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Parametric and design analysis on thermoelectricgeneratorsShouyuan HuangPurdue University
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Shouyuan Huang
PARAMETRIC AND DESIGN ANALYSIS ON THERMOELECTRIC GENERATORS
Master of Science in Mechanical Engineering
Xianfan XuChair
Stephen D. Heister
Amy Marconnet
Xianfan Xu
Jay P. Gore 7/20/2016
i
PARAMETRIC AND DESIGN ANALYSIS ON THERMOELECTRIC GENERATORS
A Thesis
Submitted to the Faculty
of
Purdue University
by
Shouyuan Huang
In Partial Fulfillment of the
Requirements for the Degree
of
Master of Science in Mechanical Engineering
August 2016
Purdue University
West Lafayette, Indiana
ii
For my parents
iii
ACKNOWLEDGEMENTS
I can’t wait to express my appreciation to the people I met during this project, and by
the way, I cannot even understand why the template says that this page is optional.
I would like to first thank my thesis advisor, Prof. Xianfan Xu, with my most sincere
gratitude. He provided to me this intriguing and promising project and showed abundance
of brilliance, inspiration, insight, and patience that helped me through. In addition, I feel it
a great privilege to have such an expert and mentor guiding me in the nano world in my
following Ph.D. career. I would appreciate Prof. Stephen Heister for the opportunity to
work at the awesome Zucrow Lab, and also Prof. Amy Marconnet serving as my
Committee.
I would thank Dr. Sumeet Kumar for the groundbreaking work, and Andrei Dubitsky
for the startup mentoring on TEG testing. I would thank James Salvador and the GM Waste
Heat II crew for the opportunity and up-to-date TEG design ideas. I would thank Prof. Tim
Fisher and for teaching me numerical methods for heat transfer and Prof. William Crossley
for the optimization methods. I would thank Scott Meyer, Rob McGuire, Andrew Pratt,
Michael Bedard etc. for helping me with all kinds of works in Zucrow. I would also thank
the financial support of the National Science Foundation (NSF), the US Department of
Energy (DOE) [DE-EE0005432], and the National Aeronautics and Space Administration
(NASA) Aeronautics Research Institute Seedling Fund. to make this research possible.
iv
Also, my deepest gratitude to, but not limited to the hereinafter, my friends and
classmates, Xinghao Zhuang, Jiacheng Zhang, Chaolei Chen, Xinye Zhang, Li Cheng,
Collier Miers, Yuan Hu, Yuqiang Zeng, Zuyuan Wang, Guangxu Lan, Biao Lv, Jingwen
Jiang, Jieyu Lu, Wei Meng, etc. for the beneficial talks on either numerical modeling,
optimization method, thermoelectric mechanism, or simply raising me up.
Last but not least, I would thank my family, especially my parents, for continuously
support, encouragement, and tolerance all the time.
v
TABLE OF CONTENTS
Page
LIST OF TABLES ............................................................................................................. vi
LIST OF FIGURES .......................................................................................................... vii
ABSTRACT ....................................................................................................................... ix
CHAPTER 1. INTRODUCTION ..................................................................................... 1
1.1 Thermoelectric Power Generation Theory. ............................................................... 1
1.2 Development of TEGs ............................................................................................... 5
1.2.1 TEG prototypes development .......................................................................... 5
1.2.2 Numerical modeling of TEGs .......................................................................... 6
1.3 Thermoelectric Materials and Modules ..................................................................... 7
1.4 Parametric/Topological Design and Optimization of TEGs ..................................... 8
1.5 Organization ............................................................................................................ 11
CHAPTER 2. MODELS AND METHODOLOGIES ................................................... 12
2.1 Numerical Model for TEGs ..................................................................................... 12
2.2 Optimization Methodology ..................................................................................... 19
2.2.1 Response surface method .............................................................................. 19
2.2.2 Genetic algorithm .......................................................................................... 23
2.2.3 Combined RSM-GA optimization algorithm ................................................ 24
2.3 Results of the Parametric Optimization Study ........................................................ 26
2.4 Summary ................................................................................................................. 37
CHAPTER 3. REGENERATIVE THERMOELECTRIC POWER GENERATION .... 38
3.1 Regenerative Concept Description .......................................................................... 38
3.2 Results on R-TEGs Performance ............................................................................ 43
3.3 Discussion on High Performance of R-TEGs ......................................................... 45
3.4 Summary ................................................................................................................. 50
CHAPTER 4. SINGLE MODULE TEG AND TEST RESULTS ................................. 51
4.1 Single Module TEG Setup ...................................................................................... 51
4.2 HZ-20 Module Test Results .................................................................................... 56
4.3 Temperature Distribution throughout the Single Cell TEG .................................... 60
4.4 Summary ................................................................................................................. 64
CHAPTER 5. CONCLUSIONS AND FUTURE WORKS ........................................... 66
5.1 Summary and Conclusions ...................................................................................... 66
5.2 Future Works ........................................................................................................... 67
LIST OF REFERENCES .................................................................................................. 69
vi
LIST OF TABLES
Table .............................................................................................................................. Page
Table 2.1. Baseline configuration. .................................................................................... 13 Table 2.2. TEM and packaging properties (Kumar et al., 2013a, 2013b). ....................... 17 Table 2.3. Design space and its discretization. ................................................................. 20
vii
LIST OF FIGURES
Figure ............................................................................................................................. Page
Figure 2.1. Schematic of baseline design of TEG based on a gas phase heat exchanger. .13 Figure 2.2. Finite volume discretization scheme. ..............................................................15 Figure 2.3. Thermal resistance network for TEM packaging. ...........................................16
Figure 2.4. Temperature dependent ZT of Bi2Te3/filled-skutterudite-based TECs. .........18 Figure 2.5. Design of experiments when k = 3. (a) Box-Behnken design; (b) Central
composite design. ...........................................................................................22 Figure 2.6. Flowchart of combined RSM-GA approach....................................................25
Figure 2.7. Convergence of combined algorithm. (a) Counter flow TEG; (b) Cross
flow TEG. .......................................................................................................28 Figure 2.8. 2-D projection of response surface near optimum for the counter flow
TEG. ...............................................................................................................30 Figure 2.9. 2-D projection of the response surface near optimum for the cross flow
TEG. ...............................................................................................................31 Figure 2.10. 2-D projection of response surface near optimum for the counter flow
TEG, width and length of the heat exchanger chosen as parameters. ............32
Figure 2.11. Performance of optimized counter flow TEG; (a) Temperature distribution
along the flow; (b) length based power density. 𝐴𝐻𝐸𝑋 = 0.38 m2,
AR = 2.0, 𝐻𝑇𝐸 = 8.0 mm. ..............................................................................33 Figure 2.12. Performance of the optimized cross flow TEG; (a) junction temperature
difference; (b) area based power density. 𝐴𝐻𝐸𝑋 = 0.33 m2, AR = 1.22,
𝐻𝑇𝐸 = 8.0 mm. ...............................................................................................34
Figure 2.13. Performance of TEMs between heat reservoirs with different 𝐻𝑇𝐸
(𝑇ℎ𝑜𝑡, 𝑟𝑒𝑠𝑒𝑟𝑣𝑜𝑖𝑟= 800 K, 𝑇𝑐𝑜𝑙𝑑, 𝑟𝑒𝑠𝑒𝑟𝑣𝑜𝑖𝑟= 300 K). ................................36
Figure 3.1. Schematics of an R-TEG (called R-TEG1). ....................................................41 Figure 3.2. Schematics of regeneration concept 2 (R-TEG 2). ..........................................42 Figure 3.3. Optimized power output of TEGs with different designs under varied cold
air supply. .......................................................................................................43 Figure 3.4. Heat transfer rate of different designs under varied cold air supply, when
power output is optimized. .............................................................................44 Figure 3.5. Regenerated air mass flow rate of TEGs of different designs and working
condition under varied cold air supply, when power output is optimized. ....45 Figure 3.6. The averaged Carnot efficiency of TEGs of different designs and working
condition under varied cold air supply, when the power output is
optimized. .......................................................................................................46
viii
Figure ............................................................................................................................. Page
Figure 3.7. Local ZT of TE materials in high-T TEGs along the flow path. For
mc=0.1, 1.0, 2.0, 3.0 kg/s. ..............................................................................47
Figure 3.8. Power output calculated by the numerical model and Eq. (3.1). Solid lines
are results using numerical model; dashed lines are results obtained using
Eq. (3.1). .........................................................................................................48
Figure 3.9. Efficiencies of high-T TEG and R-TEG 2. (a)1st Law efficiency;
(2) absolute efficiency. ...................................................................................49 Figure 4.1. System level flowchart single module TEG test rig. .......................................52
Figure 4.2. Schematics of single module TEG. .................................................................54
Figure 4.3. Photos of the experimental setup of single module TEG. (a) single module
TEG; (b) Coolant supply system. ...................................................................55
Figure 4.4. 𝛥𝑇𝑗 − Voc of HZ-20 TEM. ..............................................................................57 Figure 4.5. Electrical performance of HZ-20 TEM. (a) Internal electrical resistance;
(b) Maximum power output. ..........................................................................58 Figure 4.6. IV sweep and correction at junction temperatures of 210 – 122 °C. ...............59 Figure 4.7. Heat absorbed by the hot side of the HZ-20 TEM. .........................................60
Figure 4.8. Energy conversion efficiency of the HZ-20 module. ......................................60 Figure 4.9. Temperature along the hot stream in HHX. ....................................................61
Figure 4.10. Heat transfer rate from HHX and enters the TEM. .......................................62 Figure 4.11. Temperature distribution of the gas in HHX and the corresponding
points on the heat exchanging plate. ..............................................................63
Figure 4.12. Temperature distribution through the TEM package. ...................................64
ix
ABSTRACT
Huang, Shouyuan. M.S.M.E., Purdue University, August 2016. Parametric and Design
Analysis on Thermoelectric Generators. Major Professor: Xianfan Xu, School of
Mechanical Engineering.
In facing the limited energy source reserves and environmental problems,
thermoelectric generators (TEGs) are one of the promising waste heat recovery systems.
The modern TEGs for exhaust stream (e.g. from automobiles) can improve the fuel
economy by around 5%, taking advantage of the recent developed thermoelectric (TE)
materials.
In this work, we aimed at designing a TEG as an add-on module for a gas-phase heat
exchanger with maximized power output, and without negative impact (e.g. maintaining a
minimum heat dissipation rate from the hot side). We first developed a parametric
optimization algorithm using response surface method (RSM) and genetic algorithm (GA)
for the numerical model. The numerical model handles varied types of heat exchangers
(cross flow and counter flow) with the finite volume method and calculates the
thermoelectric modules (TEMs) with thermal resistance network analyses. TEMs based on
filled-skutterudite and bismuth telluride are used respectively in higher and lower
temperature regions. The RSM results also provide knowledge on sensitivity and
interaction of parameters. The combined RSM-GA optimization algorithm will be
x
generally useful for the parametric design of TEGs, especially before much knowledge
acquired on the TEG parameters.
The regenerative concept for TEG (R-TEG) is then introduced. Instead of developing
advanced high figure-of-merit (ZT) high-temperature TE materials, we use a gas phase heat
exchanger (precooler) to lower the temperature of the hot gas and at the same time
regenerate hot air from the cold air supply for Bi2Te3-based TEGs, avoiding the use of
high-temperature thermoelectric materials. It is found that the regenerative TEGs can
achieve a similar power output compared with TEGs using high-temperature TE materials
such as filled-skutterudites (combined filled-skutterudites and Bi2Te3-based TE materials),
by obtaining a higher heat scavenging rate. Thus, the regenerative TEGs also show a
similar absolute efficiency, defined according to the total available enthalpy from the hot
gas. This could represent a paradigm shift in the TEG research and development, that much
lower-cost, reliable, and readily available Bi2Te3-based materials and modules can be used
for high-temperature applications, and will ultimately enable the widespread deployment
of TEGs for real world waste heat recovery applications.
Lastly, a single module TEG is developed experimentally for both characterization of
TEMs and low-cost diagnoses of component performance inside TEGs. A commercialized
Bi2Te3-based module is tested. Temperatures along the streams and across the TEM
packaging are investigated. A better-defined single module TEG with internal detailed
information available can be used as a reduced size experimental model to validate the
numerical result.
1
CHAPTER 1. INTRODUCTION
The abundance of waste heat in prime mover engines and industrial processes has been
intriguing for a long time, particularly pertaining to the limited energy reserves and
environmental problems. In connection with these facts, thermoelectric generators (TEGs)
are currently of great interest as waste heat recovery systems. Using thermoelectric effects
of certain solid state devices, TEGs convert waste heat energy from exhaust or facilities
directly into electrical power output, and thereby improve the fuel economy for engines or
reduce electricity consumption for industrial equipment. Depending on the waste heat
source, TEGs are designed based on heat exchangers or constant temperature heat reservoir.
So far, TEGs are on the way to be available as a main-street application for waste heat
recovery. For example, TEGs for vehicles are now capable of generating large enough
current to charge the battery and improve fuel economy by around 5% (Bass et al., 2001;
Crane & LaGrandeur, 2010; Liu et al., 2015).
1.1 Thermoelectric Power Generation Theory.
The introductory thermoelectric generation theory can be found in the CRC
thermoelectric handbook (Rowe, 2005) or other similar literature. Thermoelectric effect
refers to the charge and energy flow carried by electrons under varied driving forces, and
can be phenomenologically elaborated into Seebeck, Peltier, and Thomson effect, without
2
going deep into solid state electron behavior. The Seebeck effect is the building up of
voltage driven by a temperature difference 𝑇ℎ and 𝑇𝑐 , characterizing by the Seebeck
coefficient 𝛼 = 𝑉/𝛥𝑇. The Peltier effect is a heat pumping process driven by an electrical
current, and the Peltier coefficient is defined by 𝜋 = 𝑞/𝐼. The Thompson effect relates to
the rate of generation of reversible heat q resulting from the passage of a current I along
the thermoelectric (TE) material, under a temperature difference 𝛥𝑇, that 𝑞 = 𝛽𝐼𝛥𝑇, in
which the 𝛽 is called Thompson coefficient. The three coefficients are correlated and
expressed again in Eq. (1.1)-(1.5). Eq. (1.4) and Eq. (1.5) are called the Kelvin relationships.
Note that, Eq. (1.1)-(1.3) are valid for both thermoelectric couples (TECs) and single
elements of TE material, while the subscript a and b in Eq. (1.5) are for the materials in
TECs.
𝑉 = 𝛼(𝑇ℎ − 𝑇𝑐) (1. 1)
𝜋 =𝑞
𝐼(1. 2)
𝑞 = 𝛽𝐼𝛥𝑇 (1. 3)
𝛼 = 𝜋/𝑇 (1. 4)
d𝛼
d𝑇=𝛽𝑎 − 𝛽𝑏𝑇
(1. 5)
In a thermoelectric generator, thermoelectric couples (TECs) fabricated from p-type
and n-type semiconductors are put between the heat source (𝑇ℎ ) and sink (𝑇𝑐 ). The
electrical resistance R and thermal conductance K of the TEC depend on the height of TEC
legs HTE and cross-section area ATE, which are shown in Eq. (1.6), (1.7), where 𝜎 is
electrical conductivity and k is thermal conductivity:
3
𝑅 =𝐻𝑇𝐸,𝑝
𝜎𝑝𝐴𝑇𝐸,𝑝+𝐻𝑇𝐸,𝑛𝜎𝑛𝐴𝑇𝐸,𝑛
(1. 6)
𝐾 =𝑘𝑝𝐴𝑇𝐸,𝑝
𝐻𝑇𝐸,𝑝+𝑘𝑛𝐴𝑇𝐸,𝑛𝐻𝑇𝐸,𝑛
(1. 7)
The heat absorbed from the hot side Qh and released to the cold side Qc can be
calculated by Eq. (1.8) and Eq. (1.9) respectively. The Seebeck coefficient is for a TEC
that 𝛼𝑇𝐸𝐶 = 𝛼𝑝 − 𝛼𝑛, and when applying Eq. (1.1) for a TEC, the V is the open circuit
voltage Voc that only depends on temperature difference:
𝑄ℎ = 𝛼𝑇𝐸𝐶𝑇ℎ𝐼 −1
2𝐼2𝑅 + 𝐾(𝑇ℎ − 𝑇𝑐) (1. 8)
𝑄𝑐 = 𝛼𝑇𝐸𝐶𝑇𝑐𝐼 +1
2𝐼2𝑅 + 𝐾(𝑇ℎ − 𝑇𝑐) (1. 9)
Here, the first terms in either equation are energy conversion due to thermoelectric
effect. The second terms are Joule heating that separates and goes to both junctions. The
third terms are the heat conduction by Fourier’s Law. Subtracting Eq. (1.8) and (1.9), and
using Ohm’s Law, the power output depends on the load resistance RL and is given by:
𝑊 = 𝑄ℎ − 𝑄𝑐 = 𝐼2𝑅𝐿 (1. 10)
Now, the efficiency of the power generation is given by:
𝜂 =𝑊
𝑄ℎ (1. 11)
4
Plugging 𝐼 =𝑉𝑜𝑐
𝑅+𝑅𝐿 into Eq. (1.10), it can be derived that the maximum power is
achieved by taking RL=R. While, the maximum efficiency can be evaluated by taking
d𝜂/dRL=0, and given by Eq. (1.12):
𝜂𝑚𝑎𝑥 = (1 −𝑇𝑐𝑇ℎ) ×
√1 + 𝑍�̅� − 1
√1 + 𝑍�̅� +𝑇𝑐𝑇ℎ
(1. 12)
The first term in the equation is Carnot efficiency 𝜂𝐶 , and thus, the exergy efficiency
of the device under a certain junction temperature difference is only dependent on a
combination term of 𝑍�̅�, referred to as the figure-of-merit. The �̅� is simply the mean
temperature within the TEC. Z for a TEC and a single element TE leg are, respectively,
𝑍𝑇𝐸𝐶 =𝛼𝑇𝐸𝐶2
[(𝑘𝑝𝜎𝑝)1/2
+ (𝑘𝑝𝜎𝑝)1/2
]
2 (1. 13)
𝑍 =α2𝜎
𝑘 (1. 14)
The ZT is a direct measurement of energy conversion ability of TE materials. Currently,
commercialized bismuth telluride TE materials have ZTs close to 1. Material science
developments especially nanotechnology have realized high-temperature TE materials
with even higher ZT, towards 2 (Poudeu et al., 2006; Venkatasubramanian et al., 2001; Wu
et al., 2014; Zhao et al., 2016).
A prevailing approach for TEG system engineering is to employ thermoelectric
modules (TEMs) as building blocks (Min, 2005). TEMs can be designed to offer varies
overall thermal and electrical performances with the same material to satisfy the different
5
working and output conditions. Designing the modules smartly is also proven to be an
approach for cost-effective performance in real world applications (Yee et al. , 2013).
1.2 Development of TEGs
1.2.1 TEG prototypes development
The famous radioisotope thermoelectric generator projects were dated back to the
1960s, merited for their system reliability in deep-space probing applications. The first
TEG waste heat recovery system was developed by Birkholz et al. (Birkholz et al., 1988)
with FeSi2 on a Porshe 944 engine, achieving 58W of power output. Over the years,
numerous attempts on TEG waste heat recovery systems, especially for vehicles have been
presented.
Prototypes were shown for diesel engines and gasoline engines or designed to be
integrated with the vehicle. Bass et al. (Bass et al., 1994; Bass et al., 2001) showed TEG
prototypes of heavy duty truck diesel engine that uses Bi2Te3 modules to generate 1 kW
during nominal working conditions. Ikoma et al. (Ikoma et al., 1998) applied Si-Ge
modules for a gasoline engine that generated up to 1.2 kW power output under a large
temperature difference of 563 K. Matsubara et al. (Matsubara et al. 2002) designed a TEG
with stacked modules based on filled-skutterudites and Bi2Te3 that operates between 350-
750C on a Toyota Estima. Hsu et al. (Hsu et al., 2011) provided more details for a low-
temperature TEG by combining experimental and numerical investigation. Karri et al.
(Karri et al., 2011) investigated TEGs for both a gasoline-fueled SUV and a compressed
natural gas engine based on Bi2Te3 and a quantum-well TE material and showed the special
features by comparison. Instead of recovering waste heat from the exhaust, Kim et al. (Kim
6
et al., 2011) tried a design of TEG on the radiator of an SUV. It showed a simple system
design but a low power output of 75 W. Crane and collaborators (Crane et al., 2013)
showed a long-term development project on on-vehicle TEG and summarized their
roadmap, which is valuable for TEG engineering code establishment in the future. Schock
et al. (Schock et al., 2013) explored jet-impingement-based TEGs for trucks, which may
be promising for a leap for high performance due to the high heat transfer coefficient,
despite the difficulty of realization and large back pressure. Deng and collaborators started
with heat exchangers and cooling system design and integration strategies (Deng et al.,
2015; Qiang et al., 2016; Su et al., 2015), and showed a unique designed prototype
generating power up to 944W (Liu et al., 2015). Zhang et al. (Zhang et al., 2015) applied
nanostructured half-Heusler to a GMC truck diesel engine and achieved 1 kW in their
testing. Another two-staged TEG for diesel engine recently reported achieving 5.35%
energy efficiency (Liu et al., 2016).
Attempts were also made on turbines (Yazawa et al., 2013; Yodovard et al., 2001) and
industrial waste heat (Ebling et al., 2016; Ota et al., 2006). However, not as many results
were presented as for vehicles.
1.2.2 Numerical modeling of TEGs
Alongside with the testing of prototypes, numerical models also played a role in the
TEG designs. Models with varied sophistications have been developed depending on the
level of investigation and computational resource. An earlier work by Esartea et al. (Esarte
et al., 2001) modeled the heat exchangers using the ϵ-NTU method, and illustrated the
effects of heat exchanger flow patterns on TEG performance. A one-dimensional (1-D)
7
model along the flow path with given heat transfer coefficient provides knowledge on
temperature distribution along the stream and across the TEMs, and evaluates the TEG
performance in different conditions and designs (Kumar et al., 2013a, 2013b). The model
is also capable of calculating pressure drops in the heat exchangers. Three-dimensional (3-
D) modeling for a jet impingement heat exchanger was established to investigate heat
transfer enhancement of a conjugate heat transfer model of a TEG (Hu et al., 2009).
Thermal resistor network analysis for TEMs is often used for computational efficiency, in
which the power output can be obtained from the junction temperatures (Hsiao et al., 2010;
Omer & Infield, 1998; Yu & Zhao, 2007), bypassing an equivalent resistor (Kumar et al.,
2013a, 2013b), or more rigorously by applying the quadrupole method (Ezzahri et al.,
2005). Integral properties (Kumar et al., 2015) and meshed models (Shih & Hogan, 2005)
for TEC give more accurate results for TEM performance. However, the latter is
computationally too expensive for a full-sized TEG model. Transient models were also
developed for simulating variable working conditions and start-up performance (Crane,
2011; Yu et al., 2015). Besides, models based on different consideration are also developed
for fast evaluation the TEG performance in certain conditions (Zhang, 2016).
1.3 Thermoelectric Materials and Modules
The thriving of TEGs research and development is accompanied and supported by the
advances of novel TE materials. Now we have a wide spectrum of TE material available
for TEG applications in different temperatures. Bismuth telluride (family) materials
showed not only high ZT but also reliability and commercial availability for lower
temperature applications from room temperature to around 250 °C (Venkatasubramanian
8
et al., 2001; Zhao et al., 2005). Filled-skutterudites are the favorable material in a higher
temperature range between 250-550 °C (Sales et al., 1996). Half-Heuslers are now believed
to be the choice for even higher temperatures (Joshi et al., 2014; Poon, 2001), while other
types of materials including Si-Ge (Dresselhaus et al., 2007; Garg et al., 2011; Vining,
1995), oxide (Koumoto, 2005), and other materials (Pei et al., 2011; Voneshen et al., 2013;
Zhao et al., 2016) may still be competitive in the similar temperature range.
The aforementioned TE materials can synergize by using varied types of modules along
the heat exchanger flow path (Crane & LaGrandeur, 2010; Kumar et al., 2013b), or
different materials along the TEC legs (Crane, 2011) (called segment TEC or cascade
design). Stacking up TEMs may also be an option, so that each material can operate in its
own temperature range.
1.4 Parametric/Topological Design and Optimization of TEGs
Once the material is chosen, geometric parameters, including TEC cross-section area
and height, filling factor of TECs in TEMs, and the heat exchanger length and width, are
the dominant factors to the TEG performances. It is also worth noting that, though the
power output or energy conversion efficiency is the most important feature of a TEG, there
are also characteristics including thermal stress, mechanical and chemical stability,
pressure budget, minimum heat transfer requirements, cost-effective merits, etc. that
determine whether or not the TEG can be commercialized. New concepts may be especially
beneficial for resolving these concerns in additional to the parametric optimization.
9
Parametric design can be difficult since the heat transfer and thermoelectric principles
do not give us direct answers when multiple mechanisms influencing the performance at
similar magnitudes.
Running through all possible combinations of parameters is a straightforward approach
which is easy to implement, and provide enough (in fact, too many) data for analysis.
However, it is too expensive for multiple parameter investigation, and the usage is often
limited to initial single parameter analysis.
Response surface methodology (RSM) is a statistical procedure that is useful in both
optimization and parametric analysis (Montgomery, 2008). This method starts with design
of experiments (DOE), which helps obtaining a better local fitting model of the
performance with respect to the parameters, called response surface, with fewer
experimental/simulation data. The fitted response surface then can be used for optimization
with an iterative process, or sensitivity and interaction analysis among the parameters at
the vicinity of specific interested designs. However, single thread searching with the fitted
response surface model does not guarantee to find the global maximum and effectiveness
of multiple-threading largely depends on experience and knowledge of the problem.
Several works applied the RSM to the TEG design at the final stage of optimization to
analyze the parametric interactions and multi-objective investigation (Fateh et al., 2014;
Qiang et al., 2016; Su et al., 2015). It is also provided as an optimization tool in ANSYS
Workbench. The detailed procedures will be introduced in Section 2.2.
Global optimization algorithms are introduced to get rid of local extrema, and most of
which are inspired by natural process. For example, simulated annealing, particle swarm
optimization, genetic algorithm etc. These algorithms generally lack mathematical
10
convergence verification and require proper algorithm parameters input to reach global
optimum. Here we introduce the genetic algorithm, which is popular in thermal system
design (Fabbri, 1997; Gosselin et al., 2009), including thermoelectric generators
(Heghmanns & Beitelschmidt, 2015; Qiang et al., 2016; Su et al., 2015). Other global
optimization algorithms would also reach global optimum given proper algorithm
parameters. The genetic algorithm simulates the genome propagation and evolution in
nature. Designs are treated as individuals and the parameters are discretized into 0/1 digits
as genes. In each iteration, called generation, designs (individuals) experience crossover
and mutation with certain probabilities, as the real individuals do in nature. By assigning
the higher performance designs with higher fitness (more likely to survive), the optimum
design can be found. However, the genetic algorithm, as well as other nature-inspired
global algorithms, merely gives any knowledge other than the optimum design.
A combined RSM-GA algorithm is developed (Huang & Xu, 2016), which guarantees
the globality and explores the knowledge of the parameters. The algorithm is applied to
optimize the parameters in all the design problems in the thesis.
In additional to parametric analysis, topological studies are also important in the design
process for it shifts the upper limits and may address other concerns qualitatively. Kumar
et al. (Kumar et al., 2013b) studied different types of heat exchangers and concluded that
transverse heat exchanger based TEG is the most suitable for certain automobile
application. Other works (He et al., 2016; Kim & Kim, 2015; Meng & Suzuki, 2015; Qiang
et al., 2016) include designing special TEC legs or cooling elements to resolve thermal
stress, cost-effectiveness or other concerns. Also, different configurations of TEMs in a
TEG has been investigated (Favarel et al., 2015). This thesis will introduce a regeneration
11
concept of TEGs (R-TEG) in Chapter 3 that generates a similar power output to the varied
modules design using only bismuth telluride modules, while guaranteeing a larger heat
dissipation rate. The sole usage of low-temperature TEMs eliminated many reliability and
cost-effective problems.
1.5 Organization
The thesis focuses on investigation and improving performance through design and
parametric optimization of TEGs based on gas phase heat exchangers. Chapter 2 introduces
the numerical model and the combined RSM-GA optimization algorithm. The model and
the algorithm are then used to obtain the optimum design of a TEG as an add-on of a gas
phase heat exchanger, with constraints of geometry and heat transfer performance. Chapter
3 proposes the regenerative concept of TEGs. The R-TEG is optimized and compared with
previous TEG design using both high and low-temperature modules (high-T TEG) under
varied coolant supply, showing the R-TEG is capable of serving as a reliable and low-cost
alternative for certain waste heat recovery applications. Chapter 4 describes a single
module TEG test rig. Test results of a Bi2Te3 module are shown, as well as the temperature
measurements for the entire rig. Chapter 5 concludes the thesis works and provide
suggestion on future works.
12
CHAPTER 2. MODELS AND METHODOLOGIES
In this chapter, a combined optimization algorithm introduced, along with the
numerical model for performance calculation of designed TEGs. The algorithm applied
response surface analysis and genetic algorithm, providing optimizing speed, sensitivity
and interaction analysis, and globality, which is generally useful for optimizing heat-
exchanger-based TEGs. The revised numerical model is capable to simulate TEGs with 2-
D heat exchanger model on both side of the TEMs. This chapter is based on a published
work (Huang & Xu, 2016) with permission to reuse the work (Springer, 3901690971966).
2.1 Numerical Model for TEGs
A numerical model for TEGs with a plug-flow model for hot side gas phase heat
exchanger and thermal resistance analysis for TEMs has been used in previous geometric
optimization and topological study (Kumar et al., 2013a, 2013b), and is available in our
group. The numerical model in this work is revised based on the abovementioned model.
Four layers of 2-D finite volume model is developed for fluid flow and metal heat
conduction on both sides of the heat exchanger.
The baseline model is shown in Fig. 2.1. The hot air from a heat source and the cold
air with the ambient temperature are pumped into a cross flow heat exchanger. The inlet
13
temperatures of hot and cold channels are fixed in the current study as listed in Table 2.1.
Conduction in the heat exchanger is assumed only within the copper walls (brown in Figure
2.1). TEMs are allocated between the heat exchanging surfaces. Two types of TEMs,
bismuth telluride and multiple-filled skutterudite, are selected respectively for lower and
higher temperature regions. The rest is filled with insulation blankets. A steady state
working condition is studied. A similar design of TEG for a counter flow heat exchanger
is also investigated for comparison.
Figure 2.1. Schematic of baseline design of TEG based on a gas phase heat exchanger.
Table 2.1. Baseline configuration.
Parameter Value unit
Inlet temperature (hot) 800 K
Inlet temperature (cold) 300 K
Heat transfer coefficient (hot) 2500 W/m2K
14
Table 2.1. Continued.
Parameter Value unit
Heat transfer coefficient (cold) 2200 W/m2K
Mass flow rate (hot) 0.1 kg/s
Mass flow rate (cold) 0.1 kg/s
Air property Ideal gas formulation
Heat exchanger wall (copper) thickness 0.008 m
Thermal conductivity of copper 401 Wm−1𝐾−1
Heat exchanger area (𝐴𝐻𝐸𝑋) 0.12 m2
Aspect ratio (AR) 0.75 -
Heat exchanger height 0.05 m
Height of TEC legs (𝐻𝑇𝐸) 4 mm
The discretization scheme of finite volume model is illustrated in Figure. 2.2. Four
layers of 2-D finite volume models are developed for hot side fluid (subtitle h in Figure
2.2, same below), hot side metal liner (hl), cold side metal liner (cl), and cold side fluid (c),
respectively. Due to the small thickness and high conductivity of the metal liners, single
layer of grids gives satisfying result according to the grid independent test. The subscript
W, P, E (also N, S, not showing in Figure 2.2) are indicator of neighboring relationships of
the control volumes according to finite volume method conventions. Ds and Fs are
diffusion and advection terms that connect the control volumes within the same layer. The
fluid and liner grids interact according to the convection coefficient and one half of the
cross-plane conductance of the liner, by treating each other as the explicit source terms.
15
The heat transfer rates that enter and leave the TEMs are calculated from thermal resistance
network analysis and exerted to the liner grids as source terms (Qh, Qc in Figure 2.3).
Figure 2.2. Finite volume discretization scheme.
The thermal resistance network is illustrated in Figure 2.3 and solved by inverting
matrices. Iterations are required to update the temperature dependent properties. T2 and T3
are referred to as the hot and cold side junction temperature of the TEM. The thermal
resistance RTEM electrical power generation Pel and is calculated at the maximum power
point of the given junction temperatures using integral averaged properties (including
Th,P Th,ETh,W
Thl,W Thl,P Thl,E
ℎ,
ℎ,
ℎ,
ℎ,
ℎ , ℎ ,
…
…
…
…
Tc,P Tc,ETc,W
Tcl,W Tcl,P Tcl,E 𝑐 ,
𝑐,
𝑐 ,
𝑐,
𝑐, 𝑐,
…
…
…
…
Thermal resistor model
16
Seebeck coefficient 𝛼, electrical conductivity 𝜎, and thermal conductivity k). For example,
the integral averaged Seebeck coefficient between TH and TC is given by:
�̅�𝑛,𝑝(𝑇𝐻, 𝑇𝐶) =∫ 𝛼𝑛,𝑝d𝑇𝑇𝐻𝑇𝐶
𝑇𝐻 − 𝑇𝐶(2. 1)
The rest of the packaging thermal resistance are calculated according to the material
properties listed in Table 2.2. The module and packaging design is adapted from Ref.
(Kumar et al., 2013a, 2013b) and the thermoelectric properties are taken from Ref. (Rogl
et al., 2010; Tang et al., 2005; Zhao et al., 2005). The Rload is an equivalent thermal resistor
that extracts a Pel amount of energy (as heat) from the TEM without effecting the actual
heat transfer through the other thermal resistors. This scheme gives more accurate results
on the heat transfer and power generation but requires more iterations.
Figure 2.3. Thermal resistance network for TEM packaging.
Thl T1
Rliner1/2 Rinterface Rceramic
T2
RTEM Rceramic Rinterface
T3 T3 Tcl
Rliner1/2
Rrad,TEM
Rrad,insulateRinsulate
Rload
Pel
Qh Qc
17
Table 2.2. TEM and packaging properties (Kumar et al., 2013a, 2013b).
Parameter Value unit
Skutterudite module:
Module (length, width, height) (0.0508, 0.0508, 0.007) (m, m, m)
TEC (No. of TEC, length, width, height) (32, 0.004, 0.004, 0.004) (-, m, m, m)
𝜀𝑀𝑜𝑑𝑢 (ceramic) 0.55 -
Bismuth telluride:
Module (length, width, height) (0.04013, 0.04013, 0.004) (m, m, m)
TEC (No. of TEC, length, width, height) (127, 0.002, 0.002, 0.002) (-, m, m, m)
𝜀𝑀𝑜𝑑𝑢 (ceramic) 0.55 -
Thermal grease (Grafoil laminate)
thickness
0.001 m
Thermal grease conductivity 5 Wm−1𝐾−1
Thermal insulation (Min-K, Morgan
Advanced Materials Inc.) thickness
0.002 m
Thermal insulation conductivity 0.0334 Wm−1𝐾−1
𝜀𝐼𝑛𝑠𝑢 𝑎𝑡𝑖𝑜𝑛 0.75 -
The heat transfer coefficient h is chosen based on a typical intermittent corrugated plate
heat exchanger (Kays & London, 1984). h varies with the Reynolds number Re, thus varies
with the channel width 𝑑 and the mass flow rate �̇� as given in Eq. (2.2). The subscript 0
denotes reference values according to the baseline design. The value 0.35 is from the
18
regression of a similarly structured heat exchanger, according to its dependence on
Reynolds number Re, for equivalent Re between 1000 to 15000.
h = h0 (𝑅𝑒
𝑅𝑒0)0.35
= h0 (�̇�𝑑0�̇�0𝑑
)0.35
(2. 2)
The aspect ratio AR is defined as the ratio between the length along the hot air flow
direction to that across the hot air flow direction. This model assumes that TEMs cover 80%
of the total area, and the rest is covered by insulation material. The model considers both
conduction and radiation, and ε is the emissivity of ceramic/insulation surfaces.
The TE materials used in this work are from Ref. (Rogl et al., 2010; Tang et al., 2005;
Zhao et al., 2005) with their ZTs plotted in Figure 2.4.
0.2
0.4
0.6
0.8
1
1.2
1.4
200 300 400 500 600 700 800 900
Bi2Te
3
Skutterudite
ZT
(-)
Temperature (K)
Figure 2.4. Temperature dependent ZT of Bi2Te3/filled-skutterudite-based TECs.
19
In practice, the heat-exchanger-TEM can be stacked according to the space limitation.
In this way, the insulation problem of heat exchangers is easier to deal with. The stacked
design can be simulated by simply scaling up the current model.
2.2 Optimization Methodology
In this section, two optimization methods are introduced and a combined algorithm of
these two is designed. The response surface method locally fits the data and performs a fast
searching process for the optimum, and sensitivity and interaction analysis at the same time.
However, it doesn’t guarantee the global optimum. Genetic algorithm is introduced for
global optimization.
2.2.1 Response surface method
The response surface methodology (RSM) (Box & Hunter, 1957; Montgomery, 2008)
is a collection of statistical techniques for modeling and analyzing problems in which the
response of interest is affected by several variables. RSM has been used to analyze both
experimental and simulation results. By fitting the results of a limited number of sample
points, a response model can be developed. Optimization and sensitivity analysis can be
achieved through this model.
In a physical model, as shown in Eq. (2.3), objective functions 𝑦𝑗 (total number p) are
determined by factors 𝑥𝑖 (total number k), forming 𝑝 number of k-dimensional surfaces in
(𝑘 + 1)-dimensional spaces. In this study, the total power output is assigned to be the
objective function (𝑝 = 1), and 𝑘 = 3 factors are the heat exchanger area 𝐴𝐻𝐸𝑋, the aspect
ratio AR, and the height of TE leg 𝐻𝑇𝐸. Possible combinations of these three factors are
20
referred to as the design space, and any combination is called a design. Here, one possible
design space of heat-exchanger-based TEG is studied for example. The upper and lower
limits of each factor are listed in Table 2.3. The minimum heat dissipation rate from the
hot side is set to 20 kW (Table 2.3). These define the design space of this study. The result
of this optimization will be shown in Section
𝑦𝑗 = 𝑓𝑖(𝑥1, … , 𝑥𝑘) + 𝜖; 𝑗 = 1,… , 𝑝 (2. 3)
Table 2.3. Design space and its discretization.
Factor Unit Step Lower limit Upper limit GA digits
𝐴𝐻𝐸𝑋 m2 0.02 0.08 0.4 6
𝑙𝑛 (𝐴𝑅) - 0.05 -0.7 0.7 6
𝐻𝑇𝐸 mm 0.2 1.5 8 6
Minimum heat dissipation 20 kW
Because of the lack of analytical solutions, the response model 𝑓 is obtained by fitting
simulation results with certain types of functions, and the error 𝜖 accounts for both
numerical and fitting errors. Instead of calculating the absolute value, we use the Pearson
correlation coefficient r2 to show the relative significance of fitting error.
A large amount of data and a complicated fitting function are usually required to
perform a fitting for the entire design space. To simplify, we use either linear (Eq. (2.4)),
or second order (Eq. (2.5)) polynomials as the local fitting function at a design’s
neighborhood. The fitting coefficients 𝛽 are obtained by the least square method.
21
𝑓 = 𝛽0 +∑ 𝛽𝑖𝑥𝑖3
𝑖=1 (2. 4)
𝑓 = 𝛽0 +∑ 𝛽𝑖𝑥𝑖3
𝑖=1+∑ 𝛽𝑖𝑖𝑥𝑖
23
𝑖=1+ ∑ 𝛽𝑖𝑗𝑥𝑖𝑥𝑗1≤𝑖<𝑗≤3
(2. 5)
The locally fitted model is only valid within a small region in the design space. We
select appropriate steps for the factors 𝛥𝑥𝑖 so that the response model is fitted, and thus
valid, within the 3-D design region of [𝑥𝑖𝑛 − 𝛥𝑥𝑖, 𝑥𝑖
𝑛 + 𝛥𝑥𝑖]. The superscript n indicates
the n-th step during the optimization process. The steps also determine the updating of
design 𝑥𝑖𝑛 during the optimization process, i.e. the differences of 𝑥𝑖
𝑛 and 𝑥𝑖𝑛+1, or two 𝑥𝑖
𝑛
between two consecutive sub-steps (described later in steepest ascent) are less than or equal
to 𝛥𝑥𝑖. The choice of steps is a balance of resolution and convergence speed, also regarding
the size limitation of manufacturability. For this study, the step selections are listed in Table
2.3.
To obtain an effective and efficient fitting model around a design, the method of design
of experiments (DOE) (Montgomery, 2008) is used. In one DOE set, different values of a
factor, called levels, are used. For example, a 3-level DOE for 𝐻𝑇𝐸 centered at the baseline
design is 𝐻𝑇𝐸 = 3.8, 4.0, 4.2 mm according to its size of the step. Moreover, instead of
running through all combinations of the 3-factor-3-level DOE, numerical simulation is only
performed for the design points shown in Figure 2.5, and the results can still produce an
effective fitting function. The Box-Behnken design (Figure 2.5 (a)) and the central
composite design (CCD) (Figure 2.5 (b)) can be applied to both first and second order
model. In these design patterns, the CCD has 2xk outreaching levels, shown as the six nodes
out of the cube (k = 3) in Figure 2.5 (b), to obtain better prediction (Montgomery, 2008).
22
In each DOE for fitting, the center level is taken according to the existing design. The +1
and -1 levels (Figure 2.5) for each factors are given by 𝑥𝑖0 + 𝛥𝑥𝑖 and 𝑥𝑖
0 − 𝛥𝑥𝑖, and the
outreaching levels for CCD (Figure 2.5 (b)) are chosen as 𝑥𝑖0 ± 1.5𝛥𝑥𝑖.
Figure 2.5. Design of experiments when k = 3. (a) Box-Behnken design; (b) Central
composite design.
The RSM optimization operates in a sequential manner. The initial design, possibly
being far from the optimum, is fitted with the linear model and optimized with steepest
ascent, i.e. finding the gradient of the local fitting function ∇𝑓, and generating new designs
according to the direction till the increment of objective function of each step is less than
30% of that of the first step. One step of each factor in steepest ascent takes at most the
step size defined earlier. This process provides a faster converging rate since it allows the
design parameters to change by multiple steps after one fitting. The response surface is
fitted with the second order model when it is closer to the optimum. The second order
model is also used for sensitivity analysis. In some problems, the objective function (the
𝑥1
𝑥2
𝑥3
-1
+1
+1-1-1
+1
(a)
𝑥1
𝑥2
𝑥3
-1
+1
+1-1-1
+1
(b)
23
power output in this study) will be much higher when two factors have a particular relation,
and much lower when they are out of the relation. This kind of response is called a ridge
system (Montgomery, 2008) for the shape of the response surface, indicating a particular
interaction mechanism of factors dominating the performance. A ridge system can be
identified by canonical transformation, and the transformation result can provide ideas to
find the physical mechanism that explains how the certain combination of factors
dominates the performance. In this study, 𝐴𝐻𝐸𝑋 is one of the dominant factors for the power
output since it directly determines the total heat transfer rate. Based on this consideration,
𝐴𝐻𝐸𝑋 and the AR are chosen as the factors instead of length and width of the heat
exchangers channels. It is also found that the interaction of 𝐴𝐻𝐸𝑋 and HTE also forms a
ridge system. The details will be discussed in Section 2.3.
2.2.2 Genetic algorithm
Genetic algorithm (Man et al., 1996; Whitley, 1994) is used as a global optimization
tool to verify the globality of the RSM results. Inspired by the evolution and nature
selection, a particular design is referred to as an individual, its objective function as fitness,
and the group of individuals as the population of one generation. The design space is
discretized into binary genome series, indicated by GA digits in Table 2.3. New individuals
are reproduced by combining genomes of the best individuals selected from the previous
generation. This process, called crossover, preserves the possible features with better
fitness, which is the higher power output in this case. Diversity is achieved by the mutation
process that randomly flips several binary digits of genomes to create new individuals to
avoid local optimum. These processes are implemented by preset probabilities.
24
2.2.3 Combined RSM-GA optimization algorithm
In the combined RSM-GA optimization algorithm, the RSM is applied as mentioned in
Section 2.2.1. While, GA treats only the central nodes of designs in each DOE step as
individual and produce diverse designs of central nodes. The optimization process is
directed by the single step RSM results, and GA is applied to verify the globality.
The procedure of the combined RSM-GA optimization is shown in the flowchart in
Figure 2.6 and described as follows. Initially, ten designs including the baseline design are
generated forming the first generation. The number of individuals is chosen based on the
prior knowledge that the response surface has few local maxima, that several trials from
different initial designs with RSM only gave the same optimum design. A lower crossover
coefficient (0.5) and a higher mutation coefficient (0.1) than recommended value are used,
so that the GA converges slower and runs enough generations to guarantee the globality.
The response surface in the neighborhood of each individual is fitted only once per
generation. It is first fitted with the linear model and optimized by steepest ascent. The
second order model is used when the power output of the design at the center point is higher
than all other points on the edge, or when the linear model shows poor goodness-of-fitting,
𝑟2 < 0.85. Then, the next generation is generated based on the nearest neighbors in GA
discretized design space of the steepest ascent results and the crossover and mutation rule.
In each step, the designs closed to each other merge into one, and the design gives heat
dissipation lower than the constraint is naturally selected out. GA stops when the
successive three iterations give improvement smaller than a given tolerance (𝛥𝑃 < 5W).
The response surface in the neighborhood of the optimized design in the last generation is
25
then fitted using the second order model, and additional iterations are taken until the
predicted power output by the second order model is within a given tolerance (𝛥𝑃 < 0.1W).
Figure 2.6. Flowchart of combined RSM-GA approach.
Generate initial designsGenerate Box-Behnken
design for each designs
Fit with linear model
Fitting
satisfied?
Steepest ascent
Fit with 2nd-order
model, optimize within
[𝑥𝑖0 − 𝑥𝑖 ,𝑥𝑖
0 + 𝑥𝑖]
Merge/discard if any
𝑃 <
GA crossover and
mutation
CCD design, 2nd order
model. Iterate till
prediction satisfied
No
Yes
No
Yes
26
2.3 Results of the Parametric Optimization Study
According to similar works (Kumar et al., 2013a, 2013b) and our initial calculation
results, grid independence of 2-D heat exchanger model is satisfied when the grid size is
smaller than 3 mm. On the other hand, the validity of the 1-D conduction thermal resistor
network model for the TEC legs requires small temperature gradient across the cross-
section of a leg, which is true for all the cases in this study. The leg cross-section size of
Bi2Te3 (2mm × 2mm, Table 2.2) is chosen to be the grid size for calculation.
Figure 2.7 illustrates the results of the combined RSM-GA optimizing process. In
Figure 2.7 (a), for the counter flow TEG case, the first 20 pairs of circles and diamonds are
respectively, the best individuals of every generation and the averaged performance of
individuals in each generation. The trend of converging of the averaged performance
indicates that the global response surface is rather smooth. It is also observed that the
change between iterations is smaller when the output power is closer to the neighborhood
of optimum. In fact, the global response surface in the current study is a highly ridged
system. The larger curvature of the response surface model at the ridge near the optimum
results in a poor fitting of the linear model so that we use the second-order model to
approach the optimum in the combined optimization process. The last four circles represent
results of optimization process using the second-order model for response surface fitting.
The response surface is well-fitted at the optimum, with 𝑟2 = 0.94. The optimized design
for the counter flow case has 𝐴𝐻𝐸𝑋 = 0.38 𝑚2, AR = 2.0, and 𝐻𝑇𝐸 = 8.0 𝑚𝑚, giving a
power output of 1.454 kW and a heat dissipation rate of 27.42 kW. The masses of
skutterudite and Bi2Te3 are 3.2 kg and 2.7 kg, respectively.
27
A similar convergence of optimization results is shown in Figure 2.7 (b) for the cross
flow TEG. The converging trend of averaged performance towards the best individuals is
also noticeable, but not as much as the case for counter flow TEGs. This indicates that
some individuals have much worse performance. The response surface forms a steeper
peak at the neighborhood of the optimum, and the high-performance designs exist in a
smaller region. This phenomenon can be conceptually estimated by the fact that a random
combination of cross flow TEGs parameters is very likely to reduce the higher power
density region and result in a low power output. The higher merging ratio during the RSM-
GA process can also infer this phenomenon, because the individuals are more likely to
gather in the design space when high-performance designs are in a more confined region.
The response surface is fitted at the optimum with 𝑟2 = 0.90. The optimized design for a
cross flow TEG is 𝐴𝐻𝐸𝑋 = 0.33 𝑚2, AR = 1.2, 𝐻𝑇𝐸 = 8.0 𝑚𝑚, giving a power output of
1.298 kW and a heat dissipation rate of 23.43 kW. The masses of skutterudite and Bi2Te3
are 2.8 kg and 2.4 kg, respectively.
The response surfaces in the neighborhood of optimum are visualized in Figure 2.8 and
Figure 2.9. In each plot, one of the three parameters is fixed at the value of the optimized
design. The response models are developed by fitting the numerical results in regions larger
than those defined by the step sizes, introducing limited errors of fitting (𝑟2 > 0.85 for
both cases) to illustrate the interaction and sensitivity of factors in these larger regions.
28
Figure 2.7. Convergence of combined algorithm. (a) Counter flow TEG; (b) Cross flow
TEG.
It can be seen in Figure 2.8 (a) that by selecting the area 𝐴𝐻𝐸𝑋 and the aspect ratio AR
of the heat exchanger, instead of the lengths along and across the flow, as the design
parameters, the objective function is close to the canonical form. The gradients and the
0.9
1
1.1
1.2
1.3
1.4
1.5
0 5 10 15 20 25
Best fitness
Mean fitness
P (
kW
)
Generation / Iteration
(a)
0.8
0.9
1
1.1
1.2
1.3
0 5 10 15 20 25 30 35
Best fitnessMean fitness
P (
kW
)
Generation / Iteration
(b)
29
contour lines are approximately parallel or perpendicular to the parameter axes. Otherwise,
it will be harder to identify the optimum and sensitivity features in the ridge system of the
width-length design space (Figure 2.10.). Also, the interaction with 𝐻𝑇𝐸 will be abstruse if
width and length are chosen to be the parameters for the heat exchanger. Thus, Figure 2.8
(a) clearly shows that at a given 𝐻𝑇𝐸 , the 𝐴𝐻𝐸𝑋 has an optimized value, which is
approximately independent of AR. The power output increases with the aspect ratio,
because the higher aspect ratio results in a larger velocity in the heat exchanger and thus
enhance the heat transfer. This selection of parameters also improves the performance of
GA since the crossover process is more efficient when the genomes are representing
orthogonal factors. The statements above are also true for cross flow TEGs in Figure 2.9
(a), except for that AR is much less sensitive than 𝐴𝐻𝐸𝑋. This is because when convection
heat transfer is enhanced by flow speed on one side, it is reduced on the other side.
Another ridge system can be observed from Figure 2.8 (b) and Figure 2.9 (b). Here, the
power output is sensitive to both 𝐴𝐻𝐸𝑋 and 𝐻𝑇𝐸 . A synergic increase of 𝐴𝐻𝐸𝑋 and 𝐻𝑇𝐸
results in larger power output, while either increasing or decreasing one parameter with the
other fixed leads to a lower power output. Roughly, there is a line in the design space along
which direction the response surface has the smallest curvature and directional derivative.
The optimum is expected to be the intersection of this line and the pre-set limits. The
optimization under the specific constraints leads 𝐻𝑇𝐸 to its upper limit for both types of
TEGs. Also, we can simply search along this line for other optimums under different
dimensional constraints. For example, introducing cost-per-watt as a penalty function can
avoid optimized 𝐴𝐻𝐸𝑋 and 𝐻𝑇𝐸 becoming too large.
30
Figure 2.8. 2-D projection of response surface near optimum for the counter flow TEG.
31
Figure 2.9. 2-D projection of the response surface near optimum for the cross flow TEG.
32
Figure 2.10. 2-D projection of response surface near optimum for the counter flow TEG,
width and length of the heat exchanger chosen as parameters.
In the neighborhood of optimum, 𝐻𝑇𝐸 appears to have a similar level of sensitivity in
comparison to 𝐴𝐻𝐸𝑋 and is more sensitive than aspect ratio, as shown in Figure 2.8 (c) and
Figure 2.9 (c). However, during steepest ascent, the gradient fraction for 𝐻𝑇𝐸 can be over
two orders of magnitudes larger than that of the area, and nearly four orders of magnitudes
larger than that of the aspect ratio. When the resistance of TEC roughly equals to the
package and interface resistance, the junction temperature difference is very sensitive to
𝐻𝑇𝐸. Thus a small change of 𝐻𝑇𝐸 makes a noticeable difference in the power output, and a
small step size should be used to investigate the factor of 𝐻𝑇𝐸. In this work the step size of
the height of TEC leg is set to 0.2 mm, considering the accuracy can be achieved in
manufacturing.
The temperature distribution and power density of optimized designs for both types of
TEGs are shown in Figure 2.11 and Figure 2.12. As shown in Figure 2.11 (a), the
temperature difference between the hot and the code sides is nearly a constant. The junction
33
temperature difference is slightly smaller because of the axial conduction. 𝐻𝑇𝐸 has a trade-
off that a larger leg height results in a larger junction temperature difference but a less heat
flow rate and, therefore, less power output, and vice versa. When the hot and cold side
temperatures of heat reservoirs are fixed, the optimized 𝐻𝑇𝐸 has a thermal resistance
approximately equal to that of the interface and packaging materials, i.e. the junction
temperature difference is approximately a half of that between the reservoirs (Figure 2.13).
Single variable optimization of 𝐻𝑇𝐸 with other parameters fixed also shows the existence
of an optimized 𝐻𝑇𝐸. However, when 𝐴𝐻𝐸𝑋 and 𝐻𝑇𝐸 are free to vary at the same time, an
increment of the area can always provide a higher heat flux and an increase of 𝐻𝑇𝐸 can
always give a larger temperature difference. The 𝐻𝑇𝐸 is optimized to its upper limit in this
study.
Figure 2.11. Performance of optimized counter flow TEG; (a) Temperature distribution
along the flow; (b) length based power density. 𝐴𝐻𝐸𝑋 = 0.38 m2, AR = 2.0, 𝐻𝑇𝐸 = 8.0
mm.
300
400
500
600
700
800
900
1000
0 0.2 0.4 0.6 0.8 1
Thot
Tcold
TTEMhot
TTEMcold
Thot (
K)
x (m)
(a)
34
0
500
1000
1500
2000
2500
0 0.2 0.4 0.6 0.8 1
Power density (W/m)Po
we
r de
nsity (
W/m
)
x (m)
(b)
Figure 2.11. Continued.
Figure 2.12. Performance of the optimized cross flow TEG; (a) junction temperature
difference; (b) area based power density. 𝐴𝐻𝐸𝑋 = 0.33 m2, AR = 1.22, 𝐻𝑇𝐸 = 8.0 mm.
35
Figure 2.12. Continued.
Figure 2.11 (b) shows the output power density along the flow direction. Its trends
differ according to the difference types of TEM. The hotter part of TEG is equipped with
filled-skutterudite module that generates approximately constant power along the flow.
Bi2Te3 modules are at the colder part, and power density increases as the mean temperature
decreases. Since the temperature difference is almost constant, the Carnot efficiency is
higher when the average temperature is lower. The lower Carnot efficiency is balanced by
the higher ZT of skutterudite in the part of higher temperature. On the other hand, ZT of
bismuth telluride does not vary much with temperature in its operating temperature range.
Thus, the power density is higher in the colder region as shown in Figure 2.11 (b).
36
10
15
20
25
30
35
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.5 1 1.5 2 2.5 3 3.5
Power density (kW/m2)
Tjunction
/Treservior
Po
we
r d
en
sity (
kW
/m2)
T
jun
ctio
n /T
rese
rvio
r
HTE
(mm)
Figure 2.13. Performance of TEMs between heat reservoirs with different 𝐻𝑇𝐸
(𝑇ℎ𝑜𝑡,𝑟 𝑠 𝑟𝑣𝑜𝑖𝑟= 800 K, 𝑇𝑐𝑜 𝑑,𝑟 𝑠 𝑟𝑣𝑜𝑖𝑟= 300 K).
One phenomenon noted from the temperature distribution of the cross flow heat
exchanger, as shown in Figure 2.12., is that the temperature difference is large at one corner
than those at the other three corners, and thus generates more power. An improper
combination of 𝐴𝐻𝐸𝑋 and 𝐻𝑇𝐸 could result in a smaller high power density region, thus
greatly reduces the power generation.
At the end of the discussion, there are some remarks on the design space to be addressed.
The design space of this study is limited by arbitrary upper and lower bounds according to
the magnitude of real world application. However, another natural way to exert the
constraints implicitly by some other performances. For example, the high aspect ratio
design would be prevented to avoid large pressure drop, if a maximum pressure drop is
required. Similarly, a maximum cost limitation, or using cost-per-watt as a penalty function
can be a constraint so that the 𝐴𝐻𝐸𝑋 and 𝐻𝑇𝐸 is limited. The weights of both TE materials
are calculated and available for cost evaluation. However, the materials usually account
37
less than 10% of the total cost of a TEG (Joshi et al., 2014). The cost evaluation can be
very hard before standardized TEG design information is available.
2.4 Summary
In this chapter, a numerical model for heat-exchanger-based TEGs and a combined
RSM-GA optimization algorithm are introduced. The algorithm enables a fast and global
search for optimum, and provides knowledge on sensitivity and interaction of the
parameters in the vicinity of the optimum design.
Cases of TEGs with cross flow and counter flow heat exchangers are studied.
Optimization is performed to seek for high power outputs under constraints of required
heat dissipation from the hot side and geometries of heat exchanger and TEM. The response
relations including sensitivity and interaction of factors are analyzed to show effects of
varying factors on power output independently and concurrently, which has the potential
to obtain optimized designs under different constraints with less calculation.
The optimization algorithm proposed in this chapter is further applied to the parametric
optimization study in Chapter 3.
38
CHAPTER 3. REGENERATIVE THERMOELECTRIC POWER GENERATION
In this chapter, the regenerative concept for thermoelectric generator is introduced. The
regenerative thermoelectric generator (R-TEG) avoids the usage of high temperature
thermoelectric materials by regenerating the thermal energy with a precooling heat
exchanger. The properly designed R-TEG is capable to generate similar amount of power
to TEGs using high temperature thermoelectric materials (high-T TEGs), which is more
favorable for the high reliability and low-cost implementation.
3.1 Regenerative Concept Description
To broaden the application of thermoelectric generators, many research efforts have
been dedicated to the development of high temperature TE materials (Dresselhaus et al.,
2007; Garg et al., 2011; Pei et al., 2011; Poon, 2001; Sales et al., 1996; Voneshen et al.,
2013; Zhao et al., 2016) for converting high temperature heat sources to power. Up till now,
however, there are no reliable high temperature TE materials that have been made
commercially available. The much higher cost of the materials, stabilities of the materials
at high temperature, and often the requirements of using inert gas or vacuum encapsulation
in the TE module and the TEG are just some of the main barriers of using these materials
(Evident Thermoelectrics Inc., 2016). Although there are numerous high temperature TEG
demonstrations that illustrated power output as high as 1kW (Crane & LaGrandeur, 2010;
39
Hu et al., 2016; Ikoma et al., 1998; Karri et al., 2011; Rowe et al., 2011; Schock et al.,
2013; Thacher et al., 2007; Yang & Stabler, 2009; Zhang et al., 2015), in general,
implementing a high temperature TEG poses much greater engineering challenges to
ensure thermal, mechanical, electrical and chemical stabilities.
The equations on thermoelectric generation and thermodynamics have been introduced
in Section 1.1, and repeated in this chapter in slightly different forms for convenience.
In thermoelectric material research and development, the challenge is to increase 1st
efficiency, or say ZT (Eq. (3.1), 𝜂𝐶 is Carnot efficiency (Eq. (3.2)), �̅� =1
2(𝑇ℎ + 𝑇𝑐)).
However, the power output within certain constraints is the main objective for a TEG,
which involves wide varieties of engineering design problems, even when materials have
been selected, including height of TEC legs, fill factor (ratio of TEG and total cross-section
area), thermal packaging and interfacing parameters etc. The absolute efficiency, defined
as ratio of power output and available energy from heat source (Eq. (3.3)), is a better
indicator of a TEG performance, which describes both material and device performance.
𝜂 =𝑊
𝑄= 𝜂𝐶 ×
√1 + 𝑍�̅� − 1
√1 + 𝑍�̅� +𝑇𝑐𝑇ℎ
(3. 1)
𝜂𝐶 = 1 −𝑇𝑐𝑇ℎ=Δ𝑇
𝑇ℎ(3. 2)
𝜂𝑎𝑏𝑠 =𝑊
�̇�𝐶(ℎℎ𝑜𝑡,𝑖𝑛 − ℎ0)(3. 3)
The proposed R-TEG first cools the hot gas to a temperature acceptable by the low
temperature TE modules, and simultaneously raises the temperature of a stream of cold air.
40
Both the cooled hot gas and the heated air are then fed to the TEGs using low temperature
TEMs (Bi2Te3 are used in this study). Two types of regeneration designs are studied using
the previously established numerical methods (Kumar et al., 2013a, 2013b) and the
optimization algorithm (Huang & Xu, 2016). For comparison, the power outputs from a
high temperature TEG using combined filled-skutterudite and Bi2Te3 TEMs (referred to as
high-T TEG below, details described in Section 2.1) are computed. It is found that for most
cases the regenerative TEG can achieve similar performance as a high-T TEG. Given the
tremendous benefits of using low temperature TEMs for the R-TEG including much lower-
cost, reliability, and availability, the development of R-TEGs will represent a paradigm
shift in the TEG research and development, and will ultimately enable the wide spread
deployment of TEGs for real world waste heat recovery applications.
The R-TEG is designed based on a counter flow heat exchanger as shown in the gas
flow chart in Figure 3.1. The waste heat source is assumed to be hot gas (air) at 800 K with
a mass flow rate of 0.1 kg/s, and the room temperature air (300 K) is the coolant. The hot
gas first enters a gas phase heat exchanger called precooler, to cool to a temperature that is
acceptable for Bi2Te3 modules. In this work, the hot side junction temperature of the TEMs
is limited to be lower than 550 K (Zhao et al., 2005). The cooled hot air then enters a
Bi2Te3-based TEG labeled as TEG1 in Figure 3.1.
For comparison, conventional TEGs (called high-T TEG here) are also computed and
optimized, where filled-skutterudite modules are used in their higher temperature sections
and Bi2Te3 modules at the lower temperature sections, as described in Section 2.1. The hot
side junction temperatures of Bi2Te3 modules in these high-T TEGs are also kept below
41
550 K. The detailed parameters of the two types of TEMs are taken from Ref. (Kumar et
al., 2013b) and listed in Table 2.2.
Figure 3.1. Schematics of an R-TEG (called R-TEG1).
In this R-TEG design, the cold air that is used to cool the hot air in the precooler comes
from sub-TEG 1 in order to recycle (regenerate) more heat as shown in Figure 3.1. The
regenerated hot air is then fed into a second Bi2Te3-based TEG (sub-TEG2) to produce
more power. The amount of the cold air used for the precooler is chosen such that the
temperature of the output of the warmed cold air reaches the limit for being used in sub-
TEG 2, i.e., the same as the inlet temperature for sub-TEG 1. The size and cold air supply
for sub-TEG 2 are thus proportional to those of the sub-TEG 1 according to the mass flow
rate of the regenerated hot air.
A second R-TEG design is illustrated in Figure 3.2. Instead of using a fraction of the
cold air from sub-TEG1 for the precooler, the regenerated air continuously flows in a
42
closed loop as shown in Figure 3.2. One of the advantages of using the closed loop is that
other types of heat carrying fluid can be used, for example, liquid coolant, to significantly
enhance the heat transfer rate, resulting in more power output from sub-TEG 2. However,
the calculations below are based on air as the regenerating fluid.
Figure 3.2. Schematics of regeneration concept 2 (R-TEG 2)
The computational model, materials properties, and optimization method for the TEGs
is the same as Chapter 2. The precooler is calculated using the ϵ-NTU method (Bergman
et al., 2011). Among the three major design parameters studied in Chapter 2: the heat
exchanger area (𝐴𝐻𝐸), the aspect ratio (width/length), and the height of TEC legs (𝐻𝑇𝐸),
the aspect ratio of the heat exchanger has less an effect on the power output according to
the sensitivity analysis. In the studies presented here, the width of the heat exchanger
channel is selected to be 0.27 m. AHE (=0.27m× length) and HTE are selected as the
optimization factors with upper bounds set at 0.2 m2 and 8 mm, respectively. In addition
to the power output, the heat dissipation rate from the hot gas is another key parameter to
43
be evaluated. The hot side convection coefficient is set to be a constant equal to 2700
W/m2K based on a typical intermittent corrugated plate heat exchanger (Kays & London,
1984), and the cold side convection coefficient varies according to Eq. (2.2) with h0 = 2300
W/m2K, i.e. h on the cold side is only dependent on mass flow rate in this case.
3.2 Results on R-TEGs Performance
The TEGs with different design concepts are optimized to provide the maximum power
output. We assume there is abundant room temperature air for cooling and the calculations
are carried out with cold air supply up to 30 times of that of the hot air (after which the
output power does not change much as seen below). The maximum power outputs vs. the
amount of cold air are plotted in Figure 3.3, where �̇�𝑐 indicates the cold air supplied to the
sub-TEG 1.
0
500
1000
1500
2000
2500
0 0.5 1 1.5 2 2.5 3 3.5
Bi2Te
3 TEG
High-T TEGR-TEG 1R-TEG 2
Pow
er
outp
ut
(W)
Cold air mass flow rate (kg/s)
Figure 3.3. Optimized power output of TEGs with different designs under varied cold air
supply.
44
Figure 3.3 compares the optimized power output for high-T TEG, R-TEG 1 and R-TEG
2. In addition, the power output from using the Bi2Te3 TEG alone (sub-TEG 1 in the R-
TEGs) is also shown. It can be seen that high-T TEG, R-TEG 1 and R-TEG 2 have similar
power outputs when the cold air mass flow rate is low. With more cold air supplied, the
power outputs increase, and the power outputs from high-T TEG and R-TEG 2 increase
more than that from R-TEG 1. Notably, R-TEG 2 generates similar amount of power
compared with high-T TEG, and in some cases even exceeds high-T TEG.
The corresponding heat transfer rate through the TEMs are plotted in Figure 3.4. It is
shown that the heat transfer rate of R-TEG 2 can be at least 8% higher than the conventional
high-T TEG design, and is even much higher when cold air supply is insufficient. Thus, it
can be concluded that R-TEG is even more preferable when the heat transfer demand is
high and cold air supply is limited.
20
25
30
35
40
0 0.5 1 1.5 2 2.5 3 3.5
High-T TEGR-TEG 1R-TEG 2
Cold air mass flow rate (kg/s)
Heat flow
rate
(kW
)
Figure 3.4. Heat transfer rate of different designs under varied cold air supply, when
power output is optimized.
45
The regenerated mass flow rate (�̇�𝑟) of regenerated air is plotted in Figure 3.5. More
than twice the hot air can be regenerated in R-TEG 2 design than that in R-TEG 1. This
indicates that size of sub-TEG 2 of R-TEG 2 design is more than twice of that of R-TEG
1, and so is the power output, for the direct scaling up.
0
0.05
0.1
0.15
0 0.5 1 1.5 2 2.5 3
R-TEG 1R-TEG 2
Re
ge
ne
rate
d a
ir m
ass f
low
rate
(kg/s
)
Cold air mass flow rate (kg/s)
Figure 3.5. Regenerated air mass flow rate of TEGs of different designs and working
condition under varied cold air supply, when power output is optimized.
3.3 Discussion on High Performance of R-TEGs
The reason that R-TEG 2 can generate similar amount of power output compared with
high-T TEG which converts heat to power at higher temperatures is analyzed as follows. It
is known that the efficiency of converting heat to power is related to (or limited by) the
Carnot efficiency which is higher at higher operation temperature, as shown in Eq. (3.2):
The main reason that a lower temperature R-TEG 2 can achieve similar power output
is due to the larger heat transfer rate. The averaged Carnot efficiencies and heat transfer
46
rates are plotted respectively in Figure 3.6 and Figure 3.4. The averaged Carnot efficiency
is calculated based on local junction temperatures weighted by the local heat flux. It is seen
that the averaged Carnot efficiency of R-TEG (the Carnot efficiency for R-TEG 1 and R-
TEG 2 are the same) is significantly lower than that of high-T TEG. On the other hand, it
is seen from Figure 3.4, that with the generative design, R-TEG 2 is capable to scavenge
more heat from the hot gas than the high-T TEG. Comparing R-TEG 2 and R-TEG 1, R-
TEG 2 produces high power due to the closed loop design and the resulting higher
regenerated mass flow rate (Figure 3.5).
0
10
20
30
40
50
60
0 0.5 1 1.5 2 2.5 3 3.5
R-TEGHigh-T TEG
Cold air mass flow rate (kg/s)
Avera
ged C
arn
ot effic
iency (
%)
Figure 3.6. The averaged Carnot efficiency of TEGs of different designs and working
condition under varied cold air supply, when the power output is optimized.
The power output is a combined effect of the Carnot efficiency, the heat transfer rate,
and ZT as shown in Eq. (3.1) (Goldsmid, 1995). For the materials used in this study, ZT of
Bi2Te3 varies in the range from 0.83 to 0.96 (Zhao et al., 2005), while ZT of materials used
in high-T TEGs are shown in Figure 3.7. Although the value of ZT of the skutterudites
varies with temperature (Rogl et al., 2010; Tang et al., 2005), it is seen that the averaged
47
ZTs are in a similar range as that of Bi2Te3. Thus, ZT is a less influencing factor for the
power outputs.
0.6
0.7
0.8
0.9
1
1.1
0 0.2 0.4 0.6 0.8 1 1.2
0.11.02.0
3.0
ZT
Normalized x along flowpath
Figure 3.7. Local 𝑍�̅� of TE materials in high-T TEGs along the flow path. For �̇�𝑐=0.1,
1.0, 2.0, 3.0 kg/s.
Our results are consistent with Eq. (3.1). To compare the calculated data shown in Fig
3, the power output is calculated again using Eq. (3.1) and Eq. (3.2) based on the local
junction temperatures and heat transfer rate. The results are compared in Figure 3.8. It is
seen that the results obtained using Eq. (3.1) are close to that from the numerical model.
There are two reasons contributing to the slight discrepancy between the results of the two
methods. One is that using the material properties evaluated by the mean temperature
(which is used for 𝑍�̅�) results in a higher power output than using integral averaged
properties (Kumar et al., 2015), which is the method we used in this model (Huang & Xu,
2016), as explained in Section 2.1. Also, Eq. (3.1) is evaluated by the maximum efficiency,
which indicates that the TECs are working in a mode different from the maximum power
output. In the simulation, the TECs are performing in the maximum power mode so that
48
the actual efficiency should not be as high as that given by Eq. (3.1), which is another
reason for the discrepancy.
1000
1200
1400
1600
1800
2000
2200
2400
2600
0 0.5 1 1.5 2 2.5 3 3.5
High-T TEGR-TEGHigh-T TEGR-TEG
Po
we
r o
utp
ut (W
)
Cold air mass flow rate (kg/s)
Figure 3.8. Power output calculated by the numerical model and Eq. (3.1). Solid lines are
results using numerical model; dashed lines are results obtained using Eq. (3.1).
The 1st Law efficiencies and absolute efficiencies of the high-T TEG and R-TEG 2 are
analyzed to conclude the discussion, and compared in Figure 3.9. The 1st Law efficiency is
defined in Eq. (3.1). The absolute efficiency is based on the available enthalpy of heat
source with respect to the ambient temperature, as defined in Eq. (3.3), which also
evaluates the energy scavenging capability in additional to the energy conversion. ℎℎ𝑜𝑡,𝑖𝑛
and ℎ0 are enthalpies of air at hot inlet and ambient conditions.
49
Figure 3.9. Efficiencies of high-T TEG and R-TEG 2. (a)1st Law efficiency; (2) absolute
efficiency.
Generally, R-TEGs have lower 1st Law efficiencies, though not as low as their averaged
Carnot efficiencies. However, our R-TEG designs provide better energy scavenging
capabilities that can compensate for the lower 1st Law efficiencies. It is seen that the R-
5
5.5
6
6.5
7
0 0.5 1 1.5 2 2.5 3 3.5
High-T TEGR-TEG1
st L
aw
effic
iency (
%)
Cold air mass flow rate (kg/s)
(a)
2
2.5
3
3.5
4
4.5
5
0 0.5 1 1.5 2 2.5 3 3.5
High-T TEGR-TEGA
bso
lute
effic
iency (
%)
Cold air mass flow rate (kg/s)
(b)
50
TEGs have comparable absolute efficiency compared with that of high-T TEGs. Hence,
similar amount of power can be extracted from an R-TEG as from a high-T TEG.
3.4 Summary
In this chapter, the concept of regenerative TEGs using low temperature TE material
Bi2Te3 is proposed. The optimized regenerative TEG is shown to be capable of generating
a similar amount of power compared to the TEG using high temperature TE materials, due
to its higher energy scavenging capacity. The heat transfer rates and regenerated mass flow
rates, as well as Carnot efficiency and local ZTs are analyzed in details to explain the
performance of regenerative TEGs. Given the tremendous benefits of using low
temperature TEMs for R-TEG including much lower-cost, much more reliability, and
availability of commercial modules, regenerative TEGs will represent a paradigm shift in
the TEG research and development, and will contribute significantly to the use of TEGs
for real world applications of converting waste heat to power.
51
CHAPTER 4. SINGLE MODULE TEG AND TEST RESULTS
In this chapter, a single module TE test cell is described. The test cell has a hot air heat
exchanger serving as the heat source and a liquid coolant heat exchanger as the heat sink.
This setup is intended to simulate the working condition of a single TEM in a TEG. The
test cell can also serve as module performance test with copper liner exerting uniform
temperature onto the TEM. A commercialized bismuth telluride module (HZ-20, Hi-Z
Technology, Inc.) in a recommended packaging is tested for example. The temperature
measurement within the heat exchangers and TEM packaging showed that enhancement of
heat transfer in the heat exchangers is essential so that the TEM can be tested in more
varied conditions, especially for high-temperature TEMs.
4.1 Single Module TEG Setup
The single module TEG is developed with electrical heat simulating exhaust gas supply
and liquid coolant loop simulating the conditions of a TEM in a waste heat recovery TEG.
By applying components comparable to the full-size TEG, the single module TEG can
serve the low-cost diagnosis and optimization purposes during the development phases.
The system level scheme is shown in Figure 4.1.
52
Figure 4.1. System level flowchart single module TEG test rig.
The single module TEG uses the heated gas source, coolant loop, and data acquisition
system adapted from previous work (Dubitsky, 2015) and summarized as follows. The hot
gas in this study is regulated from a high-pressure nitrogen supply in Zucrow lab. The
Alicat MCR-250SLPM 250 SLMP flow controller is used to control the mass flow rate of
the regulated nitrogen. The nitrogen goes through a Sylvania 038826 6kW Style B threaded
inline air heater, controlled by Watlow DC21-24S5-0000 Din-A-Mite SSR. The generated
hot nitrogen is a good simulator of the exhausted gas according to the heat capacity, thermal
conductivity, and viscosity, in comparison with octane complete combustion product
(Dubitsky, 2015).
The home-made hot side heat exchanger has a removable plate on its bottom side and
is capable of applying varied enhancement structure (e.g. pin-fin plate) by replacing the
bottom plate. However, only a flat plate is used in this work.
High
pressure N2
Mass flow
controller
Electrical
heater Single
module
TEG
Exhaust
hood
Coolant
circulator
Centrifugal
pump
Flowmeter
53
Dilute ethylene glycol (50/50 with distilled water) is used as the coolant. A
heated/refrigerated circulator (Polyscience MX20R-30-A11B) is used to control the
coolant temperature. The coolant is further boosted by a centrifugal pump for higher
cooling capacity. The coolant flow rate is measured by a float flowmeter (OMEGA FL-
9004). The cold side heat exchanger is provided by Dana Limited. with a proprietary design.
The single module TEG design and measurements are shown in Figure 4.2, taking the
HZ-20 module test for example. The home-made heat exchanger served as the heat source
for the module. Four thermocouples (TCs) are applied along the flow path to monitor the
temperature drop, and another two on the corresponding position on the heat exchanging
surface. Fittings for pressure transducer are reserved but sealed in this study, and thus, not
shown in the schematics cartoon. A thermal flux meter (TFM, HT-50 ITI Inc.) is applied
on the hot side, between the heat exchanger and TEM package, outputting a voltage signal
proportional to the heat flux and a K-type TC signal on its hot side. The TEM package is
provided by NASA, with ceramic wafers, metal liners, and copper thermal spreaders. A
recommended compressive load (200 psi) is applied on the package to ensure good thermal
interface contact. Four TCs are applied on either hot or side copper surfaces. Two metal
sheathed TCs are cemented at the upper and lower edges of the TEM, and two thin-foil
TCs inside the package to measure the junction temperature. The thermoelectric current
may introduce an overwhelming and hard-to-determine impact on the thin-foil TCs. Thus,
the thin-foil TCs are between the ceramic wafers and metal liners. The electrical
measurement is conducted with BK Precision modular programmable DC electronic load
mainframe (BKMDL001). Another two voltmeter leads are for contact resistance
elimination with four-terminal measurement. Additional insulation material (glass fiber) is
54
put between the hot side heat exchanger and the support structure to eliminate thermal
bypass. We also use graphoil between each component to handle the thermal interface.
Figure 4.2. Schematics of single module TEG.
The data acquisition system is implemented on an NI PXIe-1078 machine with
LabVIEW virtual instruments and drivers. The hot gas supply and electrical/temperature
measurement and control systems are both integrated on LabVIEW. The analog
input/output card (NI-PXI) is capable of voltage signals, also including those from TFM
or pressure transducers, between 0-10V. The TC signals are acquired on NI TC-4353 Mini
TC Terminal block. Controlling functions of the electrical load, maximum power point
tracking (MPPT) and IV sweep, are modularized with action engine and state machine
techniques and integrated into the LabVIEW code.
The pictures of the abovementioned experimental setup are shown in Figure 4.3.
Insulation
HHX
Graphoil
TC
TFM
Cu thermal spreader
TEM
Cu thermal spreader
CHX
voltmeter
IV controller
Hot air
Leads
55
Figure 4.3. Photos of the experimental setup of single module TEG. (a) single module
TEG; (b) Coolant supply system.
Coolant circulator
Centrifugal pump Flowmete
r
HHX
HHX replaceable plate
Supportive Structure
Insulation (glass fiber)
Graphoil and TFM
Copper TEM package
CHX
(a)
(b)
56
4.2 HZ-20 Module Test Results
In this section, the attention is focused on the performance of the TEM, i.e. the junction
temperature (𝛥𝑇𝑗) – open circuit voltage (Voc) – maximum power output (P) relationship.
The electrical resistance and heat transfer rate will also be investigated. However, the
temperature distribution and heat transfer of the entire single module TEG will be discussed
in Section 4.3.
Here, altogether 11 working conditions of HZ-20 TEM along the TEG heating up
process are investigated. The coolant supply is kept as constant, with circulator set at 0 °C
and coolant flow rate at 1.2 L/min.
The Seebeck performance, i.e. 𝛥𝑇𝑗 − Voc is plotted as Figure 4.4, comparing with the
reference data. The reference data is provided by Hi-Z Inc. for troubleshooting, which is to
say that only TEMs with performance lies below the diamond dashed line is acceptable.
As mentioned in Section 4.1, the junction temperature differences measured by the thin-
foil TCs are supposed to be slightly higher than the real values. Thus, the tested module is
able to output a same open circuit voltage under an even smaller temperature difference,
indicating that the module has good quality in its Seebeck performance. The TCs at the
edge are also plotted to identify the deviation. However, these TCs failed to provide reliable
data due to poor installment and heat leakage.
The electrical resistance and power output of the TEM are plotted in Figure 4.5. IV
sweeps are conducted for each investigated working condition. At certain junction
temperatures and thus a certain open circuit voltage, the maximum power output purely
depends on the internal resistance.
57
0
20
40
60
80
100
0.2 0.4 0.6 0.8 1 1.2 1.4
CenterEdgeReference
Open curcuit voltage (V)
Ju
nctio
n t
em
pera
ture
diffe
rence
(K
)
Figure 4.4. 𝛥𝑇𝑗 − Voc of HZ-20 TEM.
Due to the finish quality of the leads, a ~0.2 Ω contact electrical resistance can be
introduced to the wirings, which is comparable with the resistance of the module. Another
two voltage probes (invert triangle “voltmeter” in Figure 4.2) are inserted to get rid of the
contact resistance by four-terminal measurement. Also due to the contact resistance, which
is supposed to be ascribed as a part of the load resistance, the IV sweep will only provide
half of the data of an ideal IV sweep curve. One example is shown in Figure 4.6. The solid
line is the IV sweep data directly from BK Precision load measurement. The dashed line is
the estimation of what the IV sweep curve supposed to have without the contact resistance
interference. There is not reliable utilization of the voltage data during the sweep due to
the heterophase DAQ system so that the accuracy of correction solely depends on the
voltage measurement during the lingering period (red cross “V probe”) when the electrical
load machine short circuits. The error is even magnified for the data prediction lever
pivoted at the open circuit condition.
58
Figure 4.5. Electrical performance of HZ-20 TEM. (a) Internal electrical resistance; (b)
Maximum power output.
0.18
0.2
0.22
0.24
0.26
0.28
0.3
10 20 30 40 50 60 70 80 90
ExperimentReference
TE
M in
tern
al re
sis
tan
ce
(
Junction temperature difference (K)
(a)
0
0.3
0.6
0.9
1.2
1.5
10 20 30 40 50 60 70 80 90
ExperimentReference
Ma
xim
um
po
wer
outp
ut (W
)
Junction temperature difference (K)
(b)
59
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 1 2 3 4 5
BK-PCorrectedV probe
Volta
ge
(V
)
Current (A)
Figure 4.6. IV sweep and correction at junction temperatures of 210 – 122 °C.
The heat transfer rate (Figure 4.7) is measured by the thermal flux meter installed on
the hot side of the TEM packaging. Though some discrepancy exists, the result is
acceptable regarding the difficulties reliability of the heat transfer rate measurement.
However, it will be good to investigate the possibility to cross-verify the heat transfer
results by a different measurement method.
Then the energy conversion efficiency of the tested module can be calculated, and
compared with the specification.
60
Figure 4.7. Heat absorbed by the hot side of the HZ-20 TEM.
Figure 4.8. Energy conversion efficiency of the HZ-20 module.
4.3 Temperature Distribution throughout the Single Cell TEG
The temperature throughout the TEG is monitored during the TEM testing. Though not
quite close to the real internal structure of a full-size TEG, the analysis and diagnose
process is shown for example.
20
40
60
80
100
120
140
160
10 20 30 40 50 60 70
ExperimentReference
Hea
t tr
ansfe
r ra
te (
W)
Junction temperature difference (K)
0
0.2
0.4
0.6
0.8
1
1.2
10 20 30 40 50 60 70 80 90
ExperimentReference
Effic
ien
cy (
%)
Junction temperature difference (K)
61
The temperature along the hot gas flow in the hot side heat exchanger (HHX) are
plotted in Figure 4.9. The position of the four TCs for the HHX are shown in Figure 4.2.
The thermal energy loss is estimated and plotted and compared with the heat that enters
the TEM and measured the thermal flux meter (TFM) in Figure 4.10. The heat loss is
estimated simply by subtracting the enthalpy flow rate at the HHX inlet and outlet
temperatures. It is observed that the heat that enters the TEM is only one-half of the total
heat loss from HHX, indicating the heat leakage is severe though thick glass fiber blankets
are applied. Due to the heat leakage, and the large heat capacity of the HHX, it is not safe
to make any assertion of the heat transfer performance, though the temperature drop is
quite linear along the stream as shown in Figure 4.9. It is also noticed that there is an
overshoot of heat loss, indicating the large thermal capacity induced transient effect, that
the HHX outlet temperature doesn’t increase as soon as the inlet temperature does.
0
100
200
300
400
500
600
700
800
0 200 400 600 800 1000
HHX inletHHX 1HHX 2HHX out
Te
mpe
ratu
re (
K)
Heat up process (-)
Figure 4.9. Temperature along the hot stream in HHX.
62
0
50
100
150
200
250
300
350
400
0 200 400 600 800 1000
Heat lossTFM
Hea
t tr
ansfe
r ra
te (
W)
Heat up process (-)
Figure 4.10. Heat transfer rate from HHX and enters the TEM.
The comparison of the temperature distribution of the gas within the heat exchanger
and the corresponding positions of the measuring points (Figure 4.11) showed that the
current heat exchanger suffers from a huge convective thermal resistance that the
temperature difference can be more than 200K even at the steady state without the transient
thermal lag. In the current setup, this poor heat transfer in hot side heat exchanger is the
main reason for the incapability of performing high-temperature TEM tests. Heat transfer
enhancement is essential to improve the current single module TEG.
It is also observed that the temperature difference between position 1 and 2 on the plate
smears approximately a half of that in the gas. Taking the higher heat transfer rate closer
to the inlet into consideration, it is notable that the axial heat conduction is playing a non-
negligible role, which is not desired for a TEG heat exchanger. Of course, it will not affect
the TEM testing results since the copper plate is specially added for the purpose of uniform
temperature distribution.
63
0
100
200
300
400
500
600
700
800
0 200 400 600 800 1000
HHX 1HHX 2
HHX plate 1HHX plate 2
Tem
pe
ratu
re (
K)
Heat up process (-)
Figure 4.11. Temperature distribution of the gas in HHX and the corresponding points on
the heat exchanging plate.
The temperature through the TEM package is illustrated in Figure 4.11. The “HHX
plate” refers to the average temperature from the two TCs on the hot side heat exchanger
plate. The TFM also provides a K-type TC signal and the temperature drop through the
TFM is claimed to be small. The temperature uniformity is checked by installing four TCs
on the copper plate on both sides. The absolute deviation of temperature measured on either
side is less than 5K and the average is shown in Figure 4.12 by “TEM P H/C”. The “TEM
J H/C” refer to the junction temperature by the thin-foil TCs installed inside the package.
Another TC is attached to the surface of the cold side heat exchanger (CHX) to check the
temperature of the heat sink.
Another noticeable temperature drop is observed between the hot side heat exchanger
plate and the TFM/TEM package. Assuming the TC signal on TFM is reliable, it is
estimated to be a severe thermal contacting problem despite much graphoil is applied.
64
0
100
200
300
400
500
600
700
800
0 200 400 600 800 1000
HHX plateTFMTEM P HTEM J HTEM J CTEM P CCHX sur
Tem
pe
ratu
re (
K)
Heat up process (-)
Figure 4.12. Temperature distribution through the TEM package.
It is also worthwhile to revisit the design of the TEM package, because the junction
temperature difference is only around 50% of the package temperature difference. Possible
contact thermal resistance may mainly occur at the metal liner because no thermal grease
is applied.
In addition, the coolant supply is already maximized during the test, leaving little space
for future testing with varied cold side conditions. It is not accessible to investigate if the
cold side heat exchanger has any blocking or fouling problem.
4.4 Summary
In this chapter, a commercialized TEM is tested in a home-made single module TEG.
The open circuit voltage measurement is satisfying and electrical performance
measurement showed that the power output is negatively impacted by a larger internal
65
resistance than specified. Heat transfer performance is studied by a thermal flux meter and
the result is satisfying.
The analysis of temperature distribution throughout the TEG is helpful to diagnose the
unsatisfied performance and identify the problems. The main problems of current setup are
clarified to be the poor performance of the hot side heat exchanger and the contact
resistance within and on the top of the TEM packaging. Heat transfer enhancement of hot
side heat exchanger and better solution of contact resistance are necessary methods to
improve the performance of the single module TEG.
66
CHAPTER 5. CONCLUSIONS AND FUTURE WORKS
5.1 Summary and Conclusions
Thermoelectric generators are promising devices for waste heat recovery. To improve
the performance, numerical and experimental methods are applied for the system level
investigation. Parametric analysis and optimization are conducted with numerical
modeling and optimization algorithms. The novel concept of regenerative thermoelectric
generators is also investigated to achieve high performance with Bi2Te3 modules. Effects
of geometric parameters and cooling powers on the TEG performance are also discussed.
A single module TEG is developed for module tests and performance diagnosis.
An existing numerical model was extended to simulate 2-D heat exchanger on both hot
and cold side with consideration on thermal diffusion. A combined RSM-GA optimization
method is developed. The response surface method analyzes the parametric sensitivity and
interaction to shed light onto the mechanisms that determine the TEG performance, in
additional to directing the optimization. The genetic algorithm is incorporated to ensure the
globality. A minimum heat dissipation rate and the limitation of geometries are taken into
consideration. The relative importance of the studied parameters including area and aspect
ratio of the heat exchanger, and height of TEC legs are clarified and the HTE – AHE synergy
is illustrated.
67
Regenerative concept of thermoelectric generation using Bi2Te3 modules only is
introduced and the optimized performance is shown to be similar to the conventional
varied-types module TEG using high-temperature materials. The high performance of the
R-TEG is analyzed by classical thermoelectric generation theory and the reason is shown
to be the higher heat scavenging capability. The roles that played by heat transfer rate,
Carnot efficiencies, and local ZT are investigated in details. The R-TEG is especially useful
when the coolant supply is insufficient or the heat dissipation rate is high. What is more,
the lower temperature of the TEMs working condition natural resolved the concerns
including thermal, mechanical, and chemical stability, and the lower-temperature Bi2Te3
modules are more readily to use. The engineering simplicity and cost-effective merits will
push thermoelectric generation closer to real world application.
A single module TEG is developed. The setup can serve both module testing and
diagnostic purposes. A commercialized thermoelectric module is tested for example. The
overall thermal performance is analyzed during the heating up process in the testing. The
main constraints to higher thermoelectric generation and test handling performance are
identified.
5.2 Future Works
Different levels of sophistication of numerical models can be developed according to
the investigators’ interests and computational resources available. Besides all that have
been mentioned in Section 1.2.2, a porous media flow model with anisotropic Darcy’s law
is expected to be an efficient and accurate way to model the pressure distribution within
the heat exchangers, in additional to current finite-volume based model.
68
On the synergy of heat exchanger area and height of thermoelectric couples’ legs, a
revisit with controlled overall heat transfer coefficient is intriguing. The overall heat
transfer rate of a heat-exchanger-based TEG separates the heat transfer performance from
the heat-transfer-vs-temperature difference trade-off (Section 2.2.3). The overall heat
transfer rate is expected to have an optimized value when other parameters for a given heat
source and sink condition. However, controlling the overall heat transfer coefficient, or the
heat transfer rate is challenging for the temperature-dependent properties. This analysis is
also valuable for further designs of R-TEGs since their high performance mostly depends
on the high heat transfer rate.
The existing problems of the single cell are investigated in Section 4.3. Heat transfer
enhancement needs to be applied to the heat exchanger and the contact resistance needs to
be reduced by different thermal interface materials. Adjustability of the cold side is also
required to be improved to variable condition TEM testing and full-size TEG simulation.
Besides the performance testing and diagnosis purpose, another direction of the single
module, or reduced-size TEG design is for validation of a numerical model. Either more
detailed measurements or simplification of the boundary conditions (e.g. realizing
adiabatic or uniform temperature distribution on certain boundaries) will make it possible
to validate the numerical models with a lower degree of complexity.
69
LIST OF REFERENCES
69
LIST OF REFERENCES
Bass, J. C., Elsner, N. B., & Leavitt, F. A. (1994). Performance of the 1 kW
thermoelectric generator for diesel engines. AIP Conference Proceedings, 316(1).
Bass, J. C., Kushch, A. S., & Elsner, N. B. (2001). Thermoelectric Generator (TEG) for
Heavy Diesel Trucks. Proceedings of the Tenth International Conference on
Thermoelectrics, 1–6.
Bergman, T. L., Incropera, F. P., DeWitt, D. P., & Lavine, A. S. (2011). Fundamentals of
heat and mass transfer. John Wiley & Sons.
Birkholz, U., GroB, E., Strohrer, U., Voss, K., Gruden, D. O., & Wurster, W. (1988).
Conversion of waste exhaust heat in automobiles using FeSi2-thermoelements. In
Proc. 7th International Conference on Thermoelectric Energy Conversion (pp. 124–
128).
Box, G. E. P., & Hunter, J. S. (1957). Multi-Factor Experimental Designs for Exploring
Response Surfaces. Ann. Math. Statist., 28(1), 195–241.
http://doi.org/10.1214/aoms/1177707047
Crane, D., Lagrandeur, J., Jovovic, V., Ranalli, M., Adldinger, M., Poliquin, E., Dean, J.,
Kossakovski, D., Mazar, B., Maranville, C. (2013). TEG on-vehicle performance
and model validation and what it means for further teg development. Journal of
Electronic Materials, 42(7), 1582–1591. http://doi.org/10.1007/s11664-012-2327-8
Crane, D. T. (2011). An introduction to system-level, steady-state and transient modeling
and optimization of high-power-density thermoelectric generator devices made of
segmented thermoelectric elements. Journal of Electronic Materials, 40(5), 561–
569. http://doi.org/10.1007/s11664-010-1451-6
Crane, D. T., & LaGrandeur, J. W. (2010). Progress Report on BSST-Led US
Department of Energy Automotive Waste Heat Recovery Program. Journal of
Electronic Materials, 39(9), 2142–2148. http://doi.org/10.1007/s11664-009-0991-0
Deng, Y. D., Chen, Y. L., Chen, S., Xianyu, W. D., & Su, C. Q. (2015). Research on
Integration of an Automotive Exhaust-Based Thermoelectric Generator and a Three-
Way Catalytic Converter. Journal of Electronic Materials, 44(6), 1524–1530.
http://doi.org/10.1007/s11664-014-3442-5
70
Dresselhaus, M. S., Chen, G., Tang, M. Y., Yang, R. G., Lee, H., Wang, D. Z., Ren,
Z. F., Fleurial, J.-P., Gogna, P. (2007). New Directions for Low-Dimensional
Thermoelectric Materials. Advanced Materials, 19(8), 1043–1053.
http://doi.org/10.1002/adma.200600527
Dubitsky, A. O. (2015). Performance Evaluation of an Automotive Thermoelectric
Generator. Purdue University. Retrieved from
http://search.proquest.com/docview/1734880548?accountid=13360
Ebling, D. G., Krumm, A., Pfeiffelmann, B., Gottschald, J., Bruchmann, J., Benim, A. C.,
Adam, M., Labs, R., Herbertz, R. R., Stunz, A. (2016). Development of a System
for Thermoelectric Heat Recovery from Stationary Industrial Processes. Journal of
Electronic Materials, 45(7), 3433–3439. http://doi.org/10.1007/s11664-016-4511-8
Esarte, J., Min, G., & Rowe, D. M. (2001). Modelling heat exchangers for thermoelectric
generators. Journal of Power Sources, 93(1), 72–76. http://doi.org/10.1016/S0378-
7753(00)00566-8
Evident Thermoelectrics Inc. (2016). TEG-HH-8-1.0 Thermoelectric Generator Module
Specification. Retrieved May 1, 2016, from
http://www.evidentthermo.com/images/docs/TEG-HH-8_module_spec_sheet.pdf
Ezzahri, Y., Dilhaire, S., Grauby, S., Patio-Lopez, L. D., Claeys, W., Zhang, Y., Bian, Z.,
Shakouri, A. (2005). Simulation of Si/SiGe micro-cooler by thermal quadrupoles
method. International Conference on Thermoelectrics, ICT, Proceedings, 2005,
241–245. http://doi.org/10.1109/ICT.2005.1519932
Fabbri, G. (1997). A genetic algorithm for fin profile optimization. International Journal
of Heat and Mass Transfer, 40(9), 2165–2172. http://doi.org/10.1016/S0017-
9310(96)00294-3
Fateh, H., Baker, C. A., Hall, M. J., & Shi, L. (2014). High fidelity finite difference
model for exploring multi-parameter thermoelectric generator design space. Applied
Energy, 129, 373–383. http://doi.org/10.1016/j.apenergy.2014.04.088
Favarel, C., Bédécarrats, J.-P., Kousksou, T., & Champier, D. (2015). Experimental
analysis with numerical comparison for different thermoelectric generators
configurations. Energy Conversion and Management, 107, 114–122.
http://doi.org/10.1016/j.enconman.2015.06.040
Garg, J., Bonini, N., Kozinsky, B., & Marzari, N. (2011). Role of Disorder and
Anharmonicity in the Thermal Conductivity of Silicon-Germanium Alloys: A First-
Principles Study. Phys. Rev. Lett., 106(4), 45901.
http://doi.org/10.1103/PhysRevLett.106.045901
71
Goldsmid, H. J. (1995). Conversion Efficiency and Figure-of-Merit. In CRC Handbook of
Thermoelectrics. CRC Press. http://doi.org/10.1201/9781420049718.ch3
Gosselin, L., Tye-Gingras, M., & Mathieu-Potvin, F. (2009). Review of utilization of
genetic algorithms in heat transfer problems. International Journal of Heat and
Mass Transfer, 52(9-10), 2169–2188.
http://doi.org/10.1016/j.ijheatmasstransfer.2008.11.015
He, W., Wang, S., Lu, C., Zhang, X., & Li, Y. (2016). Influence of different cooling
methods on thermoelectric performance of an engine exhaust gas waste heat
recovery system. Applied Energy, 162, 1251–1258.
http://doi.org/10.1016/j.apenergy.2015.03.036
Heghmanns, A., & Beitelschmidt, M. (2015). Parameter optimization of thermoelectric
modules using a genetic algorithm. Applied Energy, 155, 447–454.
http://doi.org/10.1016/j.apenergy.2015.06.034
Hsiao, Y. Y., Chang, W. C., & Chen, S. L. (2010). A mathematic model of thermoelectric
module with applications on waste heat recovery from automobile engine. Energy,
35(3), 1447–1454. http://doi.org/10.1016/j.energy.2009.11.030
Hsu, C. T., Huang, G. Y., Chu, H. S., Yu, B., & Yao, D. J. (2011). Experiments and
simulations on low-temperature waste heat harvesting system by thermoelectric
power generators. Applied Energy, 88(4), 1291–1297.
http://doi.org/10.1016/j.apenergy.2010.10.005
Hu, K. S. Y., Chi, X., Shih, T., & Schock, H. J. (2009). Heat-transfer enhancement in
thermoelectric-power generation. In 47th AIAA Aerospace Sciences Meeting
including the New Horizons Forum and Aerospace Exposition.
Hu, X., Jood, P., Ohta, M., Kunii, M., Nagase, K., Nishiate, H., Kanatzidis, M.,
Yamamoto, A. (2016). Power generation from nanostructured PbTe-based
thermoelectrics: comprehensive development from materials to modules. Energy
Environ. Sci., 9(2), 517–529. http://doi.org/10.1039/C5EE02979A
Huang, S., & Xu, X. (2016). Parametric Optimization of Thermoelectric Generators for
Waste Heat Recovery. Journal of Electronic Materials.
http://doi.org/10.1007/s11664-016-4740-x
Ikoma, K., Munekiyo, M., Furuya, K., Kobayashi, M., Izumi, T., & Shinohara, K. (1998).
Thermoelectric module and generator for gasoline engine vehicles. In
Thermoelectrics, 1998. Proceedings ICT 98. XVII International Conference on (pp.
464–467). http://doi.org/10.1109/ICT.1998.740419
72
Joshi, G., He, R., Engber, M., Samsonidze, G., Pantha, T., Dahal, E., Dahal, K., Yang, J.,
Lan, Y., Kozinsky, B., Ren, Z. (2014). NbFeSb-based p-type half-Heusler for power
generation applications. Energy & Environmental Science, 7, 4070–4076.
http://doi.org/10.1039/C4EE02180K
Karri, M. A., Thacher, E. F., & Helenbrook, B. T. (2011). Exhaust energy conversion by
thermoelectric generator: Two case studies. Energy Conversion and Management,
52(3), 1596–1611. http://doi.org/10.1016/j.enconman.2010.10.013
Kays, W. M., & London, A. L. (1984). Compact heat exchangers. McGraw-Hill, New
York, NY.
Kim, H., & Kim, W. (2015). A way of achieving a low $/W and a decent power output
from a thermoelectric device. Applied Energy, 139, 205–211.
http://doi.org/10.1016/j.apenergy.2014.11.040
Kim, S., Park, S., Kim, S., & Rhi, S. H. (2011). A thermoelectric generator using engine
coolant for light-duty internal combustion Engine-Powered Vehicles. Journal of
Electronic Materials, 40(5), 812–816. http://doi.org/10.1007/s11664-011-1580-6
Koumoto, K. (2005). Oxide Thermoelectrics. In Thermoelectrics Handbook (pp. 15–35).
CRC Press. http://doi.org/10.1201/9781420038903.ch35
Kumar, S., Heister, S. D., Xu, X., & Salvador, J. R. (2015). Optimization of
Thermoelectric Components for Automobile Waste Heat Recovery Systems.
Journal of Electronic Materials, 44(10), 3627–3636. http://doi.org/10.1007/s11664-
015-3912-4
Kumar, S., Heister, S. D., Xu, X., Salvador, J. R., & Meisner, G. P. (2013a).
Thermoelectric Generators for Automotive Waste Heat Recovery Systems Part I:
Numerical Modeling and Baseline Model Analysis. Journal of Electronic Materials,
42(4), 665–674. http://doi.org/10.1007/s11664-013-2471-9
Kumar, S., Heister, S. D., Xu, X., Salvador, J. R., & Meisner, G. P. (2013b).
Thermoelectric Generators for Automotive Waste Heat Recovery Systems Part II:
Parametric Evaluation and Topological Studies. Journal of Electronic Materials,
42(6), 944–955. http://doi.org/10.1007/s11664-013-2472-8
Liu, C., Pan, X., Zheng, X., Yan, Y., & Li, W. (2015). An experimental study of a novel
prototype for two-stage thermoelectric generator from vehicle exhaust. Journal of
the Energy Institute, 86(JANUARY), 1–11.
http://doi.org/10.1016/j.joei.2015.01.019
73
Liu, X., Deng, Y. D., Li, Z., & Su, C. Q. (2015). Performance analysis of a waste heat
recovery thermoelectric generation system for automotive application. Energy
Conversion and Management, 90, 121–127.
http://doi.org/10.1016/j.enconman.2014.11.015
Man, K. F., Tang, K. S., & Kwong, S. (1996). Genetic algorithms: concepts and
applications [in engineering design]. IEEE Transactions on Industrial Electronics,
43(5), 519–534. http://doi.org/10.1109/41.538609
Matsubara, K. (2002). Development of a high efficient thermoelectric stack for a waste
exhaust heat recovery of vehicles. International Conference on Thermoelectrics,
ICT, Proceedings, 2002-Janua, 418–423. http://doi.org/10.1109/ICT.2002.1190350
Meng, X., & Suzuki, R. O. (2015). Simulation Analysis of Tilted Polyhedron-Shaped
Thermoelectric Elements. Journal of Electronic Materials, 44(6), 1469–1476.
http://doi.org/10.1007/s11664-014-3418-5
Min, G. (2005). Thermoelectric Module Design Theories. In Thermoelectrics Handbook
(pp. 11–15). CRC Press. http://doi.org/doi:10.1201/9781420038903.ch11
Montgomery, D. C. (2008). Design and analysis of experiments. John Wiley & Sons.
Omer, S. A., & Infield, D. G. (1998). Design optimization of thermoelectric devices for
solar power generation. Solar Energy Materials and Solar Cells, 53(1), 67–82.
http://doi.org/10.1016/S0927-0248(98)00008-7
Ota, T., Fujita, K., Tokura, S., & Uematsu, K. (2006). Development of thermoelectric
power generation system for industrial furnaces. International Conference on
Thermoelectrics, ICT, Proceedings, 354–357.
http://doi.org/10.1109/ICT.2006.331253
Pei, Y., Shi, X., LaLonde, A., Wang, H., Chen, L., & Snyder, G. J. (2011). Convergence
of electronic bands for high performance bulk thermoelectrics. Nature, 473(7345),
66–69. Retrieved from http://dx.doi.org/10.1038/nature09996
Poon, G. J. (2001). Chapter 2 Electronic and thermoelectric properties of Half-Heusler
alloys. Semiconductors and Semimetals, 70, 37–75. http://doi.org/10.1016/S0080-
8784(01)80136-8
Poudeu, P. F. P., D’Angelo, J., Downey, A. D., Short, J. L., Hogan, T. P., & Kanatzidis,
M. G. (2006). High thermoelectric figure of merit and nanostructuring in bulk p-type
Na1-xPbmSbyTem+2. Angewandte Chemie (International Ed. in English), 45(23),
3835–9. http://doi.org/10.1002/anie.200600865
74
Qiang, J. W., Yu, C. G., Deng, Y. D., Su, C. Q., Wang, Y. P., & Yuan, X. H. (2016).
Multi-Objective Optimization Design for Cooling Unit of Automotive Exhaust-
Based Thermoelectric Generators. Journal of Electronic Materials, 45(3), 1679–
1688. http://doi.org/10.1007/s11664-015-4159-9
Rogl, G., Grytsiv, A., Bauer, E., Rogl, P., & Zehetbauer, M. (2010). Thermoelectric
properties of novel skutterudites with didymium: DDy(Fe1−xCox)4Sb12 and
DDy(Fe1−xNix)4Sb12. Intermetallics, 18(1), 57–64.
http://doi.org/10.1016/j.intermet.2009.06.005
Rowe, D. M. (2005). General Principles and Basic Considerations. In Thermoelectrics
Handbook (pp. 1–14). CRC Press. http://doi.org/doi:10.1201/9781420038903.sec1
Rowe, D. M., Smith, J., Thomas, G., & Min, G. (2011). Weight Penalty Incurred in
Thermoelectric Recovery of Automobile Exhaust Heat. Journal of Electronic
Materials, 40(5), 784–788. http://doi.org/10.1007/s11664-011-1571-7
Sales, B. C., Mandrus, D., & Williams, R. K. (1996). Filled Skutterudite Antimonides: A
New Class of Thermoelectric Materials. Science, 272(5266), 1325–1328. Retrieved
from http://science.sciencemag.org/content/272/5266/1325.abstract
Schock, H., Brereton, G., Case, E., D’Angelo, J., Hogan, T., Lyle, M., Maloney, R.,
Moran, K., Novak, J., Nelson, C., Panayi, A., Ruckle, T., Sakamoto, J., Shih, T.,
Timm, E., Zhang, L., Zhu, G. (2013). Prospects for Implementation of
Thermoelectric Generators as Waste Heat Recovery Systems in Class 8 Truck
Applications. Journal of Energy Resources Technology, 135(2), 22001.
http://doi.org/10.1115/1.4023097
Shih, T., & Hogan, T. (2005). Modeling and Characterization of Power Generation
Modules Based on Bulk Materials. In Thermoelectrics Handbook (pp. 12–23). CRC
Press. http://doi.org/doi:10.1201/9781420038903.ch12
Su, C. Q., Huang, C., Deng, Y. D., Wang, Y. P., Chu, P. Q., & Zheng, S. J. (2015).
Simulation and Optimization of the Heat Exchanger for Automotive Exhaust-Based
Thermoelectric Generators. Journal of Electronic Materials, 45(3), 1–9.
http://doi.org/10.1007/s11664-015-4077-x
Tang, X., Zhang, Q., Chen, L., Goto, T., & Hirai, T. (2005). Synthesis and thermoelectric
properties of p-type- and n-type-filled skutterudite
RyMxCo4−xSb12(R:Ce,Ba,Y;M:Fe,Ni). Journal of Applied Physics, 97(9).
http://doi.org/10.1063/1.1888048
Thacher, E. F., Helenbrook, B. T., Karri, M. A., & Richter, C. J. (2007). Testing of an
automobile exhaust thermoelectric generator in a light truck. Proceedings of the
Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering ,
221 (1 ), 95–107. http://doi.org/10.1243/09544070JAUTO51
75
Venkatasubramanian, R., Siivola, E., Colpitts, T., & O’Quinn, B. (2001). Thin-film
thermoelectric devices with high room-temperature figures of merit. Nature,
413(6856), 597–602. http://doi.org/10.1038/35098012
Vining, C. (1995). Silicon Germanium. In CRC Handbook of Thermoelectrics. CRC
Press. http://doi.org/10.1201/9781420049718.ch28
Voneshen, D. J., Refson, K., Borissenko, E., Krisch, M., Bosak, A., Piovano, A., Cemal,
E., Enderle, M., Gutmann, M. J., Hoesch, M., Roger, M., Gannon, L., Boothroyd, A.
T., Uthayakumar, S., Porter, D. G., Goff, J. P. (2013). Suppression of thermal
conductivity by rattling modes in thermoelectric sodium cobaltate. Nat Mater,
12(11), 1028–1032. Retrieved from http://dx.doi.org/10.1038/nmat3739
Whitley, D. (1994). A genetic algorithm tutorial. Statistics and Computing, 4(2), 65–85.
http://doi.org/10.1007/BF00175354
Wu, H. J., Zhao, L.-D., Zheng, F. S., Wu, D., Pei, Y. L., Tong, X., Kanatzidis, M. G., He,
J. Q. (2014). Broad temperature plateau for thermoelectric figure of merit ZT>2 in
phase-separated PbTe0.7S0.3. Nat Commun, 5. Retrieved from
http://dx.doi.org/10.1038/ncomms5515
Yang, J., & Stabler, F. R. (2009). Automotive Applications of Thermoelectric Materials.
Journal of Electronic Materials, 38(7), 1245–1251. http://doi.org/10.1007/s11664-
009-0680-z
Yazawa, K., Koh, Y. R., & Shakouri, A. (2013). Optimization of thermoelectric topping
combined steam turbine cycles for energy economy. Applied Energy, 109, 1–9.
http://doi.org/10.1016/j.apenergy.2013.03.050
Yee, S. K., LeBlanc, S., Goodson, K. E., & Dames, C. (2013). $ per W metrics for
thermoelectric power generation: beyond ZT. Energy & Environmental Science,
6(9), 2561. http://doi.org/10.1039/c3ee41504j
Yodovard, P., Khedari, J., & Hirunlabh, J. (2001). The Potential of Waste Heat
Thermoelectric Power Generation From Diesel Cycle and Gas Turbine Cogeneration
Plants. Energy Sources, 23(3), 213–224. http://doi.org/10.1080/00908310151133889
Yu, J., & Zhao, H. (2007). A numerical model for thermoelectric generator with the
parallel-plate heat exchanger. Journal of Power Sources, 172(1), 428–434.
http://doi.org/10.1016/j.jpowsour.2007.07.045
Yu, S., Du, Q., Diao, H., Shu, G., & Jiao, K. (2015). Start-up modes of thermoelectric
generator based on vehicle exhaust waste heat recovery. Applied Energy, 138, 276–
290. http://doi.org/10.1016/j.apenergy.2014.10.062
Zhang, T. (2016). New thinking on modeling of thermoelectric devices. Applied Energy,
168, 65–74. http://doi.org/10.1016/j.apenergy.2016.01.057
76
Zhang, Y., Cleary, M., Wang, X., Kempf, N., Schoensee, L., Yang, J., Joshi, G., Meda, L.
(2015). High-temperature and high-power-density nanostructured thermoelectric
generator for automotive waste heat recovery. Energy Conversion and Management,
105, 946–950. http://doi.org/10.1016/j.enconman.2015.08.051
Zhao, L.-D., Tan, G., Hao, S., He, J., Pei, Y., Chi, H., Chi, H., Wang, H., Gong, S., Xu,
H., Dravid, V. P., Uher, C., Snyder, G. J., Wolverton, C., Kanatzidis, M. G. (2016).
Ultrahigh power factor and thermoelectric performance in hole-doped single-crystal
SnSe. Science, 351(6269), 141–144. Retrieved from
http://science.sciencemag.org/content/351/6269/141.abstract
Zhao, X. B., Ji, X. H., Zhang, Y. H., Zhu, T. J., Tu, J. P., & Zhang, X. B. (2005). Bismuth
telluride nanotubes and the effects on the thermoelectric properties of nanotube-
containing nanocomposites. Applied Physics Letters, 86(6).
http://doi.org/10.1063/1.1863440