1. Submitted in partial fulfillment of the requirements of MENG-5136G - Intro to FEA Graduate the FALL semester,
2014
Department of Mechanical Engineering Georgia Southern University
DETERMINATION OF THE SEQUENTIAL COUPLED THERMAL - STRUCTURAL
ANALYSIS AFTERMARKET EXHAUST MANIFOLD FOR A TRANSVERSE SI
ENGINE
Mosfequr Rahman
Associate Professor
Mechanical Engineering Department
Georgia Southern University
Statesboro, Georgia 30460 – 8045
mrahman@georgiasouthern.edu
Dwight Gustard
Graduate Student
Mechanical Engineering Department
Georgia Southern University
Statesboro, Georgia 30460 – 8045
dg01119@georgiasouthern.edu
ABSTRACT
This paper present the Sequential Coupled Thermal - Structural
Analysis to investigate the associated thermal stresses and
deformations under simulated operational conditions close to
the real situation on SUS 441L grade stainless steel for an
aftermarket exhaust manifold.. Analysis carried out by
reference environmental testing conditions in “room
temperature” standard conditions. The finite element analysis
software ANSYS Workbench 15.0 used to calculate the linear
steady state temperature distribution under the thermal field &
structural analysis. Thermal analysis calculates the temperature
distributions and related thermal quantities in an exhaust
manifold. Structural analysis takes inputs from thermal analysis
to calculate deformation, stress and strain. FEM analysis is
done by using tetrahedral element of first order and
convergence test is performed for structural load. The purpose
of this analysis is to ensure the appropriateness of material for
the defined design from the view point of serviceability of the
exhaust manifold. Selected details and results of the overall
investigation are presented and discussed within the framework
of this paper.
In addition to that, the impact of temperature effect on exhaust
manifold modal analysis is analyzed in this study. Firstly, the
temperature field is mapped from results processed in the
thermal analysis of the exhaust manifold. It was found that the
natural frequency of the manifold would not impact with the
frequency given off by the engine block. Those worst case
resonant conditions were calculated and are included in the
body of this paper.
INTRODUCTION
Automobile engines are the functional backbones that
contribute to and means of terrestrial transportation.
Researchers in the automotive field have rightfully emphasized

2. 2 Copyright © 2013 by ASME
improvement of engine design since fuel economy and
environmental impact from transportation become a global
concern. With respect to national mandates in 1970, Congress
passed the Clean Air Act, which called for the first tailpipe
emissions standards. The pollutants controlled were carbon
monoxide (CO), volatile organic compounds (VOC), and
oxides of nitrogen (NOx). The new standards went into effect
in 1975 with a NOx standard for cars and light-duty trucks of
3.1 grams per mile (gpm). [1]
Some of the specific areas that have been researched are new
engine material, bio-fuel cell, spark-free operation, hybrid –
engine, and electric engine. The typical methodologies for these
types of research include both experiment-based, as well as
computer simulated models like that of this report. Engine
designs have been considerably improved by virtue of
limitations and mandates placed on this industry, and as such
the fuel economy and environmental impact are still being
promulgated as main focusses of research. [2]
In this case, the part of the vehicle that is under consideration is
the exhaust manifold specific to transversely mounted engine
with the exhaust side of the engine block being directly in front
of the firewall. It is an aftermarket manifold and, as such, the
specifics as far as parameters regarding this manifold has not
been studied in an extent that is well known or acceptable.
Typically speaking, the role of the exhaust manifold is to
convey the exhaust gas from the engine block towards the
exhaust apparatus. This is composed of the catalytic converter,
muffler, and final resonator and, of course the exhaust pipes
which connect each individual part. [3]
Since the exhaust manifold acts as a collector of exhaust gases
from the engine and is directly connected to it, the manifold
itself is constantly under duress from forces due to temperature
expansion and vibration as well as constraints placed on it by
its connection to the vehicle itself.
This is especially of importance due to considering the cabin
noise, the exhaust manifold is one of the most critical
components and consequently a strong effort in the design
phase is devoted to its vibro-acoustics optimization. Most cabin
noise is generated due to engine vibrations, which can be
transmitted to the exhaust manifold surfaces and to air flow in
the exhaust system. Due to this fact, distortion of the manifold
can contribute to the noise experienced in the cabin due to the
various frequencies the engine produces. This is where modal
analysis can help to determine, for this exhaust manifold
design, what frequencies can contribute to cabin noise as well
as the deformation of the manifold.
Modal analysis is used to study the inherent dynamic
characteristics of a system. Natural frequencies and natural
modes represent the basic dynamic characteristics of all
dynamic systems. They define the dynamic individuality of
dynamic system. [4] Vibration mode is used to show the
structure deformation corresponding to each natural frequency.
The exhaust manifold is close to the engine part in automotive
exhaust system, because the cylinder discharge gas temperature
can reach 800°C and above, the tail gas heating effect is
obvious. Because the thermal stress that tail gas heating caused
can be as high as hundreds of MPa, it can also lead to thermal
fatigue and cause structural fracture.
Temperature has great influence on material mechanical
properties, so it is necessary to take the influence of the
temperature pre-stress on exhaust manifold vibration
characteristics into account. A normal modes analysis should be
performed to make sure that the frequencies of exhaust system
does not line up with the frequencies of power train and body.
The same modal analysis is helpful to determine the hanger
locations on the exhaust system based on the nodal points
shown in animated mode shape plots. This will minimize
vibrational energy transferred to the body. [5]
The objective of this work is to develop a simplified finite
element model of the MARK4 (MKIV) aftermarket gasoline
spark-ignition engine exhaust manifold. The finite element
method (FEM) is a numerical technique for finding
approximate solutions to boundary value problems for partial
differential equations. It uses subdivision of a whole problem
domain into simpler parts, called finite elements, and variation
methods from the calculus of variations to solve the problem by
minimizing an associated error function. [5] The model
geometry was constructed from the design from OBX® exhaust
products. The model of the actual manifold was simplified to
eliminate the port for the secondary air injection. Despite this
fact, the model maintains major features of the manifold. The
model is useful to find out valued benchmark information such
as temperature distribution, localized temperature, and critical
part of the manifold where damage may occur.
The finite element analysis software ANSYS Workbench 15.0
used to calculate the linear steady state temperature distribution
under the thermal field & structural analysis. Thermal analysis
calculates the temperature distributions and related thermal
quantities in an exhaust manifold. [6] Structural analysis takes
inputs from thermal analysis to calculate deformation, stress
and strain. FEM analysis is done by using tetrahedral element
of first order and convergence test is performed for structural
load. The purpose of this analysis is to ensure the
appropriateness of material for the defined design from the
view point of serviceability of the exhaust manifold. Selected
details and results of the overall investigation are presented and
discussed within the framework of this paper.
According to Shi and Zhou, Ji et al. [8] [9], the thermal modal
analysis considering the influence of the temperature and stress
fields is based on thermal analysis and structure the basic
analysis process of thermal modal analysis is as follow and the
flow chart is shown in Fig. 1.

3. 3 Copyright © 2013 by ASME
NOMENCLATURE
B Geometric matrix
DT Elastic modulus which is related to material elastic
matrix E
G Shape function matrix
 Stress matrix
M Mass Matrix
C Damping Matrix
K Stiffness Matrix
x Displacement vector
f(t) Load vector
NUMERICAL MODEL
Governing Equations
Take the structure initial stiffness matrix per Shi and Yang. [7]

 BdDBK T
T
T
(1)
On the other hand, because the thermal stress caused by
temperature gradients, additional initial stress stiffness matrix is
needed besides structure stiffness matrix. The structure initial
stress stiffness matrix is:

 GdGK T

(2)
In summary, the structure thermal stiffness matrix is:
TKKK  
(3)
The basic equation for typical un-damped modal analysis is
classic eigenvalue problem. According to mode theory, the
structure will typically be seen as a system constituted by the
mass point, rigid body and damper and discrete it as finite
number of elastic coupling rigid bodies. Therefore, an infinite
multi-degree freedom system turns into limited multi-degree
freedom system. When the linear time-invariant system
requirements are met, the system general motion mathematical
model can be expressed as: [8]
)(tfKxxCxM 

(4)
The structural damping of exhaust pipe has little effect on the
natural frequencies and therefore do not consider the external
load and damping. Thus Eq. (4) simplifies to: [8]
02
 MK  (5)
Assumptions that follow are based on modeling done by Zhu
and LvJuncheng et al. [9]
[K (T)]{T} = {Q(T)} (6)
No transient effects are considered in a steady-state analysis
[K] can be constant or a function of temperature
{Q} can be constant or a function of temperature
Fixed temperatures represent constraints {T} on the system.
For a Linear static structural analysis, the displacements {x} are
solved for in the matrix equation below:
[K]{x} = {F} Assumptions:
[K] is constant
– Linear elastic material behavior is assumed – Small deflection
theory is used
• {F} is statically applied
– No time-varying forces are considered – No damping effects.
Methodology
Commercially available software ANSYS-Workbench was used
to solve structural modal problem. The exhaust manifold finite
element model is shown in Fig. 2. The mesh was generated
using a medium sized mesh as the fine mesh would return
errors due to the collector section of the manifold. This mesh
was done with 3-D quadratic structural elements (SOLID186,
and SOLID187), where INTER204 simulates an interface
between any two surfaces and the subsequent delamination
Figure 1 – Thermal modal process [9] [8]

4. 4 Copyright © 2013 by ASME
process, where the separation is represented by an increasing
displacement between nodes, within the interface element itself.
[9]
Figure 2 –Finite element model of exhaust header
Mesh refinement
The coupling/collector portion of the manifold requires further
detailing in order to map the thermal/structural response to the
environment. It was refined to yield results that are summarized
in Table 1.
Table 1 – Nodal and Elemental quantities
Mesh Type Nodes Elements
Medium 139378 24161
Refinement 1 16241 38390
Refinement 2 209164 69669
Refinement 3 286126 122365
Material properties
The structure material is System Usability Scale SUS 441L
stainless steel. Its yield strength is 270 MPa. The tensile
strength is rated at 480 MPa. The elongation is rated at 38% per
volume. The hardness is rated at 166 HV. The thermal
expansion coefficient is rated at 1.2E-05/℃. Maximum
operational temperature is 950℃ [10]. The Poisson’s ratio is
0.30. Thermal conductivity is 61 W/m∙ ℃. Density of the
SUS441 steel is 7850kg/m3
. A summary of this information is
found in Table 1, 2 and 3.
Table 2 - Mechanical properties for SUS 441L steel
Yield
Strength
( MPa)
Tensile Strength ( MPa) Poisson’s Ratio
270 480 0.3
Table 3 – Physical properties for SUS 441L steel
Hardness (HV) Thermal
expansion coefficient
(/°C)
Service
temperature (ºC)
166 1.2e-05 950
Table 4 – Physical properties for SUS 441L steel (cont’d)
Density
(kg/m3
)
Thermal
conductivity
(W/m∙°C)
Elongation (%)
7850 61 38
Constraints and load description
The following constrains are based on the parameters set by
Zuo, Hu et al. Normal displacement constraints (Y direction) on
exhaust manifold inlet flange end face and radial displacement
constraints (X, Z direction) in the inlet flange end bolt holes.
Simplify the load acting on the exhaust manifold, such as
simplify the connection relationship of the bolt and the circular
hole for the reference point and the distribution coupling of the
hole inner surface constraint and apply bolt pre-tightening
force. Temperature load is set as a predefined field through the
heat conduction results. [8]
Thermal mapping analysis
The following constrains are based on the parameters set by
Jain and Agrawal. The thermal mapping is done by solving
steady state thermal analysis of the component by using
ANSYS Workbench 15.0. Outer surface of component is
exposed to environment (i.e. air flowing in the chamber or the
still air around the engine,) on which constant heat transfer
coefficient applied with variable ambient temperatures 25°C,
35°C and 50°C. Outer heat transfer coefficient is assumed to be
30W/m² °C, to calculate thermal loads on the exhaust manifold.
Thermal analysis is done for thermal mapping on the complete
body that will calculate all the nodal thermal values dependent
on the thermal resistance of the materials. This temperature
mapping is transfer to the structural analysis for calculation of
expansion of the structure this will gives the thermal stress and
thermal strain results. [6]
RESULTS AND DISCUSSION
Thermal Analysis
The first step of the calculation is represented by a steady state
thermal analysis performed using the ANSYS Workbench 15

5. 5 Copyright © 2013 by ASME
software which is commercially available. As previously
discussed, the environmental temperature is 22 °C, which is
considered to be the average ambient temperature for a car
during a cool evening. In this phase convective heat exchange
between exhaust gas and the internal surfaces of the model, and
conductive heat exchange into the solids and through contacts
are modeled.
The temperature of the engine block at operating temperature is
to be set at 150℃ for simplicity. This is primarily due to the
water cooled engine operating at 95℃ where the exhaust gases
can get to as high as 670℃ as can be seen in Figure 3.
Figure 3 – Initial temperature setting on header flange (150℃)
The inner surfaces of the downpipes, of course, are in direct
contact with the exhaust gases. These, as previously mentioned,
are set to be 670℃. This creates another source of temperature
input for the overall header system.
The convective component of the overall analysis is next. Here
there is to be heat loss and dissemination of the temperature
along the downpipes due to contact with air. The air film
coefficient was taken as 3.0x10-5
W/mm2
℃. Ambient
temperature is also set to 22℃ and both these parameters can be
seen in Figure 4.
Figure 4 –Convection contribution to thermal stress.
As it results, the temperature gradually fades from the header
flange of 150 ℃ to a low value of 38.285℃ and can be seen in
Table 5. This is mainly due to the convection from the ambient.
This result of thermal analysis is summarized in the illustration
from Figure 5 and Figure 6.
Figure 5 – Top-iso view of temperature distribution due to
convection. Max and min temperatures are 150℃ and 38.285℃
respectively.
Figure 6 - Bottom-iso view of temperature distribution due to
convection. Max and min temperatures are 150℃ and 38.285℃
respectively.
Table 5 – Summary of max and min temperature
Maximum Temperature (℃) Minimum Temperature (℃)
150 38.285
Thermal-Stress Analysis
Temperature Mapping Results are used in conjunction with the
static structural component of the ANSYS Workbench 15. This
enables the thermal stress, strain and deformation results to be
had due solely to temperature effect. For this section, the
cylindrical constraints were placed on the holes for the head
bolts as well as the exhaust flange. The surface of the header
flange itself was constrained with regard to displacement. This
is illustrated in Figure 6.

6. 6 Copyright © 2013 by ASME
Figure 7 – Displacement constraint placed on engine block flange
Since the header has to be mounted to the engine block, the
typical fastener used to do this is bolts protruding from the back
of the engine (exhaust side) and nuts that would secure to the
back end of the header. As such, there is a cylindrical constraint
that is places on the holes for the manifold flange (Figure 8) as
well as the back end of the manifold that mounts to the rest of
the exhaust system (Figure 9).
Figure 8 – Cylindrical constraint placed on header bolt holes
Figure 9 - Cylindrical constraint placed on exhaust pipe bolt holes
Static Structural Analyses
Temperature Mapping Results are transfer to the ANSYS static
structural solver for calculation of expansion of the structure
this will gives the thermal stress, strain and deformation results.
The material used is stainless steel SUS 441L and from those
characteristics described in Table 2 – 4 the equivalent von
misses stress and equivalent elastic strain are calculated.
Figures (10, 11 & 12) show the stress distribution of the header
due to the thermal analysis.
Figure 10 – Equivalent stress on manifold (Maximum of 1353MPa
and minimum 0.1147MPa)
Figure 11 - Equivalent stress on manifold (Maximum of 1353MPa
and minimum 0.1147MPa) – Bottom view.
Figure 12 - Equivalent stress on manifold (Maximum of 1353MPa
and minimum 0.1147MPa) – minimum stress shown.

7. 7 Copyright © 2013 by ASME
As one can easily see, the maximum stresses exceed that of the
yield stress for the material property. The stress concentration is
about the bolt opening for the exhaust manifold engine flange.
The total deformation is important as it determines how much
shift is made by a particular part of the manifold. This is critical
for clearances within the engine bay and may need to be taken
into consideration for the firewall and radiator portion of the
engine. The Figures (13, 14 &15) illustrate the total
deformation due to thermal stress. The maximum and minimum
total deformations were found to be 0.36mm and no deflection
respectively. Summary of the max stress and deformation can
be found in Table 6.
Figure 13 – Total deformation on manifold (Maximum of 0.36mm
and minimum 0mm respectively)
Figure 14 - Total deformation on manifold (Maximum of 0.36mm
and minimum 0mm respectively). Bottom view shown
Figure 15 - Total deformation on manifold (Maximum of 0.36mm
and minimum 0mm respectively). Side view shown
Table 6 – Summary of maximum stresses and deformation due to
thermal variation
Maximum Von mises (MPa) Maximum deformation (mm)
1353 .36
Modal System Response
First six orders of the system of frequencies are shown in
figures in this section. Exhaust manifold temperature effect is
mainly reflected in two aspects. On the one hand, the
temperature reduce the material stiffness and uneven
temperature distribution lead to material nonlinearity; on the
other hand, the thermal stress that the temperature generated
can be seen as pre-stress and will reduce structure’s bending
and torsional stiffness, therefore, the structure natural frequency
will be lower under the temperature pre-stress. [11] The
exhaust manifold mainly motivated by the road and engine,
generally the road incentive is about 30 Hz and the engine
inventive is more than 200 Hz, so the design frequency of
exhaust manifold should be greater than 270 Hz.
The first mode of frequency was determined to be 1015 Hz.
Figures (16 -17) display the results of this mode where the
maximum deformation was determined to be 42mm.
Figure 16 – First modal response of manifold of 1015 Hz. 42mm
maximum deformation

8. 8 Copyright © 2013 by ASME
Figure 17 - First modal response of manifold of 1015 Hz. 42mm
maximum deformation (bottom view of max location)
The second mode of frequency was determined to be 1071 Hz.
Figures (18 -19) display the results of this mode where the
maximum deformation was determined to be 46.447mm.
Figure 18 - Second modal response of manifold of 1071.7 Hz.
46.447mm maximum deformation (top view of max location)
Figure 19 - Second modal response of manifold of 1071.7 Hz.
46.447mm maximum deformation (bottom view of max location)
The third mode of frequency was determined to be 1430.6 Hz.
Figures (20 -21) display the results of this mode where the
maximum deformation was determined to be 51.97mm.
Figure 20 - Third modal response of manifold of 1430.6 Hz.
51.97mm maximum deformation (top view of max location)
Figure 21 - Third modal response of manifold of 1430.6 Hz.
51.97mm maximum deformation (top view of max location)
The fourth mode of frequency was determined to be 1495.8 Hz.
Figures (22-23) display the results of this mode where the
maximum deformation was determined to be 47.68mm.
Figure 22 - Fourth modal response of manifold of 1495.8 Hz.
47.68mm maximum deformation (top view of max location)

9. 9 Copyright © 2013 by ASME
Figure 23 - Fourth modal response of manifold of 1495.8 Hz.
47.68mm maximum deformation (bottom view of max location)
The fifth mode of frequency was determined to be 1532.6 Hz.
Figures (24-25) display the results of this mode where the
maximum deformation was determined to be 52.876mm.
Figure 24 - Fifth modal response of manifold of 1532.6 Hz.
52.876mm maximum deformation (bottom view of max location)
Figure 25 - Fifth modal response of manifold of 1532.6 Hz.
52.876mm maximum deformation (side view of max location)
The sixth mode of frequency was determined to be 1682 Hz.
Figures (26-27) display the results of this mode where the
maximum deformation was determined to be 42.07mm.
Figure 26 - Sixth modal response of manifold of 1682 Hz. 42.07mm
maximum deformation (side view of max location)
Figure 27 - Sixth modal response of manifold of 1682 Hz. 42.07mm
maximum deformation (bottom view of max location)
It can be seen by analyzing the results that the lowest order
natural frequency of thermal modal analysis is 1015 Hz and this
is at an ambient temperature of 22℃. This meets the
requirements to avoid the resonance between exhaust manifold
and the engine or other parts. A tabular summary of the data is
in Table 7.
Table 7 – Summary of Modal Response of Manifold
Mode Frequency (Hz) Max deformation (mm)
1 1015 42.07
2 1071.7 46.447
3 1430.6 51.97
4 1495.8 47.687
5 1532.6 52.876
6 1682 42.07
In addition to that, the modes represent specific rotations about
different axes. The first mode was the rotation of the manifold
about the X-axis within the coordinate system that has been
established. It should be noted that engine displacement due to
load can also contribute to this twisting. A summary is listed in
Table 8.

10. 10 Copyright © 2013 by ASME
CONCLUSIONS
From the investigated result of Sequential Coupled Thermal -
Structural FE analysis, observed that the critical area of thermal
stress concentration and deformation using the SUS 441L
stainless steel was the yield strength. Stress concentrations can
be interpreted as significant indices for extreme temperature
levels and temperature gradients. The Results shows the steel
chosen for this manifold is appropriate. The investigated FE
model of Exhaust Manifold can be further designed to remove
stress concentrations that occur near bolt openings.
In this study, a basic analysis process of the exhaust manifold
thermal modal analysis is built. And the temperature pre-stress
is applied on the exhaust manifold modal by the coupling of
ANSYS Workbench using Steady-state thermal, static
structural and modal custom systems.
Results shown are that heating can cause the nonlinear change
of material physical property and generate thermal stress; the
combined effects of both make the structure’s natural frequency
decline after heating.
Thus, in the exhaust manifold design and evaluation, the effect
of temperature on material mechanical properties should be
taken into account.
Being that as it is, there are still some possible improvement
that can be made toward this design, which may be guide to
significant improvements in reduction of thermal stresses. The
overall dimensioning and geometry of the manifold within the
OEM specifications for fitment can be adjusted. Also, the grade
of material that can be used can be changed as well to possibly
include cast iron and other grades of stainless steel.
REFERENCES
[1] Environmental Protection Agency, "Emission,"
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using Simplified Finite Element Model," Proceedings of
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[3] R. C. a. M. Landi, "Acoustic Analysis of an Exhaust
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[4] K. Daniela, "Natural Frequencies of Railway Slab on
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[5] J. Reddy, An introduction to the finite element method,
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[6] A. A. Sweta Jain, "Coupled Thermal – Structural Finite
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[9] ANSYS, Inc, "ANSYS Mechanical APDL Element
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[10] M. A. S. A. S. S. S. Rajadurai, "Materials for Automotive
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Mode Description Frequency
1 Translation along X-axis 1015
2 Translation along Z-axis 1071.7
3 Rotation about Z-axis 1430.6
4 Vertical bending mode of manifold 1495.8
5 Vertical bending mode of UFC 1532.6
6 Translation along Y-axis 1682