A Practical Method to Determine the Temperature of a Solar Thermal Energy Storage Tank

Transcription

1 American Journal of Oil and Chemical Technologies: Volume 4. Issue 1. January 2016 Petrotex Library Archive American Journal of Oil and Chemical Technologies Journal Website: A Practical Method to Determine the Temperature of a Solar Thermal Energy Storage Tank Jamadi, F Department of physics, Mathematical College, Sirjan University of Technology, Sirjan, Iran Abstract: Solar energy (renewable energy) can play a key role in supplying the increasing energy need of humans and decrease air pollution. The production of hot water in houses for consumption is the most common use of solar energy. In the present study, a solar water heater system (SWHS) is studied using solar parabolic collector and heat exchanger. The aim of this study was to compare the theoretical and experimental temperature of a thermal energy storage tank (TEST). To achieve this goal, the temperatures of TEST were measured at constant time intervals, experimentally. Moreover, the temperatures of TEST were also estimated using the Euler integration method. The comparison of temperature values shows that the Euler method is the exact method to estimate the temperature of TEST. Also, the temperature variations of the water tank versus time show that the heat losses of the system is low, as well the heat exchanger transfer thermal energy to the water tank as well. Therefore, it can be said that the system is efficient and applicable to SWHS for building. Keyword: Solar energy, thermal energy, Euler integral, solar parabolic collector, thermal energy storage tank 1. Introduction The energy crisis in today s world has caused the conversion of solar energy to the best available clean energy to save mankind. Fossil fuels produce carbon dioxide, which intensifies air pollution and accelerates the process of ozone layer destruction and the global warming phenomenon [1]. In addition, severe fluctuations of fuel prices have rendered the economy of many countries extremely vulnerable. However, the use of renewable energies offers great economic and environmental advantages [2]. Several countries have a lot of sunny days throughout the year and as such have a high potential for utilizing solar energy; however, such energy is rarely put to use. Even when this energy is utilized, there are limited strategies for energy storage and therefore, this energy can be used only during the day (only sunny days). Solar energy is stored usually in the form of sensible liquid energy [3]. Thermal energy can be stored within fluids with high specific thermal capacity and the fluid type is selected by considering the type of application and the amount of energy needed. For SWHSs that store hot water, energy storage in the form of sensible thermal energy of water is the most appropriate and most practical choice. Each SWHS consists of a TEST and solar collector in order to convert solar energy to thermal energy [4]. The use of heat exchanger (and its location), as well as the type of collector depends on the system application mode. In order to store solar energy, numerous studies have been conducted. Wang et al. conducted a detailed research on the theory and various applications of SWHSs. In their study, they classified various types of SWHS into passive and active categories and also sorted out their performance based on energy storage system efficiency [5]. One of the ways to save energy is the use of a reservoir with a dense substrate. Schumann and Franklin, for the first time in 1929, provided the descriptive energy equations on a dense substrate according to the substrate properties (such as porosity coefficient), current fluid conditions, and volumetric heat transfer coefficient between the substrate and the fluid [6].The analytical solution of Industrial And Mining Research Centre Cycle Science & Industry Company, Tehran, Iran cs.isi.pjs@gmail.com

2 Skaman equations takes too much time and as such, it is not useful. Therefore, Kuhn et al. carried out a study using the numerical solution methods for the equations governing the energy in a reservoir with a dense substrate. They introduced the NTU method as the best and most efficient method to simulate solar systems [7]. In 1977, Karaki et al. plotted the diagrams of temperature variations in various parts of energy storage [8]. Another way to store energy in passive form is the storage of thermal energy in the walls and ceilings of buildings. These walls are often made of glass and thus they allow passage of the Sun's radiation through and enclose thermal energy within their substance or absorb it. However, studies on thermal energy storage and simulation have been carried out by various researchers, such as Balcomb et al. [9] and Ohanessian and Charters [10] using the TRNSYS software. Energy storage is also possible based on the seasons. But in this type of storage, water tanks must be very large and heat loss must be brought to the nearest minimum. Bankston designed such tanks and checked their performance to save energy in one season [11]. Sagade used a parabolic dish collector to design a SWHS with a cone-shaped helical coiled receiver and studied the temperature of the hot water tank based on various mass flows. This researcher, by spiral absorption, increased the average temperature of the receiver up to 9.2% [12]. Valan and Sornakumar used a parabolic collector to increase the temperature of the energy storage tank water from 35 to C within 8 h [13]. They simulated the water heater system with a computer simulation program in The difference between the temperatures of the actual tank and the estimated value was 9.5% [14]. Rosado and Escalante determined the efficiency of a SWHS with parabolic collectors and studied the changes in temperature of water tank with mass flow of kg/s versus time [15]. This study presents a SWHS with a parabolic collector. The aim is to observe the TEST temperature changes vs. time using both experimental and theoretical methods. The temperature of the energy storage tank was estimated using the Euler Integral. Using a L water tank along with the heat exchanger, prevents quick loss of thermal energy. In addition to household applications, this hot water can be used in buildings heating systems. 1. Materials and Methods 1.1. Materials For the design of a thermal energy storage system, the characteristics of the system should be taken into consideration. Some of these important characteristics are as follows: 1 - The temperature in which the system absorbs thermal energy or losses it to the environment. 2 System components that absorb heat and the parts that loss the heat and the temperature difference between them. 3 - TESTs and the system insulation [3]. First and foremost, the SWHS component is the solar collector. It is evident that the factors affecting the performance of collectors have great impact on the performance and efficiency of the whole energy storage system.when storing thermal energy, the temperature of the collector s output oil is definitely more than the temperature of input oil of the heat exchanger. Also, within the heat exchanger, all the oil thermal would not be transferred from the oil to water. As a result, due to the economic constraints, the system s heat loss must be minimized [16]. Increasing the energy storage capacity is one of the desirable goals, in order to increase the efficiency of the entire system. Choosing a good location for the energy storage tank plays a significant role in the amount of stored thermal energy and in the increase of storage capacity. This indicates that such a choice affects the collector s working temperature, collector s surface area, its length and ultimately the costs [3]. Moreover, if the water is used in the parabolic collector at temperatures higher than 80 C(dependent on the region's pressure), steam is formed and a dual - phase system results. Hence, oil is used in the aforementioned parabolic collector as the working fluid. As a result, TEST cannot be directly connected to the collector because the desired goal is to store the heat within the water. Therefore, a heat exchanger must be used to transfer the oil heat to the water [3]. As mentioned earlier, the perfect material for thermal energy storage across a variety of solar collectors is water. Water tank Parabolic collector Heat exchanger Figure 1. SWHS system 17

3 The system shown in Figure 1 includes a parabolic collector, a heat exchanger, and a L water tank. An absorber tube is located in the focal line of the collector and oil flows through it. The oil absorbs the heat of the Sun, then it flows through the heat exchanger. The oil has a closed cycle. Also, the water returns to the tank after absorbing the oil heat and must have passed through the heat exchanger Methods The total thermal capacity for the performance cycle (energy storage capacity) is obtained using Equation ( 1 ) : Q! = m! C! T! ( 1 ) In Equation ( 1 ), T! is the temperature range required by the process and in fact, it is the TEST temperature variations during time intervals (Water vapor pressure and the amount of heat loss increase the T! temperature range.) By using the equation energy balance, the governing equation of TEST ( 2 ) is written as such [3]: m! C!!!!!" = Q! UA ( T! T! ) (2) In Equation ( 2 ) Q! is the useful energy that oil may acquire after absorbing heat from the sun through the collector. This quantity can be defined as shown in Equation ( 3 ) : Q! = m! C! ( T!" T!" ) ( 3 ) Subscript f indicates the working fluid, which is oil. One of the most practical methods of tank temperature calculation, at the end of a period of time is by applying the Euler Integral. In this method, the system efficiency for a long time can be calculated by the integration of Equation (2) [3] : T! = T! +!!!!! [Q! UA T! T! ] (4) In Equation (4), assuming that the useful absorbed energy is Q u (during 1 hour ) and the tank heat loss is U, the tank temperature at the end of the an hour can be obtained. Equation (4) shows that by increasing the heat loss coefficient, collector surface area and the temperature difference between the tank and the environment, the tank temperature decreases more versus time. Equation (5) is used to calculate the heat loss coefficient [17] : U =!! =!!!!!!! (5) The total resistance that causes heat loss is produced by heat loss through the convective flow of air and conduction of heat loss in the walls of the tank. The heat loss by convection and conduction add up as a series of resistors. To calculate the air s convective coefficient, the Nusselt Number is defined as shown in Equation (6) [17]: Nu = C Re! Pr!! (6) First, the Nusselt Number is obtained using Equation (6) and next, the Hilpert Equation (7) gives the convective coefficient: 18

4 Nu =!!!! (7) Reynolds Number (Re) in Equation (6) is correlated with kinematic viscosity and air speed as shown in Equation (8) : Re =!!! (8) 2. Results The measurements on the target system were conducted on the 16th of June 2015 from 8 am to 16 pm in the City of Sirjan. The oil flow in this test was set as 9.5 L/h. To calculate the water tank temperature at the end of each hour, all terms of Equation (4) must be calculated. The oil thermal capacity based on change in temperature (Kelvin)is shown in Table 1. Table 1. Oil thermal capacity values based on temperature. T (k) C f 10 3 (J/kg.k) density(kg/m 3 ) The last row of Table 1 shows the mean values of density and thermal capacity. To calculate the collector s Q u, the mean values of these quantities are used. The measured temperatures of the inlet and outlet oil are shown in Table 2. Table 2. The oil collector s input and output temperatures at different hours of the day. Time (h) T fi ( C) T fo ( C) Q! (W) The thermal power changes of the collector during the day vs. time are shown in Figure 2. 19

5 400 3 Thermal power of the collecor (W) Time (h) Figure 2. Collector s thermal power changes vs. time. Table 3. Solar radiation and ambient temperature vs. time. Time (h) I (w/m 2 ) T a ( C) Changes in ambient temperature vs. time are shown in Figure 3. 20

6 45 Ambient temperature ( C) Time (h) The solar radiation changes vs. time are shown in Figure 4. Figure 3. Ambient temperature changes vs. time solar radiation (w/m2) Time (h) Figure 4. solar radiation changes vs. time. To calculate the final term of phrase (Equation 4 ), the surface area of the tank is A = 0.7 m 2 and the mass of the tank's water is equal to kg. The thickness of the tank is equal to 0.5 mm and the conductive coefficient of iron is 80.2 w/m.k. So, L w = !! k m! K 21

7 To calculate the Reynolds Number, average speed of the air in Sirjan is 3 m/s, tank diameter is 0.35 m, and the dynamic!!!! viscosity of the air is ! By using Equation (8), Re = is determined. To calculate the Nusselt Number, C = and m = and to calculate the range, Reynolds Number is above 40,000, Prandtl Number is Pr = [17]. Nu = !.!"# 0.707!! = From the phrase (Equation 7), the convective coefficient is given as: h! = !! 0.35 = 13.7 w m!. K Based on the aforementioned calculations, the heat loss of tank is obtained as U = 13.7 w/ C. Based on the fact that one hour is needed to reach a steady system state, the estimation of the temperature of the tank started from 9 o clock. The values of the initial thermal power of collector, the ambient temperature, and the temperature of the water tank are estimated as W, and 33 C, respectively. By using these values, an hour later (that is, at 10: 00 a.m.), the tank temperature of 34.4 C was estimated. Now, by using this value, the temperature is calculated again for the next hour. The measured temperature and the estimated values of the water of the storage tank temperatures using the Euler method are shown in Table 4. The water s thermal capacity is kj/kg.k and the water flow is 45 L/h. Table 4. TEST temperature changes. Time (h) T Euler method ( C) T experimental ( C) The estimates of water temperatures are shown in Figures 5. 22

8 Water temperatures of the tank ( C) time(h) Figure 5. Water temperature changes vs. time (theorical). The experimental measurement of the tank water temperature is shown in Figure tank water temperature ( C) time(h) Figure 6. Tank water temperature changes chart vs. time (experimental ). Figure 7 shows the water temperature graphs, which compares the experimental and theoretical values. 23

9 the water temperature of the tank( C) theorical experimental 0 time(h) Figure 7. Temperature graphs showing the comparison of experimental and theoretical modes. 3. Discussion and conclusion As expected in this study, radiation increased with time and after reaching its maximum value at noon, it started to decrease. In line with the illustration in Figure 2, the collector s thermal power peaked at 12 o clock and then dropped as a result of the high (maximum) amount of radiation present in this hour. Therefore, most power can be gained from the collector at noon. The temperature of the environment, like other quantities, depends on the radiation from the Sun and as shown in Figure 4, it increased from morning until noon, and then decreased.the measured water temperature increased from a minimum value of C at 8 am in the morning until it reached the maximum value of C at 16 p.m., and this could be attributed to the fact that it absorbed the heat from the hot oil of the heat exchanger (actually from the radiation). As a result of the large size of the tank, the water barely lost heat, however, despite the reduction of radiation at 13 pm, its level of heat increased and then at 14, 15 and 16 h (p.m.), its temperature remained constant. Figure 8 shows that the experimental and theoretical temperature charts are almost overlapping. At 9 a.m., the initial temperature value for the Euler method was the same as the experimental value, and thus, the values were equal at 9 a.m. At 10 and 11 a.m., variations between theoretical and experimental temperatures were observed, but the theoretical values were approximated to real values at the end of the graph. Moreover, at 13, 14, 15, and 16 h, the disagreement was only a few hundredths against the real values. The good conformity of the water temperature charts in Figure 8 means that the Euler method gives a detailed estimate of the temperature of the water tank. To determine the most exact estimation using the Euler method, further studies on measurements should be conducted under a clear sky. Acknowledgment The author wish to thank Dr. Abaslo for her generous tips. Legend Surface area of the tank, m 2 Thermal capacity, J/kg.K Diameter, m A C D 24

10 Convective coefficient, w/m 2.K Conductance, w/m.k Water mass, kg Prandtl number ( dimensionless ) Thermal power, W Resistance, Ω Reynolds Number ( dimensionless ) Heat loss, w/m 2.K Air speed, m/s h k m Pr Q R Re U V Greek symbols Kinematic viscosity, m 2 /s ϑ Subscripts Air Fluid Tank Water a f t w 4. References [1] O. Edenhofer, R. Pichs-Madruga, Y. Sokona, Renewable energy sources and climate change mitigation, Technical Support Unit Working Group III Potsdam Institute for Climate Impact Research (PIK), [2] B. Batidzirai, E. Lysen, S. V. Egmond, V. Sark, W. G. J. H. M., Potential for solar water heating in Zimbabwe, Renewable and sustainable Energy, 13, , [3] J. A. Duffi, W. A. Backman, Solar Engineering of Thermal Processes, 4 th edition, Wiley, Wisconsin Madison, [4] B. Luo, Z. Hu, X. Hong, W. He, Experimental study of the water heating performance of a novel tile shaped dualfunction solar collector, Energy Procedia, 70, 87 94, [5] Z. Wang, W. Yang, Q. Feng, X. Zhang, X. Zhao, Solar water heating: From theory, application, marketing and research, Renewable and Sustainable Energy Reviews, 41, 68 84, [6] T. E. W. Schumann, J. Franklin, Heat Transfer: A Liquid Flowing through a Porous Prism, 208, , [7] J. K. Kuhn, G. F. Von Fuchs, A. W. Warren, A. P. Zob, Developing and Upgrading of Solar System Thermal Energy Storage Simulation Models, Report of Boeing Computer Services Company to the U.S. Department of Energy, [8] S. Karaki, P. R. Armstrong, T. N. Bechtel, Evaluation of a Residential Solar Air Heating and Nocturnal Cooling System, Report COO from Colorado State University to the U.S. Department of Energy, [9] J. D. Balcomb, J. C. Hedstrom, R. D. McFarland, Simulation Analysis of Passive Solar Heated Buildings Preliminary Results, Solar Energy, 19, , [10] P. Ohanessian, W. W. S. Charters, Thermal Simulation of a Passive Solar House Using a Trombe-Michel Wall Structure, Solar Energy, 20, , [11] C. A. Bankston, The Status and Potential of Central Solar Heating Plants with Seasonal Storage, An International Report, in Advances in Solar Energy, 4, 352, New York, [12] A. Sagade, Experimental investigation of effect of variation of mass flow rate on performance of parabolic dish water heater with non-coated receiver, International Journal of Sustainable Energy, 6, 80-93,

11 [13] Valan Arasu, S. Thambu Sornakumar, Performance charecteristics of the solar parabolic trough collector with hot water generation system, Thermal science, 10, , [14] Valan Arsu, S. Thambu Sornakumar, Theretical analysis and experimental verification of parabolic trough solar collector with hot water generation system, Thermal science, 11, , [15] N. Rosado Haua, M. A. Escalante, Efficiency of a parabolic trough collector as a water heater system in Yucata n mexico, Renewable and sustainable energy, 3, 1-6, [16] Mohamad, J. Orfi, H. Alansary Heat losses from parabolic trough solar collectors, International journal of energy research, 38, 20 28, [17] F. P. Incropera, D. P. Dewitt, Introduction to heat transfer, edited by L. Bergman, S. Lavine, 5 th edition, Wiley,