The Pennsylvania State University The Graduate School Department of Aerospace Engineering COMPUTATIONAL FREE WAKE ANALYSIS OF A HELICOPTER ROTOR A Thesis in Aerospace Engineering by Christopher J Szymendera Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science May 2002 We approve the thesis of Christopher J Szymendera Date of Signature Lyle N Long Professor of Aerospace Engineering Thesis Advisor Mark D Maughmer Professor of Aerospace Engineering Dennis K McLaughlin Professor of Aerospace Engineering Head of the Department of Aerospace Engineering ABSTRACT One of the most important issues in understanding the behavior of rotorcraft is the accurate prediction of the rotor wake Understanding the complex nature of the wake is necessary for the prediction of such factors as blade loading acoustics and vibration A free wake vortex lattice method was used to predict the wake structure and blade loading for a rotor in arbitrary motion The blades were modeled as flat plates and ring vortices were distributed on the surface of the blades As the blades rotated vortices were shed into the wake and then moved with a local velocity induced by the effects of the vortices on the blades and in the wake The wake was allowed to freely deform over time into its natural structure The lift was determined from the strength of each vortex on the blade calculated by applying the boundary condition of no flow normal to the blade On a helicopter in forward flight the advancing blades usually experience high Mach numbers at the tip Therefore it is important to be able to accurately predict the blade loading in compressible flow The free wake method though calculates induced velocities using the Biot Savart Law which is only applicable to incompressible flow A Prandtl Glauert correction was applied then to the Biot Savart Law which allowed the code to accurately model compressible flow The code was validated using two experimental hover cases one in which the flow was entirely incompressible and one in which the flow was compressible at the tips and then extended to handle any arbitrary motion of the helicopter TABLE OF CONTENTS LIST OF FIGURES vi ACKNOWLEDGMENTS ix Chapter 1 INTRODUCTION 1 1 1 Overview 1 2 Rotor Wake Characteristics 1 3 Previous Research in Rotor Wake Simulation 1 3 1 Vortex Methods 1 3 2 Computational Fluid Dynamics 1 3 3 Hybrid Methods 1 3 4 Compressibility 1 4 Current Approach 1 3 10 11 13 15 16 18 Chapter 2 FUNDAMENTALS OF POTENTIAL FLOW 19 2 1 Overview 2 2 Vorticity and Circulation 2 3 Two Dimensional Vortex 2 4 Three Dimensional Vortex 2 5 Vortex Core 2 6 Compressibility Correction 2 7 Applying the Prandtl Glauert Transformation to the Biot Savart Law 19 19 21 23 28 33 41 Chapter 3 FREE WAKE METHOD 44 3 1 Overview 3 2 Free Wake Procedure 3 2 1 Discretization of the Blade and Wake 3 2 2 Determine the Lift on the Blades 3 2 3 Calculate Wake Roll Up 3 3 Implementation of the Free Wake Procedure in the Code 44 44 45 48 51 51 Chapter 4 RESULTS AND DISCUSSION 60 4 1 Overview 60 v 4 2 Code Validation 4 2 1 Case 1 Incompressible Hover 4 2 2 Case 2 Compressible Hover 4 2 2 1 Case 2a Incompressible Code vs Compressible Code 4 2 2 2 Case 2b Changing the Chordwise Panel Spacing 4 2 2 3 Case 2c Changing the Vortex Core Radius 4 2 2 4 Case 2d Changing the Number of Spanwise Panels 4 2 2 5 Case 2e Changing the Number of Chordwise Panels 4 3 Wake Visualization 4 4 Application to Other Cases 4 4 1 Axial Climb 4 4 2 Forward Climb 61 63 68 68 73 76 79 82 85 91 91 94 Chapter 5 CONCLUSIONS 96 5 1 Summary and Conclusions 5 2 Suggestions for Future Work 96 98 BIBLIOGRAPHY 101 Appendix A SAMPLE INPUT FILE 107 Appendix B COMPUTER PROGRAM SUBROUTINES 108 LIST OF FIGURES Figure 1 1 Schematic showing the wake and its interaction with the fuselage in forward flight 2 Figure 1 2 Traditional model of a rotor wake showing a concentrated tip vortex and a trailing vortex sheet 5 Figure 1 3 Schematic showing the wake and tip vortex roll up 6 Figure 1 4 Tip vortices trailed behind an E A 6B Prowler 8 Figure 1 5 Tip vortices trailed behind the blades of an AH 1W Super Cobra 8 Figure 1 6 Smoke visualization of the tip vortex locations in forward flight 9 Figure 2 1 Relation between surface integral and line integral 20 Figure 2 2 Two dimensional flow field around a solid rotating cylinder showing a streamlines and b tangential velocity of flow 22 Figure 2 3 Velocity at point P due to a vortex distribution in volume V 24 Figure 2 4 Velocity at point P induced by a vortex segment 24 Figure 2 5 Velocity at point P induced by a vortex segment 26 Figure 2 6 Laser light sheet flow visualization tip vortex and vortex sheet 28 Figure 2 7 Velocity field inside a tip vortex shown by a idealized view and b model used in vortex method 30 Figure 2 8 Comparison of different 2 D vortex models 32 Figure 2 9 Effect of Prandtl Glauert transformation a actual domain in compressible flow b stretched domain in analogous incompressible flow 40 Figure 2 10 Stretching effect on a rotating blade 41 vii Figure 2 11 Stretching effect of the distance between the vortex and control point based on the Prandtl Glauert correction a actual distance b stretched distance 43 Figure 3 1 Vortex ring model 46 Figure 3 2 Wake shedding procedure 47 Figure 3 3 Computer program flowchart 52 Figure 4 1 Configuration of the experimental rotor 61 Figure 4 2 Grid spacing on blade 62 Figure 4 3 Thrust coefficient over time 64 Figure 4 4 Spanwise lift coefficient normalized by tip speed 66 Figure 4 5 Chordwise pressure coefficient at different radial sections 67 Figure 4 6 Thrust coefficient over time 70 Figure 4 7 Spanwise lift coefficient normalized by tip speed 71 Figure 4 8 Chordwise pressure coefficient at different radial locations 72 Figure 4 9 Spanwise lift coefficient normalized by tip speed 74 Figure 4 10 Chordwise pressure coefficient at different radial sections 75 Figure 4 11 Spanwise lift coefficient normalized by tip speed 77 Figure 4 12 Chordwise pressure coefficient at different radial sections 78 Figure 4 13 Spanwise lift coefficient normalized by tip speed 80 Figure 4 14 Chordwise pressure coefficient at different radial sections 81 Figure 4 15 Sectional lift coefficient normalized by tip speed 83 Figure 4 16 Chordwise pressure coefficient at different radial sections 84 Figure 4 17 Wake trailing behind both blades 86 Figure 4 18 Wake trailing behind one blade 87 Figure 4 19 Path of tip vortices 89 viii Figure 4
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