Numerical analysis of the effects of electrical and thermal configurations of thermoelectric modules in large-scale thermoelectric generators

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1 *Revised Manuscript with No Changes Marked Click here to download Revised Manuscript with No Changes Marked: AE_full_text_Cozar_01_Rv_1_no_changes.docx Numerical analysis of the effects of electrical and thermal configurations of thermoelectric modules in large-scale thermoelectric generators I R Cózar 1*, T Pujol 1, M Lehocky 1 Polytechnic School, University of Girona, Campus Montilivi s/n, 1 Girona, Spain Gamma Technologies GmbH, Danneckerstrasse, D-01 Stuttgart, Germany *Corresponding author. address: ivan.ruiz@udg.edu Abstract The need to reduce both energy consumption and greenhouse gas emissions has boosted the interest in using thermoelectric generators (TEGs) as waste heat energy harvesters. High-power TEGs are usually formed by an array of commercial thermoelectric modules (TEMs). Recent studies have analyzed the effects of using different types of electrical connections between TEMs in TEGs to produce electric power, but the effects of using different thermal configurations between TEMs have not been fully examined. Here, both electrical and thermal effects have been investigated using a numerical model developed with GT-SUITE software, which has been validated with laboratory data. TEGs with a number of TEMs between 1 and 0 distributed in different patterns along the exhaust pipe have been simulated under three engine regimes. For a given TEM geometrical pattern and engine regime, results prove the existence of an optimum number of TEMs, beyond which the total extracted power decreases. A mixed spatial distribution of TEMs generates more power than either the pure series or the pure parallel topologies. Finally, a methodology is proposed to choose an appropriate pattern of TEMs for a TEG installed in a system with variable regimes. This method is applied to a mid-size automotive diesel engine. 1

2 Keywords: TEM; TEG; series parallel connection; electrical thermal topology 1. Introduction Internal combustion engines effectively convert one third of the fuel energy into mechanical work [1]. The remaining energy corresponds to heat losses, of which the exhaust system accounts for approximately one third of the primary energy [1]. The need to manufacture more efficient vehicles that meet environmental regulations has encouraged research focused on developing technologies to recover energy from exhaust gases []. Thermoelectric generation is among the most promising techniques []. A thermoelectric module (TEM) is a system formed by pairs of n- and p-type semiconductors that converts thermal energy into electrical energy by means of the Seebeck effect []. The assembly of one or more TEMs between a heat source (hot side) and a cooling system (cold side) in a single device and connected to an external electrical load is known as a thermoelectric generator (TEG) []. The size of this external electrical load determines the amount of power the TEG extracts. For given electrical and thermal connections of TEMs, the maximum power point (MPP) method consists in tuning the size of the external electrical load to maximize the TEG electrical output power. Most of automotive TEGs currently tested are based on commercial TEMs. With the purpose of improving the heat transfer through TEMs, new TEG designs include the use of heat pipes [] and the substitution of fins for dimples in the hot heat exchanger []. As heat is being extracted from the exhaust, the gas temperature decreases along the flow direction. This implies that TEMs of the same TEG work under substantially different hot side temperatures depending on their location. The consequences of this mismatch in the TEM working regimes have been numerically investigated either by uncoupling the electrical system from the thermal one (i.e., fluid flow calculations independent of the TEM response []) or by coupling both the electrical and the thermal systems but with some simplifications (e.g., constant heat transfer coefficients []; single and continuous thermoelectric

3 modules []; temperature-independent material properties [], etc.). These previous works have provided valuable insights into the unequal functioning of TEMs in an automotive TEG. However, a fully coupled electro-thermal model, like the one used here, is required to comprehensively simulate a realistic automotive TEG. There are multiple ways of electrically and thermally connecting TEMs in a TEG. The concepts of series, parallel and mixed electrical connections are well known. With regard to the thermal configuration, the connection in series implies an arrangement of TEMs aligned with the direction of the heat flow (i.e., along the exhaust pipe), the parallel connection implies a distribution of TEMs such that all of them are exposed to the same quantity of available heat (i.e., TEMs located in a plane perpendicular to the heat flow), and the mixed thermal array refers to any combination of TEMs distributed parallel and perpendicular to the direction of the heat flow. In TEGs formed by a large number of TEMs ( ), the effects of the electrical and thermal connections of TEMs on the output electrical power are not totally known. Thus, it is a challenging task to find a general rule to determine the best electrical and thermal configuration of TEMs in a TEG. Recently, Chen [1] numerically analyzed the output power of TEGs formed by TEMs in 1 and configurations (longitudinal perpendicular to the flow) with two mixed electrical connections (series-first-parallel-second SFPS and parallel-first-series-second PFSS). In addition, Chen [] assigned two possible values for the temperature difference across each TEM : ºC or ºC. For the case of TEMs with = ºC, he obtained a % (1%) variation of the output power when changing the location of these TEMs in the SFPS (PFSS) connection case. He concluded that the TEG design with a SFPS connection type should uniformly distribute those TEMs with low, whereas in the FPSS case, the TEMs with low should be concentrated in columns.

4 Montecucco et al. [1] studied the impact on the power generated when three TEMs, each one with a different, were electrically connected either in series or in parallel. They observed power production drops of.% (series) and 1.% (parallel) from the maximum power obtained when each TEM was controlled individually, and concluded that the electrical connection in series is the most adequate. On the other hand, Stevens et al. [1] developed a thermoelectric analytical model to determine the theoretical limit of a TEG s electrical power generation, which is obtained when each TEM has its own tunable electric external load. The configurations analyzed in [1] involved several TEMs electrically connected either in series or in parallel and thermally connected in series. They found that there is an optimum beyond which the total power extracted decreases. This maximum of the generated power becomes greater when the series electrical connection is adopted. Other studies involving TEGs have combined different electrical connections, although with a fixed thermal topology. Deng et al. [1] experimentally and numerically analyzed the impact of module property disparity (i.e., TEMs with different Seebeck coefficients and internal resistance) and of wire resistance on the maximum output power. They concluded that the parallel connection suffered larger power losses in the wiring system. Quan et al. [1] and Fang et al. [1] developed algorithms to find the electrical connection of TEMs that optimized the output power of an automotive TEG ( TEMs in [1] and 0 TEMs in [1]). Both studies concluded that the pure series electrical connection provided higher output power than the pure parallel one, with an optimal mixed electrical topology that increased the pure series figures by % [1] and 0% [1]. Recently, Negash et al. [1] experimentally studied the consequences of modifying the electrical connections of a TEG formed by TEMs exposed at different. Maximum power was obtained with balanced TEM modules and a small number of junctions. Previous works have mainly focused on studying the effects of electrical connections between TEMs. As far as we know, the only theoretical study that has investigated the implications of changing the

5 spatial distribution of TEMs in a TEG was not suitable for a heat recovery system of exhaust gases, since it neglected the interaction of TEMs with both hot (exhaust gases) and cold (cooling system) flows [1]. Therefore, the main novelty of this work is the study of the consequences of using different TEM distribution patterns on the TEG output power with a fully coupled model. For this reason, we carry out analyses with series, parallel, square hybrid and mixed configurations for both the electrical connection and the thermal one. For the thermal connection, the term square hybrid describes a mixed configuration in which the same number of TEMs is distributed in parallel and in perpendicular with respect to the heat flow direction. In the square hybrid electrical connection, a group of TEMs located in the perpendicular plane with respect to the flow direction are electrically connected in parallel and, after that, electrically connected in series with the following group of TEMs. Table 1 summarizes the main findings of these previous works. We have added an improvement ratio that considers the MPP value of the series electrical connection (MPP s ) as a baseline value. For given thermal topologies, Refs. [1 1] found that mixed electrical connections, in some cases achieved by applying optimizing algorithms, improve the value of the MPP s. Table 1. Summary of previous works focused on the effects of the electrical and thermal connections of TEMs on the TEG output power. Improvement Reference Method 1 Electrical connection Thermal connection ratio (%) [1] Num Mixed Mixed variable - [1] Exp Series and parallel Series fixed 0 [1] 1 to 0 Num Series and parallel Series fixed 0 [1] Exp Series and parallel Parallel fixed 0

6 [1] Exp Series, square hybrid and Square hybrid fixed mixed [1] 0 Exp/num Series, parallel and mixed Mixed fixed 0 [1] Exp Series, parallel and mixed Mixed fixed 1 Present Num Series, parallel, square Series, parallel, square 1 to 0 0 to work hybrid and mixed hybrid and mixed 1 Num = numerical simulations; Exp = experiments. (MPP max MPP s )/MPP s 0 where MPP max is the maximum value of MPP found for all the studied configurations and MPP s is the MPP corresponding to the series electrical connection. The purpose of the present work is to determine the effects of electrical and thermal connections of TEMs on the output power of a given TEG that recovers waste energy from exhaust gases. The goal is to establish a criterion for recommending the electrical and thermal configurations of TEMs in a given TEG. The paper is organized as follows. In Section, the TEG numerical model is explained in detail. Results of a conceptual case are analyzed and discussed in Section, which includes a proposal for improving the design of TEGs formed by TEMs that work under different thermal conditions. Section develops an application of the proposed methodology. Finally, the main conclusions are summarized in Section.. TEG model Numerical simulation was carried out with the GT-SUITE software [1]. This program is a multiphysics CAE system simulation tool widely used in the automotive sector. It solves the thermoelectric equations coupled with the heat transfer equations and it has successfully been applied to studying the

7 exhaust systems of internal combustion engines. For example, Jianye et al. [0] quantified the effects that improve the brake thermal efficiency in the exhaust gas recirculation (EGR) of an internal combustion engine. A. Rahman et al. [1] studied the effect of engine speed to the heat transfer in cylinder wall and the efficiency of a waste energy harvesting system of exhaust system. M. Zhao [] et al. simulated a waste heat recovery system from exhaust gas with an organic Rankine cycle system. R. Zhao et al. [] modelled a turbocompound waste heat recovery system to analyze its thermodynamic cycle. Here, we validate the model with the manufacturer s datasheet specifications and with experimental results obtained on an engine test bench. Then, we provide thorough information about the model set-up and about the configuration of the TEGs analyzed. Finally, we explain the optimization procedure applied to find the external load resistance that maximizes the output power in each one of the configurations simulated..1 Model validation The success of a TEG numerical model depends basically upon the correct simulation of: 1) the thermoelectric effect (direct conversion of heat into electricity), and ) the heat transfer mechanisms (essentially, between fluid flows and solid elements; i.e., between exhaust gases/coolant and TEMs). For the sake of clarity, the validation procedure is shown in Appendices A and B. Appendix A focuses on the validation of point 1) by comparing simulations with TEM manufacturer s data at fixed hot- and cold-side temperatures. Appendix B focuses on the validation of point ) by comparing simulations with experimental data of a TEG installed at the exhaust line of a diesel internal combustion engine... Model overview TEGs with several topologies and (from 1 to 0) are studied to analyze the theoretical effects of electrical and thermal connections on the electrical output power. All TEGs share the same

8 dimensions to reduce the geometric effects on the cross-comparison analysis (this implies that changes in the Reynolds number, the Nusselt number and the heat transfer coefficient between different TEGs depend only on temperature). Since pure series and pure parallel thermal topologies of TEGs up to 0 TEMs are theoretically investigated, rectangular, m long conduits with cross sections of 00 0 mm for the exhaust gases and of 00 mm for the water heat sink are applied (Fig. 1). As explained above, the requirement of using the same conduit for all configurations favors the cross-comparison analysis because it keeps the flow regime steady. However, this procedure increases the ratio of the surface not covered by TEMs over covered surface to values larger than 00. Such a large surface exposed to the environment can hinder the interpretation of the effects solely due to the TEM distribution pattern. Therefore, the contribution of the surfaces not covered by TEMs to the outcomes is minimized by assuming adiabatic conditions. However, the application case in Section takes into consideration energy losses to the environment from all surfaces in a geometry fitted to the actual dimensions of the tailpipe of a mid-size vehicle. In our TEG, an aluminum heat absorber formed by straight fins mm high, 0. mm wide and with 1 mm of separation between them is inserted into the exhaust pipe. The flow of the cooling water is defined as counter-flow with respect to the exhaust gases, since this configuration is expected to generate slightly higher electrical output power than in the co-flow regime []. All models assume a fully developed flow along each pipe.

9 Fig. 1. Schematic cross-section view of the modelled TEGs (dimensions in mm). The boundary conditions of the TEG model are: 1) temperature and mass flow rate at the inlet of the exhaust pipe, ) temperature and volumetric flow rate at the inlet of the water heat sink, ) pressure at the outlet of the exhaust pipe, ) pressure at the outlet of the water heat sink, and ) electrical load resistance (see Section.). Both the electrical and the thermal connection effects are analyzed under different engine load operating points (ELOP1, ELOP and ELOP) tested in [], an analysis of the performance of a TEG installed in the exhaust pipe of an internal combustion engine. The ELOP1, ELOP and ELOP regimes are representative of low, medium and high engine load operating points, respectively (Table ). The air to fuel ratio is considered to be 1:1. Table. Input data for the numerical test (extracted from []). Units ELOP1 ELOP ELOP

10 Exhaust inlet temperature ᵒC Coolant inlet temperature ᵒC Exhaust mass flow rate g/s Coolant volumetric flow rate l/s Exhaust and coolant outlet pressures bar The TEG models are developed using the GT-SUITE libraries and implementing the following steps: 1) definition of the geometry of exhaust and coolant circuits in order to correctly reproduce the flow conditions, ) statement of the boundary conditions listed above, ) definition of each TEM by means of a submodel, and ) definition of the whole TEG by adequately replicating the submodel formed by a single TEM and the corresponding parts of the heat absorber and water heat sink. The following subsection explains the procedure for defining this submodel... Submodel The submodel is formed by a single TEM, with the same characteristics as the one used in Appendix A, and the corresponding parts of the heat absorber and water heat sink. These parts are thermally connected between them (see Fig. ). The input and the output thermal and electrical connections of the submodel are connected to the exhaust pipe, the water cooling circuit and the external load resistance of neighboring TEMs in accordance with the topologies examined.

11 Fig.. (a) Block diagram of the submodel developed with the GT-SUITE software (involving one TEM), (b) Schematic representation of the whole TEG model. The procedure of building the submodel consists in using GT-SUITE libraries to define: 1) the geometry and the effective material properties of the TEM (from Appendix A), ) the geometry and the material properties of the heat absorber and the water heat sink, ) the thermal connections between solid parts by means of thermal contact resistances (see Table ), and ) the heat transfer mechanism in fluid-solid interfaces. The average heat transfer coefficients are calculated considering uniform temperatures at all surfaces of the submodel. In the cooling circuit-heat sink interface, heat transfer is simulated using the Shah and London correlation (see []) for the average Nusselt number in laminar regions. In the exhaust gasabsorber interface, the average Nusselt number for a flat plate as employed in finned heat absorbers is calculated in laminar conditions [], and it is defined as (1) where and are the Reynolds and Prandtl numbers of the exhaust flow. The Reynolds number is defined as

12 () where and are the density, the velocity and the dynamic viscosity of the exhaust gases, respectively, and is the length of the heat absorber. The Prandtl number follows () where and are the specific heat at constant pressure and the thermal conductivity of the exhaust gases, respectively. We assume the values of the thermal contact resistances are equal to those proposed in [] (see Table ). We point out that the sensitivity of the model to changes in the value of the thermal contact resistance in the range of m K W -1 produces a variation of less than % in the output electrical power. The critical Reynolds numbers of both exhaust and cooling circuits are also summarized in Table. Table. Main constant parameters for modeling the heat transfer. Thermal contact resistance 1. - m K W -1 [] Exhaust critical Reynolds number [] Coolant critical Reynolds number [].. TEG configurations Initially, connection types in pure series, in pure parallel as well as in one square hybrid case (seriesparallel in a square hybrid configuration) were studied. In view of the results found in these cases, additional mixed configurations were analyzed with the purpose of increasing the output power (see Section.). 1

13 The nomenclature employed to identify each case first uses the number of TEMs of the TEG followed by the electrical connection type (ES, EP or EH, standing for electrical series, electrical parallel and electrical square hybrid, respectively), and by the thermal connection type (TS, TP or TH; as in the electrical case but for the thermal component; see Table ). The EP-TP connection was chosen over the ES-TP one because of its lower computational time (both cases report the same results). For the same reason, the EH-TH connection was chosen over the ES-TH one. Table. Nomenclature of the configurations studied. Case Electrical configuration Thermal configuration ES-TS Series Series EP-TP Parallel Parallel EH-TH Square hybrid Square hybrid In the ES-TS configuration all TEMs are connected electrically in pure series so that they are distributed in the same row of the TEG (see case (ES-TS) in Fig. ). The EP-TP topology has all TEMs connected electrically in pure parallel assembled in the same column of the TEG (see case (EP- TP) in Fig. ). Finally, the EH-TH configuration is applied to TEM distributed in a square hybrid configuration with each column connected electrically in pure parallel and, after that, in series with the next column. With regard to the thermal connection, there is the same in rows as in columns (see case (EH-TH) in Fig. ). The numerical test is carried out for (ES-TS), (EP-TP) and (EH-TH) configurations with = 1,,, 1,,,, 1 and 0. In addition, mixed i(es-ts) + j(eh-th) configurations 1

14 with i = j and j = m with m integer have been simulated to increase the output power of previous configurations. Fig.. Schematic representation of the (ES-TS) TEG, (a) electrical and (b) thermal connections. Fig.. Schematic representation of the (EP-TP) TEG, (a) electrical and (b) thermal connections. 1

15 Fig.. Schematic representation of the (EH-TH) TEG, (a) electrical and (b) thermal connections... Optimization procedure As in the single TEM model, the discrete-grid optimization algorithm with a 1% resolution is applied to obtain the MPP for each case. The objective function to maximize is the output electrical power whereas the electrical load resistance becomes the independent variable. The initial range of is set equal to, where refers to the current iteration, is the electrical load resistance at the MPP obtained in the previous iteration, and the scale factor takes a value comprised in the range. For the case with a single TEM, the initial value for the first iteration assumes. For the rest of the cases is estimated after applying the series-parallel electrical resistance rules and assuming that all TEMs have an electrical load resistance equal to that of the MPP obtained for a TEG with a single TEM. Since the number of simulations is very large, a Python code is developed to automatically generate and submit all the cases previously explained. First, the script generates the model of the corresponding case including the definition of the boundary conditions. After that, the model is solved using the GT- SUITE and the results are exported for analysis with a Matlab code. Finally, the Python script decides 1

16 whether to start the simulation of the next case or to reassign a new value of and run the case again. The procedure is summarized in Fig.. and are the lower and upper bounds of, respectively, and the tolerance factors and are set to 1.0 and 0., respectively. These values are chosen to keep the value far from the limits of the range. Fig.. Flowchart of the computational procedure for each TEG model. In the chart, refers to the current iteration, is the independent variable of the optimization algorithm, is the electrical load resistance at the MPP obtained in the previous iteration, is the scale factor, and are lower and upper bounds, respectively, and the tolerance factors and are set to 1.0 and 0., respectively. 1

17 Results and discussion The results for each topology studied in the conceptual analysis are presented in this section. First, simulation data under ELOP1 and ELOP working conditions are reported in pure series, pure parallel and square hybrid configurations in order to analyze the effects of the electrical and thermal connections. The ELOP regime is studied in the application case only (Section ), since here it would not provide any additional information on the analysis of the influence of the TEMs distribution on the TEG output power. After that, we carry out studies with mixed configurations consisting of series plus square hybrid configurations aimed to increase the electrical output power..1. Electrical and thermal connection effects The MPP for each TEG configuration is depicted in Fig.. Results show that, for a fixed, the ES-TS topology has a higher MPP value than either the EP-TP or the EH-TH topologies. Results confirm that there is an optimum in a TEG beyond which the total output power decreases. This optimum depends on the value of the input thermal power as well as on the topology chosen, with the pure parallel connection reaching a lower value of the optimum than the pure series one. The maximum MPP for all the pure series, pure parallel, and square hybrid cases analyzed, achieved under the ES-TS configuration, corresponds to 0.W ((ES-TS)) for the ELOP1 regime, and 1.0W ((ES-TS)) for the ELOP one. 1

18 Fig.. Electrical output power of TEGs with for different electrical and thermal configurations (see Table ). (a) ELOP1 regime, (b) ELOP regime. For the ELOP regime, and for TEGs with and 0 TEMs, respectively, simulated data for individual TEMs are presented in Figs., where we show the TEM electrical production (power, voltage and current) as well as the. The number that identifies the TEM in Figs. increases as the TEM location goes downstream (with respect to the exhaust flow). For example, TEMs from 1 to of the (EH-TH) topology correspond to TEMs located in the first column of the TEG of Fig.. TEMs from to 1 of the same configuration are located in the second column of the TEG, etc. In the ES-TS array, the first TEM generates more electrical power than the other configurations because all the thermal energy is available for a single TEM (TEM 1 in Figs. ). In this configuration, the decreases when the TEM position number increases, since less thermal energy is available. As expected, the electrical series connection causes an equal output current in all TEMs (see Figs. ). In the EP-TP topology, all the TEMs are located in the same column (i.e., perpendicular to the flow direction of the exhaust gases), which means that the thermal energy is recovered at the same point along the exhaust pipe. Therefore, all TEMs have the same. For this reason, they all have the 1

19 same internal resistance and the same current. In addition, they all have the same output voltage due to the electrical connection (see, e.g., Fig. ). This configuration implies that the first TEM produces less electrical power than in the other two topologies (ES-TS and EH-TH). In the EH-TH configuration, the changes with respect to the column, as expected from the results obtained in the ES-TS and the EP-TP cases. The contribution to the total output power is major for the TEMs located in the first columns since they have the maximum value of. The greater variation of the between columns at the beginning than at the end implies a non-linear decrease of the available heat of the exhaust gases. Fig.. (a) Electrical output power, (b), (c) output voltage and (d) output current generated by each individual TEM of the TEG. TEGs with TEMs in ELOP regime conditions. 1

20 Fig.. (a) Electrical output power, (b), (c) output voltage and (d) output current generated by each individual TEM of the TEG. TEGs with 0 TEMs in ELOP regime conditions. The electrical power generated by the first TEM in all the topologies decreases as the in the TEG increases because a counter-flow regime is used (compare Fig. with Fig. ). Eventually, the output power becomes negative in some TEMs (implying absorption of electrical energy by the TEM). For example, the electrical output power of TEM # in the 0(ES-TS) configuration in the ELOP regime is slightly less than zero (see Fig. ). Thus, in this case, TEMs from # to #0 work with negative unit output voltages and contribute to a decrease in the total output power. From the conservation equation of energy and the constitutive equations of heat fluxes and electrical field, the rate of heat absorbed at the hot side and released at the cold side of the TEM is [] 0

21 () () where, R and K are the effective Seebeck coefficient, effective electrical internal resistance and effective thermal resistance of the TEM, respectively, I is the electric current and T h and T c are the hot and cold side temperatures of the module. In Eqs. () (), the first term is the thermoelectric effect (Seebeck effect), the second term corresponds to the Joule effect, and the last one is the Fourier s law of heat conduction. The Thomson effect has been neglected in the derivation of these equations. The total electric power P generated by the TEM is calculated as follows () where the last equality is obtained after inserting Eqs. () (). From Eq. (), the electric power P corresponds to the Seebeck generation minus the Joule heating terms. Since P = I V, the voltage V at the TEM junction reads () In TEMs located upstream, the Joule heating is of minor importance in comparison with the Seebeck generation. However, in those TEMs located at the downstream tail of the device (e.g., TEMs from # to #0 in Fig. ), the available heat is low; therefore, the temperature differences at TEM sides ( ) substantially reduces. At the same time, the current flowing through the TEM is much greater than the own current generated by the Seebeck effect (i.e., ) due to the series electrical connection with other TEMs. As a consequence, the Joule heating of these TEMs is larger than the Seebeck 1

22 generation term, finally leading to a negative voltage (see Eq. ()). Note that in all of these cases, TEMs continue to absorb heat at the hot side Q h and to liberate heat at the cold side Q c. However, Q h > Q c in TEMs that contribute to increase the output power, whereas Q h < Q c in those that decrease the power generation. The condition of having a positive voltage at the TEM junctions (hence, a positive TEM contribution to the power generated) is directly correlated with the effective internal resistance of the module R (see Eq. ()). The maximum current in a TEM that does not penalize the TEG output power derives from the condition, with. Thus, two strategies can be used to avoid having TEMs with negative voltages: a) reducing the current (e.g., by modifying either the electrical connections or the thermal configurations) and b) reducing the effective internal resistance of the module R. The latter can be accomplished by using TEMs at the downstream of the TEG with p-type and n-type thermoelectric elements with different aspect ratios than those employed upstream (e.g., shorter thermoelectric legs or a larger cross-sectional area at the tail of the TEG). These reasons explain why there is, in Fig., an optimum beyond which the extracted output power decreases... Maximum output power case Mixed configurations are employed to obtain higher output power than that obtained in the previous topologies (ES-TS, EP-TP and EH-TH). This is accomplished with the aid of the information provided by each individual TEM, where the output power per TEM of the square hybrid configuration (EH-TH) exceeds that of the series one (ES-TS) in downstream TEMs beyond a critical column (see, e.g., TEM # in Fig. ). Thus, mixed i(es-ts) + j(eh-th) configurations are investigated with i = j and j = m with m integer, the upstream configuration being ES-TS. Several mixed configurations were tested. Table reports the mixed combinations of the form i(es-ts) + j(eh-th) that generate the maximum output power once the in the TEG has been fixed. The results are plotted in Fig..

23 Fig.. Comparison of the maximum output power between the mixed and the ES-TS topology for ELOP1 and ELOP regimes of TEGs with different (see Table for values of i and j). Table. Mixed i(es-ts) + j(eh-th) configurations that generate the maximum output power. ELOP1 ELOP i j i j

24 For the ELOP1 regime, the maximum output power reached with the mixed configuration is equal to. W, corresponding to the (ES-TS) + (EH-TH) case (Fig. ). However, very similar values are also reached with mixed configurations with less (e.g.,. W for the (ES-TS) + (EH-TH) configuration). For =, the mixed configuration leads to an increase of.% with respect to the (ES-TS) MPP. A much higher increment is found for a TEG with 0 TEMs. In this case, the gain reaches.% with respect to the 0(ES-TS), although with a MPP value (1.1 W) below the MPP found previously. It is remarkable that the MPP obtained with (ES-TS) and (EH-TH) combinations for large-scale TEGs attains an almost constant value independently of the being used. This is also observed for the ELOP regime (Fig. ), although in this case, the gain with respect to the pure ES-TS configuration is not as relevant due to the higher amount of available energy in the exhaust gases. The maximum output power in this case is 1. W for a TEG with ((ES-TS) + 1(EH-TH) mixed configuration). In comparison with the square hybrid configuration that, in view of the results depicted in Fig., may be a feasible option in zones with limited available space, the mixed configuration increases the output power up to %.

25 Fig.. (a) Electrical output power, (b), (c) output voltage and (d) output current generated by each individual TEM of the TEG. TEGs with TEMs in ELOP regime conditions. The behavior of each individual TEM for the mixed combination that produces the maximum output power under the ELOP regime for all the TEGs investigated is shown in Fig.. Note that the effect of changing the topology at the tail of the TEG from series to square hybrid dramatically reduces the output current in those TEMs, increasing the output voltage (which was negative for the last TEMs in the series configuration) and leading to almost constant positive values for the output power with values equal (or even lower) than those obtained in the series configuration (Fig. ).

26 Note that this mixed configuration applies strategy a) mentioned above (current reduction) to avoid TEMs with negative contribution to the total power. This can be seen in Fig. 1, where the thermoelectric generation by means of the Seebeck effect ( and the power loss by Joule heating ( ) are shown as a function of the position of each individual TEM for those cases studied in Fig.. From Eq. (), the net power provided by an individual TEM corresponds to the subtraction of these two values (Seebeck contribution minus Joule heating). Although the current is constant for all TEMs in the pure series and hybrid configurations (see Fig. d), the Joule heating monotonically decreases as a function of the TEM position. This confirms the reduction of the value of the effective internal resistance as diminishes. The Seebeck generation term is below the Joule heating in TEMs #, and for the series configuration. This implies a negative contribution to power generation, as observed in Fig. 1a. In the hybrid configuration, the smaller current prevents having local negative voltages despite the low achieved. Indeed, this low but at upstream TEMs leads to a contribution of the Seebeck generation term in the hybrid case less important than in the series one (Fig. 1b). However, the mixed configuration (Fig. 1c), due to its electrical connection, is able to reduce the Joule heating at the downstream TEMs by substantially decreasing the current, whereby defining a configuration where all TEMs contribute positively to the output power.

27 Fig. 1. Seebeck generation and Joule heating terms by each individual TEM of the TEG for those cases analyzed in Fig.. (a) (ES-TS), (b) (EH-TH), (c) (ES-TS)+1(EH-TH), all in ELOP regime conditions.. Application case The previous section has revealed the consequences of modifying the position of TEMs in a TEG. In cases where the energy source is steady, the proposal is to design a TEG with a mixed configuration of TEMs since it performs better than the series one. However, regimes are highly variable in an automotive TEG, which means that the very same configuration may be far from the optimum in many relevant engine working points. International regulations now require transient cycle tests for emission certifications of automotive engines []. A frequency analysis of the regimes involved in these transient cycles indicates the existence of few representative points. Here, we reduce the analysis to three characteristic working points corresponding to low, mid and high load requirements, although the methodology proposed can be extended to adopt a major number of principal regimes, if needed. Thus, in a simplified manner, the complex transient cycle is here interpreted as a histogram with only three regimes, the mid load (ELOP) being the longest working mode, followed by the low load (ELOP1) and, with less importance, by the high load (ELOP). Thus, the purpose of the TEG in a real case is to enhance the energy (rather than the power) produced for the whole transient cycle. Based on the results of the previous section, here we propose a methodology to achieve this target..1. Model setup The geometry of Fig. 1 is used with different dimensions. The exhaust part has an inner square crosssectional area of 0 0 mm, with individual water cooling units of an inner rectangular cross-sectional area of mm. Commercial TEMs like those described in Appendix A and simulated in previous sections are used ( mm surface area). Thus, up to TEMs in a parallel thermal configuration can

28 be installed (one TEM at each face of the square section of the TEG duct). The structure of the heat absorber (fin thickness, fin gap distance, material, etc.) follows that shown in Fig. 1. The main heat transfer parameters are those of Table, now including energy losses by convection and radiation. Convection to the environment uses Newton s law of cooling with a convective heat transfer coefficient equal to 0 W m - K -1 []. Radiation uses the gray body equation with an emissivity equal to 0. for all surfaces []. The configuration of the remaining elements, conditions and models is the same as in Section.. TEG design We have first investigated the power extracted in TEGs with numbers of TEMs in multiples of 1 (from 1 to ), electrically connected in series (ES) and, also, in different positions. These positions are: thermal series (1 TEM in the cross-sectional area of the TEG; called ES-TS) and thermal parallel with, and TEMs in the cross-sectional area (called (ES-TP), (ES-TP) and (ES-TP) respectively). Thus, for example, the 1(ES-TS), (ES-TP), (ES-TP) and (ES-TP) TEG configurations have the same number of TEMs (1), although a different total length. Note that the mixed (ES-TP) cases are not the hybrid ones (only the (ES-TP) configuration coincides with the 1(EH-TH) case). Results for the ELOP regime (mid load regime) are shown in Fig. 1. The series configuration maximizes the TEG output power when a small number of TEMs are used, satisfying the relationship P ES-TS > P (ES-TP) > P (ES-TP) > P (ES-TP) (with the same number of TEMs), where P means the generated output power and the subscript indicates the configuration type as described above. On the other hand, P (ES-TP) > P (ES-TP) > P (ES-TP) > P ES-TS when a large number of TEMs is used, mainly due to the negative contribution to the output power of downstream TEMs when the TEG is very large (as discussed in the

29 previous section). The maximum of 1. W, however, is reached at intermediate values of the number of TEMs () and occupancy of the cross-sectional area ( (ES-TP)). Fig. 1. Electrical output power of TEGs with different n TEMs for different geometrical configurations (ELOP regime). It turns out that this (ES-TP) configuration does not yield the maximum power either in ELOP1 or in ELOP conditions, as seen in Fig. 1, where only the (n TEMs /) (ES-TP) configurations have been simulated. The high load regime (ELOP) does not attain the maximum in the range of values analyzed due to its high energy source. On the contrary, the ELOP1 working mode shows a maximum with a TEG formed by less than TEMs. We now propose a modification of the distribution of TEMs to increase the maximum output power found previously and, more importantly, the total energy generated in an equivalent transient cycle. As explained above, the ELOP configuration is assumed to be the most frequent one, followed by the ELOP1 and, to a lesser extent, ELOP. This is why the ELOP scenario has been chosen to determine

30 the best mixed configuration. The behavior of the cases analyzed in Fig. 1 indicates that, at n TEMs =, the (ES-TS) and the (ES-TP) lie on the decreasing branch of output power, whereas the 1 (ES-TP) configuration lies on the increasing branch. Therefore, we combine the best configuration ((ES-TP)) with the most powerful one found on the decreasing branch ((ES-TP)). After several tests with different combinations of the chosen configurations, the best result in ELOP is found with the mixed combination (ES-TP)+(ES-TP) (output power equal to.0 W, representing a 0.% increase with respect to the (ES-TP) case although with one less TEM). Finally, when this configuration is tested under ELOP1 and ELOP conditions, power increases in ELOP1 (.0 W vs.. W) and decreases in ELOP (. W vs.. W) (see the inset in Fig. 1). Nevertheless, the total gain over one transient cycle is expected to be positive with respect to the plain (ES-TP) pattern since the duration time of ELOP is longer than that of ELOP. Note that in the present application case, the mixed configuration reports a very low gain of the output power in comparison with the former (ES-TP) design. This is caused by the fact that the output power curve of the (ES-TP) configuration presents a broad peak, so any combination with another spatial pattern of TEMs will provide a small increase. In case of having a narrower peak, like that of (ES-TS) in Fig. a or Fig. 1, the gain obtained after combining with another less powerful configuration will be substantially higher.

31 Fig. 1. Electrical output power of TEGs with different n TEMs for the (n TEMs /) (ES-TP) configuration (ELOP1, ELOP and ELOP regimes). The mixed configuration (ES-TP) + (ES-TP) is also represented and compared with the maximum of the (ES-TP) configuration in the inset. Finally, we summarize the behavior of mixing two configurations of TEMs to improve the best TEG output power. The cases schematically displayed in Fig. 1 are analyzed to explain the behavior of this procedure. In Fig.1a the maximum output power of the best configuration (black solid line) is reached using more TEMs than those employed to find the maximum output power of the second configuration (read dashed line). When this occurs, the output power increases when both configurations are suitably combined. On the other hand, in Fig. 1b, the maximum output power of two patterns of TEMs is obtained with the same number of TEMs. In this case, the output power also increases with an adequate combination of the two configurations. The last case corresponds to Fig. 1c, when the maximum output power of the best topology is reached with a smaller number of TEMs than those used to find the

32 maximum output power of the second configuration. In this case, any combination of the two patterns of TEMs leads to a decrease of the output power. Fig. 1. Schematic diagram to show the expected value of the maximum output power of a mixed configuration from information of the individual behavior of the two (1 black solid line, and red dashed line) configurations that form it.. Conclusions The present work aims to numerically determine the effects of modifying the electrical connections and, particularly, the spatial distributions of TEMs installed at the exhaust line of hot gases in large-scale TEGs. The complexity of the coupled electro-thermal system has led to design a conceptual study in

33 which the geometrical dimensions enable us to apply the same flow regime in TEGs with varying from 1 to 0. Results indicate that the pure series configuration produces more output power than the pure parallel or the square hybrid connection. The production in the pure parallel configuration is below 0% of the pure series configuration for most of the TEGs analyzed, whereas the output power of the square hybrid case is less than 1% below that of the pure series for all. Thus, the square hybrid configuration may be recommended when space limitations or non-negligible thermal losses in pipe zones not covered by TEMs make the series configuration unfeasible. Simulations confirm the existence of a critical beyond which the TEG production decreases. A detail analysis of the behavior of the individual TEMs reveals that those TEMs located downstream adversely affect the total output power. This is due to the high value of the heating by Joule effect that, in these TEMs, exceeds the generation obtained by the Seebeck effect. As a consequence, the individual TEM contributes negatively to the global output power, delivering a negative voltage. When this occurs, the heat extracted from the exhaust gases is less than the heat liberated to the cooling side. This effect is more relevant in exhaust gases with low enthalpy. In view of the TEM individual behavior, we propose a mixed electrical and thermal configuration of TEMs to increase the overall electrical output power. The purpose is to avoid having TEMs in the TEG that contribute negatively to the total energy production. This can be accomplished by reducing either the current or the internal resistance. In our case, we propose a local reduction of the electrical current by substituting the best configuration at the tail of the TEG (downstream position) with the second best topology. This method increases the maximum output power of the pure series configuration, using the same, since all individual TEMs contribute positively to the global output power. The mixed

34 configuration (series + square hybrid) maintains almost the same output power value irrespective of the being used. In a real application case, with a square cross-sectional area of a TEG fitting an automotive exhaust pipe, the model indicates that the best option for TEGs where a small number of TEMs are used, is the thermal series configuration. For TEGs with a large number of TEMs, the thermal configuration with the maximum occupancy of TEMs per cross-sectional area ( in our case) is the best. However, the maximum power output may correspond to an intermediate configuration ( TEMs thermally connected in parallel in the square cross-sectional area). For actual working conditions, where the thermal flows are variable, the solution proposed consists of a mixed configuration that maximizes the production at the most repeatable working mode. We provide a simple method to determine this maximum based on the relative position of the maximum power points of the two configurations that form the mixed pattern. Acknowledgements This work has been partially funded by the University of Girona under grant MPCUdG01-. The authors gratefully acknowledge fruitful discussions with Dr. Lino Montoro, Dr. Eduard Massaguer, Albert Massaguer and Martí Comamala. Sergi Saus and Jordi Vicens provided very helpful technical assistance. References [1] Fu J, Liu J, Feng R, Yang Y, Wang L, Wang Y. Energy and exergy analysis on gasoline engine based on mapping characteristics experiment. Appl Energ 01;:-. [] Karvonen M, Kapoor R, Uusitalo A, Ojanen V. Technology competition in the internal combustion energy waste heat recovery: a patent landscape analysis. J Clean Prod 01;:-. [] Armstead J R, Miers S A. Review of waste heat recovery mechanisms for internal combustion

35 engines. J Therm Sci Eng Appl 01;:01-1. [] Rowe D. Thermoelectric Handbook: Macro to Nano. CRC Press, Boca Raton, FL, 00. [] McCarty R. Thermoelectric power generator design for maximum power: It's all about ZT. J Electronic Mater 01;:-. [] Li B, Huanga K, Yana Y, Li Y, Twahaa S, Zhua J. Heat transfer enhancement of a modularised thermoelectric power generator for passenger vehicles. Appl Energ 01; 0:-. [] Wang Y, Li S, Xie X, Deng Y, Liu X, Su C. Performance evaluation of an automotive thermoelectric generator with inserted fins or dimpled-surface hot heat exchanger. Appl Energ 01;1:1-1. [] Zhu DC, Su CQ, Deng YD, Wang YP, Liu X. The influence of the inner topology of cooling units on the performance of automotive exhaust-based thermoelectric generators. J Electronic Mater 01;:0-. [] He W, Wang S, Lu C, Zhang X, Li Y. Influence of different cooling methods on thermoelectric performance of an engine exhaust gas waste heat recovery system. Appl Energ 01;1:11-. [] He W, Wang S, Yue L. High net power output analysis with changes in exhaust temperature in a thermoelectric generator system. Appl Energ 01;1:-. [] Meng J-H, Wang X-D, Chen W-H. Performance investigation and design optimization of a thermoelectric generator applied in automobile exhaust waste heat recovery. Energ Convers Manage 01;:1-0. [1] Chen M. Realistic optimal design of thermoelectric battery bank under partial lukewarming. In: (I&CPS) 01. th Ind Commer Power, IEEE; 01, p. 1-. [1] Montecucco A, Siviter K, Knox A R. The effect of temperature mismatch on thermoelectric generators electrically connected in series and parallel. Appl Energ 01;1:-. [1] Stevens R J, Weinstein S J, Koppula K S. Theoretical limits of thermoelectric power generation from exhaust. Appl Energ 01;1:0-. [1] Deng Y D, Zheng S J, Su C Q, Yuan X H, Yu C G, Wang Y P. Effect of thermoelectric Modules topological connection on automotive exhaust heat recovery system. J Electron Mater 01;:1-0. [1] Quan R, Tang X, Quan S, Huang L. A novel optimization method for the electric topology of thermoelectric modules used in an automobile exhaust thermoeletric generator. J Electron Mater 01;:1-.

36 [1] Fang W, Quan S H, Xie C J, Ran B, Li X L, Wang L, Jiao Y T, Xu T W. Effect of topology structure on the output performance of an automobile exhaust thermoelectric generator. ACPEE 01, IOP Conf Ser-Mat Sci. 01;1:0. [1] Negash A A, Kim T Y, Cho G. Effect of electrical array configuration of thermoelectric modules on waste heat recovery of thermoelectric generator. Sensor and Actuators A: Physical 01;0:1-. [1] Gamma Technologies LLC. December 01. < [0] Su J, Xu M, Li T, Gao Y, Wang J. Combined effects of cooled EGR and a higher geometric compression ratio on thermal efficiency improvement of a downsized boosted spark-ignition direct-injection engine. Energ Convers Manage 01;:-. [1] Rahman A, Razzak F, Afroz R, Mohiuddin A K M, Hawlader M N A. Power generation from waste of IC engines. Renew Sust Energ Rev 01;1:-. [] Zhao M, Wei M, Song P, Liu Z, Tian G. Performance evaluation of a diesel engine integrated with ORC system. Appl Therm Eng 01;:1-. [] Zhao R, Li W, Zhuge W, Zhang Y, Yin Y. Numerical study on steam injection in a turbocompound diesel engine for waste heat recovery. Appl Ener 01;1:0-1. [] Du Q, Diao H, Niu Z, Zhang G, Shu G, Jiao H. Effect of cooling design on the characteristics and performance of thermoelectric generator used for internal combustion engine. Energ Convers Manage 01;1:-1. [] Kim T Y, Negash A A, Cho G. Waste heat recovery of a diesel engine using a thermoelectric generator equipped with customized thermoelectric modules. Energ Convers Manage 01;1:0-. [] Bergman TL, Lavine AS, Incropera F P, DeWitt D P. Fundamentals of Heat and Mass Transfer. th Ed. John Willey & Sons, NJ 0. [] Corrigendum to Regulation No of the Economic Commission for Europe of the United Nations (UN/ECE). Official Journal of the European Union 00;0:-. [] II-VI Marlow. December 01. < [] N. Instruments. [Online]. Available: [Accessed 1 June 01]. [] Omega. [Online]. Available: [Accessed 1 June 01]. [] Sensus. [Online]. Available: [Accessed 1 June 01].

37

38 APPENDIX A The thermoelectric mathematical basis of GT-SUITE [1] is confirmed by reproducing the manufacturer s performance curve of a single TEM (Marlow TG1--01LS []). The model uses a mesoscale approach in which the whole TEM is modeled as a single element with effective material properties. The effective thermoelectric material properties obtained from the manufacturer s datasheet are summarized in Table A1. The effective Seebeck coefficient is obtained as, where is the open circuit voltage, the effective electrical internal resistance is, where is the short circuit current at the same hot and cold side TEM temperature as that applied to obtain, and the effective thermal resistance is directly provided by the manufacturer []. Table A1. Effective thermoelectric material properties of the TEM (Marlow TG1--01LS []). Effective thermal Effective Seebeck coefficient Effective electrical internal resistance (ºC) (mv ºC -1 ) resistance ( ) (ºC W -1 ) The numerical model consists of a TEM electrically connected to an external electrical load resistance. The boundary conditions are both hot and cold side TEM temperatures and the value of the electrical load resistance. The discrete-grid optimization algorithm with a 1% resolution is applied to obtain the

39 MPP. The objective function to maximize is the electrical output power whereas the electrical load resistance becomes the independent variable. The electrical output power and voltage found numerically at the MPP are compared with the manufacturer s datasheet (Fig. A1). The numerical prediction at 0ºC cold side temperature matches the optimum power of the datasheet in the whole range of hot side temperatures simulated. Voltage values are underestimated by % maximum (point at ºC TEM hot side temperature). These small discrepancies cannot be attributed to a flawed model since the analytical results obtained after applying the thermoelectric equations [] and using the data of Table A1 (interpolating as needed) reproduce the GT-SUITE values (see Fig. A1). The uncertainty of data provided by the manufacturer is not available. For this reason, the discrepancies between datasheet values and analytical/numerical ones are difficult to quantify. All in all, such discrepancies do not alter the implications of our analysis since we carry out an crosscomparison study of the MPP values for different topologies.

40 Fig. A1. Comparison between the simulated results, analytical predictions and manufacturer s data of optimum output power (a) and voltage (b) as a function of the TEM hot side temperature. TEM cold side temperature equal to 0ºC.

41 APPENDIX B B1. Experimental set up The experiment uses a Schenck W1 dynamometer, a PSA XUD 1. liter diesel engine, an external cold water loop, a TEG, an electrical load resistance, sensors and a data acquisition system (Fig. B1). The TEG is formed by an aluminum heat absorber with rectangular fins (Fig. B), a single mm TEM (Marlow TG1--01LS []) and a mm BXQINLENX water heat sink isolated at its upper side (Fig. B). Thermal paste is applied at both contact surfaces of the TEM to reduce the contact thermal resistance. The TEG is installed in the exhaust line at 0 cm from the cylinder head. The hydraulic diameter of the pipe is equal to. mm at the point where the heat absorber is in contact with the exhaust gas. TEM hot temperature mainly depends on the temperature and flow rate of the exhaust gas, being indirectly controlled by the engine speed, the external torque applied to the crankshaft. On the other hand, TEM cold temperature depends on the temperature and flow rate of the coolant. (a) (b)

42 Fig. B1. (a) Laboratory and (b) schematic set up. The electrical load resistance is regulated by a rheostat and its value is calculated from current and voltage data. These signals are acquired by a National Instruments (NI) Compact Rio system with and 1 modules. Type K thermocouples are used to record temperatures of 1) the TEM at its cold and hot sides, ) the exhaust gas at the TEG inlet and outlet, and ) the water at the inlet and the outlet of the TEG cooling circuit. Thermocouples are connected to the NI Compact Rio with modules. LabVIEW software is used to monitor all data. Fig. B. Dimensions of the heat absorber (mm). The dashed line shows the position of the TEM.

43 Fig. B. Illustration of the assembly of the experimental TEG. The volumetric flow rate of the cooling system is measured with a Sensus S water meter and a stopwatch. The mass flow rate of the exhaust gas is calculated as the sum of the inlet mass flow rate of the air plus that of the fuel. The inlet air mass flow rate is obtained by measuring the intake air pressure with a TG- nozzle according to the ISO 1-1: standard. The mass flow rate of diesel fuel is calculated by using a cylinder of calibrated volume. From the above, we assume that all the mass flow entering the engine exits through the exhaust pipe. The experimental procedure consists in: 1) adjusting the pumping system of the TEG cooling circuit, ) starting the engine and setting its speed, ) setting the external torque applied to the crankshaft to reach the target temperatures of exhaust gas and coolant, and ) acquiring data during a minimum time period of 1 minute at a rate of 1 sample per second once the signals have reached stationary behavior. B. Experimental uncertainty The uncertainties due to the experiment and to the measurement equipment are calculated as follows. The experimental error of the data series acquired is defined as (B1)