Numerical simulation and experimental validation of an outdoor-swimming-pool solar heating system in warm climates

Solar Energy 189 (2019) 45–56

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Numerical simulation and experimental validation of an outdoor-swimmingpool solar heating system in warm climates

T

S. Lugoa, L.I. Moralesb, R. Bestc, V.H. Gómezc, O. García-Valladaresc,

⁎

a

Posgrado en Ingeniería UNAM, Privada Xochicalco S/N, Temixco, Morelos C.P. 62580, Mexico Facultad de Ciencias Química de Ingeniería, Universidad Autónoma del Estado de Morelos, Av. Universidad 1001, Col. Chamilpa, Cuernavaca, Morelos C.P. 62209, Mexico1 c Instituto de Energías Renovables-UNAM, Privada Xochicalco S/N, Temixco, Morelos C.P. 62580, Mexico

b

ARTICLE INFO

ABSTRACT

Keywords: Solar energy Outdoor swimming pool Experimental validation TRNSYS Numerical model Solar thermal systems

This paper presents a mathematical model developed in TRNSYS to simulate the performance of a solar heating system for an outdoor swimming pool in regions with a warm climate. For this purpose, a new type for TRNSYS was developed. The model was validated using experimental data collected from an outdoor 53.8 m3 swimming pool in Cuernavaca, Morelos, Mexico. The data used to confirm the model’s components and the full model were gathered from March 2016 to June 2017. This pool is located in a hotel surrounded by trees and vegetation that cause shading on the pool’s surface throughout the day, thus reducing the heat gain from direct solar radiation. A shading factor equation for the shading over the pool was developed, introduced, and validated in the model to consider variations in pool temperature. For evaluating the evaporative losses, six empirical correlations obtained from the literature were tested. The model margin error was estimated at less than ± 2% (an average of ± 0.41%) with a temperature differential of less than ± 0.5 °C (an average of ± 0.12 °C, root of the mean quadratic error (RMSE) = 0.148 °C, mean bias error (MBE) = −0.058 °C, and coefficient of determination (R2) = 0.9723) between the measured and simulated pool temperatures. Therefore, the model adequately reproduced the pool’s temperature under different working conditions, and can be a valuable tool for generating a technical and economic analysis of solar heating systems in outdoor pools for regions with similar climatic conditions.

1. Introduction Pool heating has been an issue for several centuries; Roman records indicate the use of solar water heating in public baths since 200 B.C. There is a constant requirement for comfortable temperatures in residential and public pools, and amongst the most frequently used technologies in pool heating are water heaters that use fossil fuels such as diesel, liquefied petroleum (LP) gas, and natural gas. However, the combustion of such fuels generates greenhouse emissions, which are a critical factor affecting climate change. In addition, the cost of fossil fuels have increased considerably in recent years. These factors have created an opportunity for the use of renewable energy technology, which aligns with the requirement of reducing costs, using energy more efficiently, and reducing CO2 emissions into the atmosphere (Govaer and Zarmi, 1981; Singh et al., 1989; Molineaux et al., 1994; Barbato et al., 2018; Li et al., 2018). Solar water heating systems (SWHS) have been proven to work very successfully for pool heating in places with

adequate solar radiation, and can achieve an expected investment return in less than 2 years in warm climates. SWHS can also be combined with other technologies such as heat pumps and photovoltaic/thermal (PV/T) systems (Chow et al., 2012; Katsaprakaki, 2015) to maintain the pool temperature at desired values, even in colder months or under other conditions. Since 1980, several theoretical models for outdoor swimming pools have been published (Govind and Sodha, 1983), and the most common programs used are MATLAB’s Simulink and TRNSYS. The purpose of these models is to predict the pool temperature under various operating and meteorological conditions and obtain an economic analysis of the return time of investment. Govaer and Zarmi developed an analytical model to determine the long-term thermal performance of an outdoor pool, and their results show that the model is applicable to indoor pools after making an adequate modification to the parameters (Govaer and Zarmi, 1981). Govind and Sodha presented an analysis of the heat transfer

Corresponding author. E-mail address: [email protected] (O. García-Valladares). 1 Posdoctoral stay at Instituto de Energías Renovables-UNAM. ⁎

https://doi.org/10.1016/j.solener.2019.07.041 Received 19 February 2019; Received in revised form 8 July 2019; Accepted 11 July 2019 0038-092X/ © 2019 International Solar Energy Society. Published by Elsevier Ltd. All rights reserved.

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Nomenclature

A Ac c COPr Cp f SF h h¯

H I Ic k L m N P q Q Q T t V X w

emissivity (dimensionless) humidity (%) Stefan–Boltzmann constant (5.67 × 10 8W/m2K4 )

surface area (m2) solar collector array area (m2) constant from function f (t ) (h) coefficient of performance ratio specific heat at constant pressure (J/kg K) factor (dimensionless) solar fraction (%) enthalpy (kJ/kg) average convective heat transfer coefficient (W/m2 K) monthly average solar irradiation (MJ/m2 day) solar irradiance (W/m2) solar irradiance at collector plane (W/m2) thermal conductivity (W/m K) length (m) mass flow (kg/s) number of data points pressure (Pa) conduction speed, (dimensionless) heat flow or power (W) heat (J) temperature (°C or K) time (s) pool volume (m3) variable data wind speed (m/s)

Subscripts

a aux ave col conv cond exp eva gain in losses max rad refill s sat sim sol sky soil p pump out v w

Greek letters pool water absorbance (dimensionless) density (kg/m3) processes in the solar heating of a pool in two analytical models, one for an outdoor pool and another for a pool with a polyvinyl chloride (PVC) cover. The solar insolation and atmospheric air temperature are assumed to be periodic. The experimental water temperature in a pool in Victoria, Australia, showed close agreement with these theoretical calculations (Govind and Sodha, 1983). Hahne and Kluber’s model emphasises that losses due to heat conduction are equivalent to 1% of the total heat loss from pools, and they can thus be neglected. In contrast, evaporative heat losses can account for up to 60% of the total pool heat loss. Furthermore, this model also takes into consideration that not all the solar radiation is absorbed by the pool surface. Therefore, it includes factors that represent the solar radiation fraction absorbed by the pool surface as a function of the incidence angle. However, this model has only been validated for the German climate with solar fractions below 50% (Hahne and Klüber’s, 1994). Ahmad and Khane performed a gains and losses analysis for an outdoor pool. The results of their thermal analysis indicates that a comfortable temperature can be maintained in the pool if a plastic cover is used during the winter season (Ahmad and Khan, 2009). Ruiz and Martínez used different correlations for the evaporative coefficient one of which was developed by Richter. Richter's correlation had the lowest standard deviation value (0.036) for evaporative heat losses as compared to other correlations. However, this model does not take into consideration the losses due to water replacement and conductive heat losses, and the experimental validation was only performed for three consecutive days. Further, the pool temperature was the only parameter compared (Ruiz and Martínez, 2010). Woolley et al. evaluated the effect of solar radiation on an outdoor pool without a solar heating system. This model demonstrated that the equations used in previous models can be adjusted to obtain a deviation

ambient auxiliary average solar collector convective conduction experimental evaporation gain inlet losses maximum radiation replacement water shade saturation simulated solar sky ground pool pump outlet steam water

value of ± 0.6 °C, and includes calculations for conductive heat losses. It takes into consideration that the total conductive losses can be greater than 1% of the total losses, because the soil temperature is not constant. The pool was used as a heat sink for air conditioners (Woolley et al., 2011). Cunio and Sproul investigated the theoretical and experimental performance of solar collectors for outdoor pool heating without glazing and at low flow rates. They observed that the performance was heavily penalised until the flow drops below 50 l/min. Therefore, the efficiency for 60 l/min is approximately 15% of that obtained for 140 l/ min. A simple cost analysis also showed that the energy savings result in significant cost savings over a lifetime of 10 years (Cunio and Sproul, 2012). Zsembinszki et al. simulated the thermal behaviour of water in the presence and absence of a PCM (phase-change material) storage system and studied the effects of PCM under comfort conditions. Two methods of PCM used for heating are presented: the first comprised the use of the heat in the sidewalls and bottom of the pool, and the second comprised the use of an external heat exchanger with a PCM. The results showed at difference between the temperature values of the registered and simulated pool of less than 0.2 °C, and a deviation of 0.009. The implementation of a PCM storage system in an outdoor pool can produce an increase in the water temperature of up to 2 °C even for a limited number of days which occurs during periods of adverse weather conditions such as low sunlight, low air temperatures, or high wind speeds. In contrast, when the weather is warm, and the pool water is sufficiently warm such that it reaches a comfortable value, the PCMs have the effect of reducing the pool temperature by absorbing excess heat (Zsembinszki et al., 2012). Zayed et al. presented that a significant improvement in energy of flate plate solar collectors can be obtained using carbon based 46

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nanofluids compared to metal oxides nanofluids under the same conditions (Zayed et al., 2019a) and they also presented a review of the novel and most recent developments of PCM and cascade thermal storage (multiple PCM in descending order of their melting temperatures) and their implementation in solar water collectors storage tanks (Zayed et al., 2019b). Santos et al. proposed a hybrid structure for simulating the thermodynamic behaviour of pools using neural computational models to incorporate the climatic information of regions in Brazil. Although, the neural representation takes into consideration the latitude, longitude, and elevation, locations that are geographically distinct from the training data set cannot be represented, thus making the simulation structure inconsistent (Santos et al., 2013). Buonomano et al. developed a model for two different cases: indoor and outdoor pools heated using a PV/T system in which the electricity and water heating are produced simultaneously and a heat exchanger is used to heat the pool. This model makes use of seven correlations for estimating the evaporative coefficient and three for the convective coefficient. Furthermore, in addition to testing ASHRAE’s equation for total heat loss, it also takes into consideration the heat loss due to water replacement and conduction. An economic analysis was also performed. However, this model has not been validated experimentally (Buonomano et al., 2015). Kaci et al. developed a dynamic model for an outdoor pool heating while comparing two types of solar collector arrays: one with and another without a glass cover. The results showed that the collector without a glass cover had an annual solar fraction of approximately 47% against the collector with a cover with 27%. The economic assessment indicates that the first system is profitable with a return period of 9 years (Kaci et al., 2017). Zuccari et al. calculated through an ad_hoc developed algorithm (named EnerPool) the potential savings in terms of non-renewable primary energy consumption that are achievable through energy efficiency actions involving heating, filtration, and water replacement for indoor swimming pools in Italy. This work analyses in detail some possible solutions for reducing the heating requirement, while facilitating high non-renewable primary energy savings (up to more than 50%) at a low cost and with a payback time of less than 2 years by means of renewable sources (solar collectors, photovoltaic panels, and pool covers), thus achieving economic and energy savings but with much higher initial costs. They found that 60% of the losses are due to evaporation in this type of system. The case of the outdoor swimming pools has not been analysed or experimental validated (Zuccari et al., 2017). Foncubierta et al. presented an experimental procedure at the laboratory scale that was developed to validate a new computationalfluid-dynamic-based (CFD-based) methodology for the estimation of the water evaporative rate in indoor swimming pools. The comparison between the simulated and experimental results shows that the modelling strategy proposed is a promising tool, with average relative errors of 9% for the typically mixed convection flows in indoor swimming pools (Foncubierta et al., 2018). With the information supplied by theoretical models, it is possible to determine the energy savings generated by the solar system during its operation. According to different authors, the important variable in these models are the evaporative heat losses as these have a great impact on the pool’s total energy balance. Therefore, some authors have developed semi-empirical equations for estimating the evaporative losses under various conditions such as in use, without use, indoor, and outdoor pools (Smith et al., 1994; Shah, 2003, 2012). The location is another main factor affecting the pool temperature, considering factors such as microclimate, constructions, and shadings. For example, a pool located in an open space will be affected by evaporative losses due to air currents that have an impact on the heat transfer and greater radiative losses to the sky; in contrast, a shaded pool will have a lower heat gain from direct solar radiation than a pool

without shading. It was found in the literature review that there are no models that take into consideration shading factors, which are commonly present in actual cases, and the majority of models have been developed and validated for indoor and outdoor pools in cold climates with low solar fractions and high return of investment periods. Few works have been developed for countries with warm climates wherein outdoor pools are very common, and they are used throughout the year. For this reason, in these locations the return on investment is very interesting to use solar technology in a massive way. In this work, a mathematical model was developed using TRNSYS, which has been validated using data collected from an outdoor pool located in a hotel in the city of Cuernavaca, Morelos, Mexico. This city has a yearly solar radiation average of 5.3 kW h/m2day (19 MJ/m2day) with an average ambient temperature of 21.4 °C, data collected from the National Meteorological Service, and in the months of April and May, the average maximum temperature can reach 28 °C. Owing to optimal meteorological conditions, the use of solar energy systems has been increasing in Mexico for the last few years. The technology used in this hotel’s pool is unglazed, flat plate collectors fabricated from high-density polypropylene with ultra-violet protection treatment. The pool’s temperatures and the inlet and outlet water temperature for the solar array were measured without the use of a thermal cover. As mentioned above, an additional factor was included to take into consideration the shading on the pool generated by the dense trees and vegetation present at the hotel. The model used was generated with TRNSYS version 16 (TRNSYS, 2005) and validated with data collected from March 2016 to June 2017. The main contributions of this work are the development of a new type (pool) of TRNSYS model in order to calculate the pool temperature; a shading factor is included in this model, which has not been reported in other models of solar pool heating analysis and is useful for pools with similar conditions and for the experimental validation of the model. Further, a validation for each component of the system (and for the system as a whole) is performed, which has also not been reported in prior published models. Finally, with respect to the experimental validation of the model, the validation for each component of the system including the solar collector array as well as the system as a whole is performed and compared against the measured pool temperature, which has also not been presented in previously published models. This facilitates the evaluation of the uncertainty of the solar collector array model, which is not restricted to the swimming pool model. The validated model can be used as a good tool for determining the thermal performance of outdoor pools in warm climates throughout the year. 2. System description The thermal analysis was conducted on an outdoor swimming pool at “Las Quintas” hotel in the city of Cuernavaca, Morelos, Mexico, located at 18.9192°N 99.2181°W and an altitude of 1510 m above sea level. The pool surface area is 44.4 m2, and it has a volume of 53.8 m3. Owing to its location, this pool is partially shaded throughout the day. Buildings and vegetation generate this shading around the pool, which results in a decrease in the energy gained by the pool from direct solar radiation (Fig. 1). This factor is taken into consideration in the proposed model because it has a relevant effect on the temperature of the pool. The pool is heated by a solar thermal system comprised of a 2.18 kW pump and 12 unglazed polypropilene flate plate solar collectors. The system configuration comprises two arrays connected in series, wherein the first array consists of five collectors in parallel, and the second consists of seven collectors in parallel. The total collector area is 45.6 m2 and is located on top of one of the buildings close to the pool, as shown in Fig. 2. The solar heating system has an angle of 35° SE and an inclination of 11.5°. It is considered that the surface of the installed collector field (45.6 m2) is similar to the pool surface (44.4 m2) as per a 47

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direction and speed, ambient temperature, humidity, and precipitation; the characteristics of all the data acquisition devices are included in Table 1. The solar heating system pump is controlled (switch on and switch off of the pump) by a differential temperature control between the outlet section of the collector array and pool temperature; it switches on with a temperature difference of 4 °C and switches off when this temperature difference falls below 2 °C. The pump also switches off when the pool temperature is greater than 31 °C. The solar system and monitoring diagram are presented in Fig. 3. This system has been in operation since July 31st, 2015, and has produced 194393 MJ and mitigated 18.29 Ton of CO2, which translates into savings of 6250 kg of LP gas savings of 4254 USD as reported on April 2nd, 2019 (Las Quintas, 2019). Table 2 presents technical information and the characteristics of the solar collectors used in the system. The efficiency curve for the solar collector clearly shows how the efficiency is affected by wind speed (w ) in the case of an unglazed flat plate collector.

Fig. 1. Aerial view of the pool.

3. Mathematical model in TRNSYS 3.1. Collectors The mathematical model for solar collectors was developed using the dynamic simulation software TRNSYS version 16. The mathematical model for solar collectors corresponds to Type 1 for a flat plate solar collector with a quadratic efficiency curve. On applying the thermal efficiency equation and using the average water temperature in the collector and climate data (wind speed, solar irradiance, and ambient temperature), it is possible to obtain the efficiency value for a given instant within a time interval and, therefore, obtain the collector-array useful heat and the outlet temperature for that time interval. Efficiency values obtained using the ISO 9806:2013 standard (Table 2) were modified using correction factors that apply when: (a) the mass flow used differs from the mass flow reported during testing for the efficiency curve; (b) more than one collector is connected in series; and (c) the solar incidence is not perpendicular to the collector.

Fig. 2. Solar collector installation.

rule of thumb practice used by some installation technicians that assumes that the thermal losses in the pool are equivalent to the energy gain by the solar collector array for most of the year in warm climates. The solar installation of this pool was not sized by the authors of this work. This system was equipped with a mass flow rate sensor and several temperature sensors, which send a signal to a monitoring system that can be viewed in real time via a web page (Las Quintas, 2019). For obtaining the atmospheric data, a meteorological station was installed to measure the values of the variables such as solar radiation, wind

3.2. Pool The mathematical model for an outdoor pool comprises a balance of energy gains and losses, as shown in Eq. (1). In Table 3, various correlations for heat gains and losses reported by different authors are presented.

Table 1 Data acquisition instrumentation. Pool measuring instruments Variable

Sensor

Characteristics

Temperature

PT-1000

Mass flow

Magnetic flowmeter

Accuracy: ± 0.3 °C Measurement range: −50 °C-750 °C Accuracy: ± 0.5% Measurement range: 0–830 kg/min

Weather station measuring instruments Temperature and humidity

Temperature and humidity transducer

Solar irradiance

Spectral pyranometer

Wind speed

Anemometer

Rainfall

Rainfall sensor

48

Temperature accuracy: ± 0.5 °C Measurement range: −20-60 °C Humidity accuracy: ± 0.3% Measurement range: 0–100% Measurement range: 0–2000 W/m2 Sensibility: 5-20 µV/W/m2 Accuracy: ± 5% Measurement range: 0.5–89.0 m/s Accuracy: ± 4% Measurement range: 0–999.8 mm/m2

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Fig. 3. Solar system and monitoring schematic.

A new type (Pool) of model for TRNSYS version 16 was developed in order to calculate the pool temperature. The parameters and input and output data are presented in Table 4.

Table 2 Characteristics of solar collectors. Parameter

Specification

Collector type Material Area [m2] Fluid capacity [litres] Test conditions mass flow [kg/h m2] Optical efficiency [–] First order thermal losses coefficient [W/m2 K]

Unglazed flat plate Polypropylene 3.65 11.54 288 0.9248–0.0512w 15 + 6.3w

3.3. Pool solar heating system The model of the complete heating system was developed in TRNSYS; the solar collector and pool model were incorporated to operate in conjunction while simulating the performance of the entire system. Fig. 4 shows the layout of the complete system for simulating the complete performance of an outdoor pool with a solar heating system. In the modelling, Type 9 was included to input the experimental data from the meteorological station obtained during the test time interval in order to calculate the theoretical pool temperatures from the model and compare them to the experimental data. Type 9 can be replaced with Type 109 for inputting the meteorological data of the region for a full typical year in the TMY format in order to perform a feasibility and profitability analysis of the installation for a complete operational year. The TMY file was generated using the Meteonorm 7.0 software and the climate data for Cuernavaca, Morelos, obtained from the UNAM database (ESOLMET-IER, 2018).

The pool energy balance is

Vp

w Cpw

dTp dt

=

Qgain dt

Qlosses dt

(1)

The heat gain is

Qgain = Qsol + Qcol + Qaux

(2)

The heat losses are

Qlosses = Qeva + Qrad + Qconv + Qcond + Qrefill

(3)

In the pool’s energy balance Eq. (1), Vp represents the pool volume, is the pool water density, and Cpw is the specific heat at the constant pressure of the pool's water, the heat gains due to direct solar radiation on the pool’s surface are represented by Qsol , gains at the solar collector array are Qcol , and auxiliary heat is denoted by Qaux , heat losses due to Qeva , Qrad evaporation are radiative losses are with Tsky = 0.0552(Ta + 273.15)1.5 273.15(oC), convective losses are Qconv , conductive losses are Qcond , and losses due to water replacement are Qrefill . In this model, the conductive losses (Qcond ), replacement water (Qrefill ), and pump power were considered to be negligible (Buonomano et al., 2015) given that their magnitudes were considerably small as compared to the other coefficients. The pool model developed in this article is based on the equations presented by Ruiz and Martínez (2010), except for the evaporation correlation. The evaporative losses presented in Table 3 were considered in order to determine the one that best fit the experimental data. w

3.4. Piping heat losses The piping heat loss modelling was based on Type 204 previously used by the authors for another case study (Lugo et al., 2019). Nevertheless, the piping heat losses were considered irrelevant owing to the flow rate (100–180 l/min), piping distance (10 m), piping diameter (0.0381 m), piping material (PVC), and operating conditions, which in this case amounted to losses lower than 0.1 °C. 4. Experimental validation The experimental data obtained from March 2016 to June 2017 were analysed to validate the model, and the representative days of this period are presented in this section. To validate the complete model, it was essential to validate each component separately against the experimental data. Further, while considering the necessary input data for 49

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Does not apply

No solar heating

Tw )

=

mCp (Tout Tin) Qsolar = Ic Ac + Qpump Ic Ac + Qpump

(4)

No solar heating

where Ic is the solar irradiance at solar collector plane (W/m2), Ac is the area of the solar collector array (m2), Qsolar is the power transfer to the water for the solar collector array (W), and Qpump is the pump power (W). The coefficient of performance ratio (COPr) is evaluated using Eq. (4), while considering IcAc = 0. The margin of error for each simulated data point was obtained using Eq. (5).

Does not apply

Qsol = Ap Idt Qsol = Ap Idt

Qrad =

1 qksoil Ap (Tp Tsoil ) 2 Lc 4 Ap w (T p4 Tsky ) dt

Qrefill = mw Cpw (Tp Not considered

Rbowen =

Qcond =

{ h conv Tp Ta Pv, sat (Tp ) Pv, amb p Cbowen a po

Qconv = Qeva Rbowen

1 Qcond = qksoil Ap (Tp Tsoil ) 2 Lc 4 Qrad = Ap w (T p4 Tsky ) dt

2.8 + 3.0w = 3.1 + 4.1w

Qconv = hconv Ap (Tp

Ta) dt

Pv, a ] dt h eva = 0.036 + 0.025w

%Error =

Tp)

4 Tsky ) dt

Xsim

Xexp

100

X exp

N i=1

RMSE =

Qcol = mcol Cpw (Tcol

(5)

Xexp, i )2

(Xsim, i

(6)

N

where N represents the number of data points. The mean bias error (MBE) was calculated using the following equation:

Does not apply

Qsol = Ap Idt

(T p4 w

Qrad = Ap

Not relevant

Not considered

Ta ) dt Qconv = hconv Ap (Tp

h conv = 3.1 + 4.1w

Qeva = Ap h eva [Pv, sat (Tp) Pv, a ] dt

h eva = 0.036 + 0.025w

Pv, a ] dt

Qeva = Ap h eva [Pv, sat (Tp)

To validate the solar collector model, the following input data were used: solar radiation on a horizontal plane, ambient temperature, wind speed, inlet temperature to collectors, mass flow rate, area, and collector array. The values compared were the outlet temperature from the solar collector array as well as the energy gain by the pool (experimental and simulated), and the instantaneous thermal efficiency of the solar collector array was calculated using the following equation.

The variable X can be the temperature (°C) or energy (J). In the same manner, the root of the mean quadratic error was calculated using Eq. (6). h eva = 0.0423 + 0.0565w 0.5

dt dt

Qeva = Ap h eva [Pv, sat (Tp)

Qlosses dt dt

Q gain

= dTp w Cpw dt

QHE1, QHE 2 are heat exchangers

Vp Qlosses dt Q gain

= dTp dt w Cpw

Vp Qlosses dt Q gain

= dTp dt w Cpw

Vp

Ta ) Qlosses = 0.06Ap (Tp

Qgain = Qsol + QHE1 + QHE 2

Qgain = Qsol Qgain = Qcol + Qsol

Qlosses = Qrad + Qeva + Qconv + Qcond + Qrefill Qlosses = Qrad + Qeva + Qconv + Qcond

Qlosses = Qrad + Qeva + Qconv

MBE =

N i=1

(Xsim, i

Xexp, i )

(7)

N

The coefficient of determination R was calculated using Eq. (8):

Tp)

Tp)

Qcol = mcol Cpw (Tcol

Qaux = mw Cpw (Taux

R2 = 1

N (Xsim, i i=1 N ( Xexp, i i=1

X exp, i ) 2 Xexp, ave ) 2

(8)

Fig. 5 shows a comparison between the experimental outlet temperatures from the solar collector array and the simulated temperatures as well as the instantaneous thermal efficiency of the solar collector array and the solar irradiance measured at the collector plane. It can be observed that there is a good correlation between the simulated and experimental data. The average deviation between the simulated and experimental outlet solar collector temperature was ± 0.17 °C, and the error was ± 0.53% (RMSE = 0.194 °C, MBE = −0.12 °C, and R2 = 0.9805). With respect to the difference between the numerical and experimental data for the useful energy gain of the solar systems (in this case between 31.37 and 8.53 kW), the average deviation was ± 5.67% (RMSE = 1.48 kW, MBE = −0.94 kW, and R2 = 0.9461). The average mass flow rate was 6549 kg/h, the values of the instantaneous thermal efficiency of the solar collector array Eq. (4) are between 52.9% and 75.6% with an average of 67.6%, and the coefficient of performance ratios (COPr) are between 4.5 and 14.4 with an average of 10.6, with a solar irradiance at the collector plane between 331.6 W/m2 and 866.5 W/m2 with an average of 696.9 W/m2.

Collector heat gain

Auxiliary heat gain

= Reflectedsolar radiation factor

Direct solar gain on the pool surface Qsol = Ap (1

w

) Idt

Tw )

4 Tsky ) dt

Refill losses

(T p4 Qrad = Ap

Qrefill = mw Cpw (Tp

Radiative losses

h conv = 3.1 + 4.1w

Not relevant, less than 1% of total heat loss Conductive losses

Convective losses

Qconv = hconv Ap (Tp

Ta ) dt

Pv, a ] dt h eva = 5.058 + 6.69w

Qeva = Ap h eva [Pv, sat (Tp) Evaporative losses

dt

Qlosses dt Q gain

= dTp dt w Cpw

Qlosses = Qrad + Qeva + Qconv + Qcond + Q w Energy balance

Vp

Evaluation of eight outdoor pools with solar heating and auxiliary heating System description

Qgain = Qcol + Qsol + Qaux

1 outdoor and 1 indoor pool heated with PV/T solar hybrid system

4.1. Solar collector model

2

Hahne and Klüber (1994)

100-m2 outdoor pool with solar heating Outdoor pool without solar heating

each component model, the solar collector model and outdoor pool model were validated separately and then simulated in a coupled configuration, to obtain the validation for the complete system.

Reference

Table 3 Summary of pool energy balances reported in the literature.

Ruiz and Martínez (2010)

Woolley et al. (2011)

Buonomano et al. (2015)

S. Lugo, et al.

4.2. Outdoor pool model Climate variables. To validate the model, the experimental data 50

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Table 4 Parameters of the new type of model for TRNSYS. Parameters

Input

Output

Initial temperature of pool water

Ambient temperature (Ta ) Relative humidity ( )

Pool surface area ( Ap ) Pool volume (Vp )

Wind speed (w )

Height at which wind speed measurement is obtained

Solar irradiance (I )

Pool temperature (Tp )

.

Power gain from auxiliary heat (Qaux ) .

Power loss by evaporation (Qeva ) .

Mass flow rate supply by solar collectors (mcol ) Temperature supply by solar collectors (Tcol )

Power loss by convection (Qconv ) .

Power loss by radiation (Qrad )

.

Power gain by solar collectors (Qcol )

.

Power gain by direct solar radiation (Qsol )

was measured from March 2016 to June 2017. Corrections to this experimental data were made to take into consideration the meteorological station being 7 m above the pool level, and it was necessary to obtain the humidity, wind speed, and ambient temperature data at the pool level for implementing the model. Solar contribution. As mentioned in previous sections of this work, a shading factor ( fs ) was considered in the model to adjust the direct solar contribution (Qsol ). The pool is in a section of the hotel with considerable shading from buildings and vegetation. The amount of shading varies depending on the time of day and year; for example, in spring and autumn, the shading begins at 12:00 h, and by 15:20 h, the pool is completely shaded, while in summer and winter, the shading starts at 13:00 h, and by 16:20 h, the pool is completely shaded. The shading factor ( fs ) was introduced into the solar gain equation as shown in the following equation.

Qsol = (1

fs ) Ap Idt

(9)

The shading factor ( fs ) takes a value from 0 to 1 during the shaded period. However, the shade varies according to the season of the year as mentioned above. Therefore, the value of fs in Eq. (9) is estimated according to Table 5. The function f (t ) is given by Eq. (10).

f (t ) = 0.3(t

c)

Fig. 5. Solar irradiance, solar collector array efficiency, and comparison between simulated and experimental data for the outlet solar collector temperature for October 14th, 2016.

(10). Fig. 7 shows the experimental pool temperature profile (T2) according to Fig. 3, and the simulated pool temperatures using several semi-empirical equations for the evaporative coefficient in the pool for April 25th, 2017. The error analysis between the experimental results and the different empirical correlations used for the evaporation losses

(10)

where t is the solar time in decimal form (for example, 13:20 would be 13.333 h), and c is a constant equal to 12 h. Fig. 6 shows the map of the pool shade obtained according to Eq.

Fig. 4. TRNSYS layout for simulating the outdoor pool performance with a solar heating system. 51

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Table 5 Values of fs according to the season of the year. fs

Spring–autumn

Summer–winter

0 f(t) 1

t (c + 3.333)

t < (c + 1) (c + 1) ≤ t ≤ (c + 4.333) t > (c + 4.333)

Table 6 Comparison of average errors of pool temperature for the different evaporative losses equations against experimental data. Evaporative losses equation

Error (%)

ΔT (°C)

RMSE (°C)

MBE (°C)

R2

Richter (1979) ISO, McMillan (1971), ISO (1995) Smith et al. (1994) Rohwer (1931) ASHRAE (2003)

0.10 0.20

0.03 0.07

0.0436 0.0843

−0.0018 −0.0636

0.9979 0.9920

0.48 0.94 1.02

0.16 0.31 0.34

0.1868 0.3573 0.3893

−0.1608 −0.3147 −0.3434

0.9607 0.8563 0.8294

The solar heating system was in operation from 10:00 h to 17:00 h, local time. The performance for simulated temperatures and experimental data can be observed with an average margin of error of ± 0.14% (RMSE = 0.05 °C, MBE = −0.02 °C, and R2 = 0.9974), and a temperature difference error of ± 0.04 °C. If the shading factor was not taken into consideration in the numerical model (see Tsim_without shadow in Fig. 8), the margin of error between the simulated and experimental data was ± 0.83% (RMSE = 0.31 °C, MBE = +0.21 °C, and R2 = 0.9124) with a temperature difference of ± 0.26 °C. The margin of error indicates that the model accurately reproduces the values of the pool temperature and the importance of considering the pool shading factor. It can also be confirmed that the model accurately simulates the pool data for days with clear skies and high levels of solar irradiance. The highest irradiance value for this specific day was 923.3 W/m2, with an average irradiance of 732.5 W/m2 and an average ambient temperature of 33.5 °C. The average and final value of pool temperature are 30.4 °C and 31.8 °C, the instantaneous thermal efficiency of the solar collector array is 60.1% (COPr = 7.7) with a maximum value of 81.4% (COPr = 13.0). If the shading factor was not taken into consideration in the numerical model, the average and final value of pool temperature are 31.0 °C and 32.8 °C, the instantaneous thermal efficiency of the solar collector array is 57.6% (COPr = 7.4) with a maximum value of 75.0% (COPr = 12.3). As shown in Fig. 8, there is a decline in the solar irradiance after 15:00 h; nevertheless, this does not affect the behaviour of the pool temperature because the pool is completely shaded by this time. Fig. 9 shows a temperature comparison for April 25th, 2017; for this date, a complete energy balance for the collector system was calculated along with the pool heat gains and heat losses. The margin of error between the simulated and experimental data was ± 0.11% (RMSE = 0.044 °C, MBE = +0.035 °C, and R2 = 0.9978) with a temperature difference of ± 0.035 °C, an average instantaneous thermal

Fig. 6. Map of pool shades in percentage.

are shown in order of priority in Table 6. The Richter’s correlation (Richter, 1979) provides the best adjustments for obtaining real values with an error of ± 0.10%, RMSE = 0.0436 °C, and MBE = −0.0018 °C with a temperature difference of ± 0.03 °C. This is followed by the correlation used by McMillan (1971) and ISO (1995) with an error of ± 0.20%, and RMSE = 0.0843 °C with a temperature difference of ± 0.07 °C. After these are the correlations of Smith et al. (1994), Rohwer (1931), and ASHRAE (2003). Fig. 8 shows the results obtained for May 19th, 2017. For this day, the same shading factor was used as that used in the month of April.

Fig. 8. Pool temperature and solar collector array efficiency comparison for the model with and without shading factor with solar irradiance for May 19th, 2017.

Fig. 7. Pool temperature profiles obtained using various empirical correlations for the evaporative losses against experimental data. 52

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reached during the day time. 4.3. Solar heating system for the outdoor pool Figs. 9 and 10 show the results for the simulated pool temperatures against the measured pool temperatures; with the previous results presented, both the models were validated separately, and the pool temperatures for both the linked models will be presented in the following figures. Once the separate models were validated, the complete model was assembled to validate its performance (solar collector model and pool heat gains and losses model) to obtain a complete model that simulates an outdoor pool that is heated using a solar thermal system. Fig. 11 shows a comparison between the simulated temperatures and experimental data for April 25th, 2017. There is a very close approximation between the model and the measured results, and the margin of error is ± 0.24% (RMSE = 0.099 °C, MBE = −0.029 °C, and R2 = 0.9888), which is equivalent to a ± 0.08 °C temperature differential. The solar irradiance and efficiency of the solar collector array for this day can be observed in Fig. 9. Fig. 12 shows the comparison between the model simulation and measured data for 47 h for 3 consecutive days, while considering the initial pool temperature for day one and the climate data for each time interval. An average deviation of ± 0.73% (RMSE = 0.246 °C, MBE = −0.061 °C, and R2 = 0.9223) is observed between the simulated results and measured data, which translates into a ± 0.20 °C temperature difference. The solar irradiance and efficiency of the solar collector array for these days can be observed in Fig. 10. It is important to mention that several simulations for other days during different seasons were performed (four in spring, one in summer, four in autumn, and one in winter), and the average error for these data was ± 0.41% (RMSE = 0.148 °C, MBE = −0.058 °C, and R2 = 0.9723), which is equivalent to a temperature difference of ± 0.12 °C.

Fig. 9. Pool temperature comparison, solar collector array efficiency, and solar irradiance for April 25th, 2017.

5. Case study After a complete evaluation of the pool simulation model and verifying its reliability, the operation of the pool was analysed for an entire year, for which the monthly climate data are presented in Table 7. An analysis was performed for the two study cases: the first case did

Fig. 10. Pool temperature comparison, solar collector array efficiency, and solar irradiance for June 14th–16th, 2017.

efficiency of the solar collector array of 56.25% (COPr = 9.7) with a maximum value of 85.82% (COPr = 15.8), an average reported irradiance of 733.1 W/m2 with a maximum and minimum value of 1014.3 W/m2 and 429.3 W/m2, respectively, and an average ambient temperature of 31.1 °C. This confirms a good performance of the pool model as compared with the experimental data. Once the model was adjusted to simulate the pool temperature during the day, simulations were run for 47 h while taking into consideration nocturnal heat losses, and the dates used were June 14th to 16th, 2017. For these dates and the shading factor used in the model, the shading started at 13:00 h because summer begins on June 20th. Fig. 10 shows the results for this simulation: the margin of error for the pool temperature was ± 0.65% (RMSE = 0.214 °C, MBE = −0.129 °C, and R2 = 0.9411) with a temperature difference of ± 0.18 °C. In this figure, the thermal efficiency of the solar collector array is obtained for June 15th, the solar irradiance is obtained for the partially cloudy days of June 14th and 15th, and the pump is switched off on June 14th. A decline in the temperature can be observed to start at 15:20 h because of the pool shading factor, and the maximum pool temperature measured was 28.6 °C, which is within the acceptable pool temperatures for the hotel. Owing to cloudy skies, the temperatures did not reach as high as those in April or May (maximum temperature measured was 34.1 °C), and it can also be observed that the nocturnal temperature losses were approximately 2 °C in June with reference to the highest temperature

Fig. 11. Comparison between pool temperature of complete model simulation and measured data for April 25th, 2017. 53

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Fig. 12. Pool temperature comparison for the complete model simulation versus measured data for June 14th–16th, 2017.

Fig. 13. Average pool temperatures during operation hours during different seasons.

Table 7 Monthly climate data for the typical meteorological year in Cuernavaca, Morelos (ESOLMET-IER, 2018). Month

Ta (°C)

Tmin (°C)

Tmax (°C)

(%)

w (m/s)

H (MJ/m2 day)

January February March April May June July August September October November December

19.4 20.55 22.55 23.95 24.25 22.45 21.6 21.45 20.95 20.95 20.6 19.8

12.9 13.65 15.4 16.95 17.85 17.1 16.2 16.15 15.95 15.3 14.35 13.4

26 27.35 29.75 30.95 30.75 27.85 26.95 26.8 25.95 26.6 26.8 26.15

52.9 48.4 44.2 46.2 56.6 71.8 68.9 68.6 73.6 67.8 61 56.3

3.15 3.1 3.02 2.92 2.39 2.21 2.36 2.24 2.17 2.5 2.91 3.17

16.45 19.21 22.00 22.73 19.48 19.23 22.19 20.06 15.40 18.71 17.07 15.06

Average

21.54

15.43

27.66

59.69

2.68

18.97

5.1. Solar heating system without auxiliary power Table 8 shows the monthly results obtained by the model for each component throughout a typical year without auxiliary power and without the use of a thermal pool cover. Fig. 13 shows the average pool temperature for all the operation days during the hours of pool operation from 10:00 to 18:00 h for the different seasons; spring and summer are evidently the best seasons for pool operation as the temperatures reached were greater than 25 °C. The main advantage of installing solar systems is determined based on an analysis of the cost and return on investment. The following assumptions were made for this analysis:

• Analysis is performed for 15 years of the useful life of the solar system. • Input economics assumptions (see Table 9). • Calorific power of the LP gas is 24.12 MJ/lt LP gas (INECC-SEMARNAT, 2014). • Emission factor is 1.58 kg CO /lt LP gas (INECC-SEMARNAT, 2014). • Efficiency of the auxiliary LP gas heater is 82% at sea level and 70%

Table 8 Monthly heat gains and losses without auxiliary power and thermal pool cover. Month

Qeva GJ

Qrad GJ

Qconv GJ

Qsol GJ

Qcol GJ

Qaux GJ

SF %

January February March April May June July August September October November December

−14.16 −14.73 −20.76 −21.60 −17.39 −12.28 −13.82 −12.75 −9.40 −13.31 −13.04 −12.87

−11.66 −10.47 −11.25 −11.34 −10.86 −11.60 −12.23 −11.97 −11.39 −12.26 −11.74 −11.54

−1.51 −1.47 −1.71 −2.08 −1.49 −2.02 −2.12 −1.93 −1.62 −2.09 −1.76 −1.35

6.12 6.42 9.38 11.22 9.32 8.41 8.18 7.06 5.81 8.58 −7.32 6.45

20.87 20.86 25.29 23.09 20.62 17.31 20.91 19.98 15.34 20.03 19.00 19.19

0 0 0 0 0 0 0 0 0 0 0 0

100 100 100 100 100 100 100 100 100 100 100 100

TOTAL

−176.11

−138.30

−21.13

94.26

242.51

0

100

2

in Temixco, Morelos (altitude of 1510 m above sea level).

For this case, the heat gains are estimated at 336 GJ (see Table 8). The energy supplied by the solar collector system was 242.5 GJ (67.4 MW h) per year, which is equivalent to the energy obtained from 14363 litres of LP gas or 7182 USD. On taking into consideration the cost variables (Table 9), we obtain a 5-month payback period for the solar heating system with an internal rate of return of 286% and a net present value in 15 years of 294586 USD and an annual avoided emissions of 22.69 Ton of CO2. 5.2. Solar heating system with auxiliary power In the second case study, an auxiliary LP gas water heating system was considered to supplement the solar collector system to maintain the pool temperature at 28 °C during the operation hours throughout the year. The system operates without a thermal pool cover. Table 10 shows the results for this analysis, where it is evident that the solar fraction is reduced owing to a higher operating temperature, thus reducing the collector efficiency. This also results in an additional

not consider the use of auxiliary power for heating, while the second case considered the use of an LP gas heater to supply the energy required to maintain a minimum temperature of 28 °C in the pool during sunny hours throughout the year. 54

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Table 9 Input economic assumptions. Variable

Value

SWHS key on hand price LP gas price Annual increment of LP gas (January 2017–January 2018) Annual inflation

3223 USD (MÓDULO SOLAR, 2019) $9.55 MX/litre (∼0.50 USD/litre) (CRE, 2018) 19.5% (CRE, 2018) 6.77% (Banco de México, 2017)

an internal rate of return of 218%, and the net present value of 218,745 USD are obtained for an operation period of 15 years. Fig. 14 shows the pool temperatures reached during operating hours with the use of the solar heating system and auxiliary power; the minimum set point is constant, and the pool temperature can rise to 30 °C. The use of a thermal pool cover during the night time can significantly reduce the heat losses from the pool. A comparison made for case study 1 reveals that the heat losses can be reduced by 15.2% through the use of a thermal pool cover, which would increase the minimum pool temperatures to 26 °C throughout the year during the pool operating hours. This could also help to reduce the number of required collectors or increase the pool temperature.

Table 10 Monthly heat gains and losses with auxiliary power without thermal pool cover. Qeva GJ

Qrad GJ

Qconv GJ

Qsol GJ

Qcol GJ

Qaux GJ

SF %

January February March April May June July August September October November December

−22.38 −21.35 −26.08 −24.49 −20.73 −16.83 −18.23 −17.67 −15.18 −18.55 −19.11 −20.65

−14.89 −12.93 −13.10 −12.30 −11.99 −13.27 −13.84 −13.92 −13.76 −14.34 −14.14 −14.68

−4.30 −3.66 −3.43 −2.97 −2.47 −3.42 −3.44 −3.44 −3.44 −3.67 −3.67 −3.91

6.12 6.42 9.38 11.22 9.32 8.41 8.18 7.06 5.81 8.58 7.32 6.45

14.93 16.08 21.50 21.05 18.12 14.07 17.69 16.18 10.81 16.20 14.79 13.44

21.17 15.99 12.59 7.38 7.86 11.41 10.38 11.88 15.73 12.32 15.08 19.61

41.4 50.1 63.1 74.0 69.7 55.2 63.0 57.7 40.7 56.8 49.5 40.7

TOTAL

−241.25

−163.18

−41.81

94.26

194.86

161.40

54.7

6. Conclusions The objective of this work was to formulate a mathematical model that could simulate pool temperatures. Therefore, the model could be used to estimate the amount of energy required to maintain comfort conditions in an outdoor, partly shaded pool with a solar heating system. Based on the models found in the literature, a program was developed on TRNSYS 16 to simulate the heat gains and losses from the pool, in addition to modelling an array of solar collectors and the amount of energy that it contributes. To simulate the pool, it was necessary to program a new type of model in TRNSYS. This model type integrates validated equations and the shading factor for the swimming pools in warm climates. The new model type can be used by other authors to simulate swimming pools with similar characteristics to those described in this work. As an integral part of the validation for this model, the experimental data obtained from the pool’s monitoring system for the months of March 2016 through June 2017 were used. The validation was performed for each of the model’s components as well as for the complete model, to ensure an adequate reproduction of the measured data. As shading can be a relevant factor affecting outdoor pools owing to the reduction in important heat gains from direct solar radiation at the pool’s surface, an equation for the shading factor was developed according to the profile of the shading at the pooĺs surface for each season. The analysis of the different evaporation equations proposed showed that Richteŕs correlation best fits the experimental data and is followed by the correlation of McMillan and ISO. For May 19th, 2017, the simulated and experimental pool temperature data have an average margin of error of ± 0.14% (RMSE = 0.05 °C, MBE = −0.02 °C, and R2 = 0.9974), and a temperature difference error of ± 0.04 °C. If the shading factor is not taken into consideration, the margin of error between the simulated and experimental data was ± 0.83% (RMSE = 0.31 °C, MBE = +0.21 °C, and R2 = 0.9124) with a temperature difference of ± 0.26 °C. This behaviour is similar for other test days. The margin of error indicates that the model accurately reproduces the pool temperature values and also indicates the importance of considering the pool shading factor. The results of the validation of the solar collector array model present an average deviation of ± 0.53% (RMSE = 0.194 °C, MBE = −0.12 °C, and R2 = 0.9805) in the collector outlet temperature simulation and a ± 5.67% margin of error (RMSE = 1.48 kW,

Fig. 14. Average pool temperatures during operation hours during different seasons with auxiliary power.

heat loss of 450.7 GJ (125.2 MW h) and, therefore, more energy is required to maintain the set temperature of 28 °C. The energy supplied by the solar system is 195 GJ (54 MW h) and reaches a total solar fraction of 54.7% (solar fraction is the amount of energy provided by the solar technology divided by the total energy required) with a fuel savings of 11541 litres of LP gas (5770 USD) and annual avoided emissions of 18.24 Tons of CO2. The solar fraction of Table 10 is less than that obtained in Table 8 owing to the higher pool temperature required and the use of auxiliary power in this case in order to reach the established pool temperature around the year. The total energy supplied by the auxiliary power was 161.4 GJ (44.8 MW h), which is equivalent to 9560 L of LP gas (5353 USD) and annual avoided emissions of 15.10 Tons of CO2. On applying the same analysis as that presented in Section 5.1, a payback period of 6 months, 55

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MBE = −0.94 kW, and R2 = 0.9461) in the useful energy gain of the simulated solar collector array. This represents a temperature difference of ± 0.17 °C. The experimental instantaneous thermal efficiencies of the solar collector array including the pump power are between 52.9% and 75.6% with an average of 67.6%. With respect to the complete model (pool + solar heating system), a margin of error of ± 0.41% is reported in the simulated pool temperature (RMSE = 0.148 °C, MBE = −0.058 °C, and R2 = 0.9723), which represents a difference of temperature of ± 0.12 °C. Therefore, it can be concluded that this model adequately simulates the behaviour of the pool temperature as well as the pool heat gains and losses. Overall, from the results obtained on comparing this model with the experimental data, it can be concluded that this model can be used as a powerful tool for designing and optimising solar thermal systems for outdoor pool heating applications and for generating feasibility and cost effectiveness proposals for the potential users of this technology. It has been proven that the use of a solar thermal collector for pool heating applications is viable in Mexico both technically and economically and realises adequate temperatures for pool use and returns on investment of less than 1 year.

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Acknowledgements This paper was partially supported by the projects CEMIESOL P09, CEMIESOL P12, and PAPIIT IT102618. Laura Morales is thankful for the SENER-CONACYT postdoctoral scholarship. The authors are thankful to Iris Santos and Rodrigo Cuevas for their support in the experimental work. References Ahmad, I., Khan, N., 2009. Solar swimming pool heating in Pakistan. In: Proceedings of ISES World Congress 2007, vol. I–V. Springer, Berlin Heidelberg, pp. 2033–2037. ASHRAE, 2003. ASHRAE Applications Handbook. Banco de México, 2017. Inflación. < http://www.anterior.banxico.org.mx/portalinflacion/index.html > . Barbato, M., Cirillo, L., Menditto, L., Moretti, R., Nardini, S., 2018. Feasibility study of a geothermal energy system for indoor swimming pool in Campi Flegrei area. J Sci Therm. Sci. Eng. Prog. 6, 421–425. Buonomano, A., De Luca, G., Figaj, R.D., Vanoli, L., 2015. Dynamic simulation and thermo-economic analysis of a PhotoVoltaic/Thermal collector heating system for an indoor–outdoor swimming pool. Energy Convers. Manage. 99, 176–192. Chow, T.T., Bai, Y., Fong, K.F., Lin, Z., 2012. Analysis of a solar assisted heat pump system for indoor swimming pool water and space heating. J. Sci. Appl. Energy 100, 309–317. CRE, 2018. Energy Regulatory Commision. < https://www.gob.mx/cre/documentos/ precios-al-publico-de-gas-lp-reportados-por-los-distribuidores > . Cunio, L.N., Sproul, A.B., 2012. Performance characterisation and energy savings of uncovered swimming pool solar collectors under reduced flow rate conditions. Solar Energy 86, 1511–1517. ESOLMET-IER, 2018. Estación Solarimétrica y Meteorológica del IER-UNAM. Consulted in June 2018. < http://esolmet.ier.unam.mx/index.html > . Foncubierta, B., Lázquez, J.L., Maestre, I.R., González Gallero, F.J., Álvarez, Gómez P., 2018. Experimental test for the estimation of the evaporation rate in indoor swimming pools: validation of a new CFD-based simulation methodology. Build. Environ. 138, 293–299.

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