Performance investigation and design optimization of a thermoelectric generator applied in automobile exhaust waste heat recovery

Energy Conversion and Management 120 (2016) 71–80

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

Performance investigation and design optimization of a thermoelectric generator applied in automobile exhaust waste heat recovery Jing-Hui Meng a,b, Xiao-Dong Wang a,b,⇑, Wei-Hsin Chen c a

State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, China School of Energy, Power and Mechanical Engineering, North China Electric Power University, Beijing 102206, China c Department of Aeronautics and Astronautics, National Cheng Kung University, Tainan 70101, Taiwan b

a r t i c l e

i n f o

Article history: Received 4 January 2016 Received in revised form 19 April 2016 Accepted 23 April 2016

Keywords: Thermoelectric generator Automobile exhaust Output power Design optimization

a b s t r a c t This work develops a multiphysics thermoelectric generator model for automobile exhaust waste heat recovery, in which the exhaust heat source and water-cooling heat sink are actually modeled. Special emphasis is put on the non-uniformity of temperature difference across thermoelectric units along the streamwise direction, which may affect the performance of exhaust thermoelectric generator systems significantly. The main findings are: (1) The counter flow cooling pattern is recommended, although it cannot elevate the overall output power as compared with the parallel flow counterpart, it reduces the temperature non-uniformity effectively, and hence ensures the system reliability. (2) The temperature non-uniformity strikingly deteriorates the output power of thermoelectric unit along the streamwise direction; meanwhile, an additional lateral heat conduction effect exists within the exhaust channel wall, the both mechanisms leads to that the maximum output power of the system is not enhanced but is actually reduced when too many thermoelectric units are adopted. (3) When the exhaust channel length is fixed, the maximum output power of the system can be elevated by increasing the thermoelectric unit number but keeping thermoelectric unit spacing unchanged. This means that the system performance can be improved under the condition of less thermoelectric materials consumption. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction In recent years, research on waste heat recovery techniques is a very active field because of the global energy crisis [1]. Among various waste heat recovery techniques, thermoelectric generators (TEGs), which can directly convert heat into electricity utilizing Seebeck effect of semiconductor materials, are regarded as one of the most promising ways in the future, mainly because they have the advantages of simplicity, ruggedness, silent operation, as well as absence of compression-expansion moving parts and working fluid [2]. Different sources of waste heats can be supplied to TEGs. Li et al. [3] proposed that combining the solar concentrating thermoelectric generation with micro-channel heat pipe can save the quantity of thermoelectric generation and reduce the cost significantly. Barma et al. [4] estimated the amount of electrical power produced by a TEG placed between flue gas duct and fresh air duct of an industrial thermal oil heater. Xie et al. [5] presented a technical solution to ⇑ Corresponding author at: State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, China. E-mail address: [email protected] (X.-D. Wang). http://dx.doi.org/10.1016/j.enconman.2016.04.080 0196-8904/Ó 2016 Elsevier Ltd. All rights reserved.

the power resource problem of sensors placed on seafloors by recycling the thermal energy of hydrothermal fluids using TEGs. Automobiles are the most important means of transportation nowadays, which are quite convenient but also generate a lot of waste heat. According to the statistics, two thirds of the automobiles fuel combustion energy is lost and diffused as heat, and 40% of the heat is discharged to the atmosphere in the form of automobile exhaust [6]. Effective re-using of the waste heat from automobiles will not only improve the use efficiency of existing energy sources, but also can reduce emissions and improve the environmental quality. Research suggests that for an engine with 50 kW mechanical power, harvesting less than 2% of the power wasted in exhaust alone could provide electric supply of 1 kW, sufficient for the devices in the vehicle supplied by alternator [7]. For a long period of time, relatively low thermoelectric conversion efficiency limited the development and application of TEGs. Although the conversion efficiency of TEGs is much lower than conventional power generation devices, the thermoelectric power generation technology still receives many attentions worldwide, and the reason of which is that the acquisition of automobile exhaust virtually has no cost. For applications of TEGs on automobile waste heat recovery, Royale and Simic [8] pointed out that a

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comprehensive investigation of the TEG technology limitations, new TEG design and development, together with the simulations and testing are the current and future research objectives. In the late 1980s, Birkholz et al. [9] for the first time applied a single FeSi2-based TEG module on a vehicle and successfully produced 1 W electric power. Only a few years later (1995), Bass et al. [10] obtained 1 kW of output power with TEG designed for exhaust of 14 L diesel engine. Subsequently, Ikoma et al. [11] applied an array with 72 pieces of TEG module to gasoline engine vehicles. By maintaining 563 K temperature difference between hot and cold sides of the module, 35.6 W electric power was generated. Thacher et al. [12] found that insulating the exhaust and lowering the coolant temperature had dramatic effects on the power production through testing on a light truck. Ibrahim et al. [13] recommended that packing of the exhaust duct by inserting aluminum wool material can enhance heat transfer and hence improve the TEG performance. Aranguren et al. [14] built a TEG prototype, which can roughly obtain 100 W m
2 of usable energy from the exhaust of a combustion chamber with an efficiency of 2.2%. Through experiments on a micro-combustor, Yadav et al. [15] found that the overall conversion efficiency increased with the number of TEG modules, which was 1.2% for one module, 2.56% for two modules and 4.6% for four modules. Adopting a two-stage TEG design, the system conversion efficiency can reach 5.35% [16]. With the average exhaust temperature of 823 K and the mass flow rate of 480 g s
1, the TEG system constructed by Zhang et al. [17] generated 1002.6 W electricity with a 2.1% heat-to-electricity efficiency. The maximum output power of 944 W for the TEG application on automobiles was reported by Liu et al. [18] Subsequently, Liu et al. [19] designed a new system called the ‘‘four-TEGs” system and assembled the system into a prototype vehicle called ‘‘Warrior”. Their testing showed great potential for application of this technology in future vehicles. Moreover, some famous auto manufacturers worldwide, e.g., Hi-Z Technology in USA [20] and Nissan in Japan [21], had been attempting to improve the conversion efficiency of thermoelectric modules. Based on Bi2Te3 materials, Hi-Z Technology’s goal for a practical device was an conversion efficiency of about 11%, which could save 5–12% fuel consumption if the 1 kW TEG module was used; however, the experimental conversion efficiency of the Hz-14 modules was only 5% [22]. Overall, previous studies were mostly based on experiments [6– 22], only a few works [23–29] simulated the performance of automobile exhaust TEG systems. It is well known that the numerical simulation technique, as one of the most important research methods, can directly evaluate the device performance and suggest the direction of design optimization in a short research cycle. Weng and Huang [23] numerically investigated effects of the heat exchanger length and the thermoelectric module coverage on the automobile exhaust TEG system performance. In their study, the TEG module was simplified to a block with a thickness of 2.8 mm and an equivalent thermal conductivity of 3.26 W m
1 K
1, the real TEG structure however was not modeled. Hsiao et al. [24] established a mathematical model of TEG modules applied on an automobile, and they concluded that the output power and conversion efficiency could be improved by increasing engine speed or coolant temperature. However in Ref. [24], they simplified the automobile exhaust TEG system as a thermal resistance network, so that the heat source, the cold source, and the TEG module were treated as three blocks with certain thermal resistances. Deng et al. [25] focused on the structure design of the heat exchange attached on the TEG module. He et al. [26] presented that a thinplate exchanger should be used in the TEG system owing to its high power output. They expected to improve the performance of automobile TEG systems by further increasing the heat amount transferred into the TEG module. However, the TEG module were not modeled and investigated in their works.

Moreover, some previous studies [24,27] assumed that the performance of per TE unit in automobile exhaust TEG systems was the same; thus, only one TE unit was modeled, and then the overall performance of TEG systems was obtained by multiplying the number of TE units. However, for a TEG module applied on an automobile, the flow of the exhaust in the automobile pipe, as well as the coolant in the heat sink, is unidirectional. As the TEG module absorbs heat from the exhaust and dissipates heat into the heat sink, the temperature of exhaust will decrease while the temperature of coolant will increase along their respective streamwise direction, leading to a significant drop of the temperature difference supplied to each TE unit. As a result, the output powers of TE units are deteriorated along the exhaust flow direction, and hence the overall output power of TEG module cannot be characterized by one TE unit. In order to reflect the temperature nonuniformity, Wang et al. [28] divided the entire automobile exhaust TEG system into N subsystems along the streamwise direction and assumed that the outlet temperature of exhaust for (i
1)th subsystem was equal to the inlet temperature of exhaust for ith subsystem. Tatarinov et al. [29] adopted the similar approach. In these studies [28,29], the convective heat transfer between exhaust and TE units was actually not solved. Instead, constant convective heat transfer coefficients were introduced into the exhaust and coolant channels and a set of algebraic equations was used to iteratively solve the inlet/outlet temperatures of exhaust in each subsystem based on the energy conservation between exhaust and TE units. Furthermore, the output powers of TE units were evaluated by the thermal resistance model. However, because the convective heat transfer in the channels as well as the heat conduction and electrical conduction in TE units are inherently coupled, the inlet/outlet temperatures determined by the above method must be inaccurate, which inevitably will lead to a significant deviation of the predicted output powers of TEC units from the their practical values. To avoid this issue, the temperature variation of exhaust along its streamwise direction can be determined through experimental measurements. An alternative approach is to develop a coupled multiphysics model, in which the convective heat transfer of exhaust and coolant in channels, as well as the heat conduction and electrical conduction in thermoelectric materials are coupled solved. Unfortunately, up to now such coupled model for automobile exhaust TEG systems has not been built in the open literature. Based on the above analysis, a practical TEG system for the automobile exhaust waste heat recovery is first modeled numerically, wherein the exhaust is considered as the actual heat source and a water-cooling heat sink is used as the cold source. Using the established model, the overall performance of the automobile exhaust TEG system is then investigated for various cooling patterns and TE unit numbers to highlight the effect of temperature non-uniformity in TE units. Finally, at the condition of constant exhaust channel length, the arrangement of TE units in the system is optimized under two constraints, i.e. fixed volume of TE materials and fixed spacing between TE units.

2. Model The TEG devices can be installed on two potential positions, i.e. exhaust pipe and radiator. Hsiao et al. [24] demonstrated that the TEG module presents better performance on the exhaust pipe than on the radiator. Therefore, the automobile exhaust TEG system is investigated in this work, which consists of three parts: an automobile exhaust channel, a TEG module and a water cooling heat sink. One TEG module generally has r rows and each row has m TE units. Due to the structure periodicity of automobile TEG system, the performance of each row along the streamwise direction

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should be the same. Hence, only one row of the system is extracted as the computational domain (Fig. 1a). For easy analysis, the TE units in the computational domain is consecutively numbered along the streamwise direction as k (k = 1, 2, . . . , m). The exhaust channel and coolant channel are simplified as hollow square pipes with a wall thickness of Ht. The exhaust channel has a length Lg and a cross-sectional area Ag = Wg  Hg. For the coolant channel, the length and the cross-section dimension are Lw and Aw = Ww  Hw, respectively. The TEG module is sandwiched between two electrically insulating ceramic plates with the same thickness of Hce, and the exhaust channel and coolant channel are attached to the top and bottom ceramic plates, respectively. Fig. 1b shows the schematic of one TE unit, which is composed of p- and n-type semiconductor legs with the same square cross-section sandwiched between two metallic connectors. The heights of the semiconductor legs and connectors are respectively Hpn and Hm, and the crosssectional area for the semiconductor legs is Apn = Wpn  L2 with the spacing of L1 between the p- and n-type legs. It should be noted that the automobile exhaust TEG system shown in Fig. 1a contains only four TE units; however, the TE unit number is variable and ranges from 6 to 20 in this work. The initial geometric parameters are designed as follows: Hce = Ht = Hm = 0.2 mm, Hg = 4Hw = 1.2 mm, Hpn = 1.2 mm, Wg = Ww = Wpn = 0.5 mm, L1 = 0.2 mm, L2 = 0.5 mm, and Lg = Lw = L = m  Lpn, where Lpn = 2(L1 + L2) = 1.4 mm is the length of one TE unit. The exhaust with a temperature of Tg,in and a velocity of vg,in flows into the system through the inlet of exhaust channel, while the coolant (Tw,in, vw,in) through the inlet of coolant channel. As the high temperature exhaust flows in the channel, the hot side of the TEG module will absorb heat from the exhaust, while the

cold side will dissipate heat to the heat sink. Thus a temperature difference will be formed between the cold and hot sides of the TEG module, which will produce electricity under the action of Seebeck effect. 2.1. Governing equations The numerical model of automobile exhaust TEG system established in this work includes the flow equation, the energy equation and the electric potential equation. The following assumptions are adopted in the model: (1) The flow features single phase, laminar, incompressible, and steady state. (2) The gravitational force is ignored. (3) The properties of fluids and solids are constant. (4) The heat radiation is ignored. (5) The electric and thermal contact resistances are ignored. (6) The outside surfaces of the automobile exhaust TEG system are adiabatic. 2.1.1. For the exhaust channel and coolant channel Three-dimensional solid–fluid conjugated heat transfer exists in the exhaust channel and coolant channel. With the above assumptions, the governing equations for flow and heat transfer in the channels can be described as follows. Continuity equation for the exhaust and coolant:

r~ V ¼0

ð1Þ

Momentum equation for the exhaust and coolant:

L Ht Wg

Wpn

Ww

(a) Automobile exhaust TEG system Lpn Hm

Hpn

P

N

Hm L1/2

L2

L1

L2

L1/2

(b) TE unit Fig. 1. Schematic of automobile exhaust TEG system.

Hg

Hpn

Hw

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V qi ð~ V  rÞ~ V ¼
rp þ li r2 ~

ð2Þ

Qg is the heat supplied to the hot side of the TEG from the automobile exhaust.

ð3Þ

2.2. Boundary conditions

Energy equation for the exhaust and coolant:

V  rT ¼ ki r2 T qi cp;i ~ Energy equation for the solid wall:

ks r2 T ¼ 0

ð4Þ

where ~ V is the velocity vector; p is the pressure; qi, li, cp,i, and ki are the density, dynamic viscosity, specific heat, and thermal conductivity of fluid, respectively, and the subscript i is g for the exhaust, w for the water coolant; and ks is the thermal conductivity of solid wall. 2.1.2. For the TEG module The three-dimensional multi-physics model with coupling of heat conduction and electrical conduction is adopted to solve the temperature and electric potential in the TEG module. The energy equations of the metal connector, p-type semiconductor, n-type semiconductor, and ceramic plate are as follow:

kj r2 T þ

J2

rj

J  rT ¼ 0
bj~

ð5Þ

where kj is the thermal conductivity, rj is the electric conductivity, and bj is the Thomson coefficient. The subscript j is conn for the connector, p for the p-type semiconductor, n for the n-type semiconductor, ce for the ceramic plate. The first term on the left side in Eq. (5) denotes the Fourier heat conduction, the second and third terms denote the internal heat sources due to the Joule heating and Thomson effect. J(x, y, z) is the local current density, and J = 0 for the ceramic plate. The Thomson coefficient can be expressed as b = T(da/dt), where a is the Seebeck coefficient of semiconductors. Thus, with the constant properties assumption, the Thomson heat in Eq. (5) will vanish. It is worth noting that the Thomson effect is actually taken into account in our numerical code; however, temperature-dependent properties of semiconductor materials used in this work were not reported in the open literature, so that the constant properties assumption is adopted here. The driving force for carriers transport within semiconductors is the electrochemical potential, which can be solved by the following equation:

r  ðrðr/
arTÞÞ ¼ 0

ð6Þ

where / is the electrochemical potential, and arT is the Seebeck electromotive force coming from the Seebeck effect. The current density in Eq. (5) can be calculated as follows:

~ J ¼ rð
r/ þ arTÞ

ð7Þ

Thus, the performance of automobile exhaust TEG system can be evaluated by the output power, Ps, and the conversion efficiency, gs, which are defined as:

Ps ¼ IV

ð8Þ

Ps Qg

ð9Þ

gs ¼

where I is the load current, V is the output voltage which can be calculated by the electric potential difference across the TEG module,

For the exhaust, a uniform flow of vg,in = 10 m s
1 maintained at Tg,in = 773 K is set as the inlet boundary condition. For the coolant, the inlet velocity is vw,in = 0.1 m s
1 and the inlet temperature is Tw, in = 300 K. At the outlets of the exhaust and coolant channels, the pressure is pout = 0.10 MPa. On the interfaces between channel and solid wall, the velocity, temperature, and heat flux are continuous. For the TEG module, constant current and zero electric potential are respectively specified to the current inlet and outlet, as shown in Fig. 1a. Except of the current inlet and outlet, the current cannot flow out of the other outside surfaces of TEG module, hence, ~ J ~ n ¼ 0 is specified to these surfaces with n denoting their normal direction. On the internal interfaces between any two adjacent materials, the temperature and heat flux are assumed to be continuous. 2.3. Material properties and model validation The exhaust pipe and heat sink are made of aluminum. The ptype and n-type legs are assumed to be made of bismuth telluride alloys which have been extensively adopted in TEG module for automobile exhaust waste heat recovery [10,12]. However, temperature-dependent material properties were not reported in the open literature, so that constant properties assumption is adopted here. Copper is selected as the connector, and aluminum oxide is selected as the material of ceramic plates. All the materials properties used in this work are listed in Table 1. The working fluid is assumed to be air for the exhaust channel and water for the coolant channel; their properties are listed in Table 2. The TEG model has been validated by self-consistency examination in our previous study [30], which also has been validated by comparing the prediction with the experimental data [31] and the analytical solution [32]. Its accuracy is found to be greatly improved as compared with the conventional thermal resistance model [33]. More details of the model can be found in Refs. [30–33]. 3. Results and discussion 3.1. Effects of cooling pattern In this section, the performance of automobile exhaust TEG system with m = 8, 12, and 16 is compared for the parallel flow and counter flow cooling patterns. The parallel (counter) flow cooling pattern is defined as that the coolant flows along the direction as same as (opposite to) the exhaust. The simulations are carried out for the geometry and operation conditions of the system described in Section 2, as well as with the material properties in Tables 1 and 2. The output power, Ps, and conversion efficiency, gs, for the two cooling patterns are shown in Fig. 2. It can be seen that for the system with the same m, the cooling patterns have little impact on Ps and gs. This can be explained as follow. For the parallel flow cooling

Table 1 Material properties used in this work. Parameters

p-type

n-type

Connector (Cu)

Ceramic plate (Al2O3)

Exhaust pipe/heat sink (Al)

a (V K
1) q (X m)

2  10
4 9  10
6 1.6


2  10
4 9  10
6 1.6

– 1.695  10
9 350

– – 35

– – 270

k (W K
1 m
1)

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J.-H. Meng et al. / Energy Conversion and Management 120 (2016) 71–80 Table 2 Thermophysical properties of the fluids. Materials

q (kg m
3)

cp (J kg
1 K
1)

k (W m
1 K
1)

l (kg m
1 s
1)

Water Air

997 1.161

4179 1007

0.613 0.026

0.000855 –

pattern, the temperature of exhaust reduces along the streamwise direction due to that the sensible heat of exhaust is absorbed by the TEG module; meanwhile, the heat is liberated from the TEG module to the coolant, leading to the increase in the coolant temperature. Thus, the temperature difference, DTk, supplied to the TE unit exhibits a significant drop along the streamwise direction, as shown in Fig. 3a. However, for the counter flow cooling pattern, the coolant and exhaust are flowing in the opposite direction; hence, the temperature differences are reduced for the TE units in the first-half system, while raised for the TE units in the second-half system. Fig. 3b presents the output power Pk of each TE unit for the two cooling patterns. It can be found that the variation of Pk is exactly consistent with DTk. This can be explained as follows. According to the conventional thermal resistance model [33], the output power, P, of a TE unit can be expressed as:

P ¼ Q h
Q c ¼ ðap
an ÞIðT h
T c Þ
I R 2

ð10Þ

where Qh is the heat supplied to the hot side of the TE unit, Qc is the heat liberated from the TE unit to the heat sink, Th and Tc are the temperatures of the hot and cold sides, R is the total electric resistance of the TE unit. It should be noted that for the present

automobile exhaust TEG system, it is the same for the electric current across each TE unit; moreover, each TE unit has the same geometrical structure and the assumption of constant material properties is adopted. Hence, I, ap, an, and R are exactly identical for each TE unit. As a result, the difference of Pk among the TE units is caused only by DTk across the TE units. Eventually, for the counter flow cooling pattern, the decrement of Pk in the first-half system is compensated by the increment of Pk in the second-half system. As a result, the two cooling patterns have almost the same output power. It is worth pointing out that Pk and DTk are more uniformly distributed among the TE units for the counter flow cooling pattern, which ensures safe operation and long lifetime of the system due to the low thermal stress, and consequently this cooling pattern should be recommended for practical automobile exhaust TEG systems. In a recent study, Bejan et al. [34] presented an opposite result that the parallel pattern is more advantageous than the counter flow. In their work, the output power at maximum conversion efficiency for a TE unit was expressed as

Pjg¼gmax ¼ ðT h
T c Þ2

190

(a)

Solid icons: Parallel flow Hollow icons: Counter flow

180

ΔTk (K)

PS (mW)

80 60

150 140 130

Square: NUM= 8 Circle : NUM=12 Triangle : NUM=16

40 20

120 110 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

1

I (A)

(b)

7

10

6

9

5 4

2 1 0 0.0

Square: NUM= 8 Circle : NUM=12 Triangle : NUM=16 0.1

0.2

0.3

3

4

5

6

7

8

9 10 11 12 13 14 15 16

(b)

Parallel flow Counter flow

11

Pk (mW)

ηS (%)

12

Solid icons: Parallel flow Hollow icons: Counter flow

8

2

the k th TE unit

10

3

Parallel flow Counter flow

160

100

9

(a)

170

120

0 0.0

ð11Þ

where ZT is the figure-of-merit of thermoelectric materials, and Rth is the thermal resistance of the TE unit held between Th and Tc. Bejan et al. proposed that for a TEG system, when its hot and cold sides are not isothermal, the integral of the square of the local temR perature difference, (Th
Tc)2dx, along the flow path should be maximized to yield the maximum output power of the system. When calculating the local temperature difference Th
Tc, the

160 140

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ ZT
1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Rth ðT h 1 þ ZT þ T c Þ

8 7 6 5

0.4

0.5

0.6

0.7

I (A) Fig. 2. The overall performances for the parallel and counter flow cooling patterns: (a) output power; and (b) conversion efficiency.

4

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16

the k th TE unit

Fig. 3. (a) Temperature difference and (b) output power of each TE unit for the system with m = 16 when the overall output power is maximized.

J.-H. Meng et al. / Energy Conversion and Management 120 (2016) 71–80

3.2. Effects of TE unit number Bell [35] presented that there are two important approaches to enhance the performance of TE devices. One is to improve the TE materials’ figure-of-merit. The other is to reasonably design and manage TE devices. Theoretically, if uniform temperatures are maintained at the hot and cold sides of a TEG module, better performance can be obtained through increasing the number of TE units. For the automobile exhaust TEG system, however, the output power of TE unit reduces along the streamwise direction due to the decreased exhaust temperature. Hence, it may be not an economically effective way to elevate the output power by increasing the number of TE units. To verify this, the performances of automobile exhaust TEG systems with various TE unit numbers are compared in this section. The maximum values of overall conversion efficiency and overall output power for automobile exhaust TEG systems with m = 8, 10, 12, 16 and 20 at the counter flow pattern are shown in Fig. 4. The maximum conversation efficiency, gs,max, decreases with the increase in TE unit number. For example, gs,max is 8.14% for m = 6, it decreases to 5.13% for m = 20. However, it is astonishing that the maximum output power, Ps,max, does not increase monotonously when more TE units are installed into the system. The optimal number is found to be 16 in the present simulation conditions, as shown in Fig. 4. This result indicates that when too many TE units are adopted in automobile exhaust TEG systems, the output power is not enhanced but is actually deteriorated. In the work by Weng and Huang [23], the number and the coverage rate on the heat-exchanger of TE units were studied. Their results showed that implementing more TE units may not be worthwhile economically, which is consistent with the present conclusion. When the systems with m = 6, 8, 10, 12, 16, and 20 reach the maximum output power, the corresponding electric currents are respectively 0.34, 0.32, 0.28, 0.26, 0.22, and 0.20 A, indicating that the electric current at the maximum output power becomes small as the TE unit number increases. The reason can be explained as follows. For a TE unit, the maximum output power and the electric current at the maximum output power both reduce when a small temperature difference is supplied to the TE unit, as shown in Fig. 5. For the present exhaust TEG system, TE units are connected electrically in series and the temperature difference across each TE unit gradually decreases along the exhaust flow direction; thus, a smaller electric current can ensure a higher overall output power of the system when the system includes more TE units. The temperature difference, DTk, of each TE unit for the systems with m = 8, 12, and 16 at the maximum overall output power is shown in Fig. 6. The geometry, arrangement, and convective heat

135

8.5 Geometry of TEG module with m=6, 8, 10,12, 16, and 20

130

8.0

125

7.5

120

7.0

115

6.5

Output power

110

Conversion efficiency

105

ηs,max (%)

Ps,max (mW)

_ p , for the cold (coolant) and hot (exhaust) fluids capacity rates, mc _ is the mass flow rate and were assumed to be the same, where m cp is the specific heat. Apparently, Bejan et al.’s result can only apply to a very specific combination of exhaust/coolant velocities. More importantly, according to Eq. (11), it can be seen that the output power at maximum conversion efficiency is dependent not only on (Th
Tc)2 but also on Th and Tc. It is impossible to only change R (Th
Tc) but keep Th and Tc unchanged. Thus, (Th
Tc)2dx cannot be adopted as the objective function. It is worth emphasizing that the present study uses a comprehensive multiphysics model to study the optimal cooling pattern, so that the results can be expected to be more convincing. To further verify the effect of flow patterns, the various combinations of exhaust/coolant inlet velocities (10 m s
1/0.08 m s
1, 10 m s
1/0.12 m s
1, 8 m s
1/0.10 m s
1, 12 m s
1/0.10 m s
1) are used. The results again show that the two patterns yield almost the same Ps,max, while the counter flow pattern leads to more uniform Pk and DTk.

6.0 5.5

100

5.0

95 4

6

8

10

12

14

16

18

20

m Fig. 4. The maximum values of conversion efficiency and output power for systems with various m.

transfer in the exhaust and coolant channels are the same for the first eight TE units in the three systems, it can be expected that DTk (k = 1, 2, 3, . . . , 8) should also be the same [36]. However, it is interesting that DTk differs from the first TE unit and the difference becomes more significant at the eighth TE unit. Fig. 6 shows that DTk (k = 1, 2, 3, . . . , 8) is the largest for the system with m = 8, then followed by m = 12 and 16. The above variation of DTk can be explained as follows. Fig. 7 illustrates the temperature variations of the exhaust and the top and bottom surfaces of the exhaust channel wall, where Tg denotes the exhaust temperature, Twall,top the top surface temperature of the exhaust channel wall, and Twall,bottom the bottom surface temperature of the exhaust channel wall. As shown in Fig. 7, when the exhaust flows through the channel, Tg gradually reduces. The sensible heat of exhaust is transferred to the exhaust channel wall by forced convection. Since the flow rate of exhaust and the convective heat transfer coefficient keep unchanged along the channel when the thermal entrance effect is ignored, the variation of Twall,top can be regarded to be almost consistent with Tg. However, since there is a lateral temperature difference along the exhaust channel wall and the wall is made of Al with a very high thermal conductivity of 210 W m
1 K
1, an additional lateral heat conduction effect will take place within the wall. Thus, a more significant drop in Twall,bottom occurs at the channel upstream than at the channel downstream. For a longer channel, the lateral temperature

18

ΔT=120 K ΔT=130 K ΔT=140 K ΔT=150 K ΔT=160 K ΔT=170 K ΔT=180 K ΔT=190 K

15 12

P (W)

76

9 6 3 0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

I (A) Fig. 5. Electric current-output power curves for a TE unit at various temperature differences.

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ation of Pk is exactly consistent with DTk. Thus, when m = 8, the system has the largest Pk (k = 1, 2, 3, . . . , 8) and hence the largest P8 P8 k¼1 P k , while for m = 16, Pk (k = 1, 2, 3, . . . , 8) and k¼1 P k are the smallest. The overall output power, Ps, for the system with m TE units is equal to the sum of Pk (k = 1, 2, 3, . . . , m). Consequently, when the number of TE units increases from m1 to m2, the total output power of the system can be elevated if and only if the P 1 Pm2 reduced m k¼1 P k could be compensated by k¼m1 þ1 P k . On the other

220

m=8 m=12 m=16

200 180 160

ΔTk (K)

140 120 100 80 60 40 20 0

0

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17

the k th TE unit Fig. 6. Temperature difference of each TE unit for systems with m = 8, 12 and 16 when the overall output power is maximized.

difference becomes larger, which causes a stronger lateral heat conduction effect, and hence at the channel upstream a lower Twall,bottom appears as compared with the shorter channel. Accordingly, the largest DTk (k = 1, 2, 3, . . . , 8) for the system with m = 8 is attributed to the weakest lateral heat conduction due to its shortest channel length. For a TE unit, a larger DTk can yield a higher conversion efficiency [33]. Accordingly, the system with m = 8 has the highest gk (k = 1, 2, 3, . . . , 8), then with m = 12 and 16. Furthermore, gk (k = 9, 10, 11, 12) for m = 12 and gk (k = 9, 10, 11, . . . , 16) for m = 16 gradually decrease along the streamwise direction and are both lower than gk (k = 1, 2, 3, . . . , 8) due to the reduced DTk. Thus, the overall conversion efficiency gs,max is the highest for the system with m = 8, and it deteriorates with increasing m. The output power, Pk, of each TE unit for the systems with m = 8, 12, and 16 is shown in Fig. 8. The result again shows that the vari-

Exhaust channel

Tg

Tg, in

Tg, out

Twall, top Exhaust channel wall

hand, Pk becomes smaller and smaller along the streamwise direction due to the reduced DTk. When m2 is large enough, this compensation fails, and hence there must exist an optimal m at which the system has the largest overall output power. It should be noted that for a single TE unit operating at constant temperature difference, the electrical current leading to maximum power depends on both temperature difference and electrical load resistance [37]. In the present system, TE units are connected electrically in series, the current going through each unit is identical; however, the temperature difference across each unit is different, as shown in Fig. 5. Accordingly, it is impossible that all TE units work at maximum performance at the same time when the overall output power of the system is maximized. 3.3. Design optimization For an actual exhaust TEG system, the TEG modules are generally installed on the outside of the automobile’s exhaust pipe or radiator, thus, the installation space is very limited. Based on this consideration, Section 3.3 will mainly focus on the arrangement optimization of TE units when the exhaust channel length is fixed. In Sections 3.3.1 and 3.3.2, the exhaust channel length is fixed at L = 21.6 mm. Section 3.3.1 mainly discusses the overall performance of the exhaust TEG system under the constraint of fixed TE materials volume, and Section 3.3.2 under the constraint of fixed spacing between TE units. 3.3.1. Constraint of fixed TE materials volume The total TE materials volume is taken as 10.08 mm3. Because constant Hpn = 1.2 mm and Wpn = 0.5 mm for p- or n-type legs are adopted here, L1 and L2 will be determined only by the TE unit number m. The performance of exhaust TEG system is simulated for m = 9, 12, 15, and 18. The corresponding L1 and L2 of the systems are listed in Table 3. The overall output power, Ps, for m = 9, 12, 15, and 18 at the counter flow pattern is shown in Fig. 9. The four systems have

Qlateral 16

Twall, bottom

15 750

m=8: m=16:

700

Tg, Tg,

Twall,top, Twall,top,

13

Pk (mW)

12

650

T (K)

m =8 m =12 m =16

14

Twall,bottom Twall,bottom

600 550

11 10 9 8

500

7

450

6 0.0

0.5

1.0

1.5

2.0

2.5

3.0

L (mm) Fig. 7. Temperature variation for exhaust and exhaust channel wall along the streamwise direction.

5

0

2

4

6

8

10

12

14

16

18

the k th TE unit Fig. 8. Output power of each TE unit for systems with m = 8, 12 and 16 when the overall output power is maximized.

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700

Table 3 Geometric parameters of TE unit for systems with various TE unit numbers under two constraints.

Fixed spacing

L1 L2 L1 L2

(mm) (mm) (mm) (mm)

9

12

15

18

0.26 0.94 0.20 1.00

0.20 0.70 0.20 0.70

0.16 0.56 0.20 0.52

0.13 0.47 0.20 0.40

almost the same Ps,max = 101.5 mW, indicating that Ps,max is independent of m. This can be explained by the temperature difference, DTk, supplied to TE units. Taking m = 9 and 18 as examples, the hot side temperature Th,k, cold side temperature Tc,k, and the corresponding DTk are different for the two systems, as shown in Fig. 10. Interestingly, however, all DTk for the two systems collapse into a single curve, and the curve can be approximated as a straight line. Accordingly, DT1,18
DT1,9  DT1,9
DT2,18 holds, where the first subscript denotes the numbering of TE units and the second denotes the total TE unit number. It should be noted that the cross-sectional area of semiconductor legs for m = 18 is one half of that of m = 9, and the electric current for m = 18 is 0.18 A which is also one half of that for m = 9. Thus, the current density in all the TE units are the same for the TEG systems with m = 9 and 18. Fig. 11a shows the output power for systems with m = 9 and 18. Assuming that the output power of the first TE unit for m = 9 is P1,9, the output powers of the first and second TE units for m = 18 are P1,18 and P2,18. It can be seen that P1,9 is approximately equal to the sum of P1,18 and P2,18 due to the same current density supplied to each TE unit. The same relation also holds for other TE units; thus, the maximum output power for the system with m = 9 is identical to that with m = 18. The normalized output power of each TE unit for the TEG systems with m = 9 and 18 is shown in Fig. 11b. Here, the normalized output power is defined as Pk/Pk,max with Pk,max denoting the maximum output power for the same one TE unit. The results confirm that all TE units do not work with maximum power when the overall output power of the system is maximized, as pointed out before. Furthermore, it is found that although the TE unit with a smaller temperature difference has a lower output power, its normalized output power is higher; thus, its Pk is closer to Pk,max.

500 400

T (K)

Fixed TE materials volume

300 200 100 0

0

5

10

15

20

L (mm) Fig. 10. The hot side temperature, cold side temperature, and temperature difference of TE units for the system with m = 9 and 18 when the overall output power is maximized.

3.3.2. Constraint of fixed spacing between TE units The performance of exhaust TEG system with m = 9, 12, 15, and 18 is simulated and a constant spacing of L1 = 0.2 mm between TE units is adopted as the constraint in this subsection. Thus, the

(a)

14

Pk with m =18

Pk with m =9

12 10

Pk (mW)

m

Th,k with m=18 Tc,k with m=18 ΔTk with m=18

Th,k with m=9 Tc,k with m=9 ΔTk with m=9

600

8 6 4 2 0

0

5

10

15

20

L (mm) 1.00

120

0.98

100

m=9 m=12 m=15 m=18

60 40

Pk /Pk,max

0.96

80

Ps (mW)

(b)

0.94 0.92 0.90

m=9 m=18

20 0.88 0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

I (A) Fig. 9. Overall output power of the systems with various m under the constraint of fixed TE materials volume.

2

4

6

8

10

12

14

16

18

the k th TE unit Fig. 11. Output power and normalized output power of each TE unit for systems with m = 9 and 18 when the overall output power is maximized: (a) output power; and (b) normalized output power.

J.-H. Meng et al. / Energy Conversion and Management 120 (2016) 71–80

120

(3) For an exhaust channel with fixed length, the maximum output power of the system keeps unchanged under the constraint of fixed TE materials volume, however, it can be enhanced under the constraint of fixed TE unit spacing, when the TE unit number increases. This finding is especially useful, because higher output power of the exhaust TEG system can be achieved by less TE material consumption.

100

Ps (mW)

80 60

m=9 m=12 m=15 m=18

40 20 0 0.0

79

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

I (A) Fig. 12. Overall output power of the systems with various m under the constraint of fixed TE unit spacing.

geometries with m = 12 for the two constraints are exactly identical. The overall output power, Ps, for m = 9, 12, 15 and 18 at the counter flow pattern is shown in Fig. 12. It can be seen that Ps,max is improved as m increases. Ps,max is 98.3 mW for m = 9, it rises up to 101.5 mW for m = 12, 104.8 mW for m = 15, and 108.2 mW for m = 18. With the fixed channel length and TE unit spacing, less TE material is consumed for a larger m. Thus, higher output power of the exhaust TEG system can be achieved by less TE material consumption. Similar result was also reported for thermoelectric coolers [38], where the cooling capacity was found to be enhanced by increasing the TE unit number when the ratio of cross-sectional area to length of the TE unit keeps constant. 4. Conclusions Recycling of automobiles exhaust waste heat through thermoelectric generators (TEGs) can efficiently improve fuel consumption efficiency. In this work, a complete multiphysics model for the TEG applied in automobile exhaust waste heat recovery is developed for the first time, wherein the exhaust is modeled as the actual heat source with a water-cooling heat sink as the cold source, and convective heat transfer, heat conduction, as well as electrical conduction are solved simultaneously. Hereafter, the established model was utilized to study the influences of cooling pattern and thermoelectric (TE) unit number on the overall system performance. The main conclusions are as follows: (1) The temperature difference, DTk, across TE units remarkably decreases along the steamwise direction, because the sensible heat of the exhaust is adsorbed by TE units. Although the parallel and counter flow cooling patterns yield the same overall output power, the non-uniformity of DTk can be reduced significantly by means of the counter flow cooling pattern. Therefore, this cooling pattern is suggested for practical automobile exhaust TEG systems. (2) The non-uniformity of DTk leads to striking deterioration of TE unit performance along the streamwise direction; thus, it is not an economically effective way to improve the overall output power of the system. More importantly, the present study reveals that the maximum output power is not enhanced but is actually reduced when too many TE units are installed to the system due to the additional lateral heat conduction within the exhaust channel wall.

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