An Investigation on Buffeting Problems from Rectangular Cavities (landing gear section) During Takeoff or Landing

By Ir. Gan Chun Chet

He holds a Master of Science in Operations Management, University of Manchester Institute of Science and Technology UMIST, United Kingdom and a Bachelor of Science degree in Mechanical Engineering, University of Manchester, United Kingdom.

Introduction

Aircraft surfaces are design to avoid damage by shear layer resonating at peak frequency during flight time cause damages to the aircraft surface. This 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 rectangular cavity.

The rectangular cavity on aircraft surfaces in this case implies to landing gear section. When it comes to landing gear section, it does cause a noise nuisance nowadays to the surrounding, during takeoff or landing. This energy generated is the problem faced in modern aircraft design. In this article, it is highlighted here in a short explanation of what this noise (energy) nuisance is from a fluid dynamic point of view.

The Background Study : Boundary Layer Separation

In the late 1970’s, an area that aerospace researchers have 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 cavity (landing gear section) during takeoff or landing.

As the fluid passes through a rectangular cavity, the boundary layer of define thickness forms oscillating vortices hits the downstream edge of the cavity and surfaces releasing nuisance noise (energy). This is shown in picture 1.

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Free stream velocity, U

Upstream edge Downstream edge

Pressure waves

vortices

Boundary layer,

Noise emission

Vortices across cavityBoundary layer separation

Picture 1 : Sketch of Pressure Oscillation Across Cavity

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.

Subsonic Wind Tunnel : Model of Cavity

The location of the model in the subsonic wind tunnel is shown in sketch 1. In the subsonic wind tunnel, the model of cavity is rectangular in the working section.

Sketch 1 : Schematic Diagram of Subsonic Wind Tunnel

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Rectangular Cavity At Subsonic Flow (up to 40m/sec, or 150km/hr)

In this article, it is shown in a graphical manner a few evidences of peak resonance frequency formation in an experiment of varying length (L) to depth (D) ratio applicable during takeoff or landing speeds.

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Graph 1a, b, c & d : Boundary Layer Resonance Frequency of Distinct Peak Amplitude at Subsonic Flow in Rectangular Cavity

Also for various rectangular cavities of defined L/D ratios, as results shown on graphs 2a, b, c; are different flow speeds that pass the cavity and forms reasonable low pressure region in the cavity.

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Graph 2 : Pressure Distribution Across the Rectangular Cavity at Subsonic Flow

Boundary Layer Oscillation and Low Pressure Region Across Rectangular Cavity

It is noticed from here that boundary layer forms vortices which oscillates across the cavity to the downstream edge. This periodical impacts the downstream edge, leading to nuisance noise emission.

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It is also found that low pressure region exist at the downstream edge of every rectangular cavities. The low pressure region inside of the cavity makes the situation worst as it creates sizable vortices.

Depicted from these graphs, that pressure oscillation and low pressure region in rectangular cavity giving rise to nuisance noise and buffeting problem is inevitable.

Noise Emission : A Form of Energy

Thus noise emission due to pressure fluctuation is a form of energy that is dangerous that could also damage the aircraft surface. The turbulent force would cause damage to aircraft surfaces, give rise to buffeting problem.

For noise emission from rectangular cavity (landing area), it is also known of its turbulent characteristics discuss in the next section, a source of energy that might turn harmful in aircraft design.

A Discussion of This Phenomenon : During Takeoff or Landing

As the speeds reaches between 20 to 40 m/sec (equivalent to approx 70 to 150 km/hour) resonance frequency between 50 to 148 Hz, depending on the length to depth L/D ratio, will be formed (see figure 1, table 1 & 2).

Pressure coefficient Cp of low 0.2 (negative) ( Cp=p−pref12ρU❑

2 ) shows that the pressure is lower

than the reference pressure in the cavity (refer to graph 2a, b & c) permits shedding of vortices across the cavity.

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0.5 1 1.5 2 2.5 3 3.50

20

40

60

80

100

120

140

160

Figure 1 : Resonance Frequency of Rectangular Cavity at Respective Length to Depth (L/D) Ratios

f [Hz] (Read-ings)

Length to Depth L/D Ratio

Frequency [Hz]

Table 1 : Resonance Frequency of Rectangular Cavities at Respective L/D Ratio

Length to Depth (L/D) Ratio

f [Hz] (Readings)

y (Line of Regression) Error %

1 148 148.4 -0.4 -0.24581.2 129 128.4 0.6 0.49752 80 78.6 1.4 1.74933 50 52.9 -2.9 -5.8722

Line of Regression, Equationy = A + B * exp(C * x * -1)

A B C38 300 1

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

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80 100 27.6 0.29

50 150 35.2 0.21

These are speeds of aircraft taking off or landing. As the aircraft reaches these speeds, distinct boundary layer oscillation occurs, the magnitude measured in miliVolt (mV) using constant temperature hot wire anemometer, indicates that it is resonating. In addition, low pressure edge in the cavity enlarges the vortices. This might cause structural fatigue due to this situation.

Conclusion

The basis of investigation from a fluid dynamic view point shows that peak resonance frequency formation and low pressure region in the cavity at the downstream edge cannot be avoided. The continuous vortices strength that forms from boundary layer separation (buffeting problems) and amplified in the cavity is responsible for contributing to nuisance noise during takeoff or landing.

Affiliation

University of Manchester, England, United Kingdom.

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