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Analysis of Water Cooling of CPV Cells Mounted on Absorber Tube of a Parabolic Trough Collector
Available online at www.sciencedirect.com
ScienceDirect Energy Procedia 90 (2016) 78 – 88
5th International Conference on Advances in Energy Research, ICAER 2015, 15-17 December 2015, Mumbai, India
Analysis of water cooling of CPV cells mounted on absorber tube of a Parabolic Trough Collector Nikhil Gakkhar1,*, M.S.Soni1, Sanjeev Jakhar1 1
Center for Renewable Energy and Environment Development, Birla Institute of Technology and Science, Pilani, Rajasthan, India 333031
Abstract In the present paper, an analytical approach has been developed and presented to estimate the thermal performance of multijunction solar panel under high concentration with liquid cooling on both sides of the panel. For such system, the receiver of parabolic collector is modified to incorporate solar cells. A long panel of flexible solar cells is mounted on the outer side of circular receiver. The water is allowed to flow from inside as well as outside of receiver, thus reducing the temperature of the panel significantly. Analytical model is developed and thermal analysis has been carried out using MATLAB (vR2012a). The thermal model predicts the temperature variation of the cell along its length, which given the improved efficiency of the panel. To validate the proposed model, the simulation is performed in COMSOL (v5.1). The results show that temperature of the liquid can be maintained up-to 85 °C, thus reducing the temperature of panel from initial temperature (without liquid cooling) of above 134 °C, under stagnant air in the annulus conditions. The results obtained are within the close approximation. The future scope would include the experimental validation of the proposed system. ©©2016 Authors. Published by Elsevier Ltd. This 2016The The Authors. Published by Elsevier Ltd.is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ICAER 2015. Peer-review under responsibility of the organizing committee of ICAER 2015 Keywords: Parabolic Trough Collector; Concentrator photovoltaic; Liquid immersion cooling; MATLAB
* Corresponding author. Tel.: +91-1596-515225; fax: +91-1596-244183. E-mail address: [email protected] (Nikhil Gakkhar) mssoni@@pilani.bits-pilani.ac.in (M.S. Soni)
1876-6102 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ICAER 2015 doi:10.1016/j.egypro.2016.11.172
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Nomenclature A area (m2) D diameter (m) g gravitational constant (9.8 m/s2) h convective heat transfer coefficient (W/m2.K) k thermal conductivity (W/m.K) T temperature (K) L length (m) P perimeter (m) rate of heat transfer per unit length (W/m) Greek letters θ incident angle ƞ optical efficiency α absorptance ρ reflectance ε emissivity μ refractive index τ transitivity ν kinematic viscosity σ Stefan-Boltzmann constant (5.67 x 10-7 W/m2K4) Indices cond conduction conv convection rad radiation i irradiance m mean g glass t absorber tube f fluid (HTF) b bracket r receiver 1. Introduction Solar thermal energy utilization can be done with the help of Parabolic Trough Collectors (PTC). Many researchers tested and validated the application of PTCs with various application like power generation, desalination etc [1,2]. Parabolic trough technology has proven to be the most mature and low cost solar thermal technology available today. Concentrated sunlight using linear Fresnel lens can also be used to drive Concentrated Photovoltaic (CPV) cells [3]. The application of CPV using various techniques has already been discussed in the literature [4–7]. Concentrated Photovoltaic Thermal (CPV/T) which includes thermal system for CPV cooling has also been used for utilization of electrical as well as thermal energy [8,9]. Conventry [10] investigated the performance of a CPV/T collector where the row of cells were cooled by liquid flowing through an internally finned aluminum pipe with optical concentration of 37 suns. He found out that the thermal and electrical efficiency of the system was affected by high temperatures. The main problem with the CPV cells is the high temperature with increase in concentrated solar radiation. This increase in temperature leads to reduction in the cell efficiency and too high of a temperature may damage the cell’s integrity. If the temperature exceeds a certain limit its life-span would reduce rapidly [11], so proper cooling system is required to maintain the temperature within the limit. A simple cooling system design may also help to reduce the maintenance costs. While a variety of approaches have been used to the keep the cells cool, most of them are based
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upon removal of heat from the back of the cell (opposite surface of the incident flux exposed surface) [12,13]. The both side cooling of the flat CPV cell was discussed by Zhu et al. [14]. Liquid immersion cooling of concentrated PV cells has also been discussed by Han et al. [15,16], Zhu et al. [17], Han et al. [18], Xiang et al. [12] etc. The presented research work proposes the modified receiver system for effective cooling. Since, circular geometry has large surface area as compared to flat plate the circular tube is consideration [19]. The CPV cells are assumed to be mounted on the absorber tube of PTC where the liquid is allowed to flow though the annulus as well, thus allowing the cooling to occur from both sides of the cells. 2. Proposed system In this section, a proposed novel design for the liquid immersion cooling system of CPV along with PTC is presented. The designed receiver consists of non evacuated glass tube, absorber tube and flexible multi-junction CPV cells mounted on absorber tube with the help of epoxy. The Heat Transfer Fluid (HTF) flows through inside as well as outside of absorber tube, thus cooling the CPV cells from both sides for better performance. The schematic diagram of the system is shown in Fig. 1. For the design estimation, the energy balance has performed on such receiver system as discussed further in the section. 3. Thermal analysis of the proposed model 3.1. Energy balance model In this section, the thermal model for proposed novel design is presented. For the design estimation, the energy balance has performed on receiver system using one-dimensional methods by taking followings assumptions: • • • •
The solar radiation falling on the receiver is always taken normal to the surface. Uniform heat flux over the glass envelope and absorber tube. The flexible CPV cell is perfectly mounted along the irradiance side. The scattering and attenuation of solar radiation within the liquid is assumed to be negligible.
Fig. 1 One dimensional steady state energy balance
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As shown in Fig. 1, the energy balance is performed on receiver which consists of glass tube and absorber pipe. The flexible CPV cells are mounted on irradiance side of absorber tube so that it receives maximum solar radiation. For the simplicity, the cell and epoxy thickness has been neglected and is overall thermal conductivity of the joint is taken for consideration. The HTF flows inside the absorber tube as well as through annulus. The one dimensional energy balance method is taken similar to the evacuated absorber tube which are available in the literature [20,21]. The energy model is modified by balancing the incoming solar radiation and optical losses. In this novel receiver, uniform circumferential heat flux is assumed by taking the average of solar radiation from concentrated and non concentrated side. All the temperatures and thermodynamic properties are also assumed to be uniform across the circumference. Six surfaces are identified for the heat transfer analysis across the receiver. The incoming solar ), which is glass envelope outer surface, as well as on surface 3 ( ) which is radiation falls on the surface 5 ( outer surface of absorber tube. Across the glass tube, the absorbed energy is transferred through conduction ( ) and by convection ( ) from surface 4. The surface 4 which is inner surface of glass envelop allows convection heat transfer through HTF (which is flowing within the annulus and taken as bulk surface 9). The surface 3 transfers the heat through convection ( ) and conduction ( ) to the HTF and inner surface of tube respectively as shown in Fig. 1. From surface 2 the heat transfer occurs by convection ( ) to the inner fluid, which is taken as surface 1. The ambient and sky conditions are taken with subscript 6 and 7 respectively. Using Fig. 1, by applying the energy balance on each surface, the following equations are obtained: ' ' q5' a + q'45cond = q56 conv + q57 rad
(1)
' q'49conv = q'45cond + q34 rad ' ' q39 = q conv 49conv ' ' ' q3' a = q39 conv + q32cond + q34rad ' ' q32 cond = q21conv
(2) (3) ' + qbc
(4) (5)
3.1.1. Incident solar irradiation The incident solar absorptance on surface 5 ( ) and on surface 3 ( ) falling on the outer surface of the glass is treated as heat flux to simplify the thermal analysis. As discussed by Forristall [21], this assumption simplifies and makes the conduction equation linear across the glass and absorber tube. Although this assumption introduces minimal error, but for small absorbtance coefficient of the glass, this error can be neglected. Also, the incident irradiation is taken as uniform over the entire circumferential surface. The variation in incident angle which causes optical losses by the incident rays which are not normal to the surface are given by Incident Angle Modifier (K) as
K = cosθ + 0.000884θ − 0.00005369θ 2
(6)
The optical efficiency of the glass is given by radiation absorbed by the glass envelop by the incident normal irradiation. Forristal [21] defines the solar absorption in glass as ' q 5a = qi'η g α g
(7)
while ηg = ε t ρm K and is the estimates of effective optical efficiency as given by Price et al. [22]. is the solar radiation falling on the receiver per unit length (W/m) The solar radiation falling on the absorber tube after passing through the glass envelop and HTF can also be treated as heat flux. The equation of solar absorption becomes ' (8) q3a = qi'ηtαt
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while
ηt = ηgτ gτ f
3.2. Heat Transfer Analysis The receiver part consists of glass tube, HTF and absorber tube. The heat transfer would occur by all three modes, i.e. Conduction, Convection and Radiation. 3.2.1. Conduction heat transfer The conduction heat transfer takes place on three surfaces in the given model through the glass, absorber tube and as heat losses in the form of conduction from the support brackets. The conduction heat transfer within the glass and tube are given as:
q '45cond = ' q32 cond
2π k g (T4 − T5 )
(9)
ln( D5 / D4 ) 2π km (T2 − T3 ) = ln( D3 / D2 )
(10)
The values of thermal conductivity of glass envelope and absorber tube are assume to be uniform throughout the surface and are taken from the Incropera [23]. The thermal conductivity for eqn. (10) is taken by considering thermal resistance of absorber tube, epoxy and CPV cell in series. The conduction from the support bracket depends on the contact area between absorber tube and bracket. To estimate the heat losses, the bracket is treated as infinite long fin with base temperature 10 degree less than the T3. For the simplification the dimensions of the support bracket is assumed to be same as that of Forristal [21]. The perimeter is taken as 0.2032 m having area of 1.613 x 10-4m2. The thermal conductivity is assumed to be 50 W/m-K. The convective heat transfer coefficient depends on wind or no-wind case. From the literature it is taken within the range of 2-25 W/m2-K (for no-wind) and 25-250 W/m2-K (for wind). The conduction equation for such system is given as: ' qbc = hb Pb kb Ab × (Tb − T6 ) / Lr
(11)
3.2.2. Convection heat transfer The convection occurs at four surfaces in this model. From surface 5, the convection ) occurs from outer glass surface to the ambient conditions. The temperature difference is assumed to be ( linear here. The convection term is given by ' q56 conv = h56 D5π (T5 − T6 ) With h56 = Nu5kg / D5
(12) (13) The value of Nusselt number (Nu) for the equation (13) can be obtained by treating cross-sectional flow over the long cylinder. The flow velocity over the cylinder governs the Reynolds number and thus Nusselt number. To assess the convection coefficient, wind and no-wind cases are used. For the no-wind case, the convection from the glass surface to the surrounding will only by natural convection. To estimate the natural convection, the correlation given by Churchill and Chu [24] will be used as discussed in Ref [23].
Nu56
8 ⎫ ⎧ 9 ⎤ 27 ⎛1⎞ ⎡ ⎪ ⎪ ⎜6⎟ ⎢ ⎛ 0.559 ⎞16 ⎥ ⎪ ⎪ ⎝ ⎠ = ⎨0.60 + 0.387 × Ra56 / ⎢1 + ⎜ ⎟ ⎥ ⎬ Pr ⎪ ⎢ ⎝ 56 ⎠ ⎥ ⎪ ⎣ ⎦ ⎪ ⎪ ⎩ ⎭
2
(14)
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Ra56 =
β=
g β (T5 − T6 ) D53
(15)
α 56ν 56
1 T56
Pr56 =
(16)
ν 56 α56
(17)
where Ra is the Rayleigh number and Pr is the Prandlt number for glass outer cover, β is volumetric coefficient for thermal expansion and α is thermal diffusivity at temperature T56 which is the film temperature. The Eqn (14) is valid for 105 < Ra < 1012. In case of wind, the convection will be forced and the correlation for Nusselt number can be obtained by using Churchill and Bernstein equation. This correlation is valid for all ranges of Reynolds number with . −1/4
4/5
⎡ ⎛ Re ⎞5/8 ⎤ ⎡ 0.4 ⎤ 56 (18) ⎢1 + ⎜ Nu56 = 0.3 + 0.62 Re Pr ⎢1 + 2/3 ⎥ ⎟ ⎥ ⎢⎣ ⎝ 282000 ⎠ ⎥⎦ ⎢⎣ Pr56 ⎥⎦ This correlation assumes long horizontal cylinder with isothermal conditions. The fluid (air) properties are taken as ambient conditions, while Pr56 is evaluated at the film temperature on the surface 5. The convection within the absorber tube can be estimated by taking the fluid flow inside the tube. The correlations can be taken as Petukhov equations [25], as discussed in Ref [26] (19) q'21conv = h21D1π (T2 − T1 ) 1/2
1/3
⎛ f ⎞ 0.11 ⎜ 8 ⎟ Re Pr ⎛ Pr56 ⎞ ⎝ ⎠ Nu = ⎜ ⎟ Pr f 1.07 + 12.7 Pr 2/3 − 1 ⎝ 5 ⎠ 8
(20)
f = (0.79ln Re−1.64)−2
(21)
(
)
The other two convections occur between the annulus, from the outer surface of the absorber tube to the HTF ) and from the inner surface of the glass cover to the HTF ( ). The convective heat transfer for ( surface 3 and surface 4 can be calculated by using Petukhov correlation as discussed in eqn (20). Gnielinski [27] modified the correlation by adding the effect of characteristics length during the convection. ⎛ f ⎞ ⎜ 8 ⎟ Re Pr ⎛ ⎛ d ⎞2/3 ⎞ ⎝ ⎠ ⎜1 + ⎜ ⎟ ⎟ (22) Nu = ⎜ ⎝L⎠ ⎟ f ⎠ 1 + 12.7 Pr 2/3 − 1 ⎝ 8 (23) f = (1.8log Re−1.5)−2
(
)
In Eq (12), for (convection between surface 3 (T3) and bulk mean temperature of water (T9)) and for (convection between surface 4 (T4) and bulk mean temperature of water (T9)), the hydraulic diameter (dh) is taken as characteristics length for the estimation of Reynolds number. It is given by difference of inner glass envelope diameter to outer absorber tube diameter.
3.2.3. Radiation heat transfer ) and from the absorber tube to the glass ( ). The The radiation occurs from glass surface to the sky ( later one occurs due to high temperature of the absorber tube and is of long wavelength. It will get absorbed within
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' 4 4 q 57 rad = σε g π D5 (T5 − T7 )
(24)
The absorber tube radiation can be treated as the radiation between two concentric cylinders with participating media in between. Here, for the simplicity the scattering and attenuation effect has been neglected between the fluid molecules. The radiation equation for this case is given by Modest [28]. The Non-dimensional radiative heat flux depends upon the ratio of two cylinders diameter (D3/D4) and is taken from the Modest [28]. Further this term can be neglected if we assumed all the long wave radiation got absorbed within the next fluid layer to the absorber tube. The radiation between the fluid layer and from fluid layer to the glass can be estimated by using generic equations for long infinite concentric cylinder with participating media [23]. ' q34 rad =
σπ D2 (Tn4 − Tn4−1 ) 1 − ε g D2 1 1 + −1 + εt εt ε g D4
(25)
where Tn and Tn-1 are the intermediate fluid temperature at n and n-1 layer respectively. 3.2.4. Heat losses The heat losses in the receiver includes the convection and radiation heat loss from the outer glass envelope to the environment and the conduction losses from the support bracket. It is given as: ' ' ' q'heatloss = q57 rad = q56conv + qbc
(26)
Table 1. Receiver tube specification used in the model Parameters Receiver tube length Absorber internal diameter Emissivity of glass Absorber external diameter Absorber thermal conductivity Glass cover internal diameter Emissivity of absorber tube Optical efficiency of glass envelop Absorptance of glass envelope Thermal conductivity of glass Thermal conductivity of air Thermal conductivity of fluid Wind velocity Density of air Density of fluid Dimensionless radiative heat transfer coefficient
Value 1.2 m 0.0656m 0.82 0.07 m 411 W/mK 0.110 m 0.4 0.8 0.04 1.04 W/mK 0.026 W/mK 0.1357 W/mK 1 m/s 1.2 kg/m3 1060 kg/m3 0.96
4. Comsol Validation The validation of proposed model is done by simulating the system using Comsol (v5.1). For the simplified solution, the 3D model of the receiver is taken as 2D symmetrical model and thermal analysis is done by taking heat transfer multiphysics. The dimension of receiver tube is taken as 1.2 meter with glass envelope diameter of 125 m having thickness of 10 mm. The absorber tube diameter is 70 mm with thickness of 2.2 mm. The thickness of cell is taken as 0.5 mm is assumed to be negligible in case of analytical model. Since back side of cell is attached to the absorber tube, surface 2 (Inner side of absorber tube) which is in contact with fluid is taken as the back cell temperature. For multiphysics, simple heat transfer in solid along with laminar flow model is used. The meshing is taken with normal approach with the curvature factor of 0.3, as per the simulation tool. The two physics are coupled
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with temperature coupling. The parameters taken for the simulations are shown in Table 1. The simulated model of receiver tube is shown in Fig. 2. The temperature variation along the length is presented in the same.
Fig. 2. Temperature plot of receiver tube along the length (mm)
5.
Results and Discussion
The Comsol simulation of proposed system having flexible multijunction cells mounted on the absorber tube with HTF on both sides of the cells is simulated using parameters mentioned in Table 1. The temperature at the front surface of cell is observed to be more than the back side of the cell. The temperature variation across the six different surfaces along the length is shown in Fig. 3. 315
370
314
360 Surface 5
340
Surface 4 Surface 3
330
Surface 9
320
Surface 2
310
Surface 1
300
Temperature (K)
Temperature (K)
313 350
312 311 310 309 308
Comsol simulation Analytical model
307 306
290 0
150 300 450 600 750 900 1050 1200 Length (mm)
Fig.3. (a) Temperature variation over various surface (b) Comparison of Comsol and analytical model for same outer glass envelope temperature
It is observed from the Fig. 3(a) that the temperature at the outer glass surface (Surface 5) increases gradually as compared to inner most fluid (surface 1). The temperature at surface 2 and 3 are almost identical with the fact that it is the inner and outer surface of the absorber tube having small thickness. Similar trend is observed in inner and
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outer surface of glass tube. The temperature within the annulus goes from the inlet temperature (which is assume to be 295 K) to a converging value of around 360 K, by the end of tube length. The temperature results obtained are then compared with the results obtained by analytical model by MATLAB. The analytical approach results for fixed outer glass envelope section is compared with the Comsol results and are shown in Fig. 3(b). It shows the comparison of Comsol model (v5.1) and analytical model for same outer glass envelope The temperature value of two-dimensional model in Comsol across the length is obtained and at the point where outer temperature of glass envelope reaches 313 K, a cut cross-sectional view is obtained. The radial temperature variation is observed on each surfaces compared with one dimensional analytical results. It is found out that the analytical model shows the same trend as that of Comsol results. In Comsol case, when surface 5 is taken at 313 K, the temperature in inward direction decreases to 311 K for surface 1. The analytical model shows temperature of 309 K for surface 1 with same surface 5 temperature. The variation in the analytical model may be due to the assumptions taken in the same. Further, the Comsol model is also varied with the condition when no water flows through the annulus, by making it similar to stagnant air tube conditions. The simulations in the Comsol reveals the maximum cell temperature that could be achieved in case of no fluid within the annulus. The plot obtained in such case is shown in Fig. 4. The graph shows that without fluid within the annulus, the maximum temperature is obtained across the length as 407 K which is 46 degrees higher than the fluid flow case. Thus without fluid flow, or cooling from one side, the high cell temperature would degrade the cell. This also reduce the electrical efficiency of the cell. Hence, in such case, the HTF within the annulus would carried away by excess and the temperature of the cell can be maintained. The extracted thermal energy can be utilized for heating applications.
Fig.4. Comsol plot for no fluid flow case within the annulus
6. Conclusion In the present paper, an analytical approach has been developed and presented to estimate the thermal performance of multi-junction solar panel under high concentration with liquid cooling on both sides of the panel. The analytical model is proposed for a system where CPV cells were assumed to be mounted on the absorber tube. The HTF is flown within the annulus to allow cooling of the cell from both sides. The model is simulated considering the geometrical, optical and thermal aspect of receiver tube in MATLAB. The temperature trend obtained in the radial direction decreases from outward to inward. From outer glass envelope surface at 313 K, the temperature of inner most fluid reaches to 309 K. Across the length, the results show increase in temperature trend. This model is validated with Comsol (v5.1) where two-dimensional approach has been used for simulation. In that
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simulation sectional view (one dimension) for same outer glass temperature is taken and compared with analytical model which gives slight variation because of the assumptions taken within the model. Further the Comsol model is compared with no flow condition in the annulus, thus achieving the maximum temperature of 407 K (134 °C). This shows that fluid flow within the annulus is better case where heat can be carried away easily from the both sides of the cells. In such case, the operating temperature of cells can be maintained 46 degree less when compared to that obtained for vacuum in the annulus i.e. one side cooling. With both sides cooling not only the operating efficiency of CPV cells will increase but also the heat gained by the fluids in the annulus as well as in the absorber tube will enhance the overall utility of the system. Future scope of the research is experimental validation of such system Acknowledgements Authors gratefully acknowledge the support from the Center for Renewable Energy and Environment Development, BITS - Pilani Rajasthan, for this research. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25]
Jakhar S, Misra R, Soni MS, Gakkhar N. Parametric simulation and experimental analysis of earth air heat exchanger with solar air heating duct. Engineering Science and Technology, an International Journal 2016:1–8. Gakkhar N, Soni MS, Jakhar S. Second law thermodynamic study of solar assisted distillation system: A review. Renewable and Sustainable Energy Reviews 2016;56:519–35. Raj PS, Soni MS, Jakhar S. A Review on Photovoltaic/Thermal and Concentrated Photovoltaic/Thermal Hybrid Solar Technology. International Congress on Renewable Energy, New Delhi: 2014, p. 282–9. Lovegrove K, Stein W. Concentrating solar power technology: Principles, developments and applications. Elsevier; 2012. Kinsey GS, Bagienski W, Nayak A, Liu M, Gordon R, Garboushian V. Advancing efficiency and scale in CPV arrays. Photovoltaic Specialists Conference (PVSC), Volume 2, 2012 IEEE 38th, IEEE; 2012, p. 1–6. Du D, Darkwa J, Kokogiannakis G. Thermal management systems for Photovoltaics (PV) installations: A critical review. Solar Energy 2013;97:238–54. Kinsey GS, Stone K, Brown J, Garboushian V. Energy prediction of Amonix CPV solar power plants. Progress in Photovoltaics: Research and Applications 2011;19:794–6. Jakhar S, Soni MS, Gakkhar N. Historical and recent development of concentrating photovoltaic cooling technologies. Renewable and Sustainable Energy Reviews 2016;60:41–59. Gakkhar N, Soni MS. Techno-economic parametric assessment of CSP power generations technologies in India. Energy Procedia, vol. 54, Elsevier Ltd; 2014, p. 152–60. Coventry JS. Performance of a concentrating photovoltaic/thermal solar collector. Solar Energy 2005;78:211–22. Royne A, Dey CJ, Mills DR. Cooling of photovoltaic cells under concentrated illumination: a critical review. Solar Energy Materials and Solar Cells 2005;86:451–83. Xiang H, Wang Y, Zhu L, Han X, Sun Y, Zhao Z. 3D numerical simulation on heat transfer performance of a cylindrical liquid immersion solar receiver. Energy Conversion and Management 2012;64:97–105. Makki A, Omer S, Sabir H. Advancements in hybrid photovoltaic systems for enhanced solar cells performance. Renewable and Sustainable Energy Reviews 2015;41:658–84. Zhu L, Boehm RF, Wang Y, Halford C, Sun Y. Water immersion cooling of PV cells in a high concentration system. Solar Energy Materials and Solar Cells 2011;95:538–45. Han X, Wang Y, Zhu L. Electrical and thermal performance of silicon concentrator solar cells immersed in dielectric liquids. Applied Energy 2011;88:4481–9. Han X, Wang Y, Zhu L. The performance and long-term stability of silicon concentrator solar cells immersed in dielectric liquids. Energy Conversion and Management 2013;66:189–98. Zhu L, Wang Y, Fang Z, Sun Y, Huang Q. An effective heat dissipation method for densely packed solar cells under high concentrations. Solar Energy Materials and Solar Cells 2010;94:133–40. Han X, Everett V, Wang Y, Zhu L. Numerical analysis of direct liquid-immersed solar cell cooling of a linear concentrating photovoltaic receiver. Photovoltaic Specialists Conference (PVSC), 2010 35th IEEE, IEEE; 2010, p. 3033–8. Jakhar S, Soni MS, Gakkhar N. Performance Analysis of Photovoltaic Panels with Earth Water Heat Exchanger Cooling. MATEC Web of Conferences 2016;55:0–5. Padilla RV, Demirkaya G, Goswami DY, Stefanakos E, Rahman MM. Heat transfer analysis of parabolic trough solar receiver. Applied Energy 2011;88:5097–110. Forristall R. Heat Transfer Analysis and Modeling of a Parabolic Trough Solar Receiver Implemented in EES. 2003. Price H, Lupfert E, Kearney D, Zarza E, Cohen G, Gee R, et al. Advances in parabolic trough solar power technology. Journal of Solar Energy Engineering 2002;124:109–25. Incropera FP. Fundamentals of heat and mass transfer. John Wiley & Sons; 2011. Churchill SW, Chu HHS. Correlating equations for laminar and turbulent free convection from a horizontal cylinder. International Journal of Heat and Mass Transfer 1975;18:1049–53. Petukhov BS. Heat transfer and friction in turbulent pipe flow with variable physical properties. Advances in Heat Transfer
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ScienceDirect Energy Procedia 90 (2016) 78 – 88
5th International Conference on Advances in Energy Research, ICAER 2015, 15-17 December 2015, Mumbai, India
Analysis of water cooling of CPV cells mounted on absorber tube of a Parabolic Trough Collector Nikhil Gakkhar1,*, M.S.Soni1, Sanjeev Jakhar1 1
Center for Renewable Energy and Environment Development, Birla Institute of Technology and Science, Pilani, Rajasthan, India 333031
Abstract In the present paper, an analytical approach has been developed and presented to estimate the thermal performance of multijunction solar panel under high concentration with liquid cooling on both sides of the panel. For such system, the receiver of parabolic collector is modified to incorporate solar cells. A long panel of flexible solar cells is mounted on the outer side of circular receiver. The water is allowed to flow from inside as well as outside of receiver, thus reducing the temperature of the panel significantly. Analytical model is developed and thermal analysis has been carried out using MATLAB (vR2012a). The thermal model predicts the temperature variation of the cell along its length, which given the improved efficiency of the panel. To validate the proposed model, the simulation is performed in COMSOL (v5.1). The results show that temperature of the liquid can be maintained up-to 85 °C, thus reducing the temperature of panel from initial temperature (without liquid cooling) of above 134 °C, under stagnant air in the annulus conditions. The results obtained are within the close approximation. The future scope would include the experimental validation of the proposed system. ©©2016 Authors. Published by Elsevier Ltd. This 2016The The Authors. Published by Elsevier Ltd.is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ICAER 2015. Peer-review under responsibility of the organizing committee of ICAER 2015 Keywords: Parabolic Trough Collector; Concentrator photovoltaic; Liquid immersion cooling; MATLAB
* Corresponding author. Tel.: +91-1596-515225; fax: +91-1596-244183. E-mail address: [email protected] (Nikhil Gakkhar) mssoni@@pilani.bits-pilani.ac.in (M.S. Soni)
1876-6102 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ICAER 2015 doi:10.1016/j.egypro.2016.11.172
Nikhil Gakkhar et al. / Energy Procedia 90 (2016) 78 – 88
Nomenclature A area (m2) D diameter (m) g gravitational constant (9.8 m/s2) h convective heat transfer coefficient (W/m2.K) k thermal conductivity (W/m.K) T temperature (K) L length (m) P perimeter (m) rate of heat transfer per unit length (W/m) Greek letters θ incident angle ƞ optical efficiency α absorptance ρ reflectance ε emissivity μ refractive index τ transitivity ν kinematic viscosity σ Stefan-Boltzmann constant (5.67 x 10-7 W/m2K4) Indices cond conduction conv convection rad radiation i irradiance m mean g glass t absorber tube f fluid (HTF) b bracket r receiver 1. Introduction Solar thermal energy utilization can be done with the help of Parabolic Trough Collectors (PTC). Many researchers tested and validated the application of PTCs with various application like power generation, desalination etc [1,2]. Parabolic trough technology has proven to be the most mature and low cost solar thermal technology available today. Concentrated sunlight using linear Fresnel lens can also be used to drive Concentrated Photovoltaic (CPV) cells [3]. The application of CPV using various techniques has already been discussed in the literature [4–7]. Concentrated Photovoltaic Thermal (CPV/T) which includes thermal system for CPV cooling has also been used for utilization of electrical as well as thermal energy [8,9]. Conventry [10] investigated the performance of a CPV/T collector where the row of cells were cooled by liquid flowing through an internally finned aluminum pipe with optical concentration of 37 suns. He found out that the thermal and electrical efficiency of the system was affected by high temperatures. The main problem with the CPV cells is the high temperature with increase in concentrated solar radiation. This increase in temperature leads to reduction in the cell efficiency and too high of a temperature may damage the cell’s integrity. If the temperature exceeds a certain limit its life-span would reduce rapidly [11], so proper cooling system is required to maintain the temperature within the limit. A simple cooling system design may also help to reduce the maintenance costs. While a variety of approaches have been used to the keep the cells cool, most of them are based
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upon removal of heat from the back of the cell (opposite surface of the incident flux exposed surface) [12,13]. The both side cooling of the flat CPV cell was discussed by Zhu et al. [14]. Liquid immersion cooling of concentrated PV cells has also been discussed by Han et al. [15,16], Zhu et al. [17], Han et al. [18], Xiang et al. [12] etc. The presented research work proposes the modified receiver system for effective cooling. Since, circular geometry has large surface area as compared to flat plate the circular tube is consideration [19]. The CPV cells are assumed to be mounted on the absorber tube of PTC where the liquid is allowed to flow though the annulus as well, thus allowing the cooling to occur from both sides of the cells. 2. Proposed system In this section, a proposed novel design for the liquid immersion cooling system of CPV along with PTC is presented. The designed receiver consists of non evacuated glass tube, absorber tube and flexible multi-junction CPV cells mounted on absorber tube with the help of epoxy. The Heat Transfer Fluid (HTF) flows through inside as well as outside of absorber tube, thus cooling the CPV cells from both sides for better performance. The schematic diagram of the system is shown in Fig. 1. For the design estimation, the energy balance has performed on such receiver system as discussed further in the section. 3. Thermal analysis of the proposed model 3.1. Energy balance model In this section, the thermal model for proposed novel design is presented. For the design estimation, the energy balance has performed on receiver system using one-dimensional methods by taking followings assumptions: • • • •
The solar radiation falling on the receiver is always taken normal to the surface. Uniform heat flux over the glass envelope and absorber tube. The flexible CPV cell is perfectly mounted along the irradiance side. The scattering and attenuation of solar radiation within the liquid is assumed to be negligible.
Fig. 1 One dimensional steady state energy balance
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As shown in Fig. 1, the energy balance is performed on receiver which consists of glass tube and absorber pipe. The flexible CPV cells are mounted on irradiance side of absorber tube so that it receives maximum solar radiation. For the simplicity, the cell and epoxy thickness has been neglected and is overall thermal conductivity of the joint is taken for consideration. The HTF flows inside the absorber tube as well as through annulus. The one dimensional energy balance method is taken similar to the evacuated absorber tube which are available in the literature [20,21]. The energy model is modified by balancing the incoming solar radiation and optical losses. In this novel receiver, uniform circumferential heat flux is assumed by taking the average of solar radiation from concentrated and non concentrated side. All the temperatures and thermodynamic properties are also assumed to be uniform across the circumference. Six surfaces are identified for the heat transfer analysis across the receiver. The incoming solar ), which is glass envelope outer surface, as well as on surface 3 ( ) which is radiation falls on the surface 5 ( outer surface of absorber tube. Across the glass tube, the absorbed energy is transferred through conduction ( ) and by convection ( ) from surface 4. The surface 4 which is inner surface of glass envelop allows convection heat transfer through HTF (which is flowing within the annulus and taken as bulk surface 9). The surface 3 transfers the heat through convection ( ) and conduction ( ) to the HTF and inner surface of tube respectively as shown in Fig. 1. From surface 2 the heat transfer occurs by convection ( ) to the inner fluid, which is taken as surface 1. The ambient and sky conditions are taken with subscript 6 and 7 respectively. Using Fig. 1, by applying the energy balance on each surface, the following equations are obtained: ' ' q5' a + q'45cond = q56 conv + q57 rad
(1)
' q'49conv = q'45cond + q34 rad ' ' q39 = q conv 49conv ' ' ' q3' a = q39 conv + q32cond + q34rad ' ' q32 cond = q21conv
(2) (3) ' + qbc
(4) (5)
3.1.1. Incident solar irradiation The incident solar absorptance on surface 5 ( ) and on surface 3 ( ) falling on the outer surface of the glass is treated as heat flux to simplify the thermal analysis. As discussed by Forristall [21], this assumption simplifies and makes the conduction equation linear across the glass and absorber tube. Although this assumption introduces minimal error, but for small absorbtance coefficient of the glass, this error can be neglected. Also, the incident irradiation is taken as uniform over the entire circumferential surface. The variation in incident angle which causes optical losses by the incident rays which are not normal to the surface are given by Incident Angle Modifier (K) as
K = cosθ + 0.000884θ − 0.00005369θ 2
(6)
The optical efficiency of the glass is given by radiation absorbed by the glass envelop by the incident normal irradiation. Forristal [21] defines the solar absorption in glass as ' q 5a = qi'η g α g
(7)
while ηg = ε t ρm K and is the estimates of effective optical efficiency as given by Price et al. [22]. is the solar radiation falling on the receiver per unit length (W/m) The solar radiation falling on the absorber tube after passing through the glass envelop and HTF can also be treated as heat flux. The equation of solar absorption becomes ' (8) q3a = qi'ηtαt
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while
ηt = ηgτ gτ f
3.2. Heat Transfer Analysis The receiver part consists of glass tube, HTF and absorber tube. The heat transfer would occur by all three modes, i.e. Conduction, Convection and Radiation. 3.2.1. Conduction heat transfer The conduction heat transfer takes place on three surfaces in the given model through the glass, absorber tube and as heat losses in the form of conduction from the support brackets. The conduction heat transfer within the glass and tube are given as:
q '45cond = ' q32 cond
2π k g (T4 − T5 )
(9)
ln( D5 / D4 ) 2π km (T2 − T3 ) = ln( D3 / D2 )
(10)
The values of thermal conductivity of glass envelope and absorber tube are assume to be uniform throughout the surface and are taken from the Incropera [23]. The thermal conductivity for eqn. (10) is taken by considering thermal resistance of absorber tube, epoxy and CPV cell in series. The conduction from the support bracket depends on the contact area between absorber tube and bracket. To estimate the heat losses, the bracket is treated as infinite long fin with base temperature 10 degree less than the T3. For the simplification the dimensions of the support bracket is assumed to be same as that of Forristal [21]. The perimeter is taken as 0.2032 m having area of 1.613 x 10-4m2. The thermal conductivity is assumed to be 50 W/m-K. The convective heat transfer coefficient depends on wind or no-wind case. From the literature it is taken within the range of 2-25 W/m2-K (for no-wind) and 25-250 W/m2-K (for wind). The conduction equation for such system is given as: ' qbc = hb Pb kb Ab × (Tb − T6 ) / Lr
(11)
3.2.2. Convection heat transfer The convection occurs at four surfaces in this model. From surface 5, the convection ) occurs from outer glass surface to the ambient conditions. The temperature difference is assumed to be ( linear here. The convection term is given by ' q56 conv = h56 D5π (T5 − T6 ) With h56 = Nu5kg / D5
(12) (13) The value of Nusselt number (Nu) for the equation (13) can be obtained by treating cross-sectional flow over the long cylinder. The flow velocity over the cylinder governs the Reynolds number and thus Nusselt number. To assess the convection coefficient, wind and no-wind cases are used. For the no-wind case, the convection from the glass surface to the surrounding will only by natural convection. To estimate the natural convection, the correlation given by Churchill and Chu [24] will be used as discussed in Ref [23].
Nu56
8 ⎫ ⎧ 9 ⎤ 27 ⎛1⎞ ⎡ ⎪ ⎪ ⎜6⎟ ⎢ ⎛ 0.559 ⎞16 ⎥ ⎪ ⎪ ⎝ ⎠ = ⎨0.60 + 0.387 × Ra56 / ⎢1 + ⎜ ⎟ ⎥ ⎬ Pr ⎪ ⎢ ⎝ 56 ⎠ ⎥ ⎪ ⎣ ⎦ ⎪ ⎪ ⎩ ⎭
2
(14)
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Ra56 =
β=
g β (T5 − T6 ) D53
(15)
α 56ν 56
1 T56
Pr56 =
(16)
ν 56 α56
(17)
where Ra is the Rayleigh number and Pr is the Prandlt number for glass outer cover, β is volumetric coefficient for thermal expansion and α is thermal diffusivity at temperature T56 which is the film temperature. The Eqn (14) is valid for 105 < Ra < 1012. In case of wind, the convection will be forced and the correlation for Nusselt number can be obtained by using Churchill and Bernstein equation. This correlation is valid for all ranges of Reynolds number with . −1/4
4/5
⎡ ⎛ Re ⎞5/8 ⎤ ⎡ 0.4 ⎤ 56 (18) ⎢1 + ⎜ Nu56 = 0.3 + 0.62 Re Pr ⎢1 + 2/3 ⎥ ⎟ ⎥ ⎢⎣ ⎝ 282000 ⎠ ⎥⎦ ⎢⎣ Pr56 ⎥⎦ This correlation assumes long horizontal cylinder with isothermal conditions. The fluid (air) properties are taken as ambient conditions, while Pr56 is evaluated at the film temperature on the surface 5. The convection within the absorber tube can be estimated by taking the fluid flow inside the tube. The correlations can be taken as Petukhov equations [25], as discussed in Ref [26] (19) q'21conv = h21D1π (T2 − T1 ) 1/2
1/3
⎛ f ⎞ 0.11 ⎜ 8 ⎟ Re Pr ⎛ Pr56 ⎞ ⎝ ⎠ Nu = ⎜ ⎟ Pr f 1.07 + 12.7 Pr 2/3 − 1 ⎝ 5 ⎠ 8
(20)
f = (0.79ln Re−1.64)−2
(21)
(
)
The other two convections occur between the annulus, from the outer surface of the absorber tube to the HTF ) and from the inner surface of the glass cover to the HTF ( ). The convective heat transfer for ( surface 3 and surface 4 can be calculated by using Petukhov correlation as discussed in eqn (20). Gnielinski [27] modified the correlation by adding the effect of characteristics length during the convection. ⎛ f ⎞ ⎜ 8 ⎟ Re Pr ⎛ ⎛ d ⎞2/3 ⎞ ⎝ ⎠ ⎜1 + ⎜ ⎟ ⎟ (22) Nu = ⎜ ⎝L⎠ ⎟ f ⎠ 1 + 12.7 Pr 2/3 − 1 ⎝ 8 (23) f = (1.8log Re−1.5)−2
(
)
In Eq (12), for (convection between surface 3 (T3) and bulk mean temperature of water (T9)) and for (convection between surface 4 (T4) and bulk mean temperature of water (T9)), the hydraulic diameter (dh) is taken as characteristics length for the estimation of Reynolds number. It is given by difference of inner glass envelope diameter to outer absorber tube diameter.
3.2.3. Radiation heat transfer ) and from the absorber tube to the glass ( ). The The radiation occurs from glass surface to the sky ( later one occurs due to high temperature of the absorber tube and is of long wavelength. It will get absorbed within
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' 4 4 q 57 rad = σε g π D5 (T5 − T7 )
(24)
The absorber tube radiation can be treated as the radiation between two concentric cylinders with participating media in between. Here, for the simplicity the scattering and attenuation effect has been neglected between the fluid molecules. The radiation equation for this case is given by Modest [28]. The Non-dimensional radiative heat flux depends upon the ratio of two cylinders diameter (D3/D4) and is taken from the Modest [28]. Further this term can be neglected if we assumed all the long wave radiation got absorbed within the next fluid layer to the absorber tube. The radiation between the fluid layer and from fluid layer to the glass can be estimated by using generic equations for long infinite concentric cylinder with participating media [23]. ' q34 rad =
σπ D2 (Tn4 − Tn4−1 ) 1 − ε g D2 1 1 + −1 + εt εt ε g D4
(25)
where Tn and Tn-1 are the intermediate fluid temperature at n and n-1 layer respectively. 3.2.4. Heat losses The heat losses in the receiver includes the convection and radiation heat loss from the outer glass envelope to the environment and the conduction losses from the support bracket. It is given as: ' ' ' q'heatloss = q57 rad = q56conv + qbc
(26)
Table 1. Receiver tube specification used in the model Parameters Receiver tube length Absorber internal diameter Emissivity of glass Absorber external diameter Absorber thermal conductivity Glass cover internal diameter Emissivity of absorber tube Optical efficiency of glass envelop Absorptance of glass envelope Thermal conductivity of glass Thermal conductivity of air Thermal conductivity of fluid Wind velocity Density of air Density of fluid Dimensionless radiative heat transfer coefficient
Value 1.2 m 0.0656m 0.82 0.07 m 411 W/mK 0.110 m 0.4 0.8 0.04 1.04 W/mK 0.026 W/mK 0.1357 W/mK 1 m/s 1.2 kg/m3 1060 kg/m3 0.96
4. Comsol Validation The validation of proposed model is done by simulating the system using Comsol (v5.1). For the simplified solution, the 3D model of the receiver is taken as 2D symmetrical model and thermal analysis is done by taking heat transfer multiphysics. The dimension of receiver tube is taken as 1.2 meter with glass envelope diameter of 125 m having thickness of 10 mm. The absorber tube diameter is 70 mm with thickness of 2.2 mm. The thickness of cell is taken as 0.5 mm is assumed to be negligible in case of analytical model. Since back side of cell is attached to the absorber tube, surface 2 (Inner side of absorber tube) which is in contact with fluid is taken as the back cell temperature. For multiphysics, simple heat transfer in solid along with laminar flow model is used. The meshing is taken with normal approach with the curvature factor of 0.3, as per the simulation tool. The two physics are coupled
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with temperature coupling. The parameters taken for the simulations are shown in Table 1. The simulated model of receiver tube is shown in Fig. 2. The temperature variation along the length is presented in the same.
Fig. 2. Temperature plot of receiver tube along the length (mm)
5.
Results and Discussion
The Comsol simulation of proposed system having flexible multijunction cells mounted on the absorber tube with HTF on both sides of the cells is simulated using parameters mentioned in Table 1. The temperature at the front surface of cell is observed to be more than the back side of the cell. The temperature variation across the six different surfaces along the length is shown in Fig. 3. 315
370
314
360 Surface 5
340
Surface 4 Surface 3
330
Surface 9
320
Surface 2
310
Surface 1
300
Temperature (K)
Temperature (K)
313 350
312 311 310 309 308
Comsol simulation Analytical model
307 306
290 0
150 300 450 600 750 900 1050 1200 Length (mm)
Fig.3. (a) Temperature variation over various surface (b) Comparison of Comsol and analytical model for same outer glass envelope temperature
It is observed from the Fig. 3(a) that the temperature at the outer glass surface (Surface 5) increases gradually as compared to inner most fluid (surface 1). The temperature at surface 2 and 3 are almost identical with the fact that it is the inner and outer surface of the absorber tube having small thickness. Similar trend is observed in inner and
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outer surface of glass tube. The temperature within the annulus goes from the inlet temperature (which is assume to be 295 K) to a converging value of around 360 K, by the end of tube length. The temperature results obtained are then compared with the results obtained by analytical model by MATLAB. The analytical approach results for fixed outer glass envelope section is compared with the Comsol results and are shown in Fig. 3(b). It shows the comparison of Comsol model (v5.1) and analytical model for same outer glass envelope The temperature value of two-dimensional model in Comsol across the length is obtained and at the point where outer temperature of glass envelope reaches 313 K, a cut cross-sectional view is obtained. The radial temperature variation is observed on each surfaces compared with one dimensional analytical results. It is found out that the analytical model shows the same trend as that of Comsol results. In Comsol case, when surface 5 is taken at 313 K, the temperature in inward direction decreases to 311 K for surface 1. The analytical model shows temperature of 309 K for surface 1 with same surface 5 temperature. The variation in the analytical model may be due to the assumptions taken in the same. Further, the Comsol model is also varied with the condition when no water flows through the annulus, by making it similar to stagnant air tube conditions. The simulations in the Comsol reveals the maximum cell temperature that could be achieved in case of no fluid within the annulus. The plot obtained in such case is shown in Fig. 4. The graph shows that without fluid within the annulus, the maximum temperature is obtained across the length as 407 K which is 46 degrees higher than the fluid flow case. Thus without fluid flow, or cooling from one side, the high cell temperature would degrade the cell. This also reduce the electrical efficiency of the cell. Hence, in such case, the HTF within the annulus would carried away by excess and the temperature of the cell can be maintained. The extracted thermal energy can be utilized for heating applications.
Fig.4. Comsol plot for no fluid flow case within the annulus
6. Conclusion In the present paper, an analytical approach has been developed and presented to estimate the thermal performance of multi-junction solar panel under high concentration with liquid cooling on both sides of the panel. The analytical model is proposed for a system where CPV cells were assumed to be mounted on the absorber tube. The HTF is flown within the annulus to allow cooling of the cell from both sides. The model is simulated considering the geometrical, optical and thermal aspect of receiver tube in MATLAB. The temperature trend obtained in the radial direction decreases from outward to inward. From outer glass envelope surface at 313 K, the temperature of inner most fluid reaches to 309 K. Across the length, the results show increase in temperature trend. This model is validated with Comsol (v5.1) where two-dimensional approach has been used for simulation. In that
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simulation sectional view (one dimension) for same outer glass temperature is taken and compared with analytical model which gives slight variation because of the assumptions taken within the model. Further the Comsol model is compared with no flow condition in the annulus, thus achieving the maximum temperature of 407 K (134 °C). This shows that fluid flow within the annulus is better case where heat can be carried away easily from the both sides of the cells. In such case, the operating temperature of cells can be maintained 46 degree less when compared to that obtained for vacuum in the annulus i.e. one side cooling. With both sides cooling not only the operating efficiency of CPV cells will increase but also the heat gained by the fluids in the annulus as well as in the absorber tube will enhance the overall utility of the system. Future scope of the research is experimental validation of such system Acknowledgements Authors gratefully acknowledge the support from the Center for Renewable Energy and Environment Development, BITS - Pilani Rajasthan, for this research. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25]
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