Thermodynamic Analysis and Optimization Procedure for Domestic Solar Water Heating System

Transcription

1 American Journal of Energy and Power Engineering 2015; 2(6): Published online January 12, 2016 ( ISSN: Thermodynamic Analysis and Optimization Procedure for Domestic Solar ater Heating System Nassar Yasser Fathi Mechanical Engineering Department, Engineering and Technology Faculty, Sebha University, Brack Al-Shati, Libya address Keywords Solar Storage Tank, Solar Collector, Optimum Tank Volume, Optimum Mass Flow Rate, Solar ater Heating Received: November 26, 2015 Revised: December 17, 2015 Accepted: December 19, 2015 Citation Nassar Yasser Fathi. Thermodynamic Analysis and Optimization Procedure for Domestic Solar ater Heating System. American Journal of Energy and Power Engineering. Vol. 2, No. 6, 2015, pp Abstract The main purpose of the present work is to study the thermal behaviour of a typical domestic solar water heating system (DSHs) consists a flat-plate solar collector, thermal storage tank, pumps, piping and control unit, leading to get out the optimum design and operating parameters such as (mass flowing through the solar collector array, area of solar collectors and the volume of the storage tank) that matched the requirement of people from hot water. The idea is, all the water need flowing directly through the collector and then accumulating in the thermal storage tank, by this method we improved the thermal behaviour of the solar collector, because the inlet temperature to the collector equals to the ambient temperature, at this point we have a maximum efficiency. Furthermore, we reduce the volume of the storage tank, because some of the load will be extracted instantaneously from the collector. Equation to predict the volume of the storage tank for continuous load has been presented. To achieve this purpose a work sheet of MS-Excel was prepared in order to evaluate the influence of all mentioned above parameters on the water temperature in the storage tank. The obtained results show that, for Libyan typical family which consumed about 250 letter of water per day at temperature not less than 50 C with total daily solar radiation of 5.55 kh/m 2 /day and the average ambient air temperature is 29.7 C, the optimum parameters were found as: the solar collectors area is 2.4m 2, the mass flow rate through the collector is g/s/m 2 and the volume of the storage tank is 135 L. The maximum water temperature was found 68 C and the minimum temperature is 50.5 C. 1. Introduction Libya is located in the middle of North Africa on the south side of the Mediterranean Sea, lies between latitudes N N and longitudes 9.85 E E. The daily average solar radiation on the horizontal plane is 7.1 kh/m²/day in the coastal region, and 8.1 kh/m²/day in the southern region, with a sun duration of more than 3,500 hours per year, which gives the country a great opportunity to utilize solar energy very efficiently. Looking to the energy consumption in Libya the electricity used for water heating in the residential sector is 3,027 Gh which equal to 9.3% of the total electrical generated [1, 2]. Consequently, the reduction in this amount (by means of using DSHs) will reduce pollutants emission and oil depletion (which is presented the unique source of national income).

2 American Journal of Energy and Power Engineering 2015; 2(6): Indeed, many efforts exerted to improve the performance of solar thermal systems coincidence with the impressive growth rate of solar technology marketing around the world. One of these is, the solar heating and cooling program carried over by International Energy Agency [3]. However, most of these studies focused to the north region of the Mediterranean, The climate of this region characterised as frosted in winter and temperate in summer. In other countries located in (Africa, south America, south Asia) the climate is quite different, for this reason these equipments are not economically and technically suitable. The present work pursues the investigations leading to optimize the operating and designing parameters for DSHs Solar ater Heating Systems Solar water heating systems are classified as either passive or active and direct or indirect. Passive systems rely on natural convection to circulate the water through the collectors. Integral collector storage and thermo-siphon systems are passive systems. Active systems use electrically driven pumps and valves to control the circulation of the heat absorbing liquid. This allows greater flexibility than their passive counterparts since the hot water storage tank does not has to be above or near the collectors. All solar water heating systems can be characterized as either direct or indirect, depending on whether household water is heated directly in the collector or via a heat exchanger. In direct systems, the fluid heated in the collectors is potable water, which flows directly to the faucet. For systems including corrosion and/or freezing fluid a heat exchanger becomes essential element. The heat exchanger may be separated or located at the storage being either a mantle or a helix. An auxiliary heat source is used whenever the solar energy is insufficient to provide the desired temperature [4]. Also as the heat exchanger, the auxiliary heat source may be separated as individual tank or immersed in the storage tank. The main direct system types are integral collector storage and Drain down. The basic elements in solar water heaters can be arranged in several systems configurations [5]. The thermal performance of typical solar heating system and solar radiation calculation is well presented in many recent researches, such as [6]. The schematic diagram of the solar system is illustrated in figure 1. Flat plate collectors are used to collect the solar radiation. The thermal storage tank is employed to store the collected solar energy and to provide the stable power output when solar radiation is insufficient. hen there is a shortage in solar energy the auxiliary system will be engaged to make up for the water temperature. ater is used in both the solar energy collector and the thermal storage. The modelling of the thermal performance of the system was performed to determine the performance of the solar water heating and aid in decisions regarding optimization of operating and designing the parameters. Figure 1. Solar water heating system without heat exchanger Solar Collector Solar collector is considering as the core of any solar system. There are many types of solar collectors, and they are classified according to the operating temperature. The flatplate solar collector is suitable and the most common collector type used in solar domestic water heating. Some solar water heating systems use concentrating collectors instead of flat plate collectors. These collectors may be less effective during cloudy weather and are usually more expensive than flat plate systems, they can produce higher temperatures than flat plates. Another type of collector used for domestic water heating is the evacuated tube collector. These collectors consist of an absorber surface inside a tempered glass vacuum tube. The vacuum helps to reduce convective heat losses. The thermal analysis of a flat-plate solar collector is treated in considerable details in all text books [7, 8]. The useful energy of the collector Qu, is given by: (1) 3600/ (2) here A c is the collector area [m 2 ], Cp is the specific heat capacity [J/kg/K], mass flow rate of the water [kg/hr], T ci and T co are the inlet and outlet water temperature to and from the solar collector, respectively [ C], H is the total solar radiation incident to the solar collector [/m 2 ] and is the overall efficiency of the solar collector. The following assumptions used regarding collector calculations include: 1. Uniform solar radiation over the collector; 2. The inlet water temperature to the collector T ci equal to the ambient air temperature T and the pressure of the whole system is atmospheric pressure P =100kPa 3. Constant solar collector's efficiency, 70%, because the inlet temperature T ci equal to the ambient air temperature T, according to [7]; 4. Constant heat capacity for water, Cp=4200 J/kg/K Thermal Storage Tank In this system a sensible heat storage tank is used to store the collected solar energy. For simplicity, it is assumed that: 1. The water in the insulated storage tank is completely

3 94 Nassar Yasser Fathi: Thermodynamic Analysis and Optimization Procedure for Domestic Solar ater Heating System mixed with the water flowing from the collector [9]; 2. The water flow through the collector, stored in the tank and extracted to the load is saturated liquid; 3. The enthalpy equal to the internal energy; 4. All the entire storage tank is at the same temperature of the water in the tank, regardless the tank is full or empty; 5. Neglecting the tank material heat capacity; 6. The tank is surrounding by the ambient air at temperature of the ambient air temperature. The implicit form of the first law of thermodynamics for the thermal storage tank may be written as follows [10]: h = h + ( ) (3) here: Q s is energy loss through the storage tank to the surrounding [],, are the mass flow from the collector and to the load [kg/hr], respectively,, are the water mass in the tank for the start and the end of period time t (for this case = 3600!) [kg/hr], respectively, h, h are the enthalpy of the water coming from the collector and the extracted to the load [J/kg], respectively, ", # are the internal energy of the water coming from the collector and the extracted to the load [J/kg], respectively, and the superscripts t, +, refer to the begin and the end of the time interval, respectively. The implicit form of the terms in equation (3) were written as: = $ ( % ) (4) h = (5) h = (6) = (7) = (8) where: U s is the overall heat transfer coefficient of the storage tank [/m 2 /K], A s is the surface area of the storage tank [m 2 ]. The optimum radius r and height h of the storage tank is obtained from [11]: Table 1. Excel work sheet description. & = ' ( " *, +, h = ' -( " *, + #) ) (9) = 2/&(h + &) (10) According to the mass conservation law [10], one can write: = + (11) Regarding the considered system the mass flow through the collector is equal to the total mass of hot water needed for the load, and it divided by the working hours of the solar collector 0 [hr], so: = = " 5#- (12) The most suitable starting working regime of the solar collector is, the hour when the delivery temperature of the water from solar collector is greater than the set point temperature of the storage tank. Substituting equations (2, 3, 4, 5, 6) in equation (1) and rearranging, one can obtain the following equation for the water temperature in the storage tank as: 67889:;: @ 3C B : = (13) 67889:;: <= MSExcel ork Sheet Preparation and Calculation Procedure Excel is an effective tool for treating and solving such easy problems and presenting the results in graphical forms. Figure 2 presented a part of the work sheet of the presented work. The description of the numerical operations regarding the work sheet was presented in table 1. In where outlined the input data, the output results, the optimization procedure, the initial conditions, the governing equations and the check up of the results. Position Terminology Unit Data type Equation No: A6: A101 4 days of evaluating the system B6: B101 The time 24hours/day*4days= 96 hours, t hr C6: C101 Hourly ambient air temperature, % C given D6: D101 Hourly solar radiation, /m2 given E6: E101 ater mass flow through the collector, kg/hr (10) trial & error F6: F101 Solar useful energy, (1) G6: G101 Delivery water temperature from the collector, C (2) H6: H101 Energy losses from the storage tank, (4) I6: I101 The mass of water in the tank at time t, kg/hr the initial value is the summation of the mass load before the solar collector engaged to the system " =!(E6:E14) and then I7: I101=L6: L100 J6: J101 The delivery water mass from the collector to the tank at time t, kg/hr (10) K6: K101 The extracted water mass from the tank to the load at time t, kg/hr given

4 American Journal of Energy and Power Engineering 2015; 2(6): Position L6: L101 M6: M101 N6: N101 O6: O101 P6: P101 Q6: Q101 Terminology The mass of water in the tank at time t+ t, ater temperature in the tank, Stored energy in the tank at time t, Energy extracted to the load at time t, Energy delivered from the collector at time t, Energy lost from the tank at time t, R7: R Unit kg/hr C Data type The energy balance of the tank at time t, Q F$2 Solar collector area m2 given F$3 F$4 I$2 Solar collector efficiency Total load mass flow The over-all heat transfer coefficient of the tank $ The product of overall heat transfer coefficient into surface area of the tank ($ ) kg/day /m2/k given given =sum(k6: K29) /K = I$2*Q$3 I$4 Volume of the tank I m3 which equal to the total mass load minus the mass of load extracted during the solar collector operation period=(f$4-sum(k15: K21))/1000 L$4 Heat capacity of water Cp, The average water temperature in the tank for the third day The maximum water temperature in the tank for the third day The minimum water temperature in the tank for the third day Optimum radius of the tank, Optimum height of the tank Surface area of the tank J/kg/K given C = sum(m68: M101)/24 C = max(m68: M101) C = min(m68: M101) m m m2 = (I$4/(2/))^1/3 = (4 I$4/ /)^1/3 = 2/ $1 $1 I$3 N$1 N$2 N$3 Q$1 Q$2 Q$3 Equation No: (9) (11) =L6: L101*M6: M101*L$4/3600 =K6: K101*M6: M101*L$4/3600 =J6: J101*G6: G101*L$4/3600 =I$3*(M6: M101-C6: C101) N7: N101-(N6: N100 + P7: P101-Q7: Q101- O7: O101) it must be equal to zero in order to get the desired temperature of water in the tank, i.e. trial & error Figure 2. The work sheet of MS. Excel indicated the overall treatment of the problem. $2

5 96 Nassar Yasser Fathi: Thermodynamic Analysis and Optimization Procedure for Domestic Solar ater Heating System 2. Results and Discussion The following procedure should be followed to obtain the desired results and to avoid the instability in the answer: Total mass flow through the collector should be equal to the mass flow of the load for an average day. So we have many variants of mass flows through the collector, for a particular load, the mass flow which not achieved the required temperature will be ignored, the best candidate will be chosen according to the minimum collector area. The initial condition for the water mass in the tank equal to the summation of the mass flow to the load from the first hour to the hour just before the solar collector engaged to the system. If this step has been correctly done, zero for mass in the tank will appear at the time that solar collector engaged to the system. Since load and ambient conditions are different for various solar heating systems, the results will be different from one application to other, but the optimization principle will be the same. The information for starting the calculation are climatic and operating conditions. Figure 3, presented the climatic condition for an average day and the water mass flow to the load is established in figure 4. Figure 3. Solar radiation incident on a horizontal surface [/m 2 ] and the ambient air temperature [ C] for an average day. Figure 4. Distribution of hot water mass flow to the load [kg/hr] along a day for a typical Libyan family consumed 250 [l/day]. The mass conservation of the storage tank yields to obtain the mass of water in the tank at any time t. Figure 5 presented the mass flow of water from the collector to the tank, and from the tank to the load, also the mass of water in the tank has been plotted for a day. Looking to figure 5, zero value for the mass of water in tank is appeared at the moment that the solar collector starting delivered water to the tank. The boldfont number appeared in the figure presented the maximum water mass in the tank which, of course, equal to the capacity of the storage tank. This value is equal to the total mass load minus the quantity of that mass flow to the load at the operating period of solar collector (250- ( )=135kg of water) (see figure 2 and table 1). For a continues constant mass flow to the load [kg/hr]the volume of the tank V s [m 3 ] was found as a function of the ratio of the mass flow to the load [kg/hr] to the mass flow through the collector [kg/hr], this relation has been fitted in the form of: I = KL 1888 '1 B D * (14) The water temperature profile in the storage tank is illustrated in figure 6 for the second day as a function of the water mass flow through the collector at the best period of operating regime time for the solar collector. B3

6 American Journal of Energy and Power Engineering 2015; 2(6): Figure 5. ater mass distribution for the flow from the collector, the flow to the load Looking to figure 6, it's easy to observe that, there are only two variants satisfied the temperature above 50 C, there are water mass of 35.7 and 41.7 [kg/hr] the decision is easy to make, certainly, we chose the mass of 35.7 [kg/hr], because we provide less power to drive the pump to deliver such mass than 41.7 [kg/hr], another reason support our decision that is the volume of tank is smaller in case 35.7 [kg/hr] than that of 41.7 [kg/hr] as it illustrated in figure 7, and smaller volume means cheaper. The relationship between the volume of the tank and the operation time duration of the solar collector with the hourly mass flow rate through the and the mass of water in the tank 97 all in [kg/hr]. solar collector [kg/hr] is illustrated in figure 7. Obviously, and according to equation (12), the larger mass flow through the solar collector is leading to reduce the operating period of time of solar collector and certainly increase the tank volume, and the opposite is correct. Even more, figure 8 and 9 discuss the effect of the work starting time for the solar collector on the temperature of the water delivered from the collector and the mass of water in the storage tank, for 250 [kg/day] load, 7 hours working regime of solar collector, [kg/hr] of water mass flows through the solar collector. the ambient air temperature and the mass flows to the load is also included. Figure 6. The hourly temperature profile for the water in the storage tank with various water mass flow through the solar collector in [kg/hr].

7 98 Nassar Yasser Fathi: Thermodynamic Analysis and Optimization Procedure for Domestic Solar ater Heating System Figure 7. The variation of the volume of the storage tank and the corresponding solar collector working period regime with respect the water mass flow rate through the solar collector for mass load of 250 [kg/day]. Figure 8. The effect of start working time of the solar collector on the water temperature in the storage tank, for the mass flow through the collector = 35.7 [kg/hr]. For the prescribed data (presented in figure 2) the energy balance for the storage tanks is established in figure 10. The accumulated energy stored in the storage tank is presented as: P MNO = MNO P + NM P P QO (15) Figure 9. The effect of the work starting time of the solar collector on the water mass and the volume of the tank, the data labelled over the maximum point are the volumes.

8 American Journal of Energy and Power Engineering 2015; 2(6): Figure 10. The energy balance for the storage tank for prescribed data in figure Conclusion e successfully outlined the thermal analysis of a simple domestic solar water heating system by using a simple tool "Excel" which available in all PC even in modern mobile telephones with simple knowledge about the energy balance and access to climatic conditions. Since load and ambient conditions are different for various solar heating systems, the results will be different from one application to other, but the optimization principle will be the same. The volume of the storage tank is varying with the water mass flow rates delivered to the load and extracted from the collector furthermore it is varying with the solar collector working regime, whenever the large quantity of load lays in the domain of the solar collector operation period, the volume will be smaller. Energy and mass conservation and initial values for starting the calculation have been well established. The present paper show that, for Libyan typical family (5 to 6 persons were consumed about 250 letter of water per day at temperature not less than 50 C) with total daily solar radiation of 5.55kh/m 2 /day and the average ambient air temperature is 29.7 C, the optimum parameters were found as: the solar collectors area is 2.4 m 2, the mass flow rate through the collector is g/s/m 2 and the volume of the storage tank is 135 L. The maximum water temperature was found 68 C and the minimum temperature is 50.5 C during the day. References [1] General Electric Company Of Libya (GECOL). Annual Reports (2010). Available: [2] Erhouma M., Solar water heating systems in Libya, Publications of solar energy centre, 2011, Libya. [3] Advanced solar domestic hot water systems, final report IEA SHACP task 14, [4] Passive and Active Solar Domestic Hot ater Systems available on the Solar Centre's website the publications section, [5] Qvistgaad L. H., Energy-economic optimization of heating system with solar collector, master thesis, Norwegian university of science and technology, [6] Kyoung H. K. and Chul H. H., Thermal analysis of a solar energy system with thermal storage in different weather conditions, International Journal of Mining, Metallurgy & Mechanical Engineering (IJMMME) Volume 2, Issue 4, 2014 (Online). [7] Duffie J. A. and Beckman. A., Solar Engineering of Thermal Processes, 3 rd ed., John iley & Sons, Inc., [8] Nassar Y. F., Solar energy engineering active applications, Sebha University, Libya, "Arabic language". [9] Mohammad S., Alibakhsh K. Seyedeh S, andnastaran S., Thermal Performance Analysis of a Fully Mixed Solar Storage Tank in a ZEB Hot ater System, Sustainable Energy, 2014, Vol. 2, No. 2, pp Available online at [10] Borgnakke C., Sonntag R., Fundamentals of thermodynamics, 7 th edition, John iley & Sons, Inc, 2009, p202. [11] Yogesh Jaluria, Design and optimization of thermal systems, 2 nd edition, CRC Press, 2007, p493.