**4. Math modeling**

It is necessary to conduct a number of tests to optimize the design of ATEG in order to increase the electric power it generates and its efficiency. Building a reliable mathematical model of the automotive thermoelectric system is the most rational solution to this problem. Detailed modeling can help to find the optimal combination of ATEG parameters. In addition, the estimation of various system parameters for existing driving cycles allows predicting the appropriateness of using a generator in a specific car model.

#### **4.1. Structure of the mathematical model**

In general, the mathematical model of ATEG should describe the behavior of a system consisting of the following components: car engine, hot heat exchanger, TEM unit, cold heat exchanger, cooling system, power control system (PCU) and consumption load. Block diagram showing the interaction of these subsystems is presented in **Figure 11**.

The output ATEG model impacts, which can be calculated are: generated voltage, current and electrical power output, the temperature of exhaust gas at the exit of ATEG and efficiency

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In general, ATEG consists of several sections through which a flow of hot gas and cold coolant flows. The physical model of the ATEG section contains the following basic elements (**Figure 13**): 1 and 4 - hot and cold heat exchangers; 2 - thermal contact resistances; 3 - thermocouples,

(**Figure 12**).

**4.2. Physical model ATEG**

**Figure 12.** Input and output effects on ATEG.

**Figure 11.** Structural scheme of mathematical model.

5 - TEM container.

When simulating these subsystems, input, output impacts and parameters are set for describing the ongoing processes. The parameters include the data containing physical properties of the materials used and the geometry of system components.

As inputs to the ATEG: the temperature (*Tex in*) and mass flow (*mex*) of the exhaust gas emitted by the engine, the temperature (*Tcl in*) and the mass flow of the cold-producing (*mcl* ).

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**Figure 11.** Structural scheme of mathematical model.

**3.9. Troubleshooting**

204 Bringing Thermoelectricity into Reality

when operating the ATEG.

thermal deformations.

**4. Math modeling**

This section provides general recommendations for troubleshooting issues that may occur

Electrochemical corrosion is excluded by the selection of contacting materials with equal electrochemical potentials, qualitative isolation of electrical systems, using protective, electrically

Excessive thermal deformations can lead to plastic deformation of parts and loss of flatness of contacts. It is possible to reduce the pressure force with the help of selecting the suitable materials as per their thermal expansion coefficients and using the elastic compensators for

Fretting-wear occurs under the action of periodic tangential shifts on contacts. This process has not been fully studied. It can be eliminated by reducing the contact pressure (see para-

The thermal contact resistance can increase due to several factors which are: oxidation, degradation of the thermal grease or reduction of the pressure during heating or cooling. Using of

Cleaning and monitoring of the pH of the coolant, selection of corrosion-resistant materials or

It is necessary to conduct a number of tests to optimize the design of ATEG in order to increase the electric power it generates and its efficiency. Building a reliable mathematical model of the automotive thermoelectric system is the most rational solution to this problem. Detailed modeling can help to find the optimal combination of ATEG parameters. In addition, the estimation of various system parameters for existing driving cycles allows predicting the appro-

In general, the mathematical model of ATEG should describe the behavior of a system consisting of the following components: car engine, hot heat exchanger, TEM unit, cold heat exchanger, cooling system, power control system (PCU) and consumption load. Block dia-

When simulating these subsystems, input, output impacts and parameters are set for describing the ongoing processes. The parameters include the data containing physical properties of

*in*) and the mass flow of the cold-producing (*mcl*

*in*) and mass flow (*mex*) of the exhaust gas emitted by

).

gram showing the interaction of these subsystems is presented in **Figure 11**.

resistant materials, protective coatings and adjusting loads pressure can eliminate it.

coatings prevent heat exchangers pollution from corrosion, water deposits and soot.

insulating or corrosion-resistant coatings and observing the pH of the coolant.

graph above), using hardening or antifriction coatings or thermal grease.

priateness of using a generator in a specific car model.

the materials used and the geometry of system components.

**4.1. Structure of the mathematical model**

As inputs to the ATEG: the temperature (*Tex*

the engine, the temperature (*Tcl*

**Figure 12.** Input and output effects on ATEG.

The output ATEG model impacts, which can be calculated are: generated voltage, current and electrical power output, the temperature of exhaust gas at the exit of ATEG and efficiency (**Figure 12**).

#### **4.2. Physical model ATEG**

In general, ATEG consists of several sections through which a flow of hot gas and cold coolant flows. The physical model of the ATEG section contains the following basic elements (**Figure 13**): 1 and 4 - hot and cold heat exchangers; 2 - thermal contact resistances; 3 - thermocouples, 5 - TEM container.

The solution of operation modeling issue for the described system consists of thermal and electric circuits calculations taking into account thermoelectric processes.

**5. The ways of ATEG efficiency increasing**

**5.1. Adapting the design to variable operating modes**

tional blade-intensifier, 6 - control rod.

**5.3. About materials with a phase transition**

**5.2. Application of heat pipes**

**5.4. Temperature rise of EG**

achieved through two technical solutions.

ATEG operation is accompanied by frequent volume flow differences and EG temperature changes, and vehicle electrical load is not constant. At the same time, it is necessary to ensure the optimum flow of EG through ATEG, when, on the one hand, there is sufficient intensive heat exchange in the ATEG, and on the other hand, the pressure drop EG is not too great.

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Therefore, it is practical to use bypass for removing excessive EG through ATEG or a hot heat exchanger with variable hydraulic resistance of the flowing channel. For example, the patent [50] describes the construction of a heat exchanger using rotatable fins that allows intensifying heat transfer at low shaft speeds and reducing hydraulic resistance at high speeds. In **Figures 14**, 1- turning fins, 2- displacer, 3- TEM, 4- cold heat exchanger, 5- rota-

One of the methods to increase the efficiency of ATEG can be the use of heat pipes in its structure [51, 52]. The reduction of the thermal resistance between exhaust gases and hot junctions allows increasing the hot junction temperature and also reduces the counter-pressure in the exhaust system in some cases. In addition, the heat pipes give the possibility of a more flexible approach towards the design of ATEG and there is no need to be limited to only the surface area of the hot heat exchanger. They also help to regulate the temperature of the hot junction

There is a need to select the operating point in the ATEG design. This fact connected with: variable heat flux through TEM under different operating conditions of the internal combustion engine, the dependence of the TEM semiconductor materials ZT on the junctions' temperature and the limitations on the peak temperature of the hot junction. Optimizing ATEG for obtaining maximum power at the extreme operating conditions of the internal combustion engine leads to low efficiency at low and medium rotational rates with low engine load. In the reverse situation, there is a need to use bypass for not overheating the TEM and not creating a counter-pressure in the exhaust pipe at high engine speeds. The solution to the problem of combining these two extreme situations and, consequently, increasing the efficiency of ATEG under different operating conditions of the ICE can be the use of materials with a phase transition that store heat at high loads on the ICE and give it to ATEG with a heat flux decrease in the exhaust line [53].

It is advisable to use EG at high temperatures for efficient ATEG operating which can be

by varying their length or by using variable conductance of heat pipes.

The heat problem is solved by finding the distribution of thermal fluxes and temperatures over the entire cross-section of the ATEG section. For this purpose, the heat balance equations are used [46]. The electric current, voltage and power generated by the TEM can be calculated as a function of the electrical load using the Kirchhoff rules in accordance with the proposed electrical connection circuit for the thermoelements [47]. The amount of generated electricity is calculated using classical methods for determining the efficiency of thermoelectric conversion [48]. All characteristic values, such as the Seebeck coefficient, heat and conductivity coefficients, are taken into account.

Since the relationship between vehicle operation modes, the generated heat by exhaust gases and the generated electricity by ATEG are nonlinear, it is necessary to dynamically model these processes. To simulate the operation of ATEG under non-stationary operating conditions, the heat balance equations must be described in a differential form [45].

#### **4.3. Tests of models, city cycles**

The ATEG model allows estimating transient processes which makes it possible to use it The New European Driving Cycle (NEDC) is most often used to test the new work models ATEG. There are numerous scientific publications presenting measurements and calculations of thermoelectric generators used in cars on the basis of the NEDC [49]. It is extremely important to consider the dynamic behavior of the thermoelectric system in order to make realistic predictions of the performance of ATEG in the vehicle.

**Figure 13.** Functional diagram of ATEG section.
