Noise Control Engr. J. 61 (3), May-June 2013
Noise Control Engr. J. 61 (3), May-June 2013
Noise Control Engr. J. 61 (3), May-June 2013
discussions, stats, and author profiles for this publication at: http://www.researchgate.net/publication/260021373
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1 AUTHOR:
Nawaf Saeid
Institut Teknologi Brunei
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INTRODUCTION
GOVERNING EQUATIONS
ij
@xj @xi 3 @xl
@xj
@xi @xj
@
2
r u0 l u0 j ;
@xj
where ui and i are the mean and uctuating velocity
components (i = 1, 2, 3) and the overbar represents the
mean value. The Kronecker delta ij = 1 if i = j and
otherwise it is zero. The Reynolds-averaged approach
to turbulence modeling requires that the Reynolds
stresses in Eqn. (2) be appropriately modeled. A common method employs the Boussinesq hypothesis to
relate the Reynolds stresses to the mean velocity gradients:
@ui @uj
2
@uk
0 0
r ul uj mt
ij ; 3
rk mt
@xj @xi
@xk
3
where the turbulent (or eddy) viscosity, mt, denition
depends on the turbulence model and k is the
diffuser
Inlet pipe
inflow
outflow
turbulent kinetic energy. In the present study the standard k e turbulence model11 and the shear-stress
transport (SST) k o with near wall corrections turbulence model12 are tested for the simple silencer ow
without diffuser as discussed in the validation section.
The governing equations and the details of this turbulence models can be found in FLUENT documentation13. For the present compressible uid ow, the
density of the uid is calculated from the ideal gas equation of state. Therefore the energy equation should be
solved. For turbulent ow, neglecting the viscous heating, the energy equation can be written as:
Cp mt @T
@
@
S; 4
uj rE p
Prt @xj
@xj
@xj
where E is the total energy (E = CpT p/r + V2/2), is
the thermal conductivity, Cp is the specic heat, Prt is
the turbulent Prandtl number (Prt = 0.85) and S is the
volumetric heat source.
The aerodynamic noise theory is based on the Lighthills acoustic analogy14, which states that the exact
NavierStokes equations for turbulent uid ow are
rearranged to form the wave equation for the uctuating
uid density. Several computational approaches and
models have been proposed for aerodynamic noise
prediction for different applications. The broadband
noise source model is usually used to determine which
portion of the ow is primarily responsible for the noise
generation. This model needs what typical Reynoldsaveraged NavierStokes models would provide, such
as the mean velocity eld, turbulent kinetic energy (k)
and the dissipation rate (e). Lilley7 used the Lighthills
acoustic analogy14 to derive the formula for acoustic
power generated due to unit volume of isotropic turbulence (in W/m3) as:
W ae ro eMt5 ;
acoustic
power
Ro
Ro
Ro
12o
5Ro
Lpor
Ri
Ld
Lin
Ri (mm)
Lin (mm)
Ld (mm)
S (mm)
Ro (mm)
L (mm)
85
150
430
15
200
1000
0.6
SST k- model
0.5
k- model
0.4
0.3
0.2
0.1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.1
Fig. 4Velocity magnitudes along the length of the perforated pipe using different mesh sizes with
Lpor = 140 mm, d = 9 mm and po_inlet = 1000 kPa.
shear-stress transport (SST) k o model is employed
to generate the rest of the results in the present study.
The accuracy of the results is veried using different
mesh sizes and checking the mass balance of the ow.
The simulation of the ow through the holes along
the length of the perforated pipe in the diffuser is the
most sensitive zone to the size of the mesh elements.
Different mesh element sizes of the diffuser holes were
tested to get grid independent results for the ow in
the silencer with Lpor = 290 mm, d = 9 mm and
po_inlet = 1000 kPa. The calculated velocity magnitudes
along the length of the perforated pipe are presented in
Fig. 4 using different mesh sizes.
It can be seen that the mesh with element size of
0.5 mm generates results for the velocity magnitude
along the perforated tube with negligible discrepancy
than the smaller and larger elements. Hence the results
generated using the mesh with element size of 0.5 mm
can be considered as mesh independent results. In order
to reduce the computational time, the mesh with element
size of 0.5 mm is adopted to generate the results in all
the cases in the parametric study.
Table 1Effect of hole diameter on the average Lw (dB) with Lpor = 140 mm.
po_inlet = 250 kPa
47.0
59.3
58.6
62.8
28.3
37.6
36.6
42.0
14.3
19.6
18.7
25.1
Without Diffuser
d = 6 mm
d = 9 mm
d = 12 mm
359
Table 2Effect of length of the perforated pipe on the average Lw (dB) with d = 9 mm.
Without Diffuser
Lpor = 80 mm
Lpor = 110 mm
Lpor = 140 mm
Lpor = 170 mm
Lpor = 200 mm
47.0
57.3
59.1
58.6
64.9
66.3
28.3
32.5
34.8
36.6
39.7
41.4
14.3
15.1
16.4
18.7
22.8
23.5
CONCLUSIONS
Fig. 5Contour plots for the case of Lpor = 140 mm, d = 9 mm and po_inlet = 250 kPa.
360
Fig. 6Contour plots for the case of Lpor = 140 mm, d = 9 mm and po_inlet = 500 kPa.
the ow. In this case, the calculated transmission loss
was small and the exit sound power level was considerably high according to most standards. The numerical
results show that the hole diameter has an effect on
the values of the transmission loss. Considerable
increase in the transmission loss values is obtained for
the cases when the hole diameter increases from 9 to
12 mm. The numerical results show that increasing
the length of the perforated pipe of the diffuser leads
to improve the silencer performance and increase its
transmission loss for all the cases. This is due to
ACKNOWLEDGMENT
Fig. 7Contour plots for the case of Lpor = 140 mm, d = 9 mm and po_inlet = 1000 kPa.
Noise Control Engr. J. 61 (3), May-June 2013
361
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