SOLAR ENERGY Revista Mexicana de Fısica S59 (1) 173–178 FEBRUARY 2013

Transient thermal rating in a flat-plate solar heating system of apublic olympic pool

P. Salgado∗, R. Dorantes∗∗, G. Orellan, A. Lopez, M. Jimenez, H. Gonzalez, and J. RamırezUniversidad Autonoma Metropolitana, Departamento de Energıa,

Av. San Pablo No. 180, Col. Reynosa Tamaulipas, 02200, Mexico, D.F. Mexico,∗pau kobe@hotmail.com;∗∗rjdr@correo.azc.uam.mx

Received 30 de junio de 2011; accepted 30 de noviembre de 2011

The Azcapotzalco Reynosa’s Sports Center at Mexico City has an Olympic Pool with two heating systems: The first system has 290 flat-platesolar heaters and the other has 16 heat pumps. Since the flat-plate solar field was installed initially and the 16 heat pumps later on, bothsystems were designed to work separately. At the present time none of the systems work properly. In fact the solar field is disabled and theheat pump system does not work properly because of the lack of maintenance. A previous work using EPANET software had the plan toanalyze the water distribution of the solar heaters field, considering the complete hydraulic system. The study showed that almost 60% ofthe components had no water flux, even though the mechanic pump supplies the theoretical volumetric flow. This fact affects the solar fieldperformance even if the individual efficiency characteristics are good. This work presents the thermal evaluation results in a transitory stateto determine the possible average temperatures in several months of 2008 and 2009, the evaluation of the thermal system performance undervarious operating conditions of the pool, for example with and without a thermal cover, the water properties variation and the energy thermalbalance corresponding to the critical months.

Keywords: Thermal evaluation; solar pool heaters; thermal pool balance; the transitional regime.

La alberca olımpica del Deportivo Reynosa en la delegacion Azcapotzalco de la ciudad de Mexico tiene dos sistemas de calentamiento: unoa base de un campo solar con 290 calentadores solares planos y otro con 16 bombas de calor. Ambos sistemas estan instalados para trabajarindependientemente, aunque nunca fueron disenados para trabajar ası. Primero se instalo el campo solar y despues las bombas de calor.Actualmente ninguno de estos dos sistemas trabaja bien, de hecho el campo solar esta deshabilitado de la alberca y el de bombas de calorno opera por falta de mantenimiento adecuado. Un trabajo previo utilizando el programa EPANET tuvo por objetivo hacer un analisis dela irrigacion del campo solar considerando el sistema hidraulico completo, mostro que en cerca del 60% de estos calentadores no hay flujode agua, a pesar de que la bomba mecanica proporciona el caudal teorico necesario. Este hecho afecta el rendimiento termico del camposolar, a pesar de que cada colector plano tiene un buen rendimiento termico. En este trabajo se presentan los resultados del estudio termicoen estado transitorio para determinar las temperaturas promedio posibles de alcanzar en el agua de la alberca en diversos meses de 2008 y2009, la evaluacion del rendimiento termico del campo solar bajo diversas condiciones posibles de operacion de la alberca, con y sin cubiertatermica, con variacion de parametros de las propiedades del agua y el analisis energetico de perdidas y ganancias de calor correspondientesa los meses crıticos.

Descriptores: Evaluacion termica; calentamiento solar de albercas; balance termico de albercas; regimen transitorio.

PACS: 02.60.Cb; 05.60.Cd; 65.20.+w; 89.30.Cc

1. Introduction

In 2000 a solar heating system was installed in the sports cen-ter of the Reynosa Azcapotzalco delegation in Mexico City,replacing a steam generator heating system by burning gas,but due to high operating costs was replaced by a solar heat-ing system, composed of 290 flat-plate collectors with alu-minum fin and copper pipe, as shown in Fig. 1. For eco-nomic and technical reasons, this facility, was incorrectly de-signed and never operated properly. Subsequently a systemof 16 heat pumps was installed. The pumps worked well forsome time, but due to lack of maintenance and continuous useover the years caused the deterioration of the equipment [1,2].Currently, the solar heating system is turned off and the tem-perature of water in this pool is inappropriate to give a goodservice.

This work presents the preview of the transient thermalanalysis done by the Universidad Autonoma Metropolitana,Azcapotzalco Branch through an agreement sponsored by the

Institute of Science and Technology of the city of Mexicoto accurately establish the main technical problems the de-sign of the solar field has and proceed to assess the necessarychanges to correct it and to rehabilitate the solar field to heatthe water pool at a temperature between 28 and 32◦C, whichis an appropriate comfort range.

FIGURE 1. Panoramic view of a field of 290 solar heaters in thesports center located at the Reynosa Azcapotzalco delegation.

174 P. SALGADO, R. DORANTES, G. ORELLAN, A. LOPEZ, M. JIMENEZ, H. GONZALEZ, AND J. RAMIREZ

2. Thermal performance of the solar collectorfield

The good performance of a solar collector field is not onlybased on a good hydraulic design but also on a proper de-sign and thermal performance, which allows the solar systemto heat the pool water to the required comfort temperature,which in this case should be between 28 and 32◦C.

Obviously the problem is not easily resolved because thepools are used all year-round and usually begin their activitiesvery early (7 am) and end late at night (22 h), so the challengeof only using a solar system for water heating is enormous.Fortunately in this case there is a second heating system of16 heat pumps, which will allow us to analyze the possibilitythat both systems work in a complementary manner. For nowit is of our interest to know the range of the field of thermalsolar collectors operating at optimum irrigation and consid-ering the normal conditions of sunlight and seasonal changesin temperature.

After performing an energy balance of the pool you candetermine its thermal performance in transient state to assessits possible real-time behavior (Fig. 2). The figure shows thecontrol volume used, where the pool itself functions as heatstorage and where QU is the thermal potency provided by thecollector field, QP is the heat flow loss to the environmentand QRAD is the power gains by direct radiation and taking mas the mass of water in the pool and cP its specific heat andTa, the average temperature of the water in the pool.

∑QU +

∑Q

RAD−

∑Q

P= (mcP dT/dt)a (1)

In this differential equation all the variables on the leftside, plus the mass and the specific heat are known and willbe determined ahead. Thus there is only one unknown vari-able, which is the speed at which the water from the poolheats up,dTa/dt.

The following considerations are made in order to solvethe equation:

• The pool and solar heaters are completely exposed tothe sun.

• Incoming water temperature to the solar heaters is thesame as the water pool and it is expressed as Ta.

• Related to the pool’s depth, a temperature gradient isnot considered.

Using Euler’s method to solve Eq. (1) the following ap-proximation is made:

dTa/dt ∼= T+a − Ta/∆t (2)

where T+a is the temperature at instant i+1, and Ta is the tem-perature at the previous instant, i. The time difference be-tween both temperatures is∆t and it will have a small value(10 minutes) for the approximation to be valid.

FIGURE 2. Instantaneous power balance in the pool.

Substituting (2) in (1) we get:

T+a =Ta+(∆t/mcP )

(∑QU+

∑Q

RAD−

∑QP

). (3)

Where initial temperatures are used to solve this equa-tion, for instance, any day at sunrise and where both tem-peratures are equal and a lapse∆t of ten minutes is cho-sen. This lapse corresponds to the variation on the meteo-rological data readings. During this lapse all the values of(∑

QU +∑

QRAD−∑

QP ) are constant and evaluated at T=Ta

and all the second addend of (3) is added to Ta to obtain thenew temperature T+a . This process is repeated for a new lapseof time ∆t, where now (

∑QU +

∑QRAD −∑

QP ) will beevaluated at T+a , this is how all the daily, weekly or monthlymeteorological data is run to see the variation of the pool’swater Ta.

Heat gains∑

QU +∑

QRAD

Useful power supplied by solar heaters:∑

QU = η ∗ I ∗ Ac (4)

Where:Ac = total area of solar collection, 580 m2

I = solar radiation W/m2

η = thermal efficiency of the collector provided by the manu-facturer, such that:η = 17.483[(Te-T0/I)]3 - 36.072[(Te- T0/I)]2

- 4.7762 [(Te-T0/I)] + 0.7102 where Te is the temperature ofwater entering the collector and the ambient temperature T0.

Direct solar power gains∑

Qrad = α ∗ I ∗ As (5)

Where:As = surface area of the pool = 1,250 m2

I = solar radiation W/m2

α = absorption coefficient of water.Heat flux loss to the environmentThe heat flow losses associated with the pool’s water are

due to three important aspects, in accordance with the J. A.Manrique model [3]: losses by water evaporation to the at-mosphere, convection losses also from the water to the envi-ronment and finally the radiation losses of water to the envi-ronment, such that:

∑QP = Qevap+ Qconv + Qemi

Rev. Mex. Fis. S59 (1) (2013) 173–178

TRANSIENT THERMAL RATING IN A FLAT-PLATE SOLAR HEATING SYSTEM OF A PUBLIC OLYMPIC POOL 175

Evaporation losses:

Qevap= 1612 ∗ As ∗ hca ∗ (Pa − P0) (6)

Where:As = pool’s surface area = 1.250 m2

hca= coefficient of heat transfer by convection, and where:hca = 4.4 kW/m2◦C for wind speed below 5 km /h where hca

= 1.39 * V0.8 for speeds greater than 5 km/hPa = saturation pressure of water at the poolP0= pressure of water vapor in the air.

Losses by convection:

Qconv = As ∗ hca ∗ (Ta − T0) (7)

Where:As = pool’s surface area = 1.250 m2 poolhca= heat transfer coefficienthca= 4.4 for wind speed below 5 km/hhca = 1.39 * V0.8 for wind speed greater than 5 km / hTa = temperature of the poolT0= ambient temperature.

Heat loss by radiation from the pool to the environ-ment

Qemi = As[εσ(T4a − T4

0)] (8)

Where:As = pool’s surface area = 1.250 m2

ε = emittance coefficient of waterσ = Stefan-Boltzmann constant = 5.6697×10−8 W/m2K4

Ta = temperature of the poolT0 = ambient temperature

To graph the Eqs. (2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12), asmall Excel program was developed, using the data providedby the National Weather Service CONAGUA Azcapotzalcostation for the years 2008 and 2009, following are the valuesused:Ac= area of solar collection area = 580 m2

As = pool’s surface area = 1.250 m2

m = 2,125,000 kgcp = 4.186 kJ/kg◦Cε = emittance coefficient of the water3,4 = 0.8 to 0.95 withoutcoverε = emittance coefficient of the water3,4 = 0.2 to coverα = absorption coefficient the water3,4= 0.6 to 0.8

When the pool has the thermal cover, the following equa-tions are used:

Evaporation losses:

Qevap= 0 (9)

Convection Losses - Driving through the roof:

Qconv = (Ta − T0)/∑

R (10)

Where:∑R =

∑5n=1 Rn= sum of thermal resistances

R1 = Trapped air conduction resistance = L1/κ1 As

κ1 = Air thermal conductivity = 0.0247 + 8×10−5Ta

-4×10−8T2a

L1 = Air thickness = 0,001 mR2 = R4 = Conduction resistance between the cover and thecompressed air bubbles = L /κ As

κ = Thermal conductivity of polyethylene = 0.293 W/m◦CL = thickness of polyethylene = 0.0002 mR3 = conduction resistance of air bubbles = L3/κ1 As

L3 = thickness of compressed air = 0.005 mR5 = resistance by convection to the environment =1/As hca

hca = heat transfer coefficient (W/m2◦C)hca = 4.4 for V (wind speed) less than 5 km / hhca = 1.39 * V0.8for V more than 5 km / hAs = pool’s surface area = 1250 m2

Ta = temperature of the poolT0 = ambient temperature.

Heat loss by radiation from the pool to the environ-ment:

Qemi = As ∗ ε ∗ σ ∗ (T4a − T4

0) (11)

Where:σ = Stefan-Boltzmann constant = 5.6697×10−8 W/m2K4

As = pool’s surface area = 1.250 m2

ε = low emittance coefficient of water = 0.2Ta = pool’s temperature in Kelvin degreesTo = temperature in Kelvin degrees.

Heat gains∑

QU +∑

QRAD

Qu = 0 (12)

Qsolar = 0 (13)

3. Main results

Using the database from the ENCB1 meteorological stationlocated at the National School of Biological Sciences, IPN,

FIGURE 3. Behavior of the average water temperature of the poolof Deportivo Reynosa during December 2008 and January 2009.

Rev. Mex. Fis. S59 (1) (2013) 173–178

176 P. SALGADO, R. DORANTES, G. ORELLAN, A. LOPEZ, M. JIMENEZ, H. GONZALEZ, AND J. RAMIREZ

FIGURE 4. Behavior of the average water temperature of the poolof Deportivo Reynosa during April and May 2008.

FIGURE 5. a) Behavior of the average water temperature of thepool of Deportivo Reynosa during December 2008 and January2009, absorptance = 0.8, emittance = 0.8. b) Behavior of the aver-age water temperature of the pool of Deportivo Reynosa during De-cember 2008 and January 2009, absorptance = 0.7, emittance = 0.8.c) Behavior of the average water temperature of the pool of De-portivo Reynosa during December 2008 and January 2009, absorp-tance = 0.6, emittance = 0.8.

FIGURE 6. a) Behavior of the average water temperature of thepool of Deportivo Reynosa during December 2008 and January2009, absorptance = 0.8, emittance = 0.8. b) Behavior of the aver-age water temperature of the pool of Deportivo Reynosa during De-cember 2008 and January 2009, absorptance = 0.7, emittance = 0.8.c) Behavior of the average water temperature of the pool of De-portivo Reynosa during December 2008 and January 2009, absorp-tance = 0.6, emittance = 0.8.

located at Casco de Santo Tomas, Mexico, DF., data suchas temperature, wind speed, humidity, solar radiation andweather were taken, for the critical months of the year 2008-2009, that is the most cold and most warm months in thisdelegation, to assess the dynamic behavior of the tempera-ture Ta+, according to Eq. (2). Figure 3 shows the behaviorof water temperature (pink) and ambient temperature (blue),where, if starting from an initial water temperature of 13.8◦Cand pretending that a thermal cover is used at nights, the max-imum temperature reached is 27.2◦C, although this temper-ature is not easily stabilized and continues a trend similar tothe behavior of the ambient temperature. This chart is impor-tant because it shows the limits of the maximum water tem-

Rev. Mex. Fis. S59 (1) (2013) 173–178

TRANSIENT THERMAL RATING IN A FLAT-PLATE SOLAR HEATING SYSTEM OF A PUBLIC OLYMPIC POOL 177

FIGURE 7. a) Profit and loss performance for December 2008 andJanuary 2009. b) Profit and loss performance for April and May2008.

perature that can be achieved with the field of solar collectors,and considering that each the solar collector work in optimalconditions of irrigation, which is one of the main challengesof this work.

Figure 4 shows the simulation done for the warmestmonths of April and May, 2008. It shows that the temper-ature of water (pink) is within the comfort range and also thatit reaches a maximum temperature of 31.5◦C. In case it failsto reach the comfort range, then it will be necessary to useheat pumps, although they must be used only as supplemen-

FIGURE 8. Behavior of the average water temperature of the poolDeportivo Reynosa with and without cover for the cold months.

tary heating during the early hours of the day and late at night.In subsequent work we will present the results that will

allow us to demonstrate a solution to the longstanding sizingproblem of large solar heating systems, where the main prob-lem is not due to the good or fair solar collector efficiency,but to the poor Solar field water distribution, that does nothave a proper tool to do so.

On the graphs above the parameters absorptance andemittance of water, were varied. Figures 5a, 5b, 5c, 6a, 6band 6c show the variation of the pool’s water temperatures asthe parameters were discreetly changed.

The thermal assessment also includes an analysis of en-ergy losses and gains for each month, which are shown inFigs. 7a and 7b. The former allow us to observe the impor-tance of each term in Eq. (2) and its influence on the rise ofthe temperature of pool’s water.

At this point it is important to point out that in heat gainsthe direct radiation into the pool water is very significant, itis more significant than the thermal power supplied by thesolar field. Concerning energy losses, it stands out the largeevaporation losses when the pool does not have the cover, afact that is mitigated when the pool has the thermal blanket toreduce losses and results in an increment of the water temper-atures. Figure 8 shows the difference at night with cover (or-ange) and without cover (green). For example, in the coldermonths when the pool is covered during the night it reachesa maximum temperature of 27.4◦C and without cover it willreach 22.9◦C, there is almost 5◦C difference. This shows theimportance of a thermal blanket to minimize losses duringthe night.

4. Conclusions

We have developed a transient thermal model in theReynosa’s sports Center pool.

The model indicates that using the existing solar field thepool can achieve good water temperatures, close to comfort-able temperatures.

A gain from direct radiant heat is more important thanthose obtained by their solar water heaters.

Rev. Mex. Fis. S59 (1) (2013) 173–178

178 P. SALGADO, R. DORANTES, G. ORELLAN, A. LOPEZ, M. JIMENEZ, H. GONZALEZ, AND J. RAMIREZ

The evaporative heat loss is very important and we needto limit it.

The use of a solar cover is of great importance to achievethe required comfort temperatures in the pool.

Acknowledgments

The authors thank the authorities, officials and employees ofDeportivo Reynosa, Azcapotzalco Delegation in Mexico City

for their support. Also thank the Institute for Science andTechnology of the Federal District (ICyT) by financially sup-porting this project. Finally, the authors make special thanksto our dear UAM-A for all the support provided: technical,human and financially speaking.

1. Hydraulic and Thermal Evaluation of the field of solar collec-tors of Olympic pool. 33Proceedings of the National Solar En-ergy Week, (Guadalajara, Mexico, 2009).

2. O. G. Jimenez,Terminal Project Mechanical Engineer(UAM-A, June 24, 2009).

3. J.A. Manrique†, Solar Energy, (Editorial Harla, Mexico, 2000).

4. Duffie and Beckmann,Solar engineering for thermal processes(John Wiley and Sons. 1980).

Rev. Mex. Fis. S59 (1) (2013) 173–178