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Mathematical modeling and numerical simulation of a parabolic trough collector: A case study in thermal engineering
Accepted Manuscript Mathematical modeling and numerical simulation of a parabolic trough collector: A case study in thermal engineering Bilal Lamrani, Ahmed Khouya, Belkacem Zeghmati, Abdeslam Draoui PII: DOI: Reference:
S2451-9049(18)30149-5 https://doi.org/10.1016/j.tsep.2018.07.015 TSEP 209
To appear in:
Thermal Science and Engineering Progress
Received Date: Accepted Date:
12 March 2018 27 July 2018
Please cite this article as: B. Lamrani, A. Khouya, B. Zeghmati, A. Draoui, Mathematical modeling and numerical simulation of a parabolic trough collector: A case study in thermal engineering, Thermal Science and Engineering Progress (2018), doi: https://doi.org/10.1016/j.tsep.2018.07.015
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Mathematical modeling and numerical simulation of a parabolic trough collector: A case study in thermal engineering
Bilal LAMRANI a,c,*, Ahmed KHOUYA b , Belkacem ZEGHMATI c, Abdeslam DRAOUI a a
Equipe de recherche en Transferts Thermiques et Energétique (ETTE - UAE/E14FST) - FST de Tanger Université Abdelmalek Essâadi (UAE) –Tanger 90000, Maroc. b Laboratoire des Technologies Innovantes (LTI – ENSAtg/L02) - ENSA de Tanger - Université Abdelmalek Essâadi (UAE) –Tanger 90000 Maroc. c Laboratoire de Mathématiques et de PhySique (LAMPS), Université de Perpignan Via Domitia (UPVD) Perpignan 66000, France. * Corresponding author: [email protected] (Bilal LAMRANI)
Abstract The objective of this paper is to investigate numerically the thermal performance of a solar Parabolic Trough Collector (PTC) under transient climatic conditions. A detailed numerical model based on energy balances at the component level of the solar PTC is developed and validated with existing experimental data. The effect of some design and operation parameters, which included the mass flow rate of Heat Transfer Fluid (HTF), the length of the receiver tube and the HTF nature, on thermal performance of the solar PTC were analyzed. Results obtained show that maximum thermal efficiency of the solar collector is achieved during summer and it is about 76 %. The length of the receiver tube has a great effect on HTF outlet temperature and using synthetic oil as working fluid is suitable compared to water. Keywords: Parabolic Trough Collector; thermal performance; numerical simulation; transient climatic conditions 1
Introduction
Reducing the energy dependence and the greenhouse gas (GHG) emissions present a major objective in several countries worldwide. In this context, it is recommended that in countries where solar energy is abundant, using renewable energies could be present an appropriate solution to replace the convention sources of energy [1]. Concentrated Solar Power (CSP) using solar Parabolic Trough Collector (PTC) present an attractive solution and modeling of this technology under real weather conditions is advantageous for system design and optimization. Since the 1980s, numerical modeling of solar PTC has received increasing attention in order to investigate their thermal performance in several applications such as in industrial heat process, domestic hot water and space heating [2–4]. In order to examine the thermal performance of a PTC under climatic conditions of Morocco, a numerical model based on steady state heat transfer is proposed by Bouhal et al. [5]. They proved that the location and the climate are determinant parameters on the thermal performance of the solar collector. Another study on thermal and optical performance of a solar PTC during a year under climatic conditions of India have presented by Kumar et al. [6]. A one dimensional steady state heat transfer model is developed and validated through a comparison with the experimental results of Sandia National Laboratories (SNL) [7]. They concluded that thermal efficiency of the PTC is maximum during the month of July and could reach 66.78% and minimal values of thermal efficiency are obtained during the month of December. E. Bellos et al [8] performed a numerical investigation on thermal performance of a solar PTC under steady state thermal conditions. Numerical results show that the thermal efficiency of the solar PTC increases as the solar beam radiation increases and the Nusselt number increases. However, thermal efficiency of the solar PTC decreases as HTF inlet temperature increases. The influence of some operation parameters on the thermal performance of a solar PTC have been predicted by J. Guo et al. [9]. The steady state model is employed to carry out the numerical model and the results show that there exists an optimal mass flow rate for thermal efficiency. Furthermore, increasing ambient temperature and solar incident angle leads to decrease the heat losses of solar receiver. The thermal analysis of a solar PTC based on steady state thermal model is presented by Kalogirou [10]. The developed model is written under the Engineering Equation Solver (EES) and validated with existing experimental data in the literature. Based on heat transfer analysis, Hachicha et al. [11] have proposed a numerical model to evaluate thermal performance of a solar PTC. The thermal model is based on steady state model and the finite volume method is
used to discretize the governing equations. The validation of the developed model is realized through a comparison with experimental data of SNL [7]. In order to investigate the effect of different working fluid on thermal performance of solar PTC, Ouagued et al. [12] have presented a heat transfer numerical model. Different synthetic oils are compared and results indicate that synthetic oil (Syltherm 800) is suitable as working fluid over the year compared to the other synthetic working fluids. From the previous literature, several numerical studies are presented to investigate the thermal performance of solar PTC. However, most of the proposed numerical models are simplified and developed under steady state conditions. In the present paper, a detailed transient heat model to predict the thermal performance of a solar PTC under transient conditions is developed. Due to the abundant solar radiation, about 5.5 kWh/m2/day [13], and in order to encourage the use of this technology, meteorological data of Morocco are used. The selected city is Tangier which is represent the second most important industrial center in this country and thermal performance of the solar PTC during four periods of year is investigated. The effect of some design and operation parameters which included the mass flow rate of Heat Transfer Fluid (HTF), the length of the receiver tube and the HTF nature, on outlet temperature of the solar PTC were also analyzed. 2
System Description
The solar PTC consists of three main elements: a reflector, a receiver tube and a support structure with a sun tracking system (Fig. 1). Fig. 2 shows a cross-section of the solar PTC. The solar flux received by the concentrator is first reflected on the mirror of the reflector and then passes through the glass envelope to reach the absorber pipe. The role of the glass cover is to reduce the thermal losses by convection with the ambient air. The surface of the absorber is covered by a selective material to absorb the maximum of the solar flux. The absorbed solar flux is converted into heat and transmitted by conduction and convection to the heat transfer fluid through the tube receiver.
Glass envelope
Receiver tube Absorber tube
𝑻𝒂𝒎𝒃
𝑻𝑭
𝑻𝑨
𝑻𝑽
Reflector
Reflector
F
L
W W
Fig. 1 Physical model of the solar PTC
3
Fig. 2 Cross-section of the solar PTC
Mathematical modeling The mathematical model is based on the following assumptions:
-
The heat transfer by conduction in the receiver tube is neglected. The absorber and the glass cover are assumed to be grey bodies. The form factor between the absorber and the glass cover is considered equal to 1. The fluid is incompressible. The solar flux on the absorber tube is uniform.
The solar PTC is modeled using the time dependent energy balance. In this method, the PTC is divided into N slices perpendicular to the heat transfer fluid flow direction. The exit of the th slices is considered the inlet of the following slices. The energy balance equation in each solar PTC component can be expressed as follows:
Glass envelope (1)
It can be written as: (2)
Absorber pipe (3)
Where: (4)
Heat transfer fluid (5)
Where: (6)
To these equations, we associate the following initial and boundary conditions: - Initial conditions At (7)
Where is the component of the PTC. - Boundary conditions
(8) (9)
3.1
Thermal efficiency
The thermal efficiency of a solar PTC is defined as the ratio of useful heat gain by the HTF and the heat flux received by the concentrator [14,15]: and
3.2
=
(10)
Convection heat transfer coefficients
The convective heat transfer coefficient between the glass envelope and the ambient air without wind is determined from the correlation developed by Churchill and Ch.[16,17].
(11)
With wind, we use the correlation developed by Churchill and Bernstein[16,17] :
(12)
The convective heat transfer coefficient between the absorber and air ( ) in the annular space depends on the pressure between the glass envelope and the absorber. When there is vacuum in the annular (Pressure < 0.013 Pa), we can consider that equal to zero [17]. But if the pressure in the annular space is greater than 0.013Pa, is estimated through natural convection relations between two horizontal, concentric cylinders [16,17]: (13)
Where (14)
And (15)
(16)
The convective heat transfer coefficient between the absorber and the (HTF) is given by equation (17). To calculate the Nusselt number, the Gnielinski correlation [18] is used : (17)
(18)
With f is the friction factor defined as follows: (19)
3.3
Radiation heat transfer coefficients
The heat transfer coefficient by radiation between the absorber tube and the glass envelope is expressed as follows [15]:
(20)
The heat transfer coefficient by radiation between the glass envelope and the sky is given as follows: (21)
And (22)
4
Numerical procedure
Equations (2), (4) and (6) are discretized by an implicit finite difference method. The obtained system of algebraic equations (23) is written as: (23)
This system of algebraic equations is solved by Gauss iterative method with a convergence criterion . The space and time steps retained are and . A computer program is developed under FORTRAN language enable to simulate the thermal performance of the solar PTC under different weather conditions. The flow chart of the calculation is presented in Fig. 3. of
Start
Input data: parameters of the solar PTC, meteorological data, initials conditions, , , etc.
Time of sunrise and sunset
(i)
Calculation of the heat transfer coefficients and solving the system of equations =T
Space Loop
Time loop
Loop on hours
Calculation of absorbed solar flux, optical efficiency of the solar PTC
No
Yes
Saving Results
End
Fig. 3 Flow chart of the calculation program
5
Results and discussion
First, we validated the mathematical model and the numerical code that we developed by comparing our results with experimental results from literature [7]. Then, we applied the numerical code to investigate the thermal performance of the solar PTC under transient climatic conditions. 5.1
Model validation
The experimental study of Sandia National Laboratories (SNL) [7] is carried out on a solar PTC of type (LS2 PTC) with synthetic oil (Syltherm 800) as working fluid. The characteristics of the solar PTC used in the experimental tests are given in Table 1. The same characteristics of the solar PTC are used in the present numerical model and obtained results show that our results are in good agreement with experimental results (Fig. 4). It can be observed that the numerical results are not exceeding the dotted lines (Errors limits) and maximum discrepancy between numerical and experimental results is about 2.41%. We consider that these results validate
our numerical model and the methodology that we have developed. They can; therefore, be applied to the study of the thermal performance of the solar PTC under different operating conditions. Table 1 Characteristics of the (PTC) used in the model validation[7] Parameters Absorber length (L) Collector width (W) Focal distance (F) Absorber pipe internal diameter ( ) Absorber pipe external diameter ( ) Glass envelop internal diameter ( ) Glass envelop external diameter ( ) Absorber pipe thermal absorptance Glass envelop thermal absorptance Glass envelop transmittance Absorber pipe emittance Glass envelop emittance Reflected surface reflectivity Shape factor (
Values 7.8 m 5m 1.84 m 0.066 m 0.070 m 0.109 m 0.115 m 0.906 0.02 0.95 0.14 0.86 0.93 0.92 1
incident angle modifier
Experimental Model +/- 5%
80 75
th(%)
70 65 60 55 50 0,0
0,1
0,2
0,3
0,4
0,5
(Tin-Tamb)/Id Fig. 4 Comparison between our results and experimental results [7].
5.2
Thermal performance
In this section, the thermal performances of the solar PTC during four days of the year in Tangier city are investigated. The available meteorological data for the Tangier city such as air temperature, air velocity and solar intensity are those of 15 January, 15 April, 15 July and 14 November. The characteristics of the solar PTC used in simulations are given in Table 2 The inlet HTF temperature at the solar concentrator is assumed to be equal to the ambient temperature and the available thermo-physical properties of water and oil (syltherm 800) used in the simulations are given as a function of temperature (Table 3).
Table 2 Characteristics of the (PTC) used in this study Parameters
Values
Absorber length (L) Collector width (W) Focal distance (F) Absorber pipe internal diameter ( ) Absorber pipe external diameter ( ) Glass envelop internal diameter ( ) Glass envelop external diameter ( ) Mass flow rate ( ) Absorber pipe thermal absorptance Glass envelop thermal absorptance Glass envelop transmittance Absorber pipe emittance Glass envelop emittance Reflected surface reflectivity Shape factor (
5m 3.4 m 1.84 m 0.066 m 0.070 m 0.109 m 0.115 m 0.0278kg/s 0.906 0.02 0.95 0.14 0.86 0.93 0.92 1
incident angle modifier
Table 3 Physical proprieties of water and synthetic oil [19,20]
Water
Oil (Syltherm 800)
Fig. 5 shows the variation of the ambient temperature during four different periods of the year in Tangier city. It can be observed that maximum values of ambient temperature are obtained during summer (15th July) and the highest wind speed is observed on 15th April which is between 12.8 m/s and 19.8 m/s. However, during the 15th July, the wind speed is minimal and it does not exceed 1.75 m/s (Fig. 6). The evolution of the solar irradiance during the four days is presented in (Fig. 7). Solar irradiation reaches a maximum value of 675 W/m² on 15th July, 560 W/m² on 15th April, 472 W/m² on 14th November and 448 W/m² on 15th January 15 July 15 April 15 January 14 November
20
297
18
294
16 Wind speed (m/s)
ambient temperature (K)
300
291 288 285 282
14 12 10 8 6 4
279 276
15 July 15 April 15 January 14 November
2 6
8
10
12
14
16
18
20
Legal time (Hours)
Fig. 5 Ambient temperature on four days of the year
0
6
8
10
12
14
16
18
20
Legal time (Hours)
Fig. 6 Wind speed on four days of the year
The evolution of the water outlet temperature of the solar PTC during the day is similar to that of the solar flux (Fig. 8). It increases in the morning until reaching a maximum value and then decreases during the afternoon until reaching the ambient temperature. The water outlet temperature reaches a maximum value about 369.3 K in summer, 352.6 K in spring, 341.7 K in autumn and about 330.5 K in winter. These values are obtained at 12: 00 pm on 14th November, at 13: 00 pm on 15th July and 15th January and at 14: 00 pm on 15th
April. It will be noted that these hours correspond to the maximum values of the direct solar flux captured by the solar PTC. The hourly variation of useful heat gain by the HTF is shown in Fig. 9. It is seen that the heat flow recovered by the water is highest during the summer. It reached 8768.40 W at 13.00 pm on 15th July, 7001 W at 14.00 pm on 15th April, 5752.5 W at 12.00 pm on 14th November and 5252 W at 13.00 pm on 15th January. Fig. 10 shows the hourly thermal efficiency of the solar PTC. Thermal efficiency is maximum on 15th July and can reach 76.4%. During the winter, maximal value observed is about 69%. These results are corroborated by those of the hourly evolution of the solar flux received by the solar PTC.
15 July 15 April 15 January 14 November
360
600 500
Temperature (K)
Direct solar radiation (W/m²)
700
400 300 200 100 0
15 July 15 April 15 January 15 November
380
340 320 300 280
6
8
10
12 14 16 Legal time (Hours)
18
20
6
Fig. 7 Direct solar radiation on four days of the year
8
10
12 14 16 Legal time (Hours)
18
20
Fig. 8 Water temperature variation at the output of the absorber tube on four days of the year
The increase of the mass flow rate leads to decrease the water outlet temperature (Fig. 11). This is in good agreement with results obtained by [8].This behavior can be justified by the reduction of the water residence time in the receiver tube as the water mass flow rate increases. It is obvious that for different periods of the year, increasing the receiver tube length causes an increase of the heat transfer area between the HTF and the receiver tube. Consequently, the water outlet temperature increases as the receiver tube increases (Fig. 12). 15 July 15 April 15 January 15 November
9000 8000
80 70 Thermal efficiency (%)
Useful heat (W)
7000 6000 5000 4000 3000 2000 1000 0
15 July 15 April 15 January 14 November
60 50 40 30 20 10
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 Legal time (Hours)
Fig. 9 Useful heat gain by water on four days of the year
0
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 Legal time (Hours)
Fig. 10 Concentrator thermal efficiency on four days of the year
15 July 15 April 15 January 14 Novembre
370
390 380
350
370
340
360 Temperature (K)
Temperature (K)
360
330 320 310 300 290 280
15 July 15 April 15 January 14 November
350 340 330 320 310 300 290
0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45
1
Mass flow rate (Kg/s)
Fig. 11 Water outlet temperature at 13:00 pm of each day
2
3 4 5 Receiver tube length (m)
6
Fig. 12 Water outlet temperature at 13:00 pm of each day
Temperature (K)
Fig. 13 presents the evolution of HTF outlet temperature in Tangier city during the 15 th of July. It can be observed that outlet temperature of Oil (Syltherm 800) is higher than that of water. This result can be explained by the difference between physical properties of oil and water. Furthermore, outlet temperature of oil increase much faster than water and that is due to the lowest calorific capacity of oil.
390 380 370 360 350 340 330 320 310 300 290 280
Water Oil (Syltherm 800)
6
8
10
12
14
16
18
20
Legal time (Hours)
Fig. 13 HTF outlet temperature during the 15th July
6
Conclusions
A detailed numerical modeling of the thermal performance of a solar Parabolic Trough Collector (PTC) under transient climatic conditions is presented. A self computer program is developed under FORTRAN language to solve the governing equations and the meteorological data of Morocco are used in the simulations. The main conclusions of the present study can be summarized as follows: The amount of useful heat gain per day is highest in summer (about 71.4 kWh/day) and is minimal in winter (about 30.87 kWh/day). Thermal efficiency of the solar PTC increases with the intensity irradiation and can reach a maximum value of approximately 76 % in summer. The water outlet temperature increases with the length of the receiver tube and decreases as the mass flow rate of the fluid increases. In temperature range from 290 K to 390 K, using synthetic oil as working is suitable compared to water. The developed model is suitable to investigate thermal performance, system design and optimization of solar PTC under real climatic conditions.
Nomenclature
k
CSP EES GHG HTF PTC
Aperture area [m²] Cross sectional area [m²] Specific heat [J.kg-1.K-1] Diameter [m] Focal distance [m] Grashof number Heat transfer coefficients [W.m-² K-1] Direct solar irradiation [W.m-²] Incident angle modifier Thermal conductivity [W.m-1.K-1] Absorber length [m] Mass [kg] Mass flow rate [kg.s-1] Nusselt number Prandtl number Heat flux [W] Rayleigh number Reynolds number Temperature [K] Time [s] Collector width [m] Axial coordinate [m] Abbreviations Concentrated Solar Power Engineering Equation Solver Greenhouse gas Heat transfer fluid Parabolic trough collector
Greek Symbols Absorptance factor Thermal expansion coefficient [K-1] Transmittance Intercept factor Emittance Density [kg.m-3] Reflected surface reflectivity Dynamic viscosity [Pa.s] Stefan–Boltzmann constant Incidence angle [rad] Efficiency Time step [s] Receiver segment length [m] Subscripts Absorber pipe Absorbed Ambient air Convection Outside tube Effective Exterior Fluid Inside tube Inlet of the receiver tube Interior Outlet of the receiver tube Radiation Useful Glass envelope Sky Thermal
Declarations of interest: None. Acknowledgements The authors greatly acknowledge the financial support from the Moroccan National Center for Scientific and Technical Research (N° 31UAE2016). References [1]
[2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
the E.E. and S.C. and the C. of the R. Commission Staff Working Document accompanying the Communication from the Commission to the European Parliament, the Council, Second Strategic Energy Review : Energy sources, production costs and performance of technologies for power generation, heating and transport, 744 (2008). A. Fernández-García, E. Zarza, L. Valenzuela, M. Pérez, Parabolic-trough solar collectors and their applications, Renew. Sustain. Energy Rev. 14 (2010) 1695–1721. V.K. Jebasingh, G.M.J. Herbert, A review of solar parabolic trough collector, Renew. Sustain. Energy Rev. 54 (2016) 1085–1091. S.A. Kalogirou, Solar thermal collectors and applications, Prog. Energy Combust. Sci. 30 (2004) 231–295. T. Bouhal, Y. Agrouaz, T. Kousksou, A. Allouhi, T. El Rhafiki, A. Jamil, M. Bakkas, Technical feasibility of a sustainable Concentrated Solar Power in Morocco through an energy analysis, Renew. Sustain. Energy Rev. 81 (2018) 1087–1095. D. Kumar, S. Kumar, Year-round performance assessment of a solar parabolic trough collector under climatic condition of Bhiwani, India: A case study, Energy Convers. Manag. 106 (2015) 224–234. S.M. Dudley VE, Kolb GJ, Mahoney AR, Mancini TR, Mattews CW, Test results: SEGS LS-2 solar collector. Report of Sandia National Laboratories (SAND94-1884), 1994. E. Bellos, C. Tzivanidis, Assessment of the thermal enhancement methods in parabolic trough collectors, Int. J. Energy Environ. Eng. (2017). J. Guo, X. Huai, Z. Liu, Performance investigation of parabolic trough solar receiver, Appl. Therm. Eng. 95 (2016) 357–364. S.A. Kalogirou, A detailed thermal model of a parabolic trough collector receiver, Energy. 48 (2012) 298–306. A.A. Hachicha, I. Rodríguez, R. Capdevila, A. Oliva, Heat transfer analysis and numerical simulation of a parabolic trough solar collector, Appl. Energy. 111 (2013) 581–592. M. Ouagued, A. Khellaf, L. Loukarfi, Estimation of the temperature, heat gain and heat loss by solar parabolic trough collector
[13] [14] [15] [16] [17] [18] [19] [20]
under Algerian climate using different thermal oils, Energy Convers. Manag. 75 (2013) 191–201. T. Kousksou, A. Allouhi, M. Belattar, A. Jamil, T. El Rhafiki, Y. Zeraouli, Morocco’s strategy for energy security and low-carbon growth, Energy. 84 (2015) 98–105. E. Bellos, C. Tzivanidis, Parametric investigation of nanofluids utilization in parabolic trough collectors, Therm. Sci. Eng. Prog. 2 (2017) 71–79. J. a. Duffie, W. a. Beckman, W.M. Worek, Solar Engineering of Thermal Processes, 4nd ed., 2003. R.V. Padilla, G. Demirkaya, D.Y. Goswami, E. Stefanakos, M.M. Rahman, Heat transfer analysis of parabolic trough solar receiver, Appl. Energy. 88 (2011) 5097–5110. O. García-Valladares, N. Velázquez, Numerical simulation of parabolic trough solar collector: Improvement using counter flow concentric circular heat exchangers, Int. J. Heat Mass Transf. 52 (2009) 597–609. V. Gnielinski, On heat transfer in tubes, Int. J. Heat Mass Transf. 63 (2013) 134–140. Caractéristiques des fluides thérmiques,http://www.celsius-process.com/outils.php [Accessed : 2018-03-01], (2018). Dow, SYLTHERM 800 - Silicone Heat Transfer Fluid, (2001).
Highlights
Thermal performance of a PTC under transient conditions is successfully predicted. Design and operation parameters effect in temperature range 290-390K are examined. Maximum thermal efficiency of the PTC is achieved in summer and it is about 76%. Using synthetic oil as working is suitable compared to water.
S2451-9049(18)30149-5 https://doi.org/10.1016/j.tsep.2018.07.015 TSEP 209
To appear in:
Thermal Science and Engineering Progress
Received Date: Accepted Date:
12 March 2018 27 July 2018
Please cite this article as: B. Lamrani, A. Khouya, B. Zeghmati, A. Draoui, Mathematical modeling and numerical simulation of a parabolic trough collector: A case study in thermal engineering, Thermal Science and Engineering Progress (2018), doi: https://doi.org/10.1016/j.tsep.2018.07.015
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Mathematical modeling and numerical simulation of a parabolic trough collector: A case study in thermal engineering
Bilal LAMRANI a,c,*, Ahmed KHOUYA b , Belkacem ZEGHMATI c, Abdeslam DRAOUI a a
Equipe de recherche en Transferts Thermiques et Energétique (ETTE - UAE/E14FST) - FST de Tanger Université Abdelmalek Essâadi (UAE) –Tanger 90000, Maroc. b Laboratoire des Technologies Innovantes (LTI – ENSAtg/L02) - ENSA de Tanger - Université Abdelmalek Essâadi (UAE) –Tanger 90000 Maroc. c Laboratoire de Mathématiques et de PhySique (LAMPS), Université de Perpignan Via Domitia (UPVD) Perpignan 66000, France. * Corresponding author: [email protected] (Bilal LAMRANI)
Abstract The objective of this paper is to investigate numerically the thermal performance of a solar Parabolic Trough Collector (PTC) under transient climatic conditions. A detailed numerical model based on energy balances at the component level of the solar PTC is developed and validated with existing experimental data. The effect of some design and operation parameters, which included the mass flow rate of Heat Transfer Fluid (HTF), the length of the receiver tube and the HTF nature, on thermal performance of the solar PTC were analyzed. Results obtained show that maximum thermal efficiency of the solar collector is achieved during summer and it is about 76 %. The length of the receiver tube has a great effect on HTF outlet temperature and using synthetic oil as working fluid is suitable compared to water. Keywords: Parabolic Trough Collector; thermal performance; numerical simulation; transient climatic conditions 1
Introduction
Reducing the energy dependence and the greenhouse gas (GHG) emissions present a major objective in several countries worldwide. In this context, it is recommended that in countries where solar energy is abundant, using renewable energies could be present an appropriate solution to replace the convention sources of energy [1]. Concentrated Solar Power (CSP) using solar Parabolic Trough Collector (PTC) present an attractive solution and modeling of this technology under real weather conditions is advantageous for system design and optimization. Since the 1980s, numerical modeling of solar PTC has received increasing attention in order to investigate their thermal performance in several applications such as in industrial heat process, domestic hot water and space heating [2–4]. In order to examine the thermal performance of a PTC under climatic conditions of Morocco, a numerical model based on steady state heat transfer is proposed by Bouhal et al. [5]. They proved that the location and the climate are determinant parameters on the thermal performance of the solar collector. Another study on thermal and optical performance of a solar PTC during a year under climatic conditions of India have presented by Kumar et al. [6]. A one dimensional steady state heat transfer model is developed and validated through a comparison with the experimental results of Sandia National Laboratories (SNL) [7]. They concluded that thermal efficiency of the PTC is maximum during the month of July and could reach 66.78% and minimal values of thermal efficiency are obtained during the month of December. E. Bellos et al [8] performed a numerical investigation on thermal performance of a solar PTC under steady state thermal conditions. Numerical results show that the thermal efficiency of the solar PTC increases as the solar beam radiation increases and the Nusselt number increases. However, thermal efficiency of the solar PTC decreases as HTF inlet temperature increases. The influence of some operation parameters on the thermal performance of a solar PTC have been predicted by J. Guo et al. [9]. The steady state model is employed to carry out the numerical model and the results show that there exists an optimal mass flow rate for thermal efficiency. Furthermore, increasing ambient temperature and solar incident angle leads to decrease the heat losses of solar receiver. The thermal analysis of a solar PTC based on steady state thermal model is presented by Kalogirou [10]. The developed model is written under the Engineering Equation Solver (EES) and validated with existing experimental data in the literature. Based on heat transfer analysis, Hachicha et al. [11] have proposed a numerical model to evaluate thermal performance of a solar PTC. The thermal model is based on steady state model and the finite volume method is
used to discretize the governing equations. The validation of the developed model is realized through a comparison with experimental data of SNL [7]. In order to investigate the effect of different working fluid on thermal performance of solar PTC, Ouagued et al. [12] have presented a heat transfer numerical model. Different synthetic oils are compared and results indicate that synthetic oil (Syltherm 800) is suitable as working fluid over the year compared to the other synthetic working fluids. From the previous literature, several numerical studies are presented to investigate the thermal performance of solar PTC. However, most of the proposed numerical models are simplified and developed under steady state conditions. In the present paper, a detailed transient heat model to predict the thermal performance of a solar PTC under transient conditions is developed. Due to the abundant solar radiation, about 5.5 kWh/m2/day [13], and in order to encourage the use of this technology, meteorological data of Morocco are used. The selected city is Tangier which is represent the second most important industrial center in this country and thermal performance of the solar PTC during four periods of year is investigated. The effect of some design and operation parameters which included the mass flow rate of Heat Transfer Fluid (HTF), the length of the receiver tube and the HTF nature, on outlet temperature of the solar PTC were also analyzed. 2
System Description
The solar PTC consists of three main elements: a reflector, a receiver tube and a support structure with a sun tracking system (Fig. 1). Fig. 2 shows a cross-section of the solar PTC. The solar flux received by the concentrator is first reflected on the mirror of the reflector and then passes through the glass envelope to reach the absorber pipe. The role of the glass cover is to reduce the thermal losses by convection with the ambient air. The surface of the absorber is covered by a selective material to absorb the maximum of the solar flux. The absorbed solar flux is converted into heat and transmitted by conduction and convection to the heat transfer fluid through the tube receiver.
Glass envelope
Receiver tube Absorber tube
𝑻𝒂𝒎𝒃
𝑻𝑭
𝑻𝑨
𝑻𝑽
Reflector
Reflector
F
L
W W
Fig. 1 Physical model of the solar PTC
3
Fig. 2 Cross-section of the solar PTC
Mathematical modeling The mathematical model is based on the following assumptions:
-
The heat transfer by conduction in the receiver tube is neglected. The absorber and the glass cover are assumed to be grey bodies. The form factor between the absorber and the glass cover is considered equal to 1. The fluid is incompressible. The solar flux on the absorber tube is uniform.
The solar PTC is modeled using the time dependent energy balance. In this method, the PTC is divided into N slices perpendicular to the heat transfer fluid flow direction. The exit of the th slices is considered the inlet of the following slices. The energy balance equation in each solar PTC component can be expressed as follows:
Glass envelope (1)
It can be written as: (2)
Absorber pipe (3)
Where: (4)
Heat transfer fluid (5)
Where: (6)
To these equations, we associate the following initial and boundary conditions: - Initial conditions At (7)
Where is the component of the PTC. - Boundary conditions
(8) (9)
3.1
Thermal efficiency
The thermal efficiency of a solar PTC is defined as the ratio of useful heat gain by the HTF and the heat flux received by the concentrator [14,15]: and
3.2
=
(10)
Convection heat transfer coefficients
The convective heat transfer coefficient between the glass envelope and the ambient air without wind is determined from the correlation developed by Churchill and Ch.[16,17].
(11)
With wind, we use the correlation developed by Churchill and Bernstein[16,17] :
(12)
The convective heat transfer coefficient between the absorber and air ( ) in the annular space depends on the pressure between the glass envelope and the absorber. When there is vacuum in the annular (Pressure < 0.013 Pa), we can consider that equal to zero [17]. But if the pressure in the annular space is greater than 0.013Pa, is estimated through natural convection relations between two horizontal, concentric cylinders [16,17]: (13)
Where (14)
And (15)
(16)
The convective heat transfer coefficient between the absorber and the (HTF) is given by equation (17). To calculate the Nusselt number, the Gnielinski correlation [18] is used : (17)
(18)
With f is the friction factor defined as follows: (19)
3.3
Radiation heat transfer coefficients
The heat transfer coefficient by radiation between the absorber tube and the glass envelope is expressed as follows [15]:
(20)
The heat transfer coefficient by radiation between the glass envelope and the sky is given as follows: (21)
And (22)
4
Numerical procedure
Equations (2), (4) and (6) are discretized by an implicit finite difference method. The obtained system of algebraic equations (23) is written as: (23)
This system of algebraic equations is solved by Gauss iterative method with a convergence criterion . The space and time steps retained are and . A computer program is developed under FORTRAN language enable to simulate the thermal performance of the solar PTC under different weather conditions. The flow chart of the calculation is presented in Fig. 3. of
Start
Input data: parameters of the solar PTC, meteorological data, initials conditions, , , etc.
Time of sunrise and sunset
(i)
Calculation of the heat transfer coefficients and solving the system of equations =T
Space Loop
Time loop
Loop on hours
Calculation of absorbed solar flux, optical efficiency of the solar PTC
No
Yes
Saving Results
End
Fig. 3 Flow chart of the calculation program
5
Results and discussion
First, we validated the mathematical model and the numerical code that we developed by comparing our results with experimental results from literature [7]. Then, we applied the numerical code to investigate the thermal performance of the solar PTC under transient climatic conditions. 5.1
Model validation
The experimental study of Sandia National Laboratories (SNL) [7] is carried out on a solar PTC of type (LS2 PTC) with synthetic oil (Syltherm 800) as working fluid. The characteristics of the solar PTC used in the experimental tests are given in Table 1. The same characteristics of the solar PTC are used in the present numerical model and obtained results show that our results are in good agreement with experimental results (Fig. 4). It can be observed that the numerical results are not exceeding the dotted lines (Errors limits) and maximum discrepancy between numerical and experimental results is about 2.41%. We consider that these results validate
our numerical model and the methodology that we have developed. They can; therefore, be applied to the study of the thermal performance of the solar PTC under different operating conditions. Table 1 Characteristics of the (PTC) used in the model validation[7] Parameters Absorber length (L) Collector width (W) Focal distance (F) Absorber pipe internal diameter ( ) Absorber pipe external diameter ( ) Glass envelop internal diameter ( ) Glass envelop external diameter ( ) Absorber pipe thermal absorptance Glass envelop thermal absorptance Glass envelop transmittance Absorber pipe emittance Glass envelop emittance Reflected surface reflectivity Shape factor (
Values 7.8 m 5m 1.84 m 0.066 m 0.070 m 0.109 m 0.115 m 0.906 0.02 0.95 0.14 0.86 0.93 0.92 1
incident angle modifier
Experimental Model +/- 5%
80 75
th(%)
70 65 60 55 50 0,0
0,1
0,2
0,3
0,4
0,5
(Tin-Tamb)/Id Fig. 4 Comparison between our results and experimental results [7].
5.2
Thermal performance
In this section, the thermal performances of the solar PTC during four days of the year in Tangier city are investigated. The available meteorological data for the Tangier city such as air temperature, air velocity and solar intensity are those of 15 January, 15 April, 15 July and 14 November. The characteristics of the solar PTC used in simulations are given in Table 2 The inlet HTF temperature at the solar concentrator is assumed to be equal to the ambient temperature and the available thermo-physical properties of water and oil (syltherm 800) used in the simulations are given as a function of temperature (Table 3).
Table 2 Characteristics of the (PTC) used in this study Parameters
Values
Absorber length (L) Collector width (W) Focal distance (F) Absorber pipe internal diameter ( ) Absorber pipe external diameter ( ) Glass envelop internal diameter ( ) Glass envelop external diameter ( ) Mass flow rate ( ) Absorber pipe thermal absorptance Glass envelop thermal absorptance Glass envelop transmittance Absorber pipe emittance Glass envelop emittance Reflected surface reflectivity Shape factor (
5m 3.4 m 1.84 m 0.066 m 0.070 m 0.109 m 0.115 m 0.0278kg/s 0.906 0.02 0.95 0.14 0.86 0.93 0.92 1
incident angle modifier
Table 3 Physical proprieties of water and synthetic oil [19,20]
Water
Oil (Syltherm 800)
Fig. 5 shows the variation of the ambient temperature during four different periods of the year in Tangier city. It can be observed that maximum values of ambient temperature are obtained during summer (15th July) and the highest wind speed is observed on 15th April which is between 12.8 m/s and 19.8 m/s. However, during the 15th July, the wind speed is minimal and it does not exceed 1.75 m/s (Fig. 6). The evolution of the solar irradiance during the four days is presented in (Fig. 7). Solar irradiation reaches a maximum value of 675 W/m² on 15th July, 560 W/m² on 15th April, 472 W/m² on 14th November and 448 W/m² on 15th January 15 July 15 April 15 January 14 November
20
297
18
294
16 Wind speed (m/s)
ambient temperature (K)
300
291 288 285 282
14 12 10 8 6 4
279 276
15 July 15 April 15 January 14 November
2 6
8
10
12
14
16
18
20
Legal time (Hours)
Fig. 5 Ambient temperature on four days of the year
0
6
8
10
12
14
16
18
20
Legal time (Hours)
Fig. 6 Wind speed on four days of the year
The evolution of the water outlet temperature of the solar PTC during the day is similar to that of the solar flux (Fig. 8). It increases in the morning until reaching a maximum value and then decreases during the afternoon until reaching the ambient temperature. The water outlet temperature reaches a maximum value about 369.3 K in summer, 352.6 K in spring, 341.7 K in autumn and about 330.5 K in winter. These values are obtained at 12: 00 pm on 14th November, at 13: 00 pm on 15th July and 15th January and at 14: 00 pm on 15th
April. It will be noted that these hours correspond to the maximum values of the direct solar flux captured by the solar PTC. The hourly variation of useful heat gain by the HTF is shown in Fig. 9. It is seen that the heat flow recovered by the water is highest during the summer. It reached 8768.40 W at 13.00 pm on 15th July, 7001 W at 14.00 pm on 15th April, 5752.5 W at 12.00 pm on 14th November and 5252 W at 13.00 pm on 15th January. Fig. 10 shows the hourly thermal efficiency of the solar PTC. Thermal efficiency is maximum on 15th July and can reach 76.4%. During the winter, maximal value observed is about 69%. These results are corroborated by those of the hourly evolution of the solar flux received by the solar PTC.
15 July 15 April 15 January 14 November
360
600 500
Temperature (K)
Direct solar radiation (W/m²)
700
400 300 200 100 0
15 July 15 April 15 January 15 November
380
340 320 300 280
6
8
10
12 14 16 Legal time (Hours)
18
20
6
Fig. 7 Direct solar radiation on four days of the year
8
10
12 14 16 Legal time (Hours)
18
20
Fig. 8 Water temperature variation at the output of the absorber tube on four days of the year
The increase of the mass flow rate leads to decrease the water outlet temperature (Fig. 11). This is in good agreement with results obtained by [8].This behavior can be justified by the reduction of the water residence time in the receiver tube as the water mass flow rate increases. It is obvious that for different periods of the year, increasing the receiver tube length causes an increase of the heat transfer area between the HTF and the receiver tube. Consequently, the water outlet temperature increases as the receiver tube increases (Fig. 12). 15 July 15 April 15 January 15 November
9000 8000
80 70 Thermal efficiency (%)
Useful heat (W)
7000 6000 5000 4000 3000 2000 1000 0
15 July 15 April 15 January 14 November
60 50 40 30 20 10
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 Legal time (Hours)
Fig. 9 Useful heat gain by water on four days of the year
0
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 Legal time (Hours)
Fig. 10 Concentrator thermal efficiency on four days of the year
15 July 15 April 15 January 14 Novembre
370
390 380
350
370
340
360 Temperature (K)
Temperature (K)
360
330 320 310 300 290 280
15 July 15 April 15 January 14 November
350 340 330 320 310 300 290
0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45
1
Mass flow rate (Kg/s)
Fig. 11 Water outlet temperature at 13:00 pm of each day
2
3 4 5 Receiver tube length (m)
6
Fig. 12 Water outlet temperature at 13:00 pm of each day
Temperature (K)
Fig. 13 presents the evolution of HTF outlet temperature in Tangier city during the 15 th of July. It can be observed that outlet temperature of Oil (Syltherm 800) is higher than that of water. This result can be explained by the difference between physical properties of oil and water. Furthermore, outlet temperature of oil increase much faster than water and that is due to the lowest calorific capacity of oil.
390 380 370 360 350 340 330 320 310 300 290 280
Water Oil (Syltherm 800)
6
8
10
12
14
16
18
20
Legal time (Hours)
Fig. 13 HTF outlet temperature during the 15th July
6
Conclusions
A detailed numerical modeling of the thermal performance of a solar Parabolic Trough Collector (PTC) under transient climatic conditions is presented. A self computer program is developed under FORTRAN language to solve the governing equations and the meteorological data of Morocco are used in the simulations. The main conclusions of the present study can be summarized as follows: The amount of useful heat gain per day is highest in summer (about 71.4 kWh/day) and is minimal in winter (about 30.87 kWh/day). Thermal efficiency of the solar PTC increases with the intensity irradiation and can reach a maximum value of approximately 76 % in summer. The water outlet temperature increases with the length of the receiver tube and decreases as the mass flow rate of the fluid increases. In temperature range from 290 K to 390 K, using synthetic oil as working is suitable compared to water. The developed model is suitable to investigate thermal performance, system design and optimization of solar PTC under real climatic conditions.
Nomenclature
k
CSP EES GHG HTF PTC
Aperture area [m²] Cross sectional area [m²] Specific heat [J.kg-1.K-1] Diameter [m] Focal distance [m] Grashof number Heat transfer coefficients [W.m-² K-1] Direct solar irradiation [W.m-²] Incident angle modifier Thermal conductivity [W.m-1.K-1] Absorber length [m] Mass [kg] Mass flow rate [kg.s-1] Nusselt number Prandtl number Heat flux [W] Rayleigh number Reynolds number Temperature [K] Time [s] Collector width [m] Axial coordinate [m] Abbreviations Concentrated Solar Power Engineering Equation Solver Greenhouse gas Heat transfer fluid Parabolic trough collector
Greek Symbols Absorptance factor Thermal expansion coefficient [K-1] Transmittance Intercept factor Emittance Density [kg.m-3] Reflected surface reflectivity Dynamic viscosity [Pa.s] Stefan–Boltzmann constant Incidence angle [rad] Efficiency Time step [s] Receiver segment length [m] Subscripts Absorber pipe Absorbed Ambient air Convection Outside tube Effective Exterior Fluid Inside tube Inlet of the receiver tube Interior Outlet of the receiver tube Radiation Useful Glass envelope Sky Thermal
Declarations of interest: None. Acknowledgements The authors greatly acknowledge the financial support from the Moroccan National Center for Scientific and Technical Research (N° 31UAE2016). References [1]
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Highlights
Thermal performance of a PTC under transient conditions is successfully predicted. Design and operation parameters effect in temperature range 290-390K are examined. Maximum thermal efficiency of the PTC is achieved in summer and it is about 76%. Using synthetic oil as working is suitable compared to water.