me how to be a worthy aerodynamicist and all-round scientist with integrity - and he’s pulled me out of a few research ‘flat spins’ with a dram or two along the way. I wouldn’t have made it anywhere near this far without his guidance. My sincere gratitude is also due to Dr. Richard Green for his input throughout my work - and for his undergraduate lectures on propeller aerodynamics, which put me in excellent stead for this project. A big thank you is also due to Dr. Stewart Houston for his patience when helping me to understand inflow (particularly dynamic inflow!). My viva voce was challenging but fair, and I’m proud to have gotten through the four- and-bit hours. Thank you to Dr. Douglas Thomson for his role as the internal examiner, with fair criticism of my work. Thank you also to the external examiner, Mr. Allan Bocci for significantly more criticism (still fair, though!), and for helping me steer this work towards the version printed today. In addition, thank you to Dr. Marco Vezza for his hard work at my viva to keep things on track and stopping Allan and I from getting lost in technical debate. Dr. Josef Trchalík, Dr. Angela Knepper and Mr. Paul Methven at Dowty Propellers have been integral to the success of this project - without their support, the project wouldn’t have been possible. Thank you, also, to Mr. John Dunn at Dowty for pushing the dissertation through review! Mr. Peter Wong at ARA has provided support and guidance along the way - and eagerly took on the role of industrial supervisor at short notice. I would like to express my appreciation for the support all four have provided, and to take the opportunity to formally say ‘thank you’ here. My colleagues in the Aerospace Sciences Research Division have helped provide a productive research environment, and provided engaging conversation (and entertain- ment!) along the way. A big thank you is due to many other staff members within the division for help with niche questions - too many to name here. Thank you to all my friends for your continued support along the way - you know who you are, and I’ll always remember what you’ve done. Also, my heartfelt thank you to my family who have supported me along the way. Thank you, Katy, for always being supportive and thank you, Grandad, for the bookstand you made - I use it every day and hope I always will. Particularly, I am sincerely grateful to my parents who have always supported me, and let me live at home whilst writing up. Thank you Mum for always understanding. Thank you to my father, for his diligent proofreading (he loved the word ‘vorticity’) and for refraining from asking ‘have you figured it out yet?’ as much as possible. Thank you, Dad. iii To my parents, and to Kaya. ABSTRACT Aircraft propellers in any flight condition other than pure axial flight are subject to an incident flowfield that gives rise to time-varying forces. Means of modelling these time- dependent forces have been presented in the literature, to varying degrees of success - but a review of the different models is missing, and there is a need for an instructive means of simulation using physically realistic but computationally light methodologies. This dissertation provides a comprehensive overview of the relevant work to date, in addition to providing a logical framework in which the problem of propeller blade cyclic load variation may be assessed. Through this framework, the importance of different aerodynamic features pertinent to this problem are compared, and a new solution meth- odology based on adaptations of existing models is presented. This research project was commissioned by Dowty Propellers (DP), who chose Glasgow University and the supervisors for their rotorcraft simulation experience. Prediction of the propeller induced flowfield is shown to be of importance for the cal- culation of blade cyclic loads. Momentum models are fit for purpose owing to relative computational simplicity - this dissertation suggests a new radially-weighted implement- ation of momentum theory that provides better correlation with wind tunnel data than existing models. Swept propeller blades are discussed and the inherent problems faced by a designer or performance engineer are highlighted. An Euler transform to resolve velocities and forces between disc and blade element axes is presented, along with the assertion that ‘simple’ sweep correction methods can be deleterious to propeller aerodynamic simula- tion if used naïvely. Fundamentally, representation of a swept propeller blade by a blade element model is described as wholly more problematic than a straight propeller blade owing to the displacement of blade elements with respect to the blade pitch change axis - and that flow information will always be lost with such a representation. Installation effects are simulated and installed load fluctuations are predicted to a reasonable degree of accuracy compared to what little data is available. Different means of resolving installation velocities to disc and, subsequently, blade element axes are com- pared, and it is shown that representing installation effects by an effective incidence angle as is ‘standard practice’ will most likely underpredict installed load fluctuation. In addition to a varying blade root bending load caused directly by load fluctuation on a propeller at an angle of incidence, the reacted net loads at a propeller hub may include a constant yawing moment and in-plane force. This in-plane force has been well documented in the literature, but the equations for its calculation may miss a component of force due to a tilting of the blade tangential force. New equations for this additional force term are presented that validate well to legacy experimental data. v CONTENTS PREFACE ii ACKNOWLEDGEMENTS iii ABSTRACT v LIST OF FIGURES xii LIST OF TABLES xiii NOMENCLATURE xvi 1 INTRODUCTION 1 1.1 LITERATURE REVIEW 5 1.1.1 ROTARY NOMENCLATURE CLARIFICATION - ‘INFLOW’8 1.2 HISTORY OF PROPELLER THEORY 8 1.2.1 AXIAL MOMENTUM THEORY 9 1.2.2 GENERAL MOMENTUM THEORY 10 1.2.3 VORTEX THEORIES 11 1.2.4 PROPELLERS IN NON-AXIAL FLIGHT 16 1.2.5 SWEPT PROPELLER BLADE AERODYNAMICS 21 1.2.6 ROTARY AERODYNAMICS -FORWARD FLIGHT 21 1.2.7 UNSTEADY ROTARY AERODYNAMICS 23 1.2.8 PROPELLER STRUCTURAL-DYNAMIC MODELLING 24 1.2.9 INSTALLATION EFFECTS 24 1.2.10 PROPELLER BLADE AEROFOILS 25 1.2.11 INDUSTRY DOCUMENTS 27 1.2.12 LITERATURE SUMMARY 27 1.3 DISSERTATION OBJECTIVES 28 vi vii 1.4 CONTRIBUTION AND SCOPE 30 1.5 DISSERTATION STRUCTURE 31 2 MODELLING PROPELLERS AT INCIDENCE 33 2.1 PROBLEM STATEMENT 33 2.2 AN ISOLATED PROPELLER AT INCIDENCE 36 2.3 THE PHYSICS OF 1P AIRLOADS 39 2.4 MODEL FORMULATION AND FIRST ORDER 1P LOAD 44 2.4.1 EFFECTIVE ADVANCE RATIO AND ROTATIONAL SPEED 46 2.5 LIFTING MODEL AND HIGHER ORDER EFFECTS 53 2.5.1 LIFTING MODEL 53 2.5.2 HIGHER ORDER EFFECTS 57 2.5.3 INDUCED FLOW/UNSTEADINESS 58 2.5.4 STRUCTURAL DEFORMATIONS 65 2.5.5 SIMPLE INSTALLATION 74 2.6 THREE-DIMENSIONAL EFFECTS 78 2.6.1 PRANDTL’S,GOLDSTEIN’S AND LOCK’S FUNCTIONS FOR A PROPELLER AT INCIDENCE 79 2.7 CONCLUSIONS 85 3 INDUCED FLOW AND UNSTEADINESS 86 3.1 INTRODUCTION 86 3.2 STEADY INDUCED FLOW MODELS 93 3.2.1 B-BLADED MULTIPLICATION FACTOR 96 3.2.2 AMT VS. DMT 97 3.2.3 WEIGHTED MOMENTUM THEORY 99 3.2.4 SUMMARY OF MOMENTUM MODELS 104 3.3 UNSTEADY MODELS 105 3.4 DYNAMIC WAKE MODELS 110 3.5 SUMMARY OF MODELS 111 3.6 VALIDATION DATA 113 3.7 DISCUSSION OF RESULTS 115 3.7.1 GRAY ET AL.