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Applied Energy 363 (2024) 123047
0306-2619/© 2024 Elsevier Ltd. All rights reserved.
Innovative design for thermoelectric power generation: Two-stage
thermoelectric generator with variable twist ratio twisted tapes optimizing
maximum output
Wenlong Yang
a
,
b
, Chenchen Jin
b
, Wenchao Zhu
a
,
c
, Changjun Xie
a
,
b
,
*
, Liang Huang
b
, Yang Li
d
,
Binyu Xiong
b
a
Hubei Key Laboratory of Advanced Technology for Automotive Components, Wuhan University of Technology, Wuhan 430070, China
b
School of Automation, Wuhan University of Technology, Wuhan 430070, China
c
State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, Wuhan University of Technology, Wuhan 430070, China
d
Department of Electrical Engineering, Chalmers University of Technology, Gothenburg 41258, Sweden
HIGHLIGHTS
•Two-stage thermoelectric modules boosts power output.
•Variable twist ratio twisted tapes to boost thermal energy extraction efciency.
•Impact of tape pitch ratio and variable twist ratio on thermoelectric performance.
•Optimized thermoelectric generator net output power doubled.
ARTICLE INFO
Keywords:
Two-stage thermoelectric generator
Variable twist ratio
Twisted tape
Waste heat recovery
Heat transfer enhancement
ABSTRACT
In recent years, considerable effort has been dedicated to the development of highly efcient thermoelectric
generators for waste heat recovery and thermoelectric power generation. In this study, we present employing
twisted tapes with variable twist ratio to enhance thermal energy extraction efciency, coupled with two-stage
thermoelectric modules for heat-to-electricity conversion, resulting in a substantial increase in the power output
of the thermoelectric generator. We established an experimental system that validated the superior power
generation and heat recovery characteristics of the two-stage thermoelectric generator. Building upon these
ndings, we propose further optimizing the variable twist ratio twisted tapes to enhance the power output. We
investigated the impact of tape pitch ratio, twist ratio, and twist ratio variation range on thermoelectric per-
formance. Experimental results indicate that the inuence of ow instability is more pronounced than that of
swirl intensity, and twist tapes with the maximum twist ratio variation rate yield the highest net output power.
Compared to an unmodied thermoelectric generator, the two-stage thermoelectric generator employing twist
tapes with a twist ratio increase from
π
to 3
π
achieves a maximum net output power gain of up to 100%. These
ndings provide a practical framework for integrating innovative power generation modules and optimized heat
exchanger designs into the application of waste heat recovery thermoelectric generators, marking a signicant
advancement in the eld of thermoelectric generators.
1. Introduction
Various energy-intensive processes, such as industrial activities and
power generation, often result in the wasteful dissipation of excess heat,
leading to a signicant squandering of energy and resources. Waste heat
recovery, a pivotal research domain garnering global attention, presents
an avenue for enterprises to diminish energy consumption, carbon
emissions, and costs. The conversion of waste heat into efcient elec-
trical power is considered among the most optimal techniques for waste
heat utilization, given the substantial volume of waste heat, where even
marginal advancements may yield profound changes [1].
* Corresponding author at: Hubei Key Laboratory of Advanced Technology for Automotive Components, Wuhan University of Technology, Wuhan 430070, China.
E-mail addresses: wenlongyang@whut.edu.cn (W. Yang), jackxie@whut.edu.cn (C. Xie).
Contents lists available at ScienceDirect
Applied Energy
journal homepage: www.elsevier.com/locate/apenergy
https://doi.org/10.1016/j.apenergy.2024.123047
Received 30 December 2023; Received in revised form 23 February 2024; Accepted 15 March 2024
Applied Energy 363 (2024) 123047
2
Thermoelectric Generators (TEGs) emerges as a promising green
waste heat recovery technology, directly transforming thermal energy
into electricity. Thermoelectric generators possess unique advantages
such as solid-state conversion, absolute noiselessness, low maintenance
costs, and structural simplicity [2]. The solid-state conversion is ach-
ieved through Thermoelectric Modules (TEMs), utilizing the Seebeck
effect to directly convert temperature differentials into electrical energy.
Research on waste heat TEGs has been extensively documented, pri-
marily concentrated in the domains of automotive and marine engines
[3].
Despite the increasing prevalence of electric vehicles [4], fossil fuel-
powered automobiles emit substantial waste heat through their exhaust
systems. Due to the limitations of Carnot cycle efciency, this results in
energy wastage and environmental issues. Even a modest proportion,
such as 6%, converted into electricity could reduce fuel consumption by
10% [5], offering numerous benets to both the environment and en-
ergy efciency. Hence, efcient recovery of vehicle waste heat is
imperative to reduce emissions and enhance energy efciency. Liu et al.
[6] installed four TEGs on an off-road vehicle, achieving a maximum
output power of 944 W through road tests and dynamometer experi-
ments. Zhang et al. [7] employed a TEG constructed with nano-
structured materials for recovering waste heat from automotive diesel
engines, achieving 1 kW of electricity production with a thermoelectric
efciency of 2.1%. These studies underscore the feasibility and vast
application prospects of thermoelectric generators for vehicle waste heat
recovery. However, the generation of such signicant electrical power
comes at the cost of exacerbated weight and economic considerations
[8]. Substantial improvements in power density, economic viability, and
conversion efciency are necessary to effectively promote the wide-
spread application of automotive thermoelectric generators.
Researchers are diligently enhancing the performance of TEGs from
multiple perspectives, encompassing the development of novel ther-
moelectric materials [9], innovative thermoelectric module structures
[10], optimization of circuit topologies [11], augmented heat transfer at
the hot end [12], and optimization of heat dissipation [13]. Through
these investigations, fundamental parameters governing the perfor-
mance of exhaust waste heat recovery TEGs have gradually come to
light. Constrained by the low conversion efciency of current commer-
cial thermoelectric materials (below 5%), achieving 20 W of electricity
from a single TEM necessitates the passage of at least 400 W of heat at
the hot end [14]. This is attributed to the fact that, aside from the
intrinsic thermoelectric conversion capability of the material itself, the
power generation is contingent upon the temperature differential at
both ends. However, due to the remarkably limited convective heat
transfer coefcient at the gas-solid interface, collecting a heat ow
exceeding 400 W for each TEM proves to be particularly challenging [1].
Consequently, the heat exchange between the gas and the thermoelec-
tric module emerges as a pivotal factor determining the performance of
thermoelectric generators for exhaust waste heat recovery, constituting
one of the foremost challenges in the current landscape [15].
Through extensive research, researchers have gradually identied
solutions to the issue. A commonly employed method is optimizing the
arrangement of internal heat exchangers, aiming to minimize the ther-
mal resistance of the exchangers. The desired outcome is the reduction
of the temperature differential between the hot gas and the thermo-
electric module surface, ultimately achieving the goal of enhancing the
heat extraction rate and power generation. One of the simplest and most
effective approaches to optimize the heat exchanger arrangement in-
volves the insertion of ow disturbance elements [16]. He et al. [17]
investigated the enhanced heat transfer effects of plate n heat ex-
changers in the context of waste heat recovery TEGs from heavy-duty
diesel engines. The results indicated that the spacing and height of the
ns had a more signicant impact than the thickness of the ns,
although the study did not account for the inuence of ns on exhaust
pressure drop and net power. Pujol et al. [18] explored the thermo-
electric and ow resistance characteristics of a single TEG under forced
convection conditions, employing plate ns. They found that the net
output power was less sensitive to changes in n thickness than changes
in n spacing. Chen et al. [19] conducted a comparative study on the
effects of pin ns and plate ns in enhancing TEG performance. They
discovered that both pin ns and plate ns, compared to smooth pipes
without ns, could multiply the output power of the thermoelectric
module. Following numerical optimization, the output power of pin ns
could be up to 24.14% higher than that of plate ns. Zhao et al. [20]
investigated the impact of inserting perforated bafes into the heat
exchanger on thermoelectric performance. They found that the optimal
installation position could increase the output power by 73.4%, with
exhaust temperature and ow rate having minimal inuence on the
optimal position.
Furthermore, lling the heat exchanger with foam metal not only
maximizes the heat transfer coefcient but also improves the tempera-
ture uniformity along the TEG, alleviating the power mismatch issue to a
Nomenclature
c
p
specic heat capacity, W/(m
2
•K)
H pitch length, m
I current, A
L tape distance, m
m mass ow rate, g/s
P power, W
Q
h
hot end heat ow, W
R
L
load resistance, Ω
T temperature, K
U voltage, V
V volume ow rate, m
3
/h
W tape width, m
Δp pressure drop, Pa
ΔT temperature difference, K
Greek symbols
η
efciency, %
ρ
density, g/m
3
σ
maximum error
Subscript
out output value
p pumping value
net net value
ex exhaust gas
te thermoelectric element
hr heat recovery
in inlet value
out outlet value
max maximum value
Abbreviations
TEG thermoelectric generator
TEM thermoelectric module
ITR increasing twist ratio
DTR decreasing twist ratio
TR twist ratio
PR tape pitch ratio
TT twisted tape
W. Yang et al.
Applied Energy 363 (2024) 123047
3
certain extent [21]. Li et al. [22] analyzed the performance of a ther-
moelectric generator with the insertion of porous foam copper in the
central ow region of the heat exchanger. Compared to a thermoelectric
generator without foam metal insertion, the output power of the TEG
using high-porosity, high-volume-ratio porous foam copper could be
increased by up to 2.3 times. However, the pressure drop would rise to
over 10 kPa, posing signicant negative impacts on the engine.
In addition to inserting various structures of ow disturbance devices
in the ducts, enhancing the heat transfer between the gas and the ther-
moelectric module can also be achieved by improving the shape of the
TEG’s channels [23]. Luo et al. [24] proposed a convergent heat
exchanger where the hot-side channels converge along the direction of
uid ow. The output power of the convergent TEG was 5.9% higher
than that of a traditional at-plate TEG. Addressing a circular heat
source, Yang et al. [25] introduced a concentric circular thermoelectric
generator, where the center of the hot-side channel was lled with a
cylinder, reducing the uid space and thereby increasing the heat
transfer coefcient. Results indicated that, compared to a smooth heat
exchanger, the net output power of the concentric circular TEG could
increase by up to 65%. The commonality in these studies lies in reducing
the cross-sectional area of uid channels or increasing uid turbulence
to enhance the heat transfer coefcient. However, the improvement in
heat transfer is often accompanied by deterioration in other aspects
[26], such as friction coefcients. Currently, there is a lack of a widely
accepted heat transfer enhancement method that can effectively in-
crease the heat transfer coefcient while maintaining low pressure drop.
Net power is typically used to represent the coupled effects of heat
transfer enhancement in the TEG and the additional pressure drop. The
extra pressure drop results in pumping power losses for the engine. Net
power is generally the difference between TEG output power and
pumping power.
Due to its excellent performance, light weight, simplicity of instal-
lation, and low manufacturing/operating costs, the insertion of twisted
tapes (TTs) has recently become one of the most popular heat transfer
enhancement devices [27,28]. Twisted tapes are typically made of
metal, twisted into specic shapes and sizes, and inserted into the ow
channels. They are also considered vortex generators, serving as tur-
bulence inducers to convey vortex ow, resulting in an increase in the
heat transfer coefcient. There have been few reports on the application
of twisted tapes in TEGs.
Zhu et al. [29] inserted a typical TT into the circular tube heat
exchanger of a annular TEG and optimized the key parameters of the
tape using a genetic algorithm. The results showed that, compared to a
smooth pipe, under the optimal tape structure, the net power and ef-
ciency increased by 10.41% and 22.51%, respectively. They installed a
twisted tape in the heat exchanger that were much smaller in diameter
than the pipe, hence the improvement in TEG performance was not very
pronounced. Researchers have conducted studies on heat transfer
enhancement by inserting TTs in both circular and square tubes [30].
The results indicate that using TTs is an economical heat transfer
enhancement solution. Moreover, due to the high aspect ratio of rect-
angular ducts, their heat transfer increment is higher than that of cir-
cular ducts. This suggests that twisted tapes in at-plate heat exchangers
can achieve better performance. Karana et al. [31] investigated the ef-
fects of different pitch ratios, helix angles, and twist ratios on the ther-
moelectric performance of a diesel engine TEG. The results showed that
the optimal conguration was a pitch ratio of 8, a helix angle of 60◦, and
a twist ratio of 4, yielding the maximum net output power. At an engine
speed of 1700 rpm and a torque of 60 N⋅m, the net power could be
increased by 82% compared to a smooth heat exchanger. There is still
further potential for improvement, as there have been extensive reports
indicating that modifying the twisted tape can lead to better heat
transfer performance [28].
In addition to enhancing heat transfer, improving the thermoelectric
modules is an effective method to achieve higher power output within
the limited volume constraints of a TEG [32]. To increase power density,
a promising solution is the implementation of two-stage TEGs [33]. This
conguration involves stacking two typical thermoelectric modules
together, electrically connected in series or parallel, with typically only
a ceramic layer serving as an insulator between them. Recently, research
on two-stage thermoelectric modules has garnered increasing interest
[34,35], as it allows for better electrical energy output within the same
footprint. However, much of the research has been conned to numer-
ical simulations and simulation analyses. In the context of exhaust waste
heat recovery TEGs for internal combustion engines, there is a lack of
experimental evaluation and validation of the thermoelectric properties
of two-stage thermoelectric modules.
Table 1 summarizes recent experimental studies on TEGs used for
internal combustion engine exhaust waste heat recovery. The table in-
cludes information on the thermoelectric module sizes, quantities, heat
transfer enhancement measures, and the obtained output performance.
From the table, it is evident that all studies discussed improvements in
thermoelectric performance using single-stage thermoelectric modules.
However, detailed experimental data on the performance of two-stage
thermoelectric generators and twisted tape-enhanced heat transfer are
still lacking, making reliable optimization studies challenging through
numerical simulations.
This study differs from previous research in two aspects. Firstly, a
two-stage thermoelectric module was manufactured and implemented
to recover exhaust heat energy. Compared to typical thermoelectric
modules, it allows for higher power output within the same footprint.
Secondly, we inserted our proposed twisted tapes with variable-twist
ratio in the heat exchanger to enhance heat transfer. This swirl-
inducing device achieves better heat transfer enhancement. The study
explores the impact of twisted tape congurations on the output power,
conversion efciency, pressure drop, net power, and heat recovery rate
of a two-stage thermoelectric generator under different engine condi-
tions. The results of this research will provide valuable guidance for the
design and optimization of two-stage thermoelectric generators and
twisted tape heat exchangers.
2. Experimental platform development
2.1. Conguration of two-stage TEG
The schematic representation of the TEG is illustrated in Fig. 1(a) and
(b). It comprises a plate-type heat exchanger, two thermoelectric mod-
ule layers, and four radiators. The channel thickness of the plate-type
heat exchanger is 1.5 mm, with dimensions of 320 mm (length) ×
120 mm (width) ×20 mm (height). Twenty-four two-stage thermo-
electric modules are arranged in a 2 ×6 conguration at both ends of the
heat exchanger, interconnected in series. Surrounding the outer surface
of the thermoelectric modules are four radiators, each measuring 300
mm (length) ×50 mm (width) ×12 mm (height), covering every six
TEMs with a cooling conduit. Apart from the TEMs, other principal
components are constructed from aluminum alloy.
Two-stage thermoelectric modules were fabricated based on typical
commercially available Bi
2
Te
3
-based TEM, as illustrated in Fig. 1(c) and
(d). Under the condition of a hot-end temperature of 523 K, the pa-
rameters of a standard commercial single-stage thermoelectric module,
provided by the supplier, are shown in Table 2. The external dimensions
of the two-stage thermoelectric module are 50 mm (length) ×50 mm
(width) ×6.8 mm (height). This two-stage thermoelectric module con-
sists of upper and lower parts, with each level comprised of 198 p-type or
n-type thermoelectric legs (each measuring 1.4 mm in length, 1.4 mm in
width, and 1.6 mm in height) connected in series between 0.3 mm thick
copper electrodes. In total, there are 396 semiconductor legs, forming
198 pairs of pn thermocouples. The outer surface of the two-stage
module and the intermediate region between the two stages are insu-
lated by 0.8 mm thick Al
2
O
3
insulating plates. The Seebeck coefcient
and resistivity are approximately ±190–230
μ
V/K and 0.85 mΩ⋅cm,
respectively. Considering the thermal properties of the solder used for
W. Yang et al.
Applied Energy 363 (2024) 123047
4
connecting the thermoelectric legs to the copper electrodes and the
optimal ZT temperature range of BiTe materials, the maximum allow-
able surface temperature is 523 K.
2.2. Twisted tape with variable twist ratio
The installation of twisted tapes is exceedingly straightforward,
accomplished through the insertion into the pipeline. To facilitate the
insertion of the helical tapes, the width (W) of the tapes must align with
the height of the pipeline [28], ensuring a secure fastening within the
heat exchanger channels. When replacement becomes necessary due to
maintenance, structural upgrades, or other reasons, the inserted tapes
can be easily retracted. Following modication, the same installation
method, as described earlier, can be maintained. In this investigation, all
tested twisted tape inserts are crafted from aluminum, possessing a
width of 20 mm, a length of 300 mm, and a thickness of 1 mm.
The pitch length and twist ratio directly inuence the performance of
the twisted tape. The pitch length (depicted in Fig. 2) typically refers to
the length (H) of the tape that undergoes a 180◦rotation, used in
calculating the twist ratio. The Twist ratio (TR) determines the twisting
frequency of the tape and is calculated as the ratio of pitch length to tape
radius (TR =H/R). Furthermore, within the internal structure of a at-
type heat exchanger, multiple tapes can be inserted since multiple-twist
tapes yield higher heat transfer rates compared to single-twist tapes
[42]. The distance between adjacent tapes, denoted as L, denes the
density of the twisted tape inserts within the nite heat exchanger
channel, represented by the tape pitch ratio (PR =L/W). Fig. 2 illus-
trates the key parameters of the twisted tapes studied in this research.
Twisted tapes have the capacity to generate heightened heat transfer
rates, albeit at the cost of increased frictional losses. To strike a more
Table 1
Recent experimental studies on exhaust heat recovery TEGs for internal combustion engines.
TEM
structure
TEM
quantity
TEM size (length ×width
×height)
Methods to enhance heat transfer Maximum output
power
Maximum
efciency
Pressure
drop
Ref.
Single-stage 24 40 ×40 ×3.3 mm
3
Staggered pin ns 96.6 W 3.95% 0.37 kPa [14]
Single-stage 8 55×51.5 ×3.3 mm
3
Partially lled with copper foam 36 W N/A 5.4 kPa [22]
Single-stage 20 56×56 ×5.5 mm
3
Typical twisted ribs 94.7 W N/A N/A [31]
Single-stage 40 44 ×44 ×3.6 mm
3
Stainless steel perforated plates and plate ns 119 W 2.8% 1.4 kPa [36]
Single-stage 10 55×55 ×4 mm
3
Rectangular winglet longitudinal vortex
generators 7.1 W 1.1% N/A [37]
Single-stage 40 50 ×50 ×3.8 mm
3
Smooth at heat exchanger (4 mm in height) 29.5 W 1.25% 0.12 kPa [38]
Single-stage 30 60 ×60 ×3.3 mm
3
Flow straightener and plate ns 83 W 2.5% 1.9 kPa [39]
Single-stage 18 40 ×40 ×3.6 mm
3
Conical heat exchanger structure with
perforated plate and n 98.8 W 2.6% 2.05 kPa [40]
Single-stage 32 40 ×40 ×3.3 mm
3
Porous copper foam 5.8 W 2.05% 0.81 kPa [41]
Fig. 1. (a) TEG structure diagram. (b) TEG structure splitting diagram. (c) Two-dimensional diagrams of single-stage and two-stage TEM. (d) Manufactured two-
stage TEM.
Table 2
Parameters of single-stage TEM (TEG-19913).
Parameters Cold end temperature
300 K 323 K
Open-circuit voltage (V) 13.0 11.8
Dynamic internal resistance (Ω) 2.8 2.9
Maximum output power (W) 14.5 11.5
Conversion efciency (%) 5.7 5.0
AC internal resistance (Ω, 297 K) 1.58 1.58
Fig. 2. Key parameters of twisted tapes.
W. Yang et al.
Applied Energy 363 (2024) 123047
5
favorable balance between enhanced heat transfer rates and augmented
pressure losses, renement of the twisted tape design is imperative. In
the case of exhaust gas waste heat recovery systems where a signicant
temperature gradient is prevalent along the ow direction of the chan-
nels, the distinct temperature gradients induce uneven potential distri-
bution across the series-connected TEMs, resulting in parasitic power
losses [43]. Therefore, the objective of this study is to ameliorate this
scenario and seek the most efcient heat transfer enhancement measures
while maintaining a lower pressure drop. A novel twisted tape structure
is proposed, characterized by a variable pitch along the length of the
tape. In three-dimensional space, the structure of the twisted tape can be
represented by the following expression:
⎧
⎪
⎪
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎪
⎪
⎩
x=R⋅cos(2
π
W⋅TR t)
y=R⋅sin(2
π
W⋅TR t)
z=t
(1)
where t =[0,300].
To construct a twisted tape with variable twist ratio, one simply
needs to linearly increase or decrease 2
π
/(W⋅TR). When the TR gradu-
ally decreases along the uid ow direction, it is termed as a decreasing
twist ratio twisted tape (DTR-TT); conversely, when the TR gradually
increases along the uid ow direction, it is designated as an increasing
twist ratio twisted tape (ITR-TT).
For a standard constant twist ratio twisted tape, a general trend
suggests that as the pitch length decreases, thermodynamic performance
increases. This relationship exhibits an optimal point where the increase
in frictional losses and the improvement in convective heat transfer
reach an optimal balance. Traditionally, researchers often adopt “6” as
the optimum TR value [30]. In the realm of variable twist ratio twisted
tapes, it can be perceived as a compromise value, wherein variations in
pitch are explored based on TR =6, investigating the performance of
variable twist ratio twisted tapes under different combinations. Ac-
cording to the expression for variable twist ratio tapes, Eq. (1), its TR
alteration is associated with
π
. Consequently, we have devised specic
specications of variable twist ratio twisted tapes based on
π
, 2
π
, and 3
π
as TR boundaries. Fig. 3 illustrates schematic diagrams of typical con-
stant twist ratio twisted tapes and variable twist ratio twisted tapes.
To handle the structural characteristics of variable twist ratio twisted
tapes in a dimensionless manner, we dene the variable twist ratio
parameter (VTR) as the ratio of the twist ratio at the beginning to that at
the end of the tape. Thus, for three types of increasing twist ratio twisted
tapes, VTR =1/3, 1/2, and 2/3, while for three types of decreasing twist
ratio twisted tapes, VTR =3/2, 2, and 3. This denition can be extended
to variable twist ratio twisted tapes with different structural parameters,
where VTR <1 signies increasing twist ratio twisted tapes, VTR =1
denotes conventional constant twist ratio twisted tapes, and VTR >1
indicates decreasing twist ratio twisted tapes. As VTR approaches 1, the
rate of twist variation diminishes, whereas it increases as VTR deviates
further from 1.
2.3. Apparatus and experimental settings
The fabricated two-stage TEMs were integrated with the variable
twist ratio twisted tapes into the TEG experimental system for the
assessment of thermoelectric performance. By designing the physical
structure of the variable twist ratio twisted tapes in three-dimensional
software and subsequently employing metal 3D printing technology,
we fabricated the DTR-TT and ITR-TT. The experimental system consists
of an air heating system, TEG, a cooling water circulation system, an
electronic load, and a data acquisition system (Fig. 4).
The air heating system utilizes an industrial hot air blower (RY-P-15
A-075) as a simulated heat source, replacing an automobile engine, to
steadily provide the required ow and temperature of high-temperature
gas [24]. The industrial hot air blower comprises a blower, a heater, and
a control circuit. With a maximum power of 15 kW, the industrial hot air
blower draws in ambient air and heats it. The exhaust temperature can
be adjusted within the range of 300–633 K with a PID controller (ac-
curacy ±0.5 K). The outlet ow rate of the hot air blower can be regu-
lated within the range of 0–240 m
3
/h by adjusting the control panel.
Section 2.1 has provided a detailed description of the customized
TEG, with a detachable side of the hot-end heat exchanger, allowing the
Fig. 3. (a)Variations of the twist ratio along the length and schematic diagrams of (b) constant twist ratio, (c) decreasing twist ratio and (d) increasing twist ratio of
the twisted tapes.
W. Yang et al.
Applied Energy 363 (2024) 123047
6
insertion of the twisted tape. The TEG is connected to the industrial hot
air blower via anges. To minimize thermal resistance, the contact
surfaces between the heat exchanger, thermoelectric modules, and ra-
diators are coated with thermally conductive silicone grease. Bolts are
applied on both sides of the TEG for secure fastening.
The cooling water circulation system primarily consists of a water
tank, a water pump, and pipelines. A chilling unit (SHZ-95B) pumps cold
water from a 50 L water tank through the cold-side heat exchanger of the
TEG, maintaining a low temperature on the cold side of the TEG. The
output ow rate of the chilling unit is approximately 10 L/min, con-
nected to four radiators in the TEG system via rubber hoses. Due to the
large capacity of the cooling water tank, the cooling water temperature
remains nearly constant during the experimental process, achieving
stable output shortly after starting the TEG.
The electronic load and data acquisition system include a vortex
owmeter, a DC power supply unit, an electronic load, and a data
acquisition instrument. To measure the actual exhaust outlet ow rate,
temperature, and heat exchanger outlet pressure, a vortex owmeter
(HW-LUGA14, full range 50– 480 m
3
/h, accuracy ±1%) is installed at
the outlet of the heat exchanger. A 24 V DC power supply (RIGOL
DP832) powers the vortex owmeter. An electronic load (Array 3721 A,
resolution 0.1 mΩ, accuracy ±0.5%) is connected to the thermoelectric
modules to simulate external load conditions. All experimental data,
including the TEG’s output current, temperature, and pressure, are
measured and collected using a data acquisition device (Agilent DSO-X
2024 A).
The hot air blower, TEG, and vortex owmeter are connected using
stainless steel pipes with anges. The hot uid output from the hot air
blower ows through the TEG and vortex owmeter, discharging into
the environment. Furthermore, during the experimental process, the
TEG is enveloped in silicone felt with an extremely low thermal con-
ductivity to minimize heat losses. Given the direct connection between
the hot air blower and the TEG, the temperature at the outlet of the
blower is considered as the inlet temperature of the TEG. This temper-
ature measurement is facilitated by sensors and controllers integrated
within the blower. The outlet temperature is directly measured via the
vortex owmeter. The ow velocities at the TEG’s inlet and outlet are
directly measured by the hot air blower and the vortex owmeter,
respectively. The inlet pressure of the TEG is estimated by referencing
the performance curve provided by the manufacturer of the hot air
blower. This curve delineates the relationship between outlet pressure,
airow velocity, and power under various operating conditions. The
outlet pressure of the TEG is directly measured by the vortex owmeter.
2.4. Experimental procedure
The power output and back pressure of the TEG are signicantly
inuenced by the operational state of the engine. Kim et al. [36] con-
ducted tests on a turbocharged six-cylinder diesel engine, recording
operational parameters of the TEG system under various engine modes.
The engine had a cylinder bore of 103 mm, a stroke of 118 mm, a
compression ratio of 17:1, and a maximum power of 110 kW at 2500
rpm. Fig. 5 illustrates the impact of engine load on TEG inlet tempera-
ture and mass ow rate at different engine speeds. In the current study,
to simulate the actual operating conditions of an automotive waste heat
recovery TEG system, six typical vehicle operating conditions from
Ref. [36] were considered, as shown in Table 3. During the experiments,
the outlet temperature and ow rate of the industrial hot air blower
were adjusted through the control panel to operate the TEG under
specic engine exhaust conditions. Furthermore, the inuence of vehicle
speed on the entrance parameters of the cooling system is negligible
[44].
In each run, the TEG initially operated in an open circuit. Firstly, the
cooling water unit was activated to ensure the circulation of cooling
water. Subsequently, the industrial hot air blower was turned on and
adjusted to a xed exhaust condition. After a period of operation, the
outlet temperature of the TEG was dynamically measured, considering it
in a steady state when the rate of change over ve consecutive minutes
was within ±0.2 K. Finally, the electronic load was connected to the
TEM, and parameters such as TEG voltage, current, outlet pressure, and
ow rate were measured and recorded.
2.5. Data analysis
In the experiment, as the industrial hot air blower is directly con-
nected to the TEG, the outlet temperature of the blower is considered as
Fig. 4. Experimental conguration.
Fig. 5. Variations in exhaust temperature and mass ow rate with engine speed
and load.
W. Yang et al.
Applied Energy 363 (2024) 123047
7
the inlet temperature of the TEG (T
ex,in
). The outlet temperature (T
ex,out
)
and volumetric ow rate (V
ex
) of the TEG were measured using the
vortex owmeter. Therefore, the thermal energy extraction rate (Q
h
)
from the exhaust ow in the TEG region is calculated by the following
Eq. [45]:
Qh=mexcpex ΔTex =Vexcpex ΔTex/
ρ
ex (2)
The maximum possible energy extraction rate can be obtained by
using the atmospheric temperature as the reference temperature, as
shown below:
Qh,max =Vexcpex ΔTex,a/
ρ
ex (3)
η
hr =Qh/Qh,max (4)
where ΔT
ex
represents the temperature difference of the exhaust at the
TEG inlet and outlet, and ΔT
ex,a
represents the difference between the
exhaust temperature at the TEG inlet and the ambient temperature. The
ratio of the actual energy extraction rate (Q
h
) to the maximum possible
energy extraction rate (Q
h,max
) indicates the thermal energy recovery
efciency
η
hr
of the TEG.
The output power (P
out
) is dependent on the load resistance (R
L
) and
can be calculated by measuring the current (I) and voltage (U) across the
load resistor. The calculation formula is as follows:
Pout =UI (5)
The thermoelectric conversion efciency
η
te
is expressed as:
η
te =Pout/Qh(6)
When applying a disrupter to the hot-end heat exchanger of the TEG,
to calculate the back pressure power loss, according to [46], it can be
computed as:
Pp=VexΔp=mex Δp/
ρ
ex (7)
where Δp is the pressure drop of the hot uid through the heat
exchanger, and
ρ
ex
is the density of the exhaust gas.
Therefore, the net output power (P
net
) of the TEG is calculated as:
Pnet =Pout −Pp(8)
In addition, the measurement error is calculated based on the de-
nition of heat transfer rate and the accuracy of each measurement sensor
[38]. The specic equation is as follows:
Qh=
(
∂
Qh
∂
Vex
σ
Vex)2
+(
∂
Qh
∂
Tex,in
σ
Tex,in)2
+(
∂
Qh
∂
Tex,out
σ
Tex,out)2
√(9)
where
σ
represents the maximum error of each measurement parameter.
The calculated Q
h
error is within ±3.17%. According to the above
equation, the uncertainties of the output power, conversion efciency,
and pressure drop are calculated to be ±0.171%, ±3.181%, and ±
0.862%, respectively.
3. Results and discussion
3.1. Output performance of two-stage thermoelectric generators
Primarily, an examination was conducted within the smooth channel
devoid of twisted tapes, exploring the electrical characteristics of single-
stage TEG and two-stage TEG under varying external resistances. To
quantitatively analyze power output, power-load resistance curves for
the TEG system were obtained by altering external loads under diverse
engine modes, as depicted in Fig. 6. Irrespective of whether it was a
single-stage TEG or a two-stage TEG, the power output increased with
escalating engine speed and load. Under engine mode F, the two-stage
TEG outperformed the single-stage TEG, exhibiting a power output
enhancement of 17.3%. The enhancement rate decreases with the in-
crease of exhaust temperature and mass ow rate. This phenomenon
arises because, despite the heightened temperature gradient between
the cold and hot ends of the TEG, the enhancement in the operational
temperature difference for both the upper-level and lower-level TEMs is
not pronounced. For the single-stage TEG, characterized by lower in-
ternal resistance, the increase in temperature gradient yields a more
conspicuous improvement in output power.
With the escalation of external resistance, the output power initially
rises before diminishing. There exists an optimal load resistance,
enabling the TEG to achieve peak output power. Furthermore, from
Fig. 6, it is discernible that the operational mode of the engine signi-
cantly inuences peak output power. The optimal load exhibits a
Table 3
Selected typical TEG operating conditions.
Engine
mode
Engine Load
(MPa)
Speed
(rpm)
Mass ow rate
(g/s)
Temperature
(K)
A 0.4 1000 19.7 470.7
B 0.4 1500 26.3 509.9
C 0.4 2000 41.5 551.1
D 0.6 1000 21.3 533.1
E 0.6 1500 30.4 560.3
F 0.6 2000 49.5 598.8
Fig. 6. Output power vs. load resistance curves of (a) Single-stage TEG and (b)
Two-stage TEG under different engine modes.
W. Yang et al.
Applied Energy 363 (2024) 123047
8
marginal increase with the rise in intake temperature and ow, its
impact on the optimal load is relatively modest. This proves advanta-
geous for two-stage TEG applications, signifying that when the gener-
ator functions as an external power source, frequent adjustments to
external resistance are unnecessary, ensuring that the output power
remains close to its maximum value [47].
The optimum load resistance for the single-stage TEG is 62 Ω, while
for the two-stage TEG, it is 136 Ω. Despite the doubling of thermoelectric
legs in the two-stage TEG compared to the single-stage TEG, the optimal
load resistance is not twice that of the single-stage TEG. This disparity
arises because in the two-stage TEG, the average operating temperature
of the TEMs is lower. This, coupled with the dual effects of the high
resistivity of semiconductor materials at low temperatures and the
mismatch in internal resistance caused by the series connection of 24
two-stage thermoelectric modules, leads to the optimal load resistance
for the two-stage TEG being 2.2 times that of the single-stage TEG.
In theory, the matched load resistance equals the internal resistance
of the TEMs [48]. In contrast to these ideal conditions, this study
measured output power considering mismatches in resistance and
thermal resistance between 24 single-stage and two-stage TEGs, as well
as power losses caused by lead connections and uneven surface tem-
peratures. Consequently, the optimal load resistance does not align
perfectly with the internal resistance provided by the supplier.
Fig. 7(a) contrasts the thermoelectric conversion efciency and heat
recovery efciency of single-stage and two-stage TEGs under different
operating conditions. The results indicate that the two-stage TEG ex-
hibits a slightly higher thermoelectric conversion efciency than the
single-stage TEG, with the maximum conversion efciencies reaching
1.9% and 2.6% for single and two-stage TEG under various conditions.
As the engine speed and load increase, the thermoelectric conversion
efciency also rises, but there is a declining trend in heat recovery
performance. This is due to the fact that the actual energy extraction rate
increases by a magnitude smaller than the maximum possible energy
extraction rate. Both single and two-stage TEGs exhibit similar trends in
heat recovery performance. At the lowest engine speed and load con-
ditions, the heat recovery efciency is maximal, reaching 36.3% and
35% for single and two-stage TEGs, respectively. However, at the
highest engine speed and load conditions, the heat recovery efciency
decreases to 26.3% and 24.6% for single and two-stage TEGs. The heat
recovery performance limits the maximum output power of the TEG.
This can be elucidated by examining the temperature differentials at
the inlet and outlet of the TEG based on the exhaust. Fig. 7(b) delineates
the exhaust gas temperatures at the inlet and outlet of the TEG, as well as
the temperature differential, under various engine operating modes. It is
distinctly observable that, with the augmentation of engine speed and
load, the temperature differential increases, albeit with a discernible
trend of diminishing increments. A comparative analysis of diverse en-
gine conditions reveals that this phenomenon stems from the fact that,
despite the elevated intake temperature and mass ow rate accompa-
nying the escalation of engine speed and load, the rapid ow velocity
results in the exhaust gases bypassing the TEG without undergoing
sufcient convective heat exchange with the TEMs, thereby owing
directly out of the TEG through smooth channel.
3.2. Inuence of tape pitch ratio
The two-stage TEG manifest a notable potential for high power
density in thermal energy recovery [49]. An examination was conducted
on the inuence of employing twisted tape heat exchangers on the
performance of the two-stage TEG. Initially, an investigation was carried
out on the impact of the tape pitch ratio (PR) on the thermoelectric
performance of the two-stage TEG. In the experiments, the PR was set at
3, 2, 1.5, 1.2, and 1, with a twist ratio of
π
. As depicted in Fig. 8(a), the
variation of output power with engine modes under different PR is
illustrated. The insertion of twisted tapes exhibits an augmentation of
thermoelectric performance. In comparison to smooth channels, the
utilization of twisetd tapes at a lling ratio of PR =1, TR =
π
, can
potentially double the output power. Moreover, as the engine operating
conditions intensify, the increase in output power becomes more sub-
stantial. This arises from the elongation of the ow path by the twisted
tapes, prolonging the contact time between the uid and the tube wall,
ensuring their thorough interaction. Furthermore, the twisted tapes
induce secondary ows, segregating and obstructing uid ow, thereby
accelerating the mixing velocity of uid in the near-wall region and
increasing the ow velocity near the wall [27].
As the pitch ratio diminishes, the TEG output power increases. A
smaller tape gap gives rise to multiple swirling ows with greater in-
tensity, leading to more chaotic uid mixing and increased turbulent
kinetic energy. Consequently, a smaller gap provides a thinner thermal
boundary layer. This enhanced momentum transfer increases the heat
extracted from the hot gas, ultimately raising the temperature on the
TEG’s hot side, resulting in higher power output.
The disturbances caused by the twisted tapes not only impact heat
transfer but also inuence the friction between the channel surface and
the uid. The increased channel area blocked by the twisted tapes and in
contact with the uid contributes to pressure loss. As shown in Fig. 8(b),
under different PR, the pressure drop varies with engine modes. It is
observable that as the PR decreases, the increase in pressure drop is
more pronounced compared to the increase in power, reaching a
maximum 6.74-fold increase over smooth pipes. This is attributed to the
minimal PR signifying a heat exchanger lled with twisted tapes,
resulting in more complex uid ow and higher ow resistance.
Fig. 8(c) illustrates the impact of PR on the net output power under
Fig. 7. Comparison of (a) Thermoelectric conversion efciency and heat re-
covery efciency and (b) inlet/outlet temperatures and temperature differences
between single-stage TEG and two-stage TEG.
W. Yang et al.
Applied Energy 363 (2024) 123047
9
various engine operating conditions. Net power reects the coupled
inuence of enhanced heat transfer and frictional losses due to the
twisted tapes on TEG performance. It is evident that for different engine
conditions, net power exhibits distinct trends. At lower engine speeds,
net power increases with decreasing PR, albeit with a diminishing rate of
increase. For engine conditions A, B, D, and E, net power is nearly
equivalent at tape pitch ratios of 1.5, 1.2, and 1. As engine speed in-
creases (engine conditions C and F), the substantial increase in exhaust
ow leads to a considerable rise in channel pressure drop, causing net
power to decrease with decreasing PR.
3.3. Inuence of twist ratio
The investigation delves into the impact of constant twist ratio and
variable twist ratio twisted tapes on the output characteristics and
pressure drop of the two-stage TEG system. Fig. 9a illustrates the vari-
ation of output power under different operating conditions for twisted
tapes with PR =1.5, employing constant, decreasing, and increasing
twist ratios. For a uniform pitch, the output power increases with a
decrease in the twist tatio. This is attributed to the enhanced convective
heat transfer with a diminishing TR. Across various operating condi-
tions, the output power with TR =
π
is maximized, exhibiting a 21%
improvement over the twisted tape with TR =3
π
. The smaller TR results
in a greater number of helices, generating stronger swirling ows and
higher turbulence intensity, thereby achieving superior heat transfer. As
the exhaust temperature and ow rate decrease, the enhancement ratio
of output power with TR =
π
compared to TR =3
π
declines from 21% to
16%, owing to the superior thermal performance of twisted tapes at low
Reynolds numbers [30].
For a typical twisted tape, the thermodynamic properties vary with
the degree of looseness of the tape. Larger TR leads to a looser cong-
uration, and vice versa. According to Fig. 9, the DTR-TT of TR =3
π
to
π
is tighter than that of TR =3
π
to 2
π
, so the output power is greater. The
DTR-TT with TR =3
π
to
π
exhibits greater output power than the CTR-
TT with TR =3
π
, yet less than the twisted tape with TR =
π
. However, it
surpasses the output power of the average TR =2
π
twisted tape, indi-
cating the enhanced heat transfer performance of variable twist ratio
TTs compared to constant twist ratio TTs.
Under the same variable twist ratio combination, the output power of
Fig. 8. Inuence of different tape pitch ratios on two-stage TEG performance
under various engine modes: (a) Output power, (b) Pressure drop, and (c)
Net power.
Fig. 9. Output power and pressure drop of constant and variable twist ratios
under different engine modes.
W. Yang et al.
Applied Energy 363 (2024) 123047
10
the ITR-TT is consistently higher than that of DTR-TT. For instance, in
engine mode F, the output power of TR =
π
to 3
π
ITR-TT is 25% higher
than that of TR =3
π
to
π
DTR-TT. This is attributed to the lower pressure
drop upstream in general pipes, resulting in lower pressure loss and
higher temperature gradients. The addition of ITR-TT increases the
number and intensity of swirls upstream, yielding superior heat transfer
performance. Therefore, twisted tapes with shorter twist lengths inser-
ted upstream in the pipe achieve higher TEG output power.
An noteworthy observation is that the output power of TR =
π
to 3
π
ITR-TT is higher than that of TR =
π
to 2
π
ITR-TT. The looser variable
twist ratio TT enables TEG to attain better output performance, in
contrast to the pattern observed with DTR-TT. This is because the non-
uniform distribution of the internal vortex ow eld in TR =
π
to 3
π
ITR-TT (VTR =1/3) is more pronounced than that in TR =
π
to 2
π
ITR-
TT (VTR =1/2). This non-uniform distribution generates a larger
effective driving potential induced by the twisted tape than the one
induced by a uniform tape, resulting in higher heat and momentum
uxes. Hence, for increasing twist ratio twisted tapes, the inuence of
ow instability is more signicant than the inuence of swirl intensity.
Expanding the pitch variation range of variable twist ratio TTs can
enhance heat transfer performance.
Fig. 9(b) illustrates the variation in pressure drop under different
Fig. 10. Theoretical ow patterns under different TR and PR.
W. Yang et al.
Applied Energy 363 (2024) 123047
11
operating conditions for CTR, DTR, and ITR twisted tapes. The trend in
pressure drop mirrors the trend in TEG output power, as the effect of
enhanced heat transfer is accompanied by an increase in friction coef-
cient. The noteworthy difference is that, for DTR-TT, the impact of ow
instability on pressure drop is greater than its impact on heat transfer
performance. The output power and pressure drop of TR =3
π
to
π
DTR-
TT are 2.5% lower and 3.2% higher, respectively, compared to those of
TR =2
π
to
π
DTR-TT. The ow patterns depicted in Fig. 10 aid in un-
derstanding the inuence of twist ratio and tape pitch ratio on uid ow
and heat transfer mechanisms within the heat exchanger channels in this
study [50].
3.4. Net power analysis
The enhanced heat transfer effectiveness of variable twist ratio
twisted tapes surpasses that of typical twisted tapes, but the resulting
additional pressure drop is also signicantly higher. Once the engine
back pressure exceeds a certain level, it not only affects the normal
operation of the engine but also leads to an increase in resistance power
consumption, potentially surpassing the output power generated by the
TEG itself [51]. To assess the overall performance of variable twist ratio
twisted tapes in the TEG system, the impact of different variable twist
ratio TT on the net output power of the TEG was evaluated.
Fig. 11(a), (b), and (c) depict the variation in net output power for
TEGs employing CTR, DTR, and ITR twisted tapes with PR =1.5 under
different operating conditions. For CTR-TT, the net power increases with
a decrease in TR. However, for DTR-TT, the tape with the highest rate of
TR variation results in lower net power, particularly at high engine
speeds. This indicates that the ow instability of DTR-TT leads to infe-
rior overall performance compared to typical tapes, corroborating the
conclusions from Fig. 9. In contrast, increasing twist ratio twisted tape
yields different results. In most operating conditions, TR =
π
to 3
π
ITR-
TT achieves the best thermoelectric performance. In mode D, the net
output power of TR =
π
to 3
π
ITR-TT is 5.9% and 17.1% higher than that
of CTR-TT with twist ratios of
π
and 2
π
, respectively.
Fig. 11(d), (e), and (f) illustrate the variation in net thermoelectric
efciency (
η
net
=P
net
/Q
h
) for TEGs employing CTR, DTR, and ITR
twisted tapes with PR =1.5 under different operating conditions. The
trend in net efciency follows a similar pattern to net power. The net
efciency of ITR-TT is superior to CTR-TT at low engine speeds and
comparable at high engine speeds. From an efciency standpoint, ITR-
TT also represent the most effective enhancement for thermoelectric
performance.
To accentuate the advantages of variable twist ratio twisted tapes,
Fig. 12 compares the ratio of the net power of the TEG system after
enhanced heat transfer to the net power of the TEG system before
Fig. 11. Net power of (a) Constant twist ratio, (b) Decreasing twist ratio, and (c) Increasing twist ratio under different engine modes; as well as net conversion
efciency of (a) Constant twist ratio, (b) Decreasing twist ratio, and (c) Increasing twist ratio under different engine modes.
Fig. 12. Net power ratio of two-stage TEG with twisted tape heat exchanger
and two-stage TEG with smooth heat exchanger.
W. Yang et al.
Applied Energy 363 (2024) 123047
12
enhanced heat transfer [52]. This ratio characterizes the enhancement
in overall TEG performance relative to smooth heat exchanger. As en-
gine speed and load increase, the net power enhancement ratio of
twisted tape decreases. In engine mode A, twisted tapes with twist ratios
of 3
π
, 2
π
,
π
, 3
π
-2
π
, 3
π
-
π
, 2
π
-
π
, 2
π
-3
π
,
π
-3
π
, and
π
-2
π
yield net power
enhancements of 57.7%, 70.5%, 89%, 60%, 72.8%, 78.3%, 64.7%,
100%, and 98%, respectively, compared to a regular smooth heat
exchanger. Except for engine mode F, the enhancement ratio of TR =
π
to
3
π
ITR-TT is superior to that of CTR-TT and DTR-TT in other operating
conditions.
Finally, to highlight the novelty and advancement of this study, we
compare the two-stage TEG with the optimal variable twist ratio twisted
tapes to a typical TEG without heat transfer optimization, as shown in
Fig. 13. The typical TEG employs commercially available single-stage
thermoelectric modules and is equipped with a smooth at-plate heat
exchanger. In the two-stage TEG, the two-stage TEMs developed in
Section 2.1 are utilized, and TR =
π
to 3
π
variable twist ratio twisted
tapes with a tape pitch ratio of 1.5 are inserted into the heat exchanger,
as discussed in Section 2.1.
It is evident that, through the optimization of thermoelectric mod-
ules and heat transfer performance on the hot side, the overall perfor-
mance of the TEG has been signicantly enhanced, despite the increase
in exhaust pressure drop. Although the pressure drop has increased by
1.5 times, the output power, net power, thermoelectric conversion ef-
ciency, heat recovery efciency, and net efciency have all improved
by approximately double. It is worth noting that if the issue of internal
resistance mismatch in the two-stage thermoelectric modules is
addressed, and compatibility with various thermoelectric materials is
achieved for the temperature gradient, the comprehensive performance
of the TEG will see further substantial improvement. This will be pur-
sued in our future research endeavors. As the cost of thermoelectric
modules continues to decrease, there is a potential for the power-to-cost
ratio of two-stage thermoelectric generators to surpass that of single-
stage thermoelectric generators.
4. Conclusions
In this study, we conducted a comprehensive examination of the
experimental system for a exhaust heat recovery thermoelectric gener-
ator, comparing the thermoelectric characteristics of single-stage and
two-stage generators. Additionally, we introduced a method to enhance
heat transfer through the utilization of variable twist ratio twisted tapes
and systematically investigated its impact on the performance of the
two-stage thermoelectric generator. From our research ndings, the
following conclusions can be drawn:
1. In comparison to a single-stage thermoelectric generator, under en-
gine mode F, the two-stage thermoelectric generator leads to a 17.3%
increase in output power, and the optimum load resistance is
enhanced by approximately 2.2 times.
2. The output power and pressure drop of the two-stage thermoelectric
generator both increase with a decrease in tape pitch ratio, with the
pressure drop increase being more pronounced. Compared to a
smooth heat exchanger, the minimum tape pitch ratio results in a
6.74-fold increase in pressure drop. At low engine speeds and loads, a
smaller tape pitch ratio yields higher net output power, while at high
engine speeds and loads, net power decreases with a decrease in tape
pitch ratio.
3. Output power and pressure drop increase with a decrease in twist
ratio. Due to the more signicant inuence of ow instability
compared to swirl intensity, the output power of the twisted tape
with an increased twist ratio from
π
to 3
π
is 25% higher than that of
the twisted tape with a twist ratio increased from
π
to 2
π
.
4. The increasing twist ratio twisted tape with the highest twist ratio
variation rate exhibits the highest net output power. Under engine
operating condition A, the net output power gain can reach a
maximum of 100% compared to the unmodied thermoelectric
generator.
CRediT authorship contribution statement
Wenlong Yang: Conceptualization, Data curation, Writing – original
draft. Chenchen Jin: Investigation, Writing – original draft. Wenchao
Zhu: Methodology, Software, Validation. Changjun Xie: Funding
acquisition, Project administration, Resources, Writing – review &
editing. Liang Huang: Formal analysis, Software, Visualization. Yang
Li: Supervision, Validation, Writing – review & editing. Binyu Xiong:
Formal analysis, Methodology, Writing – review & editing.
Declaration of competing interest
The authors declare that they have no known competing nancial
interests or personal relationships that could have appeared to inuence
the work reported in this paper.
Data availability
Data will be made available on request.
Acknowledgments
This work is supported by the National Natural Science Foundation
of China (51977164) and the Postdoctoral Fellowship Program of CPSF
(GZC20232011).
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