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Power and Efficiency Calculation in Commercial TEG and Application in Wasted Heat Recovery in Automobile

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Abstract

Thermoelectric generators (TEG) make use of the Seebeck effect in semiconductors for the direct conversion of heat into electrical energy, which is of particular interest for high reliability systems or for waste heat recovery. The generator efficiency, η, is determined by comparing the amount of electricity produced (Pout) to the total amount of heat induced (Qin). A measuring system and a modeling approach which takes into account the thermal contact resistances have been developed, allowing the characterization of TEG devices under various loads and temperature gradients and thus, to evaluate material properties. These results were used to identify the appropriate positions at the exhaust pipe of a midsize vehicle for the optimum recovery of the wasted heat using a commercial TEG and to establish a set of requirements for an automotive TE waste heat recovery subsystem. Results are presented and discussed.
Power and Efficiency Calculation in Commercial TEG
and Application in Wasted Heat Recovery in Automobile
K.T. Zorbas, E. Hatzikraniotis, and K.M. Paraskevopoulos
Physics Department, Solid State Physics Section, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
evris@physics.auth.gr, Phone: +30 / 2310 99 82 16, Fax: +30 / 2310 99 82 16
Abstract
Thermoelectric generators (TEG) make use of the
Seebeck effect in semiconductors for the direct conversion
of heat into electrical energy, which is of particular interest
for high reliability systems or for waste heat recovery. The
generator efficiency,
η
, is determined by comparing the
amount of electricity produced (Pout) to the total amount of
heat induced (Qin). A measuring system and a modeling
approach which takes into account the thermal contact
resistances have been developed, allowing the
characterization of TEG devices under various loads and
temperature gradients and thus, to evaluate material
properties. These results were used to identify the
appropriate positions at the exhaust pipe of a midsize vehicle
for the optimum recovery of the wasted heat using a
commercial TEG and to establish a set of requirements for
an automotive TE waste heat recovery subsystem. Results
are presented and discussed.
Introduction
Thermoelectric generators make use of the Seebeck
effect in semiconductors for the direct conversion of heat
into electrical energy, which is of particular interest for
systems of highest reliability or for waste heat recovery [1].
A generator usually consists of several pairs of alternating p-
and n-type semiconductor blocks (generator legs), which are
arranged thermally parallel and connected electrically in a
series circuit. The heat flow, which is partly converted into
electrical power, is induced by heating one side of the
arrangement while the opposite side is cooled. The
conversion efficiency
η
is defined as the ratio of the
generated electrical power PTEG and the heat input into the
module QH:
TEGC
TEG
H
TEG
PQ
P
Q
P
+
=
η
(1)
where QC is the heat removed from the cooled side. To
accurately determine the efficiency of a generator, the heat
induced and the electrical power produced must be carefully
measured. Generator efficiencies are often calculated from
the measured material properties [2]. This method indirectly
yields generator efficiency through the figure of merit,
requiring separate measurements of absolute Seebeck,
electrical and thermal conductivities of which each is
susceptible to a tolerance of errors. More direct
measurements of the figure of merit have been demonstrated
and are useful to obtain generator efficiency, but the
measurement accuracy is limited to testing under small
temperature gradients [3-5]. Thermoelectric generator
efficiency can also be determined through comparative heat
flow, and this method offers a more direct and realistic
measurement of a generator’s efficiency [6].
The possible use of a device consisting of numerous
TEG modules in the wasted heat recovery of an internal
combustion (IC) engine can considerably help the world
effort for energy savings. Generally, the wasted heat from IC
engines is a great percentage of the fuel’s energy. In
gasoline fuelled IC engines, about 75% of the total energy of
the fuel is rejected in the environment [7]. The recovery of a
6% of the exhaust’s energy could lead to 10% saving of fuel
[8]. Furthermore, the temperatures developed vary from high
(about 900 0C at exhaust manifold) to medium (about 100 0C
in the engine coolant fluid) and thus the efficiency of the
thermoelectric elements could be sufficient.
The prevailing modern tendencies in the design of cars
lead to the continuous increase of electrically driven
elements, while simultaneously the available space for the
engine is decreased in order to minimize the aerodynamic
coefficient and to maximize the available space for the
passengers. The use of a thermoelectric generator device
will offload the alternator and thus will reduce its size.
Among the sources of rejected energy that exist in a
petrol engine, the initial application of a thermoelectric
device can be implemented at the exhaust pipe. The basic
reason for this is the high temperatures that prevail there and
the big rate of thermal power that goes through.
Nevertheless, the application of the device before the
catalyst is considered to be undesirable, because it
influences the proper operation of the catalyst and the
oxygen sensor.
This work focuses on investigating the amount of power
that could be recovered from the exhaust pipe of an
intermediate size car with the use of conventional
thermoelectric elements as well as whether such a solution
could be profitable in the automotive industry. However, the
methodology used can also be applied for thermoelectric
elements with a higher "figure of merit" ZT and respectively
higher power output. A measurement method and a
theoretical model have been developed, which allow the
calculation of gained power and efficiency of a
thermoelectric generator device under different electric
charges and temperature gradients. With the use of this
model we calculated the expected efficiency at different
positions of the exhaust pipe and investigated the possible
installation places of the device.
TEG Efficiency Calculation
Four basic physical phenomena are associated with the
operation of thermoelectric generators (TEG), namely, the
Seebeck effect, the Peltier effect, the Thomson effect and
Joule effect. Under steady state conditions, the contribution
of the four phenomena to energy flow, through a unit
volume is expressed as follows:
0
2=
+ dx
dT
dx
d
J
dx
dT
J
dx
da
TJ
κρτ
(2)
where T is the temperature, J is the electrical current
density, α is the Seebeck coefficient, τ is the Thomson
coefficient, ρ is the electrical resistivity and κ the thermal
conductivity of the material. Neglecting the contribution of
Thomson effect, as small, the equation that governs the heat
flow at the hot side is:
TEGHTEGCHTEGH RIITSTTKQ 2
2
1
)( += (3)
where KTEG is the total thermal conductance of the N couples
(KTEG=N(κn+κP)G), STEG is the total Seebeck coefficient
(STEG=N(an+aP)), RTEG is the total resistance
(RTEG=N(ρn+ρP)/G) and G is the geometry factor
(G=area/length). Similarly, the heat flow from the cold
junction is
TEGCTEGCHTEGC RIITSTTKQ 2
2
1
)( ++= (4)
and thus, the net power produced by the module (PTEG) is
[]
IVIIRTTS
RIITTSQQP
TEGTEGCHTEG
TEGCHTEGCHTEG
==
==
)(
)( 2 (5)
and the voltage produced by the module (VTEG) is
TEGCHTEGTEG IRTTSV = )( (6)
Therefore, the PTEG, QH, QC and η can easily be
calculated, if the material properties are known. In practice,
it is impossible to measure the temperature of both the hot
and the cold junction (TH and TC), as the p- and n-legs are
interconnected by metal (typically Cu) and are thermally in
parallel between two ceramic plates. However, it is feasible
to measure the temperatures T1 (hot side area) and T2 (cold
side area) at some distance of the ceramic plates. Assuming
that
WTh(H)= (Wth1+Wthcnt+Wth2+Wth3) (7)
is the total thermal resistance between T1 and TH at the hot
side, where Wth1, Wth2, Wth3 are the thermal conductivity
resistances of the copper and ceramic plate layers and Wthcnt
is the thermal contact resistance between the heater and the
ceramic plate (Fig.1), the hot junction temperature TH is
given by the equation
)(1 HThHH WQTT = (8)
Similarly, the cold junction temperature TC is given by
)(2 CThCC WQTT += (9)
where WTh(C) is the total thermal resistance between TC and
T2.
The set of equations (3)-(6) and (8)-(9) gives
AEDB
CEFB
QH
= (10)
AEDB
FADC
QC
= (11)
where
)()(
1HThTEGHThTEG WISWKA
++=
)( CThTEG WKB =
TEGTEGTEG RITISTTKC 2
2
1
121 )( +=
)(HThTEG WKD =
)()(
1CThTEGHThTEG WISWKE
+
=
TEGTEGTEG RITISTTKF 2
2
1
221 )( ++=
and TH, TC and PTEG can be easily calculated by the
equations (8), (9), (5) respectively.
T1
Heater (Cu)
Thermal grease layer
Ceramic plate
Electrical connections (Cu) TH
Wth1
Wthcnt
Wth2
Wth3
n leg
p leg
Figure 1: Thermal resistances between T1 and TH
The calculation of TH and TC assumes that the values of
α, ρ and κ are for the Tavg=(TH+TC)/2. As the values of TH
and TC are still not known, we can approach the result using
the values of α, ρ and κ for Tavg1=(T1+T2)/2 and calculating a
couple of values TH1 and TC1. Using the Tavg2=(TH1+TC1)/2
we can calculate a new pair of values TH2 and TC2 and so on.
The final values for TH and TC will result when (Tavg(n+1)
Tavg(n)) < limit (e.g. 0.1 0K) [9].
Experimental
A commercial 2.5x2.5 cm Bi2Te3 module with N=31
thermocouples (Melcor HT9-3-25) was used. The heater is
made from copper and is attached directly to the top of the
TEG module. In order to keep a constant cooling
temperature, a liquid heat exchanger was used as cooler. All
pieces were bonded together with two bolts at a pressure on
TEG’s surfaces of 4 MPa. In order to reduce the thermal
contact resistance, all surfaces lapped at a maximum
roughness of about 25 µm and a thin layer of graphite
thermal grease (Melcor GRF-159) was used.
For temperature monitoring two K-type thermocouples
were mounted, one in a hole of 1mm diameter near the
bottom surface of the heater and the other in a thin copper
plate on the bottom of the module. An Eliwell EWTR 910
temperature controller controlled the temperature of the
heater. A resistance box in combination with a Spectrol 534
potentiometer was used as external load. For the electrical
measurements, an Agilent 34401A and a Metrahit
multimeters were used as voltmeter and amperometer
respectively.
The delivered power PTEG for a module is presented in
Fig. 2 along with the calculated curves, where the top curve
(dotted) is without any thermal resistance (eq. 3 and 4 and
5). The second curve (dashed) is with the incorporation of
thermal resistance (eqs. 10, 11 and 5), including the thermal
contact resistance of the grease [10]. A substantial
improvement in the description of the PTEG is obtained.
Finally, the third curve in Fig. 2 is the calculated curve
(WTh(H)=0.1486 K/W, WTh(C)= 0.1445 K/W), taking into
account the thermal resistances of the ceramic plates and the
copper electrical contacts as well. Several experiments with
different compressions showed that although the pressure
increase generally increases the PTEG, negligible
improvement with pressures more than 4 MPa can be
achieved.
T1=140 C
T2=26,5 C
0
0,2
0,4
0,6
0,8
1
1,2
1,4
00,511,522,533,54
I (A)
PTEG (W)
w/out Thermal
Resistance
with thermal contact
recistance
with thermal resistance
of ceramic plates
Figure 2: Experimental and calculated values for Bi2Te3
TEG module.
T2=23,5-29 C
0
0,5
1
1,5
2
2,5
01 23 4
I (A)
P
TEG (W )
T1=220 C
T1=200 C
T1=180 C
T1=160 C
T1=140 C
T1=110 C
T1= 90 C
T1= 70 C
T1= 50 C
Figure 3: Measurements and calculated values for
Bi2Te3 (HT9-3-25) TEG module at various temperatures
Figure 3 shows the measured and calculated values for
the output power PTEG, for various values of hot-side
temperature. As can be seen, the maximum power (and
accordingly the maximum efficiency) increases with the
increase of the hot-side temperature. Curves correspond to
the calculated model on thermal resistance, taking the same
values (WTh(H) and WTh(C)).
Estimation of power gained at different places of exhaust
pipe with the use of TEG HT9-3-25.
Figure 4 presents the temperature distribution of the
exhaust system components for a 96 KW (BMW 318i, 1995
cm3) gasoline engine [11]. Assuming that the heat exchanger
between exhaust gases and the TEG achieves hot side
temperatures T1 equal to those of the exhaust system
components illustrated in Fig.4, the maximum power and
efficiency (Fig.5) were calculated for a Melcor HT9-3-25
TEG at different positions of the exhaust pipe after the
catalyst. The calculating model used takes into account the
thermal contact resistances between heat exchanger surfaces
and the TEG elements. As the part load operation is the most
typical operational situation for a vehicular gasoline engine,
all calculations were made for this condition. The output
power and efficiency were calculated for different cold side
temperatures T2 (0 – 120 0C), in order to have different
implementations of the cooling system covered (cooling by
ambient air or by the engine coolant, different designs of the
heat exchanger etc.). The calculation of the potentially
available thermal power at every place of the exhaust pipe
shows that, for each combination of engine load and
temperature of cold reservoir, the thermal power exceeds the
likely maximum required power from the alternator, which
can oscillate around 1000 W in modern cars with a lot of
electric accessories [12].
0
100
200
300
400
500
600
700
800
900
10 0 0
0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0
< front
Exhaust pipe L (m) rear >
T (C)
Cataly st
Center
muffler
Rear
muffler
full load
part load
Figure 4: Temperature distribution at the exhaust system
components (after exhaust manifold),( BMW 318i).
0%
1%
2%
3%
4%
5%
6%
7%
8%
1,5 2 2,5 3 3,5 4
< front E xhaust pipe L (m) rear>
n
TEG max
Center
muf f l er
Rear
muffler
Part load
T2= 0 C
T2= 30 C
T2= 60 C
T2= 90 C
T2= 120 C
Figure 5: Maximum efficiency of a TEG ΗΤ9-3-25 along
the exhaust pipe (after catalyst) for different cold side
temperatures Τ2.
The maximum number of TEG modules (of the same
type mentioned above) that could be placed for the
exploitation of the total thermal power of exhaust gases can
be consequently calculated, dividing the potentially available
thermal power Q in each point of the exhaust pipe with the
heat flow QH induced into each module. In this case, the
maximum electrical power produced from the device in each
place of the exhaust pipe and the corresponding minimal
surface required for the heat exchanger, i.e. the sum of all
TEG surfaces, are presented in Fig. 6.
0
10 0
20 0
30 0
40 0
50 0
60 0
70 0
1,5 2 2,5 3 3,5 4
< front Exhaust pipe L (m) rear>
maxPTEGtot (W)
0,05
0,06
0,07
0,08
0,09
0,1
0,11
STEG
(m2
)
T2 = 0 C
T2 = 60 C
T2 = 120
C
Center
muffler
Rear
muf f l er
>
<
<
Part load
>
<
Figure 6: Maximum TEG device output power and
required minimal surface of the heat exchanger along the
exhaust pipe (after catalyst), for different cold side
temperatures Τ2.
The total gain in fuel consumption that could be
economized with the use of a thermoelectric device can be
calculated for a 5% reduction in the fuel consumption with
current level of technology and for a 20% in future, with the
use of new thermoelectric materials (assuming an average
consumption of 7.9 lt/100 km and 10.000 km/year). With an
estimated cost of the thermoelectric device around 500 €, the
depreciation of the device could take place in 3 or 2 years
(for the more efficient devices expected in the future) also
depending on the future petrol prices.
Conclusions
In this work we developed a model for the evaluation of
performance of a thermoelectric generator (TEG). The
model, which takes into account the thermal contact
resistance and the thermal resistance of the two (top-bottom)
ceramic plates of the TEG, has been successfully applied
into a commercial TEG. The TEG module was capable to
deliver 2.6 W of power when the hot-side temperature was
220 C, which is equivalent of about 5.4 % of efficiency.
The use of thermoelectric materials in vehicular engines
for wasted heat recovery, can help considerably in the world
need for energy saving and reduction of pollutants. The
allocated power and the temperatures that prevail in the
exhaust pipe of an intermediate size car are satisfactory
enough for the efficient application of a thermoelectric
device. The most advisable place appears to be precisely
after the catalyst, where high temperatures prevail. The
output power and the efficiency of the device depend on the
operational situation of the engine and on the effective
designing of the heat exchanger. From the results it appears
that even with conventional thermoelectric elements, a
thermoelectric device with an output power of around 300
W would be feasible, with a corresponding fuel saving of
around 5%. Further improvements in the efficiency of the
thermoelectric materials, particularly for high temperature
operation, are expected to give a revolutionary impulse to
their application in the automotive industry.
Acknowledgments
It is acknowledged the financial support of the project
entitled “Application of Advanced Materials Thermoelectric
Technology in the Recovery of Wasted Heat from
automobile exhaust systems” by the Greek Secretariat of
Research and Development under the bilateral framework
with Non-European countries (Greece-USA)
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Gases of Automobiles”, Proc. 7th European Workshop on
Thermoelectrics, Pamplona, Spain 2002, p 17
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“Study of Power efficiency in Thermoelectric Power
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... The Melcor HT9-3-25 TEGs were tested in this study. The maximum power and efficiency were analysed at different points of the exhaust pipe after the catalyst used hot temperature data, particularly at partial load [20]. The temperature profile demonstrated a pattern of decreasing temperature from the section near the engine outlet to the rear muffler. ...
... The temperature profile demonstrated a pattern of decreasing temperature from the section near the engine outlet to the rear muffler. According to the graph, the TEG system should be put anywhere between the catalyst and rear muffler where the hot temperature drop ranged from 300 • C to 200 • C. The fuel consumption can be reduced up to 5% with the current technology since the TEG can always be improved to achieve better temperature difference as the TEG technology will only advance with a new combination of material that is able to withstand higher temperature and able to convert the temperature difference to a better voltage reading in the future [20]. Big companies such as BMW, General Motors (GM) and Volkswagen has begun to develop a highly efficient TEG for the recovery heat system [21]. ...
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Article
The figure of merit \mathit{ZT} of thermoelectric materials has been evaluated by the Harman method in the temperature region below room temperature. In this method only resistance measurements by both dc and ac methods are required to obtain the \mathit{ZT} values. \mathit{ZT} is given by \mathit{ZT}=(Rdc/Rac-1)/x, where Rdc, Rac and x are the resistance value by the ac and dc methods and the rate of the heat to the heat bath, respectively. The heat effect is experimentally confirmed to be negligibly small and we can use x=1 which corresponds to a sufficient adiabatic condition. Because an ambiguity due to experimental errors such as the length between the measurement terminals in the resistivity and the thermal conductivity measurements is removed, \mathit{ZT} can be determined very simply and precisely by the Harman method.
Thermoelectric technology capable of solid state electric power generation and cooling has been has been known for almost 180 years. Only in the past 50 years has this technology found its way out of the laboratory and into niche military, space, and commercial products. Most of the profitable commercial products have made their appearance in the past decade. Many of you are working hard to advance the state of the art in thermoelectric materials, and I am sure that you do not want to wait another 180 years, 50 years, or even another decade to commercialize your results. There are many potential ways to commercialize this technology, but the area that I think represents the biggest market is the automotive industry. There are over 17 million automobiles sold in the US each year and over 60 million worldwide. With the possible exception of the electric power industry, I know of no other market segment that is even close to the potential of the automotive industry for using a high volume of thermoelectric materials. Every vehicle produced has an electrical system supplied by a one to two kilowatt generator with increasing power demand as electrical features are added. A high percentage of vehicles have air conditioning systems with 3 to 5 kilowatts of cooling. Sufficiently advanced thermoelectric materials can be the heart of systems that supplement or replace the mechanical or electro-mechanical devices performing these functions today. This paper addresses the boundary conditions for the function, quantity, and value needed to commercialize thermoelectric technology. Timing to introduce subsystems with this technology is also addressed. Thermoelectric technology has to compete with the existing technologies and other emerging technologies to be successfully commercialized. While it seems out of reach today, there is even the potential that sufficiently advanced thermoelectric materials and device construction could one day replace the internal combustion engine and even rival fuel cells in energy conversion efficiency.
Article
The dimensionless thermoelectric figure-of-merit, ZT, of Bi2Te3 based alloys was investigated under a large temperature difference using a recently reported 'open/short circuit' measurement technique. It is shown that the measured ZT decreases with an increase in temperature difference. Theoretical analysis indicates that this dependence can be explained by taking into account the Thomson effect. An equation is obtained for a modified thermoelectric figure-of-merit which is valid for measurement over large temperature differences.
Article
An apparatus for measuring the conversion efficiency η and several further key properties of thermoelectric generators is presented. To achieve highest reliability and accuracy the crucial determination of the thermal energy that is supplied to the generator is done by an absolute method, i.e. by measuring the electrical power that is dissipated in a thermally guarded resistive heater. The accuracy of this method was carefully verified with a traceable calibration standard. The data evaluation is discussed for test measurements of a high efficiency Bi2Te3 module and compared to results that are estimated from the material properties. Excellent accuracy, consistency and reproducibility of the data are found, which makes the measurement a sensitive and reliable tool for the development of thermoelectric generators.
Article
A thermal contact resistance model is derived from the Whitehouse, Archard and Onions theory of contact and thermal considerations. The model used two coupled thermal resistances acting in parallel: direct contact resistance (depending on the actual dimensions of the contact spots) and interstitial contact resistance (depending on interstitial medium and mean interfacial gap). Variations of thermal contact resistance are computed as a function of the apparent pressure. The predictions are compared and agree relatively well with some experimental data. The model using non-dimensional parameters is very easy to implement.
Conference Paper
Measurements of assembled thermoelectric modules commonly include investigations of the module output power versus load resistance. Such measurements include non-ideal effects such as electrical and thermal contact resistances. Using an AC electrical measurement, a model for a thermoelectric module has been developed utilizing electrical circuits for both the thermal and electrical characteristics of the module. Measurements were taken over the frequency range of 1mHz to 500Hz using lock-in amplifiers. We present data showing the extraction of ZT from such measurements on commercially available modules. By knowing either the heat capacity of the module or the average module Seebeck coefficient, determination of the thermal conductance can also be achieved. The model proposed here provides a simple equivalent circuit which can be analyzed using an electrical simulator such as SPICE. This model makes use of the magnitude and phase of the electrical impedance measured by the lock-in amplifiers at the input terminals of the module and includes fitting parameters of the total electrical resistance, thermal conductance, heat capacitance, and module Seebeck coefficient.
Study of Power efficiency in Thermoelectric Power Generators
  • K Zorbas
  • E Hatzikraniotis
  • K M Paraskevopoulos
K. Zorbas, E. Hatzikraniotis and K.M. Paraskevopoulos, "Study of Power efficiency in Thermoelectric Power Generators", ΧΧII Greek Conference of Solid State Physics and Science of Materials, Patra Greece, September 24-27, 2006
Vehicle Fuel Economy Improvement through Thermoelectric Waste Heat Recovery
  • J Lagrandeur
J. LaGrandeur et al, "Vehicle Fuel Economy Improvement through Thermoelectric Waste Heat Recovery", 2005 Diesel Engine Emissions Reduction (DEER) Conference Presentations, Chicago, Illinois, August 21-25, 2005