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Annular thermoelectric generator performance optimization analysis based on
concentric annular heat exchanger
Wenlong Yang1ψ, WenChao Zhu1,2ψ, Yang Li1, Leiqi Zhang3, Bo Zhao3,
Changjun Xie1,2*, Yonggao Yan4, Liang Huang1
1 School of Automation, Wuhan University of Technology, Wuhan 430070, China.
2 Hubei Key Laboratory of Advanced Technology for Automotive Components, Wuhan
University of Technology, Wuhan 430070, China.
3 State Grid Zhejiang Electric Power Research Institute, Hangzhou 310014, Zhejiang Province,
China.
4 State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, Wuhan
University of Technology, Wuhan 430070, China.
ψ W. Yang and W. Zhu contributed equally to this work.
* Corresponding author
E-mail address: jackxie@whut.edu.cn (C. Xie)
Abstract
In order to increase the energy conversion efficiency of thermoelectric generators
for automobile systems where the heat sources are commonly cylindrical, a novel
concentric annular thermoelectric generator (CATEG) consisting of annular
thermocouples and a concentric annular heat exchanger is proposed. A numerical model
of the CATEG is first established using a finite-element method, based on which the
thermoelectric performances of the proposed CATEG and the conventional annular
thermoelectric generator (ATEG) with a cylindrical heat exchanger are compared. The
relationship between the size of the heat exchanger, heat transfer characteristics, and
heat flow resistances are comprehensively studied. Furthermore, to balance the
relationship between heat transmission and fluid flow resistances, and to extract the
maximum net power, the optimal design of the concentric annular exchanger is obtained
and analyzed. Simulation results show that the optimized ratio of the inner and outer
diameters of the heat exchanger is 0.94, and the new ATEG with the proposed
concentric annular heat exchanger can significantly increase the total heat transfer
coefficient as well as the pressure drop, leading to a maximum net power of 65% higher
than the conventional ATEG.
2
Keywords: Annular thermoelectric generator; Concentric annular exchanger; Waste
heat recovery; Size optimization
1. Introduction
Continuously improving the energy conversion efficiency of automobiles is one
of the major pathways to conserve precious fossil energy sources and to reduce
greenhouse gas emissions. In general, only 25% of fuel energy in the internal
combustion engine vehicles is utilized for vehicle mobility and other necessary use,
while about 30 − 40% is wasted as exhaust gas [1,2]. The wasted energy in the exhaust
gas can be potentially recovered using a thermoelectric generator (TEG) by converting
the heat into electric energy directly through thermoelectric effects. The thermal energy
recovery TEG has attracted increasing research attention in recent years due to its
advantages of simple and light-weighted structure, free of mechanical moving parts,
high safety, and high reliability [3-5]. A typical TEG consists of a heat exchanger and
many PN couples adhered to its surface [6]. However, the low conversion efficiency of
the materials currently used for TEGs has limited their applications, while optimizing
the TEG design is essential to improve its performance for practical applications and
facilitate its commercialization process [7].
One of the causes of the low efficiency of the existing TEG design is that the
temperature difference between the hot and the cold ends of the PN thermocouples is
significantly smaller than that between the hot and the cold fluids [4]. Bell [8] pointed
out that the reason for such a small temperature difference is the presence of large
thermal resistance between the fluids and the thermocouples. Therefore, many
researchers focus on enhancing the heat transfer characteristics to improve energy
conversion efficiency [9]. The most common and most effective method to improve
heat transmission characteristics is to put fillers in the exhaust channel of the hot-end
exchanger with high thermal resistance. In order to improve the heat transmission rates
and avert excessive back pressure, Wang et al. [10] investigated a hot side heat
exchanger with cylindrical grooves and studied the effects of three internal structures
on the system through numerical simulation and evaluation of efficiency and net power.
3
Kim et al. [11] fixed six 2-mm-thick plate fins on the hot surface of each thermoelectric
module, and this method improved the heat transmission performance of TEG and
increased the pressure drop on both sides of the pipe. Lu et al. [12] proved that by filling
metal foam in the hot side exchanger channel, higher efficiency and power output can
be achieved compared to using rectangular fins, whereas it leads to high back pressure
and net power loss. In addition to enhancing the heat transfer performance of the heat
exchanger, matching heat exchanger dimensions with the fluid characteristics and
optimizing the structure of the thermoelectric module can also improve the efficiency
of TEG [13,14]. For example, Fan et al. [15] developed a complete numerical model to
compute the optimal size of thermocouples, and it was found that there exists an optimal
leg length and an optimal cross-sectional area to achieve the maximum output power.
Wang et al. [16] used a pitted surface to replace the inserted groove in the traditional
heat exchanger. Compared with the heat exchanger with embedded pits, the new design
effectively reduces the pressure drop and increases the net power. Niu et al. [17] studied
the influences of gas channel size on thermoelectric performance. They found that a
medium-sized heat exchanger should be used to balance the interaction between the
pressure drop along the channel and the heat transmission.
Although considerable progress has been made on the flat-plate TEG (FTEG),
such a design is not ideal for automobile exhaust gas heat recovery where the heat
source, i.e., the exhaust pipe, is usually cylindrical [18]. The inherent geometric
mismatch can cause the problems such as high energy loss and large heat transfer
resistance, which would significantly reduce the performance of TEG. In recent years,
with the advancements in material science and engineering, thermoelectric devices can
be designed in various geometric shapes including annular thermocouples [19,20].
Unlike conventional flat-plate thermoelectric couple (FTEC), the cross-sectional area
of an annular thermoelectric couple (ATEC) changes along the radial direction, and the
contact resistance of an ATEC can be smaller than that of FTEC [21]. Shen et al. [22,23]
proposed an annular thermoelectric generator (ATEG) and theoretically analyzed the
influence of the leg’s geometric characteristics on output power and efficiency under
different temperature ratios and external loads. For cylindrical heat sources, an ATEGs
4
consisting of a cylindrical heat exchanger and many ATECs have been investigated in
the literature. For example, Ge et al. [24] proposed a liquefied natural gas power
generation system composed of an air-heated evaporator and a cylindrical ATEG, and
a comprehensive comparison was provided in [25], in which the thermoelectric
performances of ATEG and FTEG with cylindrical heat sources are analyzed from
several aspects, including the convective heat transfer coefficient, inlet velocity, and
temperature.
Although the abovementioned studies have been conducted to optimize the heat
transfer capacity and efficiency of TEG, most of the existing investigations are based
on traditional FTEGs, and the applicability of the obtained research outcomes and
design guidelines from these works to ATEGs has not been examined. Regarding the
numerical analysis and optimization of thermocouple design, recent research on TEG
focused on components such as a single PN couple or segmented annular
thermocouples for conventional design [26-28], whereas studies for structural
improvement with novel designs at system levels is lacking, especially for the ATEG
[29]. It is therefore not only beneficial but also necessary to investigate optimized
structure to improve the energy efficiency of the whole system. In this connection, the
major contributions and innovations of this paper are as follows:
1) A novel concentric annular thermoelectric generator (CATEG) composed of a
concentric annular exchanger and ATECs is proposed for the first time.
2) A high-fidelity mathematical model of the CATEG is established. The model
incorporates a thermal resistance network of CATEG considering temperature
gradient, flow resistance, and heat transmission characteristics along the flow
direction so that thermoelectric characteristics can be accurately predicted for
performance evaluation and design improvement.
3) The thermoelectric characteristics and energy conversion performance of the
CATEG system are analyzed comprehensively, and the range of the optimal design
dimension for the concentric annular heat exchanger is obtained to achieve the
maximum net power output.
The rest of the paper is structured as follows. A mathematical model of the CATEG
5
is established in Section 2 for the present investigation. The proposed model is validated
with simulation and experiment data in Section 3. The influences of dimensional
parameters of the concentric annular heat exchanger on the thermoelectric performance
are analyzed and the optimal design is obtained to maximize the net generated power
of CATEG in Section 4. Conclusions are provided in Section 5.
Nomenclature
Greek
A
cross-sectional area of the exchanger, m2
α
the Seebeck coefficient, V∙K−1
a1,a2,a3
height, inner circular arc length and width of the
PN couple, m
δ
thickness, m
λ
thermal conductivity, W∙m−1∙K−1
a4
gap between P- and N-type legs, m
ρ
density, kg m−3; resistivity, ∙m
c
specific heat capacity, J∙g−1∙K−1
µ
dynamic viscosity, Pa∙s
Dh
hydraulic diameter, m
η
efficiency, %
d
convective heat transfer coefficient, W∙m−2∙K−1
∆
difference
dev
deviation percentage
Subscript
F
Darcy resistance coefficient
Hr
surface roughness, m
c
cold side of the thermocouple
h
height of heat exchanger, m
cer
ceramic
I
electric current, A
con
connector
K
thermal conductance, W∙K−1
cu
copper
k
total heat transfer coefficient, W∙m−2∙K−1
f
hot fluid
L
length of the heat exchanger, m
h
hot side of the thermocouple
m
mass flow rate, g∙s−1
i
inner ring of heat exchanger
nx
total PN couple number in a line
L
external load
nr
total PN couple number in a single-ring
max
maximum value
Nu
Nusselt number
n
N-type semiconductor
P
power, W
net
net value
p
pressure, Pa
opt
optimal value
Pr
Prandtl number
p
P-type semiconductor
q
quantity of heat, W
per
per unit module area
R
resistance,
pn
thermocouple
Re
Reynolds number
plate
heat exchanger plate
r
radius, m
pump
consumed pump value
S
exchanger plate areas, m2
teg
TEG module value
T
temperature, °C
w
cold fluid
v
flow velocity, m∙s−1
Superscript
Abbreviations
i ( j )
line (row) number
ATEC
annular thermoelectric couple
1
Case 1
ATEG
annular thermoelectric generator
2
Case 2
TEG
thermoelectric generator
CATEG
concentric annular thermoelectric generator
6
2. Modeling of CATEG
2.1 Configuration and model assumptions
The CATEG system under investigation is shown in Fig. 1(a). It is composed of a
concentric annular heat exchanger that carries the hot fluid of automobile exhaust gas,
a coolant heat exchanger that carries the cold fluid, and many ring-shaped
thermoelectric modules mounted in between. In the figure, h, ri, and r denote the height,
inner radius, and outer radius of the concentric annular heat exchanger, respectively,
and L is the length of the CATEG/heat exchanger. The hot fluid heats the thermoelectric
modules from one side (i.e., the hot end). A part of the thermal energy transferred to the
modules is converted to electricity by the thermoelectric materials, and the rest energy
is dissipated by the cold fluid via the other side of the modules (i.e., the cold end). The
temperatures of the fluid entering the inlet of the concentric annular and coolant heat
exchangers are denoted by Tfin and Twin, respectively.
Fig. 1. Modeling of CATEG: (a) 3D view, (b) Finite element model, (c) 3D view of an elementary
unit, (d) Equivalent thermal resistance network of an elementary unit.
7
Fig. 1(b) shows a non-isothermal finite-element model of the CATEG. The system
is divided into nx nr elementary units and each unit is denoted by (i, j) where i and j
represent the indices of the row and the column, respectively. Each unit contains a
thermocouple (i.e., a PN couple) which is composed of a p-type and an n-type
semiconductor leg as shown in Fig. 1(c). The two legs are electrically connected in
series with a copper connector and sandwiched between two identical ceramic sheets
made of Al2O3, and all PN couples are connected in series. In Fig. 1(c), a1, a2, and a3
are the height, inner circular arc length, and width of p-type or n-type legs, respectively,
and a4 is the gap between the legs. The radius corresponding to the inner circular arc
length is denoted by rpn, and the thicknesses of the copper connector and the ceramic
sheet are denoted by δcu and δcer, respectively. The ceramic sheet functions as an
electrically insulating layer which is essential for achieving heat transmission from the
external thermal energy to the cooling components. The thickness of the exhaust heat
exchanger and coolant heat exchanger tube wall is denoted as δplate.
An equivalent thermal resistance network, shown in Fig. 1(d), can be used to
model and explain the heat transmission process in one elementary unit. In the ith row,
the temperatures of the hot and the cold ends of the leg are denoted by Ti
h and Ti
c,
respectively. On the one hand, as hot fluid flows through the calculation units, the
temperature of the hot fluid will drop from Ti
f to Ti+1
f. On the other hand, the temperature
of cold fluid rises from Ti
w to Ti+1
w when the cold fluid flows through the unit. When the
thermal energy released by the engine exhaust is transferred to the ATEM, the total
thermal resistance mainly consists of four components. From the inside to the outside,
they are the convective heat transfer resistance, Rf1, the heat transfer resistance across
concentric annular exchanger, Rf2, the thermal contact resistance between the surface of
the heat exchanger and ATEM, Rfcon, and heat transfer resistance across the ceramic
sheet and the copper connector, Rf3. Correspondingly, thermal resistances of the cold
end are expressed as Rw1, Rw2, Rwcon, and Rw3, respectively. Assuming that there is no air
between all PN legs, heat radiation and the Thomson effect can thus be ignored.
8
2.2 Mathematical Model
As the fluid flows through the annular heat exchanger, the temperature of the
thermocouple in the same ring is the same, so each calculation unit is marked by
superscript i. For these calculation units, due to the heat conduction, two heat transfer
components qi
h and qi
c are generated, which can be described by three sets of heat
transfer equations. The first group is obtained by the temperature difference between
fluid and thermoelectric device surface and is given by Newton's heat transfer law. The
second group is the heat transfer equation considering the conduction heat, the Peltier
effect and the Joule effect. The third group comes from the conservation of energy law,
that is, the heat released by the fluid is equal to the heat absorbed by the thermoelectric
module.
Based on the thermal resistance network and steady-state heat transmission
process in a unit, it can be obtained and described by
(1)
where qi
h and qi
c are the heat absorbed at the hot side and the heat released at the cold
side, and Sh and Sc represent the heat transmission areas of the hot and the cold ends,
respectively. mf and mw are the mass flow rates of the hot fluid and the cold fluid,
respectively. kf and kw are the total heat transfer coefficients of the heat transferred from
hot fluid and cold fluid to the surface of the thermoelectric element, and cf and cw are
the specific heat capacities for the hot fluid and the cold fluid, respectively. In addition,
αpn, Kpn, and Rpn denote the Seebeck coefficient, thermal conductance, and electrical
resistance of a PN couple, respectively, and they are determined by
(2)
(3)
1
2
1
1
2
1
()
[ ( ) 0.5 ]
[0.5( ) ]
()
[ ( ) 0.5 ]
[ 0.5( )]
i i i
h f f f f
i i i
r pn h pn h c pn
i i i
r h f f f h
i i i
c w w w w
i i i
r pn c pn h c pn
i i i
r c w c w w
q c m T T
n IT K T T I R
n S k T T T
q c m T T
n IT K T T I R
n S k T T T
+
+
+
+
=−
= + − −
= + −
=−
= + − +
= − +
pn p n
=−
2 3 1
( ) { ln[( ) ]}
pn p n pn pn pn
K a a r r a r
= + +
9
(4)
where the symbols α, λ, and ρ represent the Seebeck coefficient, electrical resistivity,
and thermal conductivity, respectively, while the subscripts “p” and “n” are attached to
the symbols to represent the corresponding quantities for the p- and n-type legs,
respectively.
The total heat transfer coefficient kf is calculated by
(5)
where λplate, λcu, and λcer represent the thermal conductivities of the heat exchanger wall,
the copper connector, and the ceramic sheets, respectively. df is the convective heat
transfer coefficient of hot fluid, obtained by
(6)
where λf is the thermal conductivity of the hot fluid, and Dh is the annulus hydraulic
diameter defined as the difference between the outer and the inner diameters of the
annulus.
In (6), the Nusselt number is determined by [30]
(7)
where Re and Pr are the Reynolds number and the Prandtl number of the hot fluid,
respectively. Tfav and Twav are the average temperatures of the hot fluid and the engine
water in the fluid-flow direction, respectively. The Reynolds number can be calculated
by
(8)
where ρf, vf, and μf represent the density, velocity, and dynamic viscosity of the hot fluid,
respectively.
Next, the fluid flow resistance characteristic of the hot side heat exchanger can be
investigated by calculating the pressure drop ∆p of the exhaust gas, i.e., [31]
(9)
1 2 3
ln[( ) ]( )
pn pn pn pn p n
R r r a r a a
= + +
1 2 3
1 ( )
1 (1 )
f f f fcon f
f plate plate fcon cu cu cer cer
k R R R R
dR
= + + +
= + + + +
f f h
d Nu D
=
0.8 0.4
2/3 0.45 6
0.0214( 100) [1
( ) ]( ) ,2300 10
h fav wav
Nu Re Pr
D L T T Re
= − +
f h f f
Re D v
=
2
4 )( 2)( ffh
LvpFD
=
10
Here, F is the Darcy resistance coefficient, determined by [32]
(10)
where Hr is the internal surface roughness of the heat exchanger.
Considering the pumping power loss due to gas resistance through the channel, it
can thus be obtained by
(11)
Finally, the current I, output power Pteg, net power Pnet, and efficiency η of the
CATEG system are evaluated as follows,
(12)
(13)
(14)
(15)
2.3 Solution method
Given the model parameters, load resistance RL, and boundary values Tfin and Twin,
the developed model (1)−(15) shall be solved to obtain the current I (which equals the
currents in all the PN couples) as well as the temperature distribution Ti of the CATEG
system. However, since the current I and the temperatures are algebraically coupled by
the highly nonlinear equations (1) and (12), the analytical solution cannot be obtained.
The problem becomes more difficult as a similar coupling relationship exists between
0.25 8/7
1.11
8/7
0.0791 59.7
, 2000 (2 )
765lg(2 )
0.5 6.8 59.7
1.8lg , 665
3.7 (2 ) 2
0.25
3.7
2lg 2
rh
rh
r
h r h r h
h
rh
F Re
Re H D
HD
HRe
Re D H D H D
F
FD
HD
=
= − + −
=
2765lg(2 )
, 665 2rh
rh
HD
Re HD
−
( )
pump f f
P p m
=
1) ( )(
x
n
pn c L p x
i
hnr
i
i
TTI R R n n
=
= − +
1)(
x
i
ii
h
n
teg c
Pqq
=
=−
net teg pump
P P P=−
1
xi
h
n
net iqP
=
=
11
the temperature distribution of TEG and the convective heat transfer coefficient kf as
shown in (1) and (6). Hence, a numerical method with double iteration loops is
proposed to efficiently solve the model, and the flowchart of the procedure is shown in
Fig. 2.
The solution procedure is initialized with the initial guess I0 and kf0 with which the
initial temperature distribution is obtained by solving (1). According to the obtained
temperature distribution, kf can be updated using (6) and it is used as the new kf0 for the
next iteration in the inner loop. The process is repeated until the convective heat transfer
coefficient kf is considered close enough to the previous inner iteration. Next, a new
current I can be determined using (12), and the current is used as the new I0 for the next
iteration in the outer loop. The process is repeated until the current I is considered close
enough to the previous outer iteration. Once I, kf, and temperature distribution have
been determined, the performance indicators of the TEG can be calculated using
(13)−(15).
Fig. 2. Flowchart of the solution procedure.
3. Model validation
3.1 Numerical and experimental validation
12
In the previous section, an accurate numerical model of CATEG is established with
the consideration of the effects of ceramic plate, copper connector, and exchanger plate
on the system. The model will be validated in this section by comparing the simulated
results with the numerical and experimental results from the literature.
First, the simulation result of the proposed model is compared with the numerical
data given in Ref. [33], where an ATEG with a hot-side cylindrical heat exchange
channel was proposed and calculated net power output of the system for the loss of
pumping power due to fluid resistance. In order to reproduce the data, we used the same
parameters as given in Ref. [33] and set the inner radius ri of the concentric annular
heat exchanger to 0. By this means, the CATEG is equivalent to a conventional ATEG
with a cylindrical heat exchanger. The maximum net powers of ATEG with different
exhaust gas mass flow rates are shown in Fig. 3(a). It is observed that the maximum
absolute error between the simulated result and data in Ref. [33] is 3.9%. This error is
due to the consideration of the copper plate, ceramic sheets, and contact thermal
resistance in our model.
For further validation of the proposed model, we compare the simulation result
with experimental data extracted from the works by Niu et al. [34] and Ge et al. [24].
In this case, we consider the fact that when the radius of the ATEG is large enough, the
curvature corresponding to the inner arc circular of the PN couple is small, and the
annular thermoelectric couples can be regarded as an FTEC. In the experiment, a
commercial Bi2Te3 thermoelectric module with the dimensions of 40 mm 40 mm
4.2 mm was used. The average thermal conductivity, resistivity, and the Seebeck
coefficient of the thermoelectric module are 1.7 W/(m·K), 9.5 10−6 ·m, and 2
10−4 V/K, respectively, all measured at room temperature. We use the same parameters
in our proposed model for model validation. The variation of power with different loads
are shown in Fig. 3(b), and it is observed that the error between the predicted results
from Ref. [24] and the experimental data was less than 10%, while the error between
the proposed model and the experimental data is less than 8%, since the effects of
ceramic plate, copper connector, and exchanger plate are considered in our model.
The proposed model structure is general, although the presented simulation results
13
still exhibit some errors compared to the experimental results, and this is mainly due to
the limitation in the model parameters. First, the parameters regarding the physical
characteristics of the PN couples are set to constant, while in practice they are highly
temperature-dependent. Second, the thermal contact resistance is set as 0.0008 m2∙K/W
in the simulation, obtained from Ref. [30], while the true value for the experiment is
not known. Furthermore, statistical approaches are beneficial for further model
evaluation by considering the design uncertainties [35].
Fig. 3. Verification of the proposed arithmetic model. (a) Comparison with numerical results from
[33]. (b) Comparison with experimental results from [34] and numerical results from [24].
3.2 Performance analysis of the theoretical model
In addition, for further model comparison, Table 1 summarizes several prevailing
modeling methods for the thermocouples or TEGs in the literature. It can be seen that
14
many theoretical models of thermocouples or thermoelectric generators have been
established using various modeling methods and implemented in different software,
from one-dimensional to three-dimensional models and from analogy model to the
thermal-electric numerical model. However, when the annular thermoelectric module
is used to recover fluid waste thermal energy, especially the waste heat of automobile
exhaust, few ATEG models can be adopted to comprehensively evaluate and optimize
the thermoelectric and output performances of the ATEG system. For example, Ref. [22]
established the mathematical model of the annular thermocouple using the finite
element method, but when multiple thermocouples are coupled together to form a
thermoelectric generator (TEG), accurate thermoelectric performance cannot be
obtained. Ref. [24] established a numerical model of ATEG by constructing a thermal
resistance network model, but the power loss caused by fluid resistance was not
considered. Ref. [38] established a three-dimensional model of an ATEG through
thermal stress analysis, and optimized the number and geometric structure of
thermocouples, but did not consider the impact of the annular heat exchanger on ATEG.
Table 1
Recent advances in modeling methods for TEC and TEG.
Research
Subject
Modeling Method and
Software
Feature
Model Type
Ref.
TEC
Numerical model /
MATLAB
1-D
short calculation
time
Thermal
resistance model
[13]
Finite-element method /
MATLAB
1-D
steady model
Thermal-electric
numerical model
[22]
ANSYS / EES
1-D
short calculation
time
Thermal
resistance model
[36]
SPICE / Mathematica
1-D steady-state
analysis and
analogies
Analogy model
[37]
TEG
Numerical simulation /
MATLAB
from 1-D to 2-D
iterative
calculation
Thermal
resistance model
[24]
Numerical simulation /
Fortran program
2-D
iterative
calculation
Thermal-electric
numerical model
[30]
Finite element approach
/ ANSYS
3-D
steady-state
Thermal stress
analyses
[38]
15
Compared to the existing TEG models as given in Table 1, the thermal resistance
model established in this work is a fluid-thermo-electric multiphysics field coupling
model, which comprehensively considers the temperature gradient, flow resistance, and
heat transmission characteristics along the flow direction. The model can accurately
predict the thermoelectric performance and net power characteristics of CATEG by
establishing a thermal resistance network model and iterative algorithms, the method
can be generalized to provide guidelines for modeling new ATEG systems in the future.
4. Results and discussion
In this section, the effects of various design factors on thermoelectric performance,
such as output power, net power, heat transfer performance, efficiency, etc., will be
analyzed via simulation studies based on the validated CATEG model developed in the
previous sections. The physical parameters of thermoelectric material (Bi2Te3) and the
dimensions of the ATEC are presented in Table 2. In the automobile coolant system, the
mass flow rate and the temperature are mw = 425 g/s and Twin = 70 ℃ [39],
respectively. The contact thermal resistance is set to 0.0008 m2·K/W. In addition, the
thickness and the thermal conductivity of the ceramic sheet, the copper sheet, and the
heat exchanger plate have significant influences on the heat transfer performance of the
TEG, and they need to be determined according to practical situations. The basic
parameters of heat source and TEG used in this work are provided in Table 3.
Table 2
Main physical and dimensional parameters of ATEC [39].
Parameters
Description
Value
Units
a1/a2/a3
P(N)-type leg height/width/inner arc circular length
5/5/5
mm
a4
Clearance between P-type and N-type legs
0.1
mm
αp
P-type Seebeck coefficient
2.03710−4
V/K
αn
N-type Seebeck coefficient
−1.72110−4
V/K
λp
P-type thermal conductivity
1.265
W/(m·K)
λn
N-type thermal conductivity
1.011
W/(m·K)
ρp
P-type resistivity
1.31410−5
·m
ρn
N-type resistivity
1.11910−5
·m
16
Table 3
Basic parameters of heat source and TEG.
Parameter
Description
Value
Unit
kw
Heat transfer coefficient of water [30]
1000
W/(m2·K)
Tfin
Exhaust gas inlet temperature
500
℃
Twin
Cooling water inlet temperature [39]
70
℃
mf
Mass flow rate of exhaust gas
50
g/s
mw
Mass flow rate of water [39]
425
g/s
Rcon
Contact thermal resistance [30]
0.0008
m2·K/W
δcer
Thickness of ceramic plate
0.05
mm
λcer
Thermal conductivity coefficient of ceramic plate
35
W/(m·K)
δcu
Thickness of copper connector
0.2
mm
λcu
Thermal conductivity coefficient of copper connector
398
W/(m·K)
δplate
Thickness of exchanger plate
0.3
mm
λplate
Thermal conductivity coefficient of exchanger plate
398
W/(m·K)
4.1 Thermoelectric performance analysis of CATEG
Fig. 4 shows the output power Pteg, voltage U, and current I of the CATEG as
functions of the module area S. Here, the height of the exchanger h is set as 5 mm. The
outer radius r of the concentric annular heat exchanger is 38 mm for an ordinary
automobile exhaust pipe, and the corresponding number of units per module is nr = 20.
It can be seen that I reduces and U increases monotonously as S increases, while both
of their rates of change decrease. Most importantly, there exists a maximum output
power Pteg,max for the CATEG. This is because, with an increased number of PN couples,
the heat transfer area from the hot end to the cold end increases, the thermal resistance
decreases, the heat conduction through the PN couples increases, and it results in a
decrease in the output power. This result is also identified by He et al. [40]. Hence, for
given parameters of the heat source, there exists an optimal module area Sopt to
maximize Pteg. According to Fig. 4, when S = Sopt = 0.34 m2, Pteg = Pteg,max = 449 W.
17
Fig. 4. Variations of Pteg, U, and I with S for h = 5 mm, nr = 20.
Next, we compare the thermoelectric characteristics of the CATEG with the
conventional cylindrical heat exchanger ATEG equipped with the cylindrical heat
exchanger. The mathematical model of the conventional ATEG was established based
on the schematic diagram shown in Fig. 5, and its parameters are selected to be the
same as the CATEG. Fig. 6(a) shows the influence of the length L of CATEG on output
power, net power, and efficiencies for these two exhaust heat exchanger structures. It is
observed that for the conventional cylindrical heat exchanger (Case 2), the difference
between the net power Pnet and the output power Pteg is small due to that the required
pumping power is low. On the other hand, for the concentric annular heat exchanger
(Case 1), although more pumping power is needed, the output power is higher than
Case 2. The reason for this is because with the concentric heat exchanger, the heat
transmission capacity of the hot side channel is increased and more thermal energy can
be converted into electricity by the thermocouples. Fig. 6(b) shows the influence of L
on pressure drop and heat transfer coefficient. It shows that, compared to the cylindrical
heat exchanger, the concentric design can significantly improve the heat transfer
coefficient, thereby increasing the output power. However, a higher pressure drop will
also cause a higher pumping power consumption. According to Fig. 6(a), the net power
of the CATEG is higher than the cylindrical design when L < 2 m, and the maximum
net power of the CATEG is 65% higher than that of the cylindrical heat exchanger
ATEG. When the peak net power is obtained, the efficiency of the CATEG is 4.7%. In
18
addition, the new type of heat exchanger can be readily adapted according to the shape
of the exhaust pipe, which can optimize the heat transfer characteristics, improve the
heat transfer performance, and accommodate more ATECs. Therefore, the ATEG based
on the concentric annular heat exchanger proposed in this paper is superior to the
conventional cylindrical heat exchanger ATEG for automobile applications.
Fig. 5. Schematic diagram of the conventional cylindrical heat exchanger ATEG system.
19
Fig. 6. Variations of (a) Pteg, Pnet, η, (b) kf, Δp with L for the same boundary condition (Case 1:
concentric annular heat exchanger ATEG; Case 2: cylindrical heat exchanger ATEG).
4.2 CATEG power output analysis based on fluid heat transfer characteristics
In this subsection, the influence of the dimension (L, r, and h) of the concentric
annular heat exchanger on the heat transmission characteristics and output power of the
CATEG will be discussed. The influence of dimension on Pteg with different design are
shown in Fig. 7(a). It can be seen that in order to increase Pteg, it requires to reduce h or
r, while an optimal heat exchanger length exists to obtain the maximum output power.
This characteristic can be explained using Fig. 7(b), where it shows that the heat transfer
coefficient kf will reduce when L, r, or h increases. However, since the cross-sectional
area A is the major factor affecting kf, according to A = πr2 – π(r−h)2, changing L is less
effective compared with changing r or h, as can be observed from Fig. 7(b).
20
Fig. 7. CATEG power output and heat transfer coefficient versus exchanger height, radius, and
length under the condition of stable heat source: (a) Output power; (b) Total heat transfer
coefficient.
Next, with A increases, the maximum output power Pteg,max, the optimal module
area Sopt, corresponding optimal total heat transfer coefficient can be obtained and the
relationships are shown in Fig. 8. It can be seen that reducing A can increase Pteg,max as
well as the corresponding kf,opt, while the corresponding Sopt will decrease almost
linearly as A reduces. In this case, when the cross-sectional area is A = 0.0011 m2, the
maximum power Pteg,max = 449 W is obtained, which is the same as that given in Fig. 4.
The corresponding optimal module area Sopt = 0.36 m2 and the optimal total heat
transfer coefficient kf,opt =177 W·m−2·K−1.
Fig. 8. Variations of Pteg,max, kf,opt, and Sopt with different A.
21
In addition, we show in Fig. 9 that radius r and height h have significant influences
on the optimal module length Lopt. It can be seen that Lopt has a positive correlation with
height h, and this relationship is similar to that between A and Sopt as shown in Fig. 8.
Therefore, in order to obtain a smaller L, the heat exchanger should be designed with a
smaller h and/or a larger r.
When the cross-sectional area A = 0.0011 m2, Fig. 10 shows the influence of h on
Lopt, Sopt, r, Pteg,max, and kf,opt. From Fig. 10(a), it can be seen that Lopt increases
approximately linearly as h increases, while h has a negligible effect on Sopt. From Fig.
10(b), both Pteg,max and the corresponding kf,opt decrease with the increase of h. Therefore,
when the cross-sectional area of the heat exchanger is fixed, a smaller height can be
selected to obtain a higher output power and a smaller module area.
Fig. 9. Variations of Lopt with different r and h.
22
Fig. 10. Variations of (a) Lopt, Sopt, r, (b) Pnet,max, and kf,opt with h for A = 0.0011 m2.
4.3 CATEG net power analysis based on flow resistance characteristics
According to the results obtained in the previous subsections, one shall reduce the
cross-sectional area A to increase the output power of the CATEG. However, a smaller
A will also cause larger heat flow resistances, which can lead to additional pump power
consumption. Such a design trade-off will be analyzed in this subsection.
Fig. 11 shows the change in pressure drop Δp as well as net power Pnet with various
exchanger dimensions. It can be seen from Fig. 11(a) that, ∆p decreases significantly
as h or r increases, while it increases as the L increases almost linearly. Fig. 11(b) shows
that there exists an optimal design for h, r, and L to achieve the maximum Pnet, and this
is different from the case as shown in Fig. 7(a) where only L has an optimal value.
23
Fig. 11. Relationship between (a) pressure drop, (b) net power, and exchanger sizes (length,
radius, and height).
This can be explained with Fig. 7(b): A small h can lead to a large kf and a large
Pteg, whereas it will also increase Δp as well as Ppump. As h increases, Δp and Ppump
gradually decrease, so Pnet first increases to the maximum value and then gradually
decreases. To obtain the optimal output characteristics, it is necessary to balance the
two factors of heat transmission as well as fluid flow resistance, so an optimal heat
exchanger height can be determined to maximize the net power.
The cross-sectional area A also significantly affects the pressure drop Δp. The
changes in the maximum net power output Pnet,max, power per unit area Pper, and the
corresponding module area Sopt with various A are shown in Fig. 11. It is observed that
Sopt increases approximately linearly with the increase of A, similar to Fig. 8. In addition,
Pnet,max first increases and then decreases as A increases. The peak Pnet,max is reached at
A = 0.0016 m2, and the corresponding Pper is high. The result is more practical than that
shown in Fig. 8, since Fig. 8 indicates that a smaller A can always lead to a higher
Pnet,max.
24
Fig. 12. Relationships of Pnet,max, Sopt, and Pper versus A.
Next, Fig. 13(a) shows the effect of height h on the optimal exchanger dimensions
for the optimal cross-sectional area Aopt = 0.0016 m2. From it, both the optimal length
Lopt and the optimal module area Sopt increase linearly as h increases. When h < 0.002
m, ropt > 13 cm; when h > 0.01 m, Lopt > 2 m. Therefore, the optimal height hopt should
be in the range of 0.002 – 0.01 m for automobile applications.
For the same Aopt = 0.0016 m2, Fig. 13(b) illustrates the influence of h on the
maximum net power, corresponding kf,opt, and degree of net power deviation devper.
Here, devper is defined as:
(16)
It can be seen that in this case the changes in kf,opt and Pnet,max are small. When h =
0.004 m, Pnet,max reaches the peak value, denoted by Pnet,peak. Therefore, in this condition,
the optimal design of heat exchanger is hopt = 0.004 m, ropt = 0.066 m, Lopt = 0.77 m,
and Sopt = 0.32 m2, and the corresponding optimal total heat transfer coefficient is kf,opt
= 108 W∙m−2∙K−1. In addition, devper < 5.2% within the optimal heat exchanger height
range of 2 –10 mm when the optimum cross-sectional area Aopt is obtained.
In the FTEG, the heat exchanger is a thin cuboid channel with an optimal height
of 5 mm, which ensures that the FTEG has improved heat transfer characteristics and
increased power output [30]. In CATEG, the fluid channel is a similar thin concentric
annular channel, the optimum height of the heat exchanger is 4 mm. This difference is
due to the use of annular thermocouples and the unconventional structure of the heat
, ,max ,
100 ( )
per net peak net net peak
dev P P P= −
25
exchanger. The optimal heat exchanger dimensions can be obtained using the design
equations in the case of variable exhaust parameters in FTEG [41]. In the CATEG, the
optimal size will also change with the parameters of the heat source. The optimum
dimension design of concentric annular heat exchanger ATEG under stable operating
conditions of automobiles is the focus of this paper, therefore, the optimization design
of automobile ATEG system under variable operating conditions will be our future work.
The conversion efficiency η is obtained with different h, shown in Fig. 13(c). It
can be observed that η > 4.5% within the optimal height range of 2 –10 mm, and for the
optimum height hopt = 0.004 m, the efficiency is η = 4.73%. Hence, with the optimal
design as presented in Fig. 13(a), excellent performance of CATEG can be obtained in
a wide range of selection of exchanger height.
To express the optimal height of the concentric annular heat exchanger more
intuitively, dimensionless analysis is carried out by defining θ as the ratio of the inner
diameter to outer diameter of the concentric annular heat exchanger:
(17)
The range of the optimal θ is found to be 0.85−0.97. When θ is 0.94, the maximum
net power of 338 W can be reached.
i
rr
=
26
Fig. 13. Variations of (a) optimal heat exchanger dimension (length, radius, height, and module
area), (b) net power, heat transfer coefficient, net power deviation, and (c) conversion efficiency
with h.
5. Conclusions
In order to recover the exhaust thermal energy from automobile waste gas
effectively, a new type of annular thermoelectric generator (ATEG) named the
concentric annular heat exchanger ATEG (CATEG) is proposed in this paper. A
comprehensive CATEG mathematical model is developed and the novel features of the
proposed CATEG system are identified and analyzed. The main findings in this work
are summarized as follows.
1) The concentric annular heat exchanger increases the total heat transfer coefficient,
27
enhances the heat transmission capacity, and improves the output power of ATEG.
Compared with the conventional cylindrical heat exchanger ATEG, the maximum
net power of CATEG can be increased by 65%.
2) When designing a concentric heat exchanger for an ATEG, it is recommended to
choose the dimensions with a small height h, a small length L, and a moderate radius
r (See Fig. 1(a) for definitions). In addition, for a given cross-sectional area, the
optimal length increases linearly with the increase of height of the heat exchanger,
and a larger height corresponds to lower power output and a longer optimal module
length.
3) According to the calculation conditions given in this paper, the peak net power can
be obtained when the cross-sectional area of the heat exchanger is 0.0016 m2. The
optimal ratio of the inner diameter to outer diameter of the heat exchanger is 0.94,
and the corresponding maximum net power is 338 W.
4) The recommended ratio of the inner diameter to outer diameter of the concentric
annular heat exchanger is in the range of 0.85−0.97. Within this range, the
maximum net power deviation can be limited below 5.2%, and the efficiency is
higher than 4.5%.
Acknowledgments
This research was supported by the National Natural Science Foundation of China
(51977164), and the Wuhan Frontier Project on Applied Research Foundation
(2019010701011405).
References
[1] S. Fan, Y. Gao, Numerical analysis on the segmented annular thermoelectric
generator for waste heat recovery, Energy 183, (2019) 35–47.
[2] X. Li, C. Xie, S. Quan, L. Huang, W. Fang, Energy management strategy of
thermoelectric generation for localized air conditioners in commercial vehicles
based on 48 V electrical system, Appl. Energy 231 (2018) 887–900.
[3] A. Elghool, F. Basrawi, T. K. Ibrahim, K. Habib, H. Ibrahim, D. M. N. D. Idris, A
28
review on heat sink for thermo-electric power generation: classifications and
parameters affecting performance, Energy Convers. Manage. 134 (2017) 260–277.
[4] Y. Li, B. Xiong, D. M. Vilathgamuwa, Z. Wei, C. Xie, C. Zou. Constrained
ensemble Kalman filter for distributed electrochemical state estimation of lithium-
ion batteries, IEEE Trans. Ind. Informat. 17 (1) (2021) 240-250.
[5] Y. Zhao, S. Wang, M. Ge, Y. Li, Z. Liang, Y. Yang, Performance analysis of a
thermoelectric generator applied to wet flue gas waste heat recovery, Appl. Energy
228 (2018) 2080–2089.
[6] X. Li, C. Xie, S. Quan, Y. Shi, Z. Tang, Optimization of thermoelectric modules’
number and distribution pattern in an automotive exhaust thermoelectric generator,
IEEE Access 7 (2019) 72143–72157.
[7] S. Huang, X. Xu, A regenerative concept for thermoelectric power generation, Appl.
Energy 185 (2017) 119–125.
[8] Bell LE. Cooling, heating, generating power, and recovering waste heat with
thermoelectric systems. Science 2008;321:1457–61.
[9] S. Vale, L. Heber, P. J. Coelho, C. M. Silva, Parametric study of a thermoelectric
generator system for exhaust gas energy recovery in diesel road freight
transportation, Energy Convers. Manage. 133 (2017) 167–177.
[10] Y. Wang, S. Li, Y. Zhang, X. Yang, Y. Deng, C. Su, The influence of inner topology
of exhaust heat exchanger and thermoelectric module distribution on the
performance of automotive thermoelectric generator, Energy Convers. Manage.
126 (2016) 266–277.
[11] T. Y. Kim, S. Lee, J. Lee, Fabrication of thermoelectric modules and heat transfer
analysis on internal plate fin structures of a thermoelectric generator. Energy
Convers. Manage. 124 (2016) 470–479.
[12] C. Lu, S. Wang, C. Chen, Y. Li, Effects of heat enhancement for exhaust heat
exchanger on the performance of thermoelectric generator, Appl. Therm. Eng. 89
(2015) 270–279.
[13] H. Tian, X. Sun, Q. Jia, X. Liang, G. Shu, X. Wang, Comparison and parameter
optimization of a segmented thermoelectric generator by using the high
29
temperature exhaust of a diesel engine, Energy 84 (2015) 121–130.
[14] C. Baker, P. Vuppuluri, L. Shi, M. Hall, Model of heat exchangers for waste heat
recovery from diesel engine exhaust for thermoelectric power generation, J.
Electron. Mater. 41 (2012) 1290-1297.
[15] L. Fan, G. Zhang, R. Wang, K. Jiao, A comprehensive and time-efficient model for
determination of thermoelectric generator length and cross-section area, Energy
Convers. Manage. 122 (2016) 85–94.
[16] Y. Wang, S. Li, X. Xie, Y. Deng, X. Liu, C. Su, Performance evaluation of an
automotive thermoelectric generator with inserted fins or dimpled-surface hot heat
exchanger, Appl. Energy 218 (2018) 391–401.
[17] Z. Niu, H. Diao, S. Yu , Investigation and design optimization of exhaust-based
thermoelectric generator system for internal combustion engine, Energy Convers.
Manage. 85 (2014) 85–101.
[18] S. Manikandan, S. C. Kaushik, Energy and exergy analysis of solar heat pipe based
annular thermoelectric generator system, Solar Energy 135 (2016) 569–577.
[19] X. Zhou, Y. Yan, X. Lu, H. Zhu, X. Han, G. Chen, Z. Ren, Routes for high-
performance thermoelectric materials, Mater. Today 21 (9) (2018) 974–988.
[20] J. L. Blackburn, A. J. Ferguson, C. Cho, J. C. Grunlan, Carbon-nanotube-based
thermoelectric materials and devices. Adv. Mater. 30 (11) (2018) 1704386.
[21] A. Bauknecht, T. Steinert, C. Spengler, G. Suck, Analysis of annular thermoelectric
couples with nonuniform temperature distribution by means of 3-D multi-physics
simulation, J. Electron. Mater. 42 (2013) 1641–1646.
[22] Z.-G. Shen, S.-Y. Wu, L. Xiao, Theoretical analysis on the performance of annular
thermoelectric couple, Energy Convers. Manage. 89 (2015) 244–250.
[23] Z.-G. Shen, S.-Y. Wu, L. Xiao, Assessment of the performance of annular
thermoelectric couples under constant heatflux condition, Energy Convers.
Manage. 150 (2017) 704–713.
[24] M. Ge, X. Wang, Y. Zhao, Performance analysis of vaporizer tube with
thermoelectric generator applied to cold energy recovery of liquefied natural gas,
Energy Convers. Manage. 200 (2019) 112112.
30
[25] M. Zhang, J. Wang, Y. Tian, Performance comparison of annular and flat-plate
thermoelectric generators for cylindrical hot source. Energy Reports 7 (2021) 413–
420.
[26] A. B. Zhang, B. L. Wang, D. D. Pang, Effects of interface layers on the performance
of annular thermoelectric generators, Energy 147 (2018) 612–620.
[27] S. Shittu, G. Li, X. Zhao, High performance and thermal stress analysis of a
segmented annular thermoelectric generator, Energy Convers. Manage. 184 (2019)
180–193.
[28] Z.-G. Shen, X. Liu, S. Chen, Theoretical analysis on a segmented annular
thermoelectric generator, Energy 157 (2018) 297–313.
[29] M. Hosseini, A. H. Abdelrazek, R. Sadri, Numerical study of turbulent heat transfer
of nanofluids containing eco-friendly treated carbon nanotubes through a
concentric annular heat exchanger, Int. J. Heat Mass Transf. 127 (2018) 403–412.
[30] W. He, S. Wang, Y. Li, Y. Zhao, Structural size optimization on an exhaust
exchanger based on the fluid heat transfer and flow resistance characteristics
applied to an automotive thermoelectric generator, Energy Convers. Manage. 129
(2016) 240–249.
[31] S. Mavridou, G. C. Mavropoulos, D. Bouris, D. T. Hountalas, G. Bergerles,
Comparative design study of a diesel exhaust gas heat exchanger for truck
applications with conventional and stage of the art heat transfer enhancements.
Appl. Therm. Eng. 30 (2010) 935–947.
[32] H. Cui, Z. Shi, S. Yang, X. Yue, J. Meng, Engineering fluid mechanics, 1th ed.
Beijing: Petroleum industry Press; 1995.
[33] Y. Yang, S. Wang, Y. Zhu, Evaluation method for assessing heat transfer
enhancement effect on performance improvement of thermoelectric generator
systems, Appl. Energy 263 (2020) 114688.
[34] Z. Niu, H. Diao, S. Yu, K. Jiao, Q. Du, G. Shu, Investigation and design
optimization of exhaust-based thermoelectric generator system for internal
combustion engine, Energy Convers. Manage. 85 (2014) 85–101.
[35] M. A. Ozgur, O. Arslan, R. Kose, K. O. Peker, Statistical evaluation of wind
31
characteristics in Kutahya, Turkey, Energy Sources Part A – Recov. Util. Environ.
Effects 31 (2009) 1450–1463.
[36] G. Fraisse, J. Ramousse, D. Sgorlon, C. Goupil, Comparison of different modeling
approaches for thermoelectric elements, Energy Convers. Manage. 65 (2013) 351–
356.
[37] D. Mitrani, J. Salazar, A. Turó, M. J. García, J. A. Chávez, One-dimensional
modeling of TE devices considering temperature-dependent parameters using
SPICE, Microelectron. J. 40 (2009) 1398–1405.
[38] S. Fan, Y. Gao, Numerical simulation on thermoelectric and mechanical
performance of annular thermoelectric generator, Energy 150 (2018) 38–48.
[39] T. K. Jack, M. M. Ojapah, Water-cooled petrol engines: a review of considerations
in cooling systems calculations with variable coolant density and specific heat, Int.
J. Adv. Eng. Technol. 6 (2013) 659–667.
[40] W. He, R. Guo, S. Liu, K. Zhu, S. Wang, Temperature gradient characteristics and
effect on optimal thermoelectric performance in exhaust power-generation systems,
Appl. Energy 261 (2020) 114366.
[41] W. He, R. Guo, H. Takasu, Y. Kato, S. Wang, Performance optimization of common
plate-type thermoelectric generator in vehicle exhaust power generation systems,
Energy 175 (2019) 1153–1163.
