A STUDY OF HELICOPTER AERODYNAMICS IN GROUND EFFECT DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Devi Prasad Pulla, B.E., M.S. * * * * * The Ohio State University 2006 Dissertation Committee: Approved by A.T. Conlisk, Adviser S.Mazumder Adviser John Yu Graduate Program in Igor Adamovich Mechanical Engineering ABSTRACT The flow around a helicopter is very complex; it becomes much more complex when it comes close to the ground. The presence of the ground changes the aerodynamic char- acteristics of the rotor and the flow environment becomes much more complex compared with that of flight out-of-ground effect (OGE) and hence the behavior of the rotor wake in the vicinity of the ground is challenging to predict. Under in-ground-effect(IGE) condi- tions, the wake collides with the ground and causes a significant perturbation to the flow near the blade. Significant interactions between the main rotor wake and the ground have been associated with the formation and passage of the ground vortex in forward flight. The presence of a ground vortex affects the handling qualities of the helicopter. The aim of this research is to capture the physics of the flow features and dynamics of ground effect flows around a rotorcraft, provide an understanding of the rotor wake/vortices near the ground, and generate rigorous models to accurately predict handling qualities, loads and moments acting on the rotor and the power requirements. A free vortex method is used to model the flowfield. The presence of the ground is modeled using the method of images and the lifting-surface theory is used to model each rotor blade. An initial wake geometry is assumed which is allowed to develop in time until the flowfield becomes periodic. The rotor wake is assumed to consist of only the tip ii vortices and the inboard sheet and the root vortex are neglected. The solution is stepped in time using an Adams-Moulton scheme with a Runge-Kutta starting formula. The wake structure after periodicity is reached is obtained for hover and different for- ward flight speeds. Also, the nature of the flowfield, as well as the formation of the ground vortex, is understood by obtaining the velocity contours on a longitudinal plane containing the rotor blade after periodicity is obtained. The unsteadiness in the velocities is quantified by obtaining the RMS deviation in velocities on different planes containing the tail rotor around the rotor disk simulating the various kinds of flight. Thrust and power requirements on the rotor disk have been predicted and have been successfully validated by comparison with experimental results obtained from Georgia Institute of Technology. A tail rotor has also been included in the current model to understand its implications on the wake struc- ture and loads. The computational results have been validated against experimental results obtained at Georgia Institute of Technology and Empey and Ormiston. iii ACKNOWLEDGMENTS Personal gratitude is extended to Professor A.T. Conlisk whose patience and guidance is greatly appreciated. I would also like to thank Mr.Alan Egolf for his helpful input regarding my research. This work is supported under Task 9.1.2 of the NASA/NTRC Rotorcraft Center of Excellence at Georgia Institute of Technology. iv VITA August 6, 1981 . Born - Visakhapatnam, India July 2002 . .B.E. Mechanical Engineering Regional Engineering College Suratkal, India December 2004 . M.S. Mechanical Engineering The Ohio State University Columbus, OH September 2002-present . Graduate Research Associate The Ohio State University Columbus, OH PUBLICATIONS Research Publications Saijo, T., Ganesh, B.A., Huang, A.B., Komerath, N.M., Bhattacharya, S., Pulla, D.P., Con- lisk, A.T, “Development of Unsteadiness in the Wake of a Rotor in Ground Effect”, Pro- ceedings of the American Helicopter Society Forum, Pheonix, AZ, May 2003. Pulla, D.P., Bhattacharyya, S., Conlisk, A.T., “Structure of the Rotor Wake in Ground ef- fect”, Annual meeting of the Division of Fluid Dynamics, APS, Meadowlands, NJ ,Novem- ber , 2003. Pulla, D.P., Conlisk, A.T., “The Long Time Structure of the Rotor Wake in Ground effect”, 43rd AIAA Aerospace Sciences Meeting, Reno, Nevada AIAA 2005-1408, January 10-13 2005. v Ganesh, B., Komerath, N.M., Pulla, D.P., Conlisk, A.T., “Unsteady Aerodynamics of Rotorcraft in Ground Effect”, 43rd AIAA Aerospace Sciences Meeting, Reno, Nevada AIAA 2005-1407, January 10-13 2005. Pulla, D.P., A.T.Conlisk., “The Unsteady Rotor Wake in Ground Effect”, Annual meeting of the Division of Fluid Dynamics, APS, Chicago, IL ,November , 2005. Pulla D.P., Vishwanath Godavarthy, Burgraff, O.R., Conlisk, A.T., “An Inviscid Model of the Formation of a Rotor Tip-Vortex”, accepted for publication by the AIAA Journal. FIELDS OF STUDY Major Field: Mechanical Engineering Studies in Fluid Mechanics: Professor A.T. Conlisk vi TABLE OF CONTENTS Page Abstract . ii Acknowledgments . iv Vita . v List of Tables . x List of Figures . xi Chapters: 1. Introduction . 1 1.1 Background . 1 1.2 Overview of Helicopter Aerodynamics . 3 1.3 Rotor Wake . 7 1.4 Wake Models . 9 1.5 Effect of the Ground on the Rotor Flow Field . 11 1.6 The Current Work . 16 2. Numerical Model for the Blade . 18 2.1 Introduction . 18 2.2 Lifting Line Theory . 19 2.3 Lifting Surface Model . 24 2.4 IGE Wake Model . 35 2.5 Summary . 42 vii 3. Results - Lifting Line . 46 3.1 Introduction . 46 3.2 Results - Lifting Line Theory . 47 3.2.1 OGE Hover for Comparison with IGE Results . 47 3.2.2 IGE Hover Lifting Line Results . 50 3.2.3 IGE Forward Flight - Single-Bladed Rotor Flow Field Results . 58 3.2.4 IGE Forward Flight - Two-Bladed Rotor . 64 3.2.5 Comparison with Experiments . 72 3.3 RMS Velocity Variations . 78 3.4 Summary . 92 4. Results - Lifting Surface Model . 95 4.1 Introduction . 95 4.2 Results - Lifting Surface . 96 4.2.1 Results - Single-Bladed Hover Lifting Surface . 96 4.2.2 Results - Two-Bladed Hover Lifting Surface . 100 4.2.3 Results - Single-Bladed Forward Flight Lifting surface . 101 4.2.4 Results - Two-Bladed Forward Flight Lifting Surface . 111 4.2.5 Comparison with Experiments . 115 4.3 Transient Velocity Variations . 123 4.4 Summary . 142 5. Loads . 144 5.1 Introduction . 144 5.2 Computation of Loads Using Lifting Line Theory in Hover . 146 5.3 Computation of Loads Using the Lifting Surface Theory . 154 5.4 Results - Lifting Line Theory . 156 5.4.1 Results in Hover . 156 5.4.2 Results - Forward Flight . 160 5.5 Results - Lifting Surface Theory . 162 5.5.1 Results - Hover . 163 5.5.2 Results - Forward Flight . 166 5.5.3 Comparison of Lifting Line and Lifting Surface Models . 167 5.6 Summary . 170 viii 6. Main Rotor - Tail Rotor Interactions . 171 6.1 Introduction . 171 6.2 Numerical Model . 173 6.3 Results . 174 6.3.1 Flow field . 174 6.3.2 Loads . 175 6.4 Summary . 185 7. Overview and Future Work . 187 7.1 Summary . 187 7.2 Future Work . 190 Appendices: A. Vortex Ring Computation . 192 Bibliography . 195 ix LIST OF TABLES Table Page 3.1 Experimental Parameters in Caradonna et al. [32] experiments. 50 3.2 Experimental parameters in Light [17] experiments. 50 3.3 Comparison of ground vortex coordinates in computation and experiment; h=R = 0:72, two-bladed rotor, µ = 0:03. 72 4.1 Comparison of ground vortex coordinates in computation and experiment; h=R = 0:72, two-bladed rotor, µ = 0:03. 121 4.2 Comparison of ground vortex coordinates in computations obtained using lifting surface and lifting line models; h=R = 0:72, two-bladed rotor, µ = 0:03. 123 x LIST OF FIGURES Figure Page 1.1 A summary of specific flow problems involving helicopter aerodynamics. From [1]. 4 1.2 A single bladed rotor in forward flight; a top view (a)Advancing and re- treating sides of the rotor disk. (b) Definition of lag and flap angles. (b) Lift and drag in forward flight. 6 1.3 Trailed and shed vorticity in rotor wake(Johnson [3]). 7 1.4 Sketch of a helicopter rotor wake for a single blade. From Gray [4]. 8 1.5 Comparison of partial and total ground effects. 12 2.1 Lifting line model for a fixed wing ; the dark areas indicate the magnitude of bound circulation; circulation has an elliptical distribution in the fixed wing case. 20 2.2 Velocity induced by the segments of a typical horseshoe element. 22 2.3 Horseshoe vortex model of a rotary wing. 26 2.4 Horseshoe-vortex panel implementation of a semi-infinite wing. The panel width is non-uniform in the spanwise direction, as discussed in the text. The velocity boundary condition is applied at the three-quarter chord line at the midspan point of each panel. (a) Definition of the local panel coordi- nates. (b) Definition of the global coordinates. 28 xi 2.5 Schematic of the trailing vortex system. Open circles denote the quarter- chord location of each panel (bound vortices), solid circles denote panel edges. Arrows denote the normal direction at the panel three-quarter chord line (normal-velocity boundary condition) [26]. 30 2.6 Bound circulation disribution along the blade in hover IGE, h=R = 0:5 and o OGE; A = 6, α0=10 . 32 2.7 Comparison of the dimensionless tip-vortex circulations for lifting line and lifting surface models in hover, h=R = 0:5. 33 2.8 Dimensionless tip-vortex circulation as a function of the aspect ratio in hover, h=R = 0:5.