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10/19/2016

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].