XXIV ICTAM, 21-26 August 2016, Montreal, Canada
TENTATIVE EXPLANATION OF THE MECHANISM OF NOISE REDUCTION FOR
TRAILING EDGE WITH CHEVRON
Caihong Su
Department of Mechanics, Tianjin University, Tianjin, China
Summary Recently, chevron appears at the trailing edge of commercial aircraft jet engines, for example, jet engine of Boeing 787.
It is believed to be for the noise reduction. So far, there is no theoretical explanations for its mechanism in published literatures,
though there were papers for this purpose for the serration appeared at the jet exit. In this paper, a simplified model is proposed,
to explore the possible cause of the noise reduction by chevron at the trailing edge of commercial aircraft jet engines.
INTRODUCTION
Aircraft noise is an important issue, especially for commercial aircraft. Jet engine exhaust is one of the main sources
during airplane take-off. One of the measure for noise reduction appears very recently is the use of chevron at the
downstream end of the engine housing. According to experimental measurements, nearly 3dB of noise reduction during
take-off can be achieved while only less than 0.5% thrust could be lost during cruise[1]. The first attention has been received
on application level in mid 1990s. However, the understanding of the physical mechanism behind and the impact of
chevrons on noise reduction still remains incomplete[2]. To date, the most popular explanation of its cause is that chevrons
generate stream-wise vortices which enhance jet mixing, leading to the reduction of the amplitude of large scale structures
in the flow field, and thus reducing the noise. However, they were mostly aiming at the case of chevron with sharp sawtooth. For smooth chevron as appeared on engines of Boeing 787, there could be another different mechanism. We believe
that the existence of chevron may well change the stability characteristics of the mean flow downstream of the engine, so
that the amplification rate of large scale vortices, which plays the dominant role of generating noise, may be significantly
reduced. In this paper, a simplified model is proposed to show how it works.
COMPUTATIONAL MODEL AND METHODS
For a real engine, the shear layer downstream of the engine is axis-symmetric. To simplify the computation and analysis,
we consider a plane shear layer instead, which is formed downstream of an infinitely thin flat plate splitting two oncoming
streams with Mach numbers 0.3 and 0.35 respectively. The length of the flat plate is assumed to be 2m, the average of the
two oncoming flow velocities and other oncoming flow quantities are used to nondimensionalize the respective quantities.
The Reynolds number so defined is 1.8h104. The oncoming temperture is 281.7K. The flow is assumed to be an ideal gas
and the viscosity coefficient is comupted using Sutherland’s law.
The governing equations are compressible unsteady Navier-Stokes equations. A 5th order upwind and a 6th order
central scheme are used to discretize the split nonlinear term and viscous term respectively. The 3rd order Runge-Kutta
scheme is used for the time advancing. The computational domain starts from the trailing edge of the flat plate and extends
far downstream. Grid points are clustered in the vicinity of trailing edge to make sure the required resolution can be
achieved. In the wall-normal direction, mesh grids are stretched gradually from the wall towards the upper and lower
boundaries. The wall is non-slip and isothermal whose temperatures on both sides are set to be 284K. The Blasius profiles
are maintained at the inlet of the computational domain and sponge zones combined with characteristic boundary conditions
are used for the top, bottom and outflow boundaries. For 3D cases periodic condition is used in the spanwise direction.
RESULTS AND DISCUSSIONS
1.
DNS: Generation of unsteady vortex
Unsteady vortex is found to appear starting from some distance downstream of the trailing edge as shown in Fig.1.
Fourier analysis is performed for time squences of transverse velocities at three locations at the centerline. As shown in
Fig.2(a), at x=0.002, very close to the trailing edge which locates at (0,0), the component with frequency 6~7Hz dominates.
Downstream at x=0.06, another peak with frequency 23~24Hz emerges. This component overtakes the one with lower
frequency and then plays a dominant role throughout the downstream region. The harmonic wave can also be observed.
2. Linear stability analysis: wake mode and shear layer mode
Spatial linear stability analysis is performed to search for the most unstable modes. In reality the flow is turbulence.
However, since the profile of the basic flow has inflection points, so at least at the initial stage, inviscid instability plays the
major role while the turbulence plays only a secondary role. So here we can ignore the turbulence as the first step. Two
types of unstable modes, that is, wake mode and shear layer mode are identified as shown in Fig.3. Fig.4(a), (b) shows the
variations of frequency and the growth rate respectively for the most unstable modes along x. We can see that at x=0.06 the
Corresponding author. Email: [email protected].
frequencies for the most unstable wave mode and shear layer mode are 6.67 and 23.4 respectively, which are in very good
agreement with what we observed in DNS. And the shear layer mode has much bigger growth rate so that it overtakes the
wake mode and plays a dominant role further downstream.
0.3
0.0006
0.2
1
0.998
0.996
0.994
0.992
0.99
0.988
0.986
0.984
y
0.1
0
0.0012
0.18
0.16
0.001
x=0.002
0.0004
x=0.06
0.14
0.0008
0.12
-0.1
0.0002
0.08
0.0004
-0.2
0.06
0.04
0.0002
-0.3
-0.1
0
0.1
0.2
x
0.3
0.4
0
0.5
0
20
40
60
80
0
100
x=0.32
0.1
0.0006
0.02
0
20
Frequency
40
60
80
0
100
0
20
Frequency
40
60
80
100
Frequency
Fig.1. Density contour at t=24.
Fig.2 Amplitude of Fourier components versus frequency (different colored lines refer to different
time periods Fourier tranform performed): (a)x=0.002, (b) x=0.06, (c) x=0.49.
1.2
35
1
25
0.6
0.4
f=23.4
20
15
10
0.2
f=6.67
-0.02
0
y
0.02
0.04
0
0.06
0
0.05
Fig.3 Eigenfunctions of streamwise velocity at x=0.06.
0.1
60
40
20
5
-0.04
shear layer mode
wake mode
80
Growth rate
Frequency
|u|
0.8
0
-0.06
100
shear layer mode
wake mode
30
wake mode
shear layer mode
x
0.15
0.2
0
0.25
0
0.05
0.1
0.15
0.2
0.25
x
(a)
Fig.4 The most unstable wave. (a) frequency, (b) growth rate.
(b)
3.
Preliminary results with chevron
We consider one chevron with a sinuous shape shown in Fig.5. Since the streamwise velocity is much bigger than the
other velocity components, the initial baseflow is approximated by the mean flow we have got without chevron, but with its
origin shifted in x direction according to the curve of the chevron. The inlet of the computational domain is shown in Fig.5
and its profiles are maintained during computation. Similarly, we performed Fourier transform for time sequencs of
transverse velocity at (0.1,0) for several spanwise positions. And compare the result with the 2D case as shown in Fig.7. It
can be seen that the existence of chevron reduces the amplitude of the dominant component. Also a temporal DNS at a
given x is performed to search for the most unstable mode to compare its growth rate with its 2D counterpart. It shows that
the growth rate also drops. More in-depth work is under way.
0.15
0.0005
0.03
z=0
z=0.026
z=0.049
z=0.75
0.02
Inlet of 3D DNS
0.01
0.0003
y
0
z
0.1
0.05
-0.01
0.0002
0.0001
-0.02
0
0
0.05
x
0.1
Fig.5 Shape of chevron
0.15
x=0.1,y=0
z=0.75
z=0.375
z=0.0
without chevron
0.0004
-0.03
0
0.2
0.4
0.6
u
0.8
Fig.6 Profiles at inlet
1
0
1.2
0
20
Frequency
40
60
Fig.7 Fourier components for cases with/without chevron
CONCLUSIONS
Vortex roll-up appears whose frequency is actually chosen by the stability characteristics of the mean flow. For the case with
chevron, the dominant unstable mode is found to be less unstable compared with the case without chevron, which may just be
the cause of noise reduction.
References
[1]
[2]
Xia H., Tucker P.G. and Eastwood S.: Large-eddy simulations of chevron jet flows with noise predictions. International Journal of Heat and Fluid Flow,
30(6):1067-1079, 2009.
Bridges J., Brown C.A.: Parametric testing of chevrons on single flow hot jets. AIAA paper 2824, 2004.