# A comparison of four modelling techniques for thermoelectric generator

TL;DR: Four ways of TEG modelling are introduced and finding the answers to three TEG related questions using STAR-CCM+, Simscape and MATLAB function based Simulink model respectively are demonstrated.

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 CO2 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.

## Summary (3 min read)

### Introduction

- Thermoelectric device is a bi-direction energy converter between thermal energy and electrical energy.
- 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].
- 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].
- In section 3, Simscape exhaust system model was developed and validated against engine test data.

### 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.
- Figure 1 shows a TEG device with four commercial TEMs was tested in a diesel engine Exhaust Gas Recirculation (EGR) path.
- Two test data set were collected at the same gas in conditions and the same clamping force.
- 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 maximum uncertainty of the voltage and current measurement is around ±0.2%.

### What is the Optimal Thickness of the Aluminum Plate?

- Now here comes a question, how much the thickness of the aluminum plate should be.
- STAR-CCM+ is an entire engineering process for solving problems involving flow (of fluids or solids), heat transfer, and stress [16].
- By using 1mm aluminum, these two curves have been not only straightened but also lifted to higher value.
- 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.
- 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.

### 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.
- A TEG unit model with one TEM has been built in GT-Power version 2016, See Figure 7.
- 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.

### Modelling the TEM

- A complete TEM is mainly made up by two ceramic wafers and the thermoelectric elements between them.
- Air-Cond is the air gap between the ceramic wafer.
- The required input parameters for the TEM block are shown in Figure 9.
- Unavoidably, there is properties loss during the manufacture process of a TEM.
- The main tuning parameter for the TEM model is the thermal contact conductance (Cond-Hot and Cond-Cold).

### 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 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.

### 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.
- A model of the exhaust system of a 2 liters GTDi gasoline engine was developed using Simscape, see Figure 11.
- The average gas temperature within the pipe was estimated using a subsystem which is displayed in Figure 12.
- This validation result using engine test data is displayed in Figure 14.

### 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.
- These two questions can be answered by using the validated exhaust system Simscape model in the previous section.
- So that the harvested electrical energy is very low.
- Subsystem for computing the average gas temperature includes the Peltier heat pumping effect.

### Model Structure

- The physical equations about the TEM multiple mechanism have been well studied [19, 20].
- As it is indicated in Figure 19, this model includes modelling the influence from the geometry of TEM and heat exchanger and the temperature dependent TEM properties and heat exchanger properties.
- The Impact of Thermal Inertia on TEG Performance.
- The sum of maximum power output of the TEG device for these 6 conditions were plotted together in Figure 25.

### Summary/Conclusions

- Four modelling techniques which are 3D CFD, GT-Power, Simscape and MATLAB function have been used in modeling TEG device.
- The existing heat exchanger template does not fit for TEG application.
- Since the GTPower is popular in modelling automotive engine, GT-power TEG model can be seamlessly integrated with engine model and then be used for system level optimization.
- Learning Simscape language needs a lot of effort.
- The conclusion is the TEG performance is not very sensitive to thermal inertia.

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##### Citations

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### Cites background from "A comparison of four modelling tech..."

...Since the thermal masses of both sides of the HXRs are significantly larger than the TEMs and dominate the thermal dynamics of the TEG system, energy transfer at the hot and cold end of the TEG system are simulated by dynamic models....

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...The heat transfer area, mass of the HXRs and aluminium plate for each control volume can be expressed as follow: =A A nhxr CV hxr CV ....

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...Thermal inertia of the HXRs is taken into account in the model so that dynamic behaviour of the system is included....

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...A comparison of power output of the systems under different scenarios underlines the importance of integration of TEM with HXRs. Based on the simulation results, around 20% average power output increase can be expected by optimizing the thermal contact conductance and the heat transfer coefficient of hot side HXR....

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...The configuration of a TEG system with counter flow type HXRs is presented in Fig....

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### Cites methods from "A comparison of four modelling tech..."

...The model structure and validation results were discussed in another paper [25]....

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### Cites background from "A comparison of four modelling tech..."

...Although aluminium plates contribute to an increase of thermal resistance, an optimal thickness of aluminium plate can increase the average delta temperature of all TEMs on the HXRs [141]....

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##### References

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### "A comparison of four modelling tech..." refers methods in this paper

...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....

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...The development of one TEM unit model is quite straightforward using GT-power [13]....

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...The development of TEG GT-power model and its validation was discussed in Section 4....

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...Since the GTPower is popular in modelling automotive engine, GT-power TEG model can be seamlessly integrated with engine model and then be used for system level optimization....

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...GT-power is a commonly used software for engine modelling....

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