Wind tunnels, subsonic speed using rectangular cavity (low MACH No., M<1) and supersonic speed using circular cavity (high MACH No., M= 2.3). Utilizing the oscillation of pressure wave to detect internal speed. Oscillation/sinusoidal wave pattern (repetitive in nature) allows amplification of signal continuously.

1. Boundary Layer Oscillation for Aircraft
Cavity/Surfaces : Calibration of Wind
Tunnels (Subsonic/Supersonic)
Chun C Gan
30th March, 2023
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. Boundary Layer Separation
• The current defined landing gear section design has shown that noise source
from the downstream edge of the cavity contributes to buffeting problem during
take-off and landing, i.e. turbulence due to oscillation of the shear layer from
upstream boundary layer separation to the downstream edge.
• The thickness of this shear layer is approximately 1.5 to 2 mm, base on wind
tunnel experiment in University of Manchester (year 1996), for the flowrate as
stated in the graph below.

3. Characteristic of Shear Layer Thickness
• It is to show here that the length of the cavity is vary to detect the sinusoidal
wave pattern of the shear layer after it separates from the surface boundary.
• Peak amplitude represents amplification of noise in the flow across cavity.
• In the landing gear section, it is advisable to detect these frequency and
amplitude for higher flow speed, pretty weak detection at low flowrate.

4. Oscillation of
Shear Layer :
Non-Dimensional
Representation
Subsonic Wind Tunnel
Upstream Boundary Layer Separation
Thickness (
𝑦
δ
) : 1.5 to 2 mm
(Wind Tunnel Experiment in the University of
Manchester)

5. Oscillation of
Shear Layer :
Influence of Free-Stream
Velocity (Real Figure)
Subsonic Wind Tunnel
For different cavity sizes
𝐿
𝐷
(as shown)
Upstream Boundary Layer Separation
Thickness δ : as shown in graph [mm]
(Wind Tunnel Experiment in the University of
Manchester)

6. Wind Tunnel Calibration
(pressure)
(P1 – P2) = ρ g h = Δ P ref
(graph plotted as shown, next slide)
P1
P2
h
Air Intake -
Bell mouth/Frictionless
with honeycomb (to
straighten flow) Rectangular Cavity –
Hot probe location
(movable, vertically)
Cylindrical Pitot
Tube
P

7. Wind Tunnel Calibration – Laboratory Course
Calibration of Wind tunnel (pressure)
1
2
𝜌 𝑉
𝑤𝑠𝑝
2
ΔPref
𝑉
𝑤𝑠𝑝
ΔPref
(P1 – P2) = ρ g h = Δ P ref
Dynamic Pressure, Pdyn = (P – Pwsp) =
1
2
𝜌 𝑉
𝑤𝑠𝑝
2
; where P = total pressure,
Pwsp = wall static pressure

10. Wind Tunnel Calibration (hot-wire probe)
(for info)
• Eo Ξ due to the natural convection when (v = 0)
• Β and η are empirical constants
• Collis-Williams Law
• 𝐸2 − 𝐸𝑜
2 = 𝐵 ∗ 𝑈𝜂
• log( 𝐸2
− 𝐸𝑜
2
) = 𝑙𝑜𝑔 𝐵 + 𝜂 log U
(graph plotted as shown, next slide)

11. Wind Tunnel Calibration – Laboratory Course
Calibration of Wind tunnel (hot-wire probe) (for info)
log( 𝐸2
− 𝐸𝑜
2
)
log U
Note : 0.35 <= η <= 0.45
Slope
𝐸𝑜
ΔPref [ proportional to
1
2
𝜌 𝑉
𝑤𝑠𝑝
2
]
E
𝐸2
= 𝐸𝑜
2
+ 𝐵 ∗ 𝑈𝜂

12. Subsonic Wind Tunnel
Low Flow
MACH < 1

14. Airflow Across Cavity:
Subsonic Flow
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
MACH <= 1
L/D = 1
>Rectangular Cavity
Specifications:
Frequency f 148 Hz
Length L 50 mm
Depth D 50 mm
Width W 460 mm

15. Airflow Across Cavity:
Subsonic Flow
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
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

16. Airflow Across Cavity:
Subsonic Flow
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
MACH <= 1
L/D = 2
>Rectangular Cavity
Specifications:
Frequency f 80 Hz
Length L 100 mm
Depth D 50 mm
Width W 460 mm

17. Airflow Across Cavity:
Subsonic Flow
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
MACH <= 1
L/D = 3
>Rectangular Cavity
Specifications:
Frequency f 50 Hz
Length L 150 mm
Depth D 50 mm
Width W 460 mm

18. Supersonic Wind Tunnel
High Flow
MACH = 2.3

22. Airflow Across Cavity:
Supersonic Flow
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
Details:
MACH 2.3
L/D = variable
> Circular CavitySpecifications:
Frequency f <see diagram>
Length L (diameter) 50 mm
Depth D <see diagram>