Thermal performance prediction of outdoor swimming pools

Building and Environment 160 (2019) 106167

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Thermal performance prediction of outdoor swimming pools a

a

b

a

c

d

D. Lovell , T. Rickerby , B. Vandereydt , L. Do , X. Wang , K. Srinivasan , H.T. Chua

T d,*

a

Department of Mechanical Engineering, University of Western Australia, 35 Stirling Hwy, Perth, WA, 6009, Australia ETH Zurich, Institut für Energietechnik, Sonneggstrasse 3, 8092, Zürich, Switzerland School of Engineering, University of Tasmania, Private Bag 65, Hobart, TAS, 7001, Australia d Department of Chemical Engineering, University of Western Australia, 35 Stirling Hwy, Perth, WA, 6009, Australia b c

A R T I C LE I N FO

A B S T R A C T

Keywords: Swimming pool Heat and mass transfer Heating capacity Geothermal

The sizing of water heating plants for outdoor community swimming pools conventionally relies on empirical methods and industry guidelines that seldom account for local climatic conditions. In the absence of a model that accounts for all modes of heat and mass transfer, the prediction of water temperature of an outdoor pool and hence the sizing of the heating plant can result in either significant over or under estimation which could impact on not only capital and operating costs but also on complying with environmental accountability and control strategy. The model developed herein accounts for numerous contributors to the thermal energy balance of pool water, notable among them being free and forced convection heat and mass transfer to/from pool and radiation cooling to the sky. Cloud and rain effects are also incorporated into the model. The role of solar and ambient weather conditions is emphasised. The first-principle and analytical model has been calibrated against data from an Olympic sized swimming pool in Perth, Australia. A comparison between various models in the literature shows that the present model is able to replicate experimental data much more closely than others, with 82% of the results being within ± 0.5 °C of the actual measured pool temperatures and with 67% of the predicted heating capacities being within ± 100 kW of the measured heating capacities.

1. Introduction Swimming pools are places where health, entertainment and recreation on one hand and energy, water and sustainability on the other hand have to be intricately balanced. The present trend of many governmental agencies is to make community swimming pools available to users throughout the year. Fédération Internationale de Natation (FINA) stipulates that the temperature of swimming pool water be maintained in the range of 25–28 °C [1] and for 50-m size pools the water inflow-outflow should be 220–250 m3/h. The range of temperature control becomes critical during winter. Specifically, in the southern region of Australia, a large number of cold fronts sweep through most of the populated areas and that period is also the rainy season. There are a number of outdoor Olympic size pools which are well patronised. Blazquez et al. [2] presented a CFD based evaporation rate calculation scheme for indoor swimming pools and estimated that about 60% of the total energy requirements of the facility was contributed by evaporation and ventilation. As a result, the importance of energy consumption to combat evaporative heat loss cannot be overemphasised. In addition, another environmental facet, namely, freshwater needs to maintain the pool water levels despite evaporation compounds the problem. Zuccari

*

et al. [3] enumerated various contributors to heating inventories in the Italian capital territory and concluded that 60% of it was due to water evaporation. A congruent factor is the consumption of 16 million m3 of water/year from the public drinking water system. It is evident that outdoor community swimming pools require substantially sized heating plants to maintain water at a desired temperature in winter. Conventionally, gas fired water heating systems are used to provide the required thermal energy. The emphasis on the reduction of greenhouse gas emissions has driven several other modes for deriving this heat, among which, geothermal water aquifers [4,5]. The Western Australian terrain is endowed with expansive shallow geothermal aquifers. Tepid groundwater (~46 °C) at a depth of ~1 km is sourced for pool heating and spent groundwater is returned to a shallower depth within the same aquifer through a pair of bore holes that are judiciously spaced apart to prevent thermal breakthrough [6,7]. Despite obvious capital costs, geothermal systems are preferred in Australia as they do not occupy large land areas as opposed to solar energy applications. Ground source heat pumps [8,9] and solar energy [10,11] are other sources explored in the past. While ideally renewable energy sources should be the sole means of heating for large pools, invariably, traditional fuel fired boilers are still

Corresponding author. E-mail address: [email protected] (H.T. Chua).

https://doi.org/10.1016/j.buildenv.2019.106167 Received 31 March 2019; Received in revised form 22 May 2019; Accepted 27 May 2019 Available online 07 June 2019 0360-1323/ © 2019 Elsevier Ltd. All rights reserved.

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Nomenclature

t U W

pool surface area (m2) empirical coefficients for evaporation losses cloud cover rating of the sky at a given time (oktas or tenths) coefficient for the determination of viscosity of dry air effect a scaling effect that occurs due to shading specific heat (kJ/kg⋅K) binary diffusion coefficient for water and air at 1 atm (m2/ s) irradiance (W/m2) view factor Grashof number heat transfer coefficient (W/m2⋅K) heat of vaporisation of water at pool temperature (kJ/kg) length of the pool (m) mass flow rate of water (kg/s) wind modification multipliers for terrain and height molecular weight of water (18 g/mol) empirical indices for evaporation losses mass transfer rate (kg/s) Nusselt number pool perimeter (m) pressure (kPa) Prandtl number thermal energy transfer rate (kW) universal gas constant (J/mol·K) characteristic gas constant of air (J/kg·K) characteristic gas constant of water vapour (J/kg·K) Rayleigh number Reynolds number Schmidt number Sherwood number temperature (K)

A a, b C8, C10 Ca Ccloud cp DAB E F Gr h hfg L m˙ M Mw n n Nu P p Pr Q R Ra Rw Ra Re Sc Sh T

temperature (°C) wind speed (m/s) width of pool (m)

Greek symbols α ε ρ σ φ ω η

absorptivity of the pool emissivity of the pool density (kg/m3) Stefan-Boltzmann constant (W/m2⋅K4) relative humidity (%) humidity ratio of air (kg/kg) viscosity of air (Pa⋅s)

Subscripts AS3634 a dew diff evap conv f fc nc hx,o m MSL rad ref refill sat s w ∞

Australian Standard 3634 air dew point diffuse evaporation convection film forced convection natural convection heat exchanger outlet mass transfer mean sea level radiation reference refill water saturated interface of pool water and air water free stream air

obtain a pragmatic pool heating capacity model, which can then be used to design an alternative energy system that will contribute toward a more sustainable and eco-friendly swimming pool sans sacrificing user comfort. This paper introduces a model based on evaporation and convection heat transfer incorporating the ephemeral wind direction, the radiative shielding by surrounding structures (especially podiums) and a facile precipitation model that will handle the mitigating effect of precipitation on radiative cooling. The present model is verified against experimental data from a geothermally heated Olympic sized swimming pool gathered over 27 months from March 2016 to December 2018, with a hiatus from March 2018 to September 2018 when the pool heating system underwent refurbishment [17]. The present model is also benchmarked against other models in vogue [11–13,15]. While the current analysis focuses on outdoor swimming pools, the present findings can be applied to other contained water systems such as aquaculture which require a stable temperature of 28 °C [18].

aplenty to supplement heating demands during colder periods. Fundamentally, this contingency stems from the inaccuracies in estimating the heating capacity of an outdoor pool exposed to highly hostile wind speeds and clear sky conditions, which are typical in Australia. To date, the methodologies for sizing the heating capacity of outdoor pools are primarily empirical [12–15], and they are seldom location specific. Further, the application of such methodologies outside geographical area of well documented ambient conditions could lead to large inaccuracies of heating plant size. A review by Jamenez et al. [16] concludes that there is a lack of a standard method for calculating losses in a pool, especially in terms of quantifying evaporation losses. There is an imminent need for generating models that calculate heat loss due to evaporation, with the aim of generating a standard model capable of delivering values closer to reality. The models should strive, above all, to solve evaporation losses in occupied outdoor and indoor pools. In the absence of a first-principle model which can predict the water temperature of an outdoor pool, deliberate over/under sizing of the heating system cannot be reliable. This will not only impact the commercial aspects but also the thermal comfort of users and control strategy of the pool water temperature. The conventional wisdom is to oversize conventional gas heating means, when boilers are comparatively cheap and fuel costs are also low. On the contrary undersized systems are the result of optimistic estimate of performance of alternative energy systems where capital costs are significant. Hence it is not uncommon to observe that large outdoor pools that adopt alternative energy systems struggle to maintain the desired temperature. In light of the above survey, the primary objective herein is to

2. Modelling evaporation and heat transfer The pool heating inventory shown in Fig. 1 has the following components Eq. (1)

Qpool = Qevap + Qconv + Qcond + Qrad + Qrefill − Qsolar

(1)

which is analogous to the one used by Ref. [3]. Conduction heat loss is negligible compared to other modes of heat loss [3], and commonly regarded as less than 1% of the total heat loss from the pool [13,14], as the present Olympic-sized pool is wet decked and set belowground as in Fig. 2 and hence will be neglected. A detailed 2

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Table 1 Values of a, b and n in eq (2) used by the various evaporation models. Model

a

b

n

McMillan [12] Woolley et al. [13] Hahne and Kübler [14] Richter [15] ASHRAE [20] AS3634 [24]

0.0360 0.0360 0.0803 0.0423 0.0890 0.0506

0.0250 0.0250 0.0583 0.0565 0.0782 0.0669

1 1 1 0.5 1 1

heat/mass transfer coefficients is prevalent and is consistently applied to evaporative losses in the generic form shown below [14] with velocity, U, in m/s and hevap in W/m2⋅Pa, which enables the evaporation mass transfer calculations, as follow Eqs. (2) and (3).

Fig. 1. Outdoor swimming pool heating capacity with approximate distributions of losses based on the present study.

hevap = a + bU n

(2)

Qevap = hevap A (pw, s − p∞ )

(3)

Evidently, coefficient a in eq (2) accounts for the case of free convection mass transfer. Table 1 lists the values of a and b as used by several researchers. AS 3634 [24] follows a different procedure for wind speed adjustment factor to account for the attenuation at the pool surface compared to meteorological measurement similar to AS/NZS 1170.2 [25] as follows Eq. (4).

UAS3634 = 0.15UBOM

(4)

The wind speed, UAS3634, is the adjusted near-surface value based on the meteorological data at site, UBOM, as supplied by the Bureau of Meteorology (BOM). For the method of AS3634, the wind speed adjustment method prescribed therein (as per eq. (4)) is exclusively implemented. For all other models (and the present model), the wind speed adjustment method will be described later. The present model calculates the evaporation rate from basic mass transfer considerations assuming thermodynamic equilibrium at the airwater interface at the pool surface. 2.1.1. Forced convection mass transfer For the selected site, the surrounding buildings, drainage system around the pool and other significant constructions result in the flow conditions being turbulent, and hence the appropriate empirical correlations have been used. The mass transfer coefficient therein is obtained from Sherwood number which is correlated as shown below [26] Eq. (5).

Sh = 0.037Re 0.8Sc1/3

(5)

For the calculation of Schmidt number, the diffusion coefficient for moist air is expressed as follows [27] Eq. (6). Fig. 2. Views of Beatty Park 50 m 10 lane outdoor swimming pool (circled in red in (b)) with depths from 1.2 to 1.8 m [17]. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

DAB =

1.049 × 10−4T1.774 f 1000pMSL

(6)

where Tf is the average of pool surface and free stream air temperatures in K. The Reynolds number needs a detailed treatment as it involves the velocity near the surface of water and a characteristic length that depends on the angle of incidence of wind. A detailed derivation of the angle-of-incident dependent correlations is given in the supplementary material of this article. The basic Reynolds number definition based on pool length is retained.

discussion on other contributors follows. 2.1. Evaporation (Qevap) Several researchers [11,19–22] dealing with this mode of heat transfer had concluded that it was the major contributor to the total heat load and required special attention. The evaporation has two components, one stemming from forced convection when there is a finite wind velocity and another from free convection, which is independent of wind velocity. Sartori [23] provided a comprehensive review of equations for the calculation of evaporation rates. The use of empirical formulae for the evaluation of evaporative

2.1.2. Wind speed adjustment The wind speed data are obtained from the Bureau of Meteorology (BOM) website which is based on measurements at a height of 10 m above sea level. This has to be corrected for the pool surface. The terrain specific multipliers are given in Table 2. 3

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The free stream moist air density, ρa,∞, is also determined analogously with temperature and humidity values being that of free stream air. Since the pool surface is horizontal, the following characteristic length has been adopted [12] Eq. (17).

Table 2 Terrain category multipliers [25]. Height (m)

Category 1

Category 2

Category 3

Category 4

≤3 10

0.61 0.71

0.48 0.60

0.38 0.44

0.35 0.35

(17)

Lnc = A/ P

Free convection mass transfer coefficient is then calculated from the Sherwood number which is in turn used along with eq (13) or (14) to evaluate the free convection mass transfer Eq. (18).

For the suburban location of Beatty Park Leisure Centre (Fig. 2b), the corrections are as per category 3 terrain. The multipliers for the terrain classifications are applied as follows Eq. (7).

U=

n w, s = hevap, nc A (ρw, s − φρw, ∞)

M3, cat 3 UBOM M10, cat 3

(7)

Subsequently, the heat transfer due to this mass transfer is evaluated as follows Eq. (19).

A crucial factor is the choice of characteristic length used in the Reynolds number. This has to be the length in the direction of wind which is highly variable. When the wind direction is not along the pool's length or width, the variability of the wind path across the pool has to be accounted for. A salient feature of this analysis is that the primary Reynolds number is defined based on the pool length and adjustment factors are calculated based on the angle of incidence of the wind (details are in supplementary material). The angles used in the present analysis are defined in Table 3. For those angles the correction factors are calculated as shown in the supplementary material and the summary of forced convection evaporation heat transfer equations is given below. For angle of incidence of θ = 22.5° or 45° Eq. (8),

Qevap, fc = 2cm [W sin(θ)]9/5 + dm W 4/5 [L − W tan(θ)]cos1/5 (θ)

Qevap, nc = n w, s hfg

This also has two components, namely due to forced and free convection. For convection heat transfer calculations, various groups used the Bowen ratio [29]. McMillan [12], ASHRAE [20] and AS3634 [24] used the following empirical relation for the heat transfer coefficient Eq. (20).

where U is m/s and hconv in W/m ⋅K. The convection thermal energy transfer rate can then be determined as follows Eq. (21). 2

(8)

p Qconv t − ta ⎞ = CBowen a ⎜⎛ w ⎟ Qevap pref ⎝ pw, s − pw, ∞ ⎠

4/5

0.37 2 ⎤ (ρw, s − φρw, ∞) DAB Sc1/3 Re 4/5 ⎡ ⎢ 9 ⎣ sin(2θ) ⎥ ⎦

hfg

(10)

Just as the Reynolds number, the characteristic length of the Sherwood number is retained as the length of the pool, L. 2.1.3. Free convection mass transfer When assessing the experimental data of pool temperatures, it was found that a perfunctory treatment of free convection proved to be a significant reason for deviations in heat and mass transfer. Hence it was decided to include its full effects in the calculation scheme. The Rayleigh mass transfer number is defined in the conventional way as below Eq. (12).

2.3. Forced convection heat transfer

(12)

The effects of wind directions are treated exactly the same way as for forced convection mass transfer. Here the Sherwood number is replaced by the Nusselt number and Schmidt number by Prandtl number in eq (5) such that Eq. (23)

It is used to evaluate the Sherwood number for mass transfer based on the following conditions Eqs. (13) and (14) (13)

If 107 < Ram < 1011, Sh = 0.15Ram1/3

(14)

The corresponding forced convection heat transfer equivalence are reproduced below. For angle of incidence of θ = 22.5° or 45° Eq. (24),

3 g (ρa, s − ρa, ∞) Lnc

ρa, ∞ ν 2

Table 3 Summary of wind angles at the pool as a function of wind directions.

(15)

The density for moist air at the surface, ρa,s, is determined as follows [28] Eq. (16).

ρa, s =

ρa, dry (1 + ωs ) 1 + ωs (Rw / Ra)

(23)

Nu = 0.037Re 0.8Pr 1/3

The Grashof number required therein is evaluated as follow [26] Eq. (15).

Gr =

(22)

Although these methods lead to good results at specific sites, extending them as a rule may be associated with limited success. Thus, it is imperative that such empirical models have to account for site-specific correlations. In the absence of which one may resort to the best fitting correlations from the literature [9]. The models of McMillan [12], Woolley et al. [13], Richter [15], ASHRAE [20] and AS3634 [24] are chosen for comparison with the present results for evaporation and convection heat transfer. In addition a common solar irradiance, radiation heat loss and precipitation model are also taken into account.

(11)

If 10 4 < Ram < 107, Sh = 0.54Ram1/4

(21)

Woolley et al. [13] used the same methodology via an explicit application of the Bowen ratio, with CBowen being 61.3 Pa/°C [29] Eq. (22).

(9)

where Eqs. (10)and (11)

Ram = Gr Sc

(20)

hconv = 3.1 + 4.1U

Qconv = hconv A (tw − ta)

Qevap, fc = cm [L cos(θ)]9/5 + dm WL4/5 [1 − 1/tan(θ)]sin1/5 (θ)

dm = 0.037(ρw, s − φρw, ∞) DAB Sc1/3Re 4/5hfg

(19)

2.2. Convection heat transfer (Qconv)

For angle of incidence of θ = 67.5° Eq. (9),

cm =

(18)

(16) 4

Wind angle, θ

Wind direction (as recorded by BOM)

22.5° 45° 67.5°

NNE, ENE, SSW, WSW N, E, S, W ESE, SSE, WNW, NNW

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Qconv, fc = 2cfc [W sin(θ)]9/5 + dfc W 4/5 [L − W tan(θ)]cos1/5 (θ)

surrounding structures provide a shielding effect to radiative heat transfer to the sky and attenuate radiative heat transfer considerably. The calculation scheme is given in the supplementary material.

(24)

For angle of incidence of θ = 67.5°Eq 25,

Qconv, fc = cfc [L cos(θ)]9/5 + dfc WL4/5 [1 − 1/tan(θ)]sin1/5 (θ)

(25) 2.7. Water refill

whereEqs. (26) and (27) 4/5

cfc =

0.37 2 ⎤ (tw − t∞) ka, f Pr 1/3 Re 4/5 ⎡ ⎢ 9 ⎣ sin(2θ) ⎥ ⎦

dfc = 0.037(tw − t∞) ka, f

Pr 1/3Re 4/5

The need for water refill to the pool arises for two reasons. The first and major one is due to the evaporation losses as described above and the second minor one is due to skin surface adhesion with users. Typically, the temperature of refill water is 20 °C. Accordingly the heating requirements for the refill process is as follow Eq. (34).

(26) (27)

For the Nusselt number the characteristic length is retained as the length of the pool, L. The thermophysical properties of moist air are consulted from Ref. [30].

Qrefill = (nfc + nnc ) cp, w (tw − trefill )

2.4. Free convection heat transfer

2.8. Solar radiation (Qsolar)

This item is also treated the same way as the one described for mass transfer in section 2.1.3 with the Sherwood number being replaced by Nusselt number and Schmidt number by Prandtl number in eqs 12–14, so that Eq. (28)

Both the beam and diffuse components of solar radiation are taken into account. Apart from the geothermal heat source, this is the main heat gain of the pool. The procedure is largely based on ASHRAE methodology [33]. The sum of beam component normal to the pool surface and diffuse component need to be adjusted to account for the effect of cloud cover Eq. (35).

Qnc = hnc A (tw − t∞)

(28)

2.5. Combination of free and forced convection heat and mass transfer

Qsolar = αpool A (Ebeam + Ediffuse ) Ccloud effect

Free convection heat and mass transfer have a standalone contribution to total heat and mass transfer as well as a synergetic contribution to forced convection heat and mass transfer. The synergetic effect of forced and free convection heat and mass transfer is determined by combining the respective contributions through a power law relation as given below [26]Eqs. (29a) and (29b). 7/2 7/2 Qconv = (Qconv , fc + Qconv, nc ) 7/2 7/2 Qevap = (Qevap , fc + Qevap, nc )

7/2

7/2

2.8.1. Cloud cover adjustment The BOM cloud cover data are available in octas (C8) twice daily at 9 am and 3 pm whereas the model requires data at 30 min intervals. It was therefore assumed that the cloud cover between 12 midnight to 9 am is as at 9am and that between 3 and 12 midnight is that at 3pm. Between 9 am and 3 pm, a linear trend was assumed. The cloud cover expression was developed by considering the ratio measurements over clear sky reference values from the literature and plotting against the cloud coverage in octas [34]. Then a third order polynomial was fitted to allow for interpolation so as to retrieve the cloud cover values, as follows Eq. (36)

(29a) (29b)

The radiative losses are calculated as follow Eq. (30). 4 σεw A (Tw4 − Tsky )(1 − Fw − structure )

(1 − εw )(1 − Fw − structure ) + εw

(30)

Ccloud effect = −0.0024C83 + 0.0108C82 − 0.0242C8 + 1.0001

The emissivity of the pool surface εw is taken as 0.96. The temperature of the sky is determined as a function of ambient free stream air temperature and sky emissivity as shown below [31] Eq. (31).

Tsky = (εsky T∞4 )1/4

(31)

A schematic of the water circulation system is shown in Fig. 4. When the pool water temperature drops below 26.0 °C, pump P2 turns on automatically, which is activated by an on-off control. The pool water is then passed through a heat exchanger with the tepid groundwater being the heating medium. This groundwater at approximately 50 °C is pumped up from the bore hole. Accordingly the heat transfer rate is calculated as follows Eq. (37).

(32)

The clear sky emissivity in the above equation is determined as shown below [31] Eq. (33).

T εcs = 0.787 + 0.764 ln ⎛ dew ⎞ ⎝ 273.15 ⎠

(36)

2.9. Geothermal heating effects

The emissivity of sky is derived from the clear sky emissivity based on the cloud cover as expressed in oktas (C8), which is made available by BOM Eq. (32).

εsky = εcs (1 + 0.17792C8 − 0.224C82 + 1.4336C83)

(35)

The shading by the surrounding podium has been accounted for by considering its angular relationship with the pool, so that the beam radiation will only be considered when the altitude of the solar disk is more than 0.16 rad after sunrise and 0.28 rad before sunset.

2.6. Radiative losses (Qrad)

Qrad =

(34)

˙ p, w (Thx , o − Tw ) Qgeo = mc

(33)

(37)

Table 4 Dimensions of pool sides for view factor calculations.

2.6.1. View factor The pool is surrounded by several structures on each side as seen in Fig. 2 and their dimensions are shown in Table 4, which is to be read in conjunction with Fig. 3. The view factor from the pool to the proximate structures is calculated following Gross et al. [32], which results in being 31%. The 5

Side

Length (m)

Height (m)

1 2 3 4

62.0 61.5 62.0 61.5

18 18 18 9

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Table 5 Beatty park pool parameters. Length (m)

50

Width (m) Average depth (m) Set temperature of pool (°C) Pool pump design flowrate (l/s) Pool orientation (0° is E-W) Latitude Longitude Height above MSL (m) Total volume (m3) Annual rainfall (mm)

25.5 1.5 26.5 8.5 45° −31.9°S 115.85°E 24 1912 786

temperature which are set at a constant flow rate of 8.5 l/s. The key pool information is outlined below in Table 5. All the required parameters were recorded at half hourly intervals over a substantial period from March 2016 to December 2018, with a hiatus from March 2018 to September 2018 when the pool heating system underwent refurbishment. Thermistors are used for temperature measurements which have an uncertainty of ± 0.2 °C. 3.1. Weather data The local meteorological data which are required as inputs, were obtained from BOM which operates the nearest Perth Metro weather station to Beatty Park Leisure Centre.

Fig. 3. Orientation of the pool for calculation of view factors.

4. Results and discussion 4.1. Temperature prediction model comparison The first objective of the model is to compare it against experimental pool temperature data collected from a pool described above from March 2016 to February 2018. In Fig. 5, all the models are compared with measured data of water temperature during a typical winter month of June 2017. On average, there were about 23 swimmers per hour in the pool during the winter months. Evidently, the effect of users in the pool has not been actively incorporated in all the models, including the present model. Regardless, the present model broadly tracks the measured values to within experimental uncertainties. The AS3634 model [24] consistently overpredicts the water temperature while the ASHRAE model [20] underpredicts it. The Woolley et al. model [13] overestimates the pool temperature by about 2 °C. The McMillan and Richter models [12,15], while predicting values quite close to the measured temperatures, suffer from variances that are larger than that of the present model. In June 2017, rainfall occurred from 7pm on 21st to 8am on 22nd. During this period the present model is able to track the water temperatures fairly well. Fig. 6 shows the corresponding heat exchanger water supply temperature to the pool during the same period as in Fig. 5. As mentioned before, the pool pump is subject to on-off control, the effect of which is reflected in the intermittency of the heat exchanger water supply temperature. However, it is evident that the water supply temperature remains constant at ostensibly 42 °C when the pool pump is fully activated. Consistently, when the pool pump is dormant, the heat exchanger water supply temperature reduces to ostensibly 26.5 °C. This temporal series of water supply temperature is applied commonly to all the pool models so as to achieve a consistent comparison. The histograms in Fig. 7 demonstrate another facet of the temperature variations for each of the models against the recorded pool temperature. The frequency covers all the data recorded over experimental days stretching over many months. The present model can be seen to be fairly consistent with 82% of all the data being within ±

Fig. 4. The Process & Instrumentation Diagram of the geothermal heating system.

2.10. Precipitation Earlier models in the literature have seldom given a detailed treatment of the effects of rain. Precipitation affects solar inputs and radiative cooling losses. In the present model, during precipitation, the direct beam radiation is considered to be fully absorbed by the raindrops and only the diffuse radiation is assumed to be absorbed by the pool. During precipitation, the raindrops are assumed to be at ambient temperature and act as a blackbody to effectively shield the pool from the cold sky. Ignoring the insignificant radiative heat exchange between the pool and raindrops, during precipitation, there will be no radiative cooling. 3. Description of the experimental swimming pool The analytical model described above is verified against experimental data from a 50-m outdoor swimming pool at Beatty Park Leisure Centre in Perth, Western Australia. This swimming pool does not use a pool cover. The pool uses a geothermal system to heat the pool water when the temperature of the pool water falls below the set point. A conventional boiler supplements further heat inventories. An on-off control strategy has been adopted for the pumps to achieve the set pool 6

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Fig. 5. Comparison of measured water temperatures with calculations from various models during June 2017. Legend: ─── – measured; ─●─ – present model;×– [12]; —♦— – [13]; * – [15]; ──▪── – [20]; •••▲••• – [24].

The diurnal solar radiation inputs are cyclic, with some days peaking at a lower value due to rain/overcast conditions. Under minimal inputs from the solar component, the geothermal heating system is seen to cover the heating requirements, especially when the evaporative losses are large. Convection and radiation losses are fairly constant, but evaporative losses tend to fluctuate primarily due to the varying wind speed. The energy implication of water refill is insignificant and hence not shown in this figure. The histograms of differences between measured and predicted heating demands for the various models over the entire period of experimentation are shown in Fig. 9. Again it can be seen that the present model has a high frequency around zero deviation and the distribution is fairly Gaussian. Note that the comparison with experimental heating capacities can only be done when the geothermal pump is switched on at a period when the pool is in use, so that the number of data sets is a lot lesser than that for Fig. 7, which was obtained over a 24/7 basis on a half hourly interval. Table 7 compares the success of the various models in terms of their percentages of the difference between modeled and experimental heating capacities being within ± 100 kW, which essentially stem from the different treatment of evaporation by the various models.

0.5 °C of the measured temperature. The McMillan model (tile B in Fig. 6) [12] is the second best with 62% of the results being within the same ± 0.5 °C range. The AS3634 model [24] over-predicts the pool temperature which could result in under-sizing of the pool heating plant. Conversely, the ASHRAE model [20] under-predicts the temperature which may result in over-sizing of the pool heating plant. The consequences of over and under sizing will be demonstrated in the next section. Table 6 compares the success of the various models in terms of their percentages of the differences between modeled and measured pool water surface temperatures being within ± 0.5 °C, which essentially stem from the different treatment of evaporation by the various models. 4.2. Heating capacity prediction comparison All the six models considered above were used to transform the temperature deviations to heating requirements over the winter season as this time of the year has the largest heating requirement. A consolidated distribution of the various contributors to heating over a few days in a typical winter month (June 2017) is shown in Fig. 8.

Fig. 6. The temporal evolution of the heat exchanger water supply temperature to the pool during June 2017. Its intermittency reflects the on-off control strategy of the pool pump. 7

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Fig. 7. Frequency distribution of variations between the various models and measured pool water surface temperatures. In all the figures the abscissa is the variation in temperature in °C and the ordinate is frequency. Legend: A: Present model, B: [12]; C: [13]; D: [15]; E: [20]; F [24].

the present model can be expected to significantly reduce design margins of heating plant capacity which are otherwise conventionally applied to compensate for uncertainties in calculations by various empirical models.

Table 6 Comparison of the accuracy of the various models in predicting the pool water surface temperature to within ± 0.5 °C of the measured heating capacity. Model

%

Present McMillan [12] Woolley et al. [13] Richter [15] ASHRAE [20] AS3634 [24]

82 62 46 54 2 7

4.3. Free convection contribution During winters, the contribution to the total heat loss due to evaporation, convection and radiation is approximately 59%, 20% and 21% respectively as shown below in Fig. 11. The total energy loss due to evaporation is due to both forced and free evaporation, with free evaporation amounting to 75% that of forced evaporation. Also the total energy loss due to pure convection heat loss is due to both forced and free convection, with free convection amounting to 81% that of forced convection. Importantly, the total energy loss is not a simple linear summation of both the apparent forced and free components, rather the latter two are combined via a power-law relation as per equation (29a and b). The results shown in Fig. 11 for losses due to evaporation heat transfer qualitatively reaffirm previous literature results which predict them to be 50–60% of total losses [3]. The conventional methods of assigning a constant empirical value is inadequate to capture the significant effects of free convection heat and mass transfer (See Section 1.2.1). Table 8 shows how the different models predict the effects of free convection over a winter that is averaged over the winters of 2016 and 2017. Comparing the various models, the present model is the most successful. It correctly models the changing behaviour of free convection heat and mass transfer over the seasons resulting in its producing the most accurate pool temperature prediction, with 82% of the results being within ± 0.5 °C, and 67% of the results being within ± 100 kW. It is often appreciated that energy and water are intricately interlinked. The heat and mass transfer analysis presented herein can be transformed to calculate the water consumption to compensate for

The prediction of pool heating capacity is the key issue from the energy and efficiency point of view. Fig. 10 shows a distribution of heating plant capacity requirements according to the various models over the course of one year. The present model predicts a distinct peak at 550 kW, while for example, in the ASHRAE model [20] (tile E in Fig. 10), even though the peak heating capacity is also at 550 kW, the large variance does not help with engineering decision making in terms of the designed heating capacity to anticipate the variation in climatic conditions. Interestingly, the standing AS3634 significantly under predicts the peak load, which is consistent with its systematic under prediction of the heating capacity by 100 kW as in Fig. 9 Tile F. The model of Richter [15] significantly over predicts the peak load, again, this is consistent with its systematic over prediction of the heating capacity by 100 kW as in Fig. 9 Tile D. The histogram format of presenting predicted pool heating capacity provides a user friendly facet of design and operation of heating plant for pools. Maximum, minimum, range and frequency of their occurrence can help in formulating an automated control strategy. It also helps to decide if one has to go for a baseload plant supplemented by peak load ones and configure their tandem operation. In this context,

8

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Fig. 8. Calculated and measured heat flow distributions over a few days in June 2017. Legend: ─•──: Solar radiation; —▪—: geothermal heating; •••▲•••: convection; × : radiation; –◆–: evaporation.

5. Conclusions

evaporation losses. Over the two winters of 2016 and 2017 alone (months of June–August) it averages to about 827 klitres per winter. This is equivalent to a daily consumption of about 38 households in Perth metro area as per the statistics of Water Corporation [35].

A model has been developed to predict the swimming pool water temperature and estimate the heating plant capacity of an outdoor Olympic-sized swimming pool under active use. The results are

Fig. 9. Frequency distribution of variations between a model and measured heating capacity demands. In all the figures the abscissa is the variation between measured and calculated heating demands (kW) and the ordinate is frequency. Legend: A: Present model, B: [12]; C: [13]; D: [15]; E: [20]; F [24]. 9

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Table 7 Comparison of the accuracy of the various models in predicting the heating capacity of the pool to within ± 100 kW of the measured heating capacity. Model

%

Present McMillan [12] Woolley et al. [13] Richter [15] ASHRAE [20] AS3634 [24]

67 47 52 58 26 58

Fig. 11. Comparison of contributions to heat loss mechanisms in a winter, averaged over the winters of 2016 and 2017. The percentage above the column indicate the relative contribution of a particular heat loss mechanism.

compared with the measured data over a period ranging from March 2016 to December 2018, with a hiatus from March 2018 to September 2018 when the pool heating system underwent refurbishment. 82% of the results are within ± 0.5 °C of the actual measured pool temperatures and 67% within ± 100 kW of the measured heating capacities. The strength of the model arises from

Table 8 Comparison of the heat losses due to free convection effecta according to the various models.

Convection (kW) Evaporation (kW) Total (kW)

(a) consideration of diurnal variance in meteorological data, (b) assessment of heat and mass transfer explicitly accounting for wind directions, (c) segregation of free and forced convection effects on heat and mass transfer, (d) accounting for the effects of precipitation on solar insolation, and (e) appropriation of radiative heat loss due to adjacent structural shading.

Present model

[12]

[13]

[15]

[20]

[24]

76.2 206.2 282.4

64.5 119.5 184.0

48.9 149.2 198.1

76.2 155.9 232.0

59.7 250.0 309.8

75.1 241.8 316.9

a Note that in the present model, the actual heat losses need to be ascertained together with forced convection effect according to equation (29a and b).

that, broadly, evaporation cooling constitutes the dominant share of the energy bill. Radiative and sensible convection cooling also contribute significantly to the heating capacity of the pool. When viewed with the requirements of makeup water to compensate for evaporative losses which is invariably potable water, one can understand the magnitude of swimming pool operation from the energy and water aspects.

This model is benchmarked against several models existing in the literature through data collected over 27 months from a swimming pool located at Beatty Park Leisure Centre in Perth, Australia. In line with qualitative predictions of other researchers it can be concluded again

Fig. 10. Frequency distribution of heating plant capacity needs over one year. In all the figures the abscissa is calculated heating capacity (kW) and the ordinate is frequency. Legend: A: Present model, B: [12]; C: [13]; D: [15]; E: [20]; F [24]. 10

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Funding This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. Acknowledgement The authors gratefully acknowledge the generous assistance of Mr. David Lister, Facilities Manager at Beatty Park Leisure Centre, for kindly availing the pool performance data for the present study. Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.buildenv.2019.106167. References [1] Fédération Internationale de Natation (FINA), Swimming pool certification guide, [Online]. Available: https://www.fina.org/sites/default/files/fina_certificate_fr2. pdf. [2] J.L.F. Blázquez, I.R. Maestre, F.J.G. Gallero, P.Á. Gómez, A new practical CFD-based methodology to calculate the evaporation rate in indoor swimming pools, Energy Build. 149 (2017) 133–141. [3] F. Zuccari, A. Santiangeli, F. Orecchini, Energy analysis of swimming pools for sports activities: cost effective solutions for efficiency improvement, Energy Procedia 126 (2017) 123–130. [4] Swim Club, Australian swimming pool, [Online] Available at http://www. swimclub.com.au/pool/QLD_pools/y_qld_swimming_pools.htm (2017) , Accessed date: 28 October 2017. [5] M. Pujol, R.P. Ludovic, G. Bolton, 20 years of exploitation of the Yarragadee aquifer in the Perth basin of Western Australia for direct-use of geothermal heat, Geothermics 57 (2015) 39–55. [6] A. Christ, B. Rahimi, K. Regenauer-Lieb, H.T. Chua, Techno-economic analysis of geothermal desalination using hot sedimentary aquifers: a pre-feasibility study for Western Australia, Desalination 404 (2017) 167–181. [7] X. Wang, A. Bierwirth, A. Christ, P. Whittaker, K. Regenauer-Lieb, H.T. Chua, Application of geothermal absorption air-conditioning system: a case study, Appl. Therm. Eng. 50 (2013) 71–80. [8] A. Chiasson, Residential Swimming Pool Heating with Geothermal Heat Pump Systems, Geo-Heat Center, Oregon Institute of Technology, Klamath Falls, OR, 2005. [9] A. Hepbasli, L. Ozgener, Development of geothermal energy utilization in Turkey: a review, Renew. Sustain. Energy Rev. 8 (2004) 433–460. [10] M. Dongellini, S. Falcioni, A. Martelli, G.L. Morini, Dynamic simulation of outdoor swimming pool solar heating, Energy Procedia 81 (2015) 1–10. [11] E. Ruiz, P.J. Martinez, Analysis of an open-air swimming pool solar heating system by using an experimentally validated TRNSYS model, Sol. Energy 84 (2010) 116–123.

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