FEA Final Project
Heat Transfer and Stress
Distribution in a Direct Injection
2-Stroke Cylinder Head
Submitted By: Austin Welch
Submitted To: Dr. Gabriel Potirniche
For: ME 404 Finite Element Analysis
Table of Contents
Introduction
Model
Loading
Amplitude of Loads
Amplitude Graphs
Interactions
Boundary Conditions
Material Properties
Mesh
Temperature Distribution
Stress Distribution
Appendix A – MatWeb
Appendix B – EES Code
Introduction
Snowmobiling is a recreational activity that many enjoy. However, with the
implementation of the EPA's reduced emission phases scheduled for completion in 2012,
enthusiasts and manufactures are looking for ways to make their sleds more eco-friendly. The
problem with many 2-stroke engines is that they historically pollute more than their 4-stroke
counterparts. Yet 2-strokes are lighter, less complex, easier to manufacture, and maintain a
higher power to weight ratio making them perfect for such recreational vehicles as
snowmobiles, dirt bikes, and atvs. Our goal in completing this project is to produce a cylinder
head design that dramatically reduces harmful emissions such as Carbon Monoxide,
Hydrocarbons, and NOx.
As part of the design process, a Finite Element Analysis is being implemented. With the
FE analysis, two parameters of this cylinder head will be evaluated. The first parameter of
interest is the temperature distribution within the cylinder head resulting from the combustion
process. This is of great importance because hot spots within the cylinder head, especially
around the combustion chamber, can cause detonation leading to poor emissions and
efficiency as well as mechanical problems. The second parameter is the stress distribution
within the cylinder head as it undergoes detonation. This is important because detonation is
certain to occur during the initial tuning and mapping of engine parameters allowing us to
ensure that the cylinder head can undergo a certain amount of detonation without failure.
Model
For the model I am modeling only half of the cylinder head because of the symmetry
about its center. I also am only interested in the temperature distribution outside of the
combustion chamber and eliminating half of the cylinder head cuts down on the number of
nodes that encompass “empty space” dramatically.
Figure 1 Model
Loading
There are three separate loads being applied to combustion chamber. First, I placed a
surface heat flux on the inside of the combustion chamber. To calculate the value of this heat
flux I applied an energy balance to the engine assuming fuel entering at a given rate and
enough air to complete the combustion process. I also assumed that the fuel being used was
Octane. The following analysis was performed:
𝐶8 𝐻18 + 12.5 𝑂2 = 8 𝐶𝑂2 + 9𝐻2 0
̅̅̅𝑝 − ℎ
̅̅̅𝑟 )
𝑄̇ = 𝑊̇ + 𝑛̇ (ℎ
𝑊̇ = 130 𝐻𝑃
𝑛̇ = 5.343 𝐸 − 7
̅̅̅
ℎ𝑝 = −1.752 𝐸 6
𝑙𝑏𝑚𝑜𝑙
𝑠
𝐵𝑡𝑢
𝐵𝑡𝑢
̅̅̅𝑟 = −1.075 𝐸 5
𝑎𝑛𝑑 ℎ
𝑙𝑏𝑚𝑜𝑙
𝑙𝑏𝑚𝑜𝑙
𝑄̇ = 3.27 𝐸 5
𝐵𝑡𝑢
ℎ𝑟
All supporting work is shown in Appendix A. I then assumed that all of the heat generated
during combustion was sent directly into the cylinder head and distributed evenly. The next
loading that was applied was the internal pressure that the cylinder head experiences during
combustion. I assumed that this pressure was distributed evenly over the entire surface of the
combustion chamber. The maximum in cylinder pressure during normal operation is
approximately 1000 psi. The final loading applied to the model was an overload pressure of 1.5
times the normal operating pressure. This value was a spike overload applied over the entire
internal surface area of the combustion chamber. The reason that this is a spike overload and is
1.5 times greater than normal operating pressures is that when the cylinder undergoes
detonation the fuel air mixture is spontaneously ignited by the pressure and heat within the
engine. This causes the flame front to move at supersonic speeds, resulting in the spike;
instead of subsonic speeds, as in normal operation when the combustion process is initiated by
the spark plug.
Figure 2 Loading Area
Amplitude of Loads
Because of the cyclical nature of an engine the loads that I have applied are not
constant. As a first round approach I assumed that they were of constant amplitude so that I
could verify my model. In reality they are somewhat sinusoidal with a maximum and minimum
value reached within each stroke of the engine. Therefore for both the heat flux and normal
operating pressures within the model I added a variable amplitude load of the form
𝑦=
sin(𝜔𝑡)
+ .5
2
𝑦 = ℎ𝑒𝑎𝑡 𝑓𝑙𝑢𝑥 𝑜𝑟 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒
𝑡 = 𝑡𝑖𝑚𝑒
𝐸𝑛𝑔𝑖𝑛𝑒 𝑆𝑝𝑒𝑒𝑑 = 7800 𝑟𝑝𝑚
𝜔 = 816.81
𝑟𝑎𝑑
𝑠
This allows the maximum and minimum to vary between their respective values and zero at a
rate equal to that of the actual engine under operating conditions. For the spike overload
however, the amplitude was changed to happen like a step function that was only on for
approximately 1/5 the time the sinusoidal function took to reach a maximum value. This I
assumed would compensate for the flame front moving at supersonic speeds instead of
subsonic speeds and give enough of a spike overload to properly analysis the cylinder head.
Amplitude Graphs
Figure 3 Pressure and Head Flux Amplitude Graph
Interactions
Since the cylinder head on the snowmobile is liquid cooled, that aspect of performance
was incorporated into the model. By using a convective heat transfer coefficient and the
average temperature of the cooling system during normal operation, I was able to introduce an
interaction that mimicked the performance of the actual engine. To establish a convective heat
transfer coefficient I used the following analysis.
ℎ𝑤 =
𝑁𝑢𝑠𝑠𝑒𝑙𝑤
𝑑ℎ
𝑁𝑢𝑠𝑠𝑒𝑙𝑤 = 0.23𝑅𝑒 0.8 𝑃𝑟 0.4
𝑅𝑒 =
Pr =
𝑄̇ 𝑑ℎ
𝑤 𝐴
𝐶𝑝,𝑤 𝜇𝑤
𝑘𝑤
ℎ𝑤 = 9228
𝐵𝑡𝑢
ℎ𝑟 𝑓𝑡 2 𝐹
These calculations are also supported in Appendix A. The physical parameters were measured
from our designed cylinder head and the volumetric flow rate was researched and found to be
approximately eight gal per min for a two cylinder 2-stroke engine of similar size and power
output.
Figure 4 Convection Interaction surface
Boundary Conditions
For the boundary conditions I initially thought to constrain all six bolt holes but after
further thought and research I concluded that the only direction in which the model is
constrained because of the bolt holes is in the z-direction. This is because as the cylinder head
is heated the engine block that it is attached to is also heated at the same rate due to the
cooling system. It acts not only to remove heat from the combustion process but also to evenly
distribute the remaining heat. Also the engine block and cylinder head are both made of an
aluminum alloy I assumed that the coefficient of thermal expansion for the two would be
approximately the same. Therefore, in the xy plane the two pieces move together and the only
reaction force is in the z-direction. To keep the model fixed in space I fixed one bolt hole in the
xyz direction.
Figure 5 Sealing Surface Boundary Conditions
Figure 6 Head Bolt Boundary Conditions
Material Properties
The material properties used were from MatWeb, and online material database, and are
as follows for Aluminum Alloy 7050-T7.
𝐷𝑒𝑛𝑠𝑖𝑡𝑦 = 0.102
𝑙𝑏
𝑖𝑛2
𝑇ℎ𝑒𝑟𝑚𝑎𝑙 𝐶𝑜𝑛𝑑𝑢𝑐𝑡𝑖𝑣𝑖𝑡𝑦 = 0.206
𝐵𝑡𝑢
𝑙𝑏𝑚 𝐹
𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑒𝑛𝑡 𝑜𝑓 𝑇ℎ𝑒𝑟𝑚𝑎𝑙 𝐸𝑥𝑝𝑎𝑛𝑠𝑖𝑜𝑛 = 12.8 𝐸 − 6
𝑌𝑜𝑢𝑛𝑔𝑠 𝑀𝑜𝑑𝑢𝑙𝑢𝑠 = 1.04 𝐸 6
𝑖𝑛
𝑖𝑛 𝐹
𝑙𝑏
𝑖𝑛2
𝑃𝑜𝑖𝑠𝑠𝑜𝑛𝑠 𝑅𝑎𝑡𝑖𝑜 = 0.33
𝑌𝑖𝑒𝑙𝑑 𝑆𝑡𝑟𝑒𝑛𝑔𝑡ℎ = 71000
𝑙𝑏
𝑖𝑛2
𝑈𝑙𝑡𝑖𝑚𝑎𝑡𝑒 𝑇𝑒𝑛𝑠𝑖𝑙𝑒 𝑆𝑡𝑟𝑒𝑛𝑔𝑡ℎ = 80000
𝑙𝑏
𝑖𝑛2
𝐸𝑙𝑜𝑔𝑎𝑡𝑖𝑜𝑛 𝑎𝑡 𝐹𝑟𝑎𝑐𝑡𝑢𝑟𝑒 = 11%
Mesh
Because of the complicated geometry of this model the only type of elements that were
allowed were tetrahedral elements. For this analysis, since I am evaluating both thermal and
mechanical properties, Temp-Displacement Tetrahedral Elements were chosen. For the mesh I
used a total of 153,725 Elements and 34,867 Nodes. This many elements were necessary to
properly mesh the model and for the analysis to solve without convergence issues.
Figure 7 Meshed Model
Temperature Distribution
The steady state temperature distribution is shown below. To achieve a convergence
temperature, the simulation was run over several time steps starting with 1 sec out to 1,000
seconds. The final step would be equivalent to an approximate fifteen minute ride. This allows
for sufficient heating of the cylinder head to a temperature slightly above that of the cooling
fluid, which is to be expected. A hot spot has developed under the exhaust side spark plug
with the maximum temperature near 320 degrees. This is enough of a temperature spike that
the hot spot could potentially lead to detention within the combustion chamber. However,
because it is located on the edge of the spark plug hole we believe that there is little to worry
about. Once the engine is assembled the spark plugs inserted through those holes will act much
like another pin fin and remove most of the heat buildup in this location. Because of the this
pin fin effect of the spark plug the slight increase in the temperature around this area will be
ignored. Since there are no other hot spots that have developed, it is assumed that there will
be no evident causes of detonation because of hot spots within the combustion chamber.
Figure 8 Steady State Temperature
Stress Distribution
During the normal operation of the engine with a max variable in-cylinder pressure of 1000 psi,
the stress distribution within the cylinder head is at a maximum of 25 Ksi. This is approximately
35 percent of the value needed to cause initial yielding. Therefore under normal operating
condition the model is well within the elastic portion of the stress strain curve and we should
have no foreseeable problems with our design.
Figure 9 Normal Stress Distribution
However, when detonation occurs, there is a huge jump in the maximum stress as can be seen
below. The maximum value of the Von Mesis Stress is over 71 Ksi. This stress is near the stress
needed to cause initial yielding under the Von Mesis Failure Theory. This theory states that as
the Von Mesis Stress approaches the yield stress of the material, yielding begins. Now with this
simulation it is interesting to note that this was only a single occurrence of detonation. It would
be interesting to see what happens as detonation continues to occur. Also, if failure does occur
because of detonation, how many cycles would it take to cause final failure of the cylinder
head.
Figure 10 Spike Stress Distribution
/w EPDw UJOTExO
Aluminum 7050-T7651
Categories: Metal; Nonferrous Metal; Aluminum Alloy; 7000 Series Aluminum Alloy
Material
7050 has very high strength coupled with high resistance to exfoliation corrosion and
Notes:
stress-corrosion cracking, high fracture toughness, and fatigue resistance. This leads to
applications in aircraft structures.
Data points with the AA note have been provided by the Aluminum Association, Inc. and
are NOT FOR DESIGN.
Composition Notes:
Composition information provided by the Aluminum Association and is not for design.
Key Words: UNS A97050; ISO AlZn6CuMgZr; Aluminium 7050-T7651; AA7050-T7651
Vendors:
No vendors are listed for this material. Please click here if you are a supplier and would like
information on how to add your listing to this material.
Physical
Properties
Density
Mechanical
Properties
Hardness,
Brinell
Hardness,
Knoop
Hardness,
Rockwell A
Hardness,
Rockwell B
Hardness,
Vickers
Ultimate
Tensile
Strength
Tensile Yield
Strength
Elongation at
Break
Modulus of
Elasticity
Poissons
Ratio
Fracture
Toughness
Shear
Modulus
Shear
Strength
Metric
English
Comments
2.83 g/cc
0.102 lb/in³
AA; Typical
Metric
English
Comments
147
147
187
187
500 kg load with 10 mm ball. Calculated
value.
Converted from Brinell Hardness Value
53
53
Converted from Brinell Hardness Value
86
86
Converted from Brinell Hardness Value
171
171
Converted from Brinell Hardness Value
552 MPa
80.0 ksi
AA; Typical
490 MPa
71.0 ksi
AA; Typical
AA; Typical
11.0 %
11.0 %
@Diameter 12.7 mm
@Diameter 0.500 in
71.7 GPa
10400 ksi
0.330
0.330
26.0 MPa-m½
23.7 ksi-in½
K(IC) in S-L Direction
31.0 MPa-m½
34.0 MPa-m½
26.9 GPa
28.2 ksi-in½
30.9 ksi-in½
3900 ksi
K(IC) in T-L Direction
K(IC) in L-T Direction
324 MPa
47000 psi
AA; Typical
AA; Typical; Average of tension and
compression. Compression modulus is
about 2% greater than tensile modulus.
Electrical
Properties
Electrical
Resistivity
Thermal
Properties
CTE, linear
Metric
English
Comments
0.00000440 ohm-cm
0.00000440 ohm-cm
Metric
English
Comments
23.0 µm/m-°C
12.8 µin/in-°F
AA; Typical; average over range
@Temperature 20.0 - 100 °C @Temperature 68.0 - 212 °F
25.4 µm/m-°C
14.1 µin/in-°F
average
@Temperature 20.0 - 300 °C @Temperature 68.0 - 572 °F
Specific Heat
Capacity
Thermal
Conductivity
Melting Point
Solidus
Liquidus
Processing
Properties
Annealing
Temperature
Solution
Temperature
Aging
Temperature
Component
Elements
Properties
Aluminum, Al
Chromium, Cr
Copper, Cu
Iron, Fe
Magnesium,
Mg
Manganese,
Mn
Other, each
Other, total
Silicon, Si
Titanium, Ti
Zinc, Zn
Zirconium, Zr
0.860 J/g-°C
0.206 BTU/lb-°F
153 W/m-K
1060 BTU-in/hr-ft²-°F
488 - 629.4 °C
910 - 1165 °F
488 °C
629.4 °C
AA; Typical range based on typical
composition for wrought products 1/4 inch
thickness or greater
910 °F
AA; Typical
1165 °F
AA; Typical
Metric
English
Comments
413 °C
775 °F
477 °C
890 °F
121 - 177 °C
250 - 350 °F
Metric
English
Comments
87.3 - 90.3 %
<= 0.040 %
2.0 - 2.60 %
<= 0.15 %
1.90 - 2.60 %
87.3 - 90.3 %
<= 0.040 %
2.0 - 2.60 %
<= 0.15 %
1.90 - 2.60 %
As remainder
<= 0.10 %
<= 0.10 %
<= 0.050 %
<= 0.15 %
<= 0.12 %
<= 0.060 %
5.70 - 6.70 %
0.080 - 0.15 %
<= 0.050 %
<= 0.15 %
<= 0.12 %
<= 0.060 %
5.70 - 6.70 %
0.080 - 0.15 %
References for this datasheet.
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consistant format. Users requiring more precise data for scientific or engineering calculations can click on the property value to see the
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