Investigation of Transonic Flow Around Oscillating Airflows [THESIS]

150 Pages·1977·7.533 MB·English

by  H. Tijdeman

DOCUMENT CONTROL SHEET
i
ORIGINATOR'S REF. SECURITY CLASS.
NLR TR 77090 U Unclassified
ORIGINATOR
National Aerospace Laboratory (NLR)
Amsterdam. The Netherlands
TITLE
Investigations of the transonic flow around oscillating airfoils
AUTHORS DATE PP ref
H. Tijdeman 21-x-77 146 I88
I
DESCRIPTORS
Supercritical wings Wind-tunnel tests
Ai rfoi 1 s Wind-tunnel walls
Unsteady flow Wing oscillations
Transonic flow Aerodynamic loads
Pressure distribution
Pressure measurements
ABSTRACT
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

NLR TR 77090 U
INVESTIEATIONS OF THE TRANSONIC FLOW AROUND
OSCILLATING AIRFOILS
by
H. Tijdernan
SUMMARY
Exploratory wind-tunnel experiments in high-subsonic and transonic
flow on a conventional airfoil with osciliating 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 probiem 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.
Division: Fluid Dynamics Completed : 21-X-77
6
Prepared: HT Ordernumber: 524.109/101,618
Approved: HB TYP. : H6

This report served the author as a thesis to obtain
a Ph. D. degree of Delft Technological University

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 it5 "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 smali
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.
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CONTENTS
Page
I BACKGROUND AN0 OUTLINE OF THESIS 9
I.I Background 9
1.2 Outiine of thesis 11
PART i: INTRODUCTORY CHAPTERS
2 THE FLOW AROUND OSCILLATING AIRFOILS 15
2.1 Description of unsteady airioads 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
3.4 Viscous aspects 24
PART li: 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 Principie.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 s t i l l 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 WINO-TUNNEL MODELS AND TEST SET-UP 38
6.1 NACA 64A006 airfoil with flap 38
6.2 NLR 7301 airfoil 39
6.3 Wind tunnel 41
6.4 Optical flow studies 41
7 TEST PROGRAM 42
7.1 NACA 64A006 airfoil with flap 42
7.2 NLR 7301 airfoil 42
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PART Ill: ANALYSIS OF RESULTS
8 THE INTERACTION BETWEEN THE STEADY AND UNSTEADY FLOW FIELD 47
8.1 Introductory remarks 47
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
fl.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 Additionai remarks 69
9.5.1 Some properties of the unsteady shock relations
9.5.2 Possible use of the shock-wave model
10 THE UNSTEAOY AERODYNAMIC CHARACTERISTICS OF THE "SHOCK-FREE'' NLR 7301 AIRFOIL 70
10.1 Introductory remarks 70
71
10.2 Unsteady pressure distributions
10.2.1 Fully subsonic flow (condition I)
10.2.2 Transonic flow with shock wave (condition 11)
10.2.3 The "shock-free'' design condition (condition Ill)
10.3 Unsteady aerodynamic coefficients 75
10.4 Remarks on the motion of the shock wave 78
81
10.5 The influence of the transition Strip
10.6 Some additional effects 83
10.6.1 The effect of Mach number
10.6.2 The effect of the amplitude of oscillation
84
10.7 Concluding remarks
I1 SOME CONSIDERATIONS ON A LINEARIZED TREATMENT OF UNSTEADY TRANSONIC FLOWS 86
I 1.1 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
li.3.i "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
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PART IV: THE CURRENT STATUS OF UNSTEADY FLOW THEORY ANO EVALUATION OF SOME NEW METHODS Page
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 ioad distribution
12.2.2 The Kernel-function method
12.2.3 The Doublet-Lattice method
12.3 Hethods for high-subsonic fiow 1 O0
12.3.1 Local-Mach-number corrections in linearized lifting-surface theory
12.3.2 Methods based on the iinearized transonic small-perturbation equation
12.4 Wethods for near-sonic flow without shock waves 102
12.5 Methods for transonic fiow 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-wal i interference
13.2.2 Subsonic fiow
13.2.3 Transonic flow with shock wave
13.2.4 "Shock-free" flow
13.3 Comparisons between theory and experiment in unsteady flow Ill
13.3.1 Pressure distributions
13.3.2 Aerodynamic coefficients
13.3.) Shock-wave motions
13.4 Concluding remarks 117
14 IMPACT OF THE NLR INVESTIGATIONS AND FUTURE PROSPECTS i i8
14.1 Impact of the NLR investigations 118
14.2 Future prospects 118
i5 REFERENCES 1 19
APPENDIX A: DEFINITION OF STEADY AND UNSTEADY AERODYNAMIC QUANTITIES
APPENDIX E: THE DYNAMIC RESPONSE OF TUBE-TRANSDUCER SYSTEMS
APPENDIX C: DERIVATION OF THE QUASI-STEADY AN0 UNSTEADY SHOCK RELATIONS
APPENDIX D: LIST OF SYMBOLS
APPENDIX E: SUMMARY IN DUTCH (SAMENVATTING IN HET NEDERLANDS)
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