Parametric study of a thermoelectric generator system for exhaust gas energy recovery in diesel road freight transportation

Energy Conversion and Management 133 (2017) 167–177

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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman

Parametric study of a thermoelectric generator system for exhaust gas energy recovery in diesel road freight transportation S. Vale a,b, L. Heber a,⇑, P.J. Coelho b, C.M. Silva c a

German Aerospace Center (DLR), Institute of Vehicle Concepts, Germany IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Portugal c Instituto Dom Luiz, Faculdade de Ciências, Universidade de Lisboa, Portugal b

a r t i c l e

i n f o

Article history: Received 31 August 2016 Received in revised form 28 October 2016 Accepted 30 November 2016

Keywords: Energy recovery Thermoelectric generator Exhaust gas heat transfer Diesel vehicles for freight transport

a b s t r a c t A parametric study and optimization approaches of a thermoelectric generator (TEG) for the recovery of energy from the exhaust gas in Diesel vehicles used in freight transport is reported. The TEG is installed in the tailpipe of a commercial vehicle (3.5 tonnes) and a heavy-duty vehicle (40 tonnes). The exhaust gas is used as the heat source and the cooling water as the heat sink. Two different heat exchanger configurations are considered: plain fins and offset strip fins. The influence of the height, length and spacing of the fins on the electrical and net power is analysed for the fixed width and length of the TEG. The influence of the length and width of the TEG and of the height of the thermocouple legs is also investigated. According to the criteria used in this study, plain fins are the best choice, yielding a maximum electrical power of 188 W for the commercial vehicle and 886 W for the heavy-duty vehicle. The best recovery efficiency is about 2%, with an average thermoelectric material efficiency of approximately 4.4%, for the light-duty vehicle. Accordingly, there is significant room for further improvement and optimisation based on the thermoelectric modules and the system design. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction In recent years, the thermoelectric generator has emerged as a promising form of technology for waste heat recovery in the automotive industry, due to the improvement of the thermoelectric materials [1]. According to Eurostat [2], over 50% of freight transportation in Europe is performed by road. This is typically executed by vehicles with Diesel engines and represented a total of about 1.7 trillion tonne-kilometres in 2014. Most of the goods are carried over distances between 300 km and 1000 km, with average vehicle loads of 13.8 tonnes. Considering 50 L/100 km energy consumption and 13% overall efficiency, this potentially resulted in an overall tailpipe wasted heat energy amounting to 1330 million MJ. The use of a TEG could help with the reduction of the waste heat. From the literature review, it is concluded that most studies focused on gasoline engines due to their higher exhaust gas temperatures (e.g. see Table 1). However, the mass flow rate and the available energy in the exhaust gas are greater for Diesel heavy-duty vehicles. In addition, the space constraints for installation of a TEG in the

⇑ Corresponding author at: German Aerospace Center (DLR), Institute of Vehicle Concepts, Pfaffenwaldring 38-40, 70569 Stuttgart, Germany. E-mail address: [email protected] (L. Heber). http://dx.doi.org/10.1016/j.enconman.2016.11.064 0196-8904/Ó 2016 Elsevier Ltd. All rights reserved.

tailpipe are lower for the former vehicles. Moreover, the driving durations are longer and the velocities are steadier for heavyduty vehicles than for passenger cars. The present study focus on Diesel vehicles for freight transport, particularly the heat exchanger numerical simulation has been tackled. The energy transfer from the engine exhaust of two vehicles is investigated: a commercial 3.5 tonne and a heavy-duty 40 tonne vehicle, both simulated in ADVISOR [3] in constant speed and world harmonized transient cycle (WHTC) [4]. The influence of two different heat exchanger structures, with either plain fins or offset strip fins, on the electrical and net power output, is assessed. The influence of the height, spacing and length of the fins, as well as the effect of the width and the length of the heat exchanger, and the height of the thermocouple legs, are investigated. The recovery efficiency from the TEG configurations studied is also determined and compared with existing results.

2. State of the art Our goal is to maximize electrical output power by improving the heat exchanger and build a model for integration with a road vehicle simulator such as ADVISOR or AVL-CRUISE . Apart from the heat exchanger, the simulation and prediction of the behaviour TM

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Nomenclature A cp CV Dh f h I k K l L N M _ m p P q Q_ Ri s T u V_

area (m2) specific heat (J kg
1 K
1) control volume (–) hydraulic diameter (m) Darcy friction factor (–) convective heat transfer coefficient (W m
2 K
1) electric current (I) thermal conductivity (W m
1 K
1) thermal conductance (W K
1) fin length (m) length/height (m) number of thermocouples in x-coord. direction (–) number of thermocouples in z-coord. direction (–) mass flow rate (kg s
1) pressure (N m
2) power output (W) total heat transfer rate (W) heat power (W) load resistance (X) fin spacing (m) temperature (K) mean flow velocity (m s
1) volumetric flow rate (m3 s
1)

of the thermoelectric modules for different boundary conditions and different locations in the exhaust is essential for the development of the TEG. Yu and Zhao [5] developed a numerical model for a TEG and compared the performance of a parallel flow and a counter flow heat exchanger. They concluded that both of these tend to result in the same electrical output power, since the average temperature difference between the hot and the cold fluids is essentially equal for the two types of heat exchangers. Their results also show that the variation in temperature of the hot and cold fluids in the flow direction is approximately linear. Lu et al. [6] investigated two types of heat transfer enhancement structures, namely rectangular offset strip fins and metal foams, for the exhaust gas heat exchanger of a gasoline light-duty vehicle. They found that the electrical power from the metal foams was significantly higher (approx. 130–294 W) than that from the offset strip fins. However, the metal foams produced a higher pressure drop, and even though the total output power can significantly increase, the net power output is lower. The solution suggested by these authors, to apply in the near future, was to develop a TEG that combines simultaneously thermoelectric generation and catalytic conversion. Bai et al. [7] used a computational fluid dynamics (CFD) code to investigate the heat transfer and pressure drop for six different internal structures of the heat exchanger in a light-duty 1.2 L gasoline engine vehicle. They showed that the serial plate structure presents the highest heat transfer, but also the highest pressure drop. They concluded that there is a compromise between high heat transfer and low drop in pressure. The maximum electrical and net powers were not determined. Su et al. [8] compared three internal heat exchanger structures for automotive exhaust-based TEGs: fishbone-shaped, accordion-shaped and scatter-shaped. It was proved that the accordion-shape design presents a better uniform temperature distribution. Again, the maximum electrical and net powers were not presented. Likewise, Liu et al. [9] focused on the temperature distribution in the heat exchanger mounted on the exhaust of a 2.0 L naturally aspirated gasoline engine. They compared two internal heat exchanger geometries, fishboneshaped and chaos-shaped, and concluded that the chaos-shaped

ZT

figure of merit (–)

Greeks symbols difference between Seebeck coefficients (V K
1) efficiency (%) electrical resistivity (X m) u correction factor (–)

a g q

Subscripts/superscripts c cold d exergy destruction el electrical ex exhaust gas f fins fu fuel h hot L load loss heat loss n n-type semiconductor material net net p p-type semiconductor material pump pumping

structure leads to better results (maximum electrical power approx. 183 W). Apart from the heat exchanger, the simulation and prediction of the behaviour of the thermoelectric modules for different boundary conditions is essential for the development of the TEG. Hence, Niu et al. [10] developed two 3D numerical models to study the behaviour of the thermocouples under different prescribed boundary conditions. They concluded that these can strongly influence the results. They also investigated in detail the influence of the shape of the thermocouples on their performance and found that the temperature gradient could be enhanced if a proper cross section area is used. The shape of the thermocouples was also investigated by Rezania et al. [11]. The maximum power generation and maximum cost performance of a thermocouple are achieved when the ratio of the area of the cross section of the n-leg to that of the p-leg of the thermocouple is lower than unity. Abdelkefi et al. [12] developed an analytical electro-thermal model for thermoelectric modules and used experimental data from a previous study for validation purposes. The effect of different hot side temperatures, temperature differences, load resistances and clamping forces on the electrical output power from a single thermocouple was analysed. Häfele et al. [13] developed a numerical model for a TEG and analysed its behaviour using bismuth telluride (Bi2Te3) and lead telluride (PbTe) thermoelectric modules. A TEG prototype with 24 Bi2Te3 HZ-20 thermoelectric modules was integrated into a test vehicle and about 200 W electrical power was measured. Yu et al. [14] also developed a numerical model for a TEG and analysed its behaviour using 16 commercial Bi2Te3 HZ-20 thermoelectric modules. It was found that the vehicle speed is a significant factor affecting the TEG performance for waste heat recovery. Gou et al. [15] developed a theoretical dynamic model for a TEG with a finned heat exchanger. The temporal variation of the temperatures on the hot and cold semiconductor surfaces, maximum output power and system efficiency was analysed by means of step changes of the heat reservoir temperatures and mass flow rates. Tatarinov et al. [16] carried out a similar work, but considered four different car driving patterns, two from Europe and two from the

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S. Vale et al. / Energy Conversion and Management 133 (2017) 167–177 Table 1 Overview of representative research projects. Engine size (L)

Fuel

D T between exhaust gas and coolant (°C)

Exhaust gas mass flow rate (kg/s)

TEG electrical output (W)

Driving situation

Source

NA 2.2 3 2 5.3 1.3 11

Gasoline Gasoline Gasoline Gasoline Gasoline Diesel Diesel

517 300–700 563 250 350–550 max. 100 150–250

0.031 NA NA 0.03 (at 15.2 m/s) NA NA 0.13–0.22

37–200 Typical < 100 35.6 183 50–225 max. 125 900–1000

50, 80, 110 km/h US06 standard cycle 60 km/h, climbing Fixed engine 3000 rpm 48.3, 80.5 and 112.6 km/h City traffic average speed 31.7 km/h Paris–Lille cycle

[7] [21] [22] [10] [23] [24] [25]

USA, instead of using step changes of the heat reservoir temperatures and mass flow rates. Meng et al. [17] developed a multiphysics thermoelectric generator model in a control volume for automobile exhaust waste heat recovery. In this study a constant exhaust condition is considered and Bi2Te3 thermoelectric material is used. Especially the number and size of the thermocouples is analysed and discussed as well as the flow direction of the cold side heat exchanger. The non-uniformity of the temperatures along the streamwise direction and its impact on the TEG performance are reported. Kumar et al. [18,19] developed a numerical model for a TEG, also for steady state conditions. Average inlet conditions from a typical light-duty vehicle were used for the baseline analysis. Another steady state mathematical model of a TEG using the exhaust gas of vehicles as heat source was presented by Wang et al. [20]. The mass flow rate and the temperature of the exhaust gas were taken from the federal test procedure (FTP-75) city driving cycle. The influence of several factors, such as temperature and mass flow rate of the cooling fluid, convective heat transfer coefficients or height of the legs of the thermocouples on the output power and efficiency were investigated. Table 1 summarizes representative work using gasoline and Diesel vehicles exhaust flow and exhaust coolant boundary conditions. It is clear that freight transportation is barely exploited as well as driving conditions representative of the heavy-duty vehicles, e.g., the WHTC and extra-urban driving with 90–120 km/h. Therefore we focused on such boundary conditions. 3. Model description 3.1. Thermoelectric generator configuration The model presented next bases on algebraic equations arising from one-dimensional approximation. As seen in Fig. 1(b) the thermocouples are connected in the z-coordinative direction, wheres several thermoelectric modules are placed in parallel in the x-coordinative direction. This structure is sandwiched between a heat source and a heat sink. Additional layers of thermoelectric modules may be placed in y-direction, separated from the neighbouring ones by a heat source or a heat sink, as seen in Fig. 1(a). The TEG used in this study is symmetric with respect to its height in y-direction, and comprises 6 layers of thermoelectric modules in that direction, according to Häfele et al. [13]. The exhaust gas is used as heat source and the cooling water as heat sink. It is assumed that both fluids have the same flow direction, uniform inlet temperatures and velocity distributions, and the temperatures are assumed to remain uniform along z-direction. 3.2. Thermal and electrical behaviour of a thermocouple The thermal analysis assumes that the TEG is working in steady state and the heat losses due to radiation are negligible. The gaps between the n and p legs of the device, of the n-type and p-type

semiconductor material respectively, are perfectly insulated, and heat conduction and current flow in the thermocouple are approximated as one-dimensional. The total heat transfer rates through the hot and cold junctions of a thermocouple are given, respectively, by [26]:

qh ¼ apn T 3;h I
0:5 R I2 þ K ðT 3;h
T 3;c Þ

ð1Þ

qc ¼ apn T 3;c I þ 0:5 R I2 þ K ðT 3;h
T 3;c Þ

ð2Þ

where apn is the difference between the Seebeck coefficients of the two thermocouple legs, T3,h and T3,c are the temperatures at the hot and cold junctions respectively, and I is the electric current in the circuit. The internal electrical resistance R, and the thermal conductance of the thermocouples K, are obtained as follows:

R ¼ qp Lp =Ap þ qn Ln =An

ð3Þ

K ¼ kp Ap =Lp þ kn An =Ln

ð4Þ

whereby q represents the electrical resistivity, k the thermal conductivity, A the area of the cross section of a thermocouple leg, and L its height. The properties of the materials, which depend on the temperature, were evaluated at the mean temperature of the thermocouple junctions. The current flow in each thermoelectric module, through which maximum power is obtained, is hereby taken as constant and written as [27]:

I ¼ apn DT=ðR þ RL Þ:

ð5Þ

In this equation, RL = R represents the external load resistance supported by each thermocouple that is required to obtain the maximum electrical output power Pel, which is equal to:

Pel ¼ RL I2 :

ð6Þ

An indication of the maximum efficiency of the thermoelectric material can be given by the following equation [26], as the maximum electrical power efficiency of a thermocouple or an entire thermoelectric module with adoption of RL = R:

P

gmax;el ¼ _el ¼ Q

Th
Tc 1  : T h
T c Th 2
2T þ ZT4 h

ð7Þ

h

In this equation, ZT is the dimensionless figure of merit which represents the inherent relationship between the main material properties, the Seebeck coefficient, the thermal conductivity and the electrical resistivity of the used thermoelectric material. 3.3. Thermal and electrical behaviour of the TEG The ducts of exhaust gas and cooling water are discretised along the flow direction, i.e., x-direction, considering a number of control volumes (CVs) equal to the number of thermoelectric modules in that direction, denoted as N in Fig. 1(b). The length of the CVs in x-direction Dx, is equal to the ratio of the length of the TEG to N.

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Fig. 1. Sub-assembly of the TEG and thermoelectric module arrangement at a layer.

This level of discretisation is sufficiently accurate because the difference between the temperatures of the fluid entering and leaving a CV is small. We shall let j and j + 1 denote the temperatures at the cell faces of the jth CV, i.e., upstream and downstream of the jth thermoelectric module respectively. Assuming that the temperature of the surfaces of the ducts of the hot and cold fluids, denoted by Tb,h and Tb,c respectively, are uniform within a control volume, the energy balances for the jth control volume may be written as follows:

_ h cp;h ðT h;j Þ ðT h;j
T h;jþ1 Þ ¼ hh gf Ah ðT h;j
T b;h;j Þ m

ð8Þ

_ c cp;c ðT c;j Þ ðT c;jþ1
T c;j Þ ¼ hc Ac ðT b;c;j
T c;j Þ m

ð9Þ

_ is the mass flow rate, cp the specific heat, h the convective where m heat transfer coefficient, and A the heat transfer area, while subscripts h and c denote the hot and cold fluids respectively. In order to enhance the energy transfer from the exhaust gas to the hot surface of the thermoelectric modules, a compact plate fin heat exchanger is used. The mean temperatures of the hot and cold fluids at the jth CV are approximated by the average between the temperatures of the fluid entering and leaving that CV, i.e., T h;j ¼ ðT h;j þ T h;jþ1 Þ=2 and similarly for T c;j . Two different configurations are investigated in this study, one with plain fins and the other one with offset strip fins, as shown in Fig. 2, with fin parameters: length l, height h, spacing s and thickness t. Symbol gf in Eq. (8) stands for the efficiency of the fins. In the case of plain fins, the Nus-

selt number was evaluated using either the correlation suggested by Martin [27], in the case of laminar flow, or the Gnielinski correlation, in the case of turbulent flow. The flow regime selection is defined by the Reynolds number, which is computed using the geometry data and operation conditions of the TEG. The correlation developed by Manglik and Bergles [28] was used for offset strip fins. The Nusselt number of the cooling water was calculated using again the correlation developed by Gnielinski, since the flow is turbulent. The heat transfer in y-direction was determined using a thermal resistance network (see Fig. 1) and assuming one-dimensional steady state conduction, ignoring all thermal contact resistances, neglecting heat losses due to radiation and considering that the gaps between the legs are perfectly insulated. The heat transfer rates through the hot and cold junctions may be set equal to the heat transfer rates through the hot and cold electrical conductor strips:

ðAn þ Ap Þ kCu ðT 2;h
T 3;h Þ=LCu ¼ apn T 3;h I
0:5 R I2 þ K ðT 3;h
T 3;c Þ

ð10Þ

ðAn þ Ap Þ kCu ðT 3;c
T 2;c Þ=LCu ¼ apn T 3;c I þ 0:5 R I2 þ K ðT 3;h
T 3;c Þ

ð11Þ

whereby kCu and LCu denote the thermal conductivity and the thickness of the electrical conductor strip made of copper (Cu). Energy balance equations may be written for every inner node of the ther-

Fig. 2. Investigated heat exchanger fins structures.

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hh gf Ah ðT h
T b;h Þ ¼ ASST kSST ðT b;h
T 1;h Þ=LSST

ð12Þ

ASST kSST ðT b;h
T 1;h Þ=LSST ¼ ACl kCl ðT 1;h
T 2;h Þ=LCl

ð13Þ

the hydraulic diameter, f the Darcy friction factor, and u a correction factor for tubes of rectangular cross section, which depends on the ratio of the side lengths. The pumping power for the TEG is equal to the sum of the pumping powers for all thermoelectric modules and finally, the net power is the difference between the electrical and the pumping power,

ACl kCl ðT 1;h
T 2;h Þ=LCl ¼ ACu kCu ðT 2;h
T 3;h Þ=LCu

ð14Þ

Pnet ¼ Pel
Ppump;j :

ACu kCu ðT 3;c
T 2;c Þ=LCu ¼ ACl kCl ðT 2;c
T 1;c Þ=LCl

ð15Þ

4. Results and discussion

ACl kCl ðT 2;c
T 1;c Þ=LCl ¼ AAl kAl ðT 1;c
T b;c Þ=LAl

ð16Þ

4.1. Case study

AAl kAl ðT 1;c
T b;c Þ=LAl ¼ hc Ac ðT b;c
T c Þ

ð17Þ

mal resistance network (nodes Tb,h, T1,h, T2,h, T2,c, T1,c and Tb,c in Fig. 1 (a), yielding the following 6 equations:

where subscripts SST, Cl and Al stand for stainless steel, ceramic layer and aluminium, respectively. These six equations along with Eqs. (8)–(11) allow the calculation of the temperatures of the hot and cold fluids downstream of the jth module, and the eight interface temperatures shown in the resistance network in Fig. 1(a). This system of 10 equations is nonlinear, since the thermophysical properties of the solid materials and fluids depend on the temperature. The solution of this system was carried out using Newton’s method until the solution converges to a tolerance value of 10
6 The CVs are treated sequentially along x-direction, setting the temperature of the fluids leaving the jth CV equal to the inlet temperatures of the fluids entering the (j + 1)th CV. The electrical power for a thermocouple is calculated from Eq. (6) using the current intensity and the load resistance computed from Eqs. (5) and (3), respectively. Since a thermoelectric module is composed by M thermocouples electrically connected in series, as seen in Fig. 1(b), their electrical resistance can be added to obtain the electrical power of a thermoelectric module. The overall electrical output power of the TEG is determined by adding the electrical power of all thermoelectric modules,

Pel ¼

N X Pj :

ð18Þ

j¼1

3.4. Pressure drop The pumping power Ppump, required to overcome the pressure drop Dp, in the heat exchanger needs to be taken into account to assess the performance of the TEG, and can be evaluated as follows for the jth thermoelectric module:

Ppump;j ¼

N X u2 Dx _ hu f j V_ j Dpj ¼ m 2 Dh j¼1

ð19Þ

_ and V_ represent the mass and volumetric flow rates across where m the thermoelectric module respectively, u is the mean velocity, Dh

ð20Þ

The selected case study includes two diesel vehicles, a commercial 3.5 tonne and a heavy-duty 40 tonne, which have been chosen as representative vehicles for freight transportation. It is anticipated that the use of a TEG is of interest for these vehicles due to their higher mass flow rates and available energy amount in the exhaust gas, in addition to larger installation space and considerably longer driving periods at approximately constant speed, in comparison to passenger cars. A constant speed driving condition on a flat road was chosen for the operation of the vehicles: 120 km h
1 and 90 km h
1 for the light- and the heavy-duty vehicles respectively, representative of extra-urban driving. In order to obtain the required input parameters for the TEG model described above, the vehicles were simulated using ADVISOR [3]. The input data for ADVISOR is given in Table 2. The exhaust gas system used in the simulation includes a diesel oxidation catalyst (DOC) and a diesel particle filter (DPF), which is the common exhaust prior to 2010 for heavy-duty vehicles in US and European pre-Euro VI vehicles. The output from this simulation is summarised in Table 3. The temperatures presented were obtained immediately after the DPF, where the TEG is placed. Consequently, the performance of the TEG will be evaluated for the exhaust gas temperatures shown in Table 3. The selection of the thermoelectric materials is crucial to the efficiency of a thermoelectric device for electricity generation. These materials must be selected in accordance with the working temperature range. In the current study, the thermoelectric materials used are listed in Table 4. They were selected according to the data given in Table 3. It should be noted that these materials are still under development and only available in a laboratory scale, although it is expected that materials with such properties or even better will become available for commercial applications in the near future. 4.2. Energy and exergy analyses In order to calculate the real amount of energy present in the vehicles’ exhaust gas and to compare this energy with that recovered by the TEG, an energy and exergy analysis is presented below.

Table 2 Vehicle specifications. Vehicle (tonnes)

Frontal area (m2)

Engine displacement (L)

Power (kW)

Torque (N m)

Transmission

3.5 40

3.288 8.348

2.14 15.6

95 at 3800 rpm 380 at1600 rpm

305 at 1200–2400 rpm 2600 at 1100 rpm

Manual 5-speed Manual 5-speed

Table 3 Output results from ADVISOR for the selected target study. Vehicle (tonnes)

Exhaust gas mass flow rate (g/s)

Exhaust gas temperature at DPF (K)

Coolant fluid temperature (K)

Engine brake power (kW)

Fuel consumption (L/ 100 km)

3.5 40

80.12 201.48

568.93 710.86

368.15 368.15

25.5 127.0

7.8 39

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Table 4 Thermoelectric materials. Vehicle (tonnes)

n-type

p-type

3.5 40

Bi2Se0.3Te2.7 [29] (Bi0.001Se0.999Te)0.88(PbS)0.12 [31]

Bi0.5Sb1.5Te3 [30] AgSbTe2 [32]

It is assumed that the engine operates at steady state, the air and the combustion products are both ideal gas mixtures, changes in the potential and kinetic energy of the gas stream from the inlet of the engine to the exit through the tail pipe are negligible, and combustion is complete. The diesel fuel is treated as dodecane, C12H26, and the lower heating value and density are taken as 42.9 MJ kg
1 and 843 g L
1 respectively [33]. The reference environment properties were taken from [34], and the amount of oxygen and trace gases was combined with nitrogen for simplicity. The energy balance for a CV that includes the diesel engine and the exhaust gas system can be written as follows:

_ þ Q_ ex þ Q_ loss Q_ fu ¼ W

ð21Þ

where Q_ fu is the energy per unit time released due to the combustion, which is equal to the product of the lower heating value of the _ is the engine output power, Q_ ex fuel and the fuel mass flow rate, W is the energy per unit time of the exhaust gas, given by the product of the sensible specific enthalpy of the exhaust gas and the exhaust gas mass flow rate, and Q_ loss represents the heat loss to the environment per unit time. The output data from Table 3 and the assumptions given above allow the calculation of all terms of Eq. (21), except Q_ loss , which is therefore evaluated from that equation. Although the energy balance provides useful information about the performance of the vehicles, the heat loss cannot be entirely converted into work, according to the second law of thermodynamics. The maximum work that can be theoretically converted from the available exhaust gas heat is the exergy, which can be determined from the following exergy balance of the control volume:

_ þ E_ ex þ E_ loss þ E_ d E_ fu ¼ W

ð22Þ

where E_ fu is the exergy of the fuel, E_ ex is the exergy of the exhaust gas, E_ loss is the exergy of heat transfer from the gas to the environ-

ment, which was evaluated according to Sayin et al. [35], and E_ d is the exergy destruction, which was determined from Eq. (22). All these terms are evaluated per unit of time. Table 5 shows the energy and exergy rates computed for both vehicles. The values reported confirm the well-known rule of thumb that only about one third of the fuel power results in engine power output. They further reveal that there is a significant amount of thermal energy in the exhaust gas. Even though the rate of exergy of the exhaust gas E_ ex , is much lower than the energy per unit time Q_ ex , there is still significant potential for energy recovery.

4.3. Influence of the heat exchanger geometry on the performance of the TEG The influence of the geometry of the heat exchanger on the performance of the TEG is investigated below. Firstly, two different

internal structures of the heat exchanger are compared. Then the influence of the external dimension of the heat exchanger is studied. Finally, the recovery efficiency for the designed TEG is evaluated. The following results are obtained based on our described numerical model for the TEG, which has been validated with earlier experimental results of the DLR Institute of Vehicle Concepts reported by Häfele et al. [36]. Therefore the model was modified for the described prototype of Häfele et al. [13] (see Section 2) and conditions by considering a 3 L gasoline engine in constant driving conditions, at velocities of 70, 100 and 120 km/h. The simulation and the experimental results, of the electrical power of 56, 91 and 148 W respectively, show a similar behaviour and by inserting a correction factor for the special offset strip fins in the prototype, which are out of the range of the used correlations, the results are consistent. 4.3.1. Internal geometry: plain fins and offset strip fins The mathematical model described in Section 2 was applied to both vehicles to study the influence of the internal geometry of the heat exchanger, considering either plain fins or offset strip fins, while the external geometry is fixed: vehicle of 3.5 tonnes
width W = 0.10 m and length L = 0.15 m; vehicle of 40 tonnes
width W = 0.20 m and length L = 0.15 m. The electrical and net powers are calculated for the studied cases. The influence of plain fins on the TEG performance is shown in Fig. 3 for different combinations of fin height h and fin spacing s. Note that in this study the thickness of the fins is not varied, but rather fixed at 1 mm. It can be seen that both TEG configurations in the different vehicles behave similarly. Smaller fin spacing increases the electrical power up to nearly its maximum, while smaller fin height leads to higher electrical power. This later effect is explained due to the mean velocity increase, since the channel height decreases whereas the mass flow rate of the exhaust gases and their temperature at the inlet of the TEG is not varied. Subsequently the Reynolds number increases and so does the convective heat transfer coefficient on the hot side. Accordingly, the heat transfer rate is increased, and so is the electrical power. Moreover, for each fin height, there is a fin spacing value that maximises the net power. When the fin spacing is reduced below this value, the pumping power starts to increase faster than the electrical power, resulting in a reduction of the net power. When the fin spacing is increased above its optimum value, the net power also starts to decrease, due to the decrease of the electrical power. Given these findings, the fin geometry corresponding to the maximum net power was selected for the TEG’s heat exchanger design. However, as it can be seen in Fig. 3(b) and (d), a maximum net power exists for each height. As a result, the configuration with the smallest fin height, to guarantee compactness, and with a pumping power lower than 30% of the electrical power is selected for both vehicles: 3.5 tonnes – fin spacing s = 5 mm and fin height h = 15 mm; 40 tonnes – fin spacing s = 5 mm and fin height h = 20 mm. The height of the TEG system is influenced by the height of the fins. Consequently, in order to allow a comparison between plain fins and offset strip fins, the height of the plain fins previously selected is fixed and is also used for the offset strip fins. The offset strip fins’ influence on the electrical and net power is illustrated in Fig. 4. Two parameters, fin length l and fin spacing

Table 5 Energy and exergy rate breakdown for the considered vehicles. Vehicle (tonnes)

Q_ fu (kW)

_ (kW) W

Q_ ex (kW)

Q_ loss (kW)

E_ fu (kW)

E_ ex (kW)

E_ loss (kW)

E_ d (kW)

3.5 40

94.1 352.9

25.5 127.0

23.0 91.4

45.6 134.5

97.9 367.1

9.2 45.3

9.3 27.4

53.9 167.4

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Fig. 3. TEG electrical and net powers for 3.5 and 40 tonne vehicles as a function of the fin height and fin spacing for plain fins (⁄ negative net power, which is not shown).

Fig. 4. TEG electrical and net power for the 3.5 and 40 tonne vehicles as a function of the fin spacing and fin length for offset strip fins.

Table 6 Electrical and net output powers of the TEG for the selected internal geometry. Vehicle (tonnes)

3.5 40

Plain fins

Offset strip fins

Electrical power (W)

Net power (W)

Electrical power (W)

Net power (W)

107 480

78 357

99 430

73 320

s, are analysed. The dimensions of the fin spacing are maintained within the range of validity of the correlations used to estimate the Nusselt number [28]. Regarding the new geometrical variable,

i.e., fin length, it can be seen that a lower offset strip fin length yields higher electrical output power, but also reduces the net power due to the high pumping power associated with this geom-

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etry. In some cases, this internal heat exchanger geometry leads to a net power that represents just 1/3 of the electrical power. In conclusion, the shorter the offset strip fins, the better the heat transfer enhancement, but the higher the pumping power required. The following criterion is suggested to select the most suitable offset strip fin geometry: the combination (fin spacing, fin length) with the highest electrical power and a pumping power lower than 30% of the electrical power is selected. According to this criterion, the following geometry is selected for the vehicles: 3.5 tonnes
fin spacing s = 7.5 mm and fin length l = 83 mm; 40 tonnes
fin spacing s = 10 mm and fin length l = 50 mm. The results presented above reveal that the design of both internal heat exchanger structures must be adjusted to achieve high electrical and high net power simultaneously. Table 6 summarises the results obtained. Even though the case of offset strip fins requires a smaller pumping power, due to the wider selected fin spacing configuration s, it can be concluded that plain fins geometry with higher electrical power is a better choice for the heat exchanger in the TEG. Consequently, only these fins are considered in the remainder of this study. 4.3.2. External geometry
width and length The external dimensions of the heat exchanger significantly influence and dictate the dimensions of the TEG. In this section, the length and the width of the heat exchanger considered in Section 4.3.1 are increased to twice their values. According to the previous analysis, the fin height is set to 15 mm and 20 mm for the vehicles of 3.5 tonnes and 40 tonnes, respectively, in order to

maintain the same TEG height (y-direction), and the fin spacing is varied. Two different cases were considered: (i) the length of the heat exchanger is doubled, but the width remains fixed; (ii) the width of the heat exchanger is doubled, but the length is fixed. The results are presented in Fig. 5 and reveal that both vehicles behave similarly. As previously seen in Section 4.3.1, there is a fin spacing that maximises the net power, which is larger in case (i) than in case (ii). The electrical power is higher in case (i) than in case (ii). In fact, when the width of the heat exchanger is doubled, i.e., in case (ii), the heat transfer area in the transverse direction (y-z plane) is greater than in case (i), and so is the heat transfer rate from the exhaust gas to the cooling water. However, the mass flow rate of the exhaust gas is the same in both cases. Accordingly, the difference between the temperatures of the hot and cold fluids is higher in case (i), and the temperature of the hot fluid in xdirection decreases slower. Note that even though the slope of hot fluid temperature profiles in Fig. 5 is similar for both cases, the length of the TEG is different, and so the actual temperature gradient in the flow direction is smaller in case (i) than in case (ii). Therefore, the temperature difference between the thermocouple junctions is greater in case (i), yielding a higher electrical power. As far as the pumping power is concerned, the pressure drop must be analysed. The pressure drop shows a different evolution for double length (i) and double width (ii), as shown in Fig. 6. The area of the TEG in x-z plane is the same in both cases, but case (ii) shows a significantly lower pressure drop when compared to case (i). This can be justified by Eq. (19), which shows that the

Fig. 5. Temperatures along the TEG’s x-direction and the output power for 3.5 and 40 tonne vehicles.

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Fig. 6. Pressure drop along the TEG’s x-direction for 3.5 and 40 tonne vehicles.

Table 7 Electrical and net output powers of the TEG for the studied external geometries. Vehicle (tonnes)

Exhaust exergy rate (kW)

Double width

Double length

Electrical power (W)

Net power (W)

Electrical power (W)

Net power (W)

3.5 40

9.2 45.3

172 831

153 739

188 886

133 663

pressure drop depends on the fluid velocity. Hence, increasing the width, and therefore the frontal area, results in a higher reduction of the pressure drop. The electrical and net powers for the fin spacing corresponding to the maximum net power that satisfies the criterion specified in 4.3.1 are summarised in Table 7.

4.3.3. Recovery efficiency In the following, the exergy rate present in the exhaust gas and the effectively recovered energy in the form of electrical power are compared. In this context, the recovery efficiency of the TEG is defined as the ratio of the electrical power to the exhaust gas exergy rate. Regarding the selected plain fins geometry discussed in Section 4.3.1 and presented in Table 7, the recovery efficiencies are 1.16% and 1.06% for the vehicles of 3.5 and 40 tonnes, respectively. In the case of a heat exchanger with double width, the recovery efficiencies are 1.87%, with an average thermoelectric material efficiency of 4.22% (see Eq. (7)) for all installed thermocouples, and 1.83% with an average material efficiency of 7.87%, for the vehicles of 3.5 and 40 tonnes, respectively. In the case of a heat exchanger with double length, the recovery efficiencies are 2.04%, with an average material efficiency of 4.45%, and 1.96%, with an average material efficiency of 8.15%, for the vehicles of 3.5 and 40 tonnes, respectively. To date, with values of ZT taken from Chen and Ren [37] in the considered temperature range, maximum peak material efficiencies of up to approximately 13% for the thermoelectric material are possible. The low recovery efficiencies are also found in other works e.g. Merkisz et al. [24] found a maximum of 1.7% efficiency in city traffic for light-duty Diesel. Lu et al. [6] show a maximum of 2.7% for the higher mass flow rate of 0.049 kg/s. It is obvious that the computed TEG recovery efficiencies are low, even though there is significant room for improvement, since particular geometries were analysed in this study as a preliminary design for this type of application, and future optimisation will

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Fig. 7. Influence of the height of the thermocouple legs on the electrical power of the TEG for the vehicle of 3.5 tonnes as representative example.

improve the recovery efficiency. Nevertheless, waste heat is partially recovered by using a TEG, which is certainly positive, particularly for freight transport vehicles. Energy efficiency is essential for these, even in extra-urban operation modes where long driving periods are usual. However, the costs and benefit of the TEG system must be taken into account and the question whether the electricity recovered pays off remains uncertain. 4.4. Influence of the height of the thermocouple legs The performance of the thermocouples depends on the properties of the materials and on the geometric design. In this section, the height of the thermocouple legs, which has a significant influence on the electrical output power of the TEG, is investigated. There are two dominant effects if the height of the thermocouple legs is reduced: (i) the internal electrical resistance of the thermocouples decreases, while the electrical power increases, as one may conclude by inserting Eq. (5) into Eq. (6) and (ii) the temperature difference between the hot and cold junctions decreases, which contributes to decrease the electrical power. The vehicle of 3.5 tonnes with the internal geometry of the heat exchanger defined in sections 4.3.1 and 4.3.2 is considered. The results plotted in Fig. 7 reveal that effect (i) is dominant if the height of the thermocouple legs is large, yielding an increase of the electrical power with the reduction of that height. However, the effect (ii) prevails if the reduction of the height is large enough, causing a decrease of the electrical power. It can be concluded that a leg height exists which maximises the electrical power. This relation is also mentioned by Rowe and Min [38] and Fan et al. [39]. It can be seen that the optimum height of the thermocouple legs is influenced by the heat exchangers configuration and has to be considered by optimisation of the system. 5. Conclusions A mathematical model of a TEG system was developed and applied to commercial and heavy-duty Diesel vehicles, within the WHTC and extra-urban driving with 90–120 km/h, for the first time. A parametric study was carried out to investigate the influence of several parameters on the electrical and net power output and additionally showing optimization approaches. The analysis was performed for steady state conditions, assuming typical driving extra-urban velocities, mass flow rates and temperatures of the exhaust gas and cooling water, for the two vehicles. Energy

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and exergy analyses were conducted to determine the energy and exergy in the exhaust gas, and the consequent potential for energy recovery. In the case of plain fins, a smaller fin height leads to higher electrical power. Subsequently for a fixed height there is an optimum fin spacing that maximises the net power. Regarding the offset strip fins, it was found that the heat transfer increases with the reduction of the length of the fins, but the pumping power increases too. In both cases, plain fins and offset fins, a compromise is needed to simultaneously achieve high electrical and net power. In the cases studied and with the criteria used, plain fins provide better performance than offset strip fins, particularly as a result of the pumping power influence. The analysis of the size of the TEG shows that doubling the length in order to achieve maximum electrical power is more effective than doubling the width. On the other hand, doubling the width is more effective when the net power is considered. The analysis carried out shows that, for typical extra-urban driving conditions, and for the heat exchanger and external TEG dimensions found in the parametric study, the recovery efficiency is low. The best recovery efficiency found is approximately 2% with an average thermoelectric material efficiency of around 4.4% for the light-duty vehicle. The results obtained via the parametric analysis show more than 800 W of electrical power for the heavy-duty vehicle. This could be used to generate the vehicle’s electrical network demand. For the light-duty vehicle, such results could not be obtained by this preliminary parametric analysis. The height of the thermocouple legs plays a significant role in the thermoelectric behaviour of the thermocouples, and there is an optimum height dependent on the configuration that maximises the electrical power. It is clear that the electricity/thermal energy of the exhaust gases ratio is still very low. However 2% of the 2014 European freight transport wasted energy represents 27 million MJ which is a significant amount. Acknowledgements This work was undertaken at and supported by the German Aerospace Center (DLR), Institute of Vehicles Concepts, through a grant received by Sónia Vale, and supported by the Portuguese Science and Technology Foundation (FCT), by IDMEC, under LAETA, project UID/EMS/50022/2013, and by the Instituto Dom Luiz (IDL), project UID/GEO/50019/2013. References [1] Zhang X, Zhao L-D. Thermoelectric materials: energy conversion between heat and electricity. J Mater 2015;1:92–105. http://dx.doi.org/10.1016/j. jmat.2015.01.001. [2] Eurostat, European statistics. . Mai 2016. [3] Wipke KB, Cuddy MR, Burch SD. ADVISOR 2.1: a user-friendly advanced powertrain simulation using a combined backward/forward approach. Veh Technol IEEE Trans 1999;48(6). [4] Krishnamurthy M, Gautam M. Development of a heavy-duty engine test cycle representative of on-highway not-to-exceed operation. Proc Inst Mech Eng Part D J Automob Eng 2006;220:837–48. http://dx.doi.org/10.1243/ 09544070JAUTO217. [5] Yu J, Zhao H. A numerical model for thermoelectric generator with the parallelplate heat exchanger. J Power Sources 2007;172:428–34. http://dx.doi.org/ 10.1016/j.jpowsour.2007.07.045. [6] Lu C, Wang S, Chen C, Li Y. Effects of heat enhancement for exhaust heat exchanger on the performance of thermoelectric generator. Appl Therm Eng 2015;89:270–9. http://dx.doi.org/10.1016/j.applthermaleng.2015.05.086. [7] Bai S, Lu H, Wu T, Yin X, Shi X, Chen L. Numerical and experimental analysis for exhaust heat exchangers in automobile thermoelectric generators. Case Stud Therm Eng 2014;4:99–112. http://dx.doi.org/10.1016/j.csite.2014.07.003.

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