13-02-2013, 04:51 PM
Computer Aided Design on Single Expansion Muffler with Extended Tube under Space Constraints
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Abstract
The optimization approach of maximal STL (sound transmission loss)
and muffler dimension under space constraints within a building or machine
room is fully addressed throughout the graphic analyses as well as the
computer-aided numerical assessments in this paper. The primary set of
design data is derived by the computer graphic analysis on sensitivity, and the
successive algorithm of iteration techniques based on the initial design data
is then carried out individually. These results are moreover compared with
each other for the accuracy purpose. The theoretical and simulated results are
found in good agreements. The optimal approach on the design of single
expansion muffler with extended tube proposed in this study surely provides
a quick and economical procedure to optimize the single expansion muffler
with the maximal sound transmission loss under space limitations without redundant
testing.
Key Words: Plane Wave, Optimal Design, Single Chamber Muffler with Extended
Tube, Computer Aided Design, Numerical Assessment.
Introduction
Whilst the muffler dimension is often limited inside a
building or machine room, the consideration of maximal
sound transmission loss (STL) under space constraints becomes
important and essential to the field of acoustics.
Many researches of muffler design have been well addressed;
however, the discussion of sensitivity among design
parameters under space constraints is rarely emphasized.
Bernhard [1] has introduced the shape optimization
of simple expansion mufflers by using design sensitivity
matrices. The space volume of the reactive silencer is still
non-constrained, and the calculation of design sensitivity
matrices is difficult especially for the mufflers, which are
complicated. In the previous work [2], the optimal shape
design to improve the performance of STL on a single expansion
muffler was discussed. To increase the STL on
the muffler, a new muffler with extended tube is thus introduced
and discussed in this paper.
The trial and error method in the improvement of
muffler design is considered tedious and expensive in
optimizing the dimension of amuffler inside the machine
room that is often limited by the space constraint. Therefore,
the interest to optimize STL of the absorber under
space constraints is arising in the field. This paper provides
a quick method to obtain an optimal design data on
a muffler by using computer graphic system and numerical
assessment. A numerical case of a muffler with extended
tube is also fully illustrated in the paper. Furthermore, a
plane wave theorem is applied for the derivation of STL
by confining the shape of each tube to be slender discussed
by Munjal [3].
Tamkang Journal of Science and Engineering, Vol. 7, No 3, pp. 171181 (2004) 171
*Corresponding author
2. Nomenclature
The mathematical model in this paper is developed
on the basis of the following notations:
C1: constant (= 1)
C2: constant (1 for extended outlet ; +1 for extended
inlet)
C0: sound speed (m s1)
D: diameter (m)
gi(X): inequality constraints
hj(X): equality constraints
j: imaginary part (= 1)
k : wave number
Kc: stagnation pressure loss factor
L: length (m)
Mi: mean flow Mach number at i
P: total flow pressure (Pa)
Pc,i: aeroacoustic pressure at i (Pa)
Pi: pressure; acoustic pressure at i (Pa)
R: gas constant (kJ/kgK)
Si: section area at i (m2)
STL: sound transmission loss (dB)
SWL: sound power level (dB re1012W)
Ui: acoustic volume velocity at i (m3 s1)
ui: acoustic particle velocity at i (m s1)
V: total flow velocity (m s1)
Vi: mean flow velocity at i (m s1)
Vc,i: aeroacoustic mass velocity at i (kg s1)
i: acoustic mass velocity at i (kg s1)
Yi: characteristic impedance at i
: specific heat ratio of air
0: air density (kg m3)
3. Theoretical Background
In this paper, the 3-D cross-section of muffler with
extended tube shown in Figure 1 is focused. The muffler’s
flow condition and location are specified in Figure
2, which shows that the whole flow condition within the
muffler can be presented by eight chosen nodes (pt1 ~
pt8) and then deduced in theoretical derivation. The theoretical
derivation is illustrated as follows: