Maximum Net-power Point Tracking
of a waste heat recovery system
ALEXANDER CHABO
PETER TYSK
Master’s Degree Project
Stockholm, Sweden 2015
MMK 2015:76 MDA 499
Examensarbete MMK 2015:76 MDA 499
Sökning av maximal nettoeffekt
i ett spillvärmeåtervinning-system
Alexander Chabo
Peter Tysk
Godkänt
Examinator
Handledare
2015-10-17
Martin Grimheden
Bengt Ericsson
Uppdragsgivare
Kontaktperson
Scania
Jan Dellrud
Sammanfattning
Av den frigjorda energin för en lastbils bränsle är omkring 30% i form av
spillvärme i avgassystemet. Med implementation av ett spillvärmeåtervinningsystem går det att återvinna en del av den frigjorda energin i form av elektricitet
till lastbilens elsystem. Två termoelektriska generatorer använder avgaserna som
värmekälla och ett kylmedel som kall källa för att åstakomma en temperaturdifferans i generatorerna. Med hjälp av Seebeck-effekten går det att omvandla
temperaturdifferansen till elektricitet och på så sätt avlastas motorns generator
vilket medför en lägre bränsleförbrukning.
Detta examensarbete innefattar utvecklandet av en funktion som maximerar
nettoeffekten utvunnen från systemet. Funktionen som utvecklats är döpt till
Maximum Net-power Point Tracking (MNPT) och har som uppgift att beräkna
referensvärden som styrningen av systemet skall uppnå för att få ut maximal
nettoeffekt.
En simuleringmiljö i Matlab/Simulink är uppbyggd för att kunna implementera en kontrollstrategi för styrningen av kylmedlet samt avgasledning via
bypass-ventiler.
Systemet har blivit implementerat i en motorstyrenhet på en testrack som
kommunicerar via CAN där givare så som temperatur och tryck avläses. Systemet har ej blivit implementerat på lastbilen då samtliga fysiska komponenter
ej blev färdigställda under examensarbetets gång.
En fallstudie genomfördes i simuleringsmiljön och resultaten visade att användningen av en MNPT-funktion tillät upp till 300% ökning av den återinförda
nettoeffekten till lastbilens elsystem jämfört med utan användning av kontrollalgoritmer, och upp till 50% ökning jämfört med statiska referensvärden.
v
Master of Science Thesis MMK 2015:76 MDA 499
Maximum Net-power Point Tracking
of a waste heat recovery system
Alexander Chabo
Peter Tysk
Approved
Examiner
Supervisor
2015-10-17
Martin Grimheden
Bengt Ericsson
Commissioner
Contact person
Scania
Jan Dellrud
Abstract
About 30% of the released energy of a truck’s fuel is waste heat in the exhaust
system. It is possible to recover some of the energy with a waste heat recovery
system that generates electricity from a temperature difference by utilising the
Seebeck-effect. Two thermoelectric generators are implemented on a truck and
utilises the exhaust gas as a heat source and the coolant fluid as a cold source
to accomplish a temperature difference in the generators. The electricity is
reintroduced to the truck’s electrical system and thus reducing the load on the
electrical generator in the engine which results in lower fuel consumption.
This thesis includes the construction of a function that maximises the netpower derived from the system. The function developed is named Maximum Net
Power Point Tracking (MNPT) and has the task of calculating reference values
that the controllers of the system must achieve in order to obtain maximum
net-power.
A simulation environment has been developed in Matlab/Simulink in order
to design a control strategy to three valves and one pump.
The system has been implemented on a engine control unit that has been
mounted on a test rack. The engine control unit communicates through CAN to
connected devices. The system has not been implemented on the truck due that
all the physical components were not completed during the time of the thesis.
A case study has been conducted and the results proves that the use of an
MNPT-function allows up to 300% increase in regenerated net power into the
trucks electrical system compared with no control algorithms, and up to 50%
compared with static reference values.
vi
Contents
Sammanfattning
v
Abstract
vi
Contents
viii
Acknowledgement
ix
List of Figures
xi
List of Tables
xii
1 Introduction
1.1 Background . . . . . . . . . . . . . . .
1.1.1 Waste heat recovery . . . . . .
1.1.2 Thermoelectric generator . . .
1.1.3 TEG-demonstrator project and
1.2 Problem definition . . . . . . . . . . .
1.3 Objectives . . . . . . . . . . . . . . . .
1.4 Overview of the report . . . . . . . . .
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2 Litterature study
2.1 Business intelligence . . . . . . . . . . . . . . . . . . . . . . . . .
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3 System layout
3.1 Schematic layout of exhaust
3.2 TEG heat exchanger design
3.2.1 ATS-TEG . . . . . .
3.2.2 EGR-TEG . . . . .
3.3 Schematic layout of system
3.3.1 Exhaust gas flow . .
3.3.2 Coolant fluid flow .
3.4 Sensors . . . . . . . . . . .
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sources
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4 Modeling
4.1 Heat . . . . . . . . . . . . . .
4.1.1 The effectiveness-NTU
4.1.2 Radiator system . . .
4.1.3 TEG - Steady state .
4.1.4 TEG - Dynamic . . .
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stakeholders .
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vii
4.2
4.1.5
4.1.6
Fluid
4.2.1
4.2.2
4.2.3
4.2.4
4.2.5
4.2.6
4.2.7
Thermoelectric module . . . . . . . .
Thermal resistance . . . . . . . . . . .
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Flow divison - Exhaust gas . . . . . .
Differential equations . . . . . . . . .
Pressure drop and fluid resistance over
Pressure drop and fluid resistance over
Pressure drop and fluid resistance over
Flow division - Coolant fluid . . . . .
Three-way valve . . . . . . . . . . . .
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ATS-TEG . . . .
EGR-TEG . . .
EG bypass valve
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5 Simulation
48
5.1 Fluid properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.2 Dynamic model of TEG-system . . . . . . . . . . . . . . . . . . . 50
6 Maximum Net-power Point Tracking
6.1 Optimisation dependencies . . . . .
6.1.1 ATS-TEG . . . . . . . . . . .
6.1.2 EGR-TEG . . . . . . . . . .
6.2 Combined optimisation function . .
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7 Control
7.1 Control strategy EG mass flow . . . .
7.1.1 ATS-TEG bypass control . . .
7.1.2 EGR-TEG bypass control . . .
7.2 Control strategy CF mass flow . . . .
7.3 Control strategy CF mass flow division
7.4 Safety restraints . . . . . . . . . . . .
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8 Case study
8.1 Inputs . . . . . . . . . .
8.2 Results . . . . . . . . . .
8.2.1 Net-power . . . .
8.2.2 Power gains . . .
8.2.3 Power losses . . .
8.2.4 Extracted energy
8.3 Discussion . . . . . . . .
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9 Closure
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9.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
9.2 Conclusions and recommendations . . . . . . . . . . . . . . . . . 78
9.3 Future studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
10 References
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Appendices
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A Steady State Result
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B Approach 3 unscaled figures from case study
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viii
Acknowledgement
This master thesis has been conducted at the department Systems Predevelopment department (REP) at Scania in Södertälje, Sweden, during the
period February 2014 to July 2014.
The project supervisor is Jan Dellrud at Scania and Bengt Ericsson at the Royal
Institute of Technology in Stockholm, Sweden.
Grateful thanks to Jan Dellrud who proposed and applied for an patent application of the MNPT-function developed during the thesis.
Alexander Chabo and Peter Tysk
Stockholm, July 2014
ix
List of Figures
1.1
1.2
1.3
1.4
Input power and losses . . . . . . . . . . . . . . . . . . . . . . .
Two dissimilar metals with junctions at different temperatures
TEP1-1264-3-4 module (Thermonamic 2015) . . . . . . . . . .
Principal construction of a TEM (Jahanbakhsh 2012) . . . . .
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2
3
3
4
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
Schematic layout of exhaust sources (Svensson 2014) . . . . . . .
ATS-TEG together with the ATS and ATS Bypass valve . . . . .
One layer with eight TEMs in the ATS-TEG . . . . . . . . . . .
Countercurrent cross-flow arrangement . . . . . . . . . . . . . . .
EGR-TEG together with the EGR valve and the EGR bypass . .
Schematic of the WHR-system . . . . . . . . . . . . . . . . . . .
Schematic of the EG flow . . . . . . . . . . . . . . . . . . . . . .
Schematic of the CF flow . . . . . . . . . . . . . . . . . . . . . .
Schematic of WHR-system with required and redundant sensors .
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15
16
4.1
4.2
4.3
4.4
4.5
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4.14
4.15
4.16
Cross-flow heat exchanger with fluids unmixed . . . . . . . . . .
Schematic of radiator system . . . . . . . . . . . . . . . . . . . .
Thermal resistance model of the heat exchanger . . . . . . . . . .
One element/lump in the lumped capacitance TEG model . . . .
The chart for output voltage and output power Vs output current
under TT EM ,h = 330 ◦C and TT EM ,c = 30 ◦C . . . . . . . . . . .
Visual of rectangular straight fins (Karri 2005) . . . . . . . . . .
Visual of offset straight fins (Karri 2005) . . . . . . . . . . . . . .
Electric analogy of EG flow division . . . . . . . . . . . . . . . .
Equivalent pressure drop over each TEG and EG bypass valve . .
Offset fin layout ATS-TEG . . . . . . . . . . . . . . . . . . . . .
Orifice Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Side view of butterfly throttle bypass valve (Carlsson 2007) . . .
Normalized area as function of the throttle plate angle whith
shaft and no shaft (Carlsson 2007). . . . . . . . . . . . . . . . . .
Schematic of coolant fluid lumped system . . . . . . . . . . . . .
Simplified schematic of the coolant fluid lumped system . . . . .
Flow division three way valve . . . . . . . . . . . . . . . . . . . .
5.1
5.2
5.3
EG Temperature between 0 and 6000 [K] . . . . . . . . . . . . .
CF Temperature between 0 and 100 [◦C] . . . . . . . . . . . . . .
Dynamic model of a TEG divided in 8 lumps . . . . . . . . . . .
49
49
50
6.1
6.2
ATS-TEG power of EG and CF flow . . . . . . . . . . . . . . . .
Power consumption of CF pump as function of CF mass flow . .
53
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4.6
4.7
4.8
4.9
4.10
4.11
4.12
4.13
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6.3
6.4
6.5
6.6
Extra fuel consumption in "%" due to CAC temperature increase
by ATS-TEG . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
EGR-TEG power of EG and CF flow . . . . . . . . . . . . . . . .
Extra fuel consumption due to CAC temperature increase by
EGR-TEG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The span to search for the best reference values was changeable
and dependent on previous reference values to reduce computational time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
55
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59
7.1
Closed loop poles as a function of closing the valve . . . . . . . .
62
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
8.9
8.10
8.11
8.12
8.13
8.14
8.15
CF mass flow reference . . . . . . . . . . . . .
Percentage of the total CF mass flow diverted
EG mass flow through ATS-TEG reference .
Net-power with approach 1 . . . . . . . . . .
Net-power with approach 2 . . . . . . . . . .
Net-power with approach 3 . . . . . . . . . .
Power gains with approach 1 . . . . . . . . .
Power gains with approach 2 . . . . . . . . .
Power gains with approach 3 . . . . . . . . .
Power losses with approach 1 . . . . . . . . .
Power losses with approach 2 . . . . . . . . .
Power losses with approach 3 . . . . . . . . .
Extracted energy with approach 1 . . . . . .
Extracted energy with approach 2 . . . . . .
Extracted energy with approach 3 . . . . . .
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to the ATS-TEG
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B.1
B.2
B.3
B.4
Net power approach 3 from case study .
Power gains approach 3 from case study
Power losses approach 3 from case study
kWH approach 3 from case study . . . .
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xi
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List of Tables
5.1
Wighted factors for composition of exhaust gas . . . . . . . . . .
48
6.1
6.2
Input signals of MNPT-function . . . . . . . . . . . . . . . . . .
Output signals of MNPT-function . . . . . . . . . . . . . . . . .
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8.1
8.2
8.3
8.4
Input data for the case study
Recommended CF mass flow
Approach 2 reference values .
Approach 3 reference values .
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A.1 Long Haulage Cycle . . . . . . . . . . . . . . . . . . . . . . . . .
A.2 Steady state power with MNPT . . . . . . . . . . . . . . . . . . .
85
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xii
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List of abrevations
WHR
MNPT
TEG
TEM
DC
CAC
ECU
EMS
CAC
EGR
NOX
ATS
EG
CF
RAD
NTU
LMTD
RPM
MPP
Waste Heat Recovery
Maximum Net-power Point Tracking
ThermoElectric Generator
ThermoElectric Module
Direct Current
Charged Air Cooler
Engine Control Unit
Engine Management System
Controller Area Network
Exhaust Gas Recirculation
Nitrogen Oxide
After Treatment System
Exhaust Gas
Coolant Fluid
Radiator
Number of Transfer Units
Log Mean Temperature Difference
Revolutions per minute
Maximum Power Point
xiii
1 | Introduction
1.1
Background
One of Scanias strongest driving forces in product development is to reduce the
fuel consumption of trucks and buses to improve the operational economy and
reduce the environmental impacts. All the main components in a vehicles system needs to be utilised optimally for an acceptable overall efficiency. About
30% of the released energy of a trucks fuel is waste heat in the exhaust system (Jahanbakhsh 2012). It is possible to recover some of the energy with a
waste heat recovery (WHR) system that generates electricity from a temperature difference by utilising the Seebeck-effect. Two thermoelectric generators
where implemented in a truck and utilises the exhaust gas as a heat source and
the coolant fluid as a cold source to accomplish a temperature difference in the
generators. The electricity is reintroduced to the truck’s electrical system and
thus reducing the load on the electrical generator in the engine which results in
a decreased fuel consumption.
The thesis has been performed at the Systems Pre-development department
(REP) at Scania in Södertälje, Sweden. The thesis includes the construction of
a function that maximises the net-power derived from the system. The developed function is named Maximum Net-power Point Tracking (MNPT) and has
the task of calculating reference values that the controllers of the system must
achieve in order to obtain maximum net-power.
1.1.1
Waste heat recovery
Waste heat is non utilised heat which is generated in a process through fuel
combustion or chemical reaction, and then "dumped" into the environment
even though it could still be reused for useful and economic purpose.
The efficiency of Scania Euro 6 engines designed for the R-series heavy-duty
truck are currently reaching approximately 40%. This is considered rather high
in the industry but it can not be neglected that 60% of the energy is wasted
(Jahanbakhsh 2012). 30% of the input power is wasted in exhaust gases as can
be seen in figure 1.1 and is hence a potential for a WHR-system. The objective
of a WHR-system is to harvest this waste heat and turn it into usefully energy.
1
Figure 1.1: Input power and losses
1.1.2
Thermoelectric generator
There exists several methods to harvest energy and the method being utilised
in this project is with the aid of a thermoelectric generator (TEG). A TEG is a
solid state device that converts heat potential directly into electrical energy by
the thermoelectric effect called the Seebeck-effect. One great advantage with a
TEG is that it lacks any moving parts, which means that it requires low maintenance work and deliver high robustness. The efficiency is currently no more
than 5% with the thermoelectric materials that are commercial available. The
technology is promising where there has been thermoelectric materials developed with efficiencies up to 20% in laboratory environment (Crane and Jackson
2004).
The TEG properties was discovered in 1821 by the physicist Johann Seebeck
when two dissimilar metals with junctions at different temperatures was formed
seen in figure 1.2. The temperature difference ∆T = Th − Tc at the junctions
makes a current flow in the circuit and give rise to an open circuit voltage Uo
(Crane and Jackson 2004).
2
Figure 1.2: Two dissimilar metals with junctions at different temperatures
The phenomenon is described by the Seebeck coefficient α (1.1).
Uo
.
(1.1)
∆T
The Seebeck coefficient describes how many volts every Kelvin of temperature difference can generate when the junctions of two dissimilar materials are
held at different temperatures. Different materials have different α and the
higher α, the more voltage Uo is generated at a certain ∆T .
α=
Thermoelectric module
A thermoelectric module (TEM) can be seen as a TEG that generates a direct
current (DC) when there is a temperature difference ∆TT EM across the TEM
surfaces. The TEMs used in the TEG-project is of the model TEP1-1264-3-4
seen in figure 1.3 and is made out of the material Bismuth Telluride (Thermonamic 2015). The TEMs can work continuously up to 330 ◦C and intermittently
up to 400 ◦C and is manufactured by the company Thermonamic and is used
for converting a heat source directly into electricity.
Figure 1.3: TEP1-1264-3-4 module (Thermonamic 2015)
Commercial TEMs maximise the Seebeck-effect by providing a grid of nand p-doped semiconductor materials that are electrically connected in series
(Jahanbakhsh 2012) as can be seen in figure 1.4. This is done in order to
3
achieve maximum exposure to thermal sources and to achieve maximum output
voltage. TEMs can as a result generate usable voltage output from even the
modest temperature differentials.
Figure 1.4: Principal construction of a TEM (Jahanbakhsh 2012)
4
1.1.3
TEG-demonstrator project and stakeholders
The TEG-demonstrator project is launched by Scania and aims to demonstrate
the potentials of thermoelectric technology on heavy-duty vehicles and to document how such a system would be best implemented.
The project includes cooperation between Scania with the overall responsibility, leadership and installation of the WHR-system. TitanX and Eberspächer
Exhaust Technology with the responsibility of the design and production of the
TEGs. Swerea IVF with the responsibility of give a better understanding of
the TEMs used in the TEGs and what can be expected from future advances in
thermoelectric technology. The later is important for indicating when to start
implementing the system in commercially available trucks. KTH provides the
design of the DC-DC converter.
The project is partly funded by the Swedish Department of Energy with the
aim of generating 1 kW of electricity for a long haulage truck driving at 85 km/h
at 75% relative load.
1.2
Problem definition
Develop a control strategy for two electrically actuated bypass valves that operates the exhaust gas into two separate TEGs with the condition that the exhaust
gas do not overheat and damage the TEGs.
The power losses due the back pressure in the exhaust system needs to be
controlled in order to maximise the net-power derived from the WHR-system.
Control of a electrically actuated coolant fluid pump and a three way valve
for directing the coolant fluid flow between the two TEGs. High coolant fluid
mass flow increases the temperature difference in the TEGs and results in higher
power output but also draws more power from the electrical system due to an
higher effect is required from the coolant pump.
The coolant fluid mass flow and temperature after the passing of the TEGs
also affects the fuel consumption of the vehicle, since it influences the charged
air cooler (CAC) fluid temperature in the radiator system. An increase in
temperature of the CAC fluid results in increased fuel consumption which is
correlated to the mass flow and temperature of the coolant fluid and CAC fluid.
The complete control strategy considers all dependencies between the system
components and continuously strive to maximise the net-power being derived
from the WHR-system. This is achieved with the developed MNPT-function
which has the task to calculate reference values that the controllers in the system
must achieve in order to obtain maximum net-power.
The control algorithms being developed is going to be auto converted from
Matlab and Simulink code into C-code in order to be implemented on the vehicles engine control unit (ECU).
5
1.3
Objectives
• Create a simulation environment of the WHR-system in Simulink. Model
composition shall include:
– ATS-TEG
– EGR-TEG
– Exhaust gas - Two pipe branches
– Coolant fluid - Radiator system
– Coolant fluid - Coolant pump system
– Coolant fluid - Three way valve
• MNPT-function at run time that calculates reference values
– Case study of presumed positive effect of MNPT-function
• Design of control actuators:
– Exhaust gas - ATS-TEG Bypass valve
– Exhaust gas - EGR-TEG Bypass valve
– Coolant fluid - Pump
– Coolant fluid - Flow division
• Auto generate C-code of MNPT-function and the controllers to be implemented into an ECU.
The algorithms is not going to be tested in an physical truck during the
thesis since the components of the WHR-system has yet to be installed. The
algorithms is instead implemented in a test rack which includes all the components except the two TEGs. The sensors that would be mounted in the truck
and the TEGs is simulated with sensor values in order to test the system without
having the truck or the TEGs available.
1.4
Overview of the report
The first part of the thesis report covers the layout of the WHR-system and
brief descriptions of the included components in the system. The first part also
includes the dependencies and correlations between the components.
The second part addresses the modelling of the simulation environment, the
developed MNPT-function and the control strategy. The modelling part are
divided in two categories; Heat and Fluid.
The third and last part contains the case study of the developed MNPTfunction, discussion and future work.
6
2 | Litterature study
This thesis is a continuation of several previously done master thesis performed at Scania for the subject of using thermoelectric generators for utilise
the waste heat generated by the trucks engine. The thesis’s that builds the
foundation for the following work are "Dimensioning and control strategy of a
cooling pump in a Waste Heat Recovery system for commercial vehicles" (Svensson 2014), "A comparison of different connection techniques for thermoelectric
generators in vehicle waste heat recovery" andersson2012comparison, "Implementation of DC-DC converter with maximum power point tracking control
for thermoelectric generator applications" (Jahanbakhsh 2012), "Mild Hybrid
System in Combination with Waste Heat Recovery for Commercial Vehicles"
(Namakian 2013), "The Thermoelectric Generator An analysis of Seebeck-based
waste heat recovery in a Scania R-series truck" (Schauman 2009) and "Optimization of the electric properties of thermoelectric generators" (Shawwaf 2010).
2.1
Business intelligence
The observations made from the thesis’s this thesis builds its foundation on
is that it is not only a necessity to introduce recycled waste energy into the
system but also have a highly optimised system for it to be useful. This is not a
secret since the use for TEGs in automotive industry have been investigated by
scientist all around the world. To cite a case study that faced similar problems
this thesis is presenting:
"In recent years, because of the forecast limitations in oil supply and increasingly stringent vehicle exhaust gas emission regulations such as Euro 6,
new energy technologies are being developed to improve fuel efficiency and reduce emission; examples include hybrid vehicles as well as those powered by fuel
cells and hydrogen [1]. For gasoline engine, about 40% of the primary gasoline
energy is discharged as waste heat in exhaust gas [2]. Historically, several types
of heat exchangers and different heat transfer enhancement measures such as
ribbing, grooving and protrusions have been investigated since the first automobile thermoelectric generator (TEG) was built in 1963 [3]." ...
"However, there are compatibility problems among TEG, CC (catalytic converter) and muf (muffler). Both TEG and CC need heat to keep normal working
in the vehicle exhaust system. The pressure drop directly affects the back pressure of the engine exhaust gas, and then the intake and exhaust system of the
engine is also affected, which may reduce the engine power. The interaction
between them when they are both installed in the automobile exhaust system
would cause improper working [7]." (Liu et al. 2014).
A proper designed TEG can provide the power needed to possible replace
7
the generator and thus reduce the load on the engine which is shown in a case
study which Fiat conducted. In the study Fiat is first to equip a light commercial vehicle with a TEG. The TEG in the study did not utilise any active
optimisation as this thesis aims for (Haagh 2013).
Fiat is not the only one investigating implementations of TEGs. Vehicle
manufactures such as GM in USA and BMW in Germany have all developed
TEGs to recover the exhaust waste heat. Since the efficiency of TEMs are less
than 5% allot of work to improve the performance of the TEMs is the main
focus (Tang et al. 2015).
All the research found for TEGs in the vehicle industry and outside that industry focus on improving the TEMs performance by analysing different materials or by building a static system the TEGs are working in such as the research
study "Research on Integration of an Automotive Exhaust-Based Thermoelectric Generator and a Three-Way Catalytic Converter" (Deng et al. 2015) are
proposing.
This thesis is now changing that by a case study of an Maximum Net-power
Point Tracking function that actively seeks to dynamically control the operating
conditions in the system the TEGs are working in.
8
3 | System layout
3.1
Schematic layout of exhaust sources
The WHR-system consists of two TEGs at different locations on the truck;
EGR-TEG and ATS-TEG. Figure 3.1 shows a schematic of the exhaust channel
of a Eu6 6-cylinder Scania engine that is used for this project. It shows that
the EGR-TEG is placed behind the engine and mounted on top of the gearbox
and the ATS-TEG is mounted before the exhaust gas outlet.
Figure 3.1: Schematic layout of exhaust sources (Svensson 2014)
Exhaust gas recirculation (EGR) is a nitrogen oxide (NOx) emissions technique used in petrol/gasoline and diesel engines. The EGR-system works by
recirculating a portion of the engines exhaust gas back to the engine cylinders. Because NOx forms primarily when a mixture of nitrogen and oxygen
is subjected to high temperature, the lower combustion chamber temperatures
caused by EGR reduces the amount of NOx the combustion generates (Exhaust
gas recirculation 2015). The EGR-TEG collects heat from the EGR gases.
The temperatures are high in the EGR but the mass flow is lower than in
the after treatment system (ATS). The ATS ensures that the exhaust gases are
released with a minimum of NOx content. By injecting a urea-based additive,
AdBlue, into the exhaust, a chemical reaction takes place that converts the toxic
nitrogen oxides into harmless water and nitrogen gas (Aftertreatment System
2015). The ATS-TEG collects heat from the exhaust gases in the ATS. The
temperatures are low after the ATS but the mass flow is high as all of the
exhaust gases go through the ATS while in the EGR only 10-25% of the exhaust
mass flow is recirculated. It is expected that the heat energy to the two TEGs
will be approximately equal and between 10-20kW (Svensson 2014).
9
3.2
TEG heat exchanger design
The design and properties differs between the two TEGs since they are based
on the dimensional constraints of the truck. The ATS-TEG is designed and
manufactured by Eberspächer and the EGR-TEG by TitanX. Two dynamic
models is made of the two TEGs since they differed in dimension and properties.
3.2.1
ATS-TEG
The ATS-TEG system is mounted at the ATS outlet seen in figure 3.2, which also
displays the configuration and where the ATS Bypass valve is being positioned.
Some of the exhaust gas will still pass through the ATS-TEG even with a fully
opened bypass. A small leakage through the ATS bypass valve is expected when
the valve being completely closed and is being taken into account during the
development of the simulation models.
Figure 3.2: ATS-TEG together with the ATS and ATS Bypass valve
One of the layers that constitutes the ATS-TEG seen in figure 3.3. Eight
TEMs located between the exhaust gas ducts and the coolant fluid ducts at
each layer. The TEMs act as a heat exchanger between the exhaust gas and
coolant fluid thus experienced a temperature difference and thereby power is
being extracted from the occurred temperature difference.
10
Figure 3.3: One layer with eight TEMs in the ATS-TEG
The TEGs is modelled as countercurrent cross-flow heat exchangers. This
can be seen in figure 3.4 were the exhaust gas flow through the ducts in one
direction (orange arrows) and the coolant fluid flow orthogonal to the exhaust
gas and then turns at the end of the layer to return to the first side (blue arrow).
Figure 3.4: Countercurrent cross-flow arrangement
11
3.2.2
EGR-TEG
Figure 3.5 depicts the EGR-TEG, EGR Bypass and the EGR valve. As with
the ATS-TEG even with an fully opened bypass some of the exhaust gas is still
passing through the EGR-TEG. This is especially unwanted for the EGR-TEG
due the high risk of overheating the TEMs. The WHR-system is set to in a worst
case scenario to override the EGR valve by closing it, which stops the mass flow
in the whole EGR-system in order to protect the TEMs in the EGR-TEG.
Figure 3.5: EGR-TEG together with the EGR valve and the EGR bypass
The EGR-TEG is also modelled as a countercurrent cross-flow heat exchanger. The main difference between the modelling of the EGR-TEG and
the ATS-TEG is that the ducts in the EGR-TEG utilises parallel fins to extract (and transport) heat were the ATS-TEG uses offset fins in the ducts.
The advantage with offset fins is lower thermal resistance which means that the
fins transports heat more efficiently than the EGR-TEG. The disadvantage is
that more back pressure is being created. The choice of which fins in the heat
exchanger to use depends on the work environment of each TEG.
3.3
Schematic layout of system
The WHR-system seen in figure 3.6 consists of two main flows, the exhaust gas
flow (EG) and the coolant fluid (CF) flow. The two flows through the TEGs
must to work together to maximise the resulting net power. Too much or too
little of any of the two fluids would waste the beneficial effects of the WHRsystem and in a worst case scenario give a negative net power output from the
WHR-system.
12
Figure 3.6: Schematic of the WHR-system
3.3.1
Exhaust gas flow
The EG flow of the system seen in figure 3.7 is the heat source to the TEGs.
The EG flow is being split into two sub flows; the total EG flow and a EGR flow
which is a minor amount of recirculated EG flow that goes back to the engine
with the purpose to reduce emissions.
The green coloured "ATS", "EGR" and "EGR Valve" blocks is not modelled
in the simulation environment since they have no influence over the net power
output, but they are included in the schematic for an overview purpose.
The green engine block produces the values of RPM, torque, amount of mass
flow and temperature of the total EG and EGR flow. The block is not dynamically modelled since the engine is extremely complex to model where it operates
in different modes dependant on the current driving condition. The block uses
instead logged data from actual test driving and the feedback influences to the
engine is being applied according to thumb rules used by Scania.
Figure 3.7: Schematic of the EG flow
13
EGR-TEG
The EGR-TEG is located directly after the engine exhaust manifold where the
EG temperatures is at its maximum. The controller for the EGR-TEG strives to
keep the temperature on the hot side of the TEMs at the temperature limit of the
TEMs without overheating them. This is done by the EGR bypass valve through
bypassing a variable amount of the EG back to the engine. The temperature
boundary of damage is 330 ◦C (Thermonamic 2015).
The exhaust mass flow to the EGR-TEG is dependent on how much the
EGR system required at the current driving condition. The EGR mass flow
available to the EGR-TEG varies between 10% and 35% of the total EG mass
flow (Svensson 2014). The amount of EGR mass flow that is introduced to the
EGR-system is controlled by the EGR valve which the WHR-system has no
control over.
ATS-TEG
The ATS-TEG is located at the end of the exhaust system and has low risk of
overheating since the temperature of the EG has time to cool down from the
engine. The ATS-TEG can receive the total amount of EG mass flow.
The main purpose of the controller for the ATS-TEG is to compromise between power produced by the ATS-TEG and power losses at the engine by the
created back pressure of the WHR-system. High rate of EG mass flow equals an
higher power output from the ATS-TEG but also a higher workload for the engine to overcome the associated back pressure. This is done with the ATS bypass
valve through bypassing a variable amount of the EG out to the environment.
Exhaust gas bypass valves
Two bypass valves (EGR bypass & ATS bypass) is being controlled by the WHRsystem. The purpose of the bypass valves is to branch the EG flow in an Y-split
according to the sections 3.3.1 and 3.3.1 above.
The two bypass valves is electrically actuated. The types of valves being
used, is an exhaust brake at the ATS-TEG and a modified EGR valve at the
EGR-TEG location (Svensson 2014).
3.3.2
Coolant fluid flow
The WHR-system has its own coolant system that is disconnected from the
trucks coolant system to the engine. The CF flow of the system seen in figure
3.8 is the cold source to the TEGs.
14
Figure 3.8: Schematic of the CF flow
Radiator system
The radiator system is composed by three radiators; one CAC radiator which
cools the air from the turbo charger to the air inlet of the engine and two TEG
radiators (RAD1 and RAD2) that cools the CF flow to the TEGs.
The fuel consumption is strongly related to the air inlet temperature to the
engine, which is influenced by the TEG radiators affect on the CAC radiator.
High CF mass flow increases the efficiency of the TEGs but has the negative
side effect that the CAC fluid temperature also increases, which would increase
the fuel consumption.
The set configuration of the radiators is analysed by previous thesis work
(Svensson 2014). The configuration allows an compromise between the CAC
and TEG radiators to maximise the cooling of both fluids through the radiators
and retain low impact on the increased fuel consumption due to the increased
temperature of the CAC fluid.
Coolant pump
The coolant pump is a centrifugal electrically actuated pump that controlls the
CF mass flow to the TEGs. It is controlled so that the temperature difference
of the TEMs becomes as great as possible, minimise the power consumption of
the pump and also the influence from the two TEG radiators on the CAC fluid.
The pump is of model: "WP29 1030002229PA14 24v pump" (Engineered
Machined Products 2014).
Coolant three way valve
The three way valve controls the division ratio of the CF flow between the two
TEGs. The power being generated by the WHR-system is being maximised by
dividing the CF flow between them accordingly to desired outcome.
The model used is "Valve unit 446 091 200 0" (Wabco 2013).
3.4
Sensors
The WHR-system has a redundant set of sensors seen in figure 3.9. The purpose
is to verify developed models and hence the design of the controllers when the
15
system has been implemented on the actual test truck.
Figure 3.9: Schematic of WHR-system with required and redundant sensors
The sensors required to control the WHR-system in addition to those already
in place is:
1. Thermocouples (temperature sensor) placed at the warmest hitting point
of the most exposed TEM’s.
2. Temperature sensors at the EG inlet of the TEGs.
3. Pre and post located temperature sensors at the TEG radiators.
4. Pressure drop sensors for the TEG’s EG ducts and the coolant pump.
T. Redundant temperature sensors
P. Redundant pressure sensors
F. Redundant mass flow sensors
The purpose of the EG temperature sensors is to send information of the
temperature of the EG to the MNPT-function and to calculate the density of the
EG. The density changes significantly with temperature and is strongly related
to the mass flow and back pressure being created by the TEG’s.
The purpose of the surface mounted therocouples is to monitor the actual
temperature of the TEM’s at the warmest hitting point to evade overheating
them.
The pre-located temperature sensors at the radiators is used as an input to
the MNPT-function to calculate the influence on the CAC. The post-located
sensor measures the temperature of the CF in to the TEG’s and is also used in
the MNPT function.
16
The pressure drop sensors in combination with temperature data calculates
the mass flow through the TEG’s. The mass flow is required both in the MNPTfunction and also to control the ATS and EGR bypass valves.
The MNPT-function receives several more sensor signals as input than the
mentioned above but they originats from other systems on the truck and engine
states from the ECU. More information about the signals are in section 6.
17
4 | Modeling
The following sections describes the modelling of the dynamics incorporated
in the simulation environment and the time-independent models used for the
MNPT-function. The modelling chapter is divided into two sections: Heat and
Fluid.
4.1
Heat
Each TEG was modelled as a heat exchanger; Heat is absorbed from the hot
exhaust gas to the hot side of the TEMs and heat is transported away from the
cold side of the TEMs to the coolant fluid. The radiator system includes two
TEG radiators and one CAC radiator where each radiator were also modelled
as a heat exchanger.
All of the heat exchangers modelled in this thesis were of the type of a
cross-flow heat exchanger where the hot and cold fluid are unmixed. Figure 4.1
displays a heat exchanger with cross-flow arrangement where the hot and cold
fluid flow perpendicular to each other. Heat is absorbed from the hot fluid,
transported through the TEMs in the heat exchanger and then out to the cold
fluid.
Figure 4.1: Cross-flow heat exchanger with fluids unmixed
The effectiveness-NTU (-NTU) method was used to determine the heat
transfer rate in heat exchangers and the outlet temperature of the hot and cold
fluid (Cļengel 2007).
The heat transfer rate is needed in order to calculate the surface temperature
on the TEMs hot and cold side in the time-independent TEG model.
18
The outlet temperature was used in the radiator system where the outlet
temperature of one of the radiators was the input to the next connected radiator.
4.1.1
The effectiveness-NTU method
The number of transfer units (NTU) method was developed in 1955 by Kays and
London to eliminate the use of the log mean temperature difference (LMTD)
method that required cumbersome iterations to solve these problems (Cļengel
2007). The LMTD method is suitable to use in order to determine the size of a
heat exchanger when the mass flow rates and the inlet and outlet temperatures
of the hot and cold fluid is specified. If the size of the heat exchanger is specified
and the outlet temperatures of the hot and cold fluid is unspecified, the LMTD
method required an iterative process to determine the outlet temperatures which
the -NTU does not require (Cļengel 2007).
The -NTU method greatly simplified the analysis by defining a dimensionless parameter called effectiveness (4.1).
=
q
qmax
=
Actual heat transfer rate
Maximum possible heat transfer rate
(4.1)
The actual heat transfer rate q (4.2) is expressed from an energy balance on the
hot or cold fluid.
q = ṁh cp,h (Th,i − Th,o ) = ṁc cp,c (Tc,i − Tc,o ).
(4.2)
where ṁh|c is the mass flow rate of the hot|cold fluid, Cp,h|c is the specific heat
of the hot|cold fluid, Th|c,i is the inlet temperature of the hot|cold fluid and
Th|c,o is the outlet temperature of the hot|cold fluid. It is convenient to combine
the product of mass flow rate and specific heat as one parameter called heat
capacity rate Ch (4.3) and Cc (4.4) expressed for the hot and cold fluid.
Ch = ṁh cp,h
(4.3)
Cc = ṁc cp,c
(4.4)
where Ch|c is the heat capacity rate of the hot/cold fluid. In order to determine
the maximum possible heat transfer rate qmax (4.7), the parameters Cmin (4.5)
and Cmax (4.6) must be identified.
Cmin = min(Ch , Cc )
(4.5)
Cmax = max(Ch , Cc )
(4.6)
where Cmin is the smaller heat capacity rate of the hot and cold fluid and Cmax
is the larger heat capacity rate of the hot and cold fluid.
The maximum possible heat transfer rate qmax (4.7) will reach its maximum
value when the cold fluid is heated up to the inlet temperature of the hot fluid
or the hot fluid is cooled down to the inlet temperature of the cold fluid. These
two conditions will not occur at the same time unless the heat capacity rate of
the fluids are equal (Ch = Cc ), which usually isn’t the case.
When both fluid have different heat capacity rates (Ch 6= Cc ), the fluid with
the smaller heat capacity rate Cmin will experience a larger temperature change
and therefore it will be the first to experience the maximum temperature.
qmax = Cmin ∆Tmax
19
(4.7)
where ∆Tmax (4.8) is the maximum temperature difference that occur in the
heat exchanger.
∆Tmax = Th,i − Tc,i
(4.8)
Rearranging (4.1) and substituting in (4.7) yields (4.9).
=
q
qmax
→ q = qmax = Cmin ∆Tmax .
(4.9)
The heat transfer is now only dependent of the inlet temperatures of the hot
and cold fluid which greatly simplifies the calculation to obtain the heat transfer
and the outlet temperatures.
The last step before the outlet temperatures can be determined is to identify
the effectiveness (4.10) for a cross-flow arranged heat exchanger.
"
#
NTU0.22 exp −Cr NTU0.78 − 1
(4.10)
= 1 − exp
Cr
where NTU is the quantity number of transfer units and Cr is the capacity ratio.
The effectiveness depends on the geometry and flow arrangement of the
heat exchanger. Different effectiveness relations have been developed for a large
number of heat exchanger types (Cļengel 2007). The type of heat exchanger
that is used in the TEGs and the radiator system are designed with a cross-flow
arrangement where the hot and cold fluid is unmixed.
The dimensionless parameter called the capacity ratio Cr (4.11) is the ratio
between the fluid with the smaller heat capacity rate Cmin and the fluid with
the larger heat capacity rate Cmax .
Cr =
Cmin
Cmax
(4.11)
The quantity NTU (4.12) is a measure of the heat transfer surface area.
NTU =
UA
Cmin
(4.12)
where U is the overall heat transfer coefficient and A is the heat transfer surface
area of the heat exchanger. The outlet temperatures Th,o (4.13) and Tc,o (4.14)
of the hot and cold fluid is determined from (4.2) rearranged.
4.1.2
q
Ch
q
= Tc,i −
Cc
Th,o = Th,i −
(4.13)
Tc,o
(4.14)
Radiator system
The radiator system is composed by three radiators; one CAC radiator which
cools down the air from the turbo charger to the air inlet of the engine and two
TEG radiators that decreased the temperature of the coolant fluid to the TEGs.
The three radiators are modelled as countercurrent cross-flow heat exchangers
with the aid of the NTU-method described in section 4.1.1. Each radiator is
discretized in small elements or so called "lumps" as can be seen in figure 4.2.
20
It was crucial to discretize the radiators in the system due to that each radiator
affected significantly other underlying radiators.
Figure 4.2: Schematic of radiator system
The air temperature that flows through RAD2 affects the CAC and thereby
the temperature of the charged air in the CAC will be increased compared to
if RAD2 is not placed in front of the CAC. This increased outlet temperature
TCAC,o from the CAC will then increase the power consumption PCAC,loss because the engine will work less effective.
The inlet coolant fluid TCF,i is cooled down in RAD1 (which is affected
by the CAC) and then cooled down again in RAD2 (which is only affected
by the ambient temperature TAM B ). The model will then output the outlet
temperature TCF,o of the coolant fluid from RAD2 which simulates the inlet
temperature to the TEGs.
4.1.3
TEG - Steady state
Time-independent models of the TEGs were needed in order to calculate the
power output in the MNPT-function. The MNPT-function do not consider the
current state of the WHR-system (which the dynamic model is) but the optimum
steady state of the WHR-system, which is the steady state. The steady state
model is a thermal resistance model and can be seen in figure 4.3.
21
Figure 4.3: Thermal resistance model of the heat exchanger
The total thermal resistance (4.15) is needed in order to be able to calculate the
hot and cold surface temperature (4.17), (4.18) of the TEMs in each TEG.
R = Rh + RT EM + Rc
(4.15)
where Rh is the thermal resistance between the hot EG and the TEM, Rc is
the thermal resistance between the cold coolant fluid and the TEM and RT EM
is the thermal resistance of the TEM. Rh and Rc are identified in the section
4.1.6 and RT EM can be found in the datasheet provided by the manufacturer of
the TEMs (Thermonamic 2015). The overall heat transfer coefficient UA (4.16)
can be calculated using R.
UA =
1
,
R
(4.16)
where the overall heat transfer coefficient is utilised in the -NTU method in
section 4.1.1 to identify the heat transfer rate q in the heat exchanger. UA
is used to calculate the hot and cold surface temperature (4.17), (4.18) of the
TEMs in each TEG.
TT EM ,h = Th − qR
(4.17)
TT EM ,c = Tc + qR
(4.18)
where Th is the temperature of the EG, Tc the temperature of the CF. The
temperatures (4.17), (4.18) from the simulation was then used as inputs to the
MNPT-function.
(4.19)
22
4.1.4
TEG - Dynamic
The simulation environment utilized dynamic models of the TEGs where each
TEG is considered a thermal system. A dynamic model involves process variables that wary with respect to time, till the process gets stabilised and the
system is not disturbed by external factors (Karri 2005).
There are many solutions that can be used to simulate thermal systems
and the method being used in this thesis is with the aid of a lumped capacitance model. This model reduces a thermal system to a number of discrete
"lumps" and assumed that the temperature difference inside each lump is negligible (Karri 2005). This approximation is useful to simplify otherwise complex
differential heat equations. It is developed as a mathematical analog of electrical
capacitance, although it also included thermal analogies of electrical resistance
as well.
The initial step is to identify the energy balance in each layer in the lumped
capacitance model seen in figure 4.4. As heat flows in and out of a element,
some energy is stored in the element. The temperature is considered constant
in each element by dividing the heat exchanger in so called "lumps".
Figure 4.4: One element/lump in the lumped capacitance TEG model
23
C (4.20) is the heat capacity of each material or fluid, R is the thermal resistance
and q is the heat transfer rate between two nearby layers in the current lump.
C = mcp .
(4.20)
where m is the mass of each layer in the current lump and cp is the specific heat
capacity of each layer in the current lump. The lumped capacitance model finds
the average temperature in each layer at the current lump. The temperatures
was then used in the TEM model to calculate the power output from each
lump. The conservation of energy in each layer (4.21) - (4.25) was needed for
this purpose.
dTEG
dt
dTHS
dt
dTT EM
dt
dTCS
dt
dTCF
dt
=
=
=
=
=
qEG
CEG
1
qEG→HS
CHS
1
qHS→T EM
CT EM
1
qT EM →CS
CCS
1
qCS→CF
CCF
1
− qEG→HS
(4.21)
− qHS→T EM
(4.22)
− qT EM →CS
(4.23)
− qCS→CF
− qCF
(4.24)
,
(4.25)
The absorbed heat qEG (4.26) from the exhaust gas to the heat exchanger.
qEG = ṁEG cp,EG (TEG,i − TEG,o ),
(4.26)
where it is convenient to rewrite the first two factors in (4.26) to a thermal
resistance R1 (4.27).
R1 =
1
.
ṁEG cp,EG
(4.27)
Equation (4.26) is dependent on both the inlet and outlet temperature. The
outlet temperature is then rewritten in order to make (4.26) only dependent on
the inlet temperature of the fluid. A mean temperature approximation is used
for T EG (4.28).
T EG =
TEG,i + TEG,o
→ TEG,o = 2T EG − TEG,i
2
(4.28)
This approximation is valid to use if the heat exchanger is divided in enough
many lumpes. The new expression after inserting (4.27), (4.28) in (4.26) is then
(4.29).
qEG =
2
(TEG,i − T EG ).
R1
24
(4.29)
The heat transfer rate qEG→HS (4.30) from the exhaust gas to the hot heatsink
by convection and conduction.
qEG→HS =
1
(T EG − T HS ),
R2
(4.30)
where R2 (4.31) is the equivalent thermal resistance.
R2 = REG,conv +
RHS
.
2
(4.31)
REG,conv and RHS are identified in section 4.1.6. The heat transfer rate qHS→T EM
(4.32) from the hot heatsink to the TEM by conduction.
qHS→T EM =
1
(T HS − T T EM ),
R3
(4.32)
where R3 (4.33) is the equivalent thermal resistance.
R3 =
RHS + RT EM
.
2
(4.33)
RT EM is identified from data sheet (Thermonamic 2015). The heat transfer
rate qT EM →CS (4.34) from the TEM to the cold heat sink by conduction.
qT EM →CS =
1
(T T EM − T CS ),
R4
(4.34)
where R4 (4.35) is the equivalent thermal resistance.
R4 =
RT EM + RCS
.
2
(4.35)
RCS is identified in section 4.1.6. The heat transfer rate qCS→CF (4.36) from
the cold heatsink to the coolant fluid by convection and conduction.
qCS→CF =
1
(T CS − T CF ),
R5
(4.36)
where R5 (4.37) is the equivalent thermal resistance.
R5 = RCF ,conv +
RCS
.
2
(4.37)
RCF ,conv and RCS is identified in section 4.1.6. The absorbed heat qCF (4.38)
from the heat exchanger to the coolant fluid.
qCF = ṁCF cp,CF (TCF ,o − TCF ,i ),
(4.38)
where it is convenient to rewrite the first two factors in (4.38) to a thermal
resistance R6 (4.39).
R6 =
1
.
ṁCF cp,CF
25
(4.39)
The absorbed heat qCF is dependent on both the inlet and outlet temperature.
A mean temperature approximation T CF (4.40) is used as in (4.29) to make
(4.38) only dependent on the inlet temperature of the fluid.
T CF =
TCF ,i + TCF ,o
→ TCF ,o = 2T CF − TCF ,i .
2
(4.40)
The new expression after inserting (4.39), (4.40) in (4.38) becomes (4.41).
qCF = 2ṁCF cp,CF (TCF ,i − T CF ).
(4.41)
The final differential equations (4.42) - (4.46) that is used in the simulation
environment.
dTEG
1
2
1
=
(TEG,i − T EG ) −
(T EG − T HS )
(4.42)
dt
CEG R1
R2
dTHS
1
1
1
=
(T EG − T HS ) −
(T HS − T T EM )
(4.43)
dt
CHS R2
R3
1
1
1
dTT EM
=
(T HS − T T EM ) −
(T T EM − T CS )
(4.44)
dt
CT EM R3
R4
1
dTCS
1
1
=
(T T EM − T CS ) −
(T CS − T CF )
(4.45)
dt
CCS R4
R5
2
dTCF
1
1
(4.46)
=
(T CS − T CF ) −
(T CF − TCF ,i ) .
dt
CCF R5
R6
The temperature of the hot and cold surface of each TEM, TT EM,h (4.47) and
TT EM,c (4.48).
TT EM ,h = T HS
(4.47)
TT EM ,c = T CS .
(4.48)
TT EM,h and TT EM,c is then used in the time-dependent simulation model to
calculate the generated power from each TEG.
4.1.5
Thermoelectric module
Both the time-independent model and the dynamic model of the TEGs output a
hot and cold surface temperature of a TEM. A TEM model is developed to calculate the power generated from each TEM with a given temperature difference.
The TEM model iss fitted against experimental data done by Eberspächer Exaust Technology in Germany, who has performed performance tests to expand
the available data from the manufacture and also to validate the manufactures
data.
The model outputs a TEMs maximum power point (MPP) which is described
with the Current-Voltage-Power characteristics seen in figure 4.5. At zero current, the open circuit voltage is high but no power is produced. As the current
is increased, the power increases to a maximum where the maximum value is
the MPP. At high currents, the voltage drops to zero or below and the power
26
produced drops to zero or becomes negative (consuming instead of producing
power).
Pmax = 6.1607 W
Output Voltage
Output Power
5
5
0
Output Power [W]
Output Voltage [V]
10
0
0
0.5
1
1.5
Output Current [A]
2
Figure 4.5: The chart for output voltage and output power Vs output current
under TT EM ,h = 330 ◦C and TT EM ,c = 30 ◦C
More power is generated when the temperature difference across a TEM becomes larger and thereby the efficiency of converting heat energy into electricity
is increased. A DC/DC-converter is needed in order to maintain a TEM at it’s
MPP. The DC/DC-converter is designed by KTH and is not part of this thesis.
In order to calculate the MPP of a TEM, a mean temperature approximation
T T EM (4.49) of a TEM is used.
T T EM =
TT EM ,h + TT EM ,c
.
2
(4.49)
The internal resistance Ri (4.50) and the open circuit voltage Uo (4.51) of a
TEM must also be identified.
Ri = CRi,1 TT EM ,h + CRi,2 TT EM ,c + CRi,3
(4.50)
where the coefficients CRi,1|2|3 was obtained from Eberspächers performance
test done internally at Eberspächers. The open circuit voltage (4.51).
Uo = CU o,1 (TT EM ,h − TT EM ,c ) + CU o,2 (TT2 EM ,h − TT2 EM ,c )
+ CU o,3 (TT3 EM ,h − TT3 EM ,c ) + CU o,4 (TT4 EM ,h − TT4 EM ,c )
27
(4.51)
where the coefficients CU o,1|2|3|4 is obtained from Eberspächers performance test
done internally at Eberspächers. Since the power was a product of the terminal
voltage UT EM and the output current IT EM , the output power P (4.52) could
be expressed.
P = IT EM UT EM =
UT EM (Uo − UT EM )
.
Ri
(4.52)
Maximum power PM AX (4.53) is achieved when the load resistance matches the
internal resistance, which occurred when the terminal voltage UT EM is half the
open circuit voltage Uo .
PM AX =
Uo 2
2
Ri
(4.53)
The expression for maximum power output is then used in the simulation environment and the MNPT-function to calculate the power output from the TEGs.
4.1.6
Thermal resistance
The overall heat transfer coefficient UA is calculated as the reciprocal of the
sum of thermal resistances (4.54).
1
= Rconv + Rcond
UA
(4.54)
where U is the overall heat transfer coefficient, A is the heat transfer surface area
of the heat exchanger, Rconv is the thermal convective resistance of a material
and Rcond is the thermal conductive resistance of a material.
To enable more heat to be channelled into the TEM’s, finned heat exchangers are needed. The increase in surface area increases convection which in turn
increases the heat transferred to or from the fluid depending on which side of
the heat exchanger the fins are on. An appropriately selected material with
high thermal conductivity is needed to maintain an effective level of conduction. These extended surfaces greatly improve the system model by increasing
the value of Rcond and Rconv . When more heat is transferred to the TEG’s,
more power is removed from the WHR-system and thus, generated by the heat
exchanger (Freedman 2011).
Many fin options are available and selection of a configuration is dependent
on several reasons. The overall intent of the finned heat exchangers is to increase
surface area which will increase heat transfer. However, the increase in surface
area will increase the pressure drop of the flow of fluid passing over the heat
exchangers. This trade-off needs to be balanced as part of the design of the fin
assemblies. The fin options to be discussed include rectangular straight fins and
offset strip fins.
28
Rectangular straight fins
Rectangular straight fins are very common fin geometry because of their simplicity to manufacturer. They are commonly available in different sizes and can
be mounted to other structures fairly easily (Freedman 2011).
The following equations is used to estimate the thermal resistance regarding
convection Rconv (4.84) and conduction Rcond (4.81) for heat exchangers that
have rectangular straight fins. These parameters that can be seen in figure 4.6
are used throughout the following equations and include the number of fins Nf ,
the thickness of an individual fin tf , the length an individual fin protrudes from
its base Lf , and the thickness of the base tf . The only material property that
is needed with regards to the fins is the conductive coefficient kf in .
Figure 4.6: Visual of rectangular straight fins (Karri 2005)
The number of channels Nch (4.55) provides the area that allows fluid flow to
pass though the heat exchanger.
Nch = Nf − 1
(4.55)
where Nf is the number of fins. The pitch of a fin pf (4.56) is needed to be
known to help determine the spacing between fins Sf .
pf =
wz − tf
Nch
(4.56)
where wz is the width of the base and tf is the thickness of an individual fin.
The spacing between the fins Sf (4.57) is used for several calculations because
it represents part of the dimensioning of the flow path.
Sf = pf − tf
29
(4.57)
The wetted perimeter Pwet (4.58) of a flow path or one channel created by the
fins.
Pwet = 2Lf + 2Sf
(4.58)
where Lf is the length of a fin. The hydraulic diameter Dh (4.59) is needed to
provide the ability to use certain calculations that are typically dependent on a
diameter.
Dh =
2Lf Sf
Pwet
(4.59)
The entrance area Aent (4.60) needs to be considered for the flow paths through
the rectangular straight fins.
Aent = Sf Lf Nch
(4.60)
The characteristic length of a fin Lf,char (4.61) is needed for fin efficiency calculations.
Lf,char = Lf +
tf
2
(4.61)
The perimeter of the cross section of a fin Pf ace (4.62) is
Pf ace = 2tf + 2Lz
(4.62)
where Lz is the length of the base. The cross sectional area of a fin Ac (4.63) is
needed to assist in finding the efficiency of the fins.
Ac = tf Lz
(4.63)
The total surface area of all the fins Af,surf (4.64) is needed for finding the total
surface area that is affected by convection.
Af,surf = 2Nch Lf,char Lz
(4.64)
The total area of the base Abase (4.65) is also needed to help find the total
effective surface area.
Abase = Lz Wz
(4.65)
The total surface area of the base Ab,surf (4.66) is the base area which fluid
flow occurs and convective heat transfer is present.
Ab,surf = Abase − Ac Nf
(4.66)
The total surface area Atot,surf (4.67) is the area which fluid flow occurs and
convective heat transfer is present.
Atot,surf = Af,surf + Ab,surf
30
(4.67)
The mean velocity of the medium V (4.68) is needed to determine the Reynolds
number.
ṁ
ρAent
V =
(4.68)
where ṁ is the mass flow rate of the medium and ρ is the density of the fluid. The
definition of Reynolds number Re (4.69) is a necessary dimensionless parameter
used in determining the performance of the fin geometry.
Re =
ρV Dh
µ
(4.69)
where µ is the dynamic viscosity of the fluid. The Prandtl number Pr (4.70) is
another necessary dimensionless parameter needed for rectangular straight fin
analysis.
Pr =
cp µ
,
kf luid
(4.70)
where cp is the specific heat of the fluid and kf luid is the thermal conductivity
of the fluid.
The first application of the Reynolds number is its use in finding the friction
factor f , which is different depending on the value of the Reynolds number. If
Reynolds is less than or equal to 3000, the flow is considered to be laminar and
if Reynolds is over 3000, the flow is considered to be turbulent. Data was taken
from (Manglik and Bergles 1995) to determine the friction factor f .
With the solved friction factor f for Reynolds and Prandtl numbers, Nusselt
number is then found. The Nusselt number Nu is the ratio of convection to
pure conduction heat transfer. It is necessary to solve for Nu in order to find
the convective coefficient h. (4.77).
Laminar flow (Re ≤ 3000)
The aspect ratio χ (4.71) of the channel dimensions is found making it
so that it is always greater than one. This means that the length of the
fin is compared to the spacing between the fins and the greater value is
divided by the lesser value.
(
Lf /Sf Lf ≥ Sf
χ=
(4.71)
Sf /Lf otherwise
The aspect ratio is then used in a developed correlation f Re (4.72) that
is only valid for aspect ratios greater than or equal to one and less than
or equal to eight. For aspect ratios greater than eight, f Re is equal to
96 (Manglik and Bergles 1995).
(
−0.4673χ2 + 7.8663χ + 49.006 1 ≤ χ ≤ 8
f Re =
96
otherwise
31
(4.72)
The friction factor f (4.73) is then calculated.
f=
f Re
Re
(4.73)
The Nusselt number Nu (4.74) is then calculated. According to (Manglik
and Bergles 1995), Equation (4.74) is valid for laminar flow, combined
thermal and velocity entry, 0.6 ≤ P r ≤ 5, 0.0044 ≤ µ/µs ≤ 9.75, and
uniform surface temperature. The surface temperature being considered
constant is accurate for this analysis because each lump in the heat
exchanger is considered isothermal and the changes in temperature are
step changes by lump.
Nu = 1.86
RePr
! 13 Lz
Dh
µ
µs
0.14
.
(4.74)
Turbulent flow (3000 ≤ Re ≤ 5 · 106 )
A different set of equations are needed if it is determined that the flow is
turbulent. For turbulent, fully developed flow with a Reynolds number
greater than or equal to 3000 and less than or equal to 5 · 106 , equation
(4.75) is used to find the friction factor f (Manglik and Bergles 1995).
This is typically used for geometries with smooth surfaces which is the
assumption that must be made with regards to the paths channelling the
flow of the fluid across the fins.
f = (0.790 ln Re − 1.64)−2 .
(4.75)
According to (Manglik and Bergles 1995), equation (4.76) is used to
find the Nusselt number for turbulent flow through rectangular straight
fins. This equation is typically used for circular tubes but the use of the
hydraulic diameter has extended its use to the rectangular geometry. It is
reasonable to use this correlation with a Prandtl number greater than 0.7.
The condition of use for flow in circular tubes has 0.5 ≤ P r ≤ 2000. The
fully developed condition may add slight error to the analysis because it
is assumed and not actually fully developed flow.
Nu =
(f /8)(Re − 1000)Pr
1 + 12.7(f /8)1/2 (Pr 2/3 − 1)
.
(4.76)
Having solved the Nusselt number for either laminar (4.73) or turbulent
(4.75) flow depending on the conditions, it is now possible to determine the
convective coefficient h (4.77).
h=
Nukf luid
Dh
32
(4.77)
In order to find the fin efficiency, m (4.78) and ηf (4.79) are needed (Freedman
2011). These parameters are suitable for fins of uniform cross sectional area.
The coefficient to calculate the efficiency of one fin m (4.78) comes from a
coefficient in a second order differential equation pertaining to an energy balance
of conduction and convection in a extended surface.
s
hPf ace
,
(4.78)
m=
kf in Ac
where kf in is the thermal conductivity of the fin. ηf (4.79) is the efficiency of
one fin.
ηf =
tanh(mLf,char )
.
mLf,char
(4.79)
With the efficiency of one fin, the efficiency of an array of fins can now be found.
The overall surface efficiency η0 (4.80) is the efficiency of the array of fins as
well as the base surface to which the fins are attached (Freedman 2011).
η0 = 1 −
Af,surf
Atot,surf
(1 − ηf ).
(4.80)
The searched thermal conductive resistance of the base Rcond (4.81) can now
be calculated.
Rcond =
tb
,
kbase Abase
(4.81)
where tb is the thickness of the base. An effective area Aef f (4.82) is needed for
finding an effective convective coefficient hef f (4.83).
Aef f = η0 Atot,surf .
(4.82)
The effective area can now be used to find the effective convective coefficient
hef f (4.83).
hef f = h
Aef f
Abase
(4.83)
The searched thermal convective resistance of the heatsink Rconv (4.84) can now
be calculated.
Rconv =
1
.
Aef f hef f
33
(4.84)
Offset straight fins
Offset strip fins are common heat sink geometry because of their heat transfer
capabilities. Each row of rectangular fins is offset from the previous row to
create a staggered pattern for the flow path. This typically creates a greater
pressure drop but also allows for a substantially larger heat transfer coefficient
(Freedman 2011).
The following equations is used to estimate the thermal resistance regarding convection Rconv and conduction Rcond for heat exchangers that have offset
straight fins. These parameters that can be seen in figure 4.7 are used throughout the following equations and include the thickness of an individual fin tf , the
length an individual fin protrudes from its base Lf , the thickness of the base
tb , the number of rows of fins Nrows and the number of fins in a row across the
heat exchanger surface in the transverse direction Nf,trans . The only material
property that is needed with regards to the fins is the conductive coefficient
kf in .
Figure 4.7: Visual of offset straight fins (Karri 2005)
The number of channels representing entrance paths Nch,ent (4.85) provides the
area that allows fluid flow to pass though the heat exchanger.
Nch,ent = Nf,trans − 1
34
(4.85)
where Nf,trans is the number of fins in the transverse direction. The pitch of a
fin pf (4.86) is needed to be known to help determine the spacing between fins
Sf .
wz − tf
Nch,ent
pf =
(4.86)
where wz is the width of the base and tf is the thickness of an individual fin.
The spacing between the fins Sf (4.87) is used for several calculations because
it represents part of the dimensioning of the flow path.
Sf = pf − tf .
(4.87)
The offset strip length Lp (4.88) is the length of one strip of fin.
Lp =
Lz
Nrows
(4.88)
where Lz is the length of the base and Nrows is the number of rows. The
hydraulic diameter Dh (4.89) is needed to provide the ability to use certain
calculations that are typically dependent on a diameter. The equation factors
in all of the dimensions related to the fin including Sf , Lf , Lp and tf (Manglik
and Bergles 1995).
Dh =
4Sf Lf Lp
2(Sf Lp + Lf Lp + tf Lf ) + Sf tf
(4.89)
The entrance area Aent (4.90) needs to be considered for the flow paths through
the offset straight fins.
Aent = Sf Lf Nch,ent
(4.90)
The characteristic length of a fin is Lf,char is represented by equation (4.61).
This is needed for fin efficiency calculations and is the same as the characteristic
length for rectangular straight fins (Freedman 2011).
The perimeter of the face of the fin Pf ace (4.91) is needed to assist in finding
the efficiency of the proposed fin.
Pf ace = 2tf + 2Lp
(4.91)
The cross sectional area of a fin Ac (4.92) is needed to assist in finding the
efficiency of the fins.
Ac = tf Lp
(4.92)
The total surface area of all the fins Af,surf (4.94) is needed for finding the
total surface area that is affected by convection. Before this can be done, the
number of fins Nf (4.93) needs to be calculated, which is dependent on whether
the number of rows is odd or even as it accounts for there being one less fin in
every even numbered row (Freedman 2011).
(
−1
Nrows is an odd integer
Nrows Nf,trans − Nrows
2
(4.93)
Nf =
Nrows
Nrows Nf,trans − 2
Nrows is an even integer
35
The total surface area of all the fins Af,surf (4.94) can now be calculated.
Af,surf = 2Nf Lf,char Lp
(4.94)
The total area of the base Abase is also needed to help find the total effective
surface area and is the same as for the rectangular straight fins in equation
(4.65). The total surface area of the base Ab,surf is the base area which fluid
flow occurs and convective heat transfer is present. This is needed to calculate
the total effective surface area and is the same as for the rectangular straight
fins in equation (4.66).
The total surface area Atot,surf is the area which fluid flow occurs and convective heat transfer is present. This is simply the sum of the surface area of
the fins and base, similar to the rectangular straight fins represented in equation
(4.67).
The mean velocity of the medium V is needed to determine the Reynolds
number and is the same as for the rectangular straight fins in equation (4.68).
The common form of the Reynolds number Re seen in equation (4.69) is used for
this purpose. The Prandtl number Pr is also needed to complete the analysis
where equation (4.70) is used to find it.
Data is taken from (Manglik and Bergles 1995) to determine the Colburn
factor j, which is necessary in order to find the convective coefficient h. The
Colburn factor j is expressed different depending if the flow region is laminar or
turbulent. To determine this, Re ∗ (4.95) is needed (Manglik and Bergles 1995).
Re −0,5 i−1
L 1,23 t 0,58 h
f
p
Dh tf + 1, 328
Re ∗ = 257
Dh
Lp
Lp Dh
(4.95)
Laminar flow (Re ≤ Re ∗ )
j = 0.6522Re −0.5403
S −0.1541 t 0.1499 t −0.0678
f
Lf
f
f
Lp
Sf
(4.96)
Turbulent flow (Re ≥ Re ∗ + 1000)
j = 0.2435Re −0.4063
S −0.1037 t 0.1955 t −0.1733
f
Lf
f
f
Lp
Sf
(4.97)
Having solved the Colburn factor for either laminar (4.96) or turbulent (4.97)
flow depending on the conditions, it is now possible to determine the convective
coefficient h (4.100). In order to convert the Colburn factor j, equation (4.96)
or (4.97), to a useful value, the convective coefficient based on LMTD hlmtd
(4.98) is introduced (Manglik and Bergles 1995).
hlmtd = j(ρV cp )Pr −2/3
36
(4.98)
The number of transfer units NTU (4.99) is a dimensionless parameter is needed
as it helps relate hlmtd to the convective coefficient h.
NTU =
hlmtd Atot,surf
ṁcp
(4.99)
The convective coefficient h (4.100) can then be finally expressed.
h=
ṁcp
(1 − exp[−NTU])
Atot,surf
(4.100)
The average value for the convective coefficient is now ready for use with
some familiar analysis performed for rectangular straight fins. By utilising
the equations (4.78) to (4.84) from the rectangular straight fins analyse, the
searched thermal convective resistance of the heatsink Rconv and the conductive resistance of the base Rcond are found.
37
4.2
4.2.1
Fluid
Flow divison - Exhaust gas
The flow division of the EG fluid between the bypass valve and the TEG’s is
modelled with an electric analogy as an lumped system (Poling et al. 2001). The
equivalent schematic of the flow division can be seen in figure 4.8. The equivalent
cross variable of voltage from the electric analogy is the pressure drop dP of
the fluid system and the through variable of current is the volumetric flow Q
of the fluid. The fluid inductance L represents the inertia of the fluid and the
fluid capacitance C represents the pressure build up due to the dimensions of
the fluid system. The fluid capacitance takes into account the compressibility
of the fluid and the fluid resistance R is caused by the friction that the fluid
experience from the surrounding surfaces (Poling et al. 2001).
Figure 4.8: Electric analogy of EG flow division
The left part marked with yellow colour of figure 4.8 represents the TEG
properties and the right part coloured green represents the EG bypass valve.
It is approximated that the TEG and EG bypass valve would cause the same
pressure drop. This approximation is concluded as the outlets for the ATSTEG and the ATS bypass valve end in parallel to each other directly into the
atmosphere pressure, see the left system in figure 4.9. The same approximation
is made for the EGR-TEG since the EG channels merge back together, see the
right system in figure 4.9. These approximations are a necessity to be able to
model the dynamics of the flow division being controlled.
38
Figure 4.9: Equivalent pressure drop over each TEG and EG bypass valve
The consecutive equations (Lindeburg et al. 2013) of the lumped system
describes the behaviour of the systems components. Each component causes an
pressure drop that depends on the properties of the component: inductance,
capacitance or resistance.
The pressure drop of an inductive component in an lumped system ∆PL
(4.101) is needed because of the inertia of the fluid.
∆PL = L
dQ
dt
(4.101)
The value of the fluid inductance L (4.102) is dependent on the density ρ of the
fluid which varies with the temperature of the EG caused by the engine RPM.
L=
ρl
A
(4.102)
where A is the area of the EG channel.The fluid capacitance C (4.103) describes
the volume flow QC into cavities dependent on the pressure build up ∆PC it
was subjected to.
QC = C
d(∆PC )
dt
(4.103)
The pressure drop of the capacitive component in the lumped system ∆PC
(4.103) is caused by the pressure build up due to the compressibility of the
fluid. The fluid capacitance C (4.104) is obtained with the Area A and the
length l of the component. The bulk modulus of the fluid β represents the
property of elasticity of the EG fluid.
C=
39
Al
β
(4.104)
The pressure drop of the resistive component in an lumped system ∆PR (4.105)
occurs because of the friction between the walls of the EG ducts and the fluid.
∆PR = RQ
(4.105)
The calculation of the fluid resistance R differs between the ATS-TEG, EGRTEG and the EG bypass valves. Because the design of the ATS-TEG and the
EGR-TEG fluid system differs between them. The fluid resistance of the EG
bypass valves is set to be changeable since they are dependent on the angle of
the throttle plate inside the bypass valve which is being controlled.
In-depth calculations of the fluid resistance is described in the following
sections 4.2.3, 4.2.4 and 4.2.5 for the ATS-TEG, EGR-TEG and the EG bypass
valves.
4.2.2
Differential equations
Combining the above equations yields the differential equations (4.106), (4.107)
and (4.108) to figure 4.8.
1
d(QT EG )
=
(∆PT EG − RT EG Q2T EG )
dt
LT EG
d(QV alve )
1
=
(∆PV alve − RV alve Q2V alve )
dt
LV alve
d(∆PT EG )
1
=
Q − QT EG − Qvalve
dt
CT EG + CV alve
(4.106)
(4.107)
(4.108)
The volumetric flow QT EG is the total volumetric flow of the EG to the
TEG. The volumetric flow can not be controlled directly as the total EG flow
is depending on the torque demand of the engine.
Instead, by manipulating the Rvalve value with the angle of the throttle
plate, the flow through the TEG is controlled without having any control of
the total EG flowing into the system. Equation (4.107) describes the change
of the volumetric flow through the bypass valve where Rvalve is the resistance
the fluid is opposed by. A completely closed throttle plate gives an infinite high
fluid resistance Rvalve for the bypass valve and forces all EG fluid into the TEG.
4.2.3
Pressure drop and fluid resistance over ATS-TEG
The resistive pressure drop is needed in order to calculate the fluid resistance
of the ATS-TEG. The pressure drop for offset fin strips in the EG ducts of the
ATS-TEG, seen in figure 4.10, is calculated by an empirical correlation (Manglik
and Bergles 1995) of the friction factor.
40
Figure 4.10: Offset fin layout ATS-TEG
The correlation utilises a modified version of the hydraulic diameter Dh
(4.89) from section 4.1.6 in order to obtain the Reynolds number Re. The
modified diameter is dependent on the pitch of a fin pf , free flow height Lf , fin
thickness tf and the fin length Lp . The total length Lz of the heat sink is then
later used in the pressure drop function. The transverse spacing between the
fins s (4.87) from section 4.1.6 is also needed in order to obtain the Reynolds
number.
The friction factor f is expressed different depending if the flow region is
laminar or turbulent. To determine this, Re ∗ is needed and is the same here as
in equation (4.95) from section 4.1.6 and corresponds:
L 1,23 t 0,58 h
Re −0,5 i−1
p
f
Re ∗ = 257
Dh tf + 1, 328
Dh
Lp
Lp Dh
Laminar flow (Re ≤ Re ∗ )
f = 9.6243Re −0.7422
S −0.1856 t 0.3053 t −0.2659
f
Lf
f
f
Lp
Sf
(4.109)
Turbulent flow (Re ≥ Re ∗ + 1000)
f = 1.8699Re −0.2993
S −0.0936 t 0.6820 t −0.2423
f
Lf
41
f
f
Lp
Sf
(4.110)
The pressure drop over the EG ducts ∆PAT S−T EG (4.111) is now be calculated.
∆PAT S−T EG = 2f
Lz ρ 2
Q
Dh A2
(4.111)
The definition of the constitutive equation (4.105) is used with (4.111) to find
out the fluid resistance. Note that the pressure drop is no longer linear for the
constitutive equation (4.112).
∆PAT S−T EG = REG,AT S−T EG Q2
(4.112)
where REG,AT S−T EG (4.113) is the fluid resistance.
REG,AT S−T EG = 2f
4.2.4
ρ l
D h A2
(4.113)
Pressure drop and fluid resistance over EGR-TEG
The difference between the ATS-TEG and the EGR-TEG is the calculation of
the friction factor and the hydraulic diameter, due to that the EGR-TEG consists of rectangular straight fins. The friction factor f is calculated for laminar
case as (4.73) and the turbulent (4.75) in section 4.1. The hydraulic diameter Dh
is derived from (4.59) from the same section. By utilising these values together
with (4.111) and (4.113), the pressure drop ∆PEGR−T EG and fluid resistance
REG,EGR−T EG can be expressed.
42
4.2.5
Pressure drop and fluid resistance over EG bypass
valve
The bypass valve is modelled as an sharp edged circular orifice. An orifice
plate forces the fluid to experience an temporary area change which results in
a pressure drop over the orifice plate (Green et al. 2008). Orifices are usually
used for measuring the volume flow in pipes (Orifice plate 2014).
The effective area A2 of the orifice plate in figure 4.11 is controlled to simulate
the behaviour of an butterfly throttle valve seen in figure 4.12.
Figure 4.11: Orifice Plate
The volumetric flow Q (4.114) through the orifice plate is dependent on the
discharge coefficient Cd, the open area of the orifice plate A2 the area of the
inlet of the bypass valve A1 .
s
C d A2
2∆P
Q= q
(4.114)
ρ
1 − ( A2 )2
A1
The discharge coefficient Cd is based on the type and dimensional constraints
of the bypass valve, which is constant for an butterfly valve. Cd together with
A2 forms the effective area of the bypass valve. The open area of the orifice
plate A2 is a function of the angle α of the throttle plate inside the bypass valve
seen in figure 4.12.
Figure 4.12: Side view of butterfly throttle bypass valve (Carlsson 2007)
43
The open area of the orifice plate A2 (4.115) is considering the diameter of
the inlet D, the area of the shaft b seen from the flow direction, the angle of the
throttle plate α from a vertical view and the angle α0 from which the bypass is
fully closed (Carlsson 2007). The throttle plate is closed at an angle so that the
throttle plate do not have the ability to get stuck in a closed position.
"
"
1/2
cos(α) 2
b πD2 1−
+
cos2 (α) − b2 cos2 (α0 )
A2 =
4
cos(α0 )
π cos(α)
##
cos(α)
−1
−1 b cos(α0 )
2 1/2
+
− b(1 − b ) − sin (b)
sin
cos(α0 )
cos(α)
(4.115)
Figure 4.13 describes the area change as a function of the throttle plate
angle. It can be seen that the shaft starts to impinge the area at 80 degrees.
Figure 4.13: Normalized area as function of the throttle plate angle whith shaft
and no shaft (Carlsson 2007).
The variable fluid resistance REG,Bypass (4.116) for the throttle valve is then
defined (4.116) where A2 is an function of the throttle plate angle.
q
!2
2 2
1 − (A
A1 )
ρ
(4.116)
REG,Bypass =
2
C d A2
The control and manipulation of the fluid resistance REG,Bypass for the
bypass valve are covered in subsection 4.2.2.
44
4.2.6
Flow division - Coolant fluid
As for the EG flow, the dynamics of the CF flow is modelled with an electric
analogy seen in figure 4.14 which describes the equivalent schematic of the CF
dynamics. The consecutive equations of inductance (4.101) and capacitance
(4.103) is the same as for the EG dynamics. The fluid resistance is formed by
serial and parallel connected fluid resistances from the hoses, CF ducts in the
TEG’s and the TEG radiators.
Figure 4.14: Schematic of coolant fluid lumped system
The fluid resistance RAT S for the ATS-TEG and REGR for the EGR-TEG in the
CF ducts is obtained with the same principles as described above in subsection
4.2.3 and 4.2.4. This is because of that the TEG’s utilises the same type of
heat exchangers both in the EG ducts as in the CF ducts in each corresponding
TEG. The fluid resistances for the TEG’s is rewritten as one resistance RT EGtot
(4.117), because the two TEG’s are parallel connected since the CF was divided
by the three way valve and then the CF merged back to one flow.
RT EGtot =
1
REGR
+
1
RAT S
−1
(4.117)
In order to calculate the fluid resistance for the hoses Rhose , the pressure drop
∆Phose is needed. The pressure drop is expressed different depending if the
flow region is laminar or turbulent. (Karlsson 2011). The pressure drop ∆Phose
(4.118) for laminar flow region occurs if Re ≤ 2000.
∆Phose =
45
8
Q
πr4
(4.118)
Where r is the radius of the hose. The fluid resistance of the hose Rhose (4.119)
is then found.
Rhose =
8
πr4
(4.119)
The pressure drop ∆Phose (4.120) for turbulent flow region occurs if Re ≥ 2000.
∆P = 2f
lρ 2
Q
dA2
(4.120)
Where the Blasius friction factor f , the length of the hose l, the diameter of the
hose d and the freeflow area in the hose A are all needed in order to solve the
expression. The Blasius friction factor f (4.121) is expressed for turbulent flow
(Karlsson 2011).
f = 0, 0791Re −1/4
(4.121)
With the aid of the pressure drop for laminar flow (4.118) and turbulent
flow (4.120), the fluid resistance for the TEG radiators RRad is then obtained
by polynomial fitting data to an second order polynomial parable. The data is
gather from measured tests performed internally at Scania and contains pressure
drops depending on different mass flow. The reason for the use of polynomial
fitted data and not empirical fluid equations is that the TEG radiator had
complex structure and would be difficult to model correctly in the given time
of the thesis.
It is then possible to combine the three serial connected fluid resistances to
one single fluid resistance RCF (4.122).
RCF = Rhose + RT EGtot + RRad
(4.122)
The simplified schematic can be seen in figure 4.15 and is implemented in
the Simulink environement.
Figure 4.15: Simplified schematic of the coolant fluid lumped system
46
4.2.7
Three-way valve
The three way valve has one inlet and two outlets. The flow into the valve is
divided between the two outlets. The mass flow into the valve is always equal to
the mass flow out from the two outlets. The division ratio is non linear between
the two fluid outlets in the three way valve. The flow division is polynomial
fitted from data obtained from the three way valve data sheet (Wabco 2013).
Figure 4.16 describes the mass flows for the two outlets as the constant mass
flow in is being divided in the valve.
Threeway valve, Constant input flow 1800 [dm3 /h]
Outlet 2.1
Outlet 2.2
1800
1600
1400
flow [dm3 /h]
1200
1000
800
600
400
200
0
10
20
30
40
50
60
Flow division [%]
70
Figure 4.16: Flow division three way valve
47
80
90
5 | Simulation
The data input to the simulation environment is obtained from logged driving scenarios performed by Scania. The driving scenario used throughout the
thesis is the distance between Södertälje and Norrköping.
5.1
Fluid properties
The properties of the exhaust gas is not considered constant due to the large
range of temperature that occurs in the TEGs. The same consideration is
applied for the coolant fluid were the dynamics of the flow in the coolant system
is behaving differently with different temperatures. The fluid properties that
change with temperatures is the density ρ, the specific heat capacity cp , viscosity
µ and the thermal conductivity k of the fluid medium.
The coolant fluid R134a (Tetrafluoroethane) is often used in cooling applications at Scania. Due to lack of data over a wide range of temperatures, the
properties of pure water is used instead. The reason is that the coolant fluid
consist of a mixture of 40% R134a and 60% water and the properties of water
is approximated to be accurate within reasonable levels.
The exhaust gas is a composition of N2 , CO2 , H2 O and O2 . Each substance
is weighted accordingly to their relative mass compared to the total mass of the
exhaust gas. The weighted factors that Scania uses is seen in table 5.1.
Table 5.1: Wighted factors for composition of exhaust gas
Element
Welement
N2
0.67
CO2
0.13
48
H2 O
0.10
O2
0.10
The medium properties for EG is seen in figure 5.1 and 5.2. The green circles
represents measured data (Reid, Prausnitz, and Poling 1987) and the blue lines
represents the fitted function used in the simulation environment.
8
cp
x 10
1400
1200
Interpo lated
Data
1000
Interpolated
Data
5
0
−5
0
4
x 10
2000
4000
6000
Tem perature [K ]
µ
0
7
x 10
2
Interpola ted
Da ta
2
0
[W/ (m ·K )]
4
[Pa ·s]
ρ
10
[J/ (K g ·K )]
[J/ (K g ·K )]
1600
−2
2000
4000
6000
Tem pera ture [K ]
k
0
−2
Interpolated
Data
−4
−6
0
2000
4000
6000
Tem perature [K ]
0
2000
4000
6000
Tem pera ture [K ]
Figure 5.1: EG Temperature between 0 and 6000 [K]
cp
ρ
1020
Interpola ted
Da ta
4220
4200
[J/ (K g·K )]
[J/ (K g·K )]
4240
4180
1000
980
940
0
50
100
Tem perature [◦ C ]
−3
µ
x 10
0
2
0.75
[W/ (m ·K ])
Interpola ted
Da ta
1.5
[Pa ·s]
Interpo lated
Da ta
960
1
0.5
0
50
100
Tem pera ture [◦ C ]
k
Interpolated
Data
0.7
0.65
0.6
0.55
0
50
100
Tem perature [◦ C ]
0
50
100
Tem pera ture [◦ C ]
Figure 5.2: CF Temperature between 0 and 100 [◦C]
49
5.2
Dynamic model of TEG-system
Each TEG-system is as earlier mentioned designed as countercurrent cross-flow
heat exchangers. Each layer in the TEG-systems consists of 8 TEM’s. The layer
is divided in eight lumps seen in figure 5.3 where each lump is considered as one
heat exchanger including one TEM each.
The warmest hitting point of the TEGs is simulated as a lump that is divided
in 50 sections. The first section is approximately the first hitting point that is
affected by inlet temperatures and mass flows of the fluids.
Figure 5.3: Dynamic model of a TEG divided in 8 lumps
The inlet and outlet temperature for the EG is represented by red labels. The
first pass of the inlet temperature is through lump 5-8. The outlet temperature
from these lumps is introduced as the inlet temperature to lump 1-4. The
average outlet temperature from lump 1-4 is the EG outlet temperature out of
the TEG model.
The inlet and outlet temperature for the CF is represented by blue labels.
The first pass of the inlet temperature is through lump 1. The outlet temperature from that lump is introduced as the inlet temperature to lump 2 and so
on. The outlet temperature from lump 8 is the CF outlet temperature out of
the TEG model.
Power generated by each TEM is outputted in the orange labels. The summation of the the generated power from the eight lumps is the total generated
power by the layer. Each layer in the TEG’s is approximated as same so only
one layer is simulated. The total generated power by each TEG corresponds to
the generated power by each layer the TEG consists of.
50
6 | Maximum Net-power Point
Tracking
The objective with the MNPT-function is to calculate the reference values at
run time in the ECU. The reference values consists of the EG mass flow through
the ATS-TEG, CF mass flow and the flow division ratio of the CF mass flow in
the three way valve. The three way valve distributes the CF mass flow between
the ATS-TEG and EGR-TEG in order to achieve maximum net-power output
from the WHR-system. A numerical solution is applied to obtain the desired
reference values which would maximise the MNPT-function.
The MNPT-function is dependent on 15 inputs of which 12 of them is state
variables received from sensor signals and engine states and the remaining inputs
is then the reference values. The MNPT-function consists of nonlinear functions
that needs to be calculated in iterative loops. The input signals are seen in
table 6.1 and the output signals are seen table 6.2.
Table 6.1: Input signals of MNPT-function
Input
Torque
RPM
Vehicle speed
Ambient temperature
CAC mass flow
EG ATS temperature
EG EGR temperature
Pressure drop ATS-TEG
Pressure drop EGR-TEG
Warmest hitting point ATS/EGR-TEM
CF temperature pre TEGs
CF temperature pre radiator
CAC fluid temperature pre radiator
51
Table 6.2: Output signals of MNPT-function
Output
ATS-TEG EG mass flow reference
CF mass flow reference
CF division
6.1
Optimisation dependencies
High mass flows of CF and EG through the TEG equalled to an high power
output. At the same time, high mass flow consumes more energy to pump
the CF in the coolant system. This also leads to high back pressure for the
exhaust system resulting in harder workload for the engine. The power losses
W (6.1) from the back pressure ∆P at volumetric flow Q is calculated as an
100% effective pump.
W = ∆P Q
(6.1)
The pressure drop ∆P for the EG back pressure and CF system is obtained
in section 4.2.1. The time dependent properties is not included since the calculations needs to be of static type in the numerical solution.
6.1.1
ATS-TEG
Figure 6.1 describes the behaviour of the net power output from the ATS-TEG
with varied mass flows of CF and EG. The temperatures of the two fluids is held
constant in this example. The inlet temperature of the CF was at 20 degrees
and the inlet temperature of the EG was at 350 degrees.
52
CF [l/min]
EG [kg/h]
Figure 6.1: ATS-TEG power of EG and CF flow
With only these variables in consideration there is an optimum at 22 l/min of
CF volumetric flow and 450 kg/h of EG mass flow for the ATS-TEG. Note that
the net power output seen in figure 6.1 is from the ATS-TEG. The EGR-TEG
is not considered when calculating the power output from the ATS-TEG.
The amount of CF mass flow is lower than the figure depicts when both
TEG’s shares the same CF pump, since the power consumption of the pump
follows the exponential pressure drop curve as a function of the CF mass flow
seen in figure 6.2.
53
Power consumption as function of mass flow
45
40
Pump power required [W]
35
30
25
20
15
10
5
0
0
5
10
15
20
25
mass flow coolant [l/min]
30
35
40
Figure 6.2: Power consumption of CF pump as function of CF mass flow
Another object the MNPT-function takes account for is how the CAC fluid
is affected by different CF temperature and mass flows. The outlet CF temperature from the TEG’s is dependent on the amount of mass flow and temperature
of the CF and EG flow in to the TEG’s.
Figure 6.3 displays the extra fuel consumption in "%" due to an increase
of temperature of the CAC fluid dependent. The same variables are used as in
figure 6.1 added with additional constants of CAC fluid, ambient temperature
and mass flows. The CAC fluid mass flow is set to 0.25kg/s, with an temperature
of 150 degrees. The ambient air is set to an temperature of 20 degrees and the
mass flow to 2.8 kg/h. This represents approximately an vehicle speed of 85
km/h with the cooling fan on idle.
54
Extra fuel consumtion [%] with variable EG and CF mass flows
−3
x 10
1.99
Extra fuel consumption [%]
1.98
1.97
1.96
1.95
1.94
1.93
1.92
1.91
500
1.9
30
480
460
28
440
26
420
24
22
400
20
380
18
360
16
340
14
320
12
10
CF [l/min]
300
EG [kg/h]
EG [kg/h]
CF [l/min]
Figure 6.3: Extra fuel consumption in "%" due to CAC temperature increase
by ATS-TEG
The extra fuel consumption in "%" is calculated according a thumb rule
commonly used at Scania (Svensson 2014). The fuel consumption increases
with 0.8% for each 10K increase in temperature. The power loss PCAC,loss (6.2)
due to increased CAC fluid temperature is expressed.
PCAC,loss = PEngine
0.08
(TCAC,out,T EG − TCAC,out,REF )
100
(6.2)
where PEngine is the power usage of the engine, TCAC,out,T EG is the outlet
temperature from CAC with TEG radiators and TCAC,out,REF is the reference
outlet CAC fluid temperature without TEG-radiators. The power usage of the
engine PEngine (6.3) is dependent on the engine torque τ and the engine RPM
ω.
PEngine =
6.1.2
τ ω2π
60
(6.3)
EGR-TEG
The EGR-TEG operates with lower EG mass flow than the ATS-TEG due to
the power loss from the back pressure is very low and can be neglected and left
out from the optimisation calculations. The EG mass flow through the EGRTEG is controlled by the boundary of not overheating the TEG. The most
critical area to monitor in the EGR-TEG is the warmest hitting point where
the EG temperature is the hottest. It has been concluded that the optimum is
to have fully closed bypass when the inlet temperature of the EG was below the
boundary temperature of 330 degrees, which means that all EG passes though
the EGR-TEG.
55
Figure 6.4 describes the net power output with an constant EG temperature
of 500 degrees and CF temperature of 20 degrees with variable EG and CF mass
flows. The back pressure is included in the figure to prove the reason to neglect
the back pressure dependency. It can be seen on the "EG mass flow" axle that
the power loss never reaches a point with the available EG mass flow to create
a negative derivative as for the ATS-TEG seen in figure 6.1.
CF [l/min]
EG [kg/h]
Figure 6.4: EGR-TEG power of EG and CF flow
The extra fuel consumption in "%" due to increased CAC fluid temperature
being caused by the EGR-TEG is displayed in figure 6.5. The same variables
are used as in figure 6.4 and additional constants as with figure 6.3.
56
Extra fuel consumtion [%] with variable EG and CF mass flows
−3
x 10
Extra fuel consumption [%]
1.908
1.906
1.904
1.902
1.9
1.898
1.896
1.894
30
300
28
280
26
260
24
22
240
20
220
18
16
200
14
180
12
CF [l/min]
10
CF [l/min]
160
EG
[kg/h]
EG [kg/h]
Figure 6.5: Extra fuel consumption due to CAC temperature increase by EGRTEG
6.2
Combined optimisation function
The algorithm of the MNPT-function receives sensor signals of the current states
of temperatures and mass flows of the fluids, engine states and numerically
calculates the reference values of mass flow CF and how the CF fluid shall be
divided between the two TEG systems by the three way valve. It also outputs
the reference value of the amount of EG mass flow that shall pass through the
ATS-TEG.
The pseudo code of the numerical optimisation function in algorithm 1 describes the steps of finding the optimum values of the references.
Calculate optimum references
The first "for loop" sets an value of the CF mass flow (reference value to decide)
at the start of an changeable span and calculates the power losses at the CAC
due to temperature increase of the fluid in the CAC radiator. It also calculates
the pump losses related to the CF mass flow in the whole coolant system. All
power losses and gains in the optimisation function are dependent on the sensor
signals and the variable set by the "for loop".
Inside the first "for loop" is the second "for loop" with the purpose to divide
the CF mass flow (reference value to decide) that has been set by the first "for
loop". In the second "for loop" the power gain from the EGR-TEG is calculated
with the set CF flow division and the current EG received by the EGR-TEG.
The Third "for loop" inside the second "for loop" steps through different
mass flows of EG through the ATS-TEG (reference value to decide) and calculates the power gain and the power loss from the back pressure for the ATS-TEG
with the remaining CF mass flow after the CF division. It also sums up the all
57
the power gains and losses to an net power value. When the third "for loop"
has finished a new value of CF mass flow is set at the first "for loop" and all
the calculations are repeated.
This approach will make the net power value N ET _P ower to start small
and increase for every iteration. When the N ET _P ower begin to decrease the
iteration part is aborted. The N ET _P ower has an parabolic appearance, where
the peak provided the the answer to values of the references. The optimum
reference values are then the values set by the previous iteration by the "for
loops" which has been "remembered".
Determining the reference values
Before the reference values are sent to the controllers they are "checked" if they
lie in the allowed span. The reason is that the CF mass flow are never allowed
to go under value that would result in overheated TEG’s or that the division
sends all of the CF to just one of the TEG’s. Even though it may be optimal
in the current state. If the reference value is outside the span it is set by a
predefined value dependent on which side the of the allowed span the reference
value was calculated to be at.
Move the interval of the search for reference values
Lastly the the intervals at the "for loops" are modified and moved in the direction of where the optimum is more likely to be found the next time the
optimisation function is run. This action is illustrated in figure 6.6.
58
Figure 6.6: The span to search for the best reference values was changeable and
dependent on previous reference values to reduce computational time.
This method fulfils two advantages, the computational time reduces significantly with an small span that can be moved, it also allows a greater resolution
of the span to search in. The second advantage is that the reference values
does not jump between large values since it is limited by the range value of the
interval. The change of the reference values will then move as an slope. The
reference values is set to update at a frequency of 1 Hz.
Summarising the MNPT-function
The structure of the MNPT-function is displayed as a pseudo code in algorithm
1. The three for loops sets the searched for reference values, dependent on
where the reference values is most likely to be found. when the reference values
is found they are checked to bee an allowed value, a new range dependent on
the reference value is then set until the next time the MNPT-function is being
calculated. Finally, the reference values is outputted to the controllers.
59
Data: Input values from sensor signals
Result: Outputs optimum reference values
Calculate optimum references
for ṁCF = ṁCF,min : ṁCF,max do
Remember_ṁCF
PCAC,loss = f (...)
PCF pump,loss = f (...)
for Division = Divmin : Divmax do
Remember_Division
PEGR,gain = f (...)
for ṁEG = ṁEG,min : ṁEG,max do
Remember_ṁEG
PAT S,gain = f (...)
PBackpressure,loss = f (...)
PN ET = PEGR,gain + PAT S,gain − PCAC,loss −
PBackpressure,loss − PCF pump,loss
end
end
if PN ET < PN ET,old then
Break
end
end
Determining the reference values
if Remember_/ṁCF /Division/ṁEG in allowed span then
ṁCF _Ref = Remember_ṁCF ← previous
Division_Ref = Remember_Division ← previous
ṁEG _Ref = Remember_ṁEG ← previous
else
ṁCF _Ref = P reDef ined
Division_Ref = P reDef ined
ṁEG _Ref = P reDef ined
end
Move the interval of the search for reference values
ṁCF,min = ṁCF _Ref − rangeCF
ṁCF,max = ṁCF _Ref + rangeCF
Divmin = Division_Ref − rangeDiv
Divmax = Division_Ref + rangeDiv
ṁEG,min = ṁEG _Ref − rangeEG
ṁEG,max = ṁEG _Ref + rangeEG
Algorithm 1: Pseudo code of MNPT-function
60
7 | Control
The design of the control parameters for the EG bypass valves uses the
iterative Nicoals-Ziegler method (Glad and Ljung 2006). This proves to work
well with the dynamics in the whole span of the system. The reason to use an
iterative method for finding the parameters instead of pole placement design is
because that the poles and zeros of the plant changes with the EG temperatures
and the angles of bypass valve. Section 7.1 addresses the behaviour of the EG
closed loop system.
The parameter values for the control of CF mass flow are obtained with the
Diophantine method (Jelali 2012). The properties of CF are not sensitive of
temperature changes and compressibility. Therefor the state matrix is being
linearised around a CF temperature and mass flow. It is shown in simulations
to be a valid approach.
The main actuators communicates with the communication protocol CAN.
The EG bypass valves are controlled by receiving a throttle plate angle value
and the CF pump receives a RPM value. The three way valve expects an analog
voltage signal to regulate the angle of the valve plate.
7.1
Control strategy EG mass flow
The controller design differs from traditional control strategy. Normally the
input to the plant is controlled but in this case the EG mass flow in the plant is
controlled by changing the systems characteristics. This raised the problem that
the amount of EG mass flow to the plant is uncontrollable as it is dependent
on torque required from the engine. The problem is solved with the solution
to control the parameter of fluid resistance Rvalve in the state matrix, which
controls the EG mass flow through the TEG’s.
With a changeable parameter Rvalve in the state matrix, there are no stationary eigenvalues in the state matrix, which leads to that no pole placement
design can be done since the poles can not be placed at an stationary location.
Instead an iterative search for a compromised placement of the poles is done.
The search for the PID parameters is done by simulating the driving scenario
and test the best option for each parameter.
The inductance for the TEG’s and valves and the fluid resistance RT EG is
stationary because of the dependencies of the EG temperatures. The poles of the
system when the valve goes from closed to opened with an constant temperature
of the EG moves towards origo in the pole zero unit circle diagram. Figure 7.1
describes the moving poles of the linearised flow division system of the EG with
constant EG temperature of 400 degrees and an total EG mass flow of 1000kg/h.
61
Flow division poles ATS-TEG
1
0.8
Opened BP valve
0.6
Imaginare
0.4
0.2
Closed BP valve
0
−0.2
−0.4
−0.6
−0.8
−1
−1
−0.5
0
Real
0.5
1
Figure 7.1: Closed loop poles as a function of closing the valve
The simulations proves that even with changing poles, a stable plant behaviour can be achieved with an PI regulator for the angle of the EG throttle
plate. The PI regulator is of linear type despite figure 4.13 in section 4.2, which
shows an nonlinear area change as function of the throttle plate angle. It is
approximated to be linear because it is only in the terminal edges of the nonlinear function the effect is noticeable. At the terminal edges, the system is
undergoing an extreme scenario to either be completely open or closed.
7.1.1
ATS-TEG bypass control
The bypass valve actuator receives the desired angle from the PI controller
calculated by the MNPT-function. The EG mass flow through the TEG is
obtained by measuring the pressure drop over the TEG and the temperature of
the EG.
In an scenario where the warmest hitting point in any of the two TEG’s
exceeds the boundary temperature of 330 degrees, the MNPT-function requests
no EG mass flow through the TEG to prevent overheating.
Another feature that is implemented in the MNPT-function is to request
no EG mass flow though the ATS-TEG the first 40 seconds after start up of
the engine. The reason is that the simulations shows that the ATS-TEG needs
time to reach a high enough temperature to produce more power than is being
wasted from the back pressure created by the EG flow through the ATS-TEG.
7.1.2
EGR-TEG bypass control
Since the back pressure at the EGR-TEG is not a problem, the controller can
request all of the available EG to flow through the EGR-TEG. The EGR bypass
valve is not dependent on the MNPT-function for the reference value since the PI
controller regulates the throttle plate angle based on the temperature boundary
62
limit of 330 degrees. The PI controller acts as an ON/OFF regulator that
holds the EGR bypass valve closed when the warmest hitting point is below the
temperature boundary at the warmest hitting point. The measurement signal
for the warmest hitting point is measured by thermoelectric elements placed on
the TEM’s that are exposed to the warmest EG.
7.2
Control strategy CF mass flow
The communication between the CF pump node and the WHR-system ECU is
that the pump receives a desired RPM and sends back the power consumption
of the pump. The power consumption divided with the pressure drop over the
pump gives the measured CF mass flow (6.1), which is sent to the controller
with the CF mass flow reference from the MNPT function.
7.3
Control strategy CF mass flow division
The three way valve receives an control signal that is converted trough a digital
to analog converter on how the division should be set from the MNPT-function.
To ensure a CF mass flow in both directions from the three way valve, the
pressure drop is measured according to the schematic in figure 3.9.
7.4
Safety restraints
The MNPT-function has in addition to maximise the net-power output also
safety responsibilities. The safety restraints is to never allow the CF volumetric
flow to be less than 8 l/min to each TEG-system in order to prevent overheating.
The MNPT-function has to keep track of both the CF mass flow and the CF
division in case there would be blockade in any of the branches.
A design decision of the placement of the EGR bypass valve allows the EGR
valve (Not the bypass valve) to completely shut down the EG mass flow to
the EGR-TEG, in case the exhaust brake creates a back pressure that causes
damage the EGR-TEG. The ability to control the EGR valve is only done by
the engine management system.
63
8 | Case study
The study is conducted to investigate how much more net energy that can be
extracted and re-introduced from the WHR-system with the MNPT-function.
Three different control approaches are analysed during this study. The unit of
energy compared between the approaches is kilowatt hour kW h since the amount
of power recycled in a period of time gives a more accurate description of the
differences than comparing the net-power generated at the current moment. The
energy kW h is based on the net-power generated by the WHR-system N etpower
(8.1). Net-power is calculated as the difference between power generated by the
TEG’s and the power losses within the whole WHR-system.
N etpower = P owerGains − P owerLosses
(8.1)
The power gains and losses is simulated in the simulation environment with
the different control approaches. The simulation environment uses logged driving data and simulated sensor values which the WHR-system needs.
8.1
Inputs
The inputs to the WHR-system for all three control approaches comes from the
first 10 minutes of a logged driving scenario between Södertälje and Norrköping.
The input data includes the start up of the truck from an equilibrium state. The
inputs from the logged driving are displayed in table 8.1.
Table 8.1: Input data for the case study
Logged data
Torque
RPM
Vehicle speed
Ambient temperature
CAC mass flow
Total EG mass flow
EG ATS temperature
EG EGR mass flow
EG EGR temperature
Simulated data
Pressure drop ATS/EGR-TEG, BP
Warmest hitting point ATS/EGR-TEM
EG mass flow ATS/EGR-TEG, BP
CF pressure drop
CF mass flow
CF temperature pre/post TEGs
CF temperature pre/post radiator
CAC fluid temperature post radiator
Power consumption from CF pump
64
Approach 1
The first control approach utilises the MNPT-function which calculates reference values to the controllers based on the sensor values at different engine
states. The MNPT-function updates the reference values at 1Hz. The controllers operates at 10Hz reading the sensors and outputting a control signal
based on the reference to the actuators. The variable reference values from the
MNPT-function is the amount of CF mass flow, the flow division of CF between
the two TEG’s and the EG mass flow through the ATS-TEG.
The EGR-TEG is only controlled to not breach the 330 degree temperature
limit at the warmest hitting point. The ATS-TEG used the mass flow reference
from the MNPT-function. All the reference values is based on the first 10
minutes of the logged driving scenario.
The CF mass flow reference sent to the CF pump controller changes according to figure 8.1 which depicts the optimum CF mass flow that updates at
1Hz. The reason of the relatively slow update frequency is because of the slow
dynamics of the CF system.
CF mass flow reference
0.5
[kg/s]
0.4
0.3
0.2
0.1
0
0
100
200
300
Time [t]
400
500
600
Figure 8.1: CF mass flow reference
The total CF mass flow from figure 8.1 works in collaboration with the CF
flow division between the TEG’s. Figure 8.2 shows how much of the total CF
mass flow in "%" that is optimum for to the ATS-TEG. The remaining of the
CF mass flow then goes the EGR-TEG. The division ration in "%" is converted
to a nonlinear signal value as described in section 4.2.7.
65
% of CF mass flow that shall go to the ATS-TEG
100
90
80
70
[%]
60
50
40
30
20
10
0
0
100
200
300
Time [t]
400
500
600
Figure 8.2: Percentage of the total CF mass flow diverted to the ATS-TEG
The EG mass flow reference for the ATS-TEG in figure 8.3 shows an zero
value of the reference at the first 40 seconds, which means that the bypass is
having an fully open angle. This is set because at start up, the temperature of
EG though the ATS-TEG location is very low. Instead of generating power, the
ATS-TEG would then create a power loss from the back pressure greater than
what can be generated from having EG mass flow through the ATS-TEG. When
the temperature of the EG reaches 150 degrees, the MNPT-function starts to
optimise the reference of EG mass flow through the ATS-TEG.
66
EG mass flow through ATS-TEG reference
0.12
0.1
[kg/s]
0.08
0.06
0.04
0.02
0
0
100
200
300
Time [t]
400
500
600
Figure 8.3: EG mass flow through ATS-TEG reference
Approach 2
The second approach utilises fixed reference values of CF mass flow, CF division
and EG mass flow through the ATS-TEG. The EG mass flow through the EGRTEG is still operating by controlling against overheating the TEM’s temperature
boundary at 330 degrees.
The constant reference values comes from previous work performed by the
manufacturer and master thesis, where it recommended a 500kg/h EG mass
flow through the ATS-TEG. The value has been obtained by using ten long
haulage cycle points in steady state and use the value as an compromise that
would work better or worse in various scenarios (Svensson 2014). The values
are listed in table 8.2.
Table 8.2: Recommended CF mass flow
CF ATS-TEG
CF EGR-TEG
ṁmin [kg/s]
0.0607
0.1489
ṁmax [kg/s]
1.2258
1.5288
The values for the simulation is set according to table 8.3. The CF mass
flow is set high because it is beneficial for the cold source at the TEG’s. The
CF division is set to be equal so both TEG’s would receive the same amount of
CF mass flow.
67
Table 8.3: Approach 2 reference values
Reference
EG
CF
CF division
Value
500 [kg/h]
1 [kg/s]
50 [%]
Approach 3
The third approach is similar to the second approach but with the difference
that all of the available EG is being directed through the ATS-TEG. This is
done to examine the WHR-system without any bypass valves except for the
boundary to fully open the bypass when the warmest hitting point breached the
temperature boundary at 330 degrees. The reference values is set accordingly
to table 8.4.
Table 8.4: Approach 3 reference values
Reference
EG
CF
CF division
Constant value
All available [kg/h]
1 [kg/s]
50 [%]
68
8.2
Results
This section displays figures of the power gains and losses for comparison between the different approaches. Lastly, the figures of kilowatt hour displayed
sums up the true difference between the three control approaches.
The axis to figures representing approach 3 is scaled to match the figures
respresenting approach 1 and 2. Unscaled figures can be found in appendix B.
8.2.1
Net-power
The net-power is as previously stated the power gains subtracted with the power
losses. The power gains are the power generated by the TEG’s and the power
losses is all the losses caused in the WHR-system. The net-power for each
approach is presented in figures 8.4, 8.5 and 8.6.
The difference between the approaches is that approach 1 had an larger integral compared with approach 2 and 3. Higher peaks of net-power is generated
with while using less control in the system.
Net power
700
600
Net power [W]
500
400
300
200
100
0
0
100
200
300
T im e [t]
400
Figure 8.4: Net-power with approach 1
69
500
600
Net power
700
600
Net power [W]
500
400
300
200
100
0
0
100
200
300
T im e [t]
400
500
600
500
600
Figure 8.5: Net-power with approach 2
Net power
700
600
Net power [W]
500
400
300
200
100
0
0
100
200
300
T im e [t]
400
Figure 8.6: Net-power with approach 3
70
8.2.2
Power gains
The power gains only displays the power generated from the TEG’s with no consideration of the power losses. The power gains for each approach is presented
in figures 8.7, 8.8 and 8.9.
The result is that approach 1 which utilises the MNPT-function actually
generated the least power output from the TEG’s. The purpose of the MNPTfunction is not to only consider the power gains but also the power losses.
Excluding the consideration of the losses with fixed references, a larger mass
flow and a larger temperature difference can be allowed.
Power ga ins from AT S-T EG & EG R-T EG
500
AT S-T EG
EG R-T EG
450
400
Power gains [W]
350
300
250
200
150
100
50
0
0
100
200
300
T im e [t]
400
Figure 8.7: Power gains with approach 1
71
500
600
Power ga ins from AT S-T EG & EG R-T EG
500
AT S-T EG
EG R-T EG
450
400
Power g ains [W]
350
300
250
200
150
100
50
0
0
100
200
300
T im e [t]
400
500
600
Figure 8.8: Power gains with approach 2
Power ga ins from AT S-T EG & EG R-T EG
500
AT S-T EG
EG R-T EG
450
400
Power gains [W]
350
300
250
200
150
100
50
0
0
100
200
300
T im e [t]
400
Figure 8.9: Power gains with approach 3
72
500
600
8.2.3
Power losses
The power losses are from the CF pump, increased CAC fluid temperature and
back pressure of the ATS-TEG at the different control approaches. The power
losses for each approach is presented in figures 8.10, 8.11 and 8.12.
The most notable difference between the approaches is the power loss from
the back pressure of the ATS-TEG. The least notable difference is the CAC
influence that exhibits almost no visible difference. An important result with
the CF pump is that an high increase in CF mass flow do not give higher
increase of power gains. The conclusion comes from examining the power gains
from the EGR-TEG which exhibits almost the same behaviour in the different
approaches. The ATS-TEG needs to be excluded from the conclusion since it
is affected of the EG mass flow. The EGR-TEG receives the same amount of
EGR EG for the different approaches.
Power lo sses from B ack pressure, C F pum p & C AC
400
B ack pressure
C F pum p
C AC
350
Power losses [W]
300
250
200
150
100
50
0
0
100
200
300
T im e [t]
400
500
Figure 8.10: Power losses with approach 1
73
600
Power lo sses from B ack pressure, C F pum p & C AC
400
B ack pressure
C F pum p
C AC
350
Power lo sses [W]
300
250
200
150
100
50
0
0
100
200
300
T im e [t]
400
500
600
Figure 8.11: Power losses with approach 2
Power lo sses from B ack pressure, C F pum p & C AC
400
B ack pressure
C F pum p
C AC
350
Power losses [W]
300
250
200
150
100
50
0
0
100
200
300
T im e [t]
400
500
Figure 8.12: Power losses with approach 3
74
600
8.2.4
Extracted energy
The last comparison examines the harvested energy in kilowatt hour from the
WHR-system between the different approaches. This comparison gives the clearest answer to the question on how much more energy could be extracted by the
use of the MNPT-function. The extracted energy for each approach is presented
in figures 8.13, 8.14 and 8.15.
The important result is displayed at the right axis at the end of the simulation at 600 seconds. Approach 1 with the MNPT-function extracts 50% more
energy compared with approach 2 and also more than 300% in comparison with
to approach 3.
G ained kWh during 10 m inutes
0.06
0.05
[kWh]
0.04
0.03
0.02
0.01
0
0
100
200
300
T im e [t]
400
500
Figure 8.13: Extracted energy with approach 1
75
600
G ained kWh during 10 m inutes
0.06
0.05
[kWh]
0.04
0.03
0.02
0.01
0
0
100
200
300
T im e [t]
400
500
600
Figure 8.14: Extracted energy with approach 2
G ained kWh during 10 m inutes
0.06
0.05
[kWh]
0.04
0.03
0.02
0.01
0
0
100
200
300
T im e [t]
400
500
Figure 8.15: Extracted energy with approach 3
76
600
8.3
Discussion
It is not meaningful to just seek high power gains as it is for the third approach.
The power losses displays greater differences between the approaches than the
power gains so it is recommended to have an MNPT-function that seeks to
minimise the power losses while maximising the power gains.
It is notable that the CF mass flow can be held relatively low and still be
an beneficial cold source, with purpose to reduce the CF pump work. By the
use of an altering CF mass flow division, the low CF mass flow can be sent to
be where it is the most needed. For example, the EG mass flow reference to the
ATS-TEG in figure 8.3 is zero in the beginning so the MNPT-function sets a
20% division of the total CF mass flow to the ATS-TEG. Since the ATS-TEG
do not produce power during this time, the EGR-TEG receives the most of the
CF mass flow.
The largest power losses of the WHR-system comes from the back pressure
at the ATS-TEG. The high back pressure is created by the offset heat fins
compared to the parallel fins for the EGR-TEG. The reason to use offset fins is
to be able to extract more heat from the EG which has relative low temperature
at the ATS location. It may be more optimal to have parallel heat fins in the
ATS-TEG which results in lower power gains due to lesser heat convection and
significantly reducing the power losses from the back pressure.
The losses from the CAC does not display any significant difference between
the approaches. This is caused by the slow dynamics of the coolant system and
the fast changes of the power required of the engine. The variable that can be
controlled to minimise the CAC losses is the CF mass flow.
The final conclusion is that the use of an MNPT-function significantly increases the energy reintroduced to the truck. But there is still improvements to
do for the MNPT-function after the WHR-system has been implemented on the
truck. The improvements are dependent on finalised dimensions of the coolant
system and the exact placement of the sensors. Further recommendations are
discussed in section 9.2
Steady state results with the MNPT-function can be found in Appendix A.
77
9 | Closure
9.1
Summary
All the energy contained in the fuel in a truck is not utilised to propel the truck
forward. About 30% of the energy of the consumed fuel ends up as waste heat
in the exhaust system. By the use of thermoelectric generators, about 5% of the
waste heat energy can be extracted. But the use of thermoelectric generators
also subsequently has the effect of consuming energy from the truck.
This thesis models a complete waste heat recovery system including all the
power gains and losses. There is also a designed Maximum Net-power Point
Tracking function to maximise the energy recycled back to the truck. The
simulation environment includes simulations of the thermoelectric generators,
the flow division of EG for the TEG’s and bypass valves and the controllers
designed. Also included is the coolant system and controllers both for the CF
pump and CF flow division.
A case study is performed to examine the effects of having control with the
use of MNPT-function, fixed control and nearly no control. It is discovered
that the MNPT-function extracts up to 50% more energy than with fixed reference control, which is the traditional way of controlling WHR-systems. The
objectives of the thesis work is met with success.
9.2
Conclusions and recommendations
It is important to not only look at the specifications of what is possible to
regenerate energy of the TEG’s. All aspects of the WHR-system needs to be
considered. The main aspect of maximising the energy reintroduced to the truck
is not to have high power gains from the TEG’s, but to have as small as possible
power losses from the WHR-system.
The use of an CF flow division valve is very beneficial for reducing the power
consumed by the CF pump. To be able to send the CF to where it is most needed
reduces the total CF mass flow required from the CF pump and subsequently
the power consumption of the CF pump. The largest power losses comes from
the back pressure, therefor it is import to have proper designed EG bypass
controllers. There are further work to do of the design of the PI parameters. A
suggestion would be to dynamically change the gains of the PI-controller.
According to the simulations, the CAC can be excluded from the MNPTfunction since it is difficult to predict the negative influence in time due to the
clash of fast and slow dynamics to control. Further study could be to develop
predictive models regarding the CAC influence for power losses, as the dynamics
are hard to predict due to the slow dynamics in the system.
78
Both TEG’s has a risk of overheating the TEM’s inside. The EGR-TEG
will according to performed simulations breach the temperature boundary of
330 degrees. It is of highest importance that the ECU knows the temperature
of the warmest hitting point at the TEM’s. An idea is to have a predictive
model of the actual temperature at the warmest hitting point, but that could
be difficult to acquire due to sensitive thermal dynamics. It is recommended
that temperature sensors are placed at the warmest hitting point in a manner
to experience the same influence of temperature of the EG as the TEM’s do.
Note for the implemented system on the truck is that it will be difficult to
calculate the correct ambient air mass flow that is cooling the radiators. The
difficulty is because of the dependency on the vehicle speed. The ambient mass
flow through the radiators will be hard to calculate and is probably not possible
to measure with high accuracy. A predictive model of the TEG radiators would
be interesting to investigate in.
9.3
Future studies
Since the WHR-system has not yet been built on the physical test truck, there
are several tweaks to be made on the various functions that the MNPT-function
is constructed by. The MNPT-function operates at small margins thus accurate
functions for calculate the power gains and losses is of most importance in order
to maximise the net-power from the WHR-system.
MNPT-function
The power consumption of the CF pump is strongly related to the pressure
drop of the coolant system. Since the coolant system has not yet been built,
the length and diameter of the CF pipes has only been approximated. There
are also an unknown number of bends of the pipes that will contribute with
additional pressure drops. It is also unclear how much the pressure will drop at
the TEG radiators since the radiator models is not verified against reality but
only against KULI CFD simulations internally performed at Scania.
It is recommended to measure the pressure drop, power consumption and
CF volumetric flow for different RPM’s of the CF pump. The gathered data
can then be fitted to a polynomial function to create an accurate estimation of
the power consumption as a function of the CF volumetric flow. Then replace
the modelled power loss of the coolant system in the MNPT-function with the
polynomial function.
TEG
The thermal resistance modelling of the heat sinks has not been verified against
any experimental data. It is recommended to use a Finite Element Analysis
R to compare the results found in this report.
software such as ANSYS
The MNPT-function utilises the steady state model of the TEG’s to determine optimum reference values. The steady state function developed needs
to be verified against measured tests. The tests could be a step response with
known inputs where the interesting outputs would be electrical power and outlet
temperatures of the EG and CF.
79
The transient model of the TEG’s has not been verified against any experimental tests. It is crucial that the model is accurate since the controllers developed in the simulation environment is dependent on the transient behaviours of
the WHR-system. The transient model is currently based on a thermal lumped
system but could be described more accurately with heat spreading in two dimensions.
Fluid
Both the controllers and MNPT-function has a need of knowing the EG mass
flow through the TEG’s. The EG mass flow can not be measured with flow
sensors in the harsh environment and the EG mass flow is calculated from measuring the pressure drop and EG temperature at the TEG’s. The calculations
of the EG mass flow through the ATS-TEG and EGR-teg needs to be verified
against an implemented system. It is recommended to test the TEG’s in a blow
bench with known mass flow and temperatures where it is possible to compare
the reality with the calculations. It is preferable that the temperature is relative
high since the temperature has been discovered to have a large impact on the
calculations.
Control
It is concluded that the largest power losses comes from the back pressure,
which makes it important to have proper controllers for the EG bypass valves.
Since the dynamics of the plant of the EG flow division changes with the EG
temperatures and the angles of the throttle plate in the bypass, the parameters
of the PI controller is not able to keep the closed loop poles stable at where it is
designed to be at. It is recommended to design a controller with changeable PI
parameters dependent on the EG temperatures and the throttle plate angles.
Since the dimensions of the coolant system has a lot of approximations,
the PI parameters will need to be updated when the coolant system has been
finalised.
80
10 | References
Aftertreatment System (2015). Scania. [Online; accessed 15-february-2015]. url:
http://www.scania.com/products-services/buses-coaches/safetytechnology/engine-technology/scr/.
Carlsson, Per (2007). “Flow Through a Throttle Body: A Comparative Study
of Heat Transfer, Wall Surface Roughness and Discharge Coefficient”. In:
Cļengel, YA (2007). Heat and mass transfer: A practical approach.
Crane, Douglas T and Gregory S Jackson (2004). “Optimization of cross flow
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Appendices
84
A | Steady State Result
To compare results between projects at Scania certain engine states of different driving conditions of RPM and relative load has been defined as Long
Haulage Cycle (LHC) in table A.1.
Table A.1: Long Haulage Cycle
LHC
1
2
3
4
5
6
7
8
9
Relative load [%]
25
50
100
25
75
25
50
75
100
Engine speed [RPM]
1000
1000
1000
1150
1150
1300
1300
1300
1300
The 9 different driving conditions sets the driving data of the truck. Table
A.2 presents the power result in steady state for the 9 LHC points with the
MNPT function.
Table A.2: Steady state power with MNPT
LHC
1
2
3
4
5
6
7
8
9
Net power [W]
310
590
387
420
600
400
624
642
236
Power gains [W]
366
709
627
484
800
474
772
867
607
85
Power losses [W]
56
119
240
64
200
74
148
225
371
B | Approach 3 unscaled figures from case study
Unscaled figures of approach 3 from the case study.
Net power
800
600
400
Net power [W]
200
0
−200
−400
−600
−800
−1000
−1200
0
100
200
300
T im e [t]
400
500
Figure B.1: Net power approach 3 from case study
86
600
Power ga ins fro m AT S-T EG & EG R-T EG
700
AT S-T EG
EG R-T EG
600
Power g ains [W]
500
400
300
200
100
0
0
100
200
300
T im e [t]
400
500
600
Figure B.2: Power gains approach 3 from case study
Power lo sses from B ack pressure, C F pum p & C AC
B ack pressure
C F pum p
C AC
1600
1400
Power losses [W]
1200
1000
800
600
400
200
0
0
100
200
300
T im e [t]
400
500
Figure B.3: Power losses approach 3 from case study
87
600
G ained kWh during 10 m inutes
0.05
[kWh]
0.04
0.03
0.02
0.01
0
−0.01
0
100
200
300
T im e [t]
400
500
Figure B.4: kWH approach 3 from case study
88
600