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Optimization of thermoelectric topping combinedsteam turbine cycles for energy economyKazuaki YazawaBirck Nanotechnology Center, Purdue University, kyazawa@purdue.edu

Yee Rui KohBirck Nanotechnology Center, Purdue University, koh7@purdue.edu

Ali ShakouriBirck Nanotechnology Center, Purdue University, shakouri@purdue.edu

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Yazawa, Kazuaki; Koh, Yee Rui; and Shakouri, Ali, "Optimization of thermoelectric topping combined steam turbine cycles for energyeconomy" (2013). Birck and NCN Publications. Paper 1450.http://dx.doi.org/10.1016/j.apenergy.2013.03.050

Optimization of thermoelectric topping combined steam turbine cyclesfor energy economy

Kazuaki Yazawa ⇑, Yee Rui Koh, Ali ShakouriBirck Nanotechnology Center, Purdue University, United States

h i g h l i g h t s

� Thermoelectric on top of steam turbine cycle provides better energy economy.� There found an optimum partitioning temperature in between two engines.� Lower energy cost is found at the max-power at the beginning of operation.� Higher efficiency operation lowers the energy cost for longer hours.� Improving ZT provides a significant cost reduction for energy production.

a r t i c l e i n f o

Article history:Received 27 December 2012Received in revised form 4 March 2013Accepted 21 March 2013Available online 23 April 2013

Keywords:ThermoelectricTopping cycleSteam turbineEnergy economy

a b s t r a c t

A mismatch between the fuel combustion temperature �2250 K (adiabatic) and the high pressure steamtemperature up to 900 K, results in a large amount of thermodynamic losses in steam turbine (ST) cycles.A solid-state thermoelectric (TE) placed on top of a ST cycle will produce additional electrical power. Byselecting the right materials for the TE generator for high temperature operation, the energy productionfrom the same fuel consumption will increase. Recent nano-structured enhancements to the thermoelec-tric materials could provide practical performance benefits. We carried out a theoretical study on theoptimization of the interface temperature connecting these two idealized engines for energy economyas a combined system. We also analytically studied the optimum point-of-operation between the max-imum power output for minimizing the payback and the maximum efficiency to obtain the maximumfuel economy for each generator. The economic optimum ends up in a significant reduction in energy cost($/kW h). The combined TE topping generator system provides a lower energy cost for any period of oper-ational life and higher interface temperature compared to the ST cycle alone. The maximum power out-put is observed at around 700 K of interface temperature for 10,000 h of operation, while the minimumenergy production cost from the combined system is observed at over 900 K with ZT = 1.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

1.1. Energy cost and fuel consumption

A tragedy with a nuclear plant in Fukushima, of Japan raisedpublic concern about nuclear power, not only in Japan but in othercountries as well [1]. The national level strategy for power plantsmay have to consider many additional factors. One of the factorsis the energy price ($/kW h). Considering sustainability of oil re-sources and global warming, without a nuclear approach, we haveno choice other than increasing fuel efficiencies or exploringrenewable sources such as solar or wind. The US energy flow chart[2] shows that the energy in service is only �41.7% of the energy

input. This study represents one approach for increasing fuelefficiency in power production and lowering the energy cost($/kW h). Among various power generators, steam turbines,invented by Parsons [3] in 1884, have a long history. This particularmechanism is widely used for power generation. Steam turbinesare also one of the most effective mechanical engines [4] due toits relatively simple structure and its intrinsic energy conversionefficiency is closer to the Carnot efficiency. In addition to using sat-urated steam from a boiler, superheated steam is also used with acompressor for higher efficiency. The thermodynamic conversionefficiency however, is limited by the inlet steam temperature sincethe structural material of turbines, such as stainless steel, has atemperature-dependent mechanical yield limit at the extremelyhigh steam pressure. For example, the theoretical upper limit ther-modynamic efficiency (Carnot efficiency) for a 900 K steam tem-perature and 300 K ambient temperature is 67%. Furthermore,since the system includes irreversible thermal contacts, we cannot

0306-2619/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.apenergy.2013.03.050

⇑ Corresponding author.E-mail address: kyazawa@purdue.edu (K. Yazawa).

Applied Energy 109 (2013) 1–9

Contents lists available at SciVerse ScienceDirect

Applied Energy

journal homepage: www.elsevier .com/locate /apenergy

obtain any usable power at maximum efficiency. Theoretical effi-ciency of an ideal thermodynamic engine (with no intrinsic losses)with irreversible contacts is only 42% at the maximum power out-put based on Curzon and Ahlborn [5]. In this work, we will high-light the validity of adding a thermoelectric (TE) generator ontop of a steam turbine (ST) cycle. With an analytical approach,we will find the best operating point for fuel economy for the TEtopping ST cycles between the conditions for the maximum effi-ciency and the efficiency at maximum power output. As an imme-diate summary, the best achieved efficiencies of other technologiesas a function of heat source temperature are given by Vining [6].

1.2. Thermoelectric topping generator on a steam turbine cycle

Here we propose adding a TE power generator into the gap be-tween the flame temperature and the steam temperature. We havestudied a combined system composed of a TE generator on top of aST cycle. The TE generates an additional amount of power by usingthe large temperature gap between the source temperature andthe steam temperature. Even with a special design dedicated forhigh temperature operation for turbines [7], the steam tempera-ture is limited to <650 �C. Some of the steam turbine cycles workunder saturated steam (Rankine cycle). For higher temperature in-put, recent steam turbines use superheated steam. A Hirn cyclemaybe used as a similar cycle using a compressor to obtain asuperheated steam under high pressure before boiling, while aRankine cycle uses a pump to circulate the condensed water backinto the boiler. In this work, we simplify the ST cycle as an irrevers-ible engine since the primary interest is on the impact resultingfrom adding the TE generator on top. Then, we optimize the inter-facial temperature for the lowest energy cost.

TE generators have been receiving relatively more attention forthe waste heat recovery applications, for which the temperaturerange is similar to that of saturated steam turbines. There are sev-eral studies of TE generators and waste heat recovery systems.Chen et al. [8] reported a comprehensive review of the variousapplications. Chen et al. [9] studied two stages thermoelectric gen-erators. Caillat et al. [10] studied the graded multiple TE materialsfor maximizing the practical efficiency of power generation. Qiuand Hayden [11] studied a combined TE and organic Rankine cycles(ORCs) to effectively use the heat exhausted from an organic Ran-kine cycle turbine with three different modes of TE generators. Gouet al. [12] studied the low-temperature waste heat recovery withTE.

Unfortunately, this solid state device provides only a moderateefficiency despite the research effort spent on the material science.Thus, only the space-limited or weight-limited applications havebeen heavily investigated, in the area of vehicle exhaust heatrecovery [13–15]. However, the solid-state thermoelectric energyconversion is theoretically scalable to temperatures much higherthan superheated steam and TE materials are tunable for thetargeted temperature. This characteristic becomes an advantage

which other technologies could not accommodate. For the highertemperature application of TE generators, several different aspectsof concentrated solar TE generators have been studied by Kraemeret al. [16], Yazawa and Shakouri [17], and Xiao et al. [18].

The TE module can be designed for optimum by changing theelement thickness to match the external thermal resistances as re-ported in [19]. Using heat concentration by making the fractionalcross section area of the element smaller, orders of magnitude lessmass of the material is necessary for the same power output [20] asfar as maintaining the thermal resistance match. Earlier we alsostudied the thermal and electrical parasitic impacts [21] for theoptimal design. This optimum TE design takes into account boththe initial cost and the operating cost of the fuel.

Knowles and Lee [22] recently studied a combined system plac-ing a TE on top of a Brayton cycle and reported the efficiency at themaximum power output. They pointed out that adding TE onlyadds the power at the lower temperature range of the turbinebut the efficiency cannot exceed that of the high temperature gasturbine. They suggest that using a TE topping cycle is limited tocases for which space or price cannot be justified for a high tem-perature turbine. To look into the potential for the temperaturerange, we also extend the calculation to investigate higher inter-face temperature range.

To evaluate the energy cost of the system, we optimized the de-sign parameters for fuel economy and thus can point out thebroader advantages of the TE topping combined system as a func-tion of the operation life time and the fuel cost.

2. Materials and methods

2.1. Model of TE system

The thermal circuit model of the system is shown in Fig. 1. Tg isthe interconnecting temperature between the two engines. Thepower output from the TE is a function of the design parameterd, the thickness of the thermoelement. The parameters are alwayson a per unit area basis for this analysis.

The external thermal resistances wh and wc (K m2/W) are as-sumed to be symmetric. This simplifies the equation since thepower output is insensitive to asymmetricity of the thermal con-tacts. Thus,

wh ffi wc ð1Þ

ðTh � TcÞðTs � TgÞ

¼ ddþmb

Pw¼ d

dþ d0ð2Þ

where d is the element thickness, d0 is the optimum thickness forthe maximum power output. b is thermal conductivity of the TEmaterial and m is a ratio of the electrical load resistance againstthe internal resistance. Ts is the adiabatic flame temperature ofthe fuel, Th and Tc are the hot side and the cold side temperatureof the thermoelement, respectively. Rw is the sum of the external

Nomenclature

d thickness [m]m electrical resistance ratio [–]F fill factor [–]I initial cost [$/W m2]h life operation hours [h]G unit price [$/kg]q heat flux [W/m2]S Seebeck coefficient [V/K]

U cost per power [$/W]Y energy cost [$/W h]w power per unit area [W/m2]b thermal conductivity [W/mK]g efficiency [–]q density [m3/kg]r electrical conductivity [1/X m]w thermal resistance [K m2/W]

2 K. Yazawa et al. / Applied Energy 109 (2013) 1–9

thermal resistances thus, Rw = wh + wc. According to Ref. [19], theoptimum is found at,

d0 ¼ mbX

w ð3Þ

and

m ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ ZT

pð4Þ

where ZT is the dimensionless figure-of-merit of the TE materialand Z is defined as Z = rS/b, while r is electrical conductivity andS is Seebeck coefficient. T is the mean operating temperature acrossthe TE element. The generic power output w is found for a given Th

and Tc, as,

wTE ¼mbZðTh � TcÞ2

ð1þmÞ2dð5Þ

The efficiency gTE of the power generation from the thermoelectricdevice is found as,

gTE ¼wqin¼ mbZðTh � TcÞ2

ð1þmÞ2d

1ðTs � ThÞ=wh

ð6Þ

where qin is heat flux from the heat source flame.While g << 1 considering ZT � 1, the heat flow through the hot

side and the cold side thermal resistances are similar. Thus, (Ts -� Th) and (Tc � Tg) are approximately equal. Based on this, thepower output Eq. (5) can be rewritten as,

wTE ¼Z

ð1þmÞ2d=d0

ðd=d0 þ 1Þ21PwðTs � TgÞ2 ð7Þ

gTE ffiZ

ð1þmÞ2d=d0

ðd=d0 þ 1Þ ðTs � TgÞ ð8Þ

Here, power output is found as a function of the dimensionlessthickness d/d0. Other parameters are the given conditions Rw, Ts,and Tg. Both the extremely thin and thick thermoelement generate

nearly zero output according to Eq. (7). This supports the assump-tion that an optimum exists.

For a specific material, the material properties and Z value aretemperature dependent. However, we kept the material propertiesthe same across the temperature range. This is because once theoptimum temperature for TE is found, we can chose or developthe material match for the required temperature. Most of the cur-rently available materials show ZT � 1 for a wide temperaturerange as seen in the handbook [23]. Despite the fact that ZT is atemperature dependent factor, we keep the properties constantso as to yield ZT = 1 at the interface temperature Tg = 800 K. TheZT value goes slightly larger for a higher temperature (Tg > 800 K)and smaller for the lower (Tg < 800 K).

2.2. Energy cost model for TE

Energy cost YTE ($/kW h) for the thermoelectric section is calcu-lated as follows:

YTE ¼ITE

hwTEþ Yf

gTEð9Þ

where h is the operational life in hours for the design, Yf is the costof potential chemical energy of the fuel in units of $/kW h, and ITE

($/m2) is the initial material cost to build the system per unit area,given by:

ITE ¼ qdFGþ 2qsdsGs ð10Þ

where subscript s indicates the substrates for the thermoelectricmodule, q is density, F is fill factor, and G is the material market unitprice ($/kg). Heat sinks are not included in this part of the model,since they are already included in the Rankine cycle unit. We mayreplace them with modified versions but do not expect a differentprice, thus we did not double count the heat sink in Eq. (10).

The first term in Eq. (9) is the payoff for the initial investment.Thus longer term operation yields a smaller energy cost since theinitial investment cost is amortized over the number of operatinghours. The second term is the operating cost, which is dependenton the fuel cost and the energy conversion efficiency. Therefore,maximizing efficiency or maximizing power impacts each individ-ual term. As Eqs. (7) and (8) show, these factors are tightly relatedand therefore the relation yields a trade-off.

Substituting Eqs. (7), (8), and (10) into Eq. (9), the energy cost isfound as a function of TE leg thickness, d.

YTE ¼ðqdFGþ 2qsdsGsÞð1þmÞ2ðd=d0 þ 1Þ2

hZðd=d0ÞðTs � TgÞ2X

TE

w

þ ð1þmÞ2ðd=d0 þ 1ÞZðd=d0ÞðTs � TgÞ

Yf ð11Þ

For the further simplification, we assume the ratio of the elementthickness and the substrate thickness d/ds is a constant. Consideringthe mechanical stiffness of the substrate and the necessity of heatspreading in the substrate, it is reasonable to assume a constantrelation. Replacing d/d0 with x, the above equation becomes,

YTE ¼ðqFGþ 2qscGsÞð1þmÞ2d0ðxþ 1Þ2

hZðTs � TgÞ2X

TE

w

þ ð1þmÞ2ðxþ 1ÞZxðTs � TgÞ

Yf ð12Þ

2.3. Optimization of TE engine

By taking the derivative of Eq. (12), @@x YTE ¼ 0, we find the value

of x that will minimize YTE.

Fig. 1. Thermal network model of the entire system.

K. Yazawa et al. / Applied Energy 109 (2013) 1–9 3

The solution is found as Eq. (13) which is the only real formulaamong the possible three solutions.

x ¼ 13

X þ 1X� 1

� �ð13Þ

while,

X ¼ffiffiffi23p

Affiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�2A3 þ 27A2Bþ 3

ffiffiffi3p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

27A4B2 � 4A5Bp

3q ð14Þ

with,

A ¼ 2ðqFGþ 2qscGsÞð1þmÞ2d0

hZðTs � TgÞ2X

TE

w and B ¼ ð1þmÞ2

ZðTs � TgÞYf ð15Þ

2.4. Optimization of ST cycle

The steam turbine can be considered with a simpler model,which is comprised of an ideal engine with irreversible thermalcontacts for both hot and cold sides. The work generated by theturbine is considered as electrical power. The efficiency of thesteam turbine cycle g0ST includes all of the mechanical energy trans-fer efficiency �65% combining the turbine and the compressor/pump and the mechanical-to-electrical conversion efficiency�92% out of the thermodynamic efficiency gST. If the cycle is ideallyflexible for the ‘‘design to the target’’, the efficiency is considered asthe gST = 1 � Ta/Tg for the reversible core of the engine with a coef-ficient CST. Thus the efficiency of the ST cycle containing irrevers-ible contacts becomes g0ST=CST ¼ gST.

YST ¼IST

hwSTþ Yf

CSTgSTð16Þ

From the conservation of energy and the conservation of entropy,the relation of the power output and the efficiency is described as,

wST ¼1X

ST

w

g0ST=CSTðTg � Ta � Tgg0ST=CSTÞ1� g0ST=CST

ð17Þ

The initial cost IST is considered to build the system for maximumpower. By following Curzon–Ahlborn maximum power is given bythe contact temperatures Tg and Ta.

IST ¼ USTwST max ¼ UST1X

ST

wTg � 2

ffiffiffiffiffiffiffiffiffiffiTaTg

qþ Ta

� �ð18Þ

where,P

STw is the sum of the irreversible thermal resistance perunit area (K m2/W) within the steam turbine. Substituting Eqs.(17) and (18) into Eq. (16),

YST ¼ EðA� g0STÞðB� Cg0STÞg0ST

þ Dg0ST

ð19Þ

where,

A¼ CST;B¼ ðTg �TaÞCST;C¼ Tg ;D¼ Yf ;E¼Yi

hTg �2

ffiffiffiffiffiffiffiffiffiffiTaTg

qþTa

� �CST

ð20Þ

Similar to the thermoelectric engine, we find the efficiency. Thesolution is found as,

g0ST ¼ðAEþ BDÞ �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðAEþ BDÞ2 � BðCDþ EÞðAEþ BDÞ=C

qðCDþ EÞ ð21Þ

Due to the model simplification, the components not consideredhere are (1) the efficiency degradation through the auxiliary

components, e.g. pressure losses of working fluid, (2) temperaturedependency of thermal properties of the working fluid, and (3)non-linear mechanical losses of turbines and generators. However,in this analysis, the impact of interfacial temperature is the primaryinterest and the difference between a single ST and the TE combinedsystem. To evaluate the differences, using the theoretical upper lim-it of ST could be reasonable to measure the validity of adding TE. In-stead of considering a particular system, this model providesseamless scalability for the interfacial temperature.

2.5. Nanostructured TE materials

Returning to the TE generator, it is not obvious from Eq. (12) butcareful investigation reveals that a material with a larger figure-of-merit could provide a lower energy cost. The infinitely large ZTgives YTE ? YTE ZT¼1=ð3þ 2

ffiffiffi2pÞ at the maximum power output,

while the load resistance ratio m ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ ZTp

. Thus, improving thematerial figure-of-merit (ZT value) is an important technologicaldevelopment. As reported in [20], the thermal conductivity is themost influential parameter for the lower mass use of these expen-sive materials.

Shakouri [24] provided a comprehensive summary of recentdevelopments. Due to the nature of thermoelectric properties, itis quite difficult to find a natural material which has a very largeZT. Similar to high speed electronic applications where electricalproperties of semiconductors are engineered, thermoelectric mate-rials are also engineered by manipulating the atomic scale charac-teristics. It is well known that the thermal conductivity ofsemiconductors consists of two components. One is lattice thermalconductivity which is due to the phonon heat transport and theother is electronic thermal conductivity. The latter is constrainedto electrical conductivity by the Weidman–Franz law. Phonon scat-tering approach [25] to reduce the lattice thermal conductivity isperformed by superlattices, embedded nanoparticles and roughnanowire structures. Some semiconductors are available to workat high temperature such as Si/SiGe used in radioisotope thermo-electric generators with a maximum ZT at 900 K or higher [23].Boron compounds can work at 1300–1500 K [23]. This is one ofthe advantages of solid-state thermoelectric devices for applica-tions similar to this study.

2.6. Conditions and parameters for analysis

Material properties of thermoelement:Base line thermoelectric properties, the figure-of-merit ZT be-

comes approximately 1.

Thermal conductivity b = 1.5 (W/m K)Electrical conductivity r = 25,000 (1/X m)Seebeck coefficient S = 2 � 10�4 (V/K)Density q = 8200 (kg/m3)

Cost factors:

TE material price 500 ($/kg)Steam turbine system machine cost (overnight cost) 7000 ($/kW)Fuel cost 0.108 ($/kW h)

The machine cost of the bottoming cycle is difficult to find.Additionally, also the cost per unit power depends on the scale.We only found the unit cost of a micro-gas turbine [26]. Sincewe are interested in different interface temperatures, the extrinsicmechanisms such as heat exchangers may have similar costs. Thefuel cost is calculated based solely on the market prices of gasolineand natural gas as well as the calorific value of the fuels. The

4 K. Yazawa et al. / Applied Energy 109 (2013) 1–9

calorific value comes from [27]. To make the cost impact clear, theauxiliary costs or interposed cost are not considered for the calcu-lation. Interestingly the price for calorific value was quite similarfor gasoline and liquid propane gas (LPG). This cost value is alsothe bottom line for the electricity supply cost. As far as relyingon burning a fuel, the electricity cost cannot be lower than the va-lue, 0.108$/KW h based on the fuel price.

Performance factors:

Thermal resistances wh and wc are 0.005 (K m2/W) each.Thermal resistances in steam turbine (heat sinks) wG1 = wG2:pseudo defined (K m2/W)

Temperatures: the flame Ts = 2250 (K) and the ambient Ta = 300(K)

ST generator’s performance constant CST is assumed to be65% � 92% = 60%. The mechanical efficiency is in a similar rangeas the efficiency used in Ref. [22] for Brayton cycle turbines.

The adiabatic flame temperature is from [28]. Another parame-ter, Fill factor = 10% (fractional area coverage of TE element relativeto the cross section area of the heat flow). With this range the sub-strate cost is in a range of 10%, so that the following calculationsneglect the cost of the TE substrate.

The analysis is carried out as a function of the operational life inhours for each design h and the interface temperature Tg.

3. Results and discussion

3.1. Thermoelectric generator part

Fig. 2a shows the power output and the heat flux per unit cross-section-area of heat flow and Fig. 2b shows the energy conversionefficiency. Both are functions of the dimensionless leg thickness, d/d0. The maximum power output at time = 0 is found at d = d0. Athicker TE element leads to a larger efficiency but it significantlylimits the heat flow, thus the power output decreases as the ele-ment becomes thicker. We analytically showed this behavior inRef. [19].

Fig. 3 shows the dimensionless thickness d/d0 optimized for thelowest energy cost and energy conversion efficiency, both as thefunctions of the operation hours. Over 2000 h, the optimum thick-ness is larger than that of the maximum power output. This is dueto better fuel efficiency. As the operation hours become longer, theecono-optimum design approaches to the maximum efficiency.

3.2. Steam turbine part

The following Figs. 4–6 are based on 800 K for the interfacetemperature. Fig. 4 shows the energy cost as a function of effi-ciency for variations of operation hours. For a small amount ofhours, the energy cost is dominated by the payback for the initialcost of the generator. For longer operation, the energy cost dropgradually. The efficiency at minimum energy cost depends on theoperating hours. This cost-minimum efficiency is found to belower for longer operational life. Finally, for very long operatinghours, the energy cost continues to drop as the efficiency in-creases. The relationship between the power output and the effi-ciency of the idealized thermodynamic cycle is shown in Fig. 5.Any thermodynamic system which has irreversible thermal con-tacts exhibits similar behavior. Considering that we have thefreedom to change the internal thermal resistance starting fromzero, the power output increases as increasing the resistanceby increasing temperature difference across the generator. Atsome point, the power output will reach the maximum and thendecrease while efficiency increases since the temperature differ-

ence is still increasing. Finally, the infinitely large internal resis-tance yields the maximum efficiency, but the power goes to zerosince the heat can no longer be transferred. In this analysis, weapplied a constant factor CST to model the intrinsic thermody-namic performance to the Carnot cycle, which is shown on thecurve with maximum efficiency of 23.3%. Fig. 6 shows the econo-optimum efficiency as a function of the operation hours. Similarto the TE analysis in Fig. 3, the optimum operating efficiency isalways higher for a longer period of operation and it convergesto the maximum efficiency for an infinitely long period ofoperation.

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

0.01 0.1 1 10 100

Pow

er fl

ux [W

/m2]

d/d0

d/d0

qinqin-wout

wout

0%

5%

10%

15%

20%

0.01 0.1 1 10 100Ef

ficie

ncy

(a)

(b)

Fig. 2. (a) Power output and heat flow per unit area and (b) energy conversionefficiency as a function of the dimensionless leg thickness.

0%

4%

8%

12%

16%

20%

0

2

4

6

8

10

1.E+02 1.E+03 1.E+04 1.E+05 1.E+06

Effic

ienc

y at

Eco

no-o

pt

d/d 0

at e

cono

-opt

Operation hours [h]

η

Fig. 3. The optimum d/d0 and its efficiency vs. hours of operation.

K. Yazawa et al. / Applied Energy 109 (2013) 1–9 5

3.3. Power output of the combined system

Fig. 7a and b shows the econo-optimum power output for theTE part, ST part, and the combined system. A dotted curve showsthe econo-optimum ST alone if there was no upper temperaturelimit. Fig. 7a shows that the combined system generates morepower compare to the bottoming cycle (ST) alone from the sameheat source. The output power tends to decrease due to theecono-optimum shift to the design for efficiency at longer life oper-ation. We observe a peak for TE at around 1000 h. Fig. 7b shows theimpact of the interface temperature Tg on power output at an

operation life of 10,000 h. We observe an optimum Tg for maxi-mum power output at around 700 K. The temperature at whichthe power output peaks for the combined system is lower than thatfor the bottoming cycle (�1100 K). This is due to the continuouslydecreasing output from TE as the interface temperature increases.

3.4. Efficiency of the combined system

Fig. 8a and b shows the efficiency calculated for the same sys-tems as above. For the design for longer operation hours, both TEand ST converge to the maximum efficiency for each individualsystems.

Fig. 8b also includes the impact of enhancing the material ZTfactor (ZT = 1, 2, and 5) by changing thermal conductivity. TheZT = 2 curve corresponds to a range of advanced high-end materialsever fabricated and characterized [23] whereas ZT = 5 suggests thefuture desire for TE materials. At ZT = 5 values stand alone thermo-electric could provide similar performance to a practical vaporcompression cycle in refrigeration. In the combined system, TEprovides a minor improvement in efficiency, but plays a relativelysignificant role at lower interface temperature. Ref. [6] providedthe best practice efficiencies for Nuclear Brayton cycle + Rankinecycle. Unfortunately, based on our analysis, the theoretical com-bined system of TE (ZT = 1) on top of Rankine cycle could notachieve the best ever marked efficiency (�50%) for the same sourcetemperature. The engineering of TE materials with ZT = 4–5 may be

0.1

1

10

100

1000

0% 10% 20% 30% 40%

Ener

gy c

ost [

$/kW

h]

Efficiency

23.5%26%

32%

1,000h10,000h

100h

>> 100,000h

Fig. 4. Energy cost vs. operating efficiency for Rankine cycle. Tg = 800 K.

0

0.2

0.4

0.6

0.8

1

0% 20% 40% 60% 80%

Pow

er o

utpu

t (no

rmar

ized

)

Efficiency

STSTST C ηη =′

Carnot efficiency

Curzon-Ahlborn efficiency at wmax

Actual operation

Ideal engine

Realistic engine

Fig. 5. Power output vs. operating efficiency at Tg = 800 K while Ta = 300 K. Theshrunk curve includes the efficiency coefficient CST = 60% relative to Carnot engine.The economic optimum is found in between the conditions of the maximum poweroutput and the maximum efficiency.

0%

5%

10%

15%

20%

25%

30%

35%

40%

1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07

Econ

o-op

t effi

cien

cy

Operation hours [h]

η

η

Fig. 6. Efficiency at economic optimum condition vs. the life operation hours.

(a)

0

5

10

15

20

25

30

1.E+02 1.E+03 1.E+04 1.E+05 1.E+06

Pow

er o

utpu

t [kW

/m2 ]

Operation hours [h]

Tg=800K

(b)

0

5

10

15

20

25

30

300 800 1300 1800

Pow

er o

utpu

t [kW

/m2 ]

Interface temperature [K]

h=10,000hrs

Fig. 7. Economical optimum power output for the lowest energy cost as (a)functions of operation hours and (b) interface temperature. (a) Is a plot for 800 K ofthe interface temperature and (b) is a plot for 10,000 h of operation. ‘ST only’ pointsthe steam turbine only white ‘TE’ and ‘ST’ indicate the TE generator and the ST cyclecomponents of the combined system. ZT is approximately 1.

6 K. Yazawa et al. / Applied Energy 109 (2013) 1–9

necessary to reach the best efficiency. Similar to the single cycleefficiency of Coal Rankine cycle, Solar Brayton cycle efficiency isalso found to be �50%. Nevertheless, there is still a room to putTE on top of them to enhance the efficiency.

3.5. Energy economy analysis

The energy production cost ($/kW h) of TE part of the systemis plotted in Fig. 9 compared to the standalone ST. A variation ofthe thermoelectric properties are also considered (ZT = 1, 2, and5). The trends for operation hours in Fig. 9a shows a similar trendfor each scenario, but the trend for interface temperature inFig. 9b shows the trade-off behavior between the TE and ST.The impact of enhancing the Z factor (Z = rS2/b) is separated bythe change in power factor (rS2) indicated by dotted curves,and the change in thermal conductivity (b) indicated by dashedcurves. The difference is smaller for longer operating period andthe energy cost of ZT = 5 is projected to be comparable to ST.Fig. 10 shows the total energy production cost of the combinedsystem in comparison to the standalone ST. As seen in Fig. 10a,longer life operation always lowers the energy cost. Cost reduc-tion contribution of the TE topping cycle is approximately 20%of the combined system at infinitely long operation hours. Theinterface temperature dependency is shown in Fig. 10b. There is

a very flat valley for the energy cost between 800–1200 K inter-face temperature with ZT = 1. However, this characteristic shiftsto a lower cost at a lower interface temperature with more ad-vanced TE material. Looking at the other technologies, the marketprice of electricity, which is very low around 0.1 $/kW h in theUnited States, is the only reasonable way to compare. In this case,the Rankine cycle even with TE topping cycle may not be the firstoption for electricity production and may need an additional con-sideration for the by-product of heat (e.g. co-generationapplications).

3.6. Practical limitation of the systems

The optimum temperature (�700 K) to achieve the peak poweroutput in Fig. 7b is preferable to considering a practical machinefor the bottoming cycle since the source temperature is limitedby some structural materials as well as the pressure limit of thesuperheated steam. For the lower temperature side, the steammight be saturated steam or the steam may be replaced by an or-ganic working fluid. Under 500 K, total efficiency is already so lowit may not pay to find the optimum temperature but TE does play amajor role at the lower temperatures. It is fortunate that the peakefficiency of the combined system shows a plateau-like curve, thusthe optimum design is quite robust.

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Fig. 8. Efficiency as a function of (a) operation hours and (b) interface temperature.(a) Is a plot for an interface temperature of 800 K and (b) is a plot for 10,000 h ofoperation with approximately ZT = 1 and dashed curves shows the case ofapproximately ZT = 2 and ZT = 5.

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Fig. 9. Energy cost of steam turbine only and TE only vs. (a) operation hours and (b)interface temperature. (a) Is a plot for an interface temperature of 800 K and (b) is aplot for 10,000 h of operation, with variation of the material properties of TE (ZT = 1,2, and 5). Dotted curves show the impact of improving power factor and dashedcurves show the impact of thermal conductivity.

K. Yazawa et al. / Applied Energy 109 (2013) 1–9 7

3.7. System scale for applications

The thermoelectric generator is scalable since it can be designedin an array. Practically, we may have to wait for mass production to

mature. A lower temperature range with moderate scale ranging10s kW – a few MW of ORCs or STs would be an advantageous areafor the TE topping system in terms of energy cost. In contrast atechnology like a nuclear plant, which is a few GW in scale, cannotbe scaled to a few MW range. For the temperature scaling, evenwith a state-of-the-art material applied, reaching the gas tempera-ture of 1200 K is not easy for Brayton cycles. For the TE materials,there is already some options as stated in Section 2.5.

3.8. Efficiency reported for real systems compared to simulations

The achieved efficiencies from data reported in the literature vs.inlet temperature are shown in Fig. 11. We also plot the simulationresults based on the Rankine cycle process referring to the T–S dia-gram of water–vapor for two cases of heat exchanger designs. 10 Kand 50 K indicates the temperature difference across the hot sideand the cold side heat exchangers. Note that the ORCs performanceand temperature range differ depending on the working fluid.Among the data points, ST2 shows an irregularly high efficiencycompared to the others. The data points do not necessarily matchsince the goal of our model is to obtain the minimum energy cost.The model is however, a reasonable fit in the practical range. Thisgraph also shows the benefit of adding TE.

4. Conclusions

We developed a generic model and analyzed energy economyfor a combined TE generator on top of a steam turbine cycle. Theoptimum design/operation for the lowest energy cost both for TEand ST are analytically found. The advantage of adding a TE ontop of a ST is demonstrated. The optimum design and the optimumoperation of each engine minimize the payback of the initial costper unit power output. It also simultaneously minimizes the fuelconsumption per unit power output. The optimum balance of thedesign/operation point between the maximum power and themaximum efficiency depends on the hours of operation. Anotherfactor for optimizing the system is the interface temperature be-tween the two engines. A higher interface temperature lowersthe energy cost, but there is a practical temperature limitation.The improved thermoelectric figure-of-merit (ZT), via e.g. nano-structured material is a key to the successful increase in poweroutput and significant reduction in fuel consumption. We alsopointed out the impact of the TE properties for power generation.

Overall, the analysis demonstrated the best balance betweenlowest fuel consumption and maximum power density. By addingTE on top of the ST cycle, the energy economy increases by effec-tively reusing a large amount of collateral heat losses that wouldotherwise occur within a standalone ST cycle.

Acknowledgements

This study was supported by the Center of Energy EfficientMaterials, one of the Energy Frontier Research Centers (EFRC) ofThe Office of Science, US Department of Energy. Authors thank toDr. Braun and Mr. James for their help on the Rankine cyclesimulation.

References

[1] New York Times on-line topic, Nuclear Energy, October 12, 2012. <http://topics.nytimes.com/top/news/business/energy-environment/atomic-energy/index.html>.

[2] Lawrence Livermore National Laboratory, Energy flow chart – EstimatedEnergy Use in 2011: 97.3 Quads, 2012. <http://flowcharts.llnl.gov/>.

[3] Parsons Charles A. The steam turbine. Cambridge University Press; 1911.[4] Wiser WH. Energy resources. Springer; 2000.[5] Curzon F, Ahlborn B. Efficiency of a Carnot engine at maximum power output.

Am J Phys 1975;43(1):22.

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0.2

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0.6

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0.8

0.9

1

1.E+02 1.E+03 1.E+04 1.E+05 1.E+06

Ener

gy e

cono

my

[$/k

Wh]

Operation hours [h]

(b)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

300 800 1300 1800

Ener

gy e

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[$/k

Wh]

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Fig. 10. Energy total energy cost in comparison to the steam turbine only vs. (a)Operation hours and (b) interface temperature, with variation of ZT of TE (ZT = 1, 2,and 5).

0%

10%

20%

30%

40%

50%

300 800 1300 1800

Effic

ienc

y

Interface temperature [K]

ST modelTE+ST modelORC1ORC2ORC3ST1ST2GT1GT2Sim Hex=10KSim Hex=50K

Fig. 11. Comparison of efficiency for a variety of turbine generators to the model.The achieved data refers ORC1: Ref. [29], ORC2: Ref. [30], ORC3: Ref. [31], ST1: Ref.[32], ST2: Ref. [33], GT1: Ref. [34], GT2: Ref. [35], respectively. Also, numericalsimulation results indicated by two dashed curves are plotted.

8 K. Yazawa et al. / Applied Energy 109 (2013) 1–9

[6] Vining CB. An inconvenient truth about thermoelectrics. Nat Mater2009;8:83–5.

[7] Imano S, Saito E, Iwasaki J, Kitamura M. High-temperature steam turbinepower plant. US Patent Application 20080250790.

[8] Chen M, Lund H, Rosendahl LA, Condra TJ. Energy efficiency analysis andimpact evaluation of the application of thermoelectric power cycle to today’sCHP systems. Appl Energy 2010;87(4):1231–8. http://dx.doi.org/10.1016/j.apenergy.2009.06.009. ISSN 0306-2619.

[9] Chen L, Li J, Sun F, Wu C. Performance optimization of a two-stagesemiconductor thermoelectric-generator. Appl Energy 2005;82(4):300–12.http://dx.doi.org/10.1016/j.apenergy.2004.12.003. ISSN 0306-2619.

[10] Caillat T, Fleurial J-P, Snyder GJ, Borshchevsky A. Development of highefficiency segmented thermoelectric unicouples. In: Proceedings of ICT2001;2001. p. 282–5.

[11] Qiu K, Hayden ACS. Integrated thermoelectric and organic Rankine cycles formicro-CHP systems. Appl Energy 2012;97:667–72. http://dx.doi.org/10.1016/j.apenergy.2011.12.072. ISSN 0306-2619.

[12] Gou X, Xiao H, Yang S. Modeling, experimental study and optimization on low-temperature waste heat thermoelectric generator system. Appl Energy2010;87(10):3131–6. http://dx.doi.org/10.1016/j.apenergy.2010.02.013. ISSN0306-2619.

[13] Fairbanks JW. Vehicular thermoelectrics: a new green technology. In:Proceedings of the 2nd thermoelectrics applications, workshop; 2011.

[14] Hussain QE, Brigham DR, Maranville CW. Thermoelectric exhaust heatrecovery for hybrid vehicles. SAE Int J Eng 2009;2(1):1132–42.

[15] LaGrandeura1 JW, Bella1 LE, Crane DT. Recent progress in thermoelectricpower generation systems for commercial applications. MRS Proc 2011;1325.

[16] Kraemer D, Poudel B, Feng H-P, Caylor JC, Yu B, Yan X, et al. High-performanceflat-panel solar thermoelectric generators with high thermal concentration.Nat Mater 2011;10:532–8. http://dx.doi.org/10.1038/nmat3013.

[17] Yazawa K, Shakouri A. System optimiztion of hot water concentrated solarthermoelectric generation. In: Proceedings of the 3rd international conferenceon thermal issues in emerging technologies theory and applications (ThETA3);2010. P. 283–90.

[18] Xiao J, Yang T, Li P, Zhai P, Zhang Q. Thermal design and management forperformance optimization of solar thermoelectric generator. Appl Energy2012;93:33–8. http://dx.doi.org/10.1016/j.apenergy.2011.06.006 [ISSN 0306-2619].

[19] Yazawa K, Shakouri A. Optimization of power and efficiency of thermoelectricdevices with asymmetric thermal contacts. J Appl Phys 2012;111(2):024509. 6pages.

[20] Yazawa K, Shakouri A. Optimizing cost-efficiency trade-offs in the design ofthermoelectric power generators. Environ Sci Technol – J Am Chem Soc2011;45(17):7548–53.

[21] Yazawa K, Shakouri A. Cost-effective waste heat recovery using thermo-electric systems. Invited Feature Paper, Journal of Material Research 2012;27:1–6.

[22] Knowles CB, Lee H. Optimized working conditions for a thermoelectricgenerator as a topping cycle for gas turbine. J Appl Phys 2012;112:07351.http://dx.doi.org/10.1063/1.4757008. 8 pages.

[23] Rowe DM, editor. Thermoelectric handbook macro to nano. CRC Press; 2006.[24] Shakouri A. Recent developments in semiconductor thermoelectric physics

and materials. Annu Rev Mater Res 2011;41:399–431.[25] D. L. Nika, E. P. Pokatilov, A. A. Balandin, V. M. Fomin, A. Rastelli, and O. G.

Schmidt Reduction of lattice thermal conductivity in one-dimensionalquantum-dot superlattices due to phonon filtering, Physical Review B, Vol.84, 165415, (7 pages), (2011).

[26] You-hong Y, Feng-rui S. Thermoeconomics cost modeling of marine gasturbine generating unit. Proceedings of industrial engineering and engineeringmanagement (IEEM), IEEE; 2010. p. 2004–8.

[27] Bauer H, editor. Automotive handbook. Robert Bosch GmbH; 1996. p. 238–9.[28] van Maaren A, Thung DS, de Goey LRH. Measurement of flame temperature

and adiabatic burning velocity of methane/air Mixtures. Combust Sci Technol1994;96(4–6):327–44.

[29] Tahir MbM, Yamada N, Hoshino T. Efficiency of compact organic Rankine cyclesystem with rotary-vane-type expander for low-temperature waste heatrecovery. Int J Civil Environ Eng 2010;2(1):11–6.

[30] Turboden Heat Recovery Unit. <http://www.turboden.eu/en/products/products-hr.php>.

[31] Yamada N, Mohamad MNA, Kien TT. Study on thermal efficiency of low- tomedium-temperature organic Rankine cycles using HFO-1234yf. RenewEnergy 2012;41:368–75. http://dx.doi.org/10.1016/j.renene.2011.11.028.

[32] Energy and Environmental Analysis, Technology Characterization: SteamTurbines, Report prepared for US Environmental Protection Agency; 2008. p.13.

[33] GE D-17 Steam Turbine. <http://www.ge-flexibility.com/products-and-services/steam-turbines/d17-steam-turbine.html>.

[34] D. Thimsen, Assessment of Leading Microturbine Technologies: EPRI,1004454; 2003.

[35] Mitsubishi Power Systems M501 J series. <http://www.mpshq.com/products/gas_turbines/index.html>.

K. Yazawa et al. / Applied Energy 109 (2013) 1–9 9