Parametric optimization of a solar-driven Braysson heat engine with ...

Download PDF
6 downloads 5431 Views 364KB Size Report
Comment
Aug 15, 2009 - Parametric optimization of a solar-driven Braysson heat engine with variable heat capacity of the working fluid and radiation–convection heat ...
Renewable Energy 35 (2010) 95–100

Contents lists available at ScienceDirect

Renewable Energy journal homepage: www.elsevier.com/locate/renene

Parametric optimization of a solar-driven Braysson heat engine with variable heat capacity of the working fluid and radiation–convection heat losses Lanmei Wu, Guoxing Lin*, Jincan Chen Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen 361005, PR China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 15 August 2008 Accepted 21 July 2009 Available online 15 August 2009

An irreversible solar-driven Braysson heat engine system is presented, in which the temperaturedependent heat capacity of the working fluid, the radiation–convection heat losses of the solar collector and the irreversibilities resulting from heat transfer and non-isentropic compression and expansion processes are taken into account. Based on the thermodynamic analysis method and the optimal control theory, the mathematical expression of the overall efficiency of the system is derived and the maximum overall efficiency is calculated, and the operating temperatures of the solar collector and the cyclic working fluid and the ratio of heat-transfer areas of the heat engine are optimized. By using numerical optimization technology, the influences of the variable heat capacity of the working fluid, the radiation– convection heat losses of the solar collector and the multi-irreversibilities on the performance characteristics of the solar-driven heat engine system are investigated and evaluated in detail. Moreover, it is expounded that the optimal performance and important parametric bounds of the irreversible solardriven Braysson heat engine with the constant heat capacity of the working fluid and the irreversible solar-driven Carnot heat engine can be deduced from the conclusions in the present paper. Ó 2009 Elsevier Ltd. All rights reserved.

Keywords: Solar-driven heat engine Temperature-dependent heat capacity Radiation–convection heat loss Irreversibility Optimal analysis

1. Introduction With the sustainable development stratagem, the problems of saving energy and minimizing negative environmental impacts are becoming more prominent day by day. Solar energy is one of the renewable clean energies and more and more scholars and engineers have focused on its application research. Along with that, many conceptive designs and apparatus for exploiting solar energy have been investigated from both theory and experiment. Solardriven heat engines [1–12] are one of the important devices utilizing solar energy and a lot of attentions have also been attracted on it. In recent years, some scholars investigated the performance characteristics of the solar-driven Carnot [1–6], solar-driven Stirling and Ericsson [7,8], solar-driven Brayton heat engine [9–11] and some significant results were obtained. Meanwhile, Sogut et al. [12] explored the optimal performance of a parabolic-trough directsteam-generation solar-driven Rankine cycle power plant at maximum power and maximum power density condition by using the equivalent Carnot-like cycle heat engine. Sogut and other

* Corresponding author. E-mail address: [email protected] (G. Lin). 0960-1481/$ – see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2009.07.015

authors [6,13,14] employed ‘an entropic average temperature’ approach to analyze and evaluate the optimal performances of the solar-driven Rankine heat engine [6,12], the heat engine-driven heat pump [13] and the Rankine heat engine [14], in which the process of heat transfer between the high temperature reservoir and the working fluid was dealt with as an isothermal one. In fact, the heat addition process of the Rankine cycle generally consists of the two or three isotonic processes [12,15], while the heat addition process of the supercritical Rankine cycle [15,16] includes one isotonic process. In these processes, the heat supplied by the external heat sources, such as the solar collector, is non-isothermally added to heat engine cycle. Except for the equivalent Carnotlike heat engine cycle, there may be other equivalent cycle models for solar-driven Rankine heat engine cycles. For example, heattransfer process between the heat source and the cyclic working fluid is considered to be an isotonic heat addition one, which is closer to the practice than an isothermal heat addition one. Thus, one may put forward an equivalent Braysson-like cycle heat engine of solar-driven Rankine heat engine. The Braysson heat engine cycle, which was proposed and investigated by Frost et al. [17], is a hybrid power cycle based on a conventional Brayton cycle for the high temperature heat addition and an Ericsson cycle for the low temperature heat rejection. The performance characteristics of the new style Braysson heat

L. Wu et al. / Renewable Energy 35 (2010) 95–100

Nomenclature A Aa Ar A1/A2 Cp G I _ m qh/qa ql Ta

overall heat-transfer area of heat engine (m2) aperture area of collector (m2) absorber area of collector (m2) heat-transfer area between working fluid and hot/cold reservoir (m2) specific heat at constant pressure (J/mol K) solar irradiance (W/m2) internal irreversibility parameter mass flow rate of the working substance (mol/s) heat-transfer rate between working fluid and hot/cold reservoir (W) heat loss rate of collector (W) ambient temperature (K)

engines have been studied [18–23]. For example, Zheng et al. [23] presented the irreversible solar-driven Braysson heat engine and its optimal performance characteristics were evaluated and discussed. In that investigation, the heat loss of the solar collector was considered to result from convection between the solar collector and its surroundings. Actually, for some solar-driven thermal devices, besides the convection heat loss, there still exists radiation heat loss. Thus, it is necessary to take into account the radiation– convection mode of heat losses from the solar collector to the ambient. On the other hand, the constant heat capacity of the cyclic working fluid was supposed in the above solar-driven heat engines’ investigations. In fact, the heat capacities of the cyclic working fluid are often variable. Some authors have applied the variable heat capacities of the working fluid to the other engines’ study [24–29] in which the heat capacities of the working fluid are considered to be linear [24–28] or fourth order polynomial [29] functions of temperature. In the present paper, a developed solar-driven Braysson heat engine system is presented, in which the multi-irreversibilities existing in the heat engine are taken into account. On the basis of thermodynamic analysis method, the relationship between the operating temperature of the solar collector and the overall efficiency of the solar-driven heat engine system is derived. By using numerical optimization technology, the maximum overall efficiency of the system and the optimal values of the main performance parameters including the operating temperature of the solar collector, the temperatures of the cyclic working fluid, and the ratios of the related heat-transfer areas to the total heat-transfer area of the heat engine are calculated and the effects of the temperature-dependent heat capacity, radiation–convection heat losses, internal irreversibility parameter, etc., on the performance characteristics of the solar-driven Braysson heat engine system are revealed and depicted quantitatively. Some special cases are also discussed.

2. An irreversible solar-driven Braysson heat engine system A solar-driven Braysson heat engine system consisting of a solar collector and an irreversible Braysson heat engine is shown in Fig. 1, where Th is the temperature of the solar collector, Ta is the ambient temperature, 2–3 and 4–1 are two irreversible adiabatic processes, 1–2 and 3–4 are, respectively, the isobaric and isothermal processes, T1S and T3S are the final temperatures of the reversible adiabatic compression and expansion processes, Ti (i ¼ 1, 2,3, 4) are the temperatures of the working fluid at state points 1, 2, 3, and 4, T3 ¼ T4 ¼ T3S because of the isothermal process, and qh and qa are,

Th Th,opt T1S/T3S Ti UL U1/U2

sa e h hs hh

temperature of collector (K) optimally operating temperature of collector (K) final temperature of reversible adiabatic compression/expansion process (K) temperature of working fluid at state points i (i ¼ 1, 2, 3, 4) (K) convective heat loss coefficient (W/m2 K) heat-transfer coefficient between working fluid and hot/cold reservoir (W/m2 K) effective transmittance–absorbance product effective emissivity of collector overall efficiency of solar-driven heat engine system efficiency of collector efficiency of heat engine

respectively, the heat-transfer rates from the solar collector at temperature Th to the heat engine and from the heat engine to the heat sink at temperature Ta. The overall efficiency h of the solardriven heat engine system is equal to the product of the efficiency hs of the solar collector and the efficiency hh of the heat engine, i.e.

h ¼ hs hh

(1)

For a solar collector in a solar-driven heat engine system, when its heat losses are dominated by the radiation and convection, the energy balance equation and efficiency of the solar collector are, respectively, given by

  qh ¼ saGAa ql ¼ saGAa  esAr Th4 Ta4 UL Ar ðTh Ta Þ

(2)

hs ¼ qh =ðGAa Þ ¼ saD

(3)

 M2 ½rðTh4 =Ta4  1Þ þ M2 ¼ UL Ta =ðsaGCÞ,

where D ¼ 1 ðTh =Ta  1Þ, r ¼ M1 =M2 ,M1 ¼ esTa4 =ðsaGCÞ, G is the solar irradiance, C ¼ Aa =Ar is the concentration ratio, Aa and Ar are, respectively, the aperture and absorber areas, sa is the effective transmittance– absorbance product, ql is the heat loss rate, e is the effective emissivity of the collector, s ¼ 5.67  108 W/(m2 K4) is the Stefan– Boltzmann constant, and UL is the convective heat loss coefficient. In most solar-driven heat engine cycle models, the working fluid is assumed to behave as an ideal gas with constant specific heats. But this assumption can be valid only for the small temperature differences. For the large temperature differences encountered in

solar collector

Th

qh 1s

1

2

Cp(T)

T

96

4

qa

Ta

3s

3

S Fig. 1. The T–S diagram of an irreversible solar-driven Braysson heat engine system.

L. Wu et al. / Renewable Energy 35 (2010) 95–100

a practical cycle, this assumption needs to be modified. According to Refs. [24–27], it can be supposed that the specific heats of the working fluid are dependent on the temperature alone and over the temperature range generally encountered for gases in heat engines (i.e., 300–2200 K), the specific heat curve is nearly linear, so the heat capacity of the working fluid at constant pressure may be closely approximated as

Cp ¼ a þ k1 T

(4)

where k1 and a are two constants. Thus, the heat-transfer rate in the isobaric process is given by

_ qh ¼ m

ZT2

_ 1 Cp dT ¼ mL

(5)

97

where h ¼ U1 A=ðsaGAa Þ. At the same time, by using Eqs. (7), (8), and (11)–(13), the efficiency of the Braysson heat engine can be expressed as

hh ¼ 1 

qa IL3 Ta ðDL2  L1 hÞ ¼ 1 qh L1 ðyIL3 D þ L2 D  L1 hÞ

(14)

It is clearly seen from Eqs. (6) and (14) that the efficiency of the heat engine is only a function of T1, A, and Th for other given parameters, i.e.

hh ¼ hh ðT1 ; A; Th Þ

(15)

Substituting Eqs. (3) and (14) into Eq. (1), we obtain the overall efficiency of the irreversible solar-driven Braysson heat engine system as

T1



IL3 Ta ðDL2  L1 hÞ L1 ðyIL3 D þ L2 D  L1 hÞ

_ is the mass flow rate. where L1 ¼ aðT2  T1 Þ þ k1 ðT22  T12 Þ=2, m Now, combining Eq. (2) with Eq. (5), it can be solved out that

h ¼ hs hh ¼ saD 1 

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  T2 ¼ k1 k21 T12 þ 2ak1 T1 þ 2k1 fD þ a2  a

Eq. (16) is an important equation of the irreversible solar-driven Braysson heat engine system, from which the optimal performance characteristics of the system can be analyzed and evaluated.

(6)

_ where f ¼ saGAa =m When finite-rate heat transfer is taken into consideration, it is often assumed that the convection heat transfer obeys Newton’s law. Thus, the heat-transfer rates qh and qa may be, respectively, expressed as

qh ¼ U1 A1 L1 =L2

(7)

qa ¼ U2 A2 ðT3  Ta Þ

(8)

where L2 ¼ ½a þ k1 Th ln½ðTh  T1 Þ=ðTh  T2 Þk1 ðT2  T1 Þ and Uj and Aj (j ¼ 1, 2) are the heat-transfer coefficients and areas related to their respective heat exchangers. Applying the second law of thermodynamics to the irreversible Braysson heat engine, one has

(9)

where L3 ¼ alnðT2 =T1 Þ þ k1 ðT2  T1 Þ. Eq. (9) indicates that the entropy flow flowing from the cycle is lager than that flowing into the cycle. In order to describe the internal irreversibility, we may introduce an internal irreversibility parameter

On the basis of Eqs. (6) and (14), one can plot the hh wT1 curves of the irreversible Braysson heat engine cycle, as shown in Fig. 2. The curves in Fig. 2 show clearly that there exists an optimal temperature T1;opt at which the efficiency of the Braysson heat engine cycle can attain its maximum. Substituting the value of T1;opt into Eq. (16), one can generate the h w Th curves of the solar-driven Braysson heat engine system, as shown in Fig. 3. The curves in Fig. 3 indicate that the overall efficiency of the solar-driven Braysson heat engine system first increases and then decreases as the collector temperature Th increases. As the temperature Th of the collector increases, the heat losses of the collector increase and result directly in the decrease of the collector efficiency hs. On the other hand, the efficiency hh of the irreversible Braysson heat engine cycle increases as Th increases. As a result, there exists an optimally operating temperature Th,opt at which the overall efficiency h of the system attains its maximum. Furthermore, based on Eqs. (6), (11)

(10)

Generally, I > 1. When the irreversibility of the adiabatic processes may be neglected, I ¼ 1. In such a case, the irreversibilities only result from the finite-rate heat transfer between the working fluid and the external reservoirs. Combining Eqs. (5) and (7) with Eq. (10), one can derive the expressions of the ratios of the hot- and cold-side heat exchanger areas to the total heat exchanger area of the heat engine as

A1 L2 ðT3  Ta Þ ¼ A yIL3 T3 þ L2 ðT3  Ta Þ

3.1. Optimization on some important parameters

Carnot

0.53

Braysson k1=0.009844 J/mol K2

0.52 h

 _ 3 L3 I ¼ U2 A2 ðT3  Ta Þ= mT

3. Optimal performance characteristics

η

_ 3  U2 A2 ðT3  Ta Þ=T3 < 0 mL

(16)

ηh,max

k1=0.005844 J/mol K2 k1=0.003844 J/mol K2

k1→ ∞

k1=0 J/mol K2

(11)

0.51

(12)

0.50 720

and

A2 yIL3 T3 ¼ A yIL3 T3 þ L2 ðT3  Ta Þ where A ¼ A1 þ A2 and y ¼ U1 =U2 . By solving Eqs. (2), (7) and (11), T3 can be expressed as

Ta ðDL2  L1 hÞ T3 ¼ yIL3 D þ L2 D  L1 h

(13)

760 T1,opt 800 T1/K

840

880

Fig. 2. The hh w T1 curves for differently given values of k1. Curves are presented for e ¼ 0.1, s ¼ 5.67  108 W/(m2 K4), G ¼ 1.353 KW/m2, sa ¼ 0.8, a ¼ 29.09 J/(mol K), r ¼ 1, M2 ¼ 0.0028, Ta ¼ 300 K, y ¼ 1.1, h ¼ 0.0092 K1, f ¼ 6.3  103 J/mol, Th ¼ 1000 K and I ¼ 1.1.

98

L. Wu et al. / Renewable Energy 35 (2010) 95–100

Braysson

Carnot

0.272

k1→ ∞

0.270

k1=0.009844J/mol K k1=0.005844J/mol K2

k1=0.003844J/mol K2

k1

I

hmax

Th,opt

T1,opt

T2,opt

T3,opt

(A1/A)opt

0

1.00 1.05 1.10

0.2952 0.2808 0.2669

986.40 998.40 1010.00

750.96 767.01 782.78

895.81 908.33 920.56

368.60 368.21 367.69

0.4790 0.4731 0.4675

0.266

0.003844

1.00 1.05 1.10

0.2961 0.2816 0.2678

985.40 997.40 1008.80

759.55 775.46 790.80

890.43 902.94 914.96

368.90 368.53 368.10

0.4809 0.4750 0.4694

0.264

0.005844

1.00 1.05 1.10

0.2965 0.2820 0.2681

984.80 996.80 1008.40

762.93 778.79 794.35

887.58 900.12 912.38

369.07 368.72 368.23

0.4817 0.4758 0.4702

0.009844

1.00 1.05 1.10

0.2971 0.2826 0.2687

983.80 996.00 1006.20

768.81 784.78 798.13

882.61 895.37 905.98

369.38 368.96 368.93

0.4830 0.4770 0.4714

N

1.00 1.05 1.10

0.3001 0.2854 0.2714

979.00 991.40 1003.40

828.46 842.72 856.73

828.46 842.72 856.73

370.66 370.28 369.75

0.4882 0.4822 0.4766

k1=0 J/mol K2

0.268 η

η

Table 1 The values of several parameters at the maximum overall efficiency, where Ta ¼ 300 K, e ¼ 0.1, s ¼ 5.67  108 W/(m2K4), sa ¼ 0.8, a ¼ 29.09 J/(mol K), r ¼ 1, M2 ¼ 0.0028, G ¼ 1.353 KW/m2, y ¼ 1.1, h ¼ 0.0092 K1 and f ¼ 6.3  103 J/mol.

2

max

0.262

980

1000 Th,opt 1020

1040

Th/K Fig. 3. The h w Th curves for differently given values of k1, where the values of the related parameters are the same as those used in Fig .2.

and (13), we can obtain the optimal values T2,opt, T3,opt and (A1/A)opt of some important parameters. The results obtained may provide some theoretical guidance for the optimal parameter design of the solar-driven heat engine. 3.2. Influence of variable heat capacities of the working fluid In fact, the influence of the variable heat capacities of the working fluid on the performance characteristics of the solardriven Braysson heat engine system has also been shown in Fig. 2. It can be seen from Fig. 2 that the maximum efficiency of the Braysson heat engine cycle hh;max and the corresponding optimal temperature T1;opt increases significantly as the parameter k1 increases. Also, it can be seen from Fig. 3 that when the parameter k1 increases, the optimally operating temperature Th;opt of the collector decreases while the maximum overall efficiency hmax of the solar-driven Braysson heat engine system increases. As an example, if I ¼ 1.1, a ¼ 29.09 J/(mol K), r ¼ 1, and M2 ¼ 0.0028 are chosen, one can see from Table 1 that when k1 ¼ 0.003844 J/ (mol K2), 0.005844 J/(mol K2) and 0.009844 J(/mol K2) [28], Th,opt ¼ 1008.8 K, 1008.4 K and 1006.2 K, and the maximum overall efficiency hmax ¼ 0.2678, 0.2681 and 0.2687, respectively. At the same time, the values of the optimal parameters T1,opt, T2,opt, T3,opt and (A1/A)opt varying with k1 are also listed in Table 1. If the heat capacities of the working fluid are constants, that is k1 ¼ 0, Eqs. (6), (14), and (16) may be simplified as

T2 ¼ T1 þ fD=a

(17)

i h T ITa ln 2 DlnTh T1 hðT2 T1 Þ T1 Th T2

hh ¼ 1 T T T1 ðT2 T1 Þ yIDln 2 þDln h hðT2 T1 Þ T1 Th T2

(18)

h ¼ hs hh 8 < ¼ saD 1 :

curve at k1 ¼ 0 is a lower bound of the solar-driven Braysson heat engine system with variable heat capacities of the working fluid. Moreover, if r ¼ 0 and k1 ¼ 0 is set, the results in the present paper correspond to those obtained in Ref. [23] in which the radiation heat loss of the collector has not been taken into consideration, where f ¼ T1 aðx1Þ=D. This implies the fact that the results obtained in Ref. [23] can be directly derived from the conclusions in the present paper. On the other hand, when the parameter k1 /N, Eqs. (6) and (14) may be simplified as

T2 ¼ T1

(20)

hh ¼ 1 

ITa ½D  hðTh  T1 Þ ðTh  T1 ÞðyID  T1 hÞ þ T1 D

In such a case, the irreversible solar-driven Braysson heat engine becomes the irreversible solar-driven Carnot heat engine. For given A and Th, using Eq. (21) and the extreme condition ðvhh =vT1 ÞA;Th ¼ 0, the temperature T1 can be determined by the following equation:

 pffiffiffiffiffi T1 ¼ Th  D 1 þ yI =h

(22)

By using Eq. (22), Eq. (21) can be expressed as

h



hh ¼ 1  ITa = Th  D 1 þ

pffiffiffiffiffi2 i yI =h

n

(19) Using Eqs. (17)–(19), one can generate the hhwT1 and hwTh curves with constant heat capacities (k1 ¼ 0), as shown in Figs. 2 and 3. It is found that the corresponding performance characteristic

(23)

Substituting Eqs. (3) and (23) into Eq. (1), the overall efficiency of the irreversible solar-driven Carnot heat engine is given by

h



h ¼ saD 1  ITa = Th  D 1 þ

h i 9 ITa ln T2 Dln Th T1 hðT2 T1 Þ = Th T2 T1

; T T T1 hðT2 T1 Þ ðT2 T1 Þ yIDln 2 þDln h T1 Th T2

(21)

pffiffiffiffiffi2 io yI =h

(24)

From Eq. (24), the performance characteristics of the irreversible solar-driven Carnot heat engine can be discussed. In fact, the relevant performance characteristic curves of the irreversible solardriven Carnot heat engine have been shown by the dash lines in Figs. 2 and 3. It can be found from these curves that the performance of the solar-driven Carnot heat engine is an upper bound of that of the solar-driven Braysson heat engine. Furthermore, if letting I ¼ 1, r ¼ 0, and k1 /N and replacing sa, G, U1, U2, and pffiffiffi ð1 þ yÞ2 =h by h0, IC, a, b, and C1, respectively, one can find that Eqs. (23) and (24) in the present paper are consistent with Eqs. (8) and

L. Wu et al. / Renewable Energy 35 (2010) 95–100

0.270

k1=0.003844 J/mol K2

a=36.01 J/mol K

Τh,opt ∼ρ

M2=0.0028

η

max

1200

M2=0.0018

0.3

900

0.2

0.266

1500

Th,opt

η

∼ρ

0.4

a=22.16 J/mol K

0.268

ηmax

0.5

a=29.09 J/mol K

99

600

0.1 0.264 0 960

980

1000 Th/ K

1020

1040

10

20

ρ

30

40

50

Fig. 6. The hmax w r and Th,opt w r curves for differently given values of M2. The values of the related parameters are the same as those used in Fig. 4.

Fig. 4. The h w Th curves for differently given values of a. Curves are presented for k1 ¼ 0.003844 J/(mol K2) and the other parameters are the same as those used in Fig. 2.

(9) in Ref. [1]. This shows once again that the irreversible solardriven Braysson heat engine system with variable heat capacity of the working fluid is a more general one and it is very significant to consider the variation of the heat capacity with temperature in the performance analysis of the solar-driven Braysson heat engine. The influence of the heat capacity parameter a on the performance of the heat engine is shown in Fig. 4. It should be pointed out that the parameter a ¼ 22.16 J/(mol K), 29.09 J/(mol K) and 36.01 J/ (mol K) is chosen in Fig. 4 , because these values correspond to the cases of the monatomic, diatomic and polyatomic gases. It can be seen from Fig. 4 that with the increase of the parameter a, the maximum overall efficiency hmax of the solar-driven Braysson heat engine increases while the optimally operating temperature Th,opt of the collector decreases. 3.3. Influence of internal irreversibility parameter I It is seen from Fig. 5 and Table 1 that the maximum overall efficiency hmax of the solar-driven Braysson heat engine system is a monotonically decreasing function of the internal irreversibility parameter I. This is very natural. The larger the parameter I is, the larger the internal irreversibility of the working fluid, and it will certainly result in the decrease of the overall efficiency of the solardriven heat engine system. Moreover, it can be also found from

I =1.00

0.30 0.28

I=1.10

η

0.26 0.24

I=1.25

900

1000 Th/K

3.4. Influence of the heat losses of the solar collector Fig. 6 shows clearly that both hmax and Th,opt decrease with the increase of the parameter r (¼M1/M2) which depends on the heat losses of the collector. For given parameter M2, the larger the parameter r is, the larger M1 or the radiation heat loss of the solar collector, such that the smaller the overall efficiency of the solardriven Braysson heat engine system. At the same time, it can be also seen from Fig. 6 that for a small M2, the maximum overall efficiency hmax of the solar-driven Braysson heat engine system and the optimally operating temperature Th,opt of the collector decrease with the increase of the parameter r more slowly than those for a large M2. 4. Conclusions

0.22 0.20 800

Table 1 that Th,opt ,T1,opt and T2,opt are monotonically increasing functions of the parameter I, while T3,opt and (A1/A)opt are monotonically decreasing functions of I . It is obvious that decreasing the internal irreversibility of the working fluid will be beneficial to the performance improvement of solar-driven heat engines. For this reason, one should pay great attention to the internal irreversibility in the research of solar-driven heat engines and try to decrease the internal irreversibility as much as possible. It should be pointed out that the parameter I summarily describes various internal irreversibilities which result from the friction, eddy, mass flow resistance and other irreversible effects inside the cyclic working fluid. The physical properties of the different working fluids may cause a difference in the entropy production of the adiabatic processes, such that the internal irreversibility parameters of solar-driven heat engines are generally different. As an example, for a typical power plant heat engine (such as a Rankine cycle engine) the parameter I may take values between 1.1 ðR ¼ 1=I ¼ 0:9Þ and 1.25 ðR ¼ 1=I ¼ 0:8Þ [30]. Thus, a number of researchers usually take I ¼ 1.1 or near 1.1 as one typical analysis in the investigation on the internal irreversibility of heat engine cycles [2,4,9,22,23,30].

1100

1200

Fig. 5. The h w Th curves for differently given values of I, where the values of the related parameters are the same as those used in Fig. 4.

In the present solar-driven Braysson heat engine system, the temperature-dependent heat capacity of the working fluid, the radiation–convection heat losses of the solar collector and the irreversibilities resulting from heat transfers between the working fluid and the reservoirs and non-isentropic compression and expansion processes have been taken into consideration. The maximum overall efficiency of the system and the optimally operating temperature of the solar collector are determined. Some other important

100

L. Wu et al. / Renewable Energy 35 (2010) 95–100

performance parameters such as the temperatures of the cyclic working fluid and ratios of the heat-transfer areas of the heat exchangers are also optimized for a typical set of operating conditions. The influences of the temperature-dependent heat capacity of the working fluid, the radiation–convection heat losses of the solar collector, and the multi-irreversibilities of the heat engine on the performance characteristics of the solar-driven Braysson heat engine system are discussed in detail. The conclusions obtained in the present paper may provide some new guidance for the parametric design of a class of solar-driven heat engines. Acknowledgements This work has been supported by the National Natural Science Foundation (No. 50776074), and the Natural Science Foundation of Fujian Province (No. 2007J0210), PR China References [1] Chen J. Optimization of a solar-driven heat engine. J Appl Phys 1992;72: 3778–80. [2] Ust Y. Effect of combined heat transfer on the thermo-economic performance of irreversible solar-driven heat engines. Renewable Energy 2007;32:2085–95. [3] Koyun A. Performance analysis of a solar-driven heat engine with external irreversibilities under maximum power and power density condition. Energy Convers Manage 2004;45:1941–7. [4] Yilmaz T, Ust Y, Erdil A. Optimum operating conditions of irreversible solar driven heat engines. Renewable Energy 2006;31:1333–42. [5] Sogut O, Durmayaz A. Ecological performance optimisation of a solar driven heat engine. J Energy Inst 2006;79:246–50. [6] Sahin B, Ust Y, Yilmaz T, Akcay I. Thermoeconomic analysis of a solar driven heat engine. Renewable Energy 2006;31(7):1033–42. [7] Badescu V. Optimization of Stirling and Ericsson cycles using solar radiation. Space Power 1992;11:99–106. [8] Chen J, Yan Z, Chen L, Andresen B. Efficiency bound of a solar-driven Stirling heat engine system. Int J Energy Res 1998;22:805–12. [9] Zhang Y, Lin B, Chen J. The unified cycle model of a class of solar-driven heat engines and their optimum performance characteristics. J Appl Phys 2005;97:084905.1–5. [10] Zhang Y, Chen J. The thermodynamic performance analysis of an irreversible space solar dynamic power Brayton system and its parametric optimum design. J Sol Energy Eng 2006;128:409–13.

[11] Zhang Y, Lin B, Chen J. Optimum performance characteristics of an irreversible solar-driven Brayton heat engine at the maximum overall efficiency. Renewable Energy 2007;32:856–67. [12] Sogut O, Durmayaz A. Performance optimization of a solar driven heat engine with finite-rate heat transfer. Renewable Energy 2005;30:1329–44. [13] Davis G, Wu C. Optimal performance of a heat engine-driven-heat pump system utilizing low grade thermal energy. Am Soc Mech Eng, AES 1994;33:271–5. [14] Khaliq A. Finite-time heat-transfer analysis and generalized power-optimization of an endoreversible Rankine heat-engine. Appl Energy 2004;79:27–40. [15] Feng Q, Li S, Zhang L. Engineering thermodynamics. Xian: Northwestern Polytechnical University Press; 2006 [in Chinese]. [16] Zhang N, Cai R, Wang W, Jin H. New near-zero CO2 emission thermal cycles with LNG cryogenic exergy utilization. J Eng Thermophys 2003;24:901–5 [in Chinese]. [17] Frost T, Anderson A, Agnew B. A hybrid gas turbine cycle (Brayton/Ericsson): an alternative to conventional combined gas and steam turbine power plant. Proc Inst Mech Eng Part A 1997;211:121–31. [18] Zheng J, Sun F, Chen L, Wu C. Exergy analysis for a Braysson cycle. Exergy Int J 2001;1:41–5. [19] Zheng J, Chen L, Sun F, Wu C. Power and efficiency performance of an endoreversible Braysson cycle. Int J Therm Sci 2002;41:201–5. [20] Zheng T, Chen L, Sun F, Wu C. Power, power density and efficiency optimization of an endoreversible Braysson cycle. Exergy 2002;2:380–6. [21] Wu C. Intelligent computer aided optimization of power and energy systems. Proc Inst Mech Eng A 1999;213:1–6. [22] Zhou Y, Tyagi S, Chen J. Performance analysis and optimum criteria of an irreversible Braysson heat engine. Int J Therm Sci 2004;43:1101–6. [23] Zheng S, Chen J, Lin G. Performance of an irreversible solar driven Braysson heat engine at maximum efficiency. Renewable Energy 2005;30:601–10. [24] Blank D, Wu C. The effect of combustion on a power optimized endoreversible Diesel cycle. Energy Convers Manage 1993;34:493–8. [25] Chen L, Zeng F, Sun F, Wu C. Heat-transfer effects on net work and/or power as functions of efficiency for air-standard Diesel cycles. Energy 1996;21:1201–5. [26] Akash B. Effect of heat transfer on the performance of an air-standard Diesel cycle. Int Commun Heat Mass Transfer 2001;28:87–95. [27] Zhao Y, Chen J. Optimum performance analysis of an irreversible Diesel heat engine affected by variable heat capacities of working fluid. Energy Convers Manage 2007;48:2595–603. [28] Ge Y, Chen L, Sun F, Wu C. Thermodynamic simulation of performance of an Otto cycle with heat transfer and variable specific heats of working fluid. Int J Therm Sci 2005;44:506–11. [29] Al-Sarkhi A, Al-Hinti I, Abu-Nada E, Akash B. Performance evaluation of irreversible Miller engine under various specific heat models. Int Commun Heat Mass Transfer 2007;34:897–906. [30] Ozkaynak S, Goktun S, Yavuz H. Finite-time thermodynamic analysis of a radiative heat engine with internal irreversibility. J Phys D Appl Phys 1994;27:1139–43.