investigations of the transonic flov\t around b oscillating airfoils hendrik tijdeman nil1 1 ia !ii lil illlli lilllll 1» lil mi j II lliiliilhiil üiiniiliill »! nil IIIU ililHiililllllUlllihlIllllllll liii o 00 f ts) o UI M o 00 1^ ._---^LLEIM INVESTIGATIONS OF THE TRANSONIC FLOW AROUND OSCILLATING AIRFOILS PROEFSCHRIFT TER VERKRIJGING VAN DE GRAAD VAN DOCTOR IN DE TECHNISCHE WETENSCHAPPEN AAN DE TECHNISCHE HOGESCHOOL DELFT, OP GEZAG VAN DE RECTOR MAGNIFICUS PROF. IR. L. HUISMAN, VOOR EEN COMMISSIE AANGEWEZEN DOOR HET COLLEGE VAN DEKANEN TE VERDEDIGEN OP WOENSDAG 21 DECEMBER 1977 TE 16.00 UUR DOOR HENDRIK TIJDEMAN vliegtuigbouwkundig ingenieur geboren te Alkmaar /5 öZ •P/ BIBLIOTHEEK TU Delft p 1181 1563 298294 C DIT PROEFSCHRIFT IS GOEDGEKEURD DOOR DE PROMOTOR PROF. IR. H. BERGH EN DE COPROMOTOR PROF. DR. IR. J.L. VAN INGEN VOOR JEANNETTE -3- ACKNOWLEDGMENTS The author is indebted to the Directors of the Nationaal Lucht- en Ruimtevaartlaboratorium (National Aerospace Laboratory NLR) for their permission to publish the results of the investigations in this form. The experiments described in this paper have been carried out in collaboration with Fokker-VFW under contract with the Netherlands Agency for Aerospace Programs (NIVR). The permission of the NIVR and Fokker-VFW to use the results for the present purpose is gratefully acknowledged. Severe gratitude is expressed to the many colleagues at NLR, who contributed in one way or another to the extensive program. The following persons should be mentioned specifically: Messrs. R.J. Zwaan, J.W. Slooff and Dr. R. Roos for the stimulating and fruitful discussions and Messrs. P. Schippers, J.W.G. van Nunen, A.J. Persoon and R. Poestkoke for their skilful assistance in preparing and executing the experiments. Further, the author owes many thanks to Mrs. Dr. A.A.C. Klaasse for critical re viewing and Mrs. J.H. Buttstedt for careful typing of the manuscript and to Messrs. H. Willigers, A. Timmer, R. Bons and J.T.A.M. Groos, who took care of the lay-out and assisted in preparing the many illustrations. -k- SUMMARY Exploratory wind-tunnel experiments in high-subsonic and transonic flow on a conventional airfoil with oscillating flap and a supercritical airfoil oscillating in pitch are described. In the analysis of the exper imental results, emphasis is placed upon the typical aspects of transonic flow, namely the interaction between the steady and unsteady flow fields, the periodical motion of the shock waves and their contribution to the overall unsteady airloads. Special attention is paid to the behaviour of the supercritical airfoil in its "shock-free" design condition. Moreover, it is discussed to what extent linearization of the unsteady transonic flow problem is allowed if the unsteady field is considered as a small perturbation superimposed upon a given mean steady-flow field. Finally, the current status of unsteady transonic flow theory is reviewed and the present test data are used to evaluate some of the recently developed calculation methods. -5- CONTENTS Page 1 BACKGROUND AND OUTLINE OF THESIS 9 1.1 Background 9 1.2 OutIine of thesis 11 PART 1: INTRODUCTORY CHAPTERS 2 THE FLOW AROUND OSCILLATING AIRFOILS 15 2.1 Description of unsteady airloads 15 2.2 Some notes on the unsteady-flow equations 16 2.2.1 The unsteady-flow equations 2.2.2 Moderately subsonic and supersonic flow 2.2.3 Transonic flow 2.3 Present status of the research on unsteady transonic flow 19 3 MAIN CHARACTERISTICS OF THE STEADY TRANSONIC FLOW AROUND AIRFOILS 20 3.1 Transonic flows with embedded shock waves 20 3.1.1 Development of flow pattern with Mach number, flap angle, and incidence 3.1.2 Characteristics of a normal shock wave 3.2 Shock-free flow 22 3.3 Some particular flow patterns on airfoils with flap 22 3.'t Viscous aspects Zk PART II: SCOPE AND DESCRIPTION OF THE EXPERIMENTAL INVESTIGATIONS 4 SCOPE OF THE NLR INVESTIGATIONS 29 4.1 Problem definition 29 4.2 Approach 29 5 TECHNIQUE FOR UNSTEADY PRESSURE MEASUREMENTS 30 5.1 Principle-of the measuring technique 30 5.2 Theoretical model for the dynamic response of tube-transducer systems 31 5.2.1 The propagation of pressure waves through cylindrical tubes 5.2.2 Solution for complete tube-transducer systems 5.3 The dynamic characteristics of tube-transducer systems 33 5.3.1 The dynamic response in still air 5.3.2 Influence of the airflow 5.3.3 Verification in a joint ONERA-NLR investigation 5.4 Practical application in wind-tunnel tests 35 5.4.1 Choice and calibration of tube-transducer systems 5.4.2 Measuring equipment and data reduction 6 WIND-TUNNEL MODELS AND TEST SET-UP 38 6.1 NACA 64AO06 airfoil with flap 38 6.2 NLR 7301 airfoil 39 6.3 Wind tunnel 4l 6.4 Optical flow studies 41 7 TEST PROGRAM 42 7.1 NACA &4A006 airfoil with flap 42 7.2 NLR 7301 airfoil 42 Page PART III: ANALYSIS OF RESULTS 8 THE INTERACTION BETWEEN THE STEADY AND UNSTEADY FLOW FIELD kj 8.1 Introductory remarks 4? 8.2 The influence of Mach number on the airloads of the NACA'64A006 airfoil with flap 47 8.2.1 Steady pressure distributions 8.2.2 Unsteady pressure distributions 8.2.3 Unsteady aerodynamic coefficients 8.3 Graphical experiment 53 8.4 The influence of incidence and mean flap angle 54 8.4.1 Unsteady pressure distributions 8.4.2 Unsteady aerodynamic coefficients 8.5 The influence of frequency 58 8.5.1 Unsteady pressure distributions 8.5.2 Unsteady aerodynamic coefficients 9 ON THE PERIODICAL MOTION OF SHOCK WAVES 62 9.1 Introductory remarks 62 9.2 Shock strength and shock position in steady flow 62 9.3 Types of shock-wave motion observed in unsteady flow 64 9.4 Introduction of an analytical model 66 9-4.1 Relation between shock position and shock strength 9.4.2 Application of the analytical model 9.5 Additional remarks 69 9.5.1 Some properties of the unsteady shock relations 9.5.2 Possible use of the shock-wave model 10 THE UNSTEADY AERODYNAMIC CHARACTERISTICS OF THE "SHOCK-FREE" NLR 7301 AIRFOIL 70 10.1 Introductory remarks 70 10.2 Unsteady pressure distributions 71 10.2.1 Fully subsonic flow (condition I) 10.2.2 Transonic flow with Shockwave (condition II) 10.2.3 The "shock-free" design condition (condition III) 10.3 Unsteady aerodynamic coefficients 75 10.4 Remarks on the motion of the shock wave 78 10.5 The influence of the transition strip 81 10.6 Some additional effects 83 10.6.1 The effect of Mach number 10.6.2 The effect of the amplitude of oscillation 10.7 Concluding remarks 84 11 SOME CONSIDERATIONS ON A LINEARIZED TREATMENT OF UNSTEADY TRANSONIC FLOWS 86 11.1 Introductory remarks 86 11.2 Flow conditions with an oscillating shock wave 86 11.2.1 Local effects of a shock wave 11.2.2 Contribution of a shock wave to the overall aerodynamic loads 11.3 Special flow conditions 89 11.3.1 "Shock-free" flow 11.3.2 Flow with a double shock 11.3.3 Flow around an airfoil with flap 11.4 Concluding remarks 92 -7- Page PART IV: THE CURRENT STATUS OF UNSTEADY FLOW THEORY AND EVALUATION OF SOME NEW METHODS FOR UNSTEADY TRANSONIC FLOW 12 REVIEW OF CALCULATION METHODS FOR TWO-DIMENSIONAL UNSTEADY FLOW 95 12.1 Classification of the various methods 95 12.2 Linearized subsonic lifting-surface theory 99 12.2.1 The integral equation relating downwash and load distribution 12.2.2 The Kernel-function method 12.2.3 The Doublet-Lattice method 12.3 Methods for high-subsonic flow 100 12.3.1 Local-Mach-number corrections in linearized lifting-surface theory 12.3.2 Methods based on the linearized transonic smal 1-perturbation equation 12.4 Methods for near-sonic flow without shock waves 102 12.5 Methods for transonic flow with shock waves 102 12.5.1 General remarks 12.5.2 Methods based on the Euler equations 12.5.3 Methods based on the potential equation 12.6 Role of the NLR results 104 13 EVALUATION OF SOME NEW CALCULATION METHODS FOR UNSTEADY TRANSONIC FLOW 105 13.1 Introductory remarks 105 13.2 Comparisons between theory and experiment in steady and quasi-steady flow 106 13.2.1 Correction for tunnel-wall interference 13.2.2 Subsonic flow 13.2.3 Transonic flow with shock wave 13.2.4 "Shock-free" flow 13.3 Comparisons between theory and experiment in unsteady flow 111 13.3.1 Pressure distributions 13.3.2 Aerodynamic coefficients 13.3.3 Shock-wave motions 13.4 Concluding remarks 117 14 IMPACT OF THE NLR INVESTIGATIONS AND FUTURE PROSPECTS 118 14.1 Impact of the NLR investigations II8 14.2 Future prospects II8 15 REFERENCES 119 APPENDIX A: DEFINITION OF STEADY AND UNSTEADY AERODYNAMIC QUANTITIES 129 APPENDIX B: THE DYNAMIC RESPONSE OF TUBE-TRANSDUCER SYSTEMS I3I APPENDIX C: DERIVATION OF THE QUASI-STEADY AND UNSTEADY SHOCK RELATIONS 143 APPENDIX D: LIST OF SYMBOLS 145 APPENDIX E: SUMMARY IN DUTCH (SAMENVATTING IN HET NEDERLANDS) 147 1 BACKGROUND AND OUTLINE OF THESIS 1.1 BACKGROUND For the transonic flight regime, with its mixed subsonic-supersonic flow patterns, these means Under certain conditions, structures like are less developed. Here the aeroelastician is airplane wings and tail surfaces may experience hampered seriously by the lack of effective cal vibrations of an unstable nature. culation methods to determine the unsteady air This phenomenon, called "flutter", is an aero- loads. For wing sections in two-dimensional flow, elastic problem, determined by the interaction of calculation methods become available at the moment, the elastic and inertial forces of the structure but the current practice for wings of general and the unsteady aerodynamic forces generated by planform still is that rather arbitrary interpola the oscillatory motion of the structure itself. tions and extrapolations are being made on the In general, two or more vibration modes are in basis of calculated airloads for pure subsonic and volved - for instance bending and torsional vibra supersonic flow. In many cases, one has to resort tion of a wing - which, under the influence of the to very expensive wind-tunnel experiments. unsteady aerodynamic forces, interact with each other such that the vibrating structure extracts SUPERSONIC TRANSPORT WING (REF.6) UNSTABLE SUBSONIC SWEPT WING (REF.5) energy from the passing airstream. This leads to SPACE SHUTTLE WING (REF.7) a progressive increase in amplitude of vibration, 1.0 usually ending up in a disintegration of the MACH CORRECTION structure. OF (REF.8 , 1946 As for a given configuration of a structure • the unsteady aerodynamic forces increase rapidly TRANSONIC DIP STABLE with flight speed, while the elastic and inertia forces remain almost unchanged, normally there 0.4 0.9 1.0 1.1 exists a critical flight speed ("flutter speed"), MACH NUMBER above which flutter occurs. Because of the dis Fig. 1.1 Flutter speed versus Mach number curve showing the "transonic dip". astrous character of the phenomenon, the aircraft manufacturers have to prove that the flutter This situation is very unsatisfactory, es speeds of their products are well outside the pecially since experience shows (Refs. 1-4) that flight envelope, and in this respect they have to flutter problems often become most critical for meet severe airworthiness requirements. transonic-flow conditions. The main reason for In many cases the demands for flutter free this is the rather peculiar behaviour of the un dom are the determining factors for the construc steady aerodynamic forces in transonic flows, in tion of wings and tail surfaces. For this reason, particular when strong shock waves are involved. much attention has been paid to the development of This is reflected, for instance, in the behaviour adequate calculation methods to predict the flut of the flutter speed for bending-torsion flutter ter characteristics of aircraft. The vibration as a function of Mach number (Fig. 1.1), which characteristics of the structure at zero airspeed shows the so-called "transonic dip", a region of can be determined accurately by sophisticated relatively low flutter speeds in the transonic calculation methods or by ground vibration tests. flight regime. In addition to the results of some Therefore, the accuracy of the flutter prediction wind-tunnel investigations (Refs. 5-7), also the depends mainly on the knowledge of the unsteady Mach-number correction as proposed in 1946 for a aerodynamic forces. flutter criterion for wing torsional stiffness In the subsonic and supersonic flight (Ref. 8) is given in figure 1.1, which illustrates regimes, the unsteady aerodynamic forces can be the presence of an old problem. predicted reasonably well by theoretical means.