2007-2008 pace collaboration vehicle: … pace collaboration vehicle: turbocharger selection jacob...

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 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.


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.


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


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


33


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


8000

7000

6000

5000

4000

3000

Garrett GT4082


42

rbobygarrett/catelog/Turbochargers/GT40/GT4082_452232_5.htm

8000

7000

6000

5000

4000

3000

43

Garrett GT4088


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

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