Performance optimization of a regenerative Brayton heat engine coupled with a parabolic dish solar collector

Energy Conversion and Management 143 (2017) 85–95

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

Performance optimization of a regenerative Brayton heat engine coupled with a parabolic dish solar collector Praveen D. Malali a, Sushil K. Chaturvedi a, Tarek Abdel-Salam b,⇑ a b

Department of Mechanical and Aerospace Engineering, Old Dominion University, Norfolk, VA, USA Department of Engineering, East Carolina University, Greenville, NC, USA

a r t i c l e

i n f o

Article history: Received 18 January 2017 Received in revised form 20 March 2017 Accepted 23 March 2017

Keywords: Brayton heat engine Regenerative Energy conservation Solar thermal power

a b s t r a c t In this study, a detailed thermodynamic analysis of a regenerative Brayton heat engine cycle coupled with a parabolic-dish solar collector is conducted. The analysis examines the thermal performance of the coupled system for power generation applications. Important non-dimensional parameters that govern the optimized performance of the coupled system are identified. The efficiency of the coupled system is expressed in terms of three parameters namely the Brayton cycle pressure ratio, the concentration ratio of the parabolic dish collector, and the maximum temperature ratio of the Brayton cycle. The efficiency of the coupled system is then optimized with respect to the aforementioned parameters by solving the resultant system of three coupled non-linear algebraic equations using a MATLAB(R) program. Optimal values for Brayton cycle pressure ratio, concentration ratio of the parabolic dish collector, and maximum temperature ratio of the Brayton cycle are obtained corresponding to the optimal efficiency of the coupled system. Effects of variation of heat exchanger efficiency, total concentrator error, rim angle and non-dimensional radiation flux parameter on the optimal performance of the coupled system are investigated. Impact of these parameters on the engine size is also presented. In addition, a procedure for preliminary design of the coupled system using performance charts is developed. Results are presented in the form of performance charts that display the effects of changing the heat exchanger efficiency, total concentrator error, rim angle and non-dimensional radiation flux parameter on the optimal efficiency of the coupled system. The analysis show that higher optimal efficiency of the coupled system is achieved for lower values of total concentrator error and higher values of the heat exchanger efficiency. It is also seen that a solar thermal power generation system using the regenerative Brayton cycle results in migration of the optimal efficiency point towards lower values of engine pressure ratio. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction The current interest in solar power conversion system comes from their ability to substantially offset carbon emission from fossil fuel power plants that currently dominate the power generation landscape [1]. Societal concerns about the global climate change and the projected sea-level rise [2] have added urgency to global efforts to reduce dependence on fossil fuels through development of renewable sources for power generation such as solar power plants [3]. Although solar energy is clean and plentiful, converting it into electric power entails two major challenges, namely the low-intensity radiation level, and the intermittency of solar radiation. The former is addressed through concentration of solar radiation by employing focusing collectors while the latter is handled ⇑ Corresponding author. E-mail address: [email protected] (T. Abdel-Salam). http://dx.doi.org/10.1016/j.enconman.2017.03.067 0196-8904/Ó 2017 Elsevier Ltd. All rights reserved.

by embedding an energy storage system for periods when solar radiation is unavailable. The technical feasibility of concentrating solar power plants was first addressed during the early part of the 20th century through development and operation of small capacity solar powered heat engines for irrigation pumps [4]. Availability of inexpensive energy – mostly from fossil fuels – during the major part of the 20th century created a substantial barrier for the development of solar power plants on a commercial scale. The energy crisis of seventies and eighties and sustained rise in energy cost provided a renewed impetus for the development of central solar power plants [5]. With the US department of Energy providing financial incentives for research and development of solar power plant components, the parabolic trough collector technology quickly matured in the eighties and nineties, and as a result several large scale power plants, using parabolic trough collectors and the Rankine steam power cycle, were built and operated [6]. The tower mounted central receiver steam power plants, Solar I and Solar II,

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Nomenclature Aa Ar C Cp Cv h Q_ abs Q_ intercept Q_ loss

Ib k P R S T T3 _ net W

a c e g gc gHEX gsys

aperture area (m2) receiver area (m2) the geometric collector concentration ratio specific heat at constant pressure (J/kg K) specific heat at constant volume (J/kg K) heat transfer coefficient (W/m2 K) heat energy absorbed by the cavity type receiver (W) intercepted heat (W) heat loss per unit time (W) the oncoming direct beam solar radiation (W/m2) ratio of specific heat pressure (N/m2) the Brayton engine pressure ratio entropy (J/kg K) temperature (K) maximum temperature of the Brayton cycle (K) net power output (W) absorptance of the receiver surface intercept factor receiver emittance efficiency (%) compressor efficiency (%) heat exchanger (regenerator) efficiency (%) efficiency of the coupled system (%)

were also built and operated in California’s Mojave Desert. These 10MW(e) size plants used a field of heliostats to focus solar energy on to the receiver which used a molten salt mixture as the heat transfer medium to absorb the concentrated solar radiation [7]. Internationally, several solar steam power plants using both parabolic trough and central tower technologies have been built and operated in Germany and Spain [8]. As noted earlier, the initial thrust of research and development efforts was for using the steam powered Rankine cycle for power generation. However, the maximum operating temperature of the cycle was limited to approximately 600 °C due to material limitation [9]. This severely limited the cycle efficiency. As noted in Ref. [10], significant potential for enhancing thermal engine cycle efficiency exists if gas-based cycles such as Brayton (gas turbine) cycle and Stirling cycle are employed for power generation. Typically these cycles provide efficiency superior to steam power cycles when the peak temperature in these cycles is in the range of 900–1200 °C. A prototype system operating on the Brayton cycle has been built and operated in Spain [11]. In future, thrust will be directed towards development of solar power plants that use regenerative open Brayton cycle due to low costs and high efficiency compared to Rankine cycle [12]. A comparison of Brayton and Rankine power cycles for solar applications has been provided by Hiller [13]. A National Renewable Energy Laboratory report also describes the potential for high efficiency solar power plants, using the high temperature point focus parabolic dish collectors [14]. The gas turbine technology for land-based power plants for peak power utility applications is quite mature. Several manufacturers currently market turnkey systems in the 10– 30 MW(e) power range that can be easily adapted for the solar power generation applications [15]. The thermal efficiency of Brayton cycle can be significantly enhanced with a heat exchanger (regenerator). Optimization of a regenerative Brayton heat engine with respect to regenerator efficiency is performed by Wu et al. [16]. A stand-alone regenerativeintercooled-reheat Brayton heat engine is optimized by Tyagi et al. [17]. Although the optimization of a coupled solar collector and Brayton heat engine is performed in [18], the effects of regenerator efficiency on the performance of the coupled system is ignored.

g sys gt

hH

q

OC Or

rm rsolar rc rt

/

modified efficiency of the coupled system (%) turbine efficiency (%) the maximum temperature ratio of the Brayton cycle mirror surface reflectance non-dimensional convection loss non-dimensional radiation flux mirror slope error solar disk apparent width (m) concentrator tracking error total concentrator error or total rms beam spread (mrad) collector rim angle (degree)

Subscripts 1 compressor inlet conditions 2 actual compressor outlet conditions 2b ideal compressor outlet conditions 3 turbine inlet conditions 4 actual turbine outlet conditions 4b ideal turbine outlet conditions a ambient opt optimum r receiver sky sky

The thermodynamic optimization of a coupled parabolic dish collector and regenerative Brayton cycle is performed for certain dish concentrator diameters by Le Roux et al. [19,20] using the method of entropy generation minimization. Le Roux et al. [21] have optimized a solar thermal regenerative Brayton cycle for a rim angle ð/Þ of 45°. The study [22] of the effect of number of heat exchanger cycles on the optimal performance of a coupled parabolic dish collector and regenerative Brayton cycle shows that a single heat exchanger cycle produces significantly more power output than a double heat exchanger cycle. In this work, the coupled parabolic dish collector and regenerative Brayton heat engine is optimized through the implementation of the first law of thermodynamics. The present work makes contributions to the state of the art by developing a comprehensive analysis that; (a) identifies important non-dimensional parameters that govern the optimized performance of the coupled system; (b) investigates the effects of changing system variables such as heat exchanger efficiency ðgHEX Þ, total concentrator error ðrt Þ, rim angle ð/Þ and a non-dimensional radiation flux parameter ðXr Þ on the optimal performance of the coupled system; (c) presents results in the form of performance charts that display effects of changing the system variables on the optimal modified efficiency of the coupled system, and (d) describes a procedure for preliminary design of the coupled system using the performance charts developed in this study. 2. The regenerative Brayton cycle The regenerative Brayton cycle is shown schematically in Fig. 1 and on a T-s diagram in Fig. 2. The cycle includes a heat exchanger to capture part of the waste heat from the cycle to improve thermal efficiency. The thermal efficiency of the regenerative Brayton cycle is given by the following expression [23].

h

gBrayton

i
 hH gt 1  1R  ðR1Þ gc h  i  ¼
 þ gHEX gt hH 1  1R ð1  gHEX Þ hH  1 þ R1 g c

ð1Þ

P.D. Malali et al. / Energy Conversion and Management 143 (2017) 85–95

87

Fig. 1. Schematic diagram of the regenerative Brayton cycle.

The system configuration investigated is the one in which the solar collector surface provides solar energy to the Brayton power plant only during the period of solar radiation availability. As a result, a storage system is not considered. During the period when solar energy is not available, a parallel loop shown in Fig. 3 supplies the fossil fuel generated thermal energy to the gas turbine combustor to sustain the system operation. It should be noted that in the fossil fuel operation mode, there is no maximum temperature limit requirement except the one arising from the material properties consideration. On the other hand, in the solar mode, the maximum temperature of the power cycle cannot exceed the solar receiver temperature. 2.1. Equations governing the thermal performance of regenerative Brayton cycle coupled to a parabolic dish solar collector

Fig. 2. Temperature-entropy diagram of the regenerative Brayton cycle.

where R ¼

 k1 P2 P1

k

, k ¼ C vpoo ; gt , gc and gHEX are turbine, compressor C

and heat exchanger efficiencies respectively. hH is the maximum temperature ratio based on the maximum temperature ðT 3 Þ of the cycle. In this study we have chosen fixed values of gc = 85%, gt = 90% and k = 1.4 for further analysis of effects of R, hH and gHEX on the cycle thermal efficiency as well as on the coupled system efficiency. One important way to increase the cycle thermal efficiency is to increase the maximum temperature of the cycle ðT 3 Þ. The steam powered Rankine cycle has limited potential for achieving higher efficiency [24]. However, Brayton cycle is operable in a certain range (700–1300 °C) with temperature below the lower limit producing low efficiency, comparable to the Rankine cycle, while the upper limit arises from the material property considerations. The downside of raising the maximum cycle temperature is that solar collector has to harness solar energy at higher temperatures and this leads to greater amount of heat loss from the solar receiver to the ambient. These counteracting tendencies namely, increasing engine efficiency and decreasing solar collector efficiency, suggest an optimal value of hH that would maximize the efficiency of the coupled system. The Brayton cycle efficiency also shows a maximum efficiency point with respect to the engine pressure ratio ðRÞ for a given hH . These two problems are coupled through hH . Finally, increasing the dish collector concentration ratio ðCÞ for a fixed receiver area, directs more solar radiation on to the receiver. However, greater spillage of directed energy results in less energy being intercepted, and consequently the net radiation collected and directed to the Brayton heat engine shows a maximum with the concentration ratio ðCÞ. This particular optimization is with respect to two variables namely hH and C. Consequently, the optimization of the coupled system efficiency is with respect to three variables namely R, hH and C.

A two-axis tracking parabolic dish collector, Fig. 3, is the source of thermal energy for the regenerative Brayton cycle power plant. The oncoming direct beam solar radiation ðIb Þ is attenuated due to several effects, namely the mirror surface reflectance ðqÞ as well as dispersion due to mirror slope error ðrm Þ, concentrator tracking error ðrc Þ and solar disk apparent width ðrsolar Þ. Dispersion of the focused solar beam due to these effects can be combined into a single parameter called the total rms beam spread or total concentrator errorc ðrt Þ, if one assumes that these dispersion errors can be characterized by a Gaussian distribution [25]. The intercept factor ðcÞ characterizes the loss of beam radiation due to the receiver not being able to capture all the incoming solar radiation in the collector plane. This is purely a geometrical effect that is characterized by the relative positioning of the reflector surface and the receiver. For the parabolic dish collectors, the intercept factor ðcÞ is a function of r2t C and the collector rim angle ð/Þ [25]. The absorption of radiation by the receiver would depend on the absorptance ðaÞ of the receiver surface. The heated receiver loses energy to surrounding through radiation, characterized by the receiver emittance ðeÞ, and convection characterized by the convective heat transfer coefficient ðhÞ. The net energy absorbed by the cavity type receiver can be expressed as,

Q_ abs ¼ Q_ intercept  Q_ loss Q_ abs ¼ Ib cqaCAr  erAr ðT 4r  T 4a Þ  hAr ðT r  T a Þ

ð2Þ

where Ar is the receiver area, T r is the receiver temperature, T a is the ambient air temperature, and C is the geometric concentration ratio defined as Aa =Ar , where Aa is the aperture area. In general, the radiation loss is characterized by the sky temperature ðT sky Þ. In this study we have made the assumption that T sky ¼ T a , the ambient air temperature. Assuming that there are no further heat losses as the heated air is transported from the receiver to the turbine inlet section, one can set T H ¼ T r in Eq. (2). The coupled system efficiency ðgsys Þ is

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Fig. 3. Schematic of a regenerative Brayton heat engine couple with a two-axis tracking parabolic dish collector.

determined by combining the Brayton cycle efficiency and solar collection Eqs. (1) and (2).

gsys ¼

Net Power Output Solar Radiation Av ailable in the Collector Plane

gsys

_ net W ¼ Ib CAr

gsys

_ net Q_ abs W ¼  _ Q abs Ib CAr 3 4 ðh  1Þ ðh  1Þ H ¼ qagBrayton 4c  HI aq  I aq 5 be C rbTe 4 C hT a a

The above equation can be expressed as,

g sys ¼

  sys @g ¼0 @R hH ;C

ð7Þ

  sys @g ¼0 @C R;hH

ð8Þ

c ¼ ð3:716  r4t C 2 Þ  ð0:35  r2t CÞ þ 1:0095; for / ¼ 60

gsys qa "

g sys ¼ gBrayton c 

ðh4H  1Þ ðhH  1Þ  C Xr C Xc

ð3Þ

Xr ¼ Ib aq=erT 4a is the non-dimensional radiation flux parameter, and Xc ¼ Ib aq=ehT a is the non-dimensional convection loss param-

eter. The intercept factor ðcÞ is a function of r2t C and the collector rim angle ð/Þ. The Brayton cycle efficiency ðgBrayton Þ is a function of R,hH , gt , gc , gHEX and k (Eq. (1)). For a given value of gc ð¼ 0:85Þ, gt ð¼ 0:9Þ and kð¼ 1:4Þ and since c is a function of C and rt , one can express Eq. (3) symbolically as,

g sys ¼ f ðhH ; R; gHEX ; C; rt ; Xr ; Xc Þ

ð4Þ

The values of gHEX and rt were changed parametrically from 0 to 0.9, and 7 mrad to 20 mrad respectively. A value of Xc equal to 0.06 was used for calculations while the non-dimensional radiation flux parameter Xr was varied between values 1.4 to 4.7.  sys with respect to hH , R and C variations, The optimal values of g for a given gHEX , rt , Xr and Xc is determined by applying the following equation.

" #    sys  sys  sys @g @g @g dhH þ dR þ dC ¼ 0 @hH R;C @R hH ;C @C R;hH

ð5Þ

ð9aÞ

c ¼ ð970:7  ðr2t CÞ Þ þ ð504:76  ðr2t CÞ Þ  ð82:67  ðr2t CÞ Þ ð9bÞ þ ð1:3674  r2t CÞ þ 0:9976; for / ¼ 30 4

#

 sys is the modified efficiency of the coupled system, where g

 sys ¼ dg

ð6Þ

Using exact results in graphical form from Ref. [24], a second order equation is obtained which provides an additional relationship between c and r2t C for certain collector rim angle ð/Þ. Eqs. (9a) and (9b) presented below are for two collector rim angles / = 60° and 30° which are both examined in this study.

2

gsys

This results in the following three equations.

  sys @g ¼0 @hH R;C

3

2

Eqs. (6)–(9) represent a system of four non-linear algebraic equations in four unknowns, namely ðhH Þopt , Ropt , C opt and copt . Eqs. (6)–(8), after differentiation can be expressed as follows.

a0 ðgHEX ; hH ÞR2 þ b0 ðgHEX ; hH ÞR þ c0 ðgHEX ; hH Þ ¼ 0

ð10Þ

a1 ðR; C; gHEX ; rt ; Xr ; Xc Þh5H þ b1 ðR; C; gHEX ; rt ; Xr ; Xc Þh4H þ c1 ðR; C; gHEX ; rt ; Xr ; Xc Þh3H þ d1 ðR; C; gHEX ; rt ; Xr ; Xc ÞhH þ ðR; C; gHEX ; rt ; Xr ; Xc Þ ¼ 0 dc ðh4H  1Þ ðhH  1Þ þ ¼0 þ dC C 2 Xr C 2 Xc

ð11Þ ð12Þ

3. Solution procedure Eqs. (9)–(12) govern the four unknowns hH , R, C and c. The coefficients in these equations are functions of variables listed in parenthesis. Solution of these equations, for given values of gHEX , rt , Xr and Xc yields the optimal values of hH , R, C and c thus max sys Þ. A MATLAB imizing the modified coupled system efficiency ðg

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P.D. Malali et al. / Energy Conversion and Management 143 (2017) 85–95

program was developed to solve Eqs. (9)–(12) iteratively. Initially, the values of all the parameters except hH , R, C and c are specified. The solution procedure is implemented by employing two nested iterative loops, the outer one for C and the inner one for hH . First, for certain values of C and hH , using Eqs. (9) and (10) values of c and R are calculated. Using these values, the 5th order equation (Eq. (11)) is solved to obtain the updated value of hH . Using this the updated value of C is calculated by solving Eq. (12). The procedure is repeated until the difference between the C and hH values of th

th

the i and ði  1Þ iteration equals 0.0001. This procedure worked very well for the zero heat exchanger efficiency case. However, for other heat exchanger efficiency cases, this method became very tedious due to unwieldy forms of coefficients a0 , b0 , c0 . . ..etc. that themselves involve dozens of terms. Consequently, for these cases an alternative method using Eq. (3) in conjunction with Eqs. (9), (10) and (12) was used. In this method, as in the case of the previous method, two nested iterative loops for C and hH values were used. The value of C is changed in the range of 200–20,000 in steps of 1. For a given value of C (the outer loop), and for an initially  sys Þ are calculated assumed value of hH , the parameters R, c and ðg from Eqs. (12), (10) and (3). The value of hH is changed continu sys Þ is detected. At this point, ously until a maximum value of ðg  sys Þ are calcuthe C value is changed in steps of one, and R, c and ðg lated by implementing the inner loop for hH . This process is contin sys Þ with respect to C is identified. This ued until a maximum in ðg results in ðhH Þopt , Ropt , C opt and copt (from Eq. (12)) being determined  sys Þ. This procedure is repeated along with the optimum value of ðg for other values of parameters such as gHEX , rt , / and Xr to generate performance charts for the coupled system.

4. Results and discussion Results consisting of numerical values for key design parame sys Þopt , ters such as optimal modified coupled system efficiency, ðg net work, wnet , optimal temperature ratio, ðhH Þopt , optimal pressure

ratio, Ropt , and optimal concentration ratio, C opt , are presented in this section. These results are obtained from simulations by varying values of parameters (shown below) such as total concentrator error ðrt Þ, heat exchanger efficiency ðgHEX Þ, rim angle ð/Þ and nondimensional radiation flux parameter ðXr Þ.

rt = f7; 10; 15; 20g mrad gHEX = f0; 0:5; 0:75; 0:9g / = f60; 30g degrees Xr = f1:4; 1:8; 2:8; 4:7g  sys Þopt , wnet , ðhH Þopt , Ropt and C opt when the aforeVariation of ðg mentioned parameters are varied is discussed in subsequent sections. Convective heat loss from the collector cavity were included in the simulation. Using the dimensional correlation [26] and assuming a wind velocity of 1 m/s, a heat transfer coefficient ðhÞ of 36 W/K m2 is used in the simulation.  sys Þopt vs. ðhH Þopt for / = 60° and aforemenThe variation of ðg

tioned values of rt and gHEX is shown in the optimized performance chart in Fig. 4. For a given value of rt one observes a significant improvement in the optimal modified coupled system efficiency when heat exchanger efficiency is increased from zero (no heat exchanger) to 0.9. It is also observed that higher modified efficiency of the coupled system is achieved when rt values are low. For instance, a collector with rt = 20 mrad, generates unacceptable  sys Þopt ranging from 0.16 to 0.24, as gHEX level of performance with ðg is increased from zero to 0.9. This is primarily due to the fact that optimal maximum temperature of the cycle is well below the level needed for superior performance. The variation of wnet vs. ðhH Þopt for / = 60° and aforementioned values of rt and gHEX is shown in the optimized performance chart in Fig. 5. It is to be noted that higher values of rt result in low values of wnet which has implication for engine size since low wnet would require higher mass flow rates for a given net power output _ net . With increasing g , wnet shows a slight decrease regardless W of the

HEX

rt value.

Ωr = 1.4; φ = 60 deg

0.4

σt = 7 mrad σt = 10 mrad

0.35

σt = 15 mrad σt = 20 mrad

0.3

ηHEX = 0.0 0.25

ηHEX = 0.5 0.2

ηHEX = 0.75 ηHEX = 0.9

0.15 2.75

3.25

3.75

4.25

 sys Þopt vs. ðhH Þopt for different values of Fig. 4. Variation of ðg

4.75

rt and gHEX .

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1.00

Ωr = 1.4; φ = 60 deg

σt = 7 mrad

0.90

σt = 10 mrad 0.80

σt = 15 mrad 0.70

σt = 20 mrad 0.60

ηHEX = 0.0 0.50

ηHEX = 0.5 0.40

ηHEX = 0.75 0.30

ηHEX = 0.9 0.20 2.75

3.25

3.75

4.25

Fig. 5. Variation of wnet vs. ðhH Þopt for different values of

4.75

rt and gHEX .

ing from 1.85 to 2.45 for values of rt ranging from 20 mrad to 7 mrad. This translates into compressor pressure ratio ranging from about 8.0 to 23. This implies larger number of compressor and turbine stages for the simple Brayton cycle as compared to the regenerative Brayton cycle with heat exchanger effectiveness. This factor coupled  sys Þopt values make the simple Brayton cycle an unattracwith low ðg

Fig. 6 shows the variation of ðhH Þopt with Ropt for different values of

rt and gHEX . One notes that for a given rt value, ðhH Þopt decreases only slightly as gHEX is increased from zero value to 0.9. This trend persists for all values of rt . However, Ropt value for a fixed rt is significantly impacted by an increasing value of gHEX . For instance, for rt = 7 mrad, Ropt decreases from 2.45 to 1.38, a decrease of approximately 44 percent. This has implications for decreased number of compressor as well as turbine stages. In fact, one observes that Ropt values for a simple Brayton cycle with no regenerator are typically quite high, rang-

tive option for solar power generation applications.  sys Þopt The performance chart in Fig. 7 shows the variation of ðg with optimal concentration ratio (C opt ). It can be noted from the

5

Ωr = 1.4; φ = 60 deg

σt = 7 mrad σt = 10 mrad

4.5

σt = 15 mrad 4

σt = 20 mrad ηHEX = 0.0

3.5

ηHEX = 0.5 3

ηHEX = 0.75 ηHEX = 0.9

2.5 1.1

1.3

1.5

1.7

1.9

2.1

Fig. 6. Variation of ðhH Þopt vs. Ropt for different values of

2.3

rt and gHEX .

2.5

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P.D. Malali et al. / Energy Conversion and Management 143 (2017) 85–95

Ωr = 1.4; φ = 60 deg

σt = 7 mrad

0.4

σt = 10 mrad 0.35

σt = 15 mrad

σt = 20 mrad

0.3

ηHEX = 0.0 0.25

ηHEX = 0.5 0.2

ηHEX = 0.75

ηHEX = 0.9 0.15

0

500

1000

1500

2000

2500

 sys Þopt vs. C opt for different values of Fig. 7. Variation of ðg

3000

rt and gHEX .

0.37

Ωr = 1.4; φ = 30 deg

σt = 7 mrad

0.32

σt = 10 mrad σt = 15 mrad

0.27

σt = 20 mrad 0.22 ηHEX = 0.0 0.17 ηHEX = 0.5 0.12

0.07 2.30

ηHEX = 0.75 ηHEX = 0.9 2.80

3.30

3.80

 sys Þopt vs. ðhH Þopt for different values of Fig. 8. Variation of ðg

 sys Þopt values are obtained for lower figure that higher ðg

rt values

and higher gHEX values. When, for gHEX = 0.9, the value of rt is  sys Þopt drops from a high of increased from 7 mrad to 20 mrad, ðg

nearly 40% to a low value of about 24%, a decrease of nearly 40%. The corresponding value of C opt drops from nearly 2300 to about 370, a decrease of about 80%. It is also evident from Fig. 7 that C opt value is not significantly affected by gHEX value. In summary, higher coupled system efficiency is achieved by employing: (a.) a high efficiency heat exchanger and (b.) a mirror surface with a

4.30

rt , gHEX and for / = 30°.

low total concentrator error. This in turn implies that high concentration ratio solar concentrator along with lower pressure ratio Brayton engine must be employed to achieve high ðhH Þopt values  sys Þopt values. that are consistent with higher ðg Although, similar trends are observed in the results for / = 30°,  sys Þopt and wnet are when compared to / = 60° case, the values of ðg

consistently lower for the chosen values of rt and gHEX (Figs. 8 and 9). This is due to lower values of intercept factor for / = 30° case compared to the / = 60° case. Also, range of hH increases typically

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0.6 σt = 7 mrad

Ωr = 1.4; φ = 30 deg

σt = 10 mrad

0.5

σt = 15 mrad 0.4 σt = 20 mrad ηHEX = 0.0

0.3

ηHEX = 0.5 0.2 ηHEX = 0.75

0.1 2.4

ηHEX = 0.9 2.7

3.0

3.3

3.6

Fig. 9. Variation of wnet vs. ðhH Þopt for different values of

within 20% for / = 60° when compared with / = 30° for the chosen  sys Þopt and wnet values in the case of / = 30° parameters. The low ðg must be compensated by using a mirror surface with a low total concentrator error. As mentioned earlier, the non-dimensional radiation flux parameter ðXr Þ was also varied. For gHEX = 0.75, the variation of  sys Þopt with Xr for different values of rt is shown in Fig. 10. ðg

It is noted that for a given heat exchanger efficiency and rt value, when Xr is increased in the range of 1.4–4.7, the value of  sys Þopt increases typically in the range of 15–25 percent dependðg

ing on the chosen rt value. Also, for a certain value of Xr , lowering  sys Þopt , a behavior also the rt value increases the value of ðg observed in Fig. 4.

3.9

4.2

rt , gHEX and for / = 30°.

This study also considers the effect of convective heat loss from the solar collector cavity on the optimal coupled system efficiency values. Fig. 11 shows results from simulations that were performed with and without convective loss by changing the value of heat transfer coefficient ðhÞ from 36 W/m2 (with convective loss) to 0 W/m2 (without convective loss). It is noted from Fig. 11, that for rt = 10 mrad, gHEX = 0.75 and / = 60°, the  sys Þopt value increases with increasing Xr for cases with ðg 2

2

ðh ¼ 36 W=km Þ and without ðh ¼ 0 W=km Þ convective heat loss. A higher value of Xr implies a higher value of Ib , a, q and a lower  sys Þopt values for the case of without convective value of . The ðg loss are relatively higher compared to the case of with convective  sys Þopt value is loss for a given Xr . For instance, when Xr = 4.7, the ðg

0.45

ηHEX = 0.75; φ = 60 deg 0.40

σt = 7 mrad 0.35

σt = 10 mrad 0.30

σt = 15 mrad 0.25

σt = 20 mrad

0.20

0.15

1

1.5

2

2.5

3

3.5

4

4.5

5

Ωr  sys Þopt vs. Xr for gHEX = 0.75 and different values of Fig. 10. Variation of ðg

rt .

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0.39

σt = 10 mrad; ηHEX = 0.75; φ = 60 deg 0.37

0.35

h = 0 W/Km2 0.33

0.31

h = 36 W/Km2 0.29

0.27

1

1.5

2

2.5

3

3.5

4

4.5

5

Ωr  sys Þopt vs. Xr with and without convective loss. Fig. 11. Variation of ðg

0.35 and 0.38 for the cases of with and without convective loss respectively. It is also seen from Fig. 11 that at higher values of Xr (lower level of radiation loss), the convective heat losses  sys Þopt as compared to lower values have a greater impact on ðg of Xr . 5. Design procedure for the coupled parabolic dish collector and Brayton heat engine cycle power generation system In this section, a brief procedure to compute optimal and nonoptimal performance of the power generation system using performance charts is provided. In the case of non-optimal performance, the chart is used for a fixed (chosen) value of the concentration ratio. However, in the case of optimal performance, the chart is used to obtain the optimal value of the concentration ratio. Also, a numerical example is provided to illustrate the usefulness of the performance charts. The procedure is encapsulated in the flow chart shown in Fig. 12. (I) Procedure for non-optimal performance. a. Specify location dependent parameters such as direct beam solar radiation ðIb Þ, ambient temperature ðT a Þ. Consider T a = 300 K and Ib = 800 W/m2. b. Specify concentrator parameters such as emittance ðeÞ, absorptance ðaÞ, mirror surface reflectance ðqÞ, concentration ratio ðCÞ, total concentrator error ðrt Þ and rim angle ð/Þ. Consider e = 0.99, a = 0.9, q = 0.9, C = 1500, rt = 7 mrad and / = 60°. c. Compute the intercept factor ðcÞ for the chosen rim angle ð/Þ using Eq. (9), concentration ratio ðCÞ and total concentrator error ðrt Þ. Therefore, intercept factor ðcÞ = 0.96. d. Include convective loss by considering a heat transfer coefficient ðhÞ value of 36 W/Km2. e. For the chosen concentrator and location dependent parameters compute the non-dimensional radiation flux parameter ðXr Þ and the non-dimensional convection loss parameter ðXc Þ. The values for the non-dimensional parameters are Xr = 1.4 and Xc = 0.06.

f. Based on ambient temperature ðT a Þ, specify the maximum temperature ðT 3 Þ of the cycle. Compute the temperature ratio ðhH Þ. Let the maximum temperature of the cycle be T 3 = 1230 K. Therefore, maximum temperature ratio hH = 4.1. g. Choose pressure ratio ðRÞ. Let R = 1.2. h. Choose heat exchanger efficiency, gHEX . Let gHEX = 0.75. i. Calculate the coupled system efficiency ðgsys Þ and net work output ðwnet Þ. The values are gsys = 0.20 and wnet = 0.38. (II) Procedure for optimal performance. a. Specify location dependent parameters such as direct beam solar radiation ðIb Þ, ambient temperature ðT a Þ. Consider T a = 300 K and Ib = 800 W/m2. b. Specify concentrator parameters such as emittance ðeÞ, absorptance ðaÞ, mirror surface reflectance ðqÞ, total concentrator error ðrt Þ and rim angle ð/Þ. Consider e = 0.99, a = 0.9, q = 0.9, rt = 7 mrad and / = 60°. c. Specify heat exchanger efficiency ðgHEX Þ. Let gHEX = 0.75. d. Using the performance charts, find optimal concentration ratio ðC opt Þ. From Fig. 7, C opt = 2398.5. e. Compute the optimal intercept factor ðcopt Þ for the chosen rim angle ð/Þ using the second order equation, optimal concentration ratio ðC opt Þ and total concentrator error ðrt Þ. Using Eq. (9), the optimal intercept factor, copt = 0.917. f. Include convective loss by considering a heat transfer coefficient ðhÞ value of 36 W/Km2. g. For the chosen concentrator and location dependent parameters compute the non-dimensional radiation flux parameter ðXr Þ and the non-dimensional convection loss parameter ðXc Þ. The values for the non-dimensional parameters are Xr = 1.4 and Xc = 0.06. h. Using the performance charts, find optimal modified cou sys Þopt , optimal coupled system effipled system efficiency, ðg ciency, ðgsys Þopt , net work, wnet , optimal temperature ratio,

ðhH Þopt , and optimal pressure ratio, Ropt . From Figs. 4, 5 and  sys Þopt = 0.34, ðgsys Þ = 0.28, 6, the optimal values are ðg opt wnet = 0.81, ðhH Þopt = 4.5 and Ropt = 1.6.

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Fig. 12. Flow chart for preliminary design procedure for non-optimal and optimal performance of the coupled system.

6. Conclusion Thermodynamic analysis of a solar thermal power generation system involving a coupled parabolic dish collector and a regenerative Brayton cycle is performed in this study. Results indicate that higher optimal efficiency of the coupled system is achieved for lower values of total concentrator error ðrt Þ and higher values of the heat exchanger efficiency ðgHEX Þ. Higher values of total concentrator error produces a very low optimal efficiency in the range of 15–20% – a performance level which is inferior even when compared to that of a system operating on the Rankine cycle. Also, higher values of rt results in low values of net work ðwnet Þ thus requiring higher mass flow rates for a given net power output _ net . It is also seen that a solar thermal power generation system W using the regenerative Brayton cycle results in the migration of the optimal efficiency point towards lower values of engine pressure ratio. This is in contrast with the case of basic Brayton heat engine (without heat exchanger) in which not only is the optimal efficiency much lower but it also occurs at much higher engine pressure ratio. This translates into much larger number of compressor and turbine stages when compared to a system configuration with a high efficiency heat exchanger.

Reduction in rim angle (/Þ is shown to have adverse effect on both the optimal efficiency of the coupled system and net work. However, these adverse effects can be mitigated by using a mirror with a lower total concentrator error. Analysis of effects of convective loss on the coupled system performance shows that increase in convective loss can lead to a moderate drop in the optimal efficiency of the coupled system. More importantly, the nondimensional radiation flux parameter ðXr Þ effectively combines several solar collector parameters such as direct beam solar radiation ðIb Þ, mirror surface reflectance ðqÞ, absorptance ðaÞ, emittance ðeÞ and ambient temperature ðT a Þ. The results show that the optimal coupled system efficiency increases for an increasing Xr . Finally, the coupled system design procedure described in the discussion section shows that the performance charts, developed as part of this study, can be used to obtain optimal values for engine pressure ratio ðRÞ, collector concentration ratio ðCÞ, maximum temperature ratio ðhH Þ, coupled system efficiency ðgsys Þ and net work ðwnet Þ for the chosen total concentrator error ðrt Þ, heat exchanger efficiency ðgHEX Þ, rim angle ð/Þ and non-dimensional radiation flux parameter ðXr Þ. These optimal values can then be used to generate a preliminary design plan for a coupled parabolic dish collector and regenerative Brayton cycle power generation system.

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References [1] Chen L, Zhang W, Sun F. Power, efficiency, entropy-generation rate and ecological optimization for a class of generalized irreversible universal heatengine cycles. Appl Energy 2007;84:512–25. [2] Church JA, White NJ. A 20th century acceleration in global sea-level rise. Geophys Res Lett 2006;33:L01602. [3] Kuravi S, Trahan J, Goswami DY, Rahman MM, Stefanakos EK. Thermal energy storage technologies and systems for concentrating solar power plants. Prog Energy Combust Sci 2013;39(4):285–319. [4] Pytlinski JT. Solar energy installations for pumping irrigation water. Sol Energy 1978;21(4):255–62. [5] Behar O, Khellaf A, Mohammedi K. A review of studies on central receiver solar thermal power plants. Renew Sustain Energy Rev 2013;23:12–39. [6] Tchanche BF, Lambrinos G, Frangoudakis A, Papadakis G. Low-grade heat conversion into power using organic Rankine cycles – a review of various applications. Renew Sustain Energy Rev 2011;15(8):3963–79. [7] Radosevich LG, Skinrood AC. The power production operation of solar one, the 10 MWe Solar Thermal Central Receiver Pilot Plant. Trans ASME J Sol Energy Eng 1989;111(2):144–51. [8] Herrmann U, Kearney DW. Survey of thermal energy storage for parabolic trough power plants. Trans ASME J Sol Energy Eng 2002;124(2):145–52. [9] Narendra S, Kaushik SC, Misra RD. Exergetic analysis of a solar thermal power system. Renewable Energy 2000;19:135–43. [10] Poullikkas A. An overview of current and future sustainable gas turbine technologies. Renew Sustain Energy Rev 2005;9(5):409–43. [11] Mills D. Advances in solar thermal electricity technology. Sol Energy 2004;76 (1–3):19–31. [12] Schwarzbozl P, Buck R, Sugarmen C, Ring A, Crespo MJM, Altwegg P, et al. Solar gas turbine systems: design, cost and perspectives. Sol Energy 2006;80 (10):1231–40. [13] Hiller CC. Introductory comparison of Brayton and Rankine power cycles for central solar power generation Report No. SAND-78-8010. Sandia National Laboratories; 1978.

95

[14] Sargent and Lundy Consulting Group. Assessment of parabolic trough and power tower solar technology cost and performance forecasts. National Renewable Energy Laboratory; 2003. [15] Romero-Alvarez M, Zarza E. Concentrating solar thermal power. Handbook Energy Efficiency Renew Energy 2007;21:1–98. [16] Wu C, Chen L, Sun F. Performance of a regenerative Brayton heat engine. Energy 1996;21(2):71–6. [17] Tyagi SK, Chen GM, Wang Q, Kaushik SC. Thermodynamic analysis and parametric study of an irreversible regenerative-intercooled-reheat Brayton cycle. Int J Therm Sci 2006;45:829–40. [18] 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. [19] Le Roux WG, Bello-Ochende T, Meyer JP. Thermodynamic optimization of the integrated design of a small-scale solar thermal Brayton cycle. Int J Energy Res 2011;36:1088–104. [20] Le Roux WG, Bello-Ochende T, Meyer JP. Operating conditions of an open and direct solar thermal Brayton cycle with optimized cavity receiver and recuperator. Energy 2011;26:6027–36. [21] Le Roux WG, Bello-Ochende T, Meyer JP. The efficiency of an open-cavity tubular solar receiver for a small-scale solar thermal Brayton cycle. Energy Convers Manage 2014;84:457–70. [22] Jansen E, Bello-Ochende T, Meyer JP. Integrated solar thermal Brayton cycles with either one or two regenerative heat exchangers for maximum power output. Energy 2015;86:737–48. [23] Decher R. Energy conversion: systems, flow physics and engineering. Oxford University Press; 1994. [24] Leibowitz LP, Hanseth EJ, Peelgreen ML. High temperature solar thermal technology. In: ASME Solar Energy division. Winter Annual Meeting, Chicago, Illinois. [25] Bendt P, Rabl A, Gaul HW, Redd KA. Optimization of line focus solar collectors. Solar Energy Research Institute Report; 1979. SERI/TR-34-092. [26] Martin Marietta Company, Central Receiver Solar Thermal Power System, Phase I: Preliminary Design Report, SAN/1110-77-2; 1977.