KTH CCGEx
Investigation and optimization of the acoustic performance of exhaust systems Sara Elsaadany Licenciate Thesis Stockholm, Sweden 2012 KTH Competence Center for Gas Exchange The Marcus Wallenberg Laboratory for Sound and Vibration Research _____________________________________________________________ Postal address Royal Institute of Technology MWL / AVE SE–100 44 Stockholm Visiting address Teknikringen 8 Stockholm Sweden Contact ssaadany@slb.com Akademisk avhandling som med tillstånd av Kungliga Tekniska Högskolan i Stockholm framlägges till offentlig granskning för avläggande av teknologie licentiatexamen den 14 Oktober 2012 kl 09.15 vid ”Faculty of Engineering, Ain Shams University”, Kairo, Egypten. TRITA‐AVE‐2012:31 ISSN 1651‐7660 Abstract
There is a strong competition among automotive manufacturers to reduce the radiated
noise levels. One important source is the engine exhaust where the main noise control
strategy is by using efficient mufflers. Stricter vehicle noise regulations combined with
various exhaust gas cleaning devices, removing space for traditional mufflers, are also
creating new challenges. Thus, it is crucial to have efficient models and tools to design
vehicle exhaust systems. In addition the need to reduce CO2 emissions puts requirements
on the losses and pressure drop in exhaust systems. In this thesis a number of problems
relevant for the design of modern exhaust systems for vehicles are addressed. First the
modelling of perforated mufflers is investigated. Fifteen different configurations were
modeled and compared to measurements using 1D models. The limitations of using 1D
models due to 3D or non-plane wave effects are investigated. It is found that for all the
cases investigated the 1D model is valid at least up to half the plane wave region. But with
flow present, i.e., as in the real application the 3D effects are much less important and then
normally a 1D model works well. Another interesting area that is investigated is the
acoustic performance of after treatment devices. Diesel engines produce harmful exhaust
emissions and high exhaust noise levels. One way of mitigating both exhaust emissions and
noise is via the use of after treatment devices such as Catalytic Converters (CC), Selective
Catalytic Reducers (SCR), Diesel Oxidation Catalysts (DOC), and Diesel Particulate Filters
(DPF). The objective of this investigation is to characterize and simulate the acoustic
performance of different types of filters so that maximum benefit can be achieved. A
number of after treatment device configurations for trucks were selected and investigated.
Finally, addressing the muffler design constraints, i.e., concerning space and pressure drop,
a muffler optimization problem is formulated achieving the optimum muffler design
through calculating the acoustic properties using an optimization technique. A shape
optimization approach is presented for different muffler configurations, and the acoustic
results are compared against optimum designs from the literature obtained using different
optimization methods as well as design targets.
Keywords Exhaust systems, noise, pressure drop, 1D models, perforated mufflers, after
treatment devices, optimization
I
Licentiate thesis
This licentiate thesis consists of an introduction with a summary and
the following papers:
Paper A
Investigation into modeling of multi-perforated mufflers, T. Elnady, S. Elsaadany and M.
Åbom, 16th International Congress of Sound and Vibration, Krakow (2009).
Paper B
Investigation of the acoustic performance of after treatment devices, T. Elnady, S.
Elsaadany and D. W. Herrin, SAE International Journal, Volume (4), Issue (2), pp. 10681075, (2011).
Paper C
Insight into exhaust systems optimization techniques, S. Elsaadany, T. Elnady, M. Åbom
and S. Boij, 17th International Congress of Sound and Vibration, Cairo (2010).
Paper D
Optimization of exhaust systems to meet the acoustic regulations and the engine
specifications, S. Elsaadany, T. Elnady, S. Boij and M. Åbom, 18th International Congress
of Sound and Vibration, Rio De Janeiro (2011).
Division of work between the authors:
The experiments in all papers were conducted using a test rig design by Elsaadany and
Elnady at Ain Shams University, Sound and Vibration Laboratory, Cairo, Egypt.
Paper A
The modeling and experiments were conducted by Elsaadany, under supervision of Elnady.
Elnady and Åbom helped in interpretation of the results. The paper was written by
Elsaadany.
Paper B
Elnady and Herrin helped in defining the scope of work. Elsaadany carried out the
experiments and simulation. The paper was written jointly by Elnady and Elsaadany.
Paper C
Boij and Åbom helped in defining the scope of work. Elsaadany formulated the
optimization problem and coded the optimization module in SIDLAB under the
supervision of Elnady. The paper was written by Elsaadany. Boij, Elnady and Åbom
reviewed the paper and helped in the results interpretation.
Paper D
Boij and Åbom helped in defining the scope of work. Elsaadany formulated the
optimization problem. The paper was written by Elsaadany. Boij, Elnady and Åbom
reviewed the paper and helped in the results interpretation.
II
Table of contents
Introduction ...................................................................................................................... 1
Theory ............................................................................................................................... 1
Two-port theory ............................................................................................................ 1
Flow calculation ............................................................................................................. 3
Optimization Technique ................................................................................................ 3
Summary of the papers ...................................................................................................... 4
Paper A: Investigation into Modeling of Multi-perforated Mufflers ............................... 4
Paper B: Investigation of the Acoustic Performance of the After Treatment Devices .... 6
Paper C: Insight into Exhaust Systems Optimization Techniques .................................. 9
Paper D: Optimization of exhaust systems to meet the acoustic regulations and the
engine specifications .................................................................................................... 12
Acknowledgments ........................................................................................................... 16
References ....................................................................................................................... 17
III
IV
Introduction
There is a strong competition among automotive manufacturers to reduce the radiated
noise levels. One important noise source is the engine exhaust system where the main noise
control strategy is by using efficient mufflers/silencers. Two principles exist for reducing
sound in exhaust systems; dissipation and reflection. The first is normally referred to as a
resistive muffler and the second as a reactive. To obtain an efficient muffler system for
automotive applications both resistive and reactive components are used since the reactive
mufflers are best for low frequencies and the resistive for mid and high frequencies.
Resistive damping can be achieved either by using absorbing (porous) material or flow
related losses, e.g., from perforates in the form of tubes or sheets. Perforated mufflers have
an increased performance with flow speed, since the acoustic resistance depends on the
flow through the perforate holes. On the other hand, perforates can deteriorate the engine
performance, if badly designed, by increasing the flow back pressure.
Due to increased environmental concerns requiring less noise emissions combined
with reduced emission of harmful gases, it is becoming very crucial to carefully design the
exhaust system mufflers for road transport applications. Maximum acoustic performance is
usually desired under the limit of space constraints. Today, a significant part of the available
space is also used by so called after treatment devices, i.e., devices used for emission
control of harmful gases. This has increased the complexity of the design task and created a
need for more advanced design approaches such as optimization.
Modeling of perforated mufflers started in the seventies when simple geometries
were used. There were two approaches to analyze two tubes connected with a perforate
(i.e. four-port), segmentation and distributed [1]. Both approaches were limited to a few
specified geometries. Recently, Elsaadany, Elnady and Åbom published a new technique
based on the segmentation approach where four ports can be replaced by a number of twoports so that it can be used in general two-port codes, see paper A.
One interesting area is to investigate the acoustic performance of after treatment
devices. Diesel engines produce harmful exhaust emissions and high exhaust noise levels.
One way of mitigating both exhaust emissions and noise is via the use of after treatment
devices such as Catalytic Converters (CC), Selective Catalytic Reducers (SCR), Diesel
Oxidation Catalysts (DOC) and Diesel Particulate Filters (DPF). One objective of this
investigation is to characterize and simulate the acoustic performance of different types of
filters so that maximum benefit can be achieved, as presented in paper B. A number of
after treatment device configurations for trucks were selected and measured.
There are several possibilities to evaluate the acoustic performance of a muffler
such as the sound transmission loss, the insertion loss, and the acoustic pressure measured
by a receiver outside the exhaust system opening. By selecting one of these design targets,
the optimum design of a specific muffler configuration in the frequency range of interest
can be obtained. Despite the obvious usefulness of muffler optimization the subject has
received little attention. Optimization of the muffler geometry is investigated in papers C
and D.
Theory
Two-port theory
For the purpose of acoustic modeling, duct systems or networks are often too
complicated to enable direct solution of the governing equations. One method to describe
1
the sound transmission along the system is called the building block method or two-port
transfer matrix method as described in references [1]. This method splits the system into
several smaller duct parts, acoustic elements, in which the sound propagation is well
defined. Plane waves are assumed to propagate between different elements and the sound
field can be characterized by two state variables. One convenient choice is to use acoustic
pressure and volume velocity. The sound propagation inside each element is analyzed
separately and higher order modes can exist inside the element.
There exists a complex 2 x 2 matrix, T, one for each frequency under investigation,
which completely describes the sound transmission within an element. The acoustic
pressure and volume velocity on each side of the element can be related with the following
expression [2-3]
 p1  T11 T12   p2   p s 
 q   T
  U    s 
T
1
21
22
  
  2  q 
(1)
where p and q are the acoustic pressure and volume velocity, while the subscript 1 refers to
the inlet side and 2 refers to the outlet side, Tii are the elements of the two-port transfer
matrix, ps is the source pressure and qs is the source volume velocity.
For modeling of perforated mufflers (which represent 4 or higher order ports in the
plane wave range), the segmentation approach can be used. The basic element to be
considered consists of two flow ducts which are joined together by a perforated duct
section of length L and specific acoustic impedance Zw. The impedance can vary along the
perforate. The main idea of the segmentation approach is to divide the perforated section
into a number of segments along the length of the ducts. Each segment consists of two
parts. The first part is two parallel hard ducts where convective plane wave motion is
assumed. The second part is a discrete impedance which can be seen as an open branch
representing a parallel coupling of all the holes in the segment.
Consider a short segment ∆x of a perforated duct. Assume that the perforated
section ∆x is much shorter than the acoustic wavelength . it can then be represented as a
lumped element. The two-port of such an element is described in matrix form by [1]
 p1  1 Z   p2 
 q   0 1    q 
  2
 1 
(2)
where Z is the lumped (‘point wise’) impedance associated with the two-port element, and
is given by Z = Zw/Sw (where Zw is the perforate acoustic impedance and Sw is the duct wall
area of the perforated segment), and 1 denotes the inlet side and 2 denotes the outlet side.
Only plane waves are assumed to propagate on each side of the perforate, and parallel to
the wall. The perforate impedance used in this work is calculated according to reference [1].
The SIDLAB code [2] used in this thesis is based on the representation of a duct
network as a network of two-ports. The two-port elements are then joined and analyzed
using the method described in reference [3]. The applied version of SIDLAB couples the
elements at each node, using the continuity of pressure and volume velocity. The
representation of perforated four-ports in the form of two-ports as described above is
attractive since two-port codes are commonly used for muffler analysis and the proposed
method makes it possible to model arbitrary complex perforated systems.
2
Flow calculation
In order to include the pressure drop related to the investigated duct systems, this
property need to be modeled. For the flow modelling applied in this work, the same
SIDLAB algorithm [4] used to calculate the sound propagation can in principle be used to
calculate the pressure drop. The difference being that since the two-matrix elements also
will depend on the flow the problem is non-linear and an iterative solution procedure is
required. Each two-port element can be described by a flow transfer matrix to relate the
stagnation pressure and volume flow, rather than the acoustic pressure and acoustic
volume flow that is used to determine the acoustic properties. This fact enables us to use
the theory of acoustic two-ports and the established algorithms to solve for the static
pressure drop in any network of arbitrary connected elements. Unlike the acoustic
calculations, the flow calculation is only performed at one “frequency”. The flow two-ports
can be described by
 P1  1
 
Q1  0
R f   P2 
 
1  Q2 
(3)
where P is the stagnation pressure, Q is the volume flow and incompressible flow is
assumed. It is important to calculate the flow resistance, Rf, for each two-port in the
network. In fluid flow handbooks, one can find the head loss or loss coefficient ke across
any element. The loss coefficient is a constant which depends on the geometry of the
element. The flow resistance is related to the loss coefficient by
R f (Q)  ke

2S
2
Q
(4)
where S is the cross-sectional area of the inlet section (1) and  is the density (constant).
Optimization Technique
The optimization problem treated in this work is represented by a specific target
acoustic performance that has to be met under space constraints and allowable engine back
pressure limit. It has been found that the insertion loss is the most appropriate quantity to
describe the exhaust system acoustic performance since it includes the engine acoustic
impedance, which varies with the engine loading and rotational speed. Usually, the
insertion loss of the exhaust system is required to satisfy a certain target performance
curve. In this thesis, a muffler optimization problem is formulated so that several shape
parameters are optimized under some specific space constraints and with flow. In the
optimization procedure, the allowable engine back pressure is introduced as a non-linear
constraint to the objective function, so that the optimum shape design will meet the engine
back pressure specifications.
The objective function used for this study is
maximize Gmin(x) = minimize –Gmin(x)
where
Gmin(x) = minimum(IL(x)-ILtarget(x))
(5)
where IL is the insertion loss vector for all frequencies, x are the shape related parameters
and ILtarget is the target insertion loss performance curve. The objective function is subject
to the following constraints:
3
–
–
–
–
–
lb ≤ x ≤ ub
Aeq . x = beq
A.x≤b
ceq(x) = 0
c(x) ≤ 0
Set of lower and upper boundaries for x
Set of linear equality constraints
Set of linear inequality constraints
Set of nonlinear equality constraints
Set of nonlinear inequality constraints
An optimization function which finds the minimum of a constrained nonlinear
multivariable function is applied in this thesis.
This function is based on an Interior Point Algorithm which is used for constrained
optimization [5-6].
The optimization performed in this thesis is obtained by means of the function in the
MATLAB optimization tool-box called "fmincon".
Summary of the papers
Paper A: Investigation into Modeling of Multi-perforated Mufflers
Perforated tubes are commonly used inside automotive mufflers. They can be
found in the form of perforated tubes to confine the mean flow in order to reduce the
back-pressure to the engine and the flow generated noise inside the muffler. They can also
be used to provide resistive damping to enhance the acoustic performance. On the other
hand, if the flow is forced through the perforates, this provides a significant back pressure
on the engine. Being able to theoretically model perforated mufflers enables car
manufacturers to optimize their performance and increase their efficiency in attenuating
engine noise, and at the same time to minimize the back pressure exerted on the engine.
Therefore, there has been a lot of interest to model the acoustics of two ducts
coupled through a perforated plate or tube. Generally, the modeling techniques can be
divided into two main groups, the distributed parameter approach and the discrete or
segmentation approach. The segmentation approach was first proposed by Sullivan [8] in
the form of four-ports.
Elnady and Åbom [9] described another technique to divide the four-port
perforated tube mufflers into a number of two-ports. It uses a two-port transfer matrix to
model both the perforated branches and the intermediate hard pipe segments. This new
technique is more flexible as it facilitates the modeling of perforated pipes with an arbitrary
configuration within a muffler. The modeling approach is implemented in the software
SIDLAB [2], which is used for the simulations presented in paper A.
In order to achieve acceptable accuracy, we need to have more segments which
results in an increased number of two-ports that have to be added to the network. Within
the work done in this paper, the technique described in reference [9] is coded into SIDLAB
so that the associated two-port network for each four or six-port element is generated
automatically and all the element properties are calculated accordingly.
The objective of paper A is to try this technique on a variety of muffler types and
configurations in order to determine its limitations, if any. A number of 15 different
muffler configurations (geometries in [mm] are shown in Figure 1 to Figure 6) were tested
and some limitations of the model were identified in some complex muffler geometries due
to 3D effects that start to deteriorate the plane wave assumption, see Figure 8. These cases
were verified by comparison to Finite Element results. Pressure drop data are presented in
Figure 7.
4
Figure 1: Through flow muffler
Figure 2: Perforated plate muffler
Chamber 1
Φ=197
Chamber 2
Φ=197
Φ=57
Φ=57
92.5
Inlet
Outlet
92.5
66
Inlet
51
54
Outlet
L=200
The thickness of the plug is
15mm
L=257
The thickness of the plug is
15mm
Figure 3: One plug flow muffler
Figure 4: Two plugs flow muffler
Chamber 1
Chamber 2
25
95
50
Outlet
61
4
Φ=197
1
Φ=57
42
161
70
3
Inlet
2
70
61
25
154
L=240
52
117
25
L=264
Figure 6: Eccentric muffler with plugs
Figure 5: Eccentric muffler
The thickness of the plugs at
the two end of pipes is:
15mm
450
5000
Simulation
Measurement
400
Simulation
Measurement
4500
4000
350
Overall Pressure Drop (Pa)
Overall Pressure Drop (Pa)
54
300
250
200
150
3500
3000
2500
2000
1500
100
1000
50
0
500
0
0.05
0.1
Inlet Mass Flow (kg/s)
0.15
0
0.2
a) Through flow muffler
0.02
0.04
0.06
0.08
Inlet Mass Flow (kg/s)
0.1
0.12
b) One plug flow muffler
4500
12000
Simulation
Measurement
Simulation
Measurement
4000
Overall Pressure Drop (Pa)
10000
Overall Pressure Drop (Pa)
0
8000
6000
4000
3500
3000
2500
2000
1500
1000
2000
500
0
0
0.02
0.04
0.06
Inlet Mass Flow (kg/s)
0.08
0
0.1
c) Two plugs flow muffler
0
0.02
0.04
0.06
0.08
Inlet Mass Flow (kg/s)
0.1
0.12
d) Eccentric muffler
Figure 7: The pressure drop curve for selected mufflers. Comparison between
measurement and simulation using SIDLAB Flow
5
18
18
Simulation
Measurement
16
14
Transmission Loss, dB
12
10
8
6
12
10
8
6
4
4
2
2
0
0
200
400
600
Frequency, Hz
800
1000
1200
0
200
a) Through flow muffler (empty)
30
Simulation
Measurement
FEM
45
600
Frequency, Hz
800
1000
1200
Simulation
Measurement
FEM
25
Transmission Loss, dB
40
400
b) One plug flow muffler
50
Transmission Loss, dB
Transmission Loss, dB
14
0
Simulation
Measurement
16
35
30
25
20
15
20
15
10
5
10
5
0
0
0
200
400
600
Frequency, Hz
800
1000
1200
0
200
400
600
Frequency, Hz
800
1000
1200
c) Two plugs flow muffler
d) Eccentric muffler
Figure 8: Comparison between the measured Transmission Loss for selected mufflers at
zero flow and simulated results using SIDLAB Acoustics. The vertical dashed line marks
the plane wave limit.
Paper B: Investigation of the Acoustic Performance of After Treatment
Devices
Protection of the environment is a concern of global interest. It is generally
acknowledged that the steady rise in all kinds of pollution cannot continue. The pollution
from internal combustion and diesel engine emissions is especially alarming, but exhaust
emissions are not the only concern. Diesel engines are also notorious for their noise levels.
Currently, trucks and heavy equipment must pass noise certifications in order to be
admitted in many markets. Moreover, noise is a major factor influencing market
attractiveness and competitiveness.
One way of mitigating both exhaust emissions and noise is via the use of after
treatment devices like catalytic converters and diesel particulate filters (DPF). The research
proposed herein will focus on DPF units. DPF units are devices which remove from 50 to
over 90 percent of diesel particulate matter from exhaust gases. Their use in both the
United States and Europe will likely be mandated by 2013. DPF units are similar to
catalytic converters, but differ by introducing a less direct path through the filter. Instead
of a straight-through path, exhaust gases must penetrate through a porous cell wall before
exiting the filter. A number of different filter materials have been used including ceramic
and silicon carbide materials, fiber wound cartridges, knitted silica fiber coils, ceramic foam,
6
wire mesh and sintered metal structures. DPF units not only filter out particulate matter,
but are also excellent noise filters due to the indirect air path plus that the filter itself
consists of sound absorbing materials.
Modeling the catalytic converters and Diesel particulate filters has been an interest
to many researches. In 1995 Ih et al. [11] introduced a theoretical formulation of acoustic
wave propagation in a narrow capillary tube with steady gas flow. The transverse variations
of the particle velocity, temperature, and viscosity are considered. A fully developed
laminar steady flow is assumed and the concept of a complex propagation constant is
introduced in the formulation.
In 1998, Selamet et al. [12] investigated the acoustical wave propagation and
attenuation in catalytic converters. The relationships for wave propagation in a catalytic
monolith are derived first and then coupled to the wave propagation in tapered ducts
which are commonly placed at either end of the monolith. In 1999, Selamet et al. [13]
carried out a study to understand the wave attenuation behavior of these elements with
firing engines, dynamometer experiments were conducted on a 3.0L V-6 engine with two
different exhaust systems: one with the catalysts in the cross-over pipe, and the other that
replaced the catalysts with equal length straight pipes.
In 2000, Peat and Kirby [14] presented a numerical study to the problem of nonisentropic acoustic wave motion in a circular capillary tube in the presence of both axial
mean flow and a background axial temperature gradient. The effects of the radial
components of the acoustic velocity are included in the analysis. The main application is in
the study of the acoustic effects of catalytic converters. The solution makes use of a series
expansion and is valid for small relative changes in the background temperature.
In 2002, Lou et al. [15] introduced a sub-structuring technique based on the
impedance matrix synthesis used along with the recently developed direct mixed-body
boundary element method (BEM) to evaluate the transmission loss (TL) of packed
silencers. Due to the single-domain nature of the direct mixed-body BEM, each
substructure does not need to be a homogeneous domain. The sub-structuring technique
presented in this paper also has the capability of modeling a catalytic converter in which a
catalytic monolith containing a stack of capillary tubes is inserted between two connecting
substructures.
In 2005, Allam and Åbom [16] carried out the first attempt to describe the acoustic
behavior of DPFs and to present models which allow the acoustic two-port to be
calculated. Also in 2005, Dickey et al. [17] developed models for visco-thermal effects in
catalytic converter substrates for time domain computational methods. The models are
suitable for use in one-dimensional (non-linear) approaches for the prediction of engine
performance.
In 2006, Allam and Åbom [18] analyzed the treatment of viscous and thermal
losses along the narrow channels in more detail, by solving the convective acoustic wave
equations for two neighboring channels simplified in the manner of the Zwikker and
Kosten theory. From the solution the acoustic two-port was calculated to predict the sound
transmission losses for an entire DPF unit. In the same year Allam and Åbom [19] studied
an acoustic model of a complete after treatment device for a passenger car. The model is
made up of four basic elements: (i) straight pipes; (ii) conical inlet/outlet; (iii) CC unit, and
(iv) DPF unit. For each of these elements, a two-port model is used and with the exception
of the DPF unit, known models from the literature are available. For the DPF unit, the
new model suggested by Allam and Åbom [18] was used. Using the models, the complete
acoustic two-port model for the investigated ATD unit was calculated and used to predict
the sound transmission loss.
In 2011 Hua et al. [20] present a finite element approach to predict the attenuation
of muffler and silencer systems that incorporate diesel particulate filters (DPF). Flow
7
effects are considered at the inlet and outlet to the DPF as well as viscous effects in the
channels themselves.
Figure 9. The DPF unit with the DOC (Diesel Oxidation Catalyst)
filter, inlet and outlet end caps.
Figure 10. The SCR (Selective Catalytic Reducer) unit with AMOX
(Ammonia Oxidation Catalyst) filter, inlet and outlet end caps.
The objective of paper C is to investigate several after treatment devices used for
large diesels shown in Figure 9 and Figure 10. The passive acoustic properties of three
different units are measured and compared to the 1D simulations using two-port
techniques. The acoustic two-port is measured at no flow, in addition to 3 different flow
conditions. The permeability of the DPF walls was estimated from the measurement of the
linear pressure drop across the filter.
A 1D model was built for these filters based on the two-port theory in the SIDLAB
software. The model is based on the division of the complete filter into a number of twoport elements. The results show that this model is capable of predicting the acoustic
performance of the after treatment devices in the low frequency region. In the high
frequency region, the model predicts the overall behavior of the performance. Figure 11 to
Figure 13 show comparison between simulation and measurement results for the no flow
case.
8
100
100
90
70
60
50
40
30
70
60
50
40
30
20
20
10
10
0
0
200
400
600
800 1000 1200
Frequency, Hz
1400
SIDLAB
Measurement
80
Transmission Loss, dB
Transmission Loss, dB
90
SIDLAB
Measurement
80
1600
1800
2000
0
0
200
400
600
800 1000 1200
Frequency, Hz
1400
1600
1800
2000
Figure 11. Comparison between the
Figure 12. Comparison between the
simulated and measured transmission loss of simulated and measured transmission loss of
the DPF unit with DOC module Type A.
the DPF unit with DOC module Type B.
60
Transmission Loss, dB
50
40
30
20
SIDLAB
Measurement
10
0
0
200
400
600
800 1000 1200
Frequency, Hz
1400
1600
1800
2000
Figure 13. Comparison between the simulated and measured transmission loss of
the SCR unit.
Paper C: Insight into Exhaust Systems Optimization Techniques
Under the continuous environmental demands to control noise emitted from IC-engines,
reduction of the exhaust system noise is an important task. Noise control can be
accomplished at three locations - at the source, in the path between the source and the
receiver and at the receiver. In this paper the noise is controlled in the path between the
source and the receiver through the shape optimization of the exhaust system mufflers.
The specific design of mufflers is driven by three paramount considerations which are:
appropriate outer geometry, low pressure drop and sufficient sound attenuation. It is thus
important to get an optimal muffler design under space constraints, an area that is not yet
so well developed.
In 1986 Bernhard [20] introduced the shape optimization of simple expansion
mufflers by using design sensitivity matrices. The volume of the reactive silencer was nonconstrained. Yeh et al. [22] presented an optimal design of a single chamber muffler with
side inlet and outlet and optimal design of single expansion muffler with extended inlet and
outlet tubes [23]. Both cases under space constraints, by using an exterior penalty function
method, an interior penalty function method and the method of feasible direction, which
9
also depend on sensitivity analysis. The calculation of design sensitivity matrices is difficult
especially for complex mufflers.
Yeh et al. also presented an optimization method for a constrained single expansion
muffler [24], a double chamber muffler [25], a double chamber muffler with extended inlet
and outlet tubes [26] and multi-segments mufflers [27], using a Genetic Algorithm based
on the principles of natural biological evolution. Recent work by Chiu et al. [28] was carried
out to determine the optimal shape design of a single expansion muffler with side
inlet/outlet using the boundary element method for calculating the acoustic properties,
combining the gradient methods and the genetic algorithm to get the optimal design.
Although with the Genetic Algorithm the sensitivity analysis is avoided, one disadvantage
of the GA is the higher computational cost [29], especially for large number of design
variables.
Barbieri and Barbieri [30], presented the shape optimization of a single expansion
muffler with extended tubes using the Zoutendijk's feasible directions method, in order to
get the maximum transmission loss at certain frequency ranges using finite element
analysis. Ih et al. [31], presented the shape optimization of a double chamber muffler using
the simulated annealing algorithm, to get a maximum insertion loss.
Paper C will deal with achieving maximum sound attenuation under space
constraints rather than optimizing a single acoustic property. This is done by searching for
the optimal designs for maximum transmission loss, maximum insertion loss, or minimum
acoustic pressure measured at a distance outside the system. It is interesting to see how the
design changes if using different optimum measures e.g. TL or IL. The optimal design for
each acoustic property will be obtained separately.
These optimal designs are compared in order to get the optimal design that gives
the best overall acoustic performance of the muffler. The acoustic properties are calculated
and conjugated with the optimization technique using “fmincon”, a function from the
MATLAB optimization tool-box, which finds the minimum of a constrained nonlinear
multivariable function. To verify the optimization technique, the results of two cases
(expansion muffler with extended inlet and outlet, and double chambers muffler shown in
Figure 14 and Figure 15) were compared with results from the literature.
Figure 14. Case 1:
Single expansion chamber muffler with
extended tube.
Figure 15. Case 2:
Double Chamber Muffler.
As shown from the results for the case of the single expansion chamber with
extended inlet/outlets, optimization of maximum transmission loss, maximum insertion
loss, and minimum sound pressure level outside the muffler, respectively, all gave the same
optimal design. This optimal design is only slightly different from the optimal design of
reference [30], however, it gave better results for the transmission loss, insertion loss and
noise reduction, as shown in Figure 16 to Figure 19 .
10
80
120
Used Model
Reference [30] Model
70
Current Optimization Results
Reference [30] Results
100
60
80
50
40
60
30
40
20
20
10
0
0
0
500
1000
1500
2000
2500
3000
Figure 16. Model comparison.
0
100
200
300
400
500
600
700
800
900
Figure 17. Comparison between optimal TL
using the procedure in paper C, and reference
[30] results.
60
120
Current Optimization Results
Reference [30] Results
100
Current Optimization Results
Reference [30] Results
40
Pressure outside, dB
80
60
40
20
0
-20
20
-40
0
-20
-60
0
100
200
300
400
500
600
700
800
900
0
100
200
300
400
500
600
Frequency, Hz
700
800
900
1000
Figure 18. Comparison between optimal IL using Figure 19. Comparison between optimal outside
the procedure in paper C, and reference [30] pressure using the procedure in paper C, and
results.
reference [30] results.
For case 2, however, on optimizing for getting maximum transmission loss,
maximum insertion loss, and minimum sound pressure level outside the muffler, the
optimal design for the transmission loss differs from the optimal design for the insertion
loss and pressure outside. Also these optimal designs differ from the optimal design of
reference [25], from which may be concluded that the optimizer has chosen a local
minimum. Results are shown in Figure 20 to Figure 23.
90
30
Used Model
Reference [5] Model
25
Design2 Results
Design1 Results
Reference [25] Results
80
70
Transmission Loss, dB
Transmission Loss, dB
20
15
10
5
60
50
40
30
20
0
10
-5
0
-10
0
200
400
600
Frequency, Hz
800
1000
1200
0
200
400
600
Frequency, Hz
800
1000
1200
Figure 20. Models comparison. N.B. model is Figure 21. Comparison design 1, design 2, and
from reference [25].
reference [25] TL results.
11
100
Design 2 Results
Design 1 Results
Reference [25] Results
80
60
Transmission Loss, dB
40
60
20
40
0
20
-20
0
Design1 Results
Design2 Results
Reference [25] Results
-40
-20
0
200
400
600
Frequency, Hz
800
1000
1200
Figure 22. Comparison design 1, design 2,
and reference [25] IL results.
-60
0
200
400
600
800
1000
1200
Figure 23. Comparison design 1, design 2, and
reference [25] outside pressure results.
From the results of the cases discussed in this paper, some points deserve attention:
 Accurate Model. Before conducting an optimization of an acoustic problem, it is
essential to choose an accurate acoustic model so that one can depend on the results
and then perform the optimization. The model accuracy is very crucial when it
comes to getting the optimal design for maximum attenuation at a single frequency.
 Multi-Optimal Designs. More than one optimal design can be found. This point is
clearly appearing in the case of the single chamber muffler with extended inlet and
outlet discussed in paper C.
 Optimized Property. It is always an important question to ask what acoustic
property is to be optimized, whether it is the transmission loss, insertion loss, or the
acoustic pressure received by a receiver outside the system. In case of the optimum
insertion loss it is very important to have information about the source and radiation
impedance for the system, while in the case of finding the optimum acoustic
pressure outside the system it is important to also have information about the source
strength.
Paper D: Optimization of exhaust systems to meet the acoustic
regulations and the engine specifications
The case study presented in paper D is a truck exhaust system (shown in Figure 24)
that consists of a diesel engine, two mufflers, intermediate pipes and a tailpipe. The first
muffler is a typical EU-regulation compliant. The dimensions and location of the second
muffler are to be optimized. A limit for the system back pressure is imposed by the engine
manufacturer. An optimum design was investigated using the formulation in paper C for
different engine speeds and loads (12 source cases). It was found that using the suggested
formulation; one can obtain a design of a muffler to meet both the acoustic regulations and
the engine specifications.
12
Figure 24. The exhaust system with an expansion chamber, paper D.
The acoustic properties are calculated using SIDLAB software [2], which is a code
to analyze low frequency sound propagation in complex duct networks based on the twoport theory. The acoustic properties calculation is conjugated with the optimization
technique using “fmincon”, a function from the MATLAB optimization tool-box that
finds the minimum of a constrained nonlinear multivariable function. The optimization
technique has been verified in earlier work [10]. This optimization technique is
implemented in SIDLAB, using the same solver of acoustics and flow simulation to find
the optimum value of any chosen shape defining property, having the option to set the
limit of engine back pressure as a non-linear constraint.
Figure 25 to Figure 29 show the insertion loss results for several iterations of the
internal design configuration of the muffler to be optimized at one source case (1200 rpm
at 25% loading). In all the figures, the dashed red curve represents the target curve to be
achieved (exceeded). Figure 25 shows the insertion loss of the exhaust system with the EU
muffler only. Although the insertion loss curve satisfies the target curve at low frequencies
(at the slope), it has a few anti-peaks at higher frequencies. The next step was to add a
simple expansion chamber, which does not enhance the performance too much, as shown
in Figure 26. When a perforated pipe is fitted inside the expansion chamber to form a
through flow muffler, it enhances the insertion loss performance at high frequencies but
the rising slope at low frequencies is not satisfied, as shown in Figure 27. When adding an
extended inlet and outlet acting as quarter wavelength resonators, it increases the slope of
the insertion loss at low frequencies, but not enough to exceed the slope of the target
curve, as shown in Figure 28.
One basic rule in muffler design to achieve higher attenuation through expansion
chambers, is to increase the ratio between the area of the chamber and the area of the inlet
pipe and not only the value of the chamber area. In our case, we are bounded by a
maximum diameter for the chamber and therefore we have to reduce the diameter of the
inlet pipe in order to achieve a higher expansion ratio. A horn was added after the EU
muffler to reduce the diameter of the intermediate pipe from 114 mm to 90 mm. This
change resulted in an increase of the insertion loss curve above the target curve at all
frequencies, as shown in Figure 29. Therefore, it can be concluded that with this internal
configuration it is possible to satisfy the target curve under the dimensional constraints and
the engine specification for the back pressure limitation.
In paper D 12 optimum designs are obtained, one for each source case. The
challenge is to choose which of these designs to implement in the exhaust system. We need
to find out which design satisfies the target insertion loss at other source cases at the same
time. One strategy is to choose the source case which corresponds to a critical operating
condition; e.g. during the pass-by noise test. In this paper, we did an exercise to predict the
insertion loss of the exhaust muffler for each of the 12 optimum designs at all source cases
resulting in 144 calculations. It was found that the optimum design at the source case of
1200 rpm and 50% loading provides the best performance for all source cases. Figure 30
shows the insertion loss results using this optimum design at all source cases.
13
70
60
60
50
50
Insertion Loss, dB
Insertion Loss, dB
70
40
30
30
20
20
10
10
0
50
100
150
200
Frequency, Hz
250
300
0
50
350
70
60
60
50
50
Insertion Loss, dB
70
40
30
10
10
150
200
Frequency, Hz
250
300
200
Frequency, Hz
250
300
350
30
20
100
150
40
20
0
50
100
Figure 26. IL for the EU muffler plus an
expansion chamber (1200 rpm, 25%
loading).
Figure 25. IL for the EU muffler only
(1200 rpm, 25% loading).
Insertion Loss, dB
40
0
50
350
Figure 27. Optimum IL for the EU muffler
plus a perforated through flow muffler
(1200 rpm, 25% loading).
100
150
200
Frequency, Hz
250
300
350
Figure 28. Optimum IL for the EU muffler
plus through flow muffler with inlet and
outlet resonators (1200 rpm, 25% loading).
70
60
Insertion Loss, dB
50
40
30
20
10
0
50
100
150
200
Frequency, Hz
250
300
350
Figure 29. Optimum IL for the EU muffler plus through flow muffler with inlet and
outlet resonators and reduced diameter of the intermediate pipe (1200 rpm, 25% loading).
14
70
Insertion Loss, dB
60
50
40
30
20
10
50
100
150
200
Frequency, Hz
250
300
350
Figure 30. IL using the 1200 rpm, 50% loading design at all source cases.
The objective of this study is to perform an exercise to optimize the acoustic
performance of an exhaust system bound to space constraints while maintaining the
pressure drop below a certain limit. In this paper a complete case study is presented, where
the insertion loss of a truck exhaust system was optimized to satisfy a target curve.
SIDLAB software was used for the acoustic and flow modeling of the exhaust system. The
optimization was performed using MATLAB built-in functions. The design steps to design
an optimum exhaust system can be summarized as follows:
–
–
–
–
–
–
Characterize the source
Determine the target performance
Define the geometrical constraints
Find the best muffler design configuration
Find the optimum dimensions for a number of source cases
Select one optimum and check it for the other source cases
15
Acknowledgments
The work has been conducted within the research projects:


SIDA and Vetenskapsrådet under the program Swedish Research Links (Contract number
348-2008-6027).
Simulation of Diesel Particulate Filters in Exhaust Systems, funded by Science and
Technology for Development Fund (STDF), Project number 866.
In addition I would like to show my gratitude to the ones who contributed in the process
of writing this thesis. The ones first to be thanked are my late parents. Before I was myself
they made me, with love, patience, and discipline, then bit by bit stepped back to set me
free. I owe my every past present and future success to them who honestly did their best
for my good. Now I'm sharing my new life with my best friend (Mohamed Mansour) who
became recently my husband, and the closest one to me. He is my supporter; his patience,
understanding, and trust to me always give me the strength to achieve whatever I want. I
dedicate him this thesis and all my future work and success.
I would also like to thank my supervisors Mats Åbom, Susann Boij, and Tamer
Elnady for the opportunity to participate in this work, and also for the continuous guidance
in all the discussions and help during the projects. They never saved their time or efforts to
help me finishing this thesis.
My thanks also goes to Hans Bodén at the MWL and Ragnar Glav at Scania trucks
for providing data for the case study data for paper D, and to Krister Svanberg, at the
KTH, Department of Mathematics for the discussions about the optimization problem
formulation.
16
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