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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

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