Rectangular Cavity L/D = 1, 1.2, 2 and 3, low speed (takeoff and landing speed), as well as Circular Cavity at MACH 2.3, high speed. Experimental study.

1. An Investigation Based On Experimental Study of
Air Flow
Across Rectangular
and Circular Cavities
(Aircraft Industry)
By Chun C Gan
4th December, 2019
MSc Operations Management
[Manchester School Management]
University of Manchester Institute of Science and Technology (UMIST),
United Kingdom.
BEng (Hons) Mechanical Engineering
[Simon Building]
University of Manchester, United Kingdom

2. Scientific Discovery
An Experimental Fluid Flow Project

3. Introduction to Experimental Study –
Fluid Flow
• The need to classify flow (fluid) whether laminar, transition or
turbulence. This is done by Osborne Reynolds, an Irish-born British
inventor. (in this situation, visualising in air flow tunnel.)
• For turbulent flow, i.e. real flow, Vincenc Strouhal, a Czech physicist,
experience vortex shedding wind tunnel, deriving relationship with
fluid frequency of vortex sheding force with respect to the bluff body.
• High Speed flow for speed of sound achieved by Pierre Gassendi, a
French scientist and philosopher in the 17th century that measured
Speed of Sound in Air.

4. Brief on Asborne Reynolds
• Osborne Reynolds
(23 August 1842 – 21 February
1912) was a prominent Irish-born
British innovator in the
understanding of fluid dynamics.
• Separately, his studies of heat
transfer between solids and fluids
brought improvements in boiler
and condenser design.
• He spent his entire career at what
is now the University of
Manchester.

5. Brief on Vincenc Strouhal
• Vincenc Strouhal
(10 April 1850 – 26 January 1922)
was a Czech physicist specializing
in experimental physics.
• He was one of the founders of the
Institute of Physics of the Czech
part of Charles University.
• In 1878 experiencing vortex
shedding and singing in the wind.
The Strouhal number is an integral
part of the fundamentals of fluid
mechanics.

6. Pierre Gassendi – Measuring the Speed of
Sound (MACH No.)
• Pierre Gassendi (22 Jan 1592 – 24 Oct 1655)
• A French scientist and philosopher, 17th
century
• Measured Speed of Sound in Air
• Although obtained was too high about 478.4
m/s, he correctly concluded that speed of
sound is independent of frequency
• MACH No. M =
𝑈
𝑎
where,
U is the Freestream Velocity, and
a is the Speed of Sound (343 m/s)

7. Hermann Ludwig Ferdinand von Helmholtz
Hermann Ludwig Ferdinand von
Helmholtz (31 August 1821 – 8
September 1894)
German physicist and physician
who made significant contributions

8. The Search for Aircraft (Surface)
Stability
New Approaches

9. • Experimental Study with data to substantiate the observed facts, with
analysis based on these approaches, making it possible.
• Design and make to enable maintenance free practises, allowing
absolutely trend prediction possible at users’ finger tips.
• Search abilities to ensure that these findings are ascertained, for
industrial delivery, documents and drawings checked.
Scientific Approaches to Achieve Stability

10. • Stable aircraft that tends to diverge from its intended flight path will
stay off its intended path during a flight path.
• An aircraft stays on its flight path to achieve its desired destination.
• Thus it is important for any design to achieve the desired degree of
stability.
• The widespread use of digital computers is increasingly common for
surface design to be inherently stable and rely on computerised
software to provide simulation based experimental facts.
Aircraft Industry – Stability, Surface Design

11. Development and Plausible Explanation
- National Body, Association, Company
- Oscillation of Shear Layer (Vortex Shedding)

12. Development in Research on Buffeting
Problems in Aircraft Industry
• 1952 - Boeing Aeroplane Company
Conducted research intensive periodic oscillation in the structure
gave rise to severe buffeting problems and was accompanied by
emission of an acoustic signal
• 1955 - National Advisory Committee For Aeronautics
Investigated buffeting problems at California Institute of Technology
which came up with remarkable flow visualisation pictures. These
pictures gave a better understanding into the problems of noise
emission from the structure
• 1970s - Investigations on other part of the aircraft, for example
landing gears, have been in particular interest in the late 70’s

13. The Facts on Boundary Layer Separation
• In the late 1970’s, an area that aerospace researchers has spent a lot
of time to understand the problem is boundary layer separation at
landing gear section.
• Boundary layer separation happens when the air flows continuously
across rectangular (landing gear section) during take off or landing.
• As the fluid passes through a rectangular cavity, the boundary layer of
the define thickness forms oscillating vortices hits the downstream
edge of the cavity and surfaces releasing nuisance noise (energy).

14. The Experimental Study – The Possible
Explanations
• The oscillation of this pressure wave at peak amplitude are of distinct
frequency (cyclical) and resonate at high magnitude of force,
exemplified the situation.
• These waves travel continuously toward the downstream edge of the
aircraft turns the situation to a buffeting problem.
• The findings shows the a distinct “cause of the source” of these
problems based on these possible pressure wave fluctuations. In this
case, the source of noise is in question.

15. The Study - The Possible Reasons (1)
• The study investigates that the problem could have been caused by
the shear layer that travels downstream, hitting the edge of the
cavity.
• Thus, it pointed to a factual point that the condition of continuous
oscillation causes these problem that arise.
• Aircraft surfaces, designed to avoid these damages cause by shear
layer, resonating at peak frequency during flight time cause to the
aircraft surface.

16. The Study - The Possible Reasons (2)
• The buffeting problem was in particular interest in the mid 20th
century. It was found that the damage is due to repetitive oscillation
of shear layer forming pressure wave at peak amplitude induced
inside the cavity.

17. The Experimental Study – A Resonance Limit
• The findings is based on ‘The Possible Results of Experimental
Findings’ utilising subsonic and supersonic wind tunnel.
• This explains that noise (energy) appears originating from the
downstream edge of the cavity.
• The hypothetical question that “noise, sourced from the downstream
cavity, damages aircraft surfaces is inferred from the findings as it is
reported based on these results.

18. Scientific Norm of the Variance Source
Past, Current and Future

19. Past, Current, Future Research
> Past Research (conventional methodology) – 1950s, 1960s, 1970s
Hot-wire anemometer was used to measure the shear layer fluctuation
for the shallow cavity which was related to noise generation.
> Current Research (approaches) - Late 1980s onwards
Noise Measurement Techniques, such as microphone (in decibel
reading), could adopted in this project to compare frequency content
of the noise obtained in this project.
> Future Research (simulations/equations) – 1990s and beyond
Online Analysis based on observable facts. Computer software
development for dynamic simulation on scientific patterns.

20. The Results - A Frequency Generator
• Shear layer resonation occurs at distinct frequency when amplitude is
at its peak. This happens as air flows downstream for different L/D
ratios.
• Energy forms during these circumstances when the “fixed or
adjustable” part / component (model) turns to be a frequency
generator.
• Subsonic (Low) and Supersonic (High) air flow.

21. Conversely,
Future Aircraft Noise Reduction Solution
• Detect Air Flow Technology DAFT – A Future Programme in Aircraft
Noise Mitigation Plan
• Approach of this system adhere to the specific requirements as stated
herein, whereby the notion of noise source as such in this situation to
ensure that it is resolved using past/current practising method.
• A programme to prevent noise source from appearing when it is not
required when in required in use. A subjective conjugate that is as
show herein.

22. Subsonic and Supersonic Wind Tunnel
Low Speed – for M<1, take-off and landing
High Speed – for M=2.3

23. The Wind Tunnels – Subsonic and Supersonic
Subsonic – Low Speed Supersonic – High Speed

24. Windtunnel Similarities
Subsonic Wind Tunnel
• Air Intake (Honeycomb inclusive –
calibration, for differential pressure
reading, using manometer
preferrably)
• Entry Length Section, Air Flow
Stabilization (section before
reaching bluff body)
• Bluff body (experimental area)
• Exist Section (Pressure Reduction)
Supersonic Wind Tunnel
• Air Intake (Bell mouth – for
calibration, pressure reading)
• MACH No. Generator
• Noise Generator (pressure reading
section), based on Helmholtz
Resonator
• Exist Section

25. Aircraft Rectangular Cavity
Subsonic Flow (M<1, where MACH 1 = 343 m/s or 1234.8 kmh)

26. Boundary Layer – Shear Layer
(By Experiment)

27. - Static Simulation of
Flow Pattern
Streamlines / Pressure Fluctuations – Air flow
across cavities of various L/D ratios simplified
in the diagram.
- Back Pressure Waves
Back Pressure – Wave pressure form at the
downstream edge of the cavity flows in the
right direction, acting on the light air as it
travels in the positive direction.
t
y(t)
Noise (energy) appears from
downstream edge of the cavity.

28. Subsonic
Wind Tunnel Profile
Low Speed
Up to 40 m/s
(3.6 KM/HR = 1 m/s; 40 – 150 KM/HR)
Signal Level
Up to 100 mV
Frequency
148, 80, 50, 129 Hz
L/D
1, 1.2, 2, 3
Feature
Fixed

29. MACH <= 1
L/D = 1
>Rectangular Cavity
Specifications:
Frequency f 148 Hz
Length L 50 mm
Depth D 50 mm
Width W 460 mm
CONFIDENTIAL

30. MACH <= 1
L/D = 1.2
>Rectangular Cavity
Specifications:
Frequency f 129 Hz
Length L 60 mm
Depth D 50 mm
Width W 460 mm
CONFIDENTIAL

31. MACH <= 1
L/D = 2
>Rectangular Cavity
Specifications:
Frequency f 80 Hz
Length L 100 mm
Depth D 50 mm
Width W 460 mm
CONFIDENTIAL

32. MACH <= 1
L/D = 3
>Rectangular Cavity
Specifications:
Frequency f 50 Hz
Length L 150 mm
Depth D 50 mm
Width W 460 mm
CONFIDENTIAL

33. Respective Frequency f with regards to
Length-to-Depth L/D Ratio
Table 1 : Resonance Frequency of Rectangular Cavities
at Respective L/D Ratio
0
20
40
60
80
100
120
140
160
0 0.5 1 1.5 2 2.5 3 3.5
Frequency [Hz]
Length to Depth L/D Ratio
Figure 1 : Resonance Frequency of Rectangular Cavity at
Respective Length to Depth (L/D) Ratios
f [Hz] (Readings)
Length to
Depth (L/D)
Ratio
f [Hz]
(Readings)
y (Line of
Regression) Error %
1 148 148.4 -0.4 -0.2458
1.2 129 128.4 0.6 0.4975
2 80 78.6 1.4 1.7493
3 50 52.9 -2.9 -5.8722
Line of Regression, Equation
y = A + B * exp(C * x * -1)
A B C
38 300 1

34. Strouhal No. for respective Frequency f at
Resonating Length-to-Depth L/D Ratio
Table 2 : Strouhal Number of Air Flow Pass Rectangular Cavity
f [Hz]
Cavity
Length L
[mm]
Free Stream Velocity,
U [m/s]
Strouhal
Number
(St=fL/U)
148 50 20.3 0.36
129 60 26.6 0.29
80 100 27.6 0.29
50 150 35.2 0.21
0.0592, 0.36
0.0776, 0.29
0.0805, 0.29
0.1026, 0.21
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.0000 0.0200 0.0400 0.0600 0.0800 0.1000 0.1200
StrouhalNo.
MACH No.
Strouhal No. Versus MACH No.

35. Aircraft Circular Cavity
Supersonic Flow (M=2.3, where MACH 2.3 = 788.9 m/s or 2840.04 kmh)

36. Supersonic
Wind Tunnel Profile
High Speed
MACH 2.3
(MACH 1 = 343 m/s; 1234.8KM/HR)
Signal Level
Up to 68 mV
Frequency
220, 440, 660, 880, 1100 Hz
L/D
Variable
Feature
Adjustable

37. MACH 2.3
L/D = variable
> Circular Cavity
Specifications:
Frequency f <see diagram>
Length L (diameter) 50 mm
Depth D <see diagram>
CONFIDENTIAL
Magnitude
mV

38. CONFIDENTIAL

39. Calculation - Strouhal No.
• Length Across Circular Cavity, L = 50 mm { for adjustable piece }
• Frequency f = 880 Hz { at peak amplitude when depth D is 89.25 mm}
• Free-stream Velocity U = 2.3 {MACH No.}
• Therefore, Strouhal No. St =
𝑓 𝐿
𝑈
=
880 ∗ 50/1000
2.3 ∗ 343
= 0.06

40. Calculation – Resonance Frequency
At Low MACH No., M<1
(utilising establish line of regression, to estimate the
free-stream velocity and resonance peak frequency)
At High MACH No., M=2.3
(circular cavity), resonance peak as follows:-
• For L = 50 mm, D = 89.25 mm
L/D = 50/89.25
= 0.56
• Resonance Peak Frequency at
880 Hz
(in this situation, MACH No.=2.3)
Line Of Regression, to calculate resonance frequency
Equation A y = A + B *exp (C * x * -1)
A B C x (=L/D)
y (=frequency,
f)
38 300 1 0.56 209.3
Linking circular cavity to low MACH No., M<1
Strouhal No. St
Equation B y = fL/U
f L U y (=Strouhal No., St)
209.3 50 19.6 0.5328
For D = 50, Free-stream velocity as such:-
L/D Speed (m/s) at Respective L/D Ratio
0.56 19.6 (see next slide)
1 20.3
1.2 26.6
2 27.6
3 35.2

41. Calculating (estimate)
free-stream velocity
• Plotting Free-stream Velocity U w.r.t.
length-to-depth L/D Ratio, the depicted
equation:-
• y = 6.2742 x + 16.131
• X, Y co-ordinate (0.56, 19.60) (O)
for L/D at high MACH No. initially passing
low MACH (M<1) region.
(O) 1, 20.3
1.2, 26.6
2, 27.6
3, 35.2y = 6.2742x + 16.131
0
5
10
15
20
25
30
35
40
0 0.5 1 1.5 2 2.5 3 3.5
Free-streamVelocity,U
L/D Ratio
Speed (m/s) at Respective L/D Ratio

42. 0.0487, 0.63
0.0592, 0.36
0.0776, 0.29
0.0805, 0.29
0.1026, 0.21
2.3000, 0.06
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.0000 0.5000 1.0000 1.5000 2.0000 2.5000
StrouhalNo.
MACH No.
Strouhal No. Versus MACH No.
Low MACH No. region
MACH No. >=1

43. Things that Works
• In order to achieve the desired objective of having stability during
supersonic speed, it is advise that the design of a particular circular
cavity does not cause resonance peak
• The L/D ratio of the circular cavity, in this situation, the depth of the
circular cavity shall not contribute to the rise in amplitude of the
resonating frequency (boundary layer oscillation)

44. Noise (Energy) - Sound Pressure
Readings
Sound Pressure Level SPL
Sound Power Level SWL
Sound Intensity Level SIL

45. Investigation Conclusion
• For it is inevitable to eliminate resonance peak at low MACH No.
(M<1)
• However for respective L/D ratio, e.g. L/D = 1 (possibly), 2, and 3, low
level amplitude detectable at millivolts readings less than 10mV at
MACH No. 2.3 (in this case)
• Achieving aircraft design criterion, stability, at supersonic speed
(M=2.3) for shallow circular cavity

46. The Equations
• Pressure Coefficient 𝐶𝑝 =
𝑝 −𝑝 𝑟𝑒𝑓
1
2
ρ𝑈∞
2
• MACH No. M =
𝑈∞
𝑎
; 𝑎 = speed of sound, 343 m/s
• Reynolds No. Re =
ρ 𝑈∞δ
μ
; μ = dynamic viscosity
• Strouhal No. St (or Sr) =
𝑓𝐿
𝑈∞

47. An Investigation Based On Experimental Study of Air
Flow Across Rectangular and Circular Cavities (Aircraft
Industry)
• Scientific Discovery - An Experimental Fluid Flow Project
• The Search for Aircraft (Surface) Stability - New Approaches
• Development and Plausible Explanation
- National Body, Association, Company
- Oscillation of Shear Layer (Vortex Shedding)
• Scientific Norm of the Variance Source - Past, Current and Future
• Subsonic and Supersonic Wind Tunnel
- Low Speed – for M<1, take-off and landing
- High Speed – for M=2.3
• Aircraft Rectangular Cavity - Subsonic Flow (M<1, where MACH 1 = 343 m/s or 1234.8 kmh)
• Aircraft Circular Cavity -Supersonic Flow (M=2.3, where MACH 2.3 = 788.9 m/s or 2840.04 kmh)
• Noise (Energy)
• Conclusion

48. about the presenter
Title: An Investigation Based On Experimental Study of Air Flow Across
Rectangular and Circular Cavities (Aircraft Industry)
Keywords : Aircraft, cavity, rectangular cavity, circular cavity
• Name : Gan Chun Chet
• Board of Engineer Malaysia Registration No. : C112539
• Branch : Mechanical
• Contact No. (HP) : 019-2938364 (whatsapp)
• Email : ccgan2906@gmail.com