Performance investigation of linear evacuated absorber of 2-stage solar Linear Fresnel Reflector module under non-uniform flux distribution

Performance investigation of linear evacuated absorber of 2-stage solar Linear Fresnel Reflector... Abstract Performance and heat loss analyses have been carried out for a 2-stage parabolic receiver system of the solar Linear Fresnel Reflector module. Performance of the system with non-uniform distribution of the flux on the absorber and the influence of the wind on the receiver system are investigated. Solar flux distribution on the surface the absorber is applied by user-defined function to analyse the heat loss under the real-time scenario. The performance of the absorber tube when coated or uncoated with a selective material is studied for different flux conditions. This provides a perception to adopt appropriate coating material for different locations under varied DNI conditions. The investigation has been carried out to analyse the heat loss effects when the absorber is placed under evacuated and non-evacuated conditions. All the modes of heat transfer are considered in the study and the dominance of each mode of heat transfer is highlighted. Performance of the numerical data with the non-uniform flux distribution on the absorber with the measured velocity and emissivity values are validated with the experimental data. Deviation of ±10 % is observed between the experimental and the numerical values. 1 INTRODUCTION Linear Fresnel Reflector (LFR) system consists of long, parallel narrow mirror strips which focus the solar rays on the absorber tube. The tube is placed in a glass tube: evacuated/non-evacuated to reduce the convective losses and the flux received by the absorber tube is uniformly distributed with the aid of the secondary reflector. The secondary reflector maximizes the number of rays falling on the absorber tube and reduces the formation of hot spots on the tube [1]. LFR has favourable prospects among the solar collector systems. This is endorsed because of the simple design, low installation cost, stability of the receiver system and the lower maintenance. Lots of work have been carried out in analysing the thermal behaviour of the receiver system considering the receiver’s boundary condition as constant temperature and constant flux. In reality, the distribution of flux is non-uniform along the circumference of the absorber. Cheng et al. [2, 3] calculated the non-uniform distribution of the solar flux on the absorber tube of a parabolic solar collector receiver using Monte Carlo Ray-Trace Method (MCRT) and coupled it with the FLUENT to determine the heat transfer with the heat transfer fluid, Syltherm 800. Validation was carried out with the test results of Dudley et al., and the average difference of 2% was observed for three typical testing conditions. Cruz et al. [4] performed the thermal and the stress analysis of a thin-wall pipe under non-uniform distribution. When the Biot number is larger (Bi > 0.3), analysis can be carried out with the one-dimensional model since the error is less than 5%. But when it is less than 0.3 one-dimensional model of thermal stress provided qualitatively unacceptable results. Beltagy et al. [5] presented a theoretical and experimental study of a 250 kW Fresnel type concentrator and a daily thermal efficiency over 40% was obtained. A LFR solar collector with modified V-shaped cavity receiver was investigated both experimentally and theoretically by Lin et al. [6]. Optical performance was analysed by Monte Carlo ray tracing method. A 2D mathematical model was developed to investigate the overall heat transfer coefficient to determine the thermal performance of the modified linear cavity receiver. Experimental results show that the overall heat loss coefficient varied from 6.25 to 7.52 W/m2 K for the tested surface temperature range, with an average deviation of about 12% when compared with simulation results. Table 1. Values of coefficients for DNI 1000 W/m2. θ  e  a  b  c  d  0° < θ < 45°  2554.8  44.01  −1.83  −1.16 × 10−2    45° < θ < 90°  9853.5  −471.59  7.55  −3.89 × 10−2    90° < θ < 180°  480.81  32.79  −8.69 × 10-2  −2.15 × 10−3  9 × 10-6  θ  e  a  b  c  d  0° < θ < 45°  2554.8  44.01  −1.83  −1.16 × 10−2    45° < θ < 90°  9853.5  −471.59  7.55  −3.89 × 10−2    90° < θ < 180°  480.81  32.79  −8.69 × 10-2  −2.15 × 10−3  9 × 10-6  The present work focuses on the heat loss study of the receiver system of a LFR module with the parabolic (PB) secondary reflector. All the three modes of heat transfer are considered for analysing the heat losses from the absorber tube placed under both the non-evacuated and evacuated conditions with non-uniform flux distribution imparted as user-defined function along the circumference of the absorber tube. Thermal losses are analysed by considering the absorber tube with and without the selective coating material. The thermal characteristics of the module under wind conditions are investigated. Numerical analyses have been carried out from the measured velocity and the emissivity data with the DNI of Vallipuram (12.65°N, 79.74°E), Tamil Nadu. The numerical result thus obtained is compared with the experimental data obtained from the on-site LFR system with the PB secondary receiver system which is numerically analysed. 2 ANALYSES OF LFR SYSTEM A pilot LFR plant of 125 kWth capacity has been developed in Vallipuram(12.65°N, 79.74°E), Tamil Nadu.The plant of 154m2 has a storage-integrated solar collector field with the variable steam output (50 bars and 350°–400°C). It has two sections namely: a saturated section with water and a superheated section. It consists of 12 primary reflectors with a mild parabolic curvature with a single axis tracking system. A selectively coated absorber tube is placed inside an evacuated glass tube. The receiver system comprises parabolic secondary reflector enclosing the absorber and the glass tube (Figure 1). Figure 1. View largeDownload slide (a) LFR module with 2-stage reflector system, (b) PB secondary reflector with solar rays on the evacuated absorber, (c) cross-sectional view of the LFR module. Figure 1. View largeDownload slide (a) LFR module with 2-stage reflector system, (b) PB secondary reflector with solar rays on the evacuated absorber, (c) cross-sectional view of the LFR module. Step by step analysis has been carried out to estimate the heat losses from the receiver system. Initially, the optical analysis is done to obtain the optimized flux along the circumference of the absorber and then the thermal study is performed. In the thermal study, firstly the thermal loss analysis of the 2-stage parabolic secondary receiver system is carried out. Secondly, with the realistic data measured from the pilot plant, the numerical analysis is carried out and the thermal performance of the system is validated with the experimental performance of the LFR system. 2.1 Investigation of the 2-stage parabolic receiver system The thermal investigation is carried out for the receiver system comprising of the parabolic secondary reflector partially enclosing the absorber tube placed in a glass tube. Numerical simulation is performed with the flux values obtained from the optical investigation. Optically optimized parameters from the earlier study namely the acceptance angle of the secondary reflector, truncation location on the secondary reflector, the focal position of the absorber tube, the ratio of the gap between the reflector and the absorber to the height of the reflector are considered for the present work. The flux thus obtained from the optical analysis is applied as a user-defined function (UDF) in the form of a polynomial curve and the curve is a function of the angular position of the flux along the circumference of the absorber as shown in Figure 2. The investigation is carried out with the thermal emissivity of the coated surface within 0.05 and 0.1 and without the coating between 0.2 and 1.0. Real-time conditions with wind velocities in the range between 0 m/s and 10 m/s are used in the study. All the three modes of heat transfer from the receiver system are considered for the investigation and the modes of heat transfer are shown in Figure 3. The numerical heat loss data thus obtained are compared with experimental data from Vallipuram, Tamil Nadu. Fluctuation in the mass flow rate between 0.06 kg/s and 0.16 kg/s were observed for varying temperature conditions during 9.30 AM to 4.30 PM. The inlet (Ti) and the outlet (To) of the fluid and the ambient temperature (T∞) were measured. Solar irradiation and the wind speed are measured. Hence, the rate of heat supplied to the heat transfer fluid (HTF) is   Qu̇=ṁCp(To−Ti), (1)where Qu̇ is the useful heat obtained from the LFR system, ṁ is the mass flow rate of the fluid, TiandTo are the inlet and outlet temperature of the fluid. The surface heat flus is calculated by   qṡ=Qu̇/As=hHTF(Tabs−Tm), (2)with As is the surface area of the absorber, hHTF is the heat transfer coefficient, Tm is the mean temperature and Tabs the surface temperature of the absorber is   Tabs=Tm+qṡ/hHTF. (3) Figure 2. View largeDownload slide (a) Local concentration ratio (LCR) along the circumference of the absorber. (b) Non-uniform flux distribution around the absorber. Figure 2. View largeDownload slide (a) Local concentration ratio (LCR) along the circumference of the absorber. (b) Non-uniform flux distribution around the absorber. Figure 3. View largeDownload slide (a) Computational grid and (b) boundary conditions PB secondary reflector system. Figure 3. View largeDownload slide (a) Computational grid and (b) boundary conditions PB secondary reflector system. The heat transfer coefficient is therefore calculated from the empirical formula correlated by Gnielinski [7]   NuHTF={4.36ReHTF≤2300(f/8)PrHTF(ReHTF−1000)1+12.7(f/8)0.5(PrHTF2/3−1)(PrHTFPrabs)0.11ReHTF>2300. (4) And the friction factor is determined based on Filonenko equation [8]:   f=⟨1.82ln(ReHTF)−1.64⟩−2. (5) Heat loss from the receiver system is hence calculated as   qlL=habs−g(Tabs−Tg)πDabs+σπDabs(Tabs4−Tg4){1εabs+DabsDg(1εg−1)} (6)  =hg−sec(Tg−Tsec)πDg+σπDgεg(Tg4−Tsec4) (7)  =hsec−∞(Tsec−T∞)AsecL+σAsecLεsec(Tsec4−Tsky4) (8) Heat transfer coefficient between the absorber tube to the evacuated glass tube calculated from the empirical formula correlated by Kalogirou [9]. Tsec is the area weighted average surface temperature of the secondary reflector. Physical properties are calculated based on area weighed average of the absorber and the evacuated glass tube temperature. Heat transfer coefficient is given by   habs−g=kvac(Dabs/2)ln(Dg−Dabs)+B0λvac(Dabs/Dg+1), (9)  B0=(2−b/2b)9λvac−5λvac+1, (10)  λvac=2.331×10−20{Tabs−g̅+273.15Pvacδvac2}, (11)where kvac = 0.02551 W/mK, b = 1.571, Pvac < 0.013 Pa, δvac = 3.55 × 10−10 m. Heat transfer coefficient between the evacuated glass tube and the secondary reflector is calculated as follows:   hg−sec=Nug−seckair/H, (12)  Nug−sec=Nuc+NuR, (13)where   Nuc=8.424(TabsT∞)−0.567(DW)−0.573ε−0.097(Gr1+Re2)−0.045, (14)  NuR=3.279(TabsT∞)1.679(DW)−1.227ε0.897(Gr1+Re2)0.004, (15)with the parameters within the range 373 K ≤ Tabs ≤ 773 K, 0.14 ≤ D/W ≤ 0.27, 0.01 ≤ ε ≤ 1, 3.23 × 107 ≤ Gr ≤ 4.83 × 107, 4.45 × 103 ≤ Re ≤ 9.79 × 104. Physical properties are calculated based on area weighed average of the evacuated glass tube and the secondary reflector temperature. Heat transfer coefficient between the secondary reflector and the ambient is calculated based on the empirical formula correlated by Hilpert [10]. Physical properties are calculated based on area weighed average of the secondary reflector and the ambient   Re=VairH/ϑ, (16)  Nu=C1Ren, (17)where H is the height of the secondary reflector. For 40<Re<4000,C1=0.615,n=0.466;4000<Re<40000,C1=0.174,n=0.618;40000<Re<400000,C1=0.0239,n=0.805 Thermal performance analyses of the LFR system have been carried out in Matlab. 2.2 Governing equations for flow and heat transfer analyses of the secondary reflector system The flow and heat transfer in the secondary reflector system is solved with the governing equations as follows: By the law of conservation of mass, the continuity equation is given by [11]   ∇.V=0. (18) Momentum equations:   V.∇V=X−∇Pρ+ϑ∇2V. (19) Energy equation is solved by   ∇.(kf∇T)=0, (20)where V represents the velocity components in the x- and the y-direction, respectively, ρ is the density of the air inside the cavity in kg/m3, X is the body force per unit volume, P is the pressure in N/m2, kf represents the thermal conductivity of the fluid in W/mK. During the wind flow, turbulence effect is observed. Hence, the turbulence model with the shear stress transport (SST) k–ω model is incorporated and the formulations are as follows [11]: k-equation:   ∂∂xi(ρkui)=∂∂xi(Γk∂k∂xi)+G̃k−Yk+Sk, (21)ω-equation:   ∂∂xi(ρωuj)=∂∂xi(Γω∂k∂xi)+Gω−Yω+Sω, (22)where k is the turbulent kinetic energy in m2/s2, ω is the specific dissipation rate, s−1. Surface-to-Surface (S2S) radiation model is used to model the radiation heat transfer of the secondary reflector system. The receiver region is considered as a non-participating medium by ignoring the emission and the scattering effects. 2.3 Boundary conditions Peers have carried out the thermal loss analyses for the closed system and hence atmospheric conditions have not been considered. But in the present work, the secondary reflector has an open aperture and hence it is open to the atmosphere. Heat is lost to the atmosphere from the secondary reflector system and hence the thermal modelling of the receiver system is carried out within a domain area which resembles the ambient condition of temperature 303 K and pressure of 1 bar. The circumference of the absorber is provided with non-uniform flux values as a user-defined function (UDF) obtained from the optical analysis in the form of a polynomial curve and the curve is a function of the angular position of the flux along the circumference of the absorber being represented as   flux=e+aθ+bθ2+cθ3+dθ4 (23)where θ is the angle along the circumference of the absorber, a, b, c, d and e are the coefficients. The values of these coefficients for DNI of 1000 W/m2 are illustrated in Table 1. Coupled conditions are provided for both the outer and inner wall of the secondary reflector and the glass tube. The non-uniform flux distribution is provided as a boundary condition and the performance of the secondary reflector system is validated with the data from the pilot plant with the 2-stage PB receiver system. 2.4 Grid independence study and numerical validation As discussed earlier, the wind effects are incorporated as considering the domain region around the receiver system. To ascertain the accuracy of the numerical results obtained for the particular domain area, the size of the domain, the distance between the inlet, outlet and the side walls from the absorber and the quantity of the mesh are varied. The sensitivity of the domain region becomes insignificant when the absorber is modelled such that it is 20D from the inlet and the side walls and 40D from the outlet of the domain where D represents the diameter of the absorber tube as shown in Figure 4. Meshing is valued such that it is fine near the receiver system of about 12, 92 356 and becomes coarse as it diverges away towards the wall of the domain. PISO algorithm is used for the Skewness–Neighbour coupling with second-order unwinding scheme for discretization of equations. Convergence criteria of 10−4, 10−4 and 10−6 are imposed on the residuals of the continuity, momentum and energy equations, respectively. The present work is validated with the experimental results of Sahoo et al. [12] with a deviation of 8% to 15% observed in the total heat loss. Figure 4. View largeDownload slide Modes of heat transfer from the PB secondary receiver system. Figure 4. View largeDownload slide Modes of heat transfer from the PB secondary receiver system. 3 RESULTS AND DISCUSSION A parametric study based on the effects of emissivity of the absorber tube and the wind velocities are considered. The non-uniform flux on the absorber tube for direct normal irradiance (DNI) ranging between 250 W/m2 and 1000 W/m2 are investigated. All the modes of heat transfer are considered for the analysis purpose. Performance analysis of the LFR system is carried out based on the on-site conditions and the numerically obtained value is compared with the experimental data. 3.1 Heat loss analysis for the absorber with emissive and non-emissive coating Temperature contour of the secondary reflector system with the non-uniform flux data provided along the circumference of the absorber with the aid of the user-defined function is shown in Figure 5. Sputtered cermet with an emissivity of 0.075 is used as a coating material. Figure 5(a) shows the temperature distribution of the cavity with the non-evacuated annular region. Buoyancy effect is observed both in the annulus and along the outer surface of the secondary reflector. The rise in the heat waves within the annular region is due to the presence of air. It can be clearly seen that as the upper part of the absorber receives negligible reflected rays, no flux is depicted in this part of the absorber tube. Figure 5(b) shows the temperature distribution in the open cavity with the evacuated annular region. Proclaiming the absence of air in the region, the stagnant heat waves are observed along the outer surface of the absorber tube. Since the heat waves are retained within the glass tube, Figure 5(b) clearly portrays the reduction in the heat waves from the outer wall of the secondary reflector. Figure 5. View largeDownload slide Temperature contour of PB secondary receiver system with non-uniform flux distribution on the absorber: (a) non-evacuated, (b) evacuated absorbers with emissivity 0.075. Figure 5. View largeDownload slide Temperature contour of PB secondary receiver system with non-uniform flux distribution on the absorber: (a) non-evacuated, (b) evacuated absorbers with emissivity 0.075. Figure 6 shows the convective and the radiative heat losses from the absorber tube coated with non-selective and the selective material. It is observed that the radiative heat losses predominate the heat losses when the emissivity is considered as a parametric factor for the uncoated absorber. When the absorber is non-evacuated, both the convective and the radiative heat transfer equally share the role of the heat losses. It is obvious and clear from Figure 4 that as the emissivity increases, the heat losses increase. Convective and radiative heat losses of about 54% and 40.6% are observed, respectively, when the absorber tube is coated with the non-emissive material. When the uncoated tube is placed under the evacuated condition, convective and radiative heat losses are reduced to 16% and 43%, respectively. Figure 6. View largeDownload slide Radiative and convective heat losses for different emissivity. Figure 6. View largeDownload slide Radiative and convective heat losses for different emissivity. 3.2 Heat loss analysis based on the wind velocity on the receiver system The temperature contour of the receiver system at different velocities and direct normal irradiance (DNI) are shown in Figure 7. As discussed earlier, when there is no wind condition, i.e. natural convection, because of the presence of air in the region between the absorber and the glass tube, the heat transfer rate is faster and due to the buoyancy effect heat waves travel upwards in the annular region around the absorber and in the outer surface of the secondary reflector. The flow direction of the wind is simulated from the inner wall of the domain towards the outer wall. Hence as the wind speed increases, circulation of air in the cavity occurs in the anti-clockwise direction around the absorber tube. This is because of the direction and velocity of the wind. The significance of the glass tube around the absorber is well proclaimed from the simulation that, though the absorber tube is evacuated or non-evacuated, the heat loss from the absorber tube can be significantly reduced when the absorber is placed in a glass tube. The figure also depicts that as the DNI increases, the temperature distribution in the annular region surrounds the entire circumference of the absorber and attains a stagnation state at the upper part of the tube. Figure 8 reveals the temperature contour of the receiver system when the absorber tube is evacuated. The heat transfer from the absorber to the cavity is completely constrained and hence the air in the cavity has less temperature gradient compared to the non-evacuated condition. This reflects the less temperature difference between the absorber and the cavity aperture opening. Hence at low wind speed, the flow of air sweeps the heat waves along the flow direction, near the aperture opening. As expected, when the velocity increases, anti-clockwise circulation of air around the absorber is observed with the transfer of heat waves from the upper part of the absorber. As the DNI increase this distribution of temperature prevails around the absorber and hence only small region is being agitated by the air circulation in the annular region. Figure 7. View largeDownload slide Temperature contours of PB secondary reflector for different velocities at DNI 250 W/m2 and 750 W/m2 for non-evacuated absorber at non-uniform flux distribution. Figure 7. View largeDownload slide Temperature contours of PB secondary reflector for different velocities at DNI 250 W/m2 and 750 W/m2 for non-evacuated absorber at non-uniform flux distribution. Figure 8. View largeDownload slide Temperature contours of PB secondary reflector for different velocities at DNI 250 W/m2 and 750 W/m2 for evacuated absorber at non-uniform flux distribution. Figure 8. View largeDownload slide Temperature contours of PB secondary reflector for different velocities at DNI 250 W/m2 and 750 W/m2 for evacuated absorber at non-uniform flux distribution. Figure 9 shows the total heat losses for different DNI for a range of velocities from 0 m/s to 10 m/s. At low DNI, 32% of heat loss is reduced because of the evacuation of the annular region. As the DNI increases, heat loss reduction of 40% can be obtained under the evacuated condition.With the increase in the velocity, 33–35% of heat loss reduction is observed for non-evacuated condition and can be further be reduced to a range of 50–75% for the evacuated condition. Figure 10 shows the amount of convective and the radiative heat losses from the 2-stage receiver system. When the region between the absorber and the glass tube is filled with air, convection heat transfer governs the heat loss because of the high heat transfer coefficient. But when the air is removed to produce a vacuum in this region, only molecular conduction exist and the convection heat transfer coefficient is low leading to negligible convection heat loss. The modes of heat transfer are only due to radiation. It is also inferred that when the tube is non-evacuated, higher the wind velocity, greater the convection heat loss and lesser the radiative heat loss. Figure 9. View largeDownload slide Total heat losses for different DNI for a range of velocities from 0 m/s to 9 m/s. Figure 9. View largeDownload slide Total heat losses for different DNI for a range of velocities from 0 m/s to 9 m/s. Figure 10. View largeDownload slide Convective and radiative heat loss for different DNI at various velocity range. Figure 10. View largeDownload slide Convective and radiative heat loss for different DNI at various velocity range. 3.3 Thermal performance analysis of linear evacuated absorber with parabolic secondary reflector On a typical solar solstice day, the DNI over a period of time from 9:30 AM to 5:00 PM is measured. From the calculations analytically made in MATLAB from the set of equations in Section 2.1, the useful heat obtained from the LFR collector is calculated. The analytical calculations for the thermal performance of the LFR system are based on the DNI on the summer solstice day in Vallipuram, Tamil Nadu with the wind velocity measured between 0.5 m/s and 2.75 m/s. The absorber emissivity is 0.075 with the transmissivity of the glass tube as 0.9. The useful heat obtained by the analytical method is compared with the experimental data obtained. Figure 11 shows the comparison of the numerical data calculated by analytical method with the experimental heat gain. For the validation of the numerical value, the performance of the LFR module is calculated from the heat loss values and is compared with the data from the pilot plant in Vallipuram, Chennai. Experimental performance of the LFR system is 10–15% less compared with the numerical data. This can be justified as the deviation caused by the natural conditions such as dust and wind flow direction. prevailing in on-site. Figure 12 shows the variation of temperature and DNI as a function of time. The deviation of the temperature of the absorber, glass tube and the secondary reflector lies in the range between 10% and 17% over the transient conditions. Figure 11. View largeDownload slide Experimental vs. numerical values of heat gain. Figure 11. View largeDownload slide Experimental vs. numerical values of heat gain. Figure 12. View largeDownload slide Transient variation of temperature and DNI. Figure 12. View largeDownload slide Transient variation of temperature and DNI. 4 CONCLUSION Numerical analysis was performed to determine the heat loss from a 2-stage receiver system under realistic conditions. The flux distribution along the circumference of the absorber was obtained by optimizing the optical parameters such as the acceptance angle, truncation points, gap between the absorber and the reflector, and tilt and the distance between the primary mirrors. The flux distribution thus acquired is applied as the boundary condition to the absorber tube with a user-defined function. Two different conditions namely, the non-evacuated and evacuated conditions were considered in the annular region between the absorber and the glass tube. A parametric study based on the emissivity of the absorber tube and the real-time conditions of the atmosphere with temperature 303 K and pressure of 1 bar with different wind velocities were analysed. The heat loss study hence reveals that the heat loss can be reduced to 65% under an evacuated condition with the emissivity of 0.075. The study provides an insight into the optimized aid of the second stage reflector with the absorber tube placed under evacuated/non-evacuated conditions proclaimed in the presence of wind. Finally, the thermal performance of the LFR system is analytically calculated. These data are compared with the experimental data obtained from Vallipuram measured on a summer solstice day. Numerical useful heat gain is found to be 10% greater than the experimental data and the temperature of the absorber tube, glass cover and the secondary reflector deviates by 10–17%. This is expected to be caused because of the dust and the wind flow direction in the on-site. ACKNOWLEDGEMENTS The financial support provided by the Department of Science and Technology (DST), Government of India through the project, DST/TM/SERI/2K11/188(G) Dt. 08/11/2012 is duly acknowledged. REFERENCES 1 Balaji S, Reddy KS, Sundararajan T. Optical modelling and performance analysis of a solar LFR receiver system with parabolic and involute secondary reflectors. App Energy  2016; 179. doi:10.1016/j.apenergy.2016.07.082. 2 Cheng ZD, He YL, Cui FQ et al.  . Numerical simulation of a parabolic trough solar collector with nonuniform solar flux conditions by coupling FVM and MCRT method. Solar Energy  2012; 86: 1770– 84. doi:10.1016/j.solener.2012.02.039. Google Scholar CrossRef Search ADS   3 Cheng ZD, He YL, Xiao J et al.  . Three-dimensional numerical study of heat transfer characteristics in the receiver tube of parabolic trough solar collector. Int Commun Heat Mass Transf  2010; 37: 782– 7. doi:10.1016/j.icheatmasstransfer.2010.05.002. Google Scholar CrossRef Search ADS   4 Marugán-Cruz C, Flores O, Santana D et al.  . Heat transfer and thermal stresses in a circular tube with a non-uniform heat flux. 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John Wiley & Sons, New York, 1996. 9 Kalogirou SA. Solar thermal collectors and applications. Prog Energy combust sci  2004. doi:10.1016/j.pecs.2004.02.001. 10 Duffie JA, Beckman WA, Worek WM, Solar Engineering of Thermal Processes, 4th edn 2003. doi:10.1115/1.2930068. 11 ANSYS Inc, ANSYS Fluent, ( 2015). 12 Sahoo SS, Varghese SM, Suresh Kumar C et al.  . Experimental investigation and computational validation of heat losses from the cavity receiver used in linear Fresnel reflector solar thermal system. Renew Energy.  2013; 55: 18– 23. doi:10.1016/j.renene.2012.11.036. Google Scholar CrossRef Search ADS   © The Author(s) 2018. Published by Oxford University Press. This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. 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Performance investigation of linear evacuated absorber of 2-stage solar Linear Fresnel Reflector module under non-uniform flux distribution

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Abstract

Abstract Performance and heat loss analyses have been carried out for a 2-stage parabolic receiver system of the solar Linear Fresnel Reflector module. Performance of the system with non-uniform distribution of the flux on the absorber and the influence of the wind on the receiver system are investigated. Solar flux distribution on the surface the absorber is applied by user-defined function to analyse the heat loss under the real-time scenario. The performance of the absorber tube when coated or uncoated with a selective material is studied for different flux conditions. This provides a perception to adopt appropriate coating material for different locations under varied DNI conditions. The investigation has been carried out to analyse the heat loss effects when the absorber is placed under evacuated and non-evacuated conditions. All the modes of heat transfer are considered in the study and the dominance of each mode of heat transfer is highlighted. Performance of the numerical data with the non-uniform flux distribution on the absorber with the measured velocity and emissivity values are validated with the experimental data. Deviation of ±10 % is observed between the experimental and the numerical values. 1 INTRODUCTION Linear Fresnel Reflector (LFR) system consists of long, parallel narrow mirror strips which focus the solar rays on the absorber tube. The tube is placed in a glass tube: evacuated/non-evacuated to reduce the convective losses and the flux received by the absorber tube is uniformly distributed with the aid of the secondary reflector. The secondary reflector maximizes the number of rays falling on the absorber tube and reduces the formation of hot spots on the tube [1]. LFR has favourable prospects among the solar collector systems. This is endorsed because of the simple design, low installation cost, stability of the receiver system and the lower maintenance. Lots of work have been carried out in analysing the thermal behaviour of the receiver system considering the receiver’s boundary condition as constant temperature and constant flux. In reality, the distribution of flux is non-uniform along the circumference of the absorber. Cheng et al. [2, 3] calculated the non-uniform distribution of the solar flux on the absorber tube of a parabolic solar collector receiver using Monte Carlo Ray-Trace Method (MCRT) and coupled it with the FLUENT to determine the heat transfer with the heat transfer fluid, Syltherm 800. Validation was carried out with the test results of Dudley et al., and the average difference of 2% was observed for three typical testing conditions. Cruz et al. [4] performed the thermal and the stress analysis of a thin-wall pipe under non-uniform distribution. When the Biot number is larger (Bi > 0.3), analysis can be carried out with the one-dimensional model since the error is less than 5%. But when it is less than 0.3 one-dimensional model of thermal stress provided qualitatively unacceptable results. Beltagy et al. [5] presented a theoretical and experimental study of a 250 kW Fresnel type concentrator and a daily thermal efficiency over 40% was obtained. A LFR solar collector with modified V-shaped cavity receiver was investigated both experimentally and theoretically by Lin et al. [6]. Optical performance was analysed by Monte Carlo ray tracing method. A 2D mathematical model was developed to investigate the overall heat transfer coefficient to determine the thermal performance of the modified linear cavity receiver. Experimental results show that the overall heat loss coefficient varied from 6.25 to 7.52 W/m2 K for the tested surface temperature range, with an average deviation of about 12% when compared with simulation results. Table 1. Values of coefficients for DNI 1000 W/m2. θ  e  a  b  c  d  0° < θ < 45°  2554.8  44.01  −1.83  −1.16 × 10−2    45° < θ < 90°  9853.5  −471.59  7.55  −3.89 × 10−2    90° < θ < 180°  480.81  32.79  −8.69 × 10-2  −2.15 × 10−3  9 × 10-6  θ  e  a  b  c  d  0° < θ < 45°  2554.8  44.01  −1.83  −1.16 × 10−2    45° < θ < 90°  9853.5  −471.59  7.55  −3.89 × 10−2    90° < θ < 180°  480.81  32.79  −8.69 × 10-2  −2.15 × 10−3  9 × 10-6  The present work focuses on the heat loss study of the receiver system of a LFR module with the parabolic (PB) secondary reflector. All the three modes of heat transfer are considered for analysing the heat losses from the absorber tube placed under both the non-evacuated and evacuated conditions with non-uniform flux distribution imparted as user-defined function along the circumference of the absorber tube. Thermal losses are analysed by considering the absorber tube with and without the selective coating material. The thermal characteristics of the module under wind conditions are investigated. Numerical analyses have been carried out from the measured velocity and the emissivity data with the DNI of Vallipuram (12.65°N, 79.74°E), Tamil Nadu. The numerical result thus obtained is compared with the experimental data obtained from the on-site LFR system with the PB secondary receiver system which is numerically analysed. 2 ANALYSES OF LFR SYSTEM A pilot LFR plant of 125 kWth capacity has been developed in Vallipuram(12.65°N, 79.74°E), Tamil Nadu.The plant of 154m2 has a storage-integrated solar collector field with the variable steam output (50 bars and 350°–400°C). It has two sections namely: a saturated section with water and a superheated section. It consists of 12 primary reflectors with a mild parabolic curvature with a single axis tracking system. A selectively coated absorber tube is placed inside an evacuated glass tube. The receiver system comprises parabolic secondary reflector enclosing the absorber and the glass tube (Figure 1). Figure 1. View largeDownload slide (a) LFR module with 2-stage reflector system, (b) PB secondary reflector with solar rays on the evacuated absorber, (c) cross-sectional view of the LFR module. Figure 1. View largeDownload slide (a) LFR module with 2-stage reflector system, (b) PB secondary reflector with solar rays on the evacuated absorber, (c) cross-sectional view of the LFR module. Step by step analysis has been carried out to estimate the heat losses from the receiver system. Initially, the optical analysis is done to obtain the optimized flux along the circumference of the absorber and then the thermal study is performed. In the thermal study, firstly the thermal loss analysis of the 2-stage parabolic secondary receiver system is carried out. Secondly, with the realistic data measured from the pilot plant, the numerical analysis is carried out and the thermal performance of the system is validated with the experimental performance of the LFR system. 2.1 Investigation of the 2-stage parabolic receiver system The thermal investigation is carried out for the receiver system comprising of the parabolic secondary reflector partially enclosing the absorber tube placed in a glass tube. Numerical simulation is performed with the flux values obtained from the optical investigation. Optically optimized parameters from the earlier study namely the acceptance angle of the secondary reflector, truncation location on the secondary reflector, the focal position of the absorber tube, the ratio of the gap between the reflector and the absorber to the height of the reflector are considered for the present work. The flux thus obtained from the optical analysis is applied as a user-defined function (UDF) in the form of a polynomial curve and the curve is a function of the angular position of the flux along the circumference of the absorber as shown in Figure 2. The investigation is carried out with the thermal emissivity of the coated surface within 0.05 and 0.1 and without the coating between 0.2 and 1.0. Real-time conditions with wind velocities in the range between 0 m/s and 10 m/s are used in the study. All the three modes of heat transfer from the receiver system are considered for the investigation and the modes of heat transfer are shown in Figure 3. The numerical heat loss data thus obtained are compared with experimental data from Vallipuram, Tamil Nadu. Fluctuation in the mass flow rate between 0.06 kg/s and 0.16 kg/s were observed for varying temperature conditions during 9.30 AM to 4.30 PM. The inlet (Ti) and the outlet (To) of the fluid and the ambient temperature (T∞) were measured. Solar irradiation and the wind speed are measured. Hence, the rate of heat supplied to the heat transfer fluid (HTF) is   Qu̇=ṁCp(To−Ti), (1)where Qu̇ is the useful heat obtained from the LFR system, ṁ is the mass flow rate of the fluid, TiandTo are the inlet and outlet temperature of the fluid. The surface heat flus is calculated by   qṡ=Qu̇/As=hHTF(Tabs−Tm), (2)with As is the surface area of the absorber, hHTF is the heat transfer coefficient, Tm is the mean temperature and Tabs the surface temperature of the absorber is   Tabs=Tm+qṡ/hHTF. (3) Figure 2. View largeDownload slide (a) Local concentration ratio (LCR) along the circumference of the absorber. (b) Non-uniform flux distribution around the absorber. Figure 2. View largeDownload slide (a) Local concentration ratio (LCR) along the circumference of the absorber. (b) Non-uniform flux distribution around the absorber. Figure 3. View largeDownload slide (a) Computational grid and (b) boundary conditions PB secondary reflector system. Figure 3. View largeDownload slide (a) Computational grid and (b) boundary conditions PB secondary reflector system. The heat transfer coefficient is therefore calculated from the empirical formula correlated by Gnielinski [7]   NuHTF={4.36ReHTF≤2300(f/8)PrHTF(ReHTF−1000)1+12.7(f/8)0.5(PrHTF2/3−1)(PrHTFPrabs)0.11ReHTF>2300. (4) And the friction factor is determined based on Filonenko equation [8]:   f=⟨1.82ln(ReHTF)−1.64⟩−2. (5) Heat loss from the receiver system is hence calculated as   qlL=habs−g(Tabs−Tg)πDabs+σπDabs(Tabs4−Tg4){1εabs+DabsDg(1εg−1)} (6)  =hg−sec(Tg−Tsec)πDg+σπDgεg(Tg4−Tsec4) (7)  =hsec−∞(Tsec−T∞)AsecL+σAsecLεsec(Tsec4−Tsky4) (8) Heat transfer coefficient between the absorber tube to the evacuated glass tube calculated from the empirical formula correlated by Kalogirou [9]. Tsec is the area weighted average surface temperature of the secondary reflector. Physical properties are calculated based on area weighed average of the absorber and the evacuated glass tube temperature. Heat transfer coefficient is given by   habs−g=kvac(Dabs/2)ln(Dg−Dabs)+B0λvac(Dabs/Dg+1), (9)  B0=(2−b/2b)9λvac−5λvac+1, (10)  λvac=2.331×10−20{Tabs−g̅+273.15Pvacδvac2}, (11)where kvac = 0.02551 W/mK, b = 1.571, Pvac < 0.013 Pa, δvac = 3.55 × 10−10 m. Heat transfer coefficient between the evacuated glass tube and the secondary reflector is calculated as follows:   hg−sec=Nug−seckair/H, (12)  Nug−sec=Nuc+NuR, (13)where   Nuc=8.424(TabsT∞)−0.567(DW)−0.573ε−0.097(Gr1+Re2)−0.045, (14)  NuR=3.279(TabsT∞)1.679(DW)−1.227ε0.897(Gr1+Re2)0.004, (15)with the parameters within the range 373 K ≤ Tabs ≤ 773 K, 0.14 ≤ D/W ≤ 0.27, 0.01 ≤ ε ≤ 1, 3.23 × 107 ≤ Gr ≤ 4.83 × 107, 4.45 × 103 ≤ Re ≤ 9.79 × 104. Physical properties are calculated based on area weighed average of the evacuated glass tube and the secondary reflector temperature. Heat transfer coefficient between the secondary reflector and the ambient is calculated based on the empirical formula correlated by Hilpert [10]. Physical properties are calculated based on area weighed average of the secondary reflector and the ambient   Re=VairH/ϑ, (16)  Nu=C1Ren, (17)where H is the height of the secondary reflector. For 40<Re<4000,C1=0.615,n=0.466;4000<Re<40000,C1=0.174,n=0.618;40000<Re<400000,C1=0.0239,n=0.805 Thermal performance analyses of the LFR system have been carried out in Matlab. 2.2 Governing equations for flow and heat transfer analyses of the secondary reflector system The flow and heat transfer in the secondary reflector system is solved with the governing equations as follows: By the law of conservation of mass, the continuity equation is given by [11]   ∇.V=0. (18) Momentum equations:   V.∇V=X−∇Pρ+ϑ∇2V. (19) Energy equation is solved by   ∇.(kf∇T)=0, (20)where V represents the velocity components in the x- and the y-direction, respectively, ρ is the density of the air inside the cavity in kg/m3, X is the body force per unit volume, P is the pressure in N/m2, kf represents the thermal conductivity of the fluid in W/mK. During the wind flow, turbulence effect is observed. Hence, the turbulence model with the shear stress transport (SST) k–ω model is incorporated and the formulations are as follows [11]: k-equation:   ∂∂xi(ρkui)=∂∂xi(Γk∂k∂xi)+G̃k−Yk+Sk, (21)ω-equation:   ∂∂xi(ρωuj)=∂∂xi(Γω∂k∂xi)+Gω−Yω+Sω, (22)where k is the turbulent kinetic energy in m2/s2, ω is the specific dissipation rate, s−1. Surface-to-Surface (S2S) radiation model is used to model the radiation heat transfer of the secondary reflector system. The receiver region is considered as a non-participating medium by ignoring the emission and the scattering effects. 2.3 Boundary conditions Peers have carried out the thermal loss analyses for the closed system and hence atmospheric conditions have not been considered. But in the present work, the secondary reflector has an open aperture and hence it is open to the atmosphere. Heat is lost to the atmosphere from the secondary reflector system and hence the thermal modelling of the receiver system is carried out within a domain area which resembles the ambient condition of temperature 303 K and pressure of 1 bar. The circumference of the absorber is provided with non-uniform flux values as a user-defined function (UDF) obtained from the optical analysis in the form of a polynomial curve and the curve is a function of the angular position of the flux along the circumference of the absorber being represented as   flux=e+aθ+bθ2+cθ3+dθ4 (23)where θ is the angle along the circumference of the absorber, a, b, c, d and e are the coefficients. The values of these coefficients for DNI of 1000 W/m2 are illustrated in Table 1. Coupled conditions are provided for both the outer and inner wall of the secondary reflector and the glass tube. The non-uniform flux distribution is provided as a boundary condition and the performance of the secondary reflector system is validated with the data from the pilot plant with the 2-stage PB receiver system. 2.4 Grid independence study and numerical validation As discussed earlier, the wind effects are incorporated as considering the domain region around the receiver system. To ascertain the accuracy of the numerical results obtained for the particular domain area, the size of the domain, the distance between the inlet, outlet and the side walls from the absorber and the quantity of the mesh are varied. The sensitivity of the domain region becomes insignificant when the absorber is modelled such that it is 20D from the inlet and the side walls and 40D from the outlet of the domain where D represents the diameter of the absorber tube as shown in Figure 4. Meshing is valued such that it is fine near the receiver system of about 12, 92 356 and becomes coarse as it diverges away towards the wall of the domain. PISO algorithm is used for the Skewness–Neighbour coupling with second-order unwinding scheme for discretization of equations. Convergence criteria of 10−4, 10−4 and 10−6 are imposed on the residuals of the continuity, momentum and energy equations, respectively. The present work is validated with the experimental results of Sahoo et al. [12] with a deviation of 8% to 15% observed in the total heat loss. Figure 4. View largeDownload slide Modes of heat transfer from the PB secondary receiver system. Figure 4. View largeDownload slide Modes of heat transfer from the PB secondary receiver system. 3 RESULTS AND DISCUSSION A parametric study based on the effects of emissivity of the absorber tube and the wind velocities are considered. The non-uniform flux on the absorber tube for direct normal irradiance (DNI) ranging between 250 W/m2 and 1000 W/m2 are investigated. All the modes of heat transfer are considered for the analysis purpose. Performance analysis of the LFR system is carried out based on the on-site conditions and the numerically obtained value is compared with the experimental data. 3.1 Heat loss analysis for the absorber with emissive and non-emissive coating Temperature contour of the secondary reflector system with the non-uniform flux data provided along the circumference of the absorber with the aid of the user-defined function is shown in Figure 5. Sputtered cermet with an emissivity of 0.075 is used as a coating material. Figure 5(a) shows the temperature distribution of the cavity with the non-evacuated annular region. Buoyancy effect is observed both in the annulus and along the outer surface of the secondary reflector. The rise in the heat waves within the annular region is due to the presence of air. It can be clearly seen that as the upper part of the absorber receives negligible reflected rays, no flux is depicted in this part of the absorber tube. Figure 5(b) shows the temperature distribution in the open cavity with the evacuated annular region. Proclaiming the absence of air in the region, the stagnant heat waves are observed along the outer surface of the absorber tube. Since the heat waves are retained within the glass tube, Figure 5(b) clearly portrays the reduction in the heat waves from the outer wall of the secondary reflector. Figure 5. View largeDownload slide Temperature contour of PB secondary receiver system with non-uniform flux distribution on the absorber: (a) non-evacuated, (b) evacuated absorbers with emissivity 0.075. Figure 5. View largeDownload slide Temperature contour of PB secondary receiver system with non-uniform flux distribution on the absorber: (a) non-evacuated, (b) evacuated absorbers with emissivity 0.075. Figure 6 shows the convective and the radiative heat losses from the absorber tube coated with non-selective and the selective material. It is observed that the radiative heat losses predominate the heat losses when the emissivity is considered as a parametric factor for the uncoated absorber. When the absorber is non-evacuated, both the convective and the radiative heat transfer equally share the role of the heat losses. It is obvious and clear from Figure 4 that as the emissivity increases, the heat losses increase. Convective and radiative heat losses of about 54% and 40.6% are observed, respectively, when the absorber tube is coated with the non-emissive material. When the uncoated tube is placed under the evacuated condition, convective and radiative heat losses are reduced to 16% and 43%, respectively. Figure 6. View largeDownload slide Radiative and convective heat losses for different emissivity. Figure 6. View largeDownload slide Radiative and convective heat losses for different emissivity. 3.2 Heat loss analysis based on the wind velocity on the receiver system The temperature contour of the receiver system at different velocities and direct normal irradiance (DNI) are shown in Figure 7. As discussed earlier, when there is no wind condition, i.e. natural convection, because of the presence of air in the region between the absorber and the glass tube, the heat transfer rate is faster and due to the buoyancy effect heat waves travel upwards in the annular region around the absorber and in the outer surface of the secondary reflector. The flow direction of the wind is simulated from the inner wall of the domain towards the outer wall. Hence as the wind speed increases, circulation of air in the cavity occurs in the anti-clockwise direction around the absorber tube. This is because of the direction and velocity of the wind. The significance of the glass tube around the absorber is well proclaimed from the simulation that, though the absorber tube is evacuated or non-evacuated, the heat loss from the absorber tube can be significantly reduced when the absorber is placed in a glass tube. The figure also depicts that as the DNI increases, the temperature distribution in the annular region surrounds the entire circumference of the absorber and attains a stagnation state at the upper part of the tube. Figure 8 reveals the temperature contour of the receiver system when the absorber tube is evacuated. The heat transfer from the absorber to the cavity is completely constrained and hence the air in the cavity has less temperature gradient compared to the non-evacuated condition. This reflects the less temperature difference between the absorber and the cavity aperture opening. Hence at low wind speed, the flow of air sweeps the heat waves along the flow direction, near the aperture opening. As expected, when the velocity increases, anti-clockwise circulation of air around the absorber is observed with the transfer of heat waves from the upper part of the absorber. As the DNI increase this distribution of temperature prevails around the absorber and hence only small region is being agitated by the air circulation in the annular region. Figure 7. View largeDownload slide Temperature contours of PB secondary reflector for different velocities at DNI 250 W/m2 and 750 W/m2 for non-evacuated absorber at non-uniform flux distribution. Figure 7. View largeDownload slide Temperature contours of PB secondary reflector for different velocities at DNI 250 W/m2 and 750 W/m2 for non-evacuated absorber at non-uniform flux distribution. Figure 8. View largeDownload slide Temperature contours of PB secondary reflector for different velocities at DNI 250 W/m2 and 750 W/m2 for evacuated absorber at non-uniform flux distribution. Figure 8. View largeDownload slide Temperature contours of PB secondary reflector for different velocities at DNI 250 W/m2 and 750 W/m2 for evacuated absorber at non-uniform flux distribution. Figure 9 shows the total heat losses for different DNI for a range of velocities from 0 m/s to 10 m/s. At low DNI, 32% of heat loss is reduced because of the evacuation of the annular region. As the DNI increases, heat loss reduction of 40% can be obtained under the evacuated condition.With the increase in the velocity, 33–35% of heat loss reduction is observed for non-evacuated condition and can be further be reduced to a range of 50–75% for the evacuated condition. Figure 10 shows the amount of convective and the radiative heat losses from the 2-stage receiver system. When the region between the absorber and the glass tube is filled with air, convection heat transfer governs the heat loss because of the high heat transfer coefficient. But when the air is removed to produce a vacuum in this region, only molecular conduction exist and the convection heat transfer coefficient is low leading to negligible convection heat loss. The modes of heat transfer are only due to radiation. It is also inferred that when the tube is non-evacuated, higher the wind velocity, greater the convection heat loss and lesser the radiative heat loss. Figure 9. View largeDownload slide Total heat losses for different DNI for a range of velocities from 0 m/s to 9 m/s. Figure 9. View largeDownload slide Total heat losses for different DNI for a range of velocities from 0 m/s to 9 m/s. Figure 10. View largeDownload slide Convective and radiative heat loss for different DNI at various velocity range. Figure 10. View largeDownload slide Convective and radiative heat loss for different DNI at various velocity range. 3.3 Thermal performance analysis of linear evacuated absorber with parabolic secondary reflector On a typical solar solstice day, the DNI over a period of time from 9:30 AM to 5:00 PM is measured. From the calculations analytically made in MATLAB from the set of equations in Section 2.1, the useful heat obtained from the LFR collector is calculated. The analytical calculations for the thermal performance of the LFR system are based on the DNI on the summer solstice day in Vallipuram, Tamil Nadu with the wind velocity measured between 0.5 m/s and 2.75 m/s. The absorber emissivity is 0.075 with the transmissivity of the glass tube as 0.9. The useful heat obtained by the analytical method is compared with the experimental data obtained. Figure 11 shows the comparison of the numerical data calculated by analytical method with the experimental heat gain. For the validation of the numerical value, the performance of the LFR module is calculated from the heat loss values and is compared with the data from the pilot plant in Vallipuram, Chennai. Experimental performance of the LFR system is 10–15% less compared with the numerical data. This can be justified as the deviation caused by the natural conditions such as dust and wind flow direction. prevailing in on-site. Figure 12 shows the variation of temperature and DNI as a function of time. The deviation of the temperature of the absorber, glass tube and the secondary reflector lies in the range between 10% and 17% over the transient conditions. Figure 11. View largeDownload slide Experimental vs. numerical values of heat gain. Figure 11. View largeDownload slide Experimental vs. numerical values of heat gain. Figure 12. View largeDownload slide Transient variation of temperature and DNI. Figure 12. View largeDownload slide Transient variation of temperature and DNI. 4 CONCLUSION Numerical analysis was performed to determine the heat loss from a 2-stage receiver system under realistic conditions. The flux distribution along the circumference of the absorber was obtained by optimizing the optical parameters such as the acceptance angle, truncation points, gap between the absorber and the reflector, and tilt and the distance between the primary mirrors. The flux distribution thus acquired is applied as the boundary condition to the absorber tube with a user-defined function. Two different conditions namely, the non-evacuated and evacuated conditions were considered in the annular region between the absorber and the glass tube. A parametric study based on the emissivity of the absorber tube and the real-time conditions of the atmosphere with temperature 303 K and pressure of 1 bar with different wind velocities were analysed. The heat loss study hence reveals that the heat loss can be reduced to 65% under an evacuated condition with the emissivity of 0.075. The study provides an insight into the optimized aid of the second stage reflector with the absorber tube placed under evacuated/non-evacuated conditions proclaimed in the presence of wind. Finally, the thermal performance of the LFR system is analytically calculated. These data are compared with the experimental data obtained from Vallipuram measured on a summer solstice day. Numerical useful heat gain is found to be 10% greater than the experimental data and the temperature of the absorber tube, glass cover and the secondary reflector deviates by 10–17%. This is expected to be caused because of the dust and the wind flow direction in the on-site. ACKNOWLEDGEMENTS The financial support provided by the Department of Science and Technology (DST), Government of India through the project, DST/TM/SERI/2K11/188(G) Dt. 08/11/2012 is duly acknowledged. 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Int J Heat Mass Transf  2016; 96: 256– 66. doi:10.1016/j.ijheatmasstransfer.2016.01.035. Google Scholar CrossRef Search ADS   5 Beltagy H, Semmar D, Lehaut C et al.  . Theoretical and experimental performance analysis of a Fresnel type solar concentrator. Renew Energy  2017; 101: 782– 93. doi:10.1016/j.renene.2016.09.038. Google Scholar CrossRef Search ADS   6 Lin M, Sumathy K, Dai YJ et al.  . Experimental and theoretical analysis on a linear Fresnel reflector solar collector prototype with V-shaped cavity receiver. Appl Therm Eng  2013; 51: 963– 72. doi:10.1016/j.applthermaleng.2012.10.050. Google Scholar CrossRef Search ADS   7 Okafor IF, Dirker J, Meyer JP. Influence of circumferential solar heat flux distribution on the heat transfer coefficients of linear Fresnel collector absorber tubes. Solar Energy  2014; 107: 381– 97. doi:10.1016/j.solener.2014.05.011. Google Scholar CrossRef Search ADS   8 Incropera DD, Dewitt FP. Introduction to Heat Transfer , 3rd edn. John Wiley & Sons, New York, 1996. 9 Kalogirou SA. Solar thermal collectors and applications. Prog Energy combust sci  2004. doi:10.1016/j.pecs.2004.02.001. 10 Duffie JA, Beckman WA, Worek WM, Solar Engineering of Thermal Processes, 4th edn 2003. doi:10.1115/1.2930068. 11 ANSYS Inc, ANSYS Fluent, ( 2015). 12 Sahoo SS, Varghese SM, Suresh Kumar C et al.  . Experimental investigation and computational validation of heat losses from the cavity receiver used in linear Fresnel reflector solar thermal system. Renew Energy.  2013; 55: 18– 23. doi:10.1016/j.renene.2012.11.036. Google Scholar CrossRef Search ADS   © The Author(s) 2018. Published by Oxford University Press. This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. 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International Journal of Low-Carbon TechnologiesOxford University Press

Published: Mar 1, 2018

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