Optimization of low temperature solar thermal electric generation with Organic Rankine Cycle in different areas

Optimization of low temperature solar thermal electric generation with Organic Rankine Cycle in different areas

Applied Energy 87 (2010) 3355–3365 Contents lists available at ScienceDirect Applied Energy journal homepage: www.elsevier.com/locate/apenergy Opti...

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Applied Energy 87 (2010) 3355–3365

Contents lists available at ScienceDirect

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

Optimization of low temperature solar thermal electric generation with Organic Rankine Cycle in different areas Li Jing, Pei Gang *, Ji Jie ** Department of Thermal Science and Energy Engineering, University of Science and Technology of China, Jinzhai Road 96#, Hefei City, Anhui Province, People’s Republic of China

a r t i c l e

i n f o

Article history: Received 19 October 2009 Received in revised form 5 May 2010 Accepted 10 May 2010 Available online 12 June 2010 Keywords: Solar thermal electric generation Compound parabolic concentrator Organic Rankine Cycle

a b s t r a c t The presented low temperature solar thermal electric generation system mainly consists of compound parabolic concentrators (CPC) and the Organic Rankine Cycle (ORC) working with HCFC-123. A novel design is proposed to reduce heat transfer irreversibility between conduction oil and HCFC-123 in the heat exchangers while maintaining the stability of electricity output. Mathematical formulations are developed to study the heat transfer and energy conversion processes and the numerical simulation is carried out based on distributed parameters. Annual performances of the proposed system in different areas of Canberra, Singapore, Bombay, Lhasa, Sacramento and Berlin are simulated. The influences of the collector tilt angle adjustment, the connection between the heat exchangers and the CPC collectors, and the ORC evaporation temperature on the system performance are investigated. The results indicate that the three factors have a major impact on the annual electricity output and should be the key points of optimization. And the optimized system shows that: (1) The annual received direct irradiance can be significantly increased by two or three times optimal adjustments even when the CPC concentration ratio is smaller than 3.0. (2) Compared with the traditional single-stage collectors, two-stage collectors connected with the heat exchangers by two thermal oil cycles can improve the collector efficiency by 8.1–20.9% in the simultaneous processes of heat collection and power generation. (3) On the use of the market available collectors the optimal ORC evaporation temperatures in most of the simulated areas are around 120 °C. Ó 2010 Elsevier Ltd. All rights reserved.

1. Introduction Thermal electric generation is one of the most important ways to utilize solar energy. In the past 20 years many solar plants have been built, such as the American SEGS. With 354 MW of installed capacity, parabolic troughs represent the most mature solar thermal electric technology [1]. In most of the present large solar thermal electric plants, steam Rankine cycle is preferred. One of the problems is that when the steam temperature drops below 370 °C the thermal efficiency becomes uneconomically low [2]. Therefore, in order to use solar energy at sufficient temperature ranges for the application of steam Rankine cycle high concentration ratio collectors are required. There are several disadvantages: (1) Tracking system is needed. (2) High concentrated systems collect little diffuse radiation. (3) A number of technical difficulties have to be overcome for high temperature heat storage. (4) The plants have to be large to be economic. Low temperature solar thermal electric generation would be able to overcome the above disadvantages by using the Organic * Corresponding author. Tel./fax: +86 551 3601641. ** Corresponding author. Tel./fax: +86 551 3601641. E-mail addresses: [email protected] (P. Gang), [email protected] (J. Jie). 0306-2619/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2010.05.013

Rankine Cycle (ORC). The ORC is named for its use of an organic, high molecular mass fluid that boils at a lower temperature than the water. Among many well-proven technologies the ORC is one of the most favorable and promising ways in low temperature applications. Compared with the steam Rankine cycle, the ORC has the ability to scale to smaller unit sizes and higher efficiencies during cooler ambient temperatures, immunity from freezing at cold winter nighttime temperatures, and the adaptability to conduct semi-attended or unattended operations [3]. In the case of a dry fluid, ORC can be used at lower temperatures and does not require superheating. This results in a practical increase in efficiency over the use of the cycle with water as the working fluid [4]. The ORC can be easily modularized and used in conjunction with various heat sources. The feasibility of the ORC technology is reinforced by the high technological maturity of most of its components, due to their extensive use in refrigeration applications [5]. The advantage of ORC for low temperature heat sources is obvious because of the more limited (in comparison to steam) volume ratio of the working fluid at the turbine outlet and inlet. This can be smaller by an order of magnitude for organic fluids than for water and hence allows the use of simpler and cheaper turbines [6]. A number of theoretical and experimental studies have been reported on the ORC for the utilization of industry waste as well as

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Nomenclature A B C Cp D G h m Nu Pr p P Q Re S T U  h v W x Y d

e / u

the first heat loss coefficient, W m2 °C1 the second heat loss coefficient, W m2 °C2 concentration ratio heat capacity, J kg1 °C1 diameter, m insolation, W m2 enthalpy, J kg1 mass ratio, kg s1 Nusselt number Prandtl number pressure, Pa power J heat, J kg1 Reynolds number collector area, m2 temperature, °C total heat transfer coefficient, W m2 °C1 heat transfer coefficient, W m2 °C1 specific volume, m3 kg1 power, J kg1 dryness length, m declination angle machine efficiency the height of sun latitude

geothermal heat sources, which can range from low temperatures of about 100 °C to medium temperatures of about 300 °C [7–12]. Yamamoto et al. designed and tested an experimental ORC. A micro-turbine and nozzle were made in order to discuss the optimum design of the turbine blade shape. It was concluded from the experimental results that the ORC could be applied to low-grade heat sources and HCFC-123 was able to improve the ORC performance significantly [13]. Badr et al. created a prototype expander by modifying an existing multi-vane pump. The expander underwent a reverse process of pumping and achieved an isentropic efficiency more than 73% [14]. James et al. presented an experimental testing of relatively cost-effective gerotor and scroll expanders. The gerotor and scroll expanders produced 2.07 kW and 2.96 kW, and had isentropic efficiencies of 0.85 and 0.83. It was determined that both expanders had significant potential to produce power from lowgrade energy [15]. Vincent and Sylvain et al. carried out an experimental study on a prototype of an open-drive oil-free scroll expander integrated into an ORC working with refrigerant HCFC123. The maximum delivered shaft power was 1.82 kW and the maximum achieved overall isentropic effectiveness is 68%. The experimental study demonstrated the viability of utilizing a mass-produced compressor as an expander in a small scale ORC [16,17]. It should be emphasized that ORC plants already exist and are commercially available in the MW power range. Examples are the plants in Altheim, Austria and in Lengfurt and Neustadt-Glewe, Germany [18,19]. The ORC plants have very low maintenance costs and by choosing an appropriate working fluid the process could be adjusted to the conditions on both the hot and the cold sides of the plant, thus achieving maximum efficiency [20]. Barbier declared that binary power plant technology with ORC had emerged as the most cost-effective and reliable way to convert large amounts of low temperature geothermal resources into electricity [21]. Both the literatures and practical examples have demonstrated that a temperature about 100 °C or somewhat higher could be sufficient for the ORC-processes. It is well-founded to choose small

c g a h

q x w f

incident angle efficiency heat capacity coefficient, J kg1 °C2 collector tilt angle density, kg m3 solar time azimuth direct irradiance increment

Subscripts 1, 2, 3, 4, 5 state point a environment b direct irradiance c CPC d diffuse irradiance f organic fluid g generator h heat transfer fluid i inlet m average n integer o outlet p pump s system t thermal/turbine

concentration ratio collectors for the solar ORC application. Compound parabolic concentrators (CPC) are non-imaging concentrators. Their potential as collectors of solar energy was pointed out by Winston [22]. Smaller concentration ratio (less than 3) CPC collectors are able to accept a large proportion of the diffuse radiation incident on their apertures and concentrate it without the need of tracking the sun [23]. Rabl summarized more than 3 years of research on non-evacuated CPC collectors. At lower concentration ratios (e.g. 3) CPC performance would be substantially better than a double glazed flat plate collector above about 70 °C while requiring only semi-annual adjustments for year-round operation [24]. Saitoch compared a CPC collector with a conventional flat plat collector and an evacuated tube collector. The experimental results indicated that the CPC collector had an excellent thermal performance for high temperature thermal electric applications in which the steam temperature should be more than 120 °C [25]. Later Saitoch proposed an advanced 3-D CPC collector. Thermal efficiency of the 3-D CPC collector was about 60% in the high temperature range from 180 °C to 200 °C and was feasible for small rating solar Rankine systems [26]. This paper combines the ORC with the CPC collectors. A simulation model of the low temperature solar thermal electric generation in areas of Canberra, Singapore, Bombay, Lhasa, Sacramento and Berlin with HCFC-123 as the working fluid is presented. The influences of the CPC collector tilt angle adjustment, the connection between the heat exchangers and the collectors, and the ORC evaporation temperature are investigated and the system performance is optimized. 2. Fundamental and structure Fig. 1 is the scheme of the novel design for the low temperature solar thermal electric generation. The system mainly consists of CPC collectors and the ORC subsystem. The ORC subsystem consists of two-stage heat exchangers, pumps and a fluid storage tank with phase change material (PCM), turbine (T), generator (G),

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Fig. 1. A novel design for low temperature solar thermal electric generation.

regenerator (R) and condenser. In contrast to the traditional solar Rankine system, there is an organic fluid storage tank with PCM set at the outlet of the second-stage heat exchanger in this novel configuration. The other novel characteristic of the configuration is that two-stage heat exchangers are adopted. The first-stage heat exchanger is an economizer where the organic fluid is heated from sub-cooled to saturated liquid conditions. The second-stage heat exchanger is a binary phase evaporator. The two-stage heat exchangers are connected with the collectors separately. The mass rate of the conduction oil in the first-stage heat exchanger (E1) is smaller than that in the second-stage heat exchanger (E2). The heat transfer configuration with two thermal oil cycles was used by Drescher and Brueggemann to avoid the constriction of the pinch point between the organic fluid and thermal oil at the beginning of vaporization in biomass power and heat plants [27]. The suggested plant design simplified fluid selection and strengthened the relationship between thermal efficiency and total heat recovery. However, the temperature–enthalpy (T–H) diagram of flue gas seemed unchanged and there was not indication that substantial improvement on the total heat recovery efficiency was achieved. Unlike the use on biomass, the application of two thermal oil cycles on the low temperature solar thermal electric generation is much more significant for the collector efficiency. The key advantages of the novel design are: (1) In case the organic fluid is not totally vaporized, the liquid will drop in the fluid storage tank and will not harm the turbine. (2) There are conduits filled with PCM in the fluid storage tank, so the stability of the ORC subsystem could be guaranteed. (3) The conduction oil from the collectors is able to exchange energy with the organic fluid without any intermediate such as heat storage equipment. Thus the temperature difference between the organic fluid and conduction oil can be effectively diminished. This is very useful for the proposed system since the temperature difference between the hot and the cold sides is only around 100 °C.

(4) Compared with the traditional one-stage evaporator, the two-stage heat exchangers can reduce the heat transfer irreversibility between the organic fluid and conduction oil. The average working temperature of collectors connected with the first-stage heat exchanger is lower and thus the overall collector efficiency will be improved. (5) In order to strengthen the heat transfer performance in the second-stage heat exchanger, the mass flow rate of the organic fluid could be increased by pump 2. And the organic fluid at the outlet of the second-stage heat exchanger does not have to be completely dry. (6) Without any complicated controlling device, the processes of heat storage or heat release can take place while electricity is being generated. The organic fluid is able to exchange energy with the PCM at a relatively low heat flux level (store heat if irradiance is stronger than that on normal condition or release heat if irradiance is weaker). The temperature difference between the organic fluid and PCM is then diminished. In the practical operating period there will be three modes: (I) The system needs to generate electricity and irradiation is available. In this mode, valves 1, 2, 3, 5 and 6 are open. Pumps 1, 3 and 4 are running. Valve 4 would be open and pump 2 would run to prevent the organic fluid from being superheated in the second-stage heat exchanger when irradiation is strong. The organic fluid is first heated in the first-stage heat exchanger and then vaporized in the second-stage heat exchanger under high pressure. The vapor flows into the turbine and expands, exporting power in the process due to the enthalpy drop. The outlet vapor is cooled down in the regenerator and condensed to a liquid state in the condenser. The liquid is pressurized by pump 1 and warmed in the regenerator. The organic fluid is then sent back to the first-stage collectors and circulates. On the use of pump 2, the system can run steadily and effectively in a wide irradiation range.

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(II) The system does not need to generate electricity but irradiation is well. Valves 8, 9 and 10 are open. Pump 3 is running. The dashed lines (except the line through valve 7) in Fig. 1 are the pipes for heat storage. In this mode, the heat storage process is separate and the conduction oil is exchanging heat with the PCM without HCFC-123. (III) The system needs to generate electricity but irradiation is very weak or unavailable. Valves 1 and 7 are open and pump 1 is running. Heat is released from the PCM. Mode I is described as the simultaneous processes of heat collection and power generation in this paper while mode II or mode III is the separate process of heat collection or power conversion. 3. Mathematical model

Fig. 2 shows the scheme of the thermodynamic cycle of HCFC123. Point 1 shows the state of HCFC-123 at the condenser outlet; point 2 at the pump 1 outlet; point 20 at the regenerator outlet; point 3 at the first-stage heat exchanger outlet; point 4 at the evaporator outlet (on the normal condition of irradiation); point 5 at the turbine outlet; point 6 at the condenser inlet. The points referred in Fig. 2 are put in Fig. 1 with circles outside the numbers (except for 20 ). The reversible processes of pressurization and expansion are described by 2s, 5s. The practical efficiency can be calculated by

ðh5s  h4 Þ  et  eg  v 1 ðp2  p1 Þ=ep h4  h20

ð1Þ

et or eg is the turbine or generator efficiency. Since the heat capacity of HCFC-123 at point 2 is higher than that at point 5 the enthalpy at point 20 should be calculated by [28]

h20 ¼ h2 þ ½h5  h6ðT 6 ¼T 2 Þ   er

There are two-phase flows in both the heat exchangers and the condenser. The heat transfer processes are similar. This section is concerned with the flow in the heat exchangers and the developed equations can easily extend to the case of the condenser. CounterCurrent concentric tubes are adopted (Fig. 3). The inner and outer diagrams are listed in Table 1. The concentric tubes could run parallel and the lines are decided by the total mass flow rate of HCFC123 and conduction oil. The following preconditions are assumed: (1) The influence of pressure drop of HCFC-123 on the saturated temperature due to the flow resistance in the heat exchanger is negligible. (2) The flow is one-dimensional.

3.2.1. Liquid-phase region of HCFC-123 The controlling equations for the energy balance of HCFC-123 and the heat transfer oil are

3.1. Calculation of the ORC cycle

gorc 

3.2. Heat transfer in the heat exchangers

ð2Þ

er is the regenerator efficiency. The enthalpy h6ðT 6 ¼T 2 Þ is obtained by assuming T6 = T2. It is noted that h6ðT 6 ¼T 2 Þ is an assumptive value but not the real enthalpy at point 6.

dT f U pDi ðT h  T f Þ ¼ dY mf C p;f dT h U pDi ðT h  T f Þ ¼ dY mh C p;h

ð3Þ ð4Þ

The total heat transfer coefficient is calculated by

 U¼1

1 1  þh o h i

 ð5Þ

where

 ¼ Nu kf h i f Di

o ¼ Nu and h h

kh ðDo  Di Þ

ð6Þ

The convectional heat transfer coefficient can be calculated with the Dittus–Boelter equations [29]. When the flow of the outer fluid is laminar the concentric tube is considered to be isothermal at the inner annulus of the cross section and insulated at the outer annulus and the heat transfer coefficient can be obtained according to the Handbook of Heat Transfer [30].

Fig. 2. Thermodynamic cycle of HCFC-123.

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Fig. 3. Concentric tube and the array.

Table 1 Specifications of the low temperature solar thermal electric generation.

Latitude

Parameters

Value

Canberra Singapore Bombay Lhasa Sacramento Berlin

35.30 1.37 19.12 29.67 38.52 52.47

Inner diameter of Di mm Turbine efficiency et Generator efficiency eg

Longitude

25 0.85 0.95

Parameters

Value

Canberra Singapore Bombay Lhasa Sacramento Berlin

149.18 103.98 72.85 91.13 121.50 13.40

Outer diameter Do mm Pump efficiency ep Regenerator efficiency er

45 0.75 0.95

3.2.2. Binary-phase region of HCFC-123 In the binary-phase region, the energy balance for conduction oil is still controlled by Eq. (4). But the energy balance for HCFC123 is controlled by

sin /h ¼ sin dn sin d þ cos dn cos d cos x

dx U pDi ¼ ðT h  T f Þ dY mf ðhf ;v  hf ;l Þ

ð7Þ

The convection heat transfer coefficient of two-phase flow can be obtained in the precious literature [31]. 3.2.3. Calculation of frictional resistance The viscosity of the oil or HCFC-123 is 3.8 mm2/s or 0.11 mm2/s at a temperature of 100 °C [32]. It can be seen that the kinematic viscosity of the oil is much larger than that of HCFC-123. For precise simulation, the flow frictional resistance of the oil should be evaluated. With N lines of the parallel concentric tubes, the required pump power is obtained by [33]

W

Z

Y2

Y1

_ 2m 128tm

pNðDo  Di Þ3 ðDo þ Di Þep

the absorber. When the CPC collector is oriented with its long axis along the east–west direction, with a little seasonal adjustment in tilt angle the collector is able to catch the sun’s rays effectively through its acceptance angle along its long axis. The height of the sun /h and the azimuth angle w relative to the collector aperture (not horizontal) are shown in Fig. 4. The plane ZOY is the cross section of the collector and OZ is normal to the aperture. OX is the long axis. In order to improve the solar energy received by the CPC collector without complicated tracking equipment, manual tilt adjustments are required. When the nth tilt adjustment is made, the actual declination of sun is described as dn and the height of the sun at noon of that day relative to the collector aperture is expected to be 90°. Then the adjusted CPC aperture would be parallel to the horizontal surface located at latitude dn on the same longitude line. The height of the sun relative to the collector aperture until the (n + 1)th adjustment can be calculated by [34].

dY

c ¼ arctan

  cos /h  cos w sin /h

ð10Þ

If c is not larger than the half acceptance angle of the CPC collector, the ray will reach the absorber. Otherwise the ray is supposed to be

ð8Þ

_ is the total mass flow rate of the oil through the tubes; t is the m viscosity of the oil, m2 s1; m is the specific volume of the oil, m3 kg1, Y2  Y1 is the length of a single tube. It is noted that Eq. (8) could easily extended to the case of HCFC-123 when the negative effect of pump 2 is considered due to increased flow rate in the high-temperature loop. The properties in Eq. (8) would then be refined and the inner or outer diameter of the concentric tube would be changed to 0 or 25 mm. 3.3. Irradiance within the acceptance angle of a CPC collector The acceptance angle of a CPC collector is defined as the angle through which a source of light can move and still converge at

ð9Þ

Generally the incidence ~ S is not parallel to the plane of ZOY. In order to judge the acceptance of the ray, the angle c between OZ and the projection of ~ S on the plane of ZOY should be known. The angle c is calculated by

Fig. 4. Scheme of the arrival of irradiance at the CPC collector surface.

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useless. Irradiance within the acceptance angle of a CPC collector of geometric concentration C is very well approximated by [24]

1 G ¼ Gb þ Gd C

ð11Þ

The increments of annual direct irradiance within the acceptance angle of the CPC collector by adjustment is calculated by

fb ¼

X

Gb =

8760

X

Gh;b

ð12Þ

8760

Gh,b is the horizontal direct irradiance intensity at the local latitude, which is independent of the collector. Gb is the direct irradiance intensity relative to the collector aperture and it would not be counted if irradiance is without the acceptance angle of the CPC collector. 3.4. Equations developed for total thermal efficiency of the collector system

h1 and h2 are the arithmetical solutions of Eq. (17) (h1 < 0, h2 > 0).

go  c1 h  c2 h2 ¼ 0:

ð17Þ

C p;a ¼ C p;0 þ aðT a  T 0 Þ

ð18Þ

The total thermal efficiency of the collector system is calculated by

gc ¼

mh;1 ðho;1  hi;1 Þ þ mh;2 ðho;2  hi;2 Þ GðS1 þ S2 Þ

ho,1  hi,1 or ho,2  hi,2 is enthalpy increment of HCFC-123 in the first-stage or second-stage heat exchanger. S1 or S2 is the first-stage or second-stage collectors area. 3.5. Annual power output The annual power generated is the product of ORC efficiency and the total heat collected

The thermal efficiency of a CPC collector module is expressed by

A G

Porc ¼

B G

gðTÞ ¼ g0  ðT  T a Þ  ðT  T a Þ2



Z

T h;o

T h;i

mh C p;h ðTÞ dT gðTÞG

ð14Þ

8760 X

Gi  S  gc  gorc

ð20Þ

i¼1

ð13Þ

The CPC collector modules available on the market have effective area between 1.0 m2 and 2.0 m2. Their thermal efficiency can be calculated by Eq. (13). The solar thermal electric generation system may demand tens or hundreds of collectors in series and the temperature differences between neighboring collectors will be small. In order to calculate the overall collector efficiency it is reasonable to assume that: (1) The average operating temperature of the collector changes continuously from one module to anther module; (2) The function of the simulated area of the collector system is integrable. In order to reach an outlet temperature Th,o of the heat transfer oil with an inlet temperature Th,i, the required collector area is obtained by

ð19Þ

The net power output is obtained by subtracting the driving power of oil pumps and pump 2 from the power generated

P ¼ Porc  Poil  Pp;2

ð21Þ

The key points of the simulation method are explained in detail in the Appendix. 4. Results and discussion The specifications of the low temperature solar thermal electric system are shown in Table 1. The properties of the conduction oil depending on the temperature are obtained in the literature [32]. The weather data is provided by EnergyPlus [35]. The weather types are: IWEC for Canberra, Singapore, Bombay and Berlin, CSWD for Lhasa and TMY2 for Sacramento. 4.1. The influence of tilt angle adjustments

When heat conduction oil is used, the heat capacity can be expressed by a first order approximation [32]

C p ðTÞ ¼ C p;0 þ aðT  T 0 Þ

ð15Þ

With c1 = A/G, c2 = B/G, the collector area according to Eqs. (13)-(15) is calculated by

 mh ðT h;o  T a  h1 Þ ðC p;a þ ah1 Þ ln T h;i  T a  h1 c2 Gðh2  h1 Þ  h2  T h;i þ T a þðC p;a þ ah2 Þ ln h2  T h;o þ T a



ð16Þ

Table 2 shows the increments fb of annual direct irradiance within the acceptance angle of the CPC collector for different areas. The fixed tilt angle means that the collector keeps stationary around the year. The optimal tilt angle adjustment means that the optimal dates of a year are selected while the simple tilt angle adjustment means that the dates are selected at equal time intervals (January 1st is firstly chosen). For the optimal fixed tilt, fb is higher than 1.0 in all the areas except Singapore when the concentration ratio is 1.3. But fb is less than 1.0 when the concentration ratio reaches 3.0. The optimal

Table 2 Increments of annual direct irradiance within the acceptance angle of a CPC collector, unit:%. C

Canberra Singapore Bombay Lhasa Sacramento Berlin

1.3 3.0 1.3 3.0 1.3 3.0 1.3 3.0 1.3 3.0 1.3 3.0

Optimal fixed tilt

119.1 72.6 99.5 60.4 102.6 68.4 110.9 65.7 124.7 72.6 153.3 88.64

Two times adjustments

Three times adjustments

Six times

Twelve times

Optimal

Simple

Optimal

Simple

Simple

Simple

122.4 92.6 101.9 79.9 105.9 92.1 114.3 85.2 129.8 100.4 160.2 125.3

117.8 72.6 98.5 59.8 98.6 49.8 108.7 60.1 123.5 71.6 150.6 75.9

123.2 94.1 102.4 81.4 106.3 93.0 115.0 87.2 130.5 102.9 161.6 129.4

110.2 61.1 91.8 52.6 98.1 57.0 101.7 51.4 110.5 53.9 137.1 67.8

119.7 80.4 99.5 68.5 101.4 67.6 112.2 75.2 119.7 80.4 156.3 111.6

126.0 109.7 104.4 90.9 107.4 96.4 118.9 102.5 126.0 109.7 164.7 149.0

Every-day

128.3 123.1 106.4 103.9 109.3 106.5 121.2 114.7 128.3 123.1 166.9 160.5

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4.2. The collector efficiencies comparison between one-stage and twostage heat exchangers system In this section, the collector parameters are needed to analyze the influence of the connection between the heat exchangers and the collectors on the overall collector efficiency of the low temperature thermal electric system. The parameters of the market available CPC collectors are proposed according to some products information [36]. The first heat loss coefficient A is 0.82 W m2 °C1 and the second heat loss coefficient B is 0.0064 W m2 °C2 and g0 is 0.661. Table 3 shows the performance comparison between the single-stage and two-stage collectors varying with solar irradiance. The number of parallel tube lines in the first or second-stage heat exchanger is 10 or 100 respectively. The evaporation or condensation temperature is 150 °C or 35 °C respectively. In the two-stage heat exchangers system, the area of the first or the second-stage collectors is 270 m2 or 410 m2, respectively. The total heat transfer area of the first or the second-stage heat exchanger is 300.0 m2 or 480.0 m2. In order to avoid the superheated state of HCFC-123, pump 2 is running. The mass flow rate driven by pump 2 is 2.0 kg/s, two times as large as that by pump 1 (1.0 kg/s). Therefore dryness of HCFC-123 should be about 0.3333 on normal condition without storing or releasing heat. Since there is a normal mass flow rate in the turbine, heat will be released from PCM if xf,o (dryness at the second-stage heat exchanger outlet) is smaller than 0.3333 or stored if xf,o is larger than 0.3333. The mass flow rate of conduction oil is 0.55 or 8.0 kg/s in the first or second-stage heat exchanger. In the single-stage heat exchanger system, the collector area is equal to that of the two-

stage system (680 m2). The mass flow rate of conduction oil is 8.55 kg/s. The mass flow rate of HCFC-123 driven by pump 2 is 2.0 kg/s. The mass flow rate of HCFC-123 driven by pump is 0.85 kg/s, which is smaller than that in the two-stage heat exchangers system. This is in the consideration that the singlestage system is compared with the two-stage system under a similar normal condition without heat release or storage when irradiance is 750 W/m2. Table 3 shows that the collector efficiency of two-stage heat exchangers system is higher than that of singlestage heat exchanger system by 8.1–20.9% and the superiority is greater when irradiance is weaker. 4.3. Annual evaporation temperature optimization Optimization of the ORC evaporation temperature is not only related to the environment temperature and annual irradiance conditions of the local area, but also to the operating mode of heat storage. In this paper, the processes of heat collection and power generation are simultaneous, e.g. electricity is generated when irradiance is stronger than 300 W/m2. Fig. 5 shows the efficiency variation of the low temperature solar thermal electric generation with ORC evaporation temperature. The curves indicate that the system electricity efficiency first goes up when the evaporation temperature increases at lower temperatures range and then drops down with further temperature increment. According to the second law of thermodynamic the ORC efficiency is improved by larger temperature difference between the hot and the cold sides. However, the collector efficiency becomes lower when the average temperature of conduction oil rises. Due to this tradeoff there is an optimal evaporation temperature Topt at which the overall electric0.0800

2

600W/m 2 700W/m 2 800W/m

0.0775 0.0750

electricity efficiency

fixed tilt angles relative to the equator for the areas are: Canberra 2.71°/8.81°, Singapore 2.09°/8.0°, Bombay 5.38°/9.67°, Lhasa 5.75°/7.99°, Sacramento 4.43°/7.46°, Berlin 2.62°/13.67°. The first numbers are the values when the concentration ratio is 1.3 while the second numbers are for a concentration ratio of 3.0. As the concentration ratio rises the CPC collector should not be titled directly towards the equator anymore. With two times optimal annual tilt angle adjustments fb can be greatly improved compared with a stationary tilt angle especially when the concentration ratio is higher. When the annual optimal adjustments increase to three times, fb is further improved but the improvement is less appreciable. The annual direct irradiance received by the CPC collector under simple adjustments is also presented. January 1st and July 2nd are chosen as the dates for two times adjustments and January 1st, May 2nd and September 1st are chosen for three times adjustments. The dates for more times simple adjustments are chosen in the same way. It is noteworthy that adjustments at regular intervals are not effective when the adjustments are less than six times. The influence of the concentration ratio on direct irradiance within the acceptance angle is little when everyday adjustment is made.

0.0725 0.0700 0.0675 0.0650 0.0625 0.0600

100

110

120

130

140

150

160

0

evaporation temperature / C Fig. 5. Efficiency variation of the low temperature solar thermal electric generation with the ORC evaporation temperature.

Table 3 Performance comparison between the single-stage and two-stage collectors. Insolation W/m2

Temperature/°C and overall collector efficiency

G

The first stage

Two-stage evaporators

600 650 700 750 800 850 900

Single-stage evaporator The second stage

Th,i

Th,o

Tf,o

Th,i

Th,o

xf,o

gc

48.8 49.7 50.6 51.5 52.4 53.3 54.1

121.6 128.0 134.2 140.4 146.6 152.5 158.5

115.9 121.7 127.3 132.8 138.4 143.6 148.9

149.9 151.0 151.9 152.7 153.4 153.9 154.4

154.0 155.8 157.3 158.8 160.2 161.4 162.5

0.118 0.190 0.256 0.326 0.400 0.464 0.537

0.399 0.411 0.422 0.432 0.440 0.449 0.456

Th,i

Th,o

xf,o

gc

144.6 145.3 145.9 146.5 147.0 147.5 148.0

151.4 153.2 154.8 156.5 158.0 159.6 161.1

0.046 0.124 0.197 0.280 0.355 0.436 0.514

0.330 0.351 0.369 0.384 0.398 0.411 0.422

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180

time to time in areas and the annual optimization of ORC evaporation temperature should be based on the fact that normally the turbines operate at constant temperature and the heat storage material is unlikely to be replaced all the year round. Therefore, once an evaporation temperature of the ORC system is evaluated the corresponding turbine and heat storage material would be considered. And this ORC evaporation temperature would keep constant for year-round operation. Fig. 6 shows the variations of annual electricity output with the ORC evaporation temperature. The optimal annual evaporation temperatures and the corresponding electricity outputs for different areas are: Canberra 118 °C, 117.4 kW h m2; Singapore 114 °C, 77.3 kW h m2; Bombay 122 °C, 106.4 kW h m2; Lhasa 116 °C, 163.4 kW h m2; Sacramento 124 °C, 119.1 kW h m2; Berlin 99 °C, 48.2 kW h m2. Fig. 7 shows the monthly distribution of the power output in different areas when the ORC evaporation temperatures are optimal. The low temperature solar thermal electric generation in Canberra is preferable from September to March of the following year. Singapore has the most uniform monthly distribution among all the areas. Although Bombay is in the northern hemisphere the lowest electricity output period is from June to September. The highest electricity output season in Lhasa is from October to January of the following year. The power output from April to September in Sacramento amounts to 70% of the annual available generation. In Berlin the power output from April to August amounts to 73% of the annual available generation and there is no more than 1.0 kW h m2 output in December or January.

Lhasa Sacramento Berlin

140

2

power output KWh/(m .a )

160

Canberra Singapore Bombay

120 100 80 60 40 20 60

80

100

120

140

160

180

0

ORC evaporation temperature / C Fig. 6. Annual output of the solar thermal electric power generation with the ORC evaporation temperature.

ity efficiency reaches its maximum. The optimal ORC evaporation temperature would be higher and the maximum overall electricity efficiency would be improved when irradiance is stronger. Each curve in Fig. 5 is shown under the conditions of constant environment temperature, constant irradiance and flow rates of conduction oil and HCFC-123. However, irradiance varies from 21

power output/ kWh

power output /kWh

15 12

9 6 3 0

21

Canberra

18

15 12 9 6 3 0

Jan F e b M ar Ap rM ayJu n Ju l Au gSep O ct N o vDec

Singapore

18

Jan F eb M ar Ap rM ayJu n Ju l Au gS ep O ct N o vDec

month 21

Bombay power output /kWh

18

power output /kWh

month

15 12 9 6 3 0

21 15 12 9 6 3 0

Jan F eb M ar Ap rM ayJu n Ju l Au gS ep O ct N o vDec

Lhasa

18

Jan F eb M ar AprM ayJu n Jul Au gSep O ct N ovD ec

month

month

15 12 9 6 3 0

21

Sacramento

18

power output/kWh

power output /kWh

21

Ja n Feb M ar Ap rM ayJu n Ju l Au gSep O ct No vD ec

month

18

Berlin

15 12 9 6 3 0

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

month Fig. 7. Monthly distribution of electricity output.

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5. Conclusion

The unknown conditions:

The connection between the heat exchangers and CPC collectors, the tilt angle adjustment and the ORC evaporation temperature and are three of the key factors for optimizing the low temperature solar thermal electric system. The following conclusions are drawn:

(1) the outlet temperature of HCFC-123 Tf,o (liquid state); (2) the inlet and outlet temperature of conduction oil Th,i, Th,o; (3) collector efficiency gc.

(1) There are several advantages in the proposed configuration of the low temperature solar thermal electric system. The two-stage heat exchangers are able to improve the collector efficiency by 8.1–20.9% in the practical operating period in comparison with the single-stage heat exchanger. (2) The influence of tilt angle adjustment on the annual direct irradiance within the acceptance angle of a CPC collector varies from area to area and is determined by both adjustment frequency and the selected dates. As the concentration ratio rises the fixed CPC collector should not be titled directly towards the equator anymore. Selecting the optimal dates is important and adjustments are desirable in periods of strong irradiance. Under two times annual optimal tilt angle adjustments the direct irradiance within the acceptance angle of a CPC collector with a concentration ratio of 3.0 can be improved by 20–40%. When the annual optimal adjustments increase to three times the improvement is less appreciable. (3) The annual electric output first climbs as the evaporation temperature rises and then falls with further increment of the ORC evaporation temperature. There is an optimal ORC evaporation temperature and a maximum power output for each area. The optimal evaporation temperatures and the corresponding annual power outputs for different areas are: Canberra 118 °C, 117.45 kW h m2; Singapore 114 °C, 77.29 kW h m2; Bombay 122 °C, 106.41 kW h m2; Lhasa 116 °C, 163.42 kW h m2; Sacramento 124 °C, 119.10 kW h m2; Berlin 99 °C, 48.15 kW h m2. In most of the areas, the optimal ORC evaporation temperatures are around 120 °C. The heat storage medium appropriate for the low temperature solar thermal electric system could be erythritol, which has melting point 120 °C and heat of fusion 339.8 kJ/kg. Magnesium chloride hexahydrate (MgCl26H2O) would be appropriate as well, which has melting point 117 °C, heat of fusion 168.6 kJ/kg and thermal conductivity 0.694 W/m K (solid). Acknowledgements The study was sponsored by National Science Foundation of China (NSFC), Project Numbers: 50978241 & 50708105 & 50974150. The National High Technology Research and Development Program of China (863 Program) Project Number: 2007AA05Z444.

The controlling equations for the energy balance of HCFC-123 and the conduction oil are Eqs. (3) and (4). A numerical approach for computation of the temperatures along the tube is used.

T f ;nþ1 ¼ T n þ

U n pDi ðT h;n  T f ;n Þ DY mf C p;f ;n

T h;nþ1 ¼ T h;n þ

ð22Þ

U n pDi ðT h;n  T f ;n Þ DY mh C p;h;n

ð23Þ

DY is discrete step length. The subscript of n or n + 1 is the discrete point. The calculation procedure is (1) Input a value for Th,i. (2) With Th,i and Tf,i (n = 1), the temperatures Th,2 and Tf,2 in the next point are calculated according to Eqs. (22) and (23). (3) With Th,2, Tf,2 and corresponding properties (heat capacity, conductivity and so on), the temperatures Th,3 and Tf,3 are calculated according to Eqs. (22) and (23). The rest can be done in the same manner until the temperatures Th,o and Tf,o have been calculated. (4) With Th,i and Th,o, the collector efficiency is calculated by

gc ¼ c2 ðh2  h1 Þ½C p;0 ðT h;o  T h;i Þ þ 0:5aðT h;o  T h;i ÞðT h;o þ T h;i  2T 0 Þ ðC p;a þ ah1 Þ ln

ðT h;o T a h1 Þ þ ðC p;a T h;i T a h1

h T

h;o

(5) With gc, S and G, the total heat available from the collectors is calculated by

Q c ¼ gc  S  G

Input a value for Th,i

Calculation of Tf,2 and Th,2 Calculation in the same manner Calculation of Tf ,o and Th,o Calculation of Qc and Qf

Appendix A. Calculation of collector efficiency Following is an example of the simulation of heat transfer in the first-stage heat exchanger (liquid-phase region). See Fig. 3a. The known conditions: (1) the mass flow rate of HCFC-123 mf and mass flow rate of conduction oil mh; (2) the inlet temperature of HCFC-123 Tf,i; (3) the heat transfer area of the tube; (4) collectors area S, irradiation G and environment temperature Ta.

þT

þ ah2 Þ ln h22T h;i þTaa

fabs(Qc -Qf)
Collector efficiency ηc

Fig. 8. Collector efficiency calculation.

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(6) On the other hand, the heat required in the evaporator is calculated by

Q f ¼ mf ðhf ;o  hf ;i Þ (7) The correct solution must fulfill energy balance. If the difference between Qc and Qf (absolute value)is smaller than f (judging parameter), then output Th,i, Th,o and Tf,o (correct values). (8) Otherwise change the value of Th,i and go to step (1). (9) With Th,o and Tf,o the collector efficiency gc is calculated. The flow charts are shown in Fig. 8. The simulation of heat transfer in the second-stage heat exchanger can be calculated in the similar way. In case of the second-stage heat exchanger the controlling Eq. (3) for HCFC-123 will be replaced by Eq. (7).

(3) With the ORC evaporation temperature the ORC efficiency gorc is calculated. (4) With S, Ta and G the total heat carried away Qc by HCFC-123 is obtained according to Appendix A. (5) With Qc the heat DQpcm that released or stored by PCM is calculated; DQpcm>0 if heat is stored while DQpcm<0 if heat is released; (6) Go to step (2) and calculate in the same manner until all the hours of a year are evaluated. P (7) Add DQpcm of all the hours together. If DQpcm
Appendix B. Calculation of annual electricity output

Reference

In this paper, the low temperature solar thermal electric generation system is simulated in the simultaneous processes of heat collection and power conversion and the system runs only when irradiation is available, e.g. stronger than 300 W/m2. The weather data is provided hourly. The calculation objective is to add the hourly produced electricity together for the annual electricity output when the ORC evaporation temperature is known. Other known parameters are the mass flow rate of HCFC-123, mass flow rate of conduction oil and the heat transfer area. It is noted that in order to achieve a balance between the processes of heat release and heat storage all the year round the corresponding collector area should be found out. Following is the key steps of the calculation method.

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(1) Input a value for the collectors area S; (2) Input the environment temperature Ta and irradiation G for one hour;

Input a value for S

Input Ta and G for one hour

Calculation of ηorc

Next hour

Calculation of Qc

Calculation of ΔQ pcm

Qpcm
Qc

Output annual electricity P

Fig. 9. Annual electricity output calculation.

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