2007-2008 PACE Collaboration Vehicle:
Turbocharger Selection
Jacob Dick
A thesis submitted in partial fulfilment
of the requirements for the degree of
BACHOLOR OF APPLIED SCIENCE
Supervisor: W.L. Cleghorn
Department of Mechanical and Industrial Engineering
University of Toronto
March 20, 2008
Working with over 200 students at 20 universities around the world on the PACE global vehicle
collaboration project was no easy task, but this is exactly the purpose of the PACE program. Dr. Greg
Jenson the head of the PACE program at Brigham Young University stated that the purpose of the PACE
program is to “prepare approximately 200 students (and 25 faculty) per year from 20 PACE institutions,
located in 10 countries, on 5 continents, speaking 7 different languages, for ‘involvement in’ and
‘leadership of’ a real-world global design/engineering and collaboration experience”. The University of
Toronto was lucky enough to be chosen as a PACE institute and to participate in this year’s PACE global
vehicle collaboration project. The following report outlines the work completed in researching, selecting
and integrating a turbocharger for the 2007-2008 PACE global vehicle. This was done by applying
learned thermodynamic equations and calculations to turbocharger theory. It was found that a Garrett
GT3782 turbocharger was suitable for this application and was purchased for this project. Although
most of the analytical work focused on selecting the turbocharger it was found that the vast majority of
this project centered on integrating the selected turbocharger into the PACE global vehicle.
i
Acknowledgments
I would like to thank Professor W.L. Cleghorn first and foremost for allowing me to participate in the
PACE program at the University of Toronto and for acting as my thesis advisor. As well I would like to
thank Ryan Udugampola for working with and alongside me on integrating the turbocharger. Much of
the work completed for this year’s PACE car was based on work already completed by the 2006-2007
University of Toronto PACE team. Without this foundation a great deal more work would have been
required this year. Most notable of the 2006-2007 team members was Thomas Cooper who took time
out of his own schedule to educate and assist me and my turbocharger team throughout this project.
I would like to thank Kenneth Mix and Drew Hasford from Brigham Young University for organizing the
PACE project. As well I would like to thank Chance Garcia at the University of Texas El Paso and
Rupinder Virk at McMaster University for working with me to integrate the turbocharger.
ii
Table of Contents
Acknowledgments .......................................................................................................................................... i
1 Introduction ............................................................................................................................................... 1
1.1 PACE Program ..................................................................................................................................... 1
1.2 2007-2008 PACE global vehicle Outline .............................................................................................. 1
1.3 University of Toronto PACE Turbocharger Team ................................................................................ 3
1.4 Collaborating Schools .......................................................................................................................... 3
1.5 Collaboration Tools ............................................................................................................................. 4
1.6 Initial Project Schedule ....................................................................................................................... 5
1.7 Revised Project Schedule .................................................................................................................... 6
1.8 Formula 1 FIA Guidelines .................................................................................................................... 7
2 Turbocharger Calculations ......................................................................................................................... 8
2.1 Internal combustion engine power characteristics ............................................................................ 8
2.2 Model of Turbocharged Engine ........................................................................................................ 10
2.3 Compressor Maps ............................................................................................................................. 11
2.4 Approach of Turbocharger Calculation ............................................................................................. 12
3 Turbocharger Sizing ................................................................................................................................. 17
3.1 Interpretation of engine characteristics ........................................................................................... 18
3.1.1 Garrett GT3571 .......................................................................................................................... 18
3.1.2 Garrett GT3782 .......................................................................................................................... 19
3.1.3 Garrett GT4082 .......................................................................................................................... 19
3.1.4 Garrett GT4088 .......................................................................................................................... 20
3.2 Selected Turbocharger ...................................................................................................................... 20
4 3D CAD Model of Turbocharger ............................................................................................................... 22
5 Layout of Turbocharger............................................................................................................................ 23
6 Oil Line Routing ........................................................................................................................................ 25
7 Engine Test Stand ..................................................................................................................................... 26
8 Work to be completed ............................................................................................................................. 27
9 Tables and Figures .................................................................................................................................... 28
Appendix A: Air mass flow rates (Kg/s) for GM Ecotec 2.2L (Gasoline) ...................................................... 39
Appendix B: Compressor Maps ................................................................................................................... 40
iii
Garrett GT3571 ....................................................................................................................................... 40
Garrett GT3782 ....................................................................................................................................... 41
Garrett GT4082 ....................................................................................................................................... 42
Garrett GT4088 ....................................................................................................................................... 43
Cited Material ............................................................................................................................................. 44
iv
List of Figures
Figure 1: 2006-2007 PACE Car .................................................................................................................... 28
Figure 2: Turbocharger and Intercooler diagram ....................................................................................... 28
Figure 3: Sample Compressor Map ............................................................................................................. 29
Figure 4: 3D CAD Model of Garrett GT4082 ............................................................................................... 30
Figure 5: Turbocharger Position Concept 1 ................................................................................................ 31
Figure 6: Turbocharger Position Concept 2 ................................................................................................ 32
Figure 7: Turbocharger Position Concept 3 ................................................................................................ 33
Figure 8: Exhaust Manifold Interface .......................................................................................................... 34
Figure 9: 2007-2008 PACE Car Oil Schematic.............................................................................................. 35
Figure 10: Engine Test Stand ....................................................................................................................... 36
v
List of Tables
Table 1: Initial Project Schedule .................................................................................................................. 37
Table 2: Engine Horse Power (HP) .............................................................................................................. 38
Table 3: Engine Torque (ft•lbf) ................................................................................................................... 38
vi
List of Symbols and Abbreviations
FEA ....................................................................................................................Finite Element Analysis
CFD ........................................................................................................Computational Fluid Dynamics
BSFC .....................................................................................................Brake Specific Fuel Consumption
fuelm& ....................................................................................................................Mass Flow Rate of Fuel
AFR ...................................................................................................................................Air Fuel Ratio
airm& ......................................................................................................................Mass Flow Rate of Air
rpm ...................................................................................................................Revolutions per Minute
V .................................................................................................................................Engine Volume
VE .......................................................................................................................Volumetric Efficiency
ρ .............................................................................................................................................Density
n ...................................................................................................Type of Engine (2 cycle or 4 cycle)
iP ............................................................................................................................Pressure at state i
iT .....................................................................................................................Temperature at state i
airR ..........................................................................................................................Gas Constant of Air
lossP∆ ..................................................................................................Pressure Loss Through Intercooler
ratioP .................................................................................Pressure Ratio Provided by the Turbocharger
ε .................................................................................................................Intercooler Effectiveness
k ......................................................................................................Ratio of Specific Heat Capacities
cη ....................................................................................................Compressor Isentropic Efficiency
1
1 Introduction
1.1 PACE Program
The Partners for the advancement of Collaborative Engineering Education (PACE) program provides
“hardware, software, training, automotive parts, industry projects, and much more to PACE Institutions
around the world”.[7] They accomplish this by connecting major sponsors including GM, EDS, HP,
Siemens PLM software and Sun Microsystems to support PACE institutes around the world.[7] The
University of Toronto is lucky enough to be included as one of these PACE institutes and was asked to
participate in the PACE global vehicle collaboration project. This is a project where many PACE institutes
from around the world collaborate to build a high performance race car.[7] This project was headed by
Brigham Young University in Provo Utah, who were responsible for overseeing the entire design process
for the PACE global vehicle collaboration project. The 2006-2007 PACE global vehicle collaboration
project resulted in the car seen in Figure 1. It was decided to continue this collaboration project for the
2007-2008 year and improve on the 2006-2007 car’s design. For the 2006-2007 PACE global vehicle the
University of Toronto was responsible for the turbocharger assembly and integration with the twin
boost system.[5] A great deal of work was completed but unfortunately the twin boost system was
never assembled and tested.
1.2 2007-2008 PACE global vehicle Outline
An email from Dr. Greg Jensen stated that the purpose of the PACE program is to “prepare
approximately 200 students (and 25 faculty) per year from 20 PACE institutions, located in 10 countries,
on 5 continents, speaking 7 different languages, for “involvement in” and “leadership of” a real-world
global design/engineering and collaboration experience”. The end result of the work completed by all
20 schools was almost a by-product of this collaboration effort.
2
This is not to say that what was created was not important. Dr. Jensen also pointed out that the scope
of this collaboration effort was to create a second iteration F-1 style car and high performance engine.
He stated that this work would be done by using the GM review of the 2006-2007 car to “drive
significant redesign and improvements”. As well as improving on the 2006-2007 car the 2007-2008 car
“will adhere strictly to the 2009 FIA formula 1 standard and should look more like current F-1 racecars”.
The University of Toronto was requested by Brigham Young University to build on the work completed
for the 2006-2007 PACE car’s engine boost system. For the 2006-2007 PACE car the boost system was
handled by one team at the University of Toronto. For the 2007-2008 PACE car, this team was split into
two with one team responsible for the turbocharger selection and the other team responsible for
turbocharger piping, control and integration with the supercharger. This report outlines the work
completed by the turbocharger selection team.
In his email Dr. Jenson stated that the deliverables requested by Brigham Young University at the
completion of this project were.
• Boost system project schedule
o Design review dates
o Assembly and test dates
• Collaboration Plan including how and when interface points would be resolved
• CAD 3D models and assemblies of all components
• Deflection and stress analysis of appropriate components
• Thermal analysis of appropriate components
• Flow analysis of appropriate components
• Motion analysis of appropriate components
• Fully dimensioned and toleranced drawings of all manufactured or modified components
3
• Fully assembled working boost system
1.3 University of Toronto PACE Turbocharger Team
Along with Jacob Dick as team leader responsible for the turbocharger team, three third year students
were assigned as members of the turbocharger team. These three students were
• Nick Berube
• Ahmed Al-Nimer
• Jacky Lau
These three students primary responsibility was to carry out the detailed tasks required for selecting
and integrating a turbocharger such as calculations, 3D CAD modeling and FEA or CFD analysis.
1.4 Collaborating Schools
Brigham Young University (BYU)
Brigham Young University’s area of responsibility was the overall project leader. All review meetings of
progress were held with Brigham Young University. Collaboration areas included project planning,
scope definition, task delegation and fund acquisition. As well Brigham Young University was
instrumental in facilitating communication between the University of Toronto and all other PACE
institutions. Kenneth Mix was the main contact between Brigham Young University and the University
of Toronto.
University of Texas El Paso (UTEP)
The University of Texas El Paso was responsible for all areas of the engine. As the turbocharger directly
related to the engine, great collaboration efforts were required with this University. Chance Garcia who
was the project leader at the University of Texas El Paso was the main contact person with the
4
University of Toronto. Several collaboration areas included engine characterization and power levels
when turbocharged.
McMaster University
McMaster University designed and built the dry sump oil system for the 2007-2008 PACE car.
Collaboration was required between McMaster University and the University of Toronto where the
turbocharger connected into the PACE car’s oil system for cooling. Rupinder Virk was the team leader at
McMaster University and the main contact with the University of Toronto. Collaboration with McMaster
University included oil system layouts and turbocharger oil connection points.
1.5 Collaboration Tools
Several tools were used to facilitate collaboration between the different PACE institutions. Meeting
between PACE institutions were primarily held using a Tandberg high definition video conference unit.
This allowed multiple people to participate in a meeting at the same time and view common
applications and presentations. The meeting host could send out both a video and audio feed of
themselves as well as a video feed of whatever application they were working on. This proved to be
very useful especially when meeting with large groups of people. Meetings were also held using phone,
Skype (internet phone) and instant messaging, although these methods proved to be far inferior to the
video conference unit. Meeting would take longs and less was understood between the parties if the
video conference unit was not used.
For sharing and organizing all the data and files created during the 2007-2008 PACE car project, Team
Center Community was used. This consisted of a web site where all data and files were uploaded to be
universally accessible by every PACE institution. Team Center Community was also used to organize
meeting, process funding requests and update team members on progress and announcements.
5
1.6 Initial Project Schedule
The first task requested by Brigham Young University was to create a schedule that would guide the
design, analysis and manufacturing of the Turbocharger and twin charger system. The date of February
13, 2008 had initially been set for when all components of the twin charger system were to be at the
University of Texas El Paso. With this February 13th
deadline a preliminary schedule Table 1 was
created. This schedule had seven key dates from when the project began in September of 2007 through
to the February 13, 2008 deadline. These dates and the progress desired included
October 25, 2007
By this point it had been planned to have completed researching turbochargers and turbo charging
systems. As well as performing a full review of the work completed for the 2006-2007 PACE car. This
would be done by collaborating with team members who worked on the 2006-2007 PACE car’s
turbocharger. With this information an appropriate turbocharger could be selected that provided the
performance desired. After selection of the turbocharger creation of 3D CAD models for layout and
analysis purposes would begin. This date was also set as a review with Brigham Young University to
update them on progress
November 8, 2007
Initially by this date it had been planned to have the modeling of all pertinent turbocharger components
completed. With these completed turbocharger models, concepting would begin for the physical layout
around the engine. This would be in conjunction and collaboration with the exhaust manifold, exhaust
pipe and oil line layout teams. It would also be determined if any sensors would be required around the
turbocharger and begin physical layout if required.
6
November 15, 2007
By this date it had been planned to have the physical location of the turbocharger set. This set location
of the turbocharger would be communicated to all concerned PACE institutions. As well it was planned
to begin FEA and CFD analysis on any component that required it by this date.
December 6, 2007
If any FEA or CFD were performed, the preliminary results would be presented by this date. After this
point less work would be completed because of final exams and the Christmas break. It was planned to
do as much work as possible over the break and reconvene in the New Year.
January 3, 2008
It was planned to present the final FEA and CFD analysis results by this date if possible. As well the oil
line layout should be completed along with the exhaust manifold and exhaust pipe interface points. If
any sensors were to be used their location would be set by this date.
January 31, 2008
With the initial schedule it had been planned to have all major components completed by this date to
present to Brigham Young University. This would include a fully modeled and purchased turbocharger
complete with oil lines. As well any FEA or CFD should be completed and presented to Brigham Young
University. All components would be shipped off close to this date to arrive at the University of Texas El
Paso by February 13, 2008.
1.7 Revised Project Schedule
As with many projects the initial schedule deadlines were not achieved. After the Christmas break the
University of Toronto had a meeting with Brigham Young University to reprioritize important
7
deliverables and to deprioritize unimportant ones. In a meeting on January 15, 2008 it was decided that
three tasks should take priority above all. These tasks were
• 3D CAD modeling of the turbocharger for layout purposes
o A date of January 21, 2008 was chosen as the desired completion date
• Layout 3D CAD model of turbocharger with engine assembly
o A date of February 1, 2008 was chosen as the desired completion date
• Selection, layout and modeling of oil lines for the turbocharger
o This would required collaboration with McMaster University and the dry sump system
o A date of February 1, 2008 was chosen as the desired completion date
As well it was decided that the other turbocharger deliverables should be deprioritized to after
completion of the above tasks. Because of this task such as FEA and CFD would only be attempted if
time allowed after the completion of the critical tasks.
These revised dates were further pushed back by the difficulty in obtaining the desired physical
turbocharger and delays in receiving engine models from GM for layout purposes.
1.8 Formula 1 FIA Guidelines
Because the 2007-2008 PACE car was to conform to the FIA Formula 1 guidelines as closely as possible
research was required to determine how this affected the turbocharger. Section 5.1.4 of the 2009 FIA
Formula 1 guideline states that “Supercharging is forbidden” [6], where in this case supercharging refers
to superchargers and turbocharger together. The guidelines also state that “all engines must have 8
cylinders arranged in a 90° ‘V’ configuration” [6]. It was decided with Brigham Young University that the
2007-2008 PACE car could deviate from the FIA Formula 1 standard in these two areas because the PACE
program was given a 4 cylinder GM Ecotec engine to use. The addition of a turbocharger and
supercharger would simulate the power produced by the high performance ‘V’ 8.
8
2 Turbocharger Calculations
Through collaboration with the University of Texas El Paso and Brigham Young University it was decided
that a maximum power output for the GM Ecotec engine in excess of 400 HP was desired. As well the
turbocharger would be used in conjunction with a supercharger to increase low rpm performance. To
select a turbocharger to fulfill these requirement calculation outlined below were used. “Boost
Requirements and Compressor Matching” written by Thomas Cooper for the 2006-2007 PACE program
was used as a guide for formulating this calculated approach. [4]
2.1 Internal combustion engine power characteristics
To characterise the power output from any internal combustion engine one property should be
examined. The brake specific fuel consumption (BSFC) is a quantity of an engine which is the mass rate
of fuel required for a given power output. The BSFC is a constant for a particular engine related to the
overall cycle efficiency. From [1] the BSFC can mathematically be defined as
Power
mBSFC
fuel&
=
1.a)
Rearranging this equation allows the power of any engine to be calculated if the mass flow rate of fuel
and BSFC are known.
BSFC
mPower
fuel&
=
1.b)
Usually it is not convenient to measure the mass flow rate of fuel into an engine, but rather the mass
flow rate of air. The mass flow rate of fuel and mass flow rate of air into an engine are related with the
air fuel ratio. From [3] it is defined as
9
fuel
air
m
mAFR
&
&=
1.c)
Rearranging for the mass flow rate of fuel and substituting into equation 1.b) yields
BSFCAFR
mPower air
•=
&
1.d)
It can be seen that the power output of any internal combustion engine is directly related to the amount
of air flowing through the engine. The mass flow rate of air for an internal combustion engine can
further be broken down into a function of the displace volume of the engine, the reciprocating speed of
the engine, the density of the air and the type of engine used. From [4] this relationship is
ρ•••= VEVn
rpmmair&
1.e)
The term n in the above equation is to account for the number of crank revolutions per power stroke. In
a 4 cycle engine, the engine must rotate through two full rotations before the exhaust gas is vented and
air is drawn in. In a 2 cycle engine air is drawn in every revolution. In general
=
=
)2(1
)4(2
cyclen
cyclen
As well volumetric efficiency (VE) is the amount of the engine volume that is changed every cycle.
Substituting equation 1.e) into 1.d) gives
10
BSFCAFR
VEVn
rpm
Power•
•••
=
ρ
1.f)
Finally assuming that the air drawn into the engine is an ideal gas the density can be determined by its
temperature, pressure and gas constant [2].
TR
P
air
=ρ
Substituting this last equation into equation 1.f) gives
n
rpm
T
P
BSFC
VEV
RAFRPower
air
•••
••
=1
1.g)
From this it can be seen that the power of any internal combustion engine is a function of chemical
properties of air and fuel, physical properties of the engine, the pressure and temperature of the intake
air and the engine speed. For an already existing engine the physical properties and maximum rpm
cannot be changed. As well with a given fuel the chemical properties cannot be changed. This leaves
just the temperature and pressure of the intake air to determine the maximum output power of the
engine.
2.2 Model of Turbocharged Engine
From the above calculations it can be seen that the power output for any engine can be maximized by
increasing the density of the intake air. This can be accomplished by either increasing the pressure,
decreasing the temperature or a combination of both. In Figure 2 a standard turbocharger intercooler
setup is shown. The process described by [5] is as follows
• Air enters the turbocharger compressor at state 1 with atmospheric conditions
• The air exits the compressor at state 2 at a higher pressure and temperature
11
• The air is then cooled as closely back to ambient temperature in a heat exchanger and exits at
state 3
• The pressurized and cooled air is fed into the intake of the engine
2.3 Compressor Maps
Figure 3 shows a typical turbocharger compressor map. This map characterises the performance of the
turbocharger’s compressor over a range of air mass flow rates and pressure ratios.[5] Most importantly
a compressor map gives the isentropic efficiency of the compression process for a given air mass flow
rate and pressure ratio.[5] To determine if a turbocharger is a good match for an engine or if it will be
able to provide a desired power output the compressor map must be consulted. Each load condition for
an engine will have a corresponding operating point on the compressor map. These operating points
need to be found to determine if they are in a useful region for a given turbocharger. Three main
regions can be found on a compressor map. These are the surge, operating and choke regions.[5] To
the left of the surge limit is the surge area. This is an area where the pressure ratio is too high to be
maintained with the low mass flow rate. The pressure ratio will fall to a level where it can be
maintained by the air mass flow rate.[3] To the right of the choke limit is the choke region. This is the
opposite of the surge region. Too much air is being forced through the compressor which will increase
the pressure ratio until equilibrium is reached.[3] In between the surge and choke limits is the operating
region. The turbocharger can provide the pressure ratio at a given air mass flow rate with varying
isentropic efficiencies. The higher the isentropic efficiency the closer the compression process is to an
ideal isentropic process.[2] With a higher isentropic efficiency less work is required for the turbocharger
and the temperature of the air at state 2 will be lower.[2] A higher isentropic efficiency is desired
because less energy is used to power the turbocharger and the density of the compressed air will be
increased because of the lower temperature. There is also a maximum speed that the turbocharger can
12
rotate. In order to prevent damage to the compressor and turbine the turbocharger needs to be limited
to below the maximum speed curve.[5]
2.4 Approach of Turbocharger Calculation
For sizing and selecting a turbocharger two properties are required. These are the mass flow rate of air
through the engine (and turbocharger) and the pressure ratio across the turbocharger compressor.[5]
The pressure ratio is the pressure at state 2 divided by the pressure at state 1. From the previous
calculations the mass flow rate of air is easily determined for a desired power output by rearranging
equation 1.d).
BSFCAFRPowermair ••=& 2.a)
To determine the pressure ratio across the turbocharger compressor required more derivations. It can
be noted that the temperature and pressure terms in equation 1.g) are the pressure and temperature at
state 3 in Figure 2. Thus solving for the desired pressure over temperature ratio at state 3 gives
airRAFRVEV
BSFCPower
rpm
n
T
P••
•••=
3
3 2.b)
This ratio can be calculated for a desired power output at a specific rpm. All other variables are set by
engine design and fuel chemistry. The next step is to formulate equations for both P3 and T3 as a
function of the pressure ratio across the turbocharger compressor where
1
2
P
PPratio = 2.c)
The equation for determining P3 is easily found. In an ideal case there would be no pressure loss across
the intercooler. As such the pressure at state 3 would be equal to the pressure at state 2.
Unfortunately this is not the case. Because of friction through the intercooler the pressure at state 3
will be less than the pressure at state 2 [5]. This pressure loss across the intercooler can either be
13
calculated with the already determined mass flow rate of air and diameter of the intercooler piping or
can be assumed to be a percentage of the pressure at state 2. [4] assumes the latter, and as such the
pressure at state 3 can be calculated by
)1(23
223
loss
loss
PPP
PPPP
∆−=
•∆−= 2.d)
Solving for P2 in equation 2.c) and substituting into equation 2.d) gives
)1(13 lossratio PPPP ∆−•= 2.e)
Next to determine the temperature at state 3 as a function of the pressure ratio requires working back
through the intercooler. The temperature drop across a heat exchanger (or intercooler) is a function of
the starting temperature and the temperature of the cooling air.[2] How close a heat exchanger cools
the working fluid to the surrounding fluid is defined as the heat exchanger effectiveness.[2] This is
mathematically defined using the states above and where Tamb is the ambient air temperature flowing
over the intercooler by [2] as
ambTT
TT
−
−=
2
32ε 2.f)
Rearranging equation 2.f) for T3 gives
ambTTT •+−= εε )1(23
2.g)
Next the temperature at state 2 can be determined by using the isentropic compression equation. An
isentropic compression process in one where there is no heat transfer to the surroundings and the
entropy of the working fluid is constant.[2] Although in an actual turbocharger there is heat transfer to
the surroundings through the compressor casing it will be neglected in this analysis. As well a
turbocharger compressor is not an isentropic device, entropy is gained during the compression process.
14
This will be taken into account with an isentropic efficiency. For an isentropic compression process from
state 1 to 2 the pressures and temperatures are related as follows from [2]
k
k
s
P
P
T
T1
1
2
1
2
−
= 2.h)
In the above equation the T2s denotes the isentropic temperature and the k term is the ratio of specific
heat capacities at constant pressure and volume of air [2].
4.1==
air
air
v
p
airC
Ck
Solving for T2s in equation 2.h) gives
k
k
sP
PTT
1
1
2
12
−
= 2.i)
Because as stated above the compression process in a turbocharger is not isentropic the isentropic
efficiency of the compressor is used to find the actual temperature at state 2. The definition of
isentropic compressor efficiency from [2] is
12
12
TT
TT
a
s
c−
−=η 2.j)
In this above equation T2a is the actual temperature at state 2 with the isentropic efficiency taken into
account. As well it should be noted that this isentropic efficiency equation assumes that the specific
heat capacity of air is constant with temperature. Although this is not the case it will be assumed for
these calculations. Rearranging equation 2.j) for the actual temperature at state 2 gives
15
1
12
2T
TTT
c
sa +
−=
η 2.k)
Substituting equation 2.i) into equation 2.k) yields
1
1
1
1
2
1
2T
TP
PT
Tc
k
k
a +
−
=
−
η
2.l)
Remembering equation 2.c) and substituting into this last equations results in
( )1
1
1
1
2T
TPTT
c
k
k
ratioa +
−=
−
η 2.m)
For the rest of the calculation T2a will be referred to as T2. Finally substituting this relation for T2 into
equation 2.g) gives
( )amb
c
k
k
ratio TTTPT
T •+−
+
−=
−
εεη
)1(1
1
1
1
3 2.n)
By dividing equation 2.e) with 2.n) and relating to equating 2.b) an expression for Pratio can be found
( )air
amb
c
k
k
ratio
lossratio RAFRVEV
BSFCPower
rpm
n
TTTPT
PPP
T
P••
•••=
•+−
+
−
∆−•=
−
εεη
)1(
)1(
1
1
1
1
1
3
3
2.o)
In this above equating the only term that is unknown is Pratio. All other terms are known or can be
approximated easily. All that needs to be done is to solve for Pratio. This cannot be done readily using
algebra because of the exponent terms that Pratio is raised to in the denominator. Instead an iterative
process such as Newton’s method or a sequential solver in Excel should be used. Initially the
compressor efficiency (ηc) needs to be estimated. After the pressure ratio is calculated and plotted with
16
the air mass flow rate on the compressor map the actual compressor efficiency can be found. A new
pressure ratio should be calculated if the compressor efficiency found is significantly different from the
initial guess.
With equations 2.a) and 2.o) the mass flow rate of air through the engine and turbocharger and the
pressure ratio across the turbocharger compressor can be found. These two equations can be used to
determine the pressure ratio and air mass flow rate required to develop a desired power output at a
given rpm for any engine.
17
3 Turbocharger Sizing
To size a turbocharger the engine characteristics need to be plotted onto a compressor map. This can
be done by plotting the values calculated from equation 2.a) and 2.o). Unfortunately all this will tell you
is if the turbocharger can provide enough pressure for the engine to produce the desired power. This
was the method used for selecting the turbocharger for the 2006-2007 PACE car. This does not tell you
the turbocharger performance over all engine speed. The turbocharger performance over all the
engine speeds can be found by creating constant speed lines on the compressor map.[5] Using
equations 2.a) and 2.o) for a range of rpms corresponding pressure ratio and air mass flow rate pairs
need to be calculated. The range of rpms used should be representative of your engine. For the case of
the 2007-2008 PACE car a GM Ecotec 2.2L engine was used. It was expected to red line at about 8000
rpm. As well a supercharger would be used at the low end of the rpm range to increase response. As
such air mass flow rate and pressure ratio pairs were calculated from 3000 rpm to 8000 rpm every 1000
rpms. This was done by substituting equation 2.a) into equation 2.o) and solving for the mass flow rate
of air.
( )
air
lossratio
amb
c
y
y
ratio
air RAFRVEV
BSFC
rpm
n
PPP
TTTPT
m •••
••∆−•
•+−
+
−
=
−
2
2
1
1
1
1
1
)1(
)1( εεη
& 2.p)
For each rpm selected, corresponding pairs of mass flow rates of air and pressure ratios were calculated.
Pressure ratios from 1.0 to 4.0 were used for sizing because 1.0 is the lowest possible and 4.0 was the
highest that most turbochargers examined could provide. The calculated air mass flow rates of air and
pressure ratios pairs for corresponding rpms for the GM Ecotec 2.2L engine are shown in Appendix A.
For these calculations gasoline was used as the fuel. New air mass flow rates and pressure ratio pairs
would need to be calculated if ethanol was used as the fuel.
18
These calculated values can then be plotted on any compressor map to see the turbocharger’s
performance over the engine rpm range. Many calculations for different sized turbochargers were
completed by the members of the turbocharger team. Appendix B shows the engine characteristics
plotted on several of these turbocharger compressor maps.
3.1 Interpretation of engine characteristics
By examining the compressor maps in Appendix B the engine characteristics can be seen for several
different sizes of turbocharger. The smallest turbocharger examined was the Garrett GT3571 and the
largest was the Garrett GT4088. By seeing where the different rpm lines intersect the surge and choke
limits the maximum power for each rpm can be found.
3.1.1 Garrett GT3571
By looking at where the 3000 rpm line intersects the surge limit it can be seen that this turbocharger
could already provide a maximum pressure ratio of about 2.25. As stated above a supercharger was
used to provide boost at the low end of the engine rpm range. In collaboration with Brigham Young
University it was decided that the supercharger would provide a pressure ratio of around 2.0 until it was
shut off. If used in conjunction with this turbocharger the supercharger could be shut off before 3000
rpm. Following the rpm lines to the right it can be seen that a maximum pressure ratio of about 3.1
occurs between 4000 and 5000 rpm. The calculated maximum power output from Table 2 and Table 3
using this turbocharger is 321 HP at 8000 rpm and a maximum torque of 283 ft•lbf between 4000 and
5000 rpm is produced. This turbocharger is a good fit for the PACE car’s engine. It provides ample
pressure at low rpms and the rpm lines are distributed over the entire operating range of the
19
compressor. Unfortunately the maximum power output is too low. A value above 400 HP was desired.
As such this was not a match for our application.
3.1.2 Garrett GT3782
This turbocharger is a litter larger than the GT3571 and as such provides less pressure ratio at lower
rpms. The supercharger would have to operate for more of the lower rpms. From Appendix B the
GT3782 reaches a pressure ratio of 2.0 at around 4000 rpm. The supercharger would have to operate
until this point. Increasing the engine speed results in a maximum power output of 432 HP at 8000 rpm
and a maximum torque output of 314 ft•lbf between 5000 and 6000 rpm. This turboharger provides
more power and more torque over almost the entire rpm range. This appears to be a good match for
the 2007-2008 PACE car. The maximum power output was above 400 HP and the supercharger could be
shut off above 4000 rpm. One drawback was that to achieve the higher pressure ratios the engine rpms
did not fit as well onto the compressor’s operating range. More of the boost at lower rpms needs to be
handled by the supercharger and the full operating range of the turbocharger is not used.
3.1.3 Garrett GT4082
Increasing the turbocharger size even more results in even higher maximum power output. From Table
2 and Table 3 the maximum power produced is 455 HP at 8000 rpm and the maximum torque is 367
ft•lbf at 6000 rpm. The main drawback was that this turbocharger is not be able to provide a pressure
ratio of 2.0 until 4000 rpm and does not produce considerable boost until over 6000 rpm. This would
result in poor performance at lower rpm. Even though this turboharger can provide the power desired,
the low end rpm performance leaves more to be desired.
20
3.1.4 Garrett GT4088
Finally the largest turbocharger examined produces the most power as expected. 514 HP is produced at
8000 rpm and 337 ft•lbf of torque is produced between 7000 and 8000 rpm. This shows the major
weakness with using an oversized turbocharger to achieve high power outputs. Maximum torque is not
produced until very high rpms. This is not ideal as high torque is desired at lower rpms right after a gear
change. Even through this turbocharger provides the highest power output it does not appear to be
suitable to this application because of the poor low rpm performance.
3.2 Selected Turbocharger
Out of the top four turbochargers discussed and all turbochargers examined the GT3782 was selected.
This was because it provided a good amount of power at high rpm but also had high torque at low rpms
and through the entire range. The smaller GT3571 did not provide enough power and the larger GT4082
and GT4088 would require the supercharger to operate for too much of the rpm range to keep torque
output to acceptable levels. As well because a standard turbocharger was selected and ordered,
engineering drawings were not required for the turbocharger.
For the 2006-2007 PACE car both the Garrett GT3782 and GT4802 were recommended by Thomas
Cooper. This was based solely on a one point analysis unlike the full engine rpm analysis preformed for
the 2007-2008 PACE car. When asked which turbocharger was purchased the University of Toronto was
told that it was the Garrett GT3782. This was ideal as it was the turbocharger selected through the
more thorough process. Unfortunately when the turbocharger was shipped to the University of Toronto
for 3D CAD modeling and further analysis it was discovered that in fact the Garrett GT4082 had been
purchased. The correct turbocharger was ordered from a supplier in Toronto but at the time of this
21
report it has not yet been received. It was decided to create parametric 3D CAD models with the
available Garrett GT4082 for overall dimension that could be easily changed when the Garrett GT3782
was acquired.
22
4 3D CAD Model of Turbocharger Using Unigraphics NX 4.0 3D CAD models of the turbine, compressor and bearing casings were created.
These three components were assigned to the three team members on the University of Toronto
turbocharger team. The created 3D CAD models can be seen if Figure 4. The internal components of
the turbocharger including the compressor, turbine, bearings and shaft were not modeled at this time
because they were not critical to the physical space layout of the turbocharger. Also disassembling the
turbocharger would be required to accurately measure the internal components. This could damage the
turbocharger and would have proved difficult to reassemble.
23
5 Layout of Turbocharger With the created 3D CAD models and a supplied 3D model of a GM Ecotec engine three initial concepts
were created for locations of the turbocharger. These layouts can be seen in Figure 5, Figure 6 and
Figure 7. The GM engine model was replaced with a block model due to confidentiality concerns. These
three concepts were created in collaboration with the turbocharger piping team headed by Ryan
Udugampola.
The first concept consists of a straight exhaust manifold with the turbocharger mounted as close to the
engine as possible. Advantages of this concept include a low pressure drop through the exhaust
manifold and relative ease of manufacturing when compared to the other concepts. A short exhaust
manifold is desired because it restricts the exhaust follow the least before it enters the turbine of the
turbocharger. A disadvantage to this concept is that the turbocharger may be mounted to high up on
the engine and interfere with the body of the car. Because at the time of this layout the body of the car
had not been finalized caution had to be used.
The second concept created had the exhaust manifold bent 90° down onto the turbocharger. This
allowed the turbocharger to be mounted lower down away for the body work of the car but still allows
the exhaust manifold to be relatively short. Although this concept is not complicated it would be harder
to make than the first concept created and would cause a larger pressure drop of the exhaust gas. This
concept could also make installing the turbocharger more difficult because it would have to be
positioned from the bottom of the car instead of from the side. Brigham Young University had stated
that the area around the engine where the turbocharger is placed should not have space constrains with
other part. Because of this, installation was not thought to be a large concern.
The final concept had the turbocharger mounted from the top onto a U bent exhaust manifold. This
concept would allow for the easiest installation of the turbocharger but at the price of the largest
24
pressure drop of the exhaust gas and the most complicated exhaust manifold of all three concepts. Like
with the first concept the turbocharger may be mounted too high up to not interfere with the body of
the car.
These three concepts were presented to Brigham Young University on February 12, 2008. The layout of
the turbocharger had been delayed from the revised schedule because of problems opening and
manipulating the engine model supplied by GM. It was decided at this meeting that the second concept
fulfilled the criteria best with the fewest drawbacks. With this decided an accurate layout of the
turbocharger could be created. Figure 8 shows the hard point locations created for an exhaust manifold
that would be designed by IPN University. This layout accommodates the turbocharger with ample
clearances to adjacent parts as well as allowing ample room for the exhaust manifold pipes.
25
6 Oil Line Routing Working in collaboration with McMaster University the oil line routing to and from the turbocharger was
decided. Oil is required to lubricate and cool the bearings in the turbocharger [5]. Without adequate
cooling the turbocharger would quickly overheat and stop functioning. Two concepts were discussed
with Rupinder Virk the team leader at McMaster University. The first concept involved plumbing the
turbocharger in line with the main oil loop of the car. This solution had several advantages most notably
the simplicity. As well this would not require many extra parts keeping the cost down. A disadvantage
to this solution was that the turbocharger would have to use the same oil as the engine. Although this
should not have been a problem the option of keeping the two systems separate was appealing. At the
suggestion of Rupinder Virk a separate oil loop for the turbocharger was developed. An oil line
schematic for the 2007-2008 PACE car can be seen in Figure 9. The oil pump selected by McMaster
University was capable of supporting multiple pump modules. This allowed the turbocharger to have a
dedicated oil pump and oil system at little extra cost. This system also would allow the flow rate and
pressure for the turbocharger to be adjusted for optimum lubrication and cooling.
Because of these advantages with little extra cost a separate oil system was chosen for the
turbocharger.
26
7 Engine Test Stand To aid with concepting when creating the turbocharger layout, a scrap GM Ecotec engine was purchased
and mounted. This would allow the turbocharger and turbocharger piping team to have a physical area
in which to work. This would complement the work done on 3D CAD and ensure that any errors were
caught with a full system assembly before it was shipped to the University of Texas El Paso. A picture of
the engine test stand can be seen in Figure 10.
27
8 Work to be completed
At the time of this report the 2007-2008 PACE collaboration vehicle project is still ongoing. The Garrett
GT3782 turbocharger was ordered but has not arrived at the University of Toronto to date. When the
turbocharger is acquired work that will be completed includes
• Update the current 3D CAD models for the dimensions of the Garrett GT3782
• Verify the turbocharger 3D CAD layout with the updated model
• Test fitting the turbocharger on the engine test stand to verify 3D CAD models and integration
with turbocharger piping
Although it is not known exactly at this time when the turbocharger will arrive at the University of
Toronto it is hoped that this scheduled work will be completed by the end of March 2008. This would
allow time for the turbocharger piping team to test fit all the system components before sending the
entire assembly to the University of Texas El Paso.
28
9 Tables and Figures
Figure 1: 2006-2007 PACE Car
Figure 2: Turbocharger and Intercooler diagram
Intercooler 3
1
2
Tamb
Compressor Engine
29
Figure 3: Sample Compressor Map
Surge Limit
Choke Limit
Max speed
30
Figure 4: 3D CAD Model of Garrett GT4082
31
Figure 5: Turbocharger Position Concept 1
32
Figure 6: Turbocharger Position Concept 2
33
Figure 7: Turbocharger Position Concept 3
34
Figure 8: Exhaust Manifold Interface
35
Figure 9: 2007-2008 PACE Car Oil Schematic
36
Figure 10: Engine Test Stand
37
Oct 25/2007
Turbo sizing/Validate of last year’s selection complete and review
-Select turbo such that power requirements are met
-Begin modeling components and physical locating of turbo
Nov 8/2007
Major turbo component modeling complete and review
-Continue to physically layout turbo location
-Begin layout of oil lines, exhaust manifold connection, exhaust pipe
connection, sensor connections
Nov 15/2007
Turbo physical location set and review
Begin FEA and CFD of turbo components
Dec 6/2007
Present preliminary FEA/CFD results
Jan 3/2007
FEA/CFD analysis complete (if possible) and review
Oil line layout, exhaust manifold connection and exhaust pipe connection,
sensor connections completed
Jan 3/2007
Begin prototyping and engineering drawings (if required) and begin to order
parts (if required)
Jan 31/2007
Present turbocharger to BYU et all
Send turbocharger to UTEP. All design and analysis complete
All design and analysis complete (if possible)
Feb 13/2007
Turbo at UTEP deadline
GANTT CHART
Task
Sep Oct Nov Dec Jan Feb March April May
Preliminary
Design/System
outline
CAD model Creation
Physical layout
FEA/CFD
Engineering
Drawings
Prototyping
Purchasing/Manufac
turing
Testing
Assembly
Table 1: Initial Project Schedule
38
rpm 3000 4000 5000 6000 7000 8000
GT3571 134 216 270 297 314 321
GT3782 86 148 299 359 399 432
GT4082 60 148 224 420 450 455
GT4088 60 131 232 337 450 514
Table 2: Engine Horse Power (HP)
rpm 3000 4000 5000 6000 7000 8000
GT3571 214 283 283 259 235 210
GT3782 150 193 314 314 299 283
GT4082 105 193 235 367 337 299
GT4088 105 172 243 295 337 337
Table 3: Engine Torque (ft•lbf)
39
Appendix A: Air mass flow rates (Kg/s) for GM Ecotec 2.2L (Gasoline)
Pratio rpm 3000 4000 5000 6000 7000 8000
4.0 24.68 32.91 41.13 49.36 57.58 65.81
3.5 22.01 29.34 36.68 44.02 51.35 58.69
3.0 19.27 25.70 32.12 38.55 44.97 51.40
2.5 16.47 21.95 27.44 32.93 38.42 43.91
2.0 13.57 18.09 22.61 27.13 31.65 36.18
1.5 10.55 14.07 17.59 21.11 24.62 28.14
1.0 7.39 9.85 12.31 14.77 17.23 19.69
40
Appendix B: Compressor Maps
Garrett GT3571
Image from http://www.turbobygarrett.com/turbobygarrett/catelog/Turbochargers/GT35/GT3571_731413_1.htm
8000
7000
6000
5000
4000
3000
41
Garrett GT3782
Image from http://www.turbobygarrett.com/turbobygarrett/catelog/Turbochargers/GT37/GT3782_452159_3.htm
8000
7000
6000
5000
4000
3000
Garrett GT4082
Image from http://www.turbobygarrett.com/turbobygarrett/catelog/Turbochargers/GT40/GT4082_452232_5.htm
42
rbobygarrett/catelog/Turbochargers/GT40/GT4082_452232_5.htm
8000
7000
6000
5000
4000
3000
43
Garrett GT4088
Image from http://www.turbobygarrett.com/turbobygarrett/catelog/Turbochargers/GT40/GT4088_703457_2.htm
8000
7000
6000
5000
4000
3000
44
Cited Material
[1] “Brake Specific fuel consumption”, Wikipedia, [Online] Sep. 2007, [2007 Nov 13], Available at HTTP:
http://en.wikipedia.org/wiki/Brake_specific_fuel_consumption
[2] Y.A. Çengel, M.A. Boles, Thermodynamics an Engineering Approach, New York: McGraw-Hill, 2002.
[3] B. Challen, R. Baranescu, Eds. Diesel Engine Reference Book 2nd Edition, Oxford: Butterworth
Heinemann, 1999.
[4] T. Cooper, Boost Requirements and Compressor Matching, PACE, 2006.
[5] T. Cooper. PACE lecture, Topic: “Compressor Maps” MB123, Oct. 11, 2007.
[6] FIA, 2009 Formula One Technical Regulations, FIA, 2006.
[7] PACE, [Online] 2005, [2008 March 15], Available at HTTP: http://www.pacepartners.org/index.html