evolution of an acoustic disturbance to transition in the boundary layer on an airfoil

219 Pages·1999·13.88 MB·English

by  Howard S. Kanner

EVOLUTION OF AN ACOUSTIC DISTURBANCE TO
TRANSITION IN THE BOUNDARY LAYER ON AN AIRFOIL
by
Howard S. Kanner
Dissertation submitted to the Faculty of
Virginia Polytechnic and State University
In partial fulfillment of the requirements of the degree of
Doctor of Philosophy
In
Aerospace Engineering
Joseph Schetz, Chairman
Richard Barnwell
Meelan Choudhari
James Marchman
Wing Ng
Richard Wlezien
22 - February 1999
Blacksburg, Virginia
Keywords: Boundary Layer, Receptivity, Tollmien-Schlichting Wave
Copyright 1999, Howard S. Kanner
EVOLUTION OF AN ACOUSTIC DISTURBANCE TO TRANSITION IN THE
BOUNDARY LAYER ON AN AIRFOIL
Howard S. Kanner
Abstract
An experiment has been conducted to examine the generation and subsequent evolution of
boundary-layer disturbances on a two-dimensional airfoil up through transition to turbulent flow.
The experiment was conducted at the NASA Langley Research Center (cid:210)2˚ft by 3˚ft Low Speed
Wind Tunnel Facility.(cid:211) The primary objective of the experiment was to generate a
comprehensive database that includes the effect of the external disturbance environment on the
transition process and can be used as a benchmark for future transition prediction tools. The
airfoil used for this experiment was custom designed. The model was a 6% thick, 4-ft chord
unswept symmetric wing. A description of the design procedure, along with the theoretical
stability characteristics of the airfoil will be presented in this paper. The experiment consisted of
establishing the mean flow conditions, forcing two-dimensional Tollmien-Schlichting (T-S)
waves in the boundary layer using modulated acoustic bursts in the free-stream, and acquiring
the mean boundary-layer data and fluctuating disturbance data using hot-wire probes. The
acoustic receptivity due to surface roughness near Branch I has been examined. The surface
roughness consisted of two-dimensional strips of tape applied at and symmetrically spaced about
Branch I. Repeated roughness elements were spaced one wavelength apart based upon the
wavelength of the primary forcing frequency as determined by linear-stability theory. The test
conditions consisted of mean flow velocities of 15 and 20˚m/s, which correspond to chord
Reynolds numbers of 1.25 and 1.68˚million, respectively. Boundary-layer disturbance profiles
and constant boundary-layer height chordwise traverses were acquired and examined at
individual frequencies and in total energy amplitude / broadband forms. The experimental
results match well with linear stability theory and linear parabolized stability equations,
indicating breakdown of disturbances between N-factors of 7 and 11 with surface roughness on
the model. It was observed that when the flow physics change, differences between linear-
stability theory and experiment are strongly apparent. An amplitude-based breakdown criterion
was defined for the developing boundary-layer responses, which were burst-type packets like the
acoustic forcing signal. A criterion was defined for the breakdown of both maxima of the T-S-
like disturbance profile. Overall, the effects of surface roughness and free-stream acoustic
forcing on boundary-layer receptivity and stability were examined in a well-documented
disturbance environment. These results will be used to validate and refine non-linear flow
theories as well as help to provide an improved understanding and improved methods to control
flow transition.
iii
Acknowledgements
I would like to thank my advisor, Professor Joseph Schetz for all of his guidance, support and
encouragement throughout this work. I would also like to thank Dr. Richard Wlezien, NASA
Langley Research Center, for all of our technical discussions and his support and guidance.
I am grateful to all whom have made this project possible including Dr. Meelan Choudhari, High
Technology Corporation, and Dr. Ronald Joslin, NASA Langley Research Center, and to Dave
Chestnutt and Rita Aguillard of the Virginia Consortium for Engineering and Science
Universities who helped make the virtual campus a smaller world.
I would like to express my appreciation to Innovative Aerodynamic Technologies for use of the
LAMDA airfoil analysis package and Fei Li of High Technology Corporation for completing
linear PSE solutions.
Finally, I would like to express my deep gratitude to my wife Amy and my daughters Quinn and
Bryce who were always there for me.
This work was performed with the support of NASA Grant NAG-1-1682
iv
Contents
Acknowledgements....................................................................................................................iv
Nomenclature.........................................................................................................................viii
Figures.......................................................................................................................................x
Tables.......................................................................................................................................xii
1 Introduction.......................................................................................................................1
1.1 Background......................................................................................................................................1
1.2 History of Boundary-Layer Stability Studies..............................................................................1
1.2.1 Receptivity...............................................................................................................................................4
1.2.1.1 Receptivity to Modulated Bursts...................................................................................................5
1.2.2 Transition Prediction...............................................................................................................................6
1.2.3 Free-Stream Disturbances.......................................................................................................................7
1.3 Experimental Disturbance Environment.....................................................................................8
1.4 Overview of this document.............................................................................................................9
2 Facility and Instrumentation...........................................................................................10
2.1 Facility............................................................................................................................................10
2.2 Instrumentation.............................................................................................................................11
2.2.1 Hot-Wire Probe Supports......................................................................................................................12
3 The Airfoil Model.............................................................................................................14
3.1 Model Installation and Alignment..............................................................................................18
3.2 Test Section Set-Up.......................................................................................................................19
3.3 Roughness Configurations...........................................................................................................20
3.4 Model Fabrication Results...........................................................................................................22
4 Experimental Techniques and Data Acquisition..............................................................25
4.1 Acoustic Forcing............................................................................................................................25
4.2 Hot-Wire Probe Measurements..................................................................................................29
4.2.1 Turbulence Intensity Measurements.....................................................................................................29
4.2.2 Boundary-Layer Profile Measurements................................................................................................30
4.2.3 Boundary-Layer Chordwise Traverse Measurements..........................................................................31
4.3 Boundary-Layer Responses to the Acoustic Excitation...........................................................32
4.4 Data Acquisition Codes................................................................................................................33
4.5 Computational Tools.....................................................................................................................34
4.6 Uncertainty Analysis.....................................................................................................................35
v
5 Results and Discussion.....................................................................................................37
5.1 Test Plan.........................................................................................................................................37
5.2 Experimental Results and Comparisons to Theory..................................................................37
5.2.1 Test Section Set-Up Results..................................................................................................................38
5.2.2 Mean Flow Results................................................................................................................................40
5.2.2.1 Model Alignment, Surface Pressure Distribution and Angle of Attack....................................40
5.2.2.2 Theoretical Mean Flow Results..................................................................................................44
5.2.2.3 Experimental Mean Flow Results with Comparisons to Theory...............................................47
5.2.2.4 Mean Boundary-Layer Velocity Profiles....................................................................................56
5.2.2.5 Flow Transition Analysis............................................................................................................61
5.2.3 Boundary-Layer Modeshape Results....................................................................................................66
5.2.3.1 Tollmien-Schlichting Modeshape Analysis................................................................................66
5.2.3.2 Frequency Spectra of Modeshape Results..................................................................................78
5.2.3.3 Comparison of Experimental and LPSE Modeshapes...............................................................81
5.2.3.4 Chordwise Traverse of Modeshape Results...............................................................................84
5.2.3.5 Total Energy Amplitude Disturbance Profiles...........................................................................86
5.2.3.6 Amplitude-Based Disturbance Breakdown Criterion from Disturbance Profile Results.......111
5.2.4 Boundary-Layer Chordwise Traverse Results....................................................................................111
5.2.4.1 Time Traces and Wave Speed Results......................................................................................112
5.2.4.2 Non-Dimensional Single-Frequency Amplitude Growth........................................................116
5.2.4.3 Receptivity Coefficient..............................................................................................................132
5.2.4.4 Comparison of Repeated Roughness Results to Flat Plate Experiments.................................142
5.2.4.5 Comparison of Single-Frequency Disturbance Amplitudes to Linear Stability Theory.........142
5.2.4.6 Boundary-Layer Response Frequency Spectra.........................................................................158
5.2.4.7 Total Energy Amplitude Results...............................................................................................165
5.2.4.8 Amplitude-Based Disturbance Breakdown Criterion for Chordwise Traverse Results..........180
6 Summary and Conclusions............................................................................................181
7 References......................................................................................................................186
vi
Appendices:
Appendix A: Model Surface and Pressure Port Coordinates...........................................A-1
Appendix A-1: Model Design Coordinates.......................................................................................A-1
Appendix A-2: Quality Assurance Measured Centerline Coordinates.........................................A-2
Appendix A-3: Surface Pressure Port Coordinates.......................................................................A-13
Appendix B: Hardware Inventory....................................................................................B-1
Appendix C: Experimental Procedure Check Lists..........................................................C-1
Appendix C-1: Everyday....................................................................................................................C-1
Appendix C-2: Mean Pressure Measurements................................................................................C-1
Appendix C-3: Install and Calibrate the Hot-Wire.........................................................................C-1
Appendix C-4: Set Up Acoustic Forcing (20˚m/s Flow Case).........................................................C-2
Appendix C-5: Set Up Acoustic Forcing (15˚m/s Flow Case).........................................................C-2
Appendix C-6: Boundary-Layer Profile Measurements................................................................C-3
Appendix C-7: Boundary-Layer Chordwise Traverse Measurements.........................................C-3
Vita........................................................................................................................................V-1
vii
Nomenclature
a, speed of sound
b, span
b, gaussian waveform coefficient
C , pressure coefficient
p
c, chord
c, convection wave speed
e, hot-wire voltage
F = 2 p ˜ n / U2 x 106, dimensionless frequency
g, gaussian envelope function
h, roughness height
M = U / a, Mach number
N-factor = ln (u / u ), logarithmic disturbance amplitude ratio
TS ref
OHR = r / r - 1, hot-wire over-heat ratio
hw cold
Re = r U x / m, Reynolds number based upon length scale x
x
SF , boundary-layer stepping scale factor for traversing inside the boundary layer
in
SF , boundary-layer stepping scale factor for traversing above the boundary layer
out
S = w r / U , Strouhal number
¥
T, temperature
t, airfoil thickness
U, mean streamwise velocity
u, fluctuating streamwise velocity component
x, chordwise or stream-wsie coordinate
y, chord-normal coordinate
a, angle of attack
a , hot-wire temperature coefficient of resistivity at reference temperature T
o o
d, boundary-layer thickness
d*, displacement thickness
˜, frequency
l, wavelength
m, absolute viscosity
n = m / r, kinematic viscosity
q, momentum thickness
r, density
viii
Subscripts
cal, calibration
c, corrected
d, disturbance
DS, downstream source
¥
fs, , free-stream
LPSE, linear parabolized stability equations
LST, linear stability theory
min, minimum
p-p, peak-to-peak amplitude
rms, root-mean-square energy amplitude
s, acoustic source signal
th, theory
T-S, Tollmien-Schlichting disturbance
US, upstream source
ix
Figures
Figure 1: NASA Langley Research Center 2 ft x 3 ft Low Speed Wind Tunnel Facility............10
Figure 2 (a,b,c) Hot Wire Probe Supports.................................................................................13
Figure 3: Model Pressure Port Layout.......................................................................................17
Figure 4: HSK-R01 Model........................................................................................................18
Figure 5: Test 10 Roughness Configuration - 5 Repeated Roughness Elements.........................22
Figure 6: Design vs. Actual Surface Coordinates Along the Model CenterLine.........................23
Figure 7: Difference between Design and Actual Airfoil Coordinates.......................................24
Figure 8: Design vs. Actual Surface Coordinates over Entire Model.........................................24
Figure 9: Determining the Tunnel Acoustic Transfer Function..................................................26
Figure 10: 300 Hz Acoustic Forcing Burst Time Trace and Power Spectral Density..................27
Figure 11: 200 Hz Acoustic Forcing Burst Time Trace and Power Spectral Density..................28
Figure 12: Test Section Ceiling Theoretical Surface Contour: Upstream Mount Location.........39
Figure 13: Test Section Ceiling Theoretical Surface Contour: Downstream Mount Location.....39
Figure 14: Test Section Ceiling Surface Pressure Distribution: Theory vs. Experiment.............40
Figure 15: Model Alignment Angle as Computed by Y Measurements.................................41
wall
Figure 16: Model Surface Pressure Distribution........................................................................43
Figure 17: Locating the Stagnation Point..................................................................................44
Figure 18: Comparison of Mean Flow Solutions.......................................................................46
Figure 19: 20 m/s Pressure Distribution Based Upon Boundary-Layer Edge Velocity...............48
Figure 20: 20 m/s Mean Flow Boundary-Layer Integral Parameters, d* and q...........................50
Figure 21: 15 m/s Pressure Distribution Based Upon Boundary-Layer Edge Velocity...............52
Figure 22: 15 m/s Mean Flow Boundary-Layer Integral Parameters, d* and q...........................53
Figure 23: 30 m/s Pressure Distribution Based Upon Boundary-Layer Edge Velocity...............54
Figure 24: 20 m/s Mean Boundary-Layer Velocity Profiles.......................................................57
Figure 25: Flow Transition Study Results.................................................................................62
Figure 26: 20 m/s Modeshape Results at Select Chordwise Stations..........................................70
Figure 27: 15 m/s Modeshape Results at Select Chordwise Stations..........................................75
Figure 28: 20 m/s Modeshape Results for Select Surface Conditions ........................................76
Figure 29: 15 m/s Modeshape Results for Select Surface Conditions ........................................77
Figure 30: 20 m/s Frequency Spectra from Modeshape Results.................................................79
Figure 31: 15 m/s Frequency Spectra from Modeshape Results.................................................79
Figure 32: 20 m/s Surface Roughness Equivalent Frequency Spectra........................................80
Figure 33: 15 m/s Surface Roughness Equivalent Frequency Spectra........................................80
Figure 34: 20˚m/s, 300˚Hz LPSE Modeshape Comparison (Lower Lobe)..................................82
Figure 35: 20˚m/s, 300˚Hz LPSE Modeshape Comparison (Upper Lobe)..................................83
Figure 35: 20 m/s Chordwise Traverse from Modeshape Results..............................................85
Figure 36: 15 m/s Chordwise Traverse from Modeshape Results..............................................85
Figure 37: 20 m/s U /U Disturbance Profiles at Select Chordwise Stations............................89
p-p ¥
Figure 38: 15 m/s U /U Disturbance Profiles at Select Chordwise Stations............................94
p-p ¥
Figure 39: 20 m/s U /U Disturbance Profiles for Select Surface Conditions..........................95
p-p ¥
Figure 40: 15 m/s U /U Disturbance Profiles for Select Surface Conditions..........................96
p-p ¥
Figure 41: 15 m/s Test 11 Peak-to-Peak Disturbance Profiles....................................................97
x