Numerical Investigation of Tonal Noise on a Transitional Airfoil under Varying Conditions

91 Pages·2015·3.3 MB·English

by  Warren W. Hiner

Dissertations and Theses
4-2015
Numerical Investigation of Tonal Noise on a
Transitional Airfoil under Varying Conditions
Warren W. Hiner
Embry-Riddle Aeronautical University - Daytona Beach
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Hiner, Warren W., "Numerical Investigation of Tonal Noise on a Transitional Airfoil under Varying Conditions" (2015).Dissertations
and Theses. 166.
https://commons.erau.edu/edt/166
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NUMERICAL INVESTIGATION OF TONAL NOISE ON A TRANSITIONAL
AIRFOIL UNDER VARYING CONDITIONS

A Thesis
Submitted to the Faculty
of
Embry-Riddle Aeronautical University
by
Warren Hiner

In Partial Fulfillment of the
Requirements for the Degree
of
Master of Science in Aerospace Engineering

May 2015
Embry-Riddle Aeronautical University
Daytona Beach, Florida

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TABLE OF CONTENTS
LIST OF TABLES .............................................................................................................. v
LIST OF FIGURES .......................................................................................................... vi
SYMBOLS ......................................................................................................................... ix
ABBREVIATIONS ............................................................................................................ x
ABSTRACT ....................................................................................................................... xi
1. Introduction .......................................................................................................... 1
1.1. Motivation ................................................................................................................... 1
1.2. Airfoil Noise ............................................................................................................... 1
1.3. Characteristics of Transitional Airfoil Noise ............................................................ 2
1.4. Proposed Theories For Explaining Tonal Noise ...................................................... 5
1.5. Objective of Current Work ........................................................................................ 9
2. Numerical Models .............................................................................................. 12
2.2. The ILES Code ......................................................................................................... 12
2.3. The Acoustic Field Computation ............................................................................ 14
2.4. The Linear Stability Calculations ............................................................................ 16
2.4.1. The Linear Stability Theory ................................................................................. 16
2.4.2. The Linear Stability Code, LASTRAC ............................................................... 19
2.5. How The Stability Results Will Be Used ............................................................... 22
3. Results ................................................................................................................ 25
3.1. Varied Angle of Attack at Re = 180,000 ................................................................ 26
3.1. Tonal cases - Incidence Angle < 6˚. ........................................................................ 27
3.1.1. Tones ..................................................................................................................... 27
3.1.2. Separation Bubbles ............................................................................................... 30
3.1.3. Linear Stability ..................................................................................................... 32
3.1.4. Correlation Between Acoustic Tones and LST Peaks ....................................... 37
3.1.5. Vortex Shedding ................................................................................................... 41
3.1.6. Correlation with the Airfoil Surface Pressure..................................................... 44
3.1.7. The Proposed Feedback Loop ............................................................................. 47
3.2. Non-tonal cases ......................................................................................................... 50
3.2.1. Acoustic-Spectra ................................................................................................... 50
3.2.2. Flow Separation .................................................................................................... 50
3.2.3. The LST Results ................................................................................................... 51
3.2.4. Vorticity ................................................................................................................ 56
3.2.5. Surface Pressure Spectra ...................................................................................... 57
3.2.6. Proposed Interpretation of the Disappearance of Tones .................................... 58
3.3. Effect of Reynolds Number at 2˚ Angle of Attack ................................................. 59
3.3.1. Tones ..................................................................................................................... 59
3.3.2. Separation Regions ............................................................................................... 61
3.3.3. The LST Results ................................................................................................... 64
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3.3.4. Vorticity Contours ................................................................................................ 67
3.3.5. Surface Pressure Spectra ...................................................................................... 68
3.3.6. Proposed Interpretation of the Effect of Reynolds Number .............................. 70
4. Conclusion .......................................................................................................... 72
4.1. Confirmation of results from prior studies .............................................................. 72
4.2. New conclusions based on current work ................................................................ 73
5. Future Work ....................................................................................................... 76
References ......................................................................................................................... 77
v

LIST OF TABLES

Table 3.1. Far-field peak tonal frequencies by case .......................................................... 29
Table 3.2. Locations of suction and pressure side separation bubbles ............................. 31
Table 3.3. Locations of suction and pressure side separation bubbles ............................. 51
Table 3.4. Near-field tonal frequencies. ............................................................................ 60
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LIST OF FIGURES

Figure 1.1. Example of tonal and broadband spectrums. .................................................... 2
Figure 1.2. Noise from transitional vortex shedding (Brooks et al., 1989). ....................... 3
Figure 1.3. Tonal peaks in acoustic spectrum (Nash et al., 1999). ..................................... 3
Figure 1.4. Ladder structure of tones (Petterson et al., 1973). ............................................ 4
Figure 1.5. Envelope of tonal noise (Arcondoulis et al., 2010). ......................................... 5
Figure 1.6. Feedback model proposed by Tam (1974). ...................................................... 6
Figure 1.7. Feedback model proposed by Arbey & Bataille (1983). .................................. 7
Figure 1.8. Feedback model proposed by Nash et al. (1999) ............................................. 8
Figure 1.9. Feedback model proposed by Desquesnes et al. (2007). .................................. 9
Figure 1.10. Effect of one-sided tripping (Golubev et al., 2014)...................................... 10
Figure 1.11. Scope of current study. ................................................................................. 11
Figure 2.1. Explanation of instability growth. .................................................................. 18
Figure 2.2. Boundary layer profile locations (Nash et al., 1999)...................................... 23
Figure 2.3. Growth rates at chordwise stations (Nash et al., 1999) .................................. 23
Figure 2.4. Instability amplification at station 12 for tonal cases (Nash et al., 1999). ..... 24
Figure 2.5. Chordwise amplification at 1048 Hz. (Nash et. al, 1999) .............................. 24
Figure 3.1. Airfoil grid and control surface (purple line). ................................................ 26
Figure 3.2. Varying angle of attack for fixed Re = 180,000 (Arcondoulis et al., 2010) ... 27
Figure 3.3. Presence of tones for varied angle of attack ................................................... 28
Figure 3.4. Far-field acoustic spectra for cases with tonal peaks at 0°, 2°, 4°, 6°. ............ 29
Figure 3.5. Near-field spectra of tonal cases at 0°, 2°, 4°, 6°. ........................................... 30
Figure 3.6. Separation regions for tonal cases. ................................................................. 32
Figure 3.7. Chordwise amplification of predicted peak for 0˚. ......................................... 34
Figure 3.8. Chordwise amplification and boundary layer statistics for 2˚ ........................ 35
Figure 3.9. Chordwise amplification and boundary layer statistics for 4˚ ........................ 36
Figure 3.10. Chordwise amplification and boundary layer statistics for 6˚. ..................... 37
Figure 3.11. 0˚ Amplification. .......................................................................................... 39
Figure 3.12. 2˚ Amplification (pressure surface left, suction surface right). .................... 39
Figure 3.13. 4˚ Amplification (pressure surface left, suction surface right). .................... 39
Figure 3.14. 6˚ Suction Surface Amplification. ................................................................ 40
Figure 3.15. Maximum amplification at the trailing edge. ............................................... 40
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Figure 3.16. Instantaneous vorticity contours compared to time averaged velocity. ....... 42
Figure 3.17. 2˚ pressure contour used to calculate vortex shedding frequency. ............... 43
Figure 3.18. Correlation between observed and predicted frequencies ............................ 44
Figure 3.19. 0° Surface pressure spectra. .......................................................................... 45
Figure 3.20. 2˚ Surface pressure spectra. .......................................................................... 45
Figure 3.21. Suction surface wall pressure spectra at 4˚. .................................................. 46
Figure 3.22. Suction surface wall pressure spectra at 6˚. .................................................. 47
Figure 3.23. Far-field acoustic spectra for cases without tonal peaks. ............................. 50
Figure 3.24. Separation regions for cases without tones. ................................................. 51
Figure 3.25. Chordwise amplification of predicted frequencies for 8˚ ............................. 52
Figure 3.26. Chordwise amplification of predicted frequencies for 10˚ ........................... 53
Figure 3.27. Chordwise amplification of predicted frequencies for 12˚ ........................... 54
Figure 3.28. 8˚ Amplification ........................................................................................... 55
Figure 3.29. 10˚ Amplification ......................................................................................... 55
Figure 3.30. 12˚ Amplification ......................................................................................... 56
Figure 3.31. Instantaneous vorticity contours. .................................................................. 57
Figure 3.32. Suction surface wall pressure spectra at 10˚. ................................................ 58
Figure 3.33. Varying Re for fixed angle (Arcondoulis et al., 2010). ................................ 60
Figure 3.34. Near-field spectrum for Re = 144,000. ........................................................ 61
Figure 3.35. Near-field spectrum for Re = 288,000. ......................................................... 61
Figure 3.36. Separation Regions with Varied Re. ............................................................ 62
Figure 3.37. Cf at Re = 268,000. ....................................................................................... 63
Figure 3.38. Peak N-factor for Re = 144,000. .................................................................. 64
Figure 3.39. Peak N-factor for Re = 288,000. .................................................................. 65
Figure 3.40. Peak N-factor for Re = 468,000. .................................................................. 65
Figure 3.41. Chordwise amplification of tonal frequency for Re = 144,000. ................... 66
Figure 3.42. Chordwise amplification of tonal frequency for Re = 288,000. ................... 66
Figure 3.43. Chordwise amplification of tonal frequency for Re = 468,000. ................... 67
Figure 3.44. Vorticity contours for Re = 144,000. ........................................................... 67
Figure 3.45. Vorticity contours for Re = 288,000. ........................................................... 68
Figure 3.46. Wall pressure spectra for Re = 144,000 ....................................................... 69
Figure 3.47. Wall pressure spectra for Re = 288,000 ....................................................... 69
viii
ix

SYMBOLS

u Tangential velocity
v Normal velocity
w Spanwise velocity
𝑉⃑ Velocity vector
𝜌 Density
T Temperature
p Pressure
Re Reynolds number
ν Viscosity
l Length scale
φ Disturbance vector
ω Nondimensional frequency
f frequency
α Complex streamwise wavenumber
−𝛼 Disturbance growth rate
𝑖
A Disturbance amplitude
𝐴 Initial disturbance amplitude
0
𝐶 Coefficient of friction
𝑓
τ Wall shear stress
w