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2017-01-0144
A Comparison of Four Modelling Techniques for Thermoelectric Generator
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Abstract
The application of state-of-art thermoelectric generator (TEG) in
automotive engine has potential to reduce more than 2% fuel
consumption and hence the CO
2
emissions. This figure is expected to
be increased to 5%~10% in the near future when new thermoelectric
material with higher properties is fabricated. However, in order to
maximize the TEG output power, there are a few issues need to be
considered in the design stage such as the number of modules, the
connection of modules, the geometry of the thermoelectric module,
the DC-DC converter circuit, the geometry of the heat exchanger
especially the hot side heat exchanger etc. These issues can only be
investigated via a proper TEG model. The authors introduced four
ways of TEG modelling which in the increasing complexity order are
MATLB function based model, MATLAB Simscape based Simulink
model, GT-power TEG model and CFD STAR-CCM+ model. Both
Simscape model and GT-Power model have intrinsic dynamic model
performance. MATLAB function based model and STAR-CCM+
model can be developed to have only steady state performance or to
include dynamic performance. Steady state model can be used in
quick assessment of TEG performance and for initial design
optimization. However, only dynamic model can give the accurate
prediction of TEG output during engine transient cycles. This paper
also demonstrates finding the answers to three TEG related questions
using STAR-CCM+, Simscape and MATLAB function based
Simulink model respectively.
Introduction
Thermoelectric device is a bi-direction energy converter between
thermal energy and electrical energy. When there is thermal gradient
developed across a couple which is consisted of one n-type leg and
one p-type leg, this couple will work as a small voltage battery which
is Seebeck mode. On the other hand, if an external voltage applied to
the two terminals of the couple, there will be heat be pumped from
one end of the legs to the other end of the legs though the legs. This
is known as Peltier mode [1]. This reversible energy conversion
property makes the thermoelectric device have big potential for being
an actuator in future thermal management systems in vehicle other
than working only in uni-function, either Thermoelectric Generator
(TEG) for thermal energy harvest or Thermoelectric Cooler (TEC)
for heating, refrigerator and air-conditioner. For example, it can be
used in heating battery, catalyst, fuel, oil and engine coolant up
before engine cold start and then it can harvest the thermal energy
when the engine works in warm and heavy load condition. This will
provide another control freedom in the online optimization of the
whole vehicle system in fuel consumption and CO
2
emissions. The
very open prediction for the future could be that most thermal
sensitive components and the whole engine surface together with the
exhaust system in the vehicle will possibly be wrapped or integrated
with thermoelectric layers.
So far, in the domain of automotive application, the majority
research efforts are focused on the optimization and prediction of the
TEG performance and the reduction of the device cost related to the
waste thermal energy harvest in both diesel and gasoline engines
[2~9]. The optimization and prediction work unavoidably has to be
based on device and system level model. There are multiple choices
of modelling technique or environment for doing both the device and
system level modelling work. If the hot side and cold side
temperature is equally distributed, the basic equations for Seebeck,
Peltier, Thomas effect and energy conservative of one thermoelectric
module (TEM) can be clearly stated and be numerically calculated
using Excel, calculator, Fortran or C language or MATLAB scripts.
However, there will be numbers of TEMs in a TEG used in engine
exhaust waste energy harvest and the boundary conditions for each
TEM are not the same. Hence, the modelling of a TEG device needs
proper software environment.
Since the TEG device has both thermal and electrical mechanism and
the thermal phenomenon can be modelled as equivalent electric
circuit, the electric circuit and analysis software SPICE can be used
for modelling the TEG device [10,11]. The temperature depended
properties of the thermoelectric material can be modelled using
polynomial function within the circuit block. But this type of model
is purely steady state. If the TEG model needs to be coupled to
engine model, MATLAB/Simulink, Simscape or GT-Power can be
chosen as the modelling environment. They all can model the TEG
dynamic behaviour. Simscape has both fundamental thermal and
electrical elements. A physical TEG model together with DC/DC
converter circuit can be built up based on the physical connections of
thermal and electrical elements [12]. A Simscape TEG model can run
directly within Simullink model frame. If the engine model is also a
Simscape model or a Mean Value Engine Model (MVEM) developed
in Simulink environment, there will be seamless integration of TEG
model with engine model. In 2016b version of MATLAB, other than
electrical and thermal elements, there are elements for gas system
which make the modelling of engine exhaust system more
convenient. GT-power is a commonly used software for engine
modelling. There is also a TEM block in the GT-Power library in
later than 2013 version. The development of one TEM unit model is
quite straightforward using GT-power [13]. The analysis of heat
flux, stress, pressure drop, heat exchanger performance is best to be
carried out using 3D CAD and CFD modelling techniques
[3,4,14,15].
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This paper presents the applications of four modelling techniques in
solving TEG related optimization problem or questions. It is
organized as this: In section 2, STAR-CCM+ was used in the analysis
of the TEG performance improved using Aluminium plate between
the hot side stainless heat exchanger and the TEMs. In section 3,
Simscape exhaust system model was developed and validated against
engine test data. This model then was used to demonstrate that only
stainless pipe without inner fins will not give acceptable TEG output
performance. The development of TEG GT-power model and its
validation was discussed in Section 4. Then it was followed by the
introduction of a Simulink dynamic TEG model which is based on
MATLAB function block. This model was also validated against
engine transient cycle and was used to explore the impact of thermal
inertia on the TEG performance.
STAR-CCM+ TEG Model
TEG Engine Test Result w/o Aluminum Plate
Since the maximum exhaust gas temperature is normal higher than
500°C, the hot side heat exchanger for TEG device is made from
stainless steel which has as low as 16 W/m.K thermal conductivity. It
can be expected that the temperature distribution within the TEM
contact surface with the hot side heat exchanger surface will be very
uneven. This prediction was proved by the experiment results. Figure
1 shows a TEG device with four commercial TEMs was tested in a
diesel engine Exhaust Gas Recirculation (EGR) path. The sandwich
assembly of this TEG device is displayed in Figure 2. Two test data
set were collected at the same gas in conditions and the same
clamping force. One is without aluminium plates, one is with adding
two 3mm aluminium plates. For the case with aluminium plates, one
aluminium plate was placed between the two top TEMs and the top
surface of hot side exchanger and the other was placed between the
two bottom TEMs and the bottom surface of the hot side exchanger.
The width and length of the aluminium plates are the same to those of
the hot side surface of the hot side heat exchanger. These four TEMs
were wired together electrically in series and with an external PWM
current sweep circuit. The comparison of power output of the top two
TEMs are shown in Figure 3. There is obvious power improvement
of both two TEMs by using the aluminium plate.
Figure 1. TEG testing in a diesel engine EGR path
The data acquisition system used in the experimental work in this
study consists of NI cRIO chassis and 16bit analog input module. The
maximum uncertainty of the voltage and current measurement is
around ±0.2%. Hence the maximum uncertainty of computed
electrical power is around ±0.3% according to the theory of the
propagation of uncertainty.
Figure 2. (a) Four TEMs and one hot side heat exchanger and two cold side
exchangers; (b) TEG consisted of four TEMs in work mode
(a) (b)
( c) (d)
Figure 3. Test results: (a) Electrical power of the first top TEM in the
upstream position; (b) increased power percentage by using aluminum plate;
(c) Electrical power of the second top TEM in the downstream position; (b)
increased power percentage by using aluminum plate;
What is the Optimal Thickness of the Aluminum Plate?
Now here comes a question, how much the thickness of the
aluminum plate should be. Instead of repeating the experimental test
with various thickness of the aluminum plate, this work was done
using a STAR-CCM+ TEG model. STAR-CCM+ is an entire
engineering process for solving problems involving flow (of fluids or
solids), heat transfer, and stress [16]. The version of the STAR-
CCM+ used in this study is 9.06. When developing the TEG model,
perfect contact between each pair surface was assumed.
Figure 4 shows the temperature distribution of three cases which are
1) without aluminum plate, 2) with 1mm aluminum plate and 3) with
7mm aluminum plate respectively. It can be seen that there is
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changes of temperature distribution pattern among these three
situations. The sampled temperatures along the middle line of the top
two TEMs along the gas flow direction are depicted in Figure 5.
Figure 5 plays an important role in the interpretation of the benefit
from using aluminum plate and the TEG performance evolves with
the thickness of the aluminum plate. When there is no aluminum
plate, the temperature along the middle line of both TEMs is very
curved toward lower temperature value. By using 1mm aluminum,
these two curves have been not only straightened but also lifted to
higher value. This can be explained as the big jump thermal
conductivity from stainless steel to aluminum plate of which the
thermal conductivity is around 237 W/m.K. The lateral thermal
conduction heat transfer has contributed to this phenomenon. When
the thickness of the aluminum plate increases, the temperature of the
upstream TEM tends to decrease, while the temperature of the
downstream TEM tends to increase. These two lines both become
more level and straight. This is also because the thicker the aluminum
plate, the more lateral heat transfer from upstream to downstream.
Figure 4. Top: the surface temperature distribution of the hot side heat
exchanger without aluminum plate; Bottom left: the surface temperature
distribution of the hot side heat exchanger using 1mm aluminum plate;
Bottom right: the surface temperature distribution of the hot side heat
exchanger using 7mm aluminum plate.
Figure 5. Temperature samples along the middle line of the TEMs along the
gas flow direction
Figure 6. The average of delta temperature along the middle line of the top
two TEMs varies with the thickness of the aluminum plate.
Figure 6 is the plot of average delta temperature of the hot side and
the cold side of two TEMs verse the thickness of the aluminum plate.
It shows that the average delta temperature reaches the plateau at
4mm. Similar simulation results have been obtained for other gas in
conditions. This suggests that placing an aluminum plate with even
only 1mm thickness will help to improve the TEG output
performance and that plate thickness greater than 4mm provides no
additional benefit. Other metal plate which has high thermal
conductivity such as copper can be used in steady of aluminum plate
but will add more into the cost of the TEG [17].
1D models do not include the lateral heat conduction mechanism and
they are developed under the assumption that there is even
temperature distribution within the contact surface area of one TEM.
2D modelling techniques like the 3D modelling techniques can be
used in this simulation work.
GT-Power TEG Model
When the system level optimization and prediction work need to be
carried out for the application of TEG in engine waste energy harvest,
GT-Power is a good choice. No only it is convenient in modelling
engine system, but also there is ready to use TEM block in the library
and its strong capability in modelling the gas and coolant flow, heat
exchanger thermal behavior etc.
A TEG unit model with one TEM has been built in GT-Power
version 2016, See Figure 7. It is a basic unit brick for building future
complete TEG device. The aim of this modelling task is to investigate
the behaviour of TEG when it works under wide range of engine
operating conditions, to explore the influence of TEG on engine
performance and to design a model-based control system to maintain
the energy balance and prevent the possible damage of the TEG. It is
a dynamic TEG model which includes the dynamic of exhaust gas,
thermal inertia of the TEM and heat exchanger. Hence, it can
simulate the transient response of the TEG device.
Figure 7. (can be found at the end of this paper)
Modelling the TEM
A complete TEM is mainly made up by two ceramic wafers and the
thermoelectric elements between them. A basic TEM unit model
which consists a hot-wafer, a cold-wafer and a TEM block is shown
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in Figure 8. There is one ceramic wafer on TEM hot side and cold
side respectively. Cond-Hot-1 and Cond-Cold-1 are used to simulate
the contact thermal resistance. Air-Cond is the air gap between the
ceramic wafer. TEM-1 is the block for emulating both thermal and
electrical behavior of a TEM. The required input parameters for the
TEM block are shown in Figure 9. These input parameters include
TEM geometrical parameters and thermoelectric properties.
Unavoidably, there is properties loss during the manufacture process
of a TEM. In order to have high accuracy of the TEM model,
validated module based thermoelectric properties should be used in
this setup.
Figure 8. A unit TEM GT-Power model
Figure 9. Setup window of input parameters for TEM Block
The main tuning parameter for the TEM model is the thermal contact
conductance (Cond-Hot and Cond-Cold). Figure 10 shows the best
tuned result of the TEM model to match a module performance given
in the datasheet for steady state conditions.
(a)
(a)
Figure 10. TEM model performance at steady state: (a) OCV; (b) Maximum
electrical power
Modelling the heat exchanger
Because the TEM is closely integrated with the heat exchanger to
form a TEG, the heat exchanger templates within the GT-Power do
not fit the TEG scenario. So that the heat exchanger has to be
modelled using pipe and thermal mass blocks. The structure of both
hot side and cold side heat exchanger can be seen in Figure 7. The
pipes are used to calculate the temperature and pressure along the
heat exchanger. The heat transfer coefficient which is correlated to
both gas flow rate and gas temperature needs to be input as known
function. The validation of a TEG GT-Power model which consists
multiple TEM units against engine test results is undergoing. This
result together with its integration into engine model for system level
optimization, prediction and control design will be discussed in
another forth coming paper.
Simscape TEG Model
Modelling the Engine Exhaust System
Simscape provides a quick way to develop physical model within
MATLAB/Simulink environment. The element blocks in Simscaps
are very basic. Users can create their own custom component models
using MATLAB based Simscape language which enables text-based
authoring of physical modelling components, domains and libraries
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[18]. A model of the exhaust system of a 2 liters GTDi gasoline
engine was developed using Simscape, see Figure 11. The exhaust
system was divided into four segments. Each segment pipe was
modelling using one internal convection heat transfer and one
external convection heat transfer element. The average gas
temperature within the pipe was estimated using a subsystem which
is displayed in Figure 12. This subsystem also gives the estimated
value for gas out temperature. Figure 13 is the diagram of this engine
which was installed on a dyno engine test bed. This validation result
using engine test data is displayed in Figure 14.
Figure 11. (can be found at the end of this paper)
Figure 12. (can be found at the end of this paper)
Figure 13. A diagram of the 2 liters GTDi gasoline engine
Figure 14. Validation result of the Simscape exhaust system model
Prediction the Output of the TEG Mounted Directly to
the External Surface of the Engine Exhaust System
It can be seen from Figure 14 that the gas out temperature after the
fourth pipe segment is still as high as 500°C. Hence, here comes a
couple of questions. The first is how is the TEG performance if the
TEMs are mounted to the external surface of the exhaust pipe without
change the exhaust pipe. The second is will the hot side temperature
of the TEMs is over the commercial module limit which is 250°C?
These two questions can be answered by using the validated exhaust
system Simscape model in the previous section. But before doing
that, the model in Figure 11 and the subsystem in Figure 12 need to
be modified to include TEM component and Peltier effect. For
simplicity, Joule heat effect and Thomas effect were neglected. To
further simplify the problem, only one pipe segment model was used
for this simulation. Two conduction heat transfer elements ware
added and to replace the external convection heat transfer element,
see Figure 15. The cold side was simulated as a constant temperature
source. Figure 16 shows the Peltier pumping heat transfer was
extracted in computing the average gas temperature within one pipe
segment.
The simulation result shows that even though the gas in temperature
is very high, the hot side temperature of the TEM is very low with
maximum value is at 50°C. So that the harvested electrical energy is
very low. It is because the heat transfer from gas to the exhaust pipe
wall is not big enough to give high hot side temperature.
In R2016b MATLAB, there is gas system element block in Simscape
, which will help to build more accurate model. However, if a
dynamic TEG model which is used for predicting TEG output during
an engine transient cycle is to be developed, customized heat
exchanger block and customized temperature dependent TEM block
need to be created first.
Figure 15 (can be found at the end of this paper)
Figure 16. Subsystem for computing the average gas temperature includes the
Peltier heat pumping effect.
A Simulink TEG Model
Model Structure
The physical equations about the TEM multiple mechanism have
been well studied [19, 20]. Figure 17 shows the energy flow within a
TEM. The heat flow cause by Thomas effect was not included. When
there is current flow through the TEM, the Peltier pumping energy
developed from hot side to cold side. The Peltier pumping thermal
energy into the hot side of the TEM is higher than the Peltier
pumping thermal energy out the cold side of the TEM. Their
difference equals to the sum of joule heating
and electrical
output power
. The energy flow within a unit TEG which consist
of one TEM is depicted in Figure 18.
are respectively
the heat exchanger thermal resistance, the hot side contact thermal
resistance and the cold side thermal resistance.
is the mass
weight of the heat exchanger.
is the maximum electrical output
of the TEM. Letter represents the thermal energy and letter
represents the temperature. The detailed physical equations for TEM
and heat exchanger used in this modelling work can be found in
reference [21].