Software for designing solar water heating systems

Renewable and Sustainable Energy Reviews 58 (2016) 361–375

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Renewable and Sustainable Energy Reviews journal homepage: www.elsevier.com/locate/rser

Software for designing solar water heating systems Carlos Eduardo Camargo Nogueira n, Magno Luiz Vidotto, Fernando Toniazzo, Gilson Debastiani College of Post-Graduation Program of Energy Engineering in Agriculture (PPGEA), from State University of Western Paraná (UNIOESTE), Cascavel, PR, Brazil

art ic l e i nf o

a b s t r a c t

Article history: Received 21 March 2015 Received in revised form 6 September 2015 Accepted 18 December 2015

This paper presents a complete development of software for sizing small solar water heating systems. The application framework was developed using the MATLAB platform, and its algorithm was structured to minimize the user intervention. The software was developed using consolidated methodologies and practices relationships, aiming at the technical and economical project optimization. The used project methodologies were the F-Chart and Brazilian Technical Standards (NBR-15569), together with an economic analysis. All of them are detailed in this work. The database was built using commercial equipment performance data, from the official tests of the Brazilian Labeling Program, and meteorological data, from the Brazilian Solarimetric Atlas and Agronomic Institute of Paraná. The developed software allows the sizing of natural and forced circulation systems, composed of flat plate collectors or evacuated collectors type U, horizontal thermal storage tank and auxiliary power supply (electric or gas). It also allows the user to modify the input parameters at any time, making possible to simulate different situations and find the best technical and economical solution. An example of the solar system design is also presented and discussed. & 2016 Elsevier Ltd. All rights reserved.

Keywords: Solar energy Water heating Economic analysis

Contents 1. 2. 3. 4.

5. 6.

n

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362 Solar water heating systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362 2.1. Auxiliary power sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363 Some computer tools for designing solar water heating systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363 Software development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364 4.1. Calculation of the daily hot water demand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365 4.2. Calculation of the monthly energy demand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365 4.3. Scaling and power consumption of electric passage heaters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365 4.4. Scaling and power consumption of gas passing heaters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365 4.5. Scaling and power consumption of electric accumulation heaters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365 4.6. Scaling and power consumption of gas accumulation heaters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365 4.7. Calculation of the collector area and thermal reservoir volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366 4.7.1. F-Chart methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366 4.7.2. Brazilian Technical Standards (NBR 15569) methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367 4.8. Scaling and power consumption of the auxiliary system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367 4.9. Determining the type of circulation and the operating pressure of the system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367 4.10. Economic analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368 Software presentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369 Scaling examples using Solardim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371 6.1. Design results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371 6.2. Energy balance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373 6.3. Economic viability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373

Corresponding author. Tel.: þ 55 45 3220 3151. E-mail address: [email protected] (C.E. Camargo Nogueira).

http://dx.doi.org/10.1016/j.rser.2015.12.346 1364-0321/& 2016 Elsevier Ltd. All rights reserved.

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7. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374

1. Introduction Currently the global demand for energy reaches worrying levels. Increasingly unbridled energy dependence and consumption are tied to population growth and modernization of production processes. In this context, the growing global demand for energy and efforts to reduce the availability of non-renewable fuels become a means of encouraging research into alternative technologies for power generation as well as for more efficient applications. In several countries, various alternative energy sources are now available and being applied: wind, biomass, small hydroelectric generators, solar thermal and photovoltaic [1]. Among those, solar thermal energy to heat water has been highlighted due to its important social, technological, economic and environmental, as well as being abundant on the surface of the planet Earth [2,3]. The application of solar thermal energy for water heating is accomplished through solar collectors. These devices are responsible for the capture of solar radiation and transferring the thermal energy to a fluid. Solar water heating systems are usually composed of: solar collector, accumulator (hot water tank), auxiliary source (electrical resistance or gas heater) and pipes for distribution of heated fluid [4,5]. Among several applications of such systems, the most common use (85%) is for domestic hot water [6]. In Brazil, the electricity consumption related to water heating in residential sector is approximately 26%, but this percentage can reach 35% of total demand of low-income families [7]. According to Passos et al. [8] showerheads consumption accounts represent 43% of the high consumption peak between 6 and 9 p.m. on the Brazilian residential sector demand profile. Many studies [8–15] have suggested that solar energy could reduce part of this demand, since Brazil has a relatively high average annual global radiation throughout its territory. Global daily radiation rates showed values ranging from 4.25 kW h/m² on the northern coast of Santa Catarina to 6.5 kW h/m² at the border of Bahia with Piauí [16]. However, one of the obstacles in Brazil for the spread of solar water heating systems has been the high initial investment compared to conventional systems [14]. Another factor is the careless projects adopted by manufacturers and national sellers. These methods are summarized in design recommendations on the

Fig. 1. (a) Flat plate solar collector; (b) “U” type vaccum solar collector. Source: [24].

number of plates (installed area) depending on the number of users and/or consumption points. This procedure may produce good results in family projects, but when it comes to a specific design or installation in different climates, they fail and compromise the reliability of solar technology [17,18]. The use of computer tools specialized in the design of solar systems can be a great option to mitigate this problem, provided that these tools do not require an advanced knowledge of the user. In this context, the present study aimed to develop a software application to assist in the design of small water solar heating systems. With the development of this tool, the design of these systems will be more accurate, taking into account the particularities of hot water consumption of the facility, the climatic characteristics of the site, the performance data of the equipment, the orientation of the collectors, alternatives and cost of the complementary energy system.

2. Solar water heating systems The simplest installation to use solar energy for hot water supply in small systems is basically composed by solar collectors, hot water tank, insulated pipes and an auxiliary power source. These systems can be classified as active systems or passive systems [19]. Active systems use a flow pump to force the fluid flow, and passive systems are characterized by not using an external power source for fluid flow, because this action is performed by natural means (thermosyphon) [20]. Solar heating systems can be further classified into direct and indirect. In direct systems the fluid stored in the thermal tank is the same that circulates in the solar collectors. In the indirect system, the collectors heat a coolant (oil, ethylene glycol or propylene glycol) that transfers heat to the water through a heat exchanger. The latter, being very expensive, are best used in areas of severe weather to prevent the occurrence of water freezing and it is uncommon in Brazil [5,21]. Currently, the most used collectors for water heating in residential sector are flat plate collectors and evacuated tube collectors (which are on the rise in the market due to excellent performance in cold climates) [6,22]. The flat solar collector (Fig. 1a)

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consists of a rectangular aluminum housing, hermetically sealed and thermally insulated by coatings of expanded polyurethane or glass wool. Inside there is a copper coil through which the fluid flows. Around the coil there is an absorbing plate, also of copper, painted matte black to facilitate absorption of heat. At the top there is a transparent cover which allows the entry of solar radiation and prevents heat from being lost to the environment. Collectors of this type reach temperatures up to 80 °C [23]. The evacuated solar tube collector is a relatively new technology and has higher efficiency than the plane collector. This collector is commonly formed by two concentric glass tubes with a double wall. The inner wall has a coating of aluminum nitrate, which has high heat absorptivity. Between both tubes there is an insulation (vacuum), responsible for mitigating heat losses. Temperatures above 80 °C can be obtained by this type of collector [24,25]. The evacuated collectors may use different forms of heat extraction, the most common being the use of heat pipes, U-tubes, and direct transfer (water-in-glass) [22]. In the extraction of the U type (Fig. 1b) a copper pipe in the form of a 'U' is mounted within the evacuated tube. Cold water enters through one end of the tube, absorbs heat and exits through the other end. Due to its flexibility and modular nature, this collector has been widely used in China [26]. As noted by Shukla et al. [22], the solar water heating is one of the most effective, developed and commercialized technology to convert solar energy into thermal energy.

To meet the energy deficit, these systems include an auxiliary energy source. This support can be located inside the hot water tank (accumulation system) or in conjunction with the output of water for consumption (passage system). In the first case, the auxiliary system is constituted by one or more armored electrical resistors, activated automatically by a thermostat, or manually by the user. In the second case, the auxiliary system can be a heater passing gas or electricity (electrical resistances). The gas passage heater consists of a heating unit in which there is a burner that allows the proper combustion of the gas, and a heat exchanger that transfers heat to the water. The electric passage heaters are usually electric heaters that use the energy dissipated by the Joule effect to heat the water. The passage heaters used in solar systems typically rely on temperature control and power devices, to provide only the power required to supplement the heating [28]. Fig. 2 shows the layout and operation of a solar system with support from passage heaters using liquefied petroleum gas (LGP). The gas passage heater can also be used in conjunction with the storage tank (Fig. 3), considered in practice as an accumulation heater, since it has the same operating principle: the tank stores a volume of hot water, at a selected temperature, available for use [28].

2.1. Auxiliary power sources

There are many tools available for designing solar water heating systems. Each one has its particularity, emphasizing certain aspects and applications, as well as a target audience. It is presented, next, a short list of such programs that inspired the software developed in this work. The F-Chart [29] is a computer tool (commercially available) for the analysis and design of active and passive systems, useful for estimating the long-term average performance of domestic water

Although based on principles of accumulation, solar water heating systems are not designed to supply 100% of the demand for heated water throughout the year. If so, oversizing would block the installation from an economic standpoint. Thus, these systems are designed to provide 60–80% of the thermal energy required [23,27].

Fig. 2. Solar system with gas passage heaters. Source: Adapted from COMGÁS [28].

3. Some computer tools for designing solar water heating systems

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Fig. 3. Conjugated heating system. Source: [28].

heating systems. The program is an application of the methods developed by Klein and Beckman in the Solar Energy Laboratory at the University of Wisconsin, United States [30]. The F-Chart has climatic data for hundreds of locations in North America and the user also has the option of adding new meteorological data. Besides the domestic heating, the software allows working with swimming pool heating, hot water storage tanks and large heating systems in general, using different types of collectors (flat, evacuated, compound parabolic concentrators and tracking system). Its other functions include the economic analysis of the systems and an option for choosing the International System units or English units. T*SOL [31] is a German commercial tool for designing and simulating solar water heating systems, with optimization of collector area and storage tank volume, and an option to add custom collectors and meteorological data. This software also works with swimming pool heating, space heating, process heat and largescale systems. It has an extensive library of collectors, boilers, hydraulic pumps, heat exchanges, climate data, storage tanks, and consumption profiles. To design and optimize a solar system, the software does a simulation based on the balance of energy flows and supplies sources, with the help of meteorological data input. Moreover, it is possible to do a financial analysis of the system considering the energy balancing, pollutant emissions and costs. Polysun is another German software (paid and spread internationally) used in the simulation and optimization of active and passive solar heating systems [32]. The program has a modern and user-friendly interface. The input of the various parameters for each component is made easily through a versatile graphical environment, very similar to tools used in the development of architectural plans. Among the systems that can be simulated by this software are: domestic hot water, space heating, swimming pools, and process heating. Polysun has an extensive catalog of components and meteorological data and also allows the user to enter new data. The output of the program includes solar fraction, energy values, temperatures, flow rate, and economic analysis [33]. The RETScreen International [34] is a Canadian tool directed to the analysis of projects involving different renewable energy sources. With this tool, one can perform comparative studies of renewable and conventional energy sources. This software

evaluates the energy production, the reduction of greenhouse gases and the economic viability of projects. It has a database of components and meteorological data for several places located in different countries of the world. RETScreen uses the F-chart method to evaluate the use of solar water heaters for domestic, commercial and industrial applications. The designing of the system is performed in a spreadsheet (the RETScreen 4 version works with Microsoft excel), in an intuitive way to understand [35]. TermoDim is a Brazilian computational tool (freeware) developed by Siqueira [36],which allows the determination of the solar collector area and the accumulator volume for small and large systems, operating on a thermosiphon system. This tool was developed based on simulations using TRNSYS (Transient System Simulation Program) and its operation requires information of geometrical parameters, types of collectors and consumption profile. The Helios-Chart [18] is another Brazilian software, commercially available, that performs the simulation, design and economic analysis of active systems for medium and large systems. This software uses the F-Chart methodology [37] for system design, technical information from the Brazilian Labeling Program [38] and meteorological data from the Brazilian Solarimetric Atlas [16]. The Solterm, developed by the National Laboratory of Energy and Geology of Portugal [39], is a commercial software used to simulate and design solar heating systems, operating in forced circulation. Also performs an economic analyzes and estimates the reduction of CO2 in the atmosphere. Another Portuguese software, freeware, named SolarEnergy [40], allows design and simulation of active and passive solar systems, considering local characteristics, type of system utilization, consumption profile data of the solar collector, economic analysis among others. It uses the F-Chart methodology for calculation.

4. Software development The software proposed in this paper was developed in the MATLAB computing environment (Matrix Laboratory, Inc., version R2012a) and was directed to the design of small solar water

C.E. Camargo Nogueira et al. / Renewable and Sustainable Energy Reviews 58 (2016) 361–375

heating systems (maximum demand of 1000 l per day of hot water). The input parameters include: the model of the collector (flat or evacuated with U tube), the form of heating (passive or active, with horizontal accumulator), the auxiliary power source (electric or gas, accumulation or passage), the local geometry and the consumption of hot water in the facility. The software also performs the design of strictly electrical or gas systems, for economic comparison. The collector area and the tank volume were scaled based on the F-Chart method [27] and on a Brazilian Technical Standards (NBR-15569) [41]. The first is widely used in solar projects, while the second is a simplification of the F-Chart, and was adopted for comparison of results. To build a database for tests, it was used the values of solar radiation and ambient temperature of some cities of Paraná State, located in the southern region of Brazil. The solar radiation data are from the Brazilian Solarimetric Atlas [16] and temperature data come from the Agronomic Institute of Paraná [42]. The technical specifications of solar collectors, hot water tanks and auxiliary heaters were based on the tables of the Brazilian Labeling Program [38]. To do the economic evaluation, real market values of the equipment were used. Below, it is presented the mathematical models used for the software development.

To calculate the consumers' hot water demand, the consumption method presented in NBR 5626 [43] was adopted. This method consists of getting the consumption of each sanitary appliance that uses hot water. The sum of the flow of each component, multiplied by the average time and frequency of use, determines the volume of hot water to be available in the building. To calculate the daily demand of hot water, Eq. (1) was used: V c ¼ Q d :t b :Nb

ð1Þ

where: Vc ¼total volume of hot water consumed in building (L day  1); Qd ¼ showerhead flow (L min  1); tv ¼average individual bath time (min); Nb ¼total of daily baths. 4.2. Calculation of the monthly energy demand The monthly energy demand for heating water was calculated by Eq. (2) [23]. Ei ¼ V c :Nd :ρ:cp ðT c  T a Þ

ð2Þ

where: Ei ¼useful energy for heating water (kW h month  1); Nd ¼ number of days in the corresponding month; ρ¼ specific mass of water (1 kg L  1); cp ¼specific heat of water (0.001163 kW h kg  1 °C  1); T c ¼consumption temperature (°C); T a ¼ monthly average ambient temperature of the installation site (°C). 4.3. Scaling and power consumption of electric passage heaters The power rating of the electric passage heater was calculated using the following equation [23]: _ max :cP :ðT c  T am Þ P APE ¼ m where:

P APE ¼rated power of electric passage heater (kW); ̇ ̇ max m ¼maximum water flow of the installation (kg h  1); T am ¼temperatura ambiente média anual (°C). The monthly energy consumption of the electric heater was calculated using Eq. (4): C APE ¼

ð3Þ

Ei ηAPE

ð4Þ

where: C APE ¼ power consumption of the electric passage heater (kWh.month  1); ηAPE ¼efficiency of the electric passage heater (decimal). 4.4. Scaling and power consumption of gas passing heaters The rated power of the gas passage heater was calculated using the following expression [28]: _ max :cP :ðT c T am Þ P APG ¼ m

ð5Þ

where: P APG ¼ rated power of the gas passage heater (kW). The monthly energy consumption of the gas passage heater was calculated using the following equation: C APG ¼

4.1. Calculation of the daily hot water demand

365

Ei ηAPG

ð6Þ

where: C APG ¼ energy consumption of the gas passage heater (kWh. month  1); ηAPG ¼ efficiency of the gas passage heater (decimal). 4.5. Scaling and power consumption of electric accumulation heaters

The rated power of the electric accumulation heater was calculated using Eq. (7) [23]. P AAE ¼

V arm 3 :cP :ðT c  T am Þ

t aq

ð7Þ

where: P AAE ¼rated power of the electric accumulation heater (kW); V arm ¼storage volume of water (kg); t aq ¼heating time (h). To calculate the monthly energy consumption of the electric accumulation heater, Eq. (8) was used: C AAE ¼

Ei ηAAE

ð8Þ

where: C AAE ¼power consumption of the electric accumulation heater (kWh.month  1); ηAAE ¼efficiency of the electric accumulation heater (decimal). 4.6. Scaling and power consumption of gas accumulation heaters The rated power of the gas accumulation heater was calculated by the following expression [28]: P AAG ¼

V arm :cP :ðT c  T am Þ t aq

ð9Þ

where: P AAG ¼ rated power of the gas accumulation heater (kW). The monthly energy consumption of the gas accumulation

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heater was calculated using Eq. (10): C AAG ¼

Ei ηAAG

ð10Þ

where: C AAG ¼average monthly power consumption of the gas heater (kW h month  1); ηAAG ¼ efficiency of the gas heater (decimal). 4.7. Calculation of the collector area and thermal reservoir volume 4.7.1. F-Chart methodology The F-Chart methodology was developed by Duffie et. al. [37] based on the collection and consolidation of the results of numerical simulations in TRNSYS software, and evaluation of operating conditions of solar heating installations. This methodology can be used both for the design of passive and active systems. To calculate the collecting area of the F-Chart method, it is required the prior selection of the solar collector, a survey of local meteorological parameters and the energy demands of the facility. With this information, the collecting area is achieved through correlations between the contribution of solar energy (solar fraction) and the monthly energy demand for water heating. The solar fraction for monthly analysis is expressed by Eq. (11). f i ¼ 1:029Y 0:065X  0:245Y 2 þ 0:0018X 2 þ 0:0215Y 3

ð11Þ

where: f i ¼monthly solar fraction for the corresponding month, adimensional. The X parameter is related to the thermal losses from the solar collector, as presented in Eq. (12)
 AC :F R U L :ðT ref  T a Þ:Δt i C ad  0:25 X¼ : ð12Þ Ei C ap where: AC ¼total area of the solar collectors (m²); F R U L ¼product of heat removal by global coefficient of solar collector thermal losses, corresponding to the slope of the instantaneous thermal efficiency curve factor (kW m  2 °C  1); T ref ¼ reference temperature, considered constant and equal to 100 °C; Δt i ¼month duration (h); C ad ¼ specific desired storage capacity (L m  2); C ap ¼ specific storage capacity adopted by the F-Chart method, corresponding to 75 L m  2. The X parameter needs to be corrected due to the diversity of the Brazilian situation, which is different from the USA reality, with regard to the need to heat water in homes. When the use of solar power is restricted to heating water, Duffie and Beckman [27] proposed the correction shown in Eq. (13).
 11:6 þ 3:86T rede þ 1:18T c  2:32T a X C ¼ X: ð13Þ 100  T a where: T rede ¼temperature at which water is admitted (°C); T c ¼temperature of usable water (°C). The Y parameter, in Eq. (11), is related to the energy absorbed by the collector plate, as shown in Eq. (14): Y¼

AC U F R ðτc αp Þθ UH T U N d Ei

ð14Þ

where: F R ðτc αp Þθ ¼ product of the removal factor, transmissivity of the glass and absorptivity of the ink collectors to average angle of direct radiation incidence;

HT ¼daily global solar radiation on average monthly incident on the plane of the collector, per unit area (kW h m  2 dia  1). To calculate the solar radiation incident on the inclined surface of the collector, Eq. (15) was used [27]. This equation implies a series of calculations presented below.


 H 1 þ cos β 1  cos β H T ¼ H 1  d Rb þ H d þHρ ð15Þ 2 2 H where: H¼ daily horizontal solar radiation on average monthly (kWh. m  2 dia  1); Hd ¼diffuse solar radiation incident on inclined plane (kWh.m  2 dia  1); ρ¼reflectance of the neighborhood near the solar collector (used ¼0.25. Values between 0.20 and 0.25 contemplate the index of reflection of most land surfaces [44]); Rb ¼ratio of the extraterrestrial radiation on horizontal and inclined plane, calculated by Eq. (16): senδðsenf cos β  cos fsenβ cos γ Þ þ cos ω0 s cos δð cos f cos β þsenfsenβ cos γ Þ þ cos δsenβsenγsenω0s

Rb ¼

senδsenf þ cos δ cos f cos ωs

ð16Þ where: δ ¼solar declination (°), represents the angular position of the sun at solar noon, with respect to the plane of the equator; Φ¼latitude (°), corresponds to the angular position (north or south), in relation to the equator (defined as zero latitude); β ¼inclination of the collector (°), corresponds to the angle between the plane of the collector surface and the horizontal; γ ¼azimuthal angle of the surface (°), corresponds to the angle between the north–south direction and the projection on the horizontal plane, normal to the surface of the solar collector; ωs – hour angle of the setting sun to the horizontal surface (°); ω0s – hour angle of the setting sun to the inclined surface (°). The solar declination was calculated using Eq. (17):
 284 þ d ð17Þ δ ¼ 23:451sen 2π: 365 where: d ¼day of the year, same as the unit, on January 1st. To minimize the error value that represents the daily average monthly solar radiation, the average day of the month, shown in Table 1, was used. The sunset time angle for the horizontal surface, in degrees, was obtained using Eq. (18). ωs ¼ arc cos ð  tgf:tgδÞ

ð18Þ

The sunset time angle set to the inclined surface was calculated by Eq. (19).   arc cos ð  tgf:tgδÞ 0 ω0s ¼ minimo ð19Þ arc cos ð  tgðf þ βÞ:tgδÞ To calculate the second term of Eq. (15), it was first necessary to calculate the extraterrestrial solar radiation (Ho), given by Eq. Table 1 Average day of the month. Source: [45]. Month

Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

Day

17

16

16

15

15

11

17

16

15

15

14

10

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collector, given by Eqs. (27) (for 15° oβ o 90°) and 28 (for β o 15°).

(20).


 24:3600:Gsc 2πd 1 þ 0:033: cos H0 ¼ ð cos f cos δsenωs 365 π þ ωs senfsenδÞ

ð20Þ

S¼

where: Gsc ¼1.367 kW m  2; H 0 ¼extraterrestrial solar radiation, corresponds to the incident radiation at the top of the atmosphere.

S¼

Then, it was necessary to decompose the solar radiation into its direct and diffuse components. For this, it was calculated the clearness index on monthly average (KT), defined by Eq. (21). KT ¼

H H0

ð21Þ

In the end, Hd was calculated using Eq. (22) [46]. Hd ¼ 0:775 þ0:00606:ðωs  90Þ  ½0:505 H þ 0:00455:ðωs  90Þ:cosð115KT  103Þ

ð22Þ

After correcting solar radiation and obtaining the X and Y parameters, the monthly solar fraction is calculated. Then, the annual solar fraction is obtained from the weighted average of the monthly contributions of solar heating and energy demand (Eq. (23)). 12 P

F ¼i¼1 12 P

f i Ei ð23Þ

i¼1

Ei

where: F¼annual solar fraction. To reach the area of solar collectors, the software calculates, initially, the volume of the thermal reservoir (VRT) using Eq. (24): 0:75 r

V RT r 1:25 Vc

ð24Þ

Then, the algorithm searches the database for a commercial tank that supplies the requirements of Eq. (24). In the sequence, Cad is varied from 50 to 250 L m  2 (with increments of 10 L m  2) and the collecting area is calculated. For each value of the area that is found, the algorithm calculates the annual solar fraction and performs an economic analysis to find the system with the lowest annual cost. In other words, it finds the optimum collector area according to the system configuration. 4.7.2. Brazilian Technical Standards (NBR 15569) methodology This methodology is a simplification of the F-Chart method and was elaborated considering a theoretical annual solar fraction of 70%. Similar to the first, it is necessary to pre-select the model of solar collector, weather data and meet the energy demand of the installation site. From this, the collecting area (Ac) is obtained using Eq. (25). 12 P

ðEi þ Ep ÞS Ac ¼ i ¼ 1 12 P EM

ð25Þ

i¼1

where: Ei ¼useful energy for heating water (kWh. month  1); Ep ¼ sum of the heat loss of the primary and secondary circuits (kWh. month  1), calculated by Eq. (26). Ep ¼ 0:15Ei

367

ð26Þ

S ¼correction factor for inclination and orientation of the solar

h

1  1:2  10

1 4

ðβ βo Þ2 þ 3:5  10  5 γ 2

i

1 h i 1  1:2  10  4 ðβ βo Þ2

ð27Þ

ð28Þ

where: β ¼inclination of the collector in relation to the horizontal plane (°); βo ¼ optimum collector slope for the installation site (latitude þ10°); γ ¼orientation angle of solar collectors in relation to geographic north (°). EM ¼average monthly production of specific energy of the solar collector (kWh. m  2), calculated by Eq. (29).   EM ¼ F R ðτc αp Þθ  ð0:0249F R U L Þ U H UN d ð29Þ where: H¼daily horizontal solar radiation on average monthly (kW h m  2 dia  1); Nd ¼number of days in the corresponding month. To scale the thermal reservoir, NBR 15569 uses the following relationship: V R Z0:75V c

ð30Þ

where: VR ¼volume of the hot water tank (L); VC ¼ daily volume of hot water consumed (L). 4.8. Scaling and power consumption of the auxiliary system The power of the auxiliary heating system (electric or gas) was calculated using Eqs. (3), (5), (7) and (9), previously presented. The monthly demand of auxiliary energy was calculated using the following equation [23]:  ð31Þ Eaux ¼ 1  f i Ei where: Eaux ¼ auxiliary energy of the solar heating system (kW h month  1); fi ¼solar fraction of the corresponding month. 4.9. Determining the type of circulation and the operating pressure of the system To specify the type of circulation the system, mathematical relationships in Fig. 4 were used as well as the considerations presented in the sequence. In Fig. 4, Hrr is the height between the bottom of the cold water tank and the top of the heat reservoir (m); Hcr is the height between the bottom of the thermal reservoir and the top of the collectors (m) and Dcr is the distance between the center of the thermal reservoir and the top of the collectors (m). According to ABRAVA [23], for a system to fit in a thermosyphon setting, it should, in addition to meeting the minimum and maximum measurements shown in Fig. 4, have a thermal tank with a volume of less than 1200 l, and a total collector area less than 12 m². Otherwise, the system is considered as forced circulation. With respect to operating pressure, the system is considered to be high pressure if H is greater than 5 m [23]. In this case, equipment that meet this particularity have to be employed.

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4.10. Economic analysis Economic analysis of scaled systems was performed considering the costs of acquisition, installation, maintenance and auxiliary power consumption. The acquisition cost includes the cost of solar

collectors, thermal reservoir, auxiliary heating system, the hot water pipes, accessories and, eventually, the hydraulic pump. The costs of installation and maintenance are calculated based on a percentage of the acquisition cost of the system. The cost of energy takes into account the monthly energy consumption and the energy rate of the auxiliary system. All costs are annualized considering the equipment useful life and the interest rate To identify the attractiveness of the project, a comparison is done between the costs generated by the solar system and the costs generated by an equivalent conventional heating. The Internal Rate of Return (TIR) and the Discounted Payback (PBD) are used as a decision criteria, obtained by Eqs. (32) and (33) [47,48]. I0 

Xn

FCi

i¼1

ð1 þ TIRÞi

¼0

ð32Þ

where: TIR ¼internal rate of return (decimal); I0 ¼initial investment (US$); i¼discount rate (decimal); n ¼period of time of the last cash flow (years); FC ¼Cash flow for a period. (US$). PBD ¼

Fig. 4. Recommended distances for a thermosyphon system. Source: [24].

 ln U UP U i lnð1 þiÞ

where: U¼annual return on investment (US$); P ¼present value (US$).

Fig. 5. Home screen and block diagram of the developed application.

ð33Þ

C.E. Camargo Nogueira et al. / Renewable and Sustainable Energy Reviews 58 (2016) 361–375

5. Software presentation The application designed in this paper is titled “Solardim”. This tool can be seen as an alternative to using calculation methods that are not precise enough and/or time consuming. In Fig. 5, it is shown the initial screen and a flowchart that illustrates the operation and principle used in the construction of Solardim. Solardim is divided into four main parts (local elements, solar system, results and economic analysis). In the first, called "Local Elements" (Fig. 6), the user selects the location (city/state) and the positioning of the solar collectors. From this, the application shows values of altitude, latitude, longitude, graphs of the monthly average environmental temperature and the monthly average horizontal solar radiation of the selected city. Initially, eight cities are available, however, the user can add a new location by entering the location and meteorological data. From this screen, it is also possible to adjust the positioning of the solar collectors, azimuthal deviations, from 0° to 30°, and slope angles from 0° to 90°. Initially, the app features a tilt equal to the latitude of the selected location. Another alternative option is "Optimize for winter", which adjusts the tilt of the collector to the local latitude þ 10°. Finally, it can be viewed, in real time, the influence of the chosen orientation of the collector in relation to solar radiation, presented in the solar radiation corrected graph. In the second part (Solar system), the user introduces the particularities of the system, such as: geometry of the installation,

369

component characteristics and consumption profile. The first step is to insert distance values to determine the pressure of the heat accumulator and the type of circulation system (Fig. 7). Considering the difficulty to obtain certain values, the application has two settings with default values. These settings (1 and 2) consist of: 1 – solar collector above the accumulator; 2 – solar collector below the accumulator. Also in "Solar system" (by clicking on "continue"), the next step refers to the heating system itself, and contains the following modules: Solar Collector, Accumulator (thermal reservoir or boiler), Auxiliary Heater (support) and Consumption. First, the user must choose the type of heater (passage or accumulation heater). With this choice, each module will be presented with the appropriate equipment. In the Solar Collector module (Fig. 8), the user can select the type of collector (flat or vacuum) for posterior access to a list with various models of collectors available in the market. Selecting a model, the application automatically displays the specific characteristics of this collector, such as catchment area, average energy efficiency, thermal resistivity and optical performance. There is even an option called "new collector", which allows the user to insert a new collector if he does not find the desired equipment. In Accumulator module (Fig. 9a), the application shows the hot water tanks present in the database. These are shown according to the working pressure of the system, defined by the difference in height between the bottom of the water tank and the upper part of

Fig. 6. Local elements.

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Fig. 7. System geometry.

Fig. 8. Solar system window.

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371

Fig. 9. (a) Thermal reservoir; (b) auxiliary heater.

the boiler. The choice of the thermal tank is a Solardim task, which selects the most suitable for the consumption profile of the building model. In a similar way to other modules, the user can insert a new element ("New Storage Tank") specifying its technical characteristics. In Auxiliary Heater module (Fig. 9b), the user must designate the type of power source that will complement the solar system. The application will show the options contained in the database, and Solardim will choose the most appropriate model for the consumption profile. The option of inserting new equipment is also available in "New Heater". The last module in this section is related to the consumption of hot water in the building (Fig. 10). In this module the user can select the temperature of the usable water (38–40°), the number of daily baths (maximum 10), the flow rate of the shower (from 1 to 10 l per minute) and eventually the number of showers functioning simultaneously (up to 3 showers). In the third part, called "Results" (Fig. 11), the results of the solar system scaling, for the two calculation methods (F-Chart and NBR 15569), are shown. This includes information about the total collector area, solar fraction, solar system energy production, auxiliary system energy production, and equipment selected by the application. There is also an option to save the design ("Generate Report"), which details the information on this screen. In the last part, called "Economic Analysis" (Fig. 12), the application presents an economically evaluation of the system using parameters such as auxiliary power prices, interest rate, operation and system installation costs. Each change can be visualized in real time on the bottom of the screen. There is also an option here called "Generate Report". Although Solardim is easy to use and does not require advanced knowledge in solar energy, its use requires attention. The user must be cautious when adding new equipment, building information or meteorological data, since the inclusion of incorrect values (e.g. greater or less than the real) will result in an erroneous design. In any case, the software has warning boxes that significantly reduce these errors. Moreover, the user can use the information displayed on the screen (charts, tables and colors) to recognize and correct any typos that passed through the filter system. Another limitation is the determination of the system operating pressure (or circulation mode) by geometry. In the current version, the Solardim has only the most common settings (collector above or below the hot water tank) and a simplified interface for entering distances. In future versions, it is intended to make this section similar to that found in CAD platforms (Computer Aided

Fig. 10. Hot water consumption of the building.

Design), allowing individual positioning of each equipment and the definition of the pipes-network. In future versions of the software, it is also intended to insert a help menu to meet any user's doubts, a selection of consumer profiles, and an option to perform a sensitivity analysis.

6. Scaling examples using Solardim Some examples of the sizing of water heating solar systems, using the application developed in this work, are presented. Table 2 contains six different scenarios, which differ from the auxiliary power source, the type of water circulation, and the type of collector. The scaling was performed with the same consumption data for all arrangements. Table 3 shows the consumption profile that is very recurrent in Brazil for small systems (families of up to five people). The economic parameters are shown in Table 4. 6.1. Design results The design results of the solar systems and auxiliary systems are listed in Table 5. The information related to solar systems are grouped according to the two methods used by the application. It can be observed, in Table 5, that the values of power of the auxiliary heater are equivalent for both methods, since the method of calculation is the same. However, the powers of the auxiliary gas heaters (systems 2, 4 and 6) are larger than the powers of the electric heaters (systems 1, 3 and 5). This is due to the performance of a gas heater, which is lower than the electric heater, and also due to the absence of lower powered gas heaters in the Brazilian market. In relation to system 3, the low value found for the electric heater power is due to the kind of accumulation, which uses an electrical resistance inside. In all cases evaluated, the volume of the thermal reservoir selected was of 300 l. This value agrees with the

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Fig. 11. Result of the scaling.

Fig. 12. Economic analysis.

C.E. Camargo Nogueira et al. / Renewable and Sustainable Energy Reviews 58 (2016) 361–375

that systems employing flat collectors (systems 1, 2, 3 and 4) showed a greater collecting area than those using evacuated collectors (systems 5 and 6). This is due to the greater energy efficiency of the latter.

Table 2 Configurations of solar systems. System Auxiliary source

1 2 3 4 5 6

Electric (220 V) – Passage GLP – Passage Electric (220 V) – Accumulation GLP – Accumulation Electric (220 V) – Passage GLP – Passage

Circulation Solar collector Type

FR(τcαp)θ FRUL (W m  2 °C  1)

Natural

Flat

0.759

7.199

Natural Forced

Flat Flat

0.759 0.759

7.199 7.199

Forced

Flat

0.759

7.199

Natural

U-type tube U-type tube

0.779

2.103

0.779

2.103

6.2. Energy balance

Natural

Table 3 Common input data to the systems. Locality Latitude, longitude and altitude Collector tilt Collector Azimuth Total baths per day Average duration of each bath Flow of shower Temperature of usable water Water storage temperature

Cascavel-Paraná 24.53°S; 53.33°O; 660 m 34.53° 0°N 5 10 min 6 l min  1 40 °C 45 °C

Table 4 Economic parameters. Annual interest rate Rate of eletricity Cost of Liquefied Petroleum (GLP) Annual maintenance of the solar system Annual maintenance of the electrical system Annual maintenance of the gas system Installation cost

10% 0.16 US$ kW h  1 1.33 US$ kg  1 2% of the equipment initial cost 2% of the equipment initial cost 15% of the equipment initial cost 15% of the equipment initial cost

Note: The installation cost includes the expenditure on manpower and the hot water hydraulic network of the solar heating system. Table 5 Design result. System

1 2 3 4 5 6

PAUX (W)

7700 11300 1500 11300 7700 11300

373

VRT (L)

300 300 300 300 300 300

NBR 15569

F-Chart

NC

ACT (m²)

NC

ACT (m²)

4 4 4 4 3 3

4 4 4 4 2.91 2.91

4 4 5 4 3 2

4 4 5 4 2.91 1.94

Note: PAUX is the nominal power of the auxiliary heater, VRT is the volume of the thermal reservoir, NC is the number of collectors and ACT is the total collecting area.

optimum size of the storage tank recommended by the studies of Rodríguez-Hidalgo et al. [49] and Çomaklı et al. [50]. Comparing the number of collectors for both design methods, the F-Chart showed the increase of one solar collector for system 3, and the reduction of one unit for system 6. The reason for this difference can be explained by the optimization performed by the algorithm, which seeks to select the system that has the lowest annual cost, including the cost of equipment, installation, maintenance and auxiliary power consumption (electricity or gas, depending on the chosen configuration). Finally, it can be observed

The energy balance for each system is shown in Table 6. It can be observed that the annual demand for energy does not change, since the consumption of hot water remains the same for all configurations. It is also noted that the solar fraction found for the NBR 15569 methodology was above 0.80. It is noteworthy that this methodology has been developed taking into account a theoretical solar fraction of 70%, however, when choosing the equipment available in the market, it is very likely that the solar fraction increases. The same observation was done by Altoé [13]. In Table 6, for NBR 15569 method, systems 3 and 4 present a greater demand for auxiliary power. The reason for this is related to the increased demand for energy to keep the water hot inside the storage tank, while in passage systems, the complementation is made at the time of consumption. In F-Chart method, system 3 presents a reduction in demand for auxiliary power (when compared with NBR 15569), and an increase in production of solar energy. This is due to the higher solar fraction, and consequently, the higher designed collector area. Finally, it can be noted that the settings using evacuated collectors (systems 5 and 6), for NBR 15569, had the lowest demand for auxiliary power, since these devices are more efficient. However, for F-Chart method, system 6 showed an increased demand for auxiliary power. This is the result of the flexibility that Solardim presents, working with the FChart methodology, which seeks to select the system with the lowest annual cost. 6.3. Economic viability To calculate the economic feasibility, Solardim compares the annualized costs of the solar system, added to the annual cost of the auxiliary system, with a conventional system. For this evaluation, it was considered two situations. In the first one, the total costs of systems 1, 3 and 5 were compared with the costs of a strictly electric water heating; in the second one, the total costs of systems 2, 4 and 6 were compared with the costs of a strictly gas water heating. The results are shown in Tables 7 and 8. It can be seen, in Tables 7 and 8, that system 1 has the shortest discounted payback (six years), followed by systems 3, 2 and 5. It can also be seen that systems 3 and 6, designed using the F-Chart method, showed a slight reduction in the total annual cost, when compared to the NBR 15569 method. Systems 4 and 6 did not show economic feasibility, even with the optimization made by the F-Chart method (the discounted payback was higher than the useful life of equipment, and the total annual cost of the system was higher than the annual cost of the conventional system). For system 4, the reason was the high cost presented in the combination of the gas accumulation system with forced circulation, while in system 6, the impracticability was due to the high cost of evacuated collectors in Brazil. As a final result, comparing all the evaluated systems, it can be verified that systems 1 and 3 presented the best economic feasibility for implementation, since they have the lowest annualized total cost (the user may choose the system 1, if the preference is for an auxiliary electric heater, or the system 2, if the preference is for an auxiliary gas heater).

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Table 6 Energy balance of the designed systems. System

1 2 3 4 5 6

QT (kWh. year  1)

3240.97 3240.97 3240.97 3240.97 3240.97 3240.97

NBR 15569

F-Chart

F

QS (kWh. year  1)

QAUX (kWh. year  1)

F

QS (kWh. year  1)

QAUX (kWh. year  1)

0.80 0.80 0.80 0.80 0.88 0.88

2578.63 2578.63 2578.63 2578.63 2864.35 2864.35

560.22 649.04 697.20 807.73 318.55 369.06

0.80 0.80 0.85 0.80 0.88 0.67

2578.63 2578.63 2763.31 2578.63 2864.35 2172.18

560.22 649.04 502.79 807.73 318.55 1047.33

Note: QT is the annual energy demand, F is the annual solar fraction, QS is the solar system energy output and QAUX is the auxiliary heater energy output.

Table 7 Economic analysis for systems designed according to the NBR 15569 methodology System

CI (US$)

CIA (US$ y  1)

CAM (US$ y  1)

CEAUX (US$ y  1)

CAT (US$ y  1)

CASC (US$ y  1)

PBD (years)

TIR (%)

VE

1 2 3 4 5 6

1491.77 1600.10 1783.44 1887.60 2388.77 2497.10

192.43 194.55 215.58 228.32 318.18 320.30

29.84 50.96 35.67 56.71 47.78 68.90

93.37 63.63 116.20 79.19 53.09 36.18

315.63 309.15 367.45 364.23 419.05 425.39

457.63 333.25 457.63 333.25 457.63 333.25

6 11 9 22 11 –

22.61 13.93 16.77 9.48 12.62 5.11

Yes Yes Yes No Yes No

Note: CI is the initial cost of the equipment, CIA is the annualized initial cost, CAM is the annual maintenance cost, CEAUX is the annual cost of auxiliary energy, CAT is the total annual cost, CASC is the annual cost of the conventional system, PBD is the discounted payback, TIR is the internal rate of return and VE is the economic viability.

Table 8 Economic analysis for systems designed according to the F-Chart methodology. System

CI (US$)

CIA (US$ y  1)

CAM (US$ y  1)

CEAUX (US$ y  1)

CAT (US$ y  1)

CASC (US$ y  1)

PBD (years)

TIR (%)

VE

1 2 3 4 5 6

1491.77 1600.10 1977.50 1887.60 2388.77 1939.35

192.43 194.55 238.38 228.32 318.18 247.99

29.84 50.96 39.55 56.71 47.78 57.75

93.37 63.63 83.80 79.19 53.09 102.68

315.63 309.15 361.72 364.23 419.05 408.42

457.63 333.25 457.63 333.25 457.63 333.25

6 11 9 22 11 –

22.61 13.93 16.45 9.48 12.62 5.00

Yes Yes Yes No Yes No

7. Conclusions

References

A review of the methodologies and some useful software used for designing solar water heating system were presented in this paper. So, in order to facilitate some design methodologies, making them more suitable for normal use in Brazil, and, at the same time, using consolidated calculation methodologies (F-Chart and NBR 15569), a new software was developed and presented in details. The application developed allows to perform, in a quick and efficient way, the scaling and economic analysis of small solar water heating systems. The software also allows the user to modify, at any time, the input parameters, in order to simulate different situations of use. In the simulation performed in this paper, it can be verified that the change of the components and the solar heating system configuration, for the same energy demand, strongly influences the economic viability of the project. The simple change of the auxiliary system, for example, may result in an uneconomical investment.

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