Design Optimization of a Non-evacuated CPC Collector

Design Optimization of a Non-evacuated CPC Collector Dariush Zare a,*, Hossein Ebadi a a Biosystems Engineering Department, College of Agriculture, Shiraz University, Shiraz, Fars, Iran * Corresponding author. Email: sanyzare@yahoo.com Abstract In this study a mathematical model based on temperature dependent coefficients was developed to predict the thermal behavior of a non-evacuated CPC collector under Shiraz climate condition (Iran). Energy balance equations for collector components were established and estimations on fluid temperature distribution along the receiver tube were done using an iterative method with a convergence criteria of ξ=10-5. In order to find the optimum design, the proposed model was applied to four different design configurations with a constant acceptance angle (θ c = 22.5 o ) and four different absorber diameters. A water mass flow rate of 0.003 kg/s was marked as the optimum point, to find the best collector length (L) and absorber diameter (Do) with maximum efficiency and 100 o C outlet water temperature. The results indicate that, D o = 3.81cm and L = 8m will have the best performance for the optimization purpose. Results were also compared to similar works and showed a good agreement with experimental studies. Keywords: CPC design, Length optimization, Thermal modeling, Performance estimation 1. Introduction Environmental effects and the ways which energy is employed are the prime factors in sustainable developments. During the history, the importance of energy availability and its relation with economic activity has been proved, but early concerns were at the cost of energy in the early 1970s (Kalogirou, 2009). After two decades when some issues like acid rain, ozone layer depletion, global climate change, etc., were discussed in international negotiations, alternative energy sources with respects to economic, environmental, and safety considerations emerged. Solar energy as one of the most reliable renewable energy sources, with a wide variety of applications, and without environmental pollution, has been gaining increased attention in recent years. Thus, it is expected that in the year 2020 solar thermal energy accounts for about 25% of the renewable energy and the solar PV electricity for about 2.3% (Galloway, 2004). Solar water heating systems are one of the common and advanced solar thermal applications. Different models and designs have been presented in literatures (Kalogirou, 2004). Various aspects can be classified for solar water heating system evaluation, and are listed as; the thermal performance, lifetime and cost, sustainability or durability, maintenance and installation devices (Choudhury et al., 1995). For thermal performance analysis many researchers investigated different types of solar collectors and they applied different simulation models. Al-Ajlan et al. (2003) proposed a simulation of forced convection solar heated water system for a flat plate collector, Ouagued et al., (2013) estimated the performance of a parabolic trough collectors under Algeria Climate conditions. For optimization investigations, Tiba and Fraidenraich (2011) studied optical and thermal optimization of stationary non-evacuated CPC solar concentrators for different concentration ratios (C<2), to find their relations with thermal performance. Furthermore, Dagougui et al., (2011) analyzed performance optimization of flat plate collectors, and examined different cover configurations for optimal condition, finally they reported that combined Plexiglas and Glass cover has the best performance. Papers reporting design optimization of the CPC are rarely found, and those published are about reflector configurations, and optical behavior (Tiba and Fraidenraich, 2011), however; Patil, et al., (2014) studied the optimum size of the receiver by investigating the critical value of different radius ratio (diameter of the glass tube per diameter of receiver tube) for minimum heat loss. Finally they reported that the value of the critical radius ratio is lower for higher values of pipe diameter and is independent of receiver temperature and wind velocity. However, to import the CPC technology into sustainable designs, more optimization studies are needed. Since meteorological conditions are constant factors, enhancements on solar water heating system components like; absorber designs, collector area, etc. need to be investigated for the optimal conditions (Dagougui et al., 2011). The main purpose of this study is to support decision makers in their designs and predictions over the CPC collector application. As different collector s parameters have been considered and their effects are well analyzed upon the efficiency, outlet temperature and overall heat losses, the designers will be assisted with the most accurate and suitable model for their needs. To achieve this aim, several procedures were done. First, a set of heat transfer coefficients were established and a mathematical model for thermal behavior of water through the collector was conducted. Then in order to evaluate of the consistency of proposed model, results were compared to similar and experimental works. Second, to support decision makers about the most cost-effective design, numerous different configurations were compared and the 1

investigation was done about the collector length and absorber diameter. All calculations were conducted over the actual and measured meteorological data from Shiraz (Iran), to show the applicability of the presented methodology. 2. Materials and Methods 2.1. Collector design Details of a compound parabolic concentrator were studied by Mc Intire (1979) and the following expressions were conducted in two sections of the curve. (The involute part of the curve) ρ(θ)=rθ, θ θ A + π 2 (1) ρ(θ)=r{{θ+θ A +π 2-cos((θ-θ A )) }/(1+sin(θ-θ A ) )} (2) where θ A + π 2 θ 3π 2-θ A The curve is generated by incrementing θ in radiant, calculating ρ, and then calculating the coordinates, X and Y, by: X=R sin θ- ρ cos θ (3) Y= -R cos θ- ρ sin θ (4) where θ A and R denote acceptance half angle and receiver radius. In order to plot a full CPC diagram, equations (1-4) has been coded using Matlab R2014a software. 2.2. Physical parameters In this study, the CPC collector is considered to be trough, with the acceptance half angle of 22.5 o and reduced to nearly two third of its full size, while its concentration ratio remains 2.5. The orientation is in the way that it tracks the sun along its East-West axis, toward south with a constant slope angle of β. The collector has a total variable aperture width and height due to absorber diameter and also different configuration for different values of CPC length L. The receiving pipes were selected from commercial copper pipe sizes and were assumed to be painted non-selective matte black. Two sealed supports were designed to stable the receiver along its axis and also eliminate conductive heat exchanging from the receiver to the ambient. For the reflective surfaces, stainless steel sheet with thickness of 0.4mm were considered. 2.3. Thermal modeling In this study, some assumptions were taken into account to simplify the analysis and the following items are made; (1) In this model the CPC concentration ratio (Cr) is calculated as a geometric concentration ratio that is to be expressed as (Hsieh, 1981) Cr = 1 sin(θ max ) (11) (2) All of the fabrication errors are neglected, because it is assumed that the CPC is ideal. (3) For the solar radiation calculations, it was assumed that the sky is isotropic for diffuse radiation considerations. (4) The physical and optical properties of materials are assumed to be independent of temperature. (5) Water properties are functions of temperature only. (6) Steady state is considered for the modeling procedure. (7) Metrological data were taken into account for 11th June of Shiraz region, Iran (29.6167 o N, 52.5333 o E) A simplified mathematical model has been made to simulate thermal behavior of the collector. In this design in order to present a convenient model for construction, non-evacuated receiver was analyzed. Fig.4, represents the schematic network of the heat exchanged occurring in the air gap between the receiver to the cover and the cover to the ambient. The one dimensional receiver heat-loss model is shown in figure 1. This is the model used in the literature most often for the calculation of the heat-loss from the receiver. Modeling of the heat-loss rates for the present study is described in detail below per unit length of the receiver. Figure 1. Thermal network for a non-evacuated CPC collector. 2

Radiative heat loss rate from cover to sky; h1 The radiative heat transfer coefficient h1 is calculated using the following relation (Tchinda et al., 1995): h1=ε c σ (T c 2 + T s 2 )(T c +T s )A a A r (12) where the T c is cover temperature and sky temperature (T s ) is assumed to be 6 o C less than the ambient temperature (Whillier, 1967). Convective heat loss rate from the cover to the ambient; h2 Duffie and Beckman (1991) reported that convective heat loss from cover to ambient has relation to wind velocity as the following equation presents: h2=(5.7+3.8υ) A a A r (13) where A a and A r are aperture and receiver area. Radiative heat loss rate from the receiver to the cover, h3 For radiation loss rate from receiver to cover the equation to be used is (Hsieh, 1981): h3=(σ(t r 2 +T c 2 )(T r +T c ))/(1 ε c +A r A c (1 ε c -1)) (14) where σ is the Stefan-Boltzmann constant and ε c represents cover emissivity. Convective heat loss rate from receiver to cover, h4 According to the Hsieh theory (1981) the convection heat loss occurs between the receiver and cover is: h4=3.25+0.0085 ((T r -T c )/4R) (15) It should be added that the flow is assumed to be fully developed at the collector inlet. The empirical expression, presents the loss coefficient for heat transfer from the receiver to the ambient is given as (Duffie and Beckman 1991): Ul=1 A r [1/((h4+h3)A r )+ 1/((h2+h1)A a )] -1 (16) To predict the collector performance, it is necessary to evaluate the collector efficiency factor F, so following equation is used (Hsieh, 1981): (17) where the hci is the convective heat transfer coefficient of inner part of receiver. Final step for calculation of collector performance is to determine the useful thermal energy Q u extracted from collector and is calculated as following (Duffie and Beckman 1991): where F R is a removal factor and is given as: (18) (19) For calculation of hourly efficiency, which presents the ratio of extracted thermal power of the collector to total power incident on the aperture area, this formula is used (Duffie and Beckman 1991): (20) 2.4. Calculation procedure The mathematical modeling used in this study was programmed in to MatlabR2014a and followed an iterative method. The temperatures of the cover and the receiver were two major factors of this model. So, first for two assumed temperatures, different temperature dependence heat transfer coefficients were calculated and by the presented equations in Appendix new temperatures were estimated. All the procedure was repeated again, using new temperatures and the iteration continues until the values converged. To ensure the accuracy of the described method, a convergence criterion was evaluated and is given by the following expression (Tchinda, 2008): (21) For indication of the best ξ, different iterations were conducted and the results were compared by the output values and the number of iterations. It was seen that for ξ=10-5 the results were accurate sufficiently. Figure 2 illustrates the flowchart of the solution procedure. 3

Figure 2. Flowchart of solution procedure. 2.5. The optimization approach Thermal analysis defined in pervious section, shows the importance of choosing the proper design components, in this section in order to find the optimal performance of the different configurations with four different commercial absorber diameters and different collector length an optimization approach is utilized. The aim is to find the optimal design of solar system that offers a high efficiency and the desire outlet temperature. Industrial heat demands are divided with different factors. Temperature level is one of the aspects for this division; therefore three different levels have been used by ECHOHEATCOOL (2006) for describing the quality of the demand for heat to be used in various industrial branches: Low temperature level is defined as lower than 100 o C, corresponding to the typical heat demands for space heating. The heat is used in low temperature industrial processes as washing, rinsing, and food preparation. Some heat is also used for space heating of industrial building and on-site hot water preparation. Medium temperature level is represented by an interval between 100 and 400 o C. This heat is normally supplied through steam as a local heat carrier. The purpose is often to evaporate or to dry. High temperature level constitutes temperature levels over 400 o C. This high quality is needed for manufacture of metals, ceramics, and glass etc. these temperatures can be created by using hot flue gases, electric induction etc. In this study, in order to find the ideal operation and design condition, the effect of water mass flow rate on each design is investigated and the efficiency, outlet temperature and overall losses were determined and compared. As it was mentioned earlier, CPC configuration is a function of acceptance angle and absorber diameter, so in this proposed optimization problems with four absorber diameters and a constant acceptance angle of 45 o, four different designs determined. According to the fact that the cost of the absorber is one of the constraints in collector design, the length of the tube would be critical in different comparisons, therefore, a range of 2 to 10m with intervals of 0.5m was assumed to be tested and the minimum length that fits the requirements, was realized as the most cost-effective choice, due to the least material consumption in the design. It also reveals that, as the collector is considered to be trough, the reduction in absorber length, leads to reduction of overall collector length and thus decreases the fabrication cost. Therefore the aim 4

was to identify the ideal design with the highest value for efficiency with the minimum length of absorber tube in order to reach outlet water temperature of 100 o C to ensure the system applicability over the industrial low level heat demands. 3. Results and Discussion 3.1. Thermal analysis results The results in figure 3 show that the water outlet temperature increases with decrease in water mass flow rate; however, the collector efficiency has the opposite effect. Figure 3. Effect of water mass flow rate on T fo and η; D o =3.81cm, L=10m. Fig. 4 illustrates the variation of the useful energy and solar radiation during the daylight hours in 11 June 2012. The figure shows that the increase in solar radiation leads to an increase in the useful energy. Figure 4. Hourly variation of Useful energy and Solar radiation; Do = 3.81cm, L = 8m, M = 0.005 kg s. Fig. 5 exhibits temperatures of collector components during a typical day. As it was expected, the receiver has the maximum temperature while cover has the minimum temperature. The figure shows that, in midday hours when the collector absorbed the highest amount of energy, water outlet temperature records as 50 o C for mass flow rate of 0.005 kg s with the length of 8m. Figure 5. Hourly variation of tempratures of the collector; Do = 3.81cm, L = 8m, M = 0.005 kg s. 3.2. Optimization results To investigate the optimal performance and design, it was essential to find the most adequate mass flow rate for maintaining good efficiency and suitable water outlet temperature. For this purpose several runs for the effects of various parameters such as collector length, absorber diameter and mass flow rate, on the efficiency and the outlet temperature were conducted and the results were compared. It has been seen that for all conditions there would be a constant value of 5

0.003 kg s for water mass flow rate, that the system maintains both the highest efficiency and the maximum water outlet temperature. In the next step, in order to find the ideal length, the effects of length in a wide range of 2 to 10m of the efficiency and the outlet water temperature for different configurations were investigated and plotted in figures (6-9). As illustrated in Fig 6 to 9, increase in collector length increases the outlet temperature and reduces the thermal efficiency which, results from the greater absorbed energy for increase in aperture area. On the other hand, the higher operating temperature, the more energy wasted, so for this reason it is acceptable to observed decrease in thermal efficiency while the length proceeds. It also can be concluded that, as the absorber diameter increase, where the aperture width grows, the higher outlet temperature is expected, however; more heat is exchanged to the surroundings and causes a decrease in thermal efficiency. Figure 6. The effect of collector length on T fo and η; D o = 1.27cm, M= 0.003kg/s. Figure 7. The effect of collector length on T fo and η; D o = 2.54cm, M = 0.003 kg s. Figure 8. The effect of collector length on T fo and η; D o = 3.81cm, M = 0.003 kg s. 6

Figure 9. The effect of collector length on T fo and η; D o = 5.08cm, M = 0.003 kg s. To solve the optimization problem, one ideal point was detected in each figure, and it was described as the location where the both lines meet each other. Hence, in this point the highest temperature estimated with the highest efficiency, as these factors have the conflicting trends along the length axis. The results of the optimization analysis for all the configurations have been summarized and the ideal points are shown in the table 1. Table 1. Summary of optimal characteristics of the collector Design characteristics Optimization characteristics D o Truncated to Aperture width L T fo η 1.27 cm 2/3 10 cm 7.5 m 33.6 54.4% 2.54 cm 2/3 20 cm 8 m 66.9 45.3% 3.81 cm 2/3 30 cm 8 m 109.5 40% 5.08 cm 2/3 40 cm 7.5 m 147 36% As it was mentioned previously the main goal is to find a design with the outlet temperatures above 100 o C, therefore as table 2 summarized, two choices qualified in this step while they have T fo =109.5 o C and 147 o C for D=3.81cm and 5.08cm respectively. For the selection of the optimal design, the second characteristic i.e. thermal efficiency was compared and the higher value was selected as 40%. Thus, the optimal collector length and absorber diameter were recognized as L=8m and D=3.81cm respectively. 4. Conclusions In this paper, the thermal behavior of a non-evacuated CPC collector has been studied. A theoretical solution procedure of the heat transfer and energy equations using a computer code for estimating the effects of different parameters on thermal performance of the present collector has been made. Reasonable agreement with pervious and experimental similar works obtained. Finally, an optimization problem has been described and solved with a comparison between different configurations, in order to determine the most cost-effective design with maximum efficiency and the require water temperature. Finally, the design with a receiver diameter of 3.81cm and 8m total length for acceptance angle of 45 o shows the best performance under Shiraz climate conditions. References Al-Ajlan, S.A., H. Al Faris, H. Khonkar, 2003. A simulation modeling for optimization of flat plate collector design in Riyadh, Saudi Arabia. Renewable Energy. 28, 1325-1339. Choudhury, C., P.M. Chauhan, H.P. Garg, 1995. Design curves for conventional solar air heaters. Renewable Energy. 6, 739-749. Dagougui, H., A.Ouammi, M. Robba, R. Salcile, 2011. Thermal analysis and performance optimization of a solar water heater flat plate collector: Application to Tetouan (Morocco). Renewable and Sustainable Energy Reviews. 15, 630-638. Galloway, T., 2004. Solar House: A Guide for the Solar Designer.Oxford, Architectural Press, 1st ed. Hsieh, C.k., 1981. Thermal analysis of CPC collectors. Solar Energy. 27, 19-29. 7

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