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Feasibility study of a PCM storage tank integrated heating system for outdoor swimming pools during the winter season
Accepted Manuscript Research Paper Feasibility study of a PCM storage tank integrated heating system for outdoor swimming pools during the winter season Yantong Li, Gongsheng huang, Huijun Wu, Tao Xu PII: DOI: Reference:
S1359-4311(17)35952-5 https://doi.org/10.1016/j.applthermaleng.2018.02.030 ATE 11812
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
15 September 2017 2 January 2018 9 February 2018
Please cite this article as: Y. Li, G. huang, H. Wu, T. Xu, Feasibility study of a PCM storage tank integrated heating system for outdoor swimming pools during the winter season, Applied Thermal Engineering (2018), doi: https:// doi.org/10.1016/j.applthermaleng.2018.02.030
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Feasibility study of a PCM storage tank integrated heating system for outdoor swimming pools during the winter season
Yantong LIa, Gongsheng HUANGa*, Huijun WUb, Tao XUb a
Department of Architecture and Civil Engineering, City University of Hong Kong Tat Chee Avenue, Kowloon, Hong Kong b
School of Civil Engineering, Guangzhou University, Guangzhou 510006, China
*The corresponding author; Tele 852-34422408; Fax 852-34420427; Email: [email protected]
ABSTRACT This feasibility study explores a heating system for outdoor swimming pools with applications for winter in subtropical weather conditions. The proposed heating system integrates air-source heat pumps, a PCM storage tank, and a thermal insulation cover; the novelty is that the storage tank is used to completely shift electrical demand from on-peak to off-peak periods, making outdoor swimming pools economically viable during the winter season. The configuration, operation, and control of the heating system are illustrated in detail. Its technical and economic feasibility is analyzed from the aspects of control performance, energy performance, thermal comfort, and economic performance by comparing it with a traditional heating system that uses electrical boilers for its heat supply. Case studies show that the proposed heating system can reduce operating costs significantly, suggesting its potential for application to outdoor swimming pools in subtropical climates during the winter.
Keywords: PCM storage tank; Air-source heat pump; Feasibility study; Swimming pool; Heating
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1. Introduction In many countries, swimming is one of the most popular sports, and both indoor and outdoor swimming pools can be found worldwide. However, in countries with cold seasons, there is often a heavy demand for heat to maintain water temperatures within a comfortable range, leading to very high operating costs if electrical or gas boilers are used, especially for outdoor pools [1, 2]. Therefore, many outdoor pools are closed during the cold season, including in Hong Kong, wasting facilities and space.
To enable outdoor swimming pools to become more available during the cold season, several techniques have been proposed. The simplest one uses a thermal insulation cover, as suggested by the United States Department of Energy (DOE) [3]. According to the DOE [3], thermal insulation covers can significantly reduce evaporation loss and loss attributed to radiation, with the former comprising 70% of total heat loss and the latter almost 20% during the night. Pools are covered at night when low ambient temperatures prevail, or generally when the pool is out of use. Mousia et al. [4] analyzed energy consumption in outdoor swimming pools in different climate zones in Greece and found that average energy consumption could be reduced from 2456.16 kWh/m2 to 1827.45 kWh/m2 by using thermal insulation covers. In addition, two types of thermal insulation covers, transparent and opaque, were compared by Francey et al. [5], who showed that transparent covers were more effective at absorbing solar energy to heat pools.
Thermal insulation covers can definitely reduce heat loss from outdoor swimming pools, but they cannot generate heat. Thus, during cold seasons, low ambient temperatures mean that a heat supply is necessary. Many methods have been developed to supply heat to outdoor swimming pools, such as the use of geothermal heat [6] and biomass heat [7], with the most popular being solar energy. Alkham et al. [8], for example, used a solar heat collector with flat plate collectors to provide heat to an outdoor Olympic size swimming pool in Miami, United States, but concluded that their solar-assisted heating system was not economical over 10 years. Cunio et al. [9] investigated the effects of reduced flow rates on the performance and
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effectiveness of domestic unglazed, uninsulated pool solar collector heaters and found that the use of a low-power pump to reduce the flow rate through a typical pool solar thermal collector was feasible. Rakopoulos et al. [10] also used a solar heat collector to supply heat to the Athens Olympic swimming pool. Buonomano et al. [11], studied a photovoltaic thermal collector that was applied to an outdoor swimming pool in Italy. They analyzed the effect of the photovoltaic thermal collector field area, the water tank volume, and the pump flow rate on the economic performance of the system and concluded that incentive policies would be required to enhance the economic profitability of this heating system. Tagliafico et al. [12] proposed a solar-assisted heat pump for heating outdoor swimming pools, which included a water-to-water heat pump and a solar collector. Climatic data from all Italian municipalities were used to evaluate the system’s primary energy saving capacity. The authors concluded that this capacity could be well correlated with degree days, as determined by the cities’ geographic locations.
The efficiency of solar energy depends on the availability and intensity of solar radiation. In cities like Hong Kong, crowded with tall buildings, the use of solar energy has been confronted with many obstacles, such as unstable solar intensity and solar radiation as a result of sunlight being blocked by neighboring tall buildings. To overcome this problem, air-source heat pumps have gained attention for their ability to supply heat to outdoor swimming pools. Considering the subtropical weather conditions (the average outdoor temperature in the winter season varies from 15°C to 20°C), Lam et al. [13, 14] used air-source heat pumps to provide heat for the outdoor pool of a four-star Hong Kong hotel. The swimming pool had a surface area of 35 m2 and a volume of 52 m3. The heat pump’s coefficient of performance (COP) was used to calculate the system’s economic index. Their work showed that the use of a heat pump system with a COP of 3.5 would lead to annual savings of about 75% over a traditional electric boiler. Lopez et al. [15] experimentally investigated an air-source heat pump to heat the swimming pool of the Aquatic Center of Azcapotzalco; they focused on an analysis of the COP curve of the air-source heat pump in different weather conditions.
Following the work of Lam et al. [13], this study proposes a new heating system for outdoor
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swimming pools for cold season application in subtropical weather conditions. The proposed system integrates an air-source heat pump (for heat supply), a phase change material (PCM) storage tank (for heat storage), and a thermal insulation cover (for heat maintenance). The configuration, operation and control of the proposed heating system is illustrated below in detail. Its technical and economic feasibility is analyzed for control performance, energy performance, thermal comfort, and economic performance by comparing it with a traditional heating system that uses electrical boilers for its heat supply.
This study is not the first to use PCM for thermal comfort in outdoor swimming pools. Zsembinszki et al. [16] previously considered its use. In their work, PCM was used to reduce the temperature variation of an outdoor pool in Spain. Compared with their work, the novelty of the proposed heating system is that a PCM thermal storage tank is used to completely shift the electrical demand of the air-source heat pumps from on-peak to off-peak periods. Combined with an insulation layer, the proposed system can reduce operation costs and make outdoor swimming pools in subtropical districts economically viable. In addition, this study establishes a general method and platform to analyze the technical and economic feasibility of the proposed heating system, which in turn provide guidelines for the design and use of the proposed heating system for outdoor swimming pools.
The remainder of this paper is organized as follows. Section 2 describes the proposed heating system. Section 3 shows the method used to analyze the technical and economic feasibility of the proposed system. Section 4 provides a case study, and concluding remarks are presented in Section 5.
2. System description 2.1 System configuration The proposed heating system consists mainly of air-source heat pumps, a PCM storage tank, heat exchangers, a thermal insulation cover, pumps, and valves. Fig. 1 is a schematic diagram of the system. The functions of the key components are listed below.
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Air-source heat pumps are used to collect heat from the ambient air. Considering the load variation, multiple heat pumps should be adopted to guarantee the efficient operation of the heat pumps at partial load conditions and to increase operating flexibility.
A PCM storage tank is used to store the heat collected from the air-source heat pumps and to discharge heat into the swimming pool as necessary. The PCM storage tank aims to shift the energy consumed during on-peak electrical periods to off-peak periods when the price of electricity is lower, thereby reducing utility costs.
A thermal insulation cover covers the swimming pool when it is not in use to reduce heat loss.
Fig. 1. Schematic of the proposed heating system for outdoor swimming pools
Tables 1 and 2 summarize the important time frames and rated operations, respectively, of the main components over a 24-hour operation cycle. The swimming pool is open from
5
to
and is covered with an insulation layer from
to
and from
to
(the start of the
next period). The PCM storage tank is charged by the air-source heat pumps to the rated maximum temperature (
) from
discharged into the swimming pool from
to
. The heat stored in the storage tank is
to
to maintain the water temperature at the
desired comfort level. The air source heat pumps are switched on from , when they are used to heat the thermal storage tank, and from
to to
: from
to
, when they are
used to preheat the swimming pool.
Table 1 Important time frames within a 24-hour period PCM charging starts
Swimming pool preheating starts
On-peak electrical use starts
Swimming pool open starts
Swimming pool close starts
Off-peak electrical use starts
Table 2 Rated operations of the main components within a 24-hour period →
→
→
→
→
→ (next)
cover with insulation Swimming pool
cover with insulation layer
open layer
PCM storage tank
charge
Air-source heat pump
on
idle
discharge
on
idle off
Fig. 2 shows the rated temperature profile of the swimming pool. temperature of the swimming pool water (for example, 28°C).
is the design
indicates the temperature
decrease from heat loss when the swimming pool is not in use.
is the increase in
temperature once the pool is preheated, and it is expected that the set of temperature reach a design point when the swimming pool reopens.
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can help the
Fig. 2. Rated temperature profile of the swimming pool 2.2 Sizing of main components The sizing procedure of the main components is explained below. First, the thermodynamic model of an outdoor swimming pool is identified and validated, which is then used to predict the hourly heating load during the open period ( → ) when the water temperature is maintained at the design point (
). Because the heat loss that occurs during the open
period is affected significantly by the weather conditions, the worst-case scenario for the weather conditions should be considered. Thus, design days should be introduced into the sizing procedure.
The hourly heating loads during the open period ( → ) on the design days are used to calculate the maximum heat energy needed for the thermal comfort of the swimming pool. The maximum heat energy is the amount of heat energy that should be stored in the PCM storage tank, and thus it can be used to determine the size of the tank. The heat energy stored in the PCM storage tank should be calculated according to the temperature difference between the swimming pool’s design temperature
(indicating that the tank is fully
discharged) and the rated maximum temperature that can be provided by the air-source heat pumps
(indicating that the tank is fully charged), shown in Eq. (1). (1)
where and
and
are the specific heat of the PCM and water, respectively;
are the mass of PCM and water in the PCM storage tank, respectively; and
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is the specific enthalpy of the PCM.
Because air-source heat pumps are used to charge the PCM storage tank during the charging period ( → ) and to provide the heat necessary to the swimming pool during the preheating period ( → ), they should be sized according to the power requirements from these two processes. For the PCM storage tank charging process, it is assumed that the temperature will be raised from
during this period ( → ), based on the minimum
to
power requirements for the heat pumps that can be estimated, denoted as
and
calculated by (2) For the swimming pool preheating process, it is assumed that the pool’s water temperature will be raised from
during this period ( → ), based on
to
the minimum power requirements for the heat pumps that can be estimated, denoted as and calculated by (3) where
and
are the specific heat and density of water, respectively;
volume of the swimming pool; and
is the
is the maximum heat energy loss of the
swimming pool during the preheating period ( → ). The larger value of
and
is used to size the total capacity of the heat pumps. By using the thermodynamic model of the swimming pool and the insulation property of the insulation cover layer, both the maximum heat energy lost during the pool’s preheating period ( → ) and the drop and rise in its temperature (
and
) can be predicted.
2.3 Thermal properties of thermal insulation cover The thermal insulation cover used in this study is inflatable (Fig. 3). The thicknesses of the upper layer, air layer, and lower layer are 5 mm, 10 mm, and 5 mm, respectively. The insulation material is a type of low-density polyethylene, and its thermal properties are shown in Table 3.
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Fig. 3. Schematic diagram of the inflatable thermal insulation cover
Table 3 Thermal properties of low-density polyethylene Properties
Value
Thermal conductivity ( Density (
)
0.36 920
)
Specific heat (
)
Emissivity coefficient
2.3 0.93
Effective solar absorptance coefficient 0.92
2.4 Control strategy Three basic controls are used in the proposed system: (i) the PCM storage charging control; (ii) the swimming pool preheating control; and (iii) the swimming pool water temperature control used during the open period.
An on/off controller is used for the PCM storage charging control. At time
, the air-source
heat pumps and their associated pumps are switched on to charge the PCM storage tank. The temperature of the tank is monitored. When the temperature reaches its design value (i.e., the rated maximum temperature that can be provided by the air-source heat pumps), the air-source heat pumps are switched off.
Another on/off controller is used for the swimming pool preheating control. At time
, the
air-source heat pumps and their associated pumps are switched on to preheat the swimming pool, and the temperature of the pool is measured. When the temperature reaches , the air-source heat pumps are switched off.
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A PI controller is used for the swimming pool water temperature control during its open period. The PI controller adjusts the water flow rate through the PCM storage tank to collect and deliver heat to the swimming pool so that the water temperature is maintained at its design value
. The water temperature is continuously measured and compared with
the design value, and the error between them is inputted into the PI controller to calculate the required water flow rate through the PCM storage tank.
3. Methodology used for the feasibility analysis Fig. 4 shows the methodology used to analyze the technical and economic feasibility of the proposed heating system. First, a simulation platform is constructed that integrates the weather data, swimming pool thermodynamic model, heating system models (including heat pumps, PCM thermal storage tank, heat exchangers, and pumps), and system control strategy. Models of the main components are then validated using the available experimental data. Next, the heating system’s control performance is tested to determine which control parameters must be adjusted until the control performance is satisfactory. When the simulation platform is ready, simulations are carried out to generate data for the analysis of the system’s energy performance and its technical and economic feasibility. It should be noted that in system modelling, the time delay and thermal inertia in the heating processes, including the processes of heat collection/supply and charging/discharging, were not considered as they were in the work of [17] because their influence as transients might be insignificant when long-time scale analysis is performed.
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Fig. 4. Method used to study the proposed heating system
3.1 Models of the main components Given that the models of pumps, valves, heat exchangers, and air-source heat pumps have been well studied [18, 19], only the thermodynamic models of the outdoor swimming pool and the PCM thermal storage tank are illustrated.
3.1.1 Outdoor swimming pool thermodynamic model The temperature of an outdoor swimming pool can be calculated with the following equations [6, 11]: (4) where
represents the swimming pool’s temperature, and
represents the
swimming pool’s total heat transfer rate calculated in two cases (shown in Fig. 5): during the open period (without thermal insulation cover) and during the thermal-insulation period (with thermal insulation cover).
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Fig. 5. Heat transfer of the swimming pool: (a) open period; and (b) thermal-insulation period
During the open period, the total heat transfer rate of the swimming pool is determined as: (5) where
and
are the heat gain and heat loss of the swimming pool, respectively.
The heat gain
is calculated by: (6)
where
and
are the heat flow rate from the heat exchanger connected to the PCM
storage tank and solar heat, respectively. The heat gain from solar heat is calculated by: (7) where
is the surface area of the swimming pool, and
absorptance coefficient, set at 0.85 [14];
is the effective solar
is the solar radiation use efficiency
considering the blockage of solar radiation by neighboring tall buildings; and
is the
solar irradiance.
The total heat loss of the swimming pool is calculated by: (8) where
,
,
,
, and
are the heat loss from evaporation, radiation,
refilling with fresh water, convection and conduction, respectively. Heat loss resulting from refilling with fresh water is calculated by: (9) where
is the mass flow rate of the refilled fresh water; and
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is the temperature of
the fresh water. The evaporative heat loss is determined by: (10) where
is the evaporation heat transfer coefficient;
is the air saturated vapor
pressure of the swimming pool surface temperature; and
is the air partial vapor
pressure of the ambient temperature. The evaporative heat transfer coefficient is determined by [11]: (11) where
is the wind velocity. The radiation heat loss is calculated by the Stefan-
Boltzmann equation, shown below: (12) where
is the water emissivity coefficient set at 0.95 [16, 20];
constant equal to 5.67×10-8W/(m2·K4) [21]; and
is the Stefan-Boltzmann
is the equivalent sky temperature,
calculated by [22, 23]: (13) where Ta is the ambient temperature. The convective heat loss is determined by: (14) where
is the convection heat transfer coefficient between the swimming pool surface and
the ambient environment, calculated by [14]: (15) The conductive heat loss is [24]: (16) where
is the characteristic length of the swimming pool;
conduction heat transfer rate; 0.52
[24].
is the dimensionless
is the thermal conductivity of the soil, assumed to be
is the conductive heat transfer area; and
is the soil temperature.
During the thermal-insulation period, the total heat transfer rate is calculated by: (17) where pumps; and
is the heat flow rate from the heat exchanger connected to the air-source heat is the heat loss from the lower surface of the thermal insulation cover.
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The heat transfer process in the upper or lower layer of the cover is [25]: (18) where
,
,
, and
are the density, specific heat, temperature, and
thermal conductivity of the cover, respectively. The heat transfer process in the air layer between the upper and lower layer of the cover is calculated by: (19) where
,
,
, and
are the density, specific heat, temperature, and thermal
conductivity of the air, respectively.
The boundary conditions of these thermodynamic models are shown as follows. The lower surface temperature of the lower layer satisfies: (20) For the contacting surface between the upper or lower layer and air layer, it is calculated by (21) For the upper surface of the upper layer, it satisfies (22) where
,
, and
are the heat gain from solar, radiative heat loss, and
convective heat loss in the upper surface, respectively. The heat gain from solar in the upper surface is: (23) where
is the effective solar absorptance coefficient of the thermal insulation cover. is the solar radiation use efficiency during thermal-insulation.
The radiative heat loss from the upper surface is: (24) where
is the emissivity coefficient of the thermal insulation cover;
temperature of the upper surface.
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is the
The convective heat loss in the upper surface is: (25) where
is the convection heat transfer coefficient between the upper surface and the
ambient environment, which is [26]: (26) (27) (28) where
,
,
, and
are the Nussle Reynolds, Rayleigh, Grashof, and Prandtl
numbers of the air, respectively; and
is the characteristic length of the upper surface; and
are the constants determined by the status of the air flow.
3.1.2 PCM storage tank thermodynamic model To simplify the mathematical model, the following assumptions are proposed: (1) the temperature of the PCM remains constant during the phase change process; (2) there is no heat loss from the storage tank; (3) no internal heat is generated inside the PCM tubes; (4) only variations in the PCM and water temperature along the water flow direction are considered; (5) the thermophysical properties of PCM and water are not affected by the temperature.
Based on the above assumptions, the governing energy balance equation for the heat transfer process between the PCM and the HTF is [27]: (29) where
is the density of the HTF;
velocity of the HTF;
is the specific heat of the HTF;
is the temperature of the HTF;
is the time;
is the mean
is the water fraction
in the energy storage tank;
is the effective convective heat transfer coefficient between
the HTF and the PCM;
is the heat transfer area of the tube wall;
temperature of the PCM;
is the volume of one element; and x is the distance.
The heat transfer process of the PCM is determined by:
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is the
(30) where
is the density of the PCM, and
is the enthalpy of the PCM. The effective
convective heat transfer coefficient between the HTF and the PCM is: (31) where
,
, and
are the thermal resistance of the HTF, the tube walls, and the PCM,
respectively. The thermal resistance of the PCM is determined by [28]:
(32)
where
and
respectively;
are the solid and liquid thermal conductivities of the PCM, and
are the solid diameters during the solidification process and the
liquid diameters during the melting process, respectively; and
is the inner diameter of the
tube walls.
The convective heat transfer coefficient of the HTF is calculated by [29]: (33) (34) where
,
, and
respectively; and
are the Nussle, Reynolds, and Prandtl numbers of the HTF, is the outer diameter of the tube walls. The finite difference method
can be used to discretize the governing equations [27]; and the discretized algebraic equations can be solved by MATLAB codes.
3.2 Performance indices To study the performance and feasibility of the proposed heating system, the following indices are adopted.
Indices for energy performance The annual energy consumption
is used to evaluate the energy performance of the
proposed system, calculated by:
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(35) where
and
are the annual energy consumption of the air-source heat pumps
and pumps, respectively. To compare with the energy use of a traditional heating system, the energy saving ratio (ESR) is adopted and defined as: (36) where
is the annual energy consumption of the traditional heating system.
Index for technical feasibility The index of total thermal comfort unmet time percentage is adopted to analyze the technical feasibility, defined as the total thermal comfort unmet time divided by the total time of the open period throughout the entire winter. This index indicates the degree to which a system is unable to cater to the thermal comfort demand. The index is expressed as: (37) where
is the total time of the open period.
, either 0 or 1, is the thermal comfort
failure of the system. It is 0 if the thermal comfort is satisfied; otherwise it is 1.
Index for economic performance To analyze the economic performance of the proposed system, its annual operating cost is calculated according to local utility prices. To compare it with the annual operating cost of a traditional heating system, the operating cost saving ratio (OCSR) is used and defined as: (38) where and are the operating costs of the proposed and traditional heating systems, respectively. Based on the annual operating cost savings, the simple payback period ( ) is also calculated, defined as: (39) where
is the initial total investment of the proposed system.
4. Case studies 4.1 Simulation platform
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The outdoor swimming pool considered in this study is located at the City University of Hong Kong. It is 50 m long and 22 m wide with a total volume of 1963.5
. Along its length, for
the first 10 m at both ends, the depth is 1.2 m, and in the middle the depth is 2.5 m, with the transition spread over 15 m. Along its width, the depth changes from 1.2 m to 2.5 m at 7.5 m from both sides. The swimming pool is always closed from the middle of November until the following April due to cold weather.
Table 4 shows the important time frames within the 24-hour operating schedule. The charging start time for the PCM storage tank was set at 21:00 ( ); the swimming pool preheating start time was set at 05:00 (
; the swimming pool open period was set between 12:00 ( ) and
20:00 ( ); and the electrical on-peak start and end times were 09:00 ( ) and 21:00 ( ), respectively.
Table 4 Important time frames in this case study 21:00
05:00
09:00
12:00
20:00
21:00
Table 5 lists the structural parameters of the PCM storage tank. The PCM of sodium acetate trihydrate was selected due to its high latent heat value. The thermophysical properties of sodium acetate trihydrate are given in Table 6 [30].
Table 5 Structural parameters of the PCM storage tank Parameters
Value
Number of PCM tubes
3000
Tube length (m)
2.5
Tube inner diameter (m) 0.098 Tube outer diameter (m) 0.1 Water fraction
0.25
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Table 6 Thermophysical properties of sodium acetate trihydrate [30] Parameters
Value 58
( ) (
)
266
(
)
1450
(
)
1.68
(
)
2.37
(
)
0.43
(
)
0.34
Table 7 Main specification/characteristics of the air-source heat pump unit Item
Unit
Value
Refrigerant
-
R410A
Heating capacity (
)
450
Input power
(
)
81.7
COP
-
Power supply
(
5.5 ) 380-400/50
Table 8 Global configuration table of the heating system Item
Number Rated capacity Rated power
PCM storage tank
1
78.5m3
-
Air-source heat pump
3
450kW
81.7kW
Thermal insulation cover
1
1100m2
-
Pump-I
3
213.9L/s
10kW
Pump-II
3
71.3L/s
4kW
Valve
4
-
-
Controller
2
-
-
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Table 7 gives the main specifications and characteristics of the air-source heat pump unit, and Table 8 shows the heating system’s global configuration table. Hong Kong meteorological data, collected by the Hong Kong Observatory from 2003 to 2012, were used in this study. The meteorological data contains dry-bulb temperatures, wet-bulb temperatures, wind speeds, and solar irradiance.
The simulation platform was established using TRNSYS 17 software as shown in Fig. 6, where Type 941 was used for air-source heat pumps, and Type 741 was adopted for variable speed pumps. The rated flow rate of the discharging pump and the preheating pump were set at 213.9 L/s, and the rated flow rate of the other pumps was set at 71.3 L/s. The heat exchanger was simulated using Type 91, in which the effectiveness of the heat exchanger was assumed to be 0.95. Type 647 and Type 649 were used to model the diverting and mixing valves, respectively. The PID controller for the swimming pool’s water temperature control was simulated using Type 23. The thermodynamic models of the PCM storage tank and the outdoor swimming pool were solved using MATLAB programs, linked into TRNSYS 17 using Type 155, the MATLAB interface.
Fig. 6. Simulation platform constructed in TRNSYS 17
4.2 Model validation The experimental data of Watanabe et al. [29] and Ruiz et al. [20] were used to validate the
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swimming pool and PCM storage tank models, respectively. The values of the parameters and work conditions used in the simulation were the same as those used by Watanabe et al. and Ruiz et al. To describe the accuracy of the adopted models for the outdoor swimming pool and the PCM storage tank, the average relative error (
) between the numerical and
experimental results was used, as defined by: (40) where
is the number of experimental samples;
and
are the experimental and
simulated temperatures, respectively. Fig. 7 gives a temperature comparison in the outdoor swimming pool model. The average relative error (
) was 0.50%, indicating that the
swimming pool model was reliable and accurate.
Fig. 8 shows a comparison of the numerical and experimental results for the PCM storage tank during the charging and discharging processes, where x is the distance from the top of the tank. The calculated
for the thermodynamic model of the PCM storage tank was 3.59%,
indicating that this model was reliable and accurate.
Fig. 7. Comparison between the temperature measured and predicted by the adopted model
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Fig. 8. Comparison between the temperatures measured and predicted by the adopted model: (a) charging process and (b) discharging process
4.2 Control performance analysis After the swimming pool and the PCM storage tank models were validated, the control performance of the proposed heating system was analyzed. The design temperature of the swimming pool was set at 28°C and
, the temperature increase necessary for preheating
was calculated at 0.2°C. Analysis of the pool’s water temperature variation show that the adopted operation and control methods could achieve the water temperature required for the open period.
As an example, Fig. 9 shows the water temperature variation for 1 week (from 05/1, 2012, to 11/1, 2012). Within a 24-hour operating period, starting at 05:00 ( , the moment preheating started), the temperature of the swimming pool rose until it reached 28.2°C (
).
This preheating process normally required 1 to 2 hours. Before the swimming pool opened to swimmers (at 12:00), the pool’s temperature was likely to first decrease from heat loss (although the insulation cover was on the pool) and then increase slightly when the heat gain from solar radiation became greater than the heat loss (05/1 to 08/1, 11/1) or to constantly decrease because the solar heat gain could not cover the heat loss (09/1, 10/1). After the swimming pool opened, the temperature dropped significantly due to evaporation (10/1). Thereafter, the water temperature was maintained at approximately 28°C by the PI controller. During the thermal-insulation period (from 20:00 until 05:00 the next morning), the
22
temperature experienced an average drop of 0.5°C before preheating due to the insulation cover
Fig. 9. Water temperature variation of the swimming pool within a week
The corresponding heat flow rates are shown in Fig. 10, where
is the heat flow rate
inside the heat exchanger connecting the air-source heat pumps and the swimming pool, and is the heat flow rate inside the heat exchanger connecting the PCM storage tank and the swimming pool. The heat flow rate of the swimming pool
was positive (heat gain)
when preheating, slightly negative (heat loss) during the thermal-insulation period, and maintained at approximately 0 (heat balanced) when the swimming pool was open.
Fig. 10. Variations in the heat flow rate during a week
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Fig. 11 shows the corresponding PCM liquid fraction. The liquid fraction decreased when the PCM storage tank was discharging and increased when the tank was charging. Because the PCM tank was sized using the worst-case scenario, the PCM tank did not fully discharge every day (but it was fully charged every day due to the control methods adopted). In this example, the PCM tank was fully discharged on only 2 days (06/1 and 07/1), and on other days it was partially discharged.
Fig. 11. Variation in PCM liquid fraction in the PCM storage tank in a week
4.3 Energy performance analysis Fig. 12 shows the annual energy use of the traditional and the proposed systems, where the traditional system used an electrical boiler to provide heat and a thermal insulation cover when the swimming pool was closed. The maximum annual energy use of the proposed system
was 8.76×108 kJ (occurring in 2010); the minimum was 8.18×109 kJ (occurring
in 2008); and the average was 8.42×108 kJ. The maximum annual energy use of the traditional system
was 3.65×109 kJ (in 2004); the minimum was 3.49×109 kJ (in 2009); and the
average was 3.57×109 kJ. Fig. 12 also shows the energy saving ratio ( for each year. The maximum
, defined by Eqn. 36)
was 77.03% (in 2007); the minimum was 75.66% (in
2010); and the average was 76.40%. Thus, the proposed system achieved significant energy savings.
24
Fig. 12. Annual energy use comparison between the traditional and proposed systems (numbers in brackets are energy saving ratios)
4.4 Technical feasibility analysis Fig. 13 shows the total thermal comfort unmet time percentage ( for the years 2003 to 2012. All
, defined by Eqn. 37)
values during these years were lower than 1%, which
means that the capacity of the proposed system could satisfy the requirements for thermal comfort. The maximum
was 0.40% (in 2010); the minimum was 0.00% (in 2006 and
2012); and the average was 0.10%.
25
Fig. 13. Total thermal comfort unmet time percentage (
) of the proposed system
4.5 Economic feasibility analysis The initial cost of the proposed system was estimated at around HK$2,016,348 according to the price quoted in the Chinese market for the major components, shown in Table 9. The majority of funds were allocated to the air-source heat pumps and the PCM storage tank, and the price of the selected PCM was HK$2250.8
, referring to [30].
Table 9 Costs of the main components of the proposed system Item
Value
PCM storage tank (
)
Air-source heat pump ( Thermal insulation cover ( Pump ( Controller (
)
190,498 )
1,709,000 )
35,000 30,600
)
Total investment (
51,250 )
2,016,348
To calculate the annual operating cost, the electricity price was referred to the bulk tariff of a local power company (CLP Hong Kong), which consisted of demand and energy charges [31], shown in Table 9. Fig. 14 shows the operating costs of the traditional and the proposed systems. The maximum operating cost for the traditional system
26
was HK$1,440,096 (in
2010); the minimum was HK$1,336,354 (in 2008); and the average was HK$1,381,543. The maximum operating cost for the proposed system
was HK$218,774 (in 2010); the
minimum was HK$204,253 (in 2008); and the average was HK$210,842. The daily average for the proposed and traditional systems was HK$1,396 and HK$9,149 respectively. Fig. 14 also shows the yearly operating cost saving ratios (
, defined by Eqn. 38). The maximum
was 84.98% (in 2012); the minimum was 84.49% (in 2004); and the average was 84.74%. The calculated simple payback period (
) was 1.72 years, suggesting that the
investment could be paid back over a short period of time. Thus, considerable economic benefits were derived from the proposed heating system.
Fig. 14. Annual cost comparison between the traditional and proposed systems (numbers in brackets are operational cost saving ratios)
Table 8 Electricity price referred to the bulk tariff in the CLP [31] On-peak period Demand charge
Range (
)
Off-peak period
Charge (
)
Range (
)
Charge (
)
[0, 650)
68.4
[0, don-peak)
0
[650, ∞)
65.4
[don-peak, ∞)
26.8
27
Energy charge
Range (
)
Charge (
)
Range (
)
Charge (
)
[0, 200000)
0.738
-
0.661
[200000, ∞)
0.722
-
-
don-peak: on-peak billing demand
5. Conclusions In this study, a heating system for outdoor swimming pools with winter application for subtropical weather conditions was proposed. The proposed system integrates a PCM thermal storage tank, air-source heat pumps and a thermal insulation cover and aims to completely shift the electrical demand from on-peak to off-peak periods, thereby rendering outdoor swimming pools economically viable during the winter season. Case studies have shown that the proposed system, with its sizing and control method, can guarantee the thermal comfort of outdoor swimming pools during winter because the total unmet thermal comfort time percentage can be maintained, on average, at around 0.10%. Compared with a traditional heating system that uses an electrical boiler, the average energy saving ratio can reach 76.40%, and the average operating cost saving ratio can reach 84.74%. Therefore, the proposed outdoor swimming pool heating system is feasible in both technical and economic aspects for winter application in subtropical weather conditions.
Acknowledgement The work described in this paper was supported by the Campus Sustainability Fund of the City University of Hong Kong (No. 6986039) and the Guangdong Basic and Applied Basic Research Fund (No. 2015A030313814).
References [1] R.M. Lazzarin, G.A. Longo, Comparison of heat recovery systems in public indoor swimming pools, Applied Thermal Engineering, 16 (1996) 561-570. [2] W.-S. Lee, C.-K. Kung, Optimization of heat pump system in indoor swimming pool using particle swarm algorithm, Applied Thermal Engineering, 28 (2008) 1647-1653.
28
[3] DOE USA, availble at https://energy.gov/energysaver/swimming-pool-covers, in. [4] A. Mousia, A. Dimoudi, Energy performance of open air swimming pools in Greece, Energy and Buildings, 90 (2015) 166-172. [5] J. Francey, P. Golding, R. Clarke, Low-cost solar heating of community pools using pool covers, Solar Energy, 25 (1980) 407-416. [6] A. Somwanshi, A.K. Tiwari, M.S. Sodha, Feasibility of earth heat storage for all weather conditioning of open swimming pool water, Energy Conversion and Management, 68 (2013) 89-95. [7] D.A. Katsaprakakis, Comparison of swimming pools alternative passive and active heating systems based on renewable energy sources in Southern Europe, Energy, 81 (2015) 738-753. [8] A. Alkhamis, S. Sherif, Performance analysis of a solar-assisted swimming pool heating system, Energy, 17 (1992) 1165-1172. [9] L. Cunio, A. Sproul, Performance characterisation and energy savings of uncovered swimming pool solar collectors under reduced flow rate conditions, Solar Energy, 86 (2012) 1511-1517. [10] C. Rakopoulos, E. Vazeos, A model of the energy fluxes in a solar heated swimming pool and its experimental validation, Energy Conversion and Management, 27 (1987) 189-195. [11] A. Buonomano, G. De Luca, R.D. Figaj, L. Vanoli, Dynamic simulation and thermo-economic analysis of a PhotoVoltaic/Thermal collector heating system for an indoor–outdoor swimming pool, Energy Conversion and Management, 99 (2015) 176-192. [12] L.A. Tagliafico, F. Scarpa, G. Tagliafico, F. Valsuani, An approach to energy saving assessment of solar assisted heat pumps for swimming pool water heating, Energy and Buildings, 55 (2012) 833-840. [13] W.W. Chan, J.C. Lam, Energy-saving Supporting Tourism Sustainability: A Case Study of Hotel Swimming Pool Heat Pump, Journal of Sustainable Tourism, 11 (2003) 74-83. [14] J.C. Lam, W.W. Chan, Life cycle energy cost analysis of heat pump application for hotel swimming pools, Energy Conversion and Management, 42 (2001) 1299-1306. [15] R. López, M. Vaca, H. Terres, A. Lizardi, J. Morales, S. Chávez, Experimental evaluation of a heat pump for the water-supply heating of a public swimming pool, in:
Journal of Physics: Conference Series, Vol. 792, IOP
Publishing, 2017, pp. 012020. [16] G. Zsembinszki, M.M. Farid, L.F. Cabeza, Analysis of implementing phase change materials in open-air swimming pools, Solar Energy, 86 (2012) 567-577. [17] Y. Allouche, S. Varga, C. Bouden, A.C. Oliveira, Dynamic simulation of an integrated solar-driven ejector
29
based air conditioning system with PCM cold storage, Applied Energy, 190 (2017) 600-611. [18] A. Handbook, Refrigerants, in, ASHARE, 2001. [19] T.D. TRNSYS, TRNSYS, 2012, Available at http://sel.me.wisc.edu/trnsys., in. [20] E. Ruiz, P.J. Martínez, Analysis of an open-air swimming pool solar heating system by using an experimentally validated TRNSYS model, Solar Energy, 84 (2010) 116-123. [21] Z. Jiang, K. Wang, H. Wu, Y. Wang, J. Du, A two-dimensional analytical model for prediction of the radiation heat transfer in open-cell metal foams, Applied Thermal Engineering, 93 (2016) 1273-1281. [22] C. Harrington, M. Modera, Swimming pools as heat sinks for air conditioners: California feasibility analysis, Energy and Buildings, 59 (2013) 252-264. [23] J. Woolley, C. Harrington, M. Modera, Swimming pools as heat sinks for air conditioners: Model design and experimental validation for natural thermal behavior of the pool, Building and Environment, 46 (2011) 187-195. [24] T.L. Bergman, F.P. Incropera, Fundamentals of heat and mass transfer, John Wiley & Sons, 2011. [25] X. Jin, M.A. Medina, X. Zhang, Numerical analysis for the optimal location of a thin PCM layer in frame walls, Applied Thermal Engineering, 103 (2016) 1057-1063. [26] T. İnan, T. Başaran, M.A. Ezan, Experimental and numerical investigation of natural convection in a double skin facade, Applied Thermal Engineering, 106 (2016) 1225-1235. [27] S. Wu, G. Fang, Dynamic performances of solar heat storage system with packed bed using myristic acid as phase change material, Energy and Buildings, 43 (2011) 1091-1096. [28] M.A. Kibria, M.R. Anisur, M.H. Mahfuz, R. Saidur, I.H.S.C. Metselaar, Numerical and experimental investigation of heat transfer in a shell and tube thermal energy storage system, International Communications in Heat and Mass Transfer, 53 (2014) 71-78. [29] T. Watanabe, H. Kikuchi, A. Kanzawa, Enhancement of charging and discharging rates in a latent heat storage system by use of PCM with different melting temperatures, Heat Recovery Systems and CHP, 13 (1993) 57-66. [30] J. Pereira da Cunha, P. Eames, Thermal energy storage for low and medium temperature applications using phase change materials – A review, Applied Energy, 177 (2016) 227-238. [31]
CLP
tariff
structure,
available
at
/business-and-other-customers/bulk-tariff, in.
30
https://www.clp.com.hk/en/customer-service/tariff
Highlights
PCM integrated heating system for outdoor swimming pool for winter use is studied The electrical load is shifted from on-peak period to off-peak period The technical and economic feasibility analysis of the proposed system is conducted Compared with traditional heating system energy can be saved by 76.40% Compared with traditional heating system operational cost can be saved by 84.74%
31
S1359-4311(17)35952-5 https://doi.org/10.1016/j.applthermaleng.2018.02.030 ATE 11812
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
15 September 2017 2 January 2018 9 February 2018
Please cite this article as: Y. Li, G. huang, H. Wu, T. Xu, Feasibility study of a PCM storage tank integrated heating system for outdoor swimming pools during the winter season, Applied Thermal Engineering (2018), doi: https:// doi.org/10.1016/j.applthermaleng.2018.02.030
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Feasibility study of a PCM storage tank integrated heating system for outdoor swimming pools during the winter season
Yantong LIa, Gongsheng HUANGa*, Huijun WUb, Tao XUb a
Department of Architecture and Civil Engineering, City University of Hong Kong Tat Chee Avenue, Kowloon, Hong Kong b
School of Civil Engineering, Guangzhou University, Guangzhou 510006, China
*The corresponding author; Tele 852-34422408; Fax 852-34420427; Email: [email protected]
ABSTRACT This feasibility study explores a heating system for outdoor swimming pools with applications for winter in subtropical weather conditions. The proposed heating system integrates air-source heat pumps, a PCM storage tank, and a thermal insulation cover; the novelty is that the storage tank is used to completely shift electrical demand from on-peak to off-peak periods, making outdoor swimming pools economically viable during the winter season. The configuration, operation, and control of the heating system are illustrated in detail. Its technical and economic feasibility is analyzed from the aspects of control performance, energy performance, thermal comfort, and economic performance by comparing it with a traditional heating system that uses electrical boilers for its heat supply. Case studies show that the proposed heating system can reduce operating costs significantly, suggesting its potential for application to outdoor swimming pools in subtropical climates during the winter.
Keywords: PCM storage tank; Air-source heat pump; Feasibility study; Swimming pool; Heating
1
1. Introduction In many countries, swimming is one of the most popular sports, and both indoor and outdoor swimming pools can be found worldwide. However, in countries with cold seasons, there is often a heavy demand for heat to maintain water temperatures within a comfortable range, leading to very high operating costs if electrical or gas boilers are used, especially for outdoor pools [1, 2]. Therefore, many outdoor pools are closed during the cold season, including in Hong Kong, wasting facilities and space.
To enable outdoor swimming pools to become more available during the cold season, several techniques have been proposed. The simplest one uses a thermal insulation cover, as suggested by the United States Department of Energy (DOE) [3]. According to the DOE [3], thermal insulation covers can significantly reduce evaporation loss and loss attributed to radiation, with the former comprising 70% of total heat loss and the latter almost 20% during the night. Pools are covered at night when low ambient temperatures prevail, or generally when the pool is out of use. Mousia et al. [4] analyzed energy consumption in outdoor swimming pools in different climate zones in Greece and found that average energy consumption could be reduced from 2456.16 kWh/m2 to 1827.45 kWh/m2 by using thermal insulation covers. In addition, two types of thermal insulation covers, transparent and opaque, were compared by Francey et al. [5], who showed that transparent covers were more effective at absorbing solar energy to heat pools.
Thermal insulation covers can definitely reduce heat loss from outdoor swimming pools, but they cannot generate heat. Thus, during cold seasons, low ambient temperatures mean that a heat supply is necessary. Many methods have been developed to supply heat to outdoor swimming pools, such as the use of geothermal heat [6] and biomass heat [7], with the most popular being solar energy. Alkham et al. [8], for example, used a solar heat collector with flat plate collectors to provide heat to an outdoor Olympic size swimming pool in Miami, United States, but concluded that their solar-assisted heating system was not economical over 10 years. Cunio et al. [9] investigated the effects of reduced flow rates on the performance and
2
effectiveness of domestic unglazed, uninsulated pool solar collector heaters and found that the use of a low-power pump to reduce the flow rate through a typical pool solar thermal collector was feasible. Rakopoulos et al. [10] also used a solar heat collector to supply heat to the Athens Olympic swimming pool. Buonomano et al. [11], studied a photovoltaic thermal collector that was applied to an outdoor swimming pool in Italy. They analyzed the effect of the photovoltaic thermal collector field area, the water tank volume, and the pump flow rate on the economic performance of the system and concluded that incentive policies would be required to enhance the economic profitability of this heating system. Tagliafico et al. [12] proposed a solar-assisted heat pump for heating outdoor swimming pools, which included a water-to-water heat pump and a solar collector. Climatic data from all Italian municipalities were used to evaluate the system’s primary energy saving capacity. The authors concluded that this capacity could be well correlated with degree days, as determined by the cities’ geographic locations.
The efficiency of solar energy depends on the availability and intensity of solar radiation. In cities like Hong Kong, crowded with tall buildings, the use of solar energy has been confronted with many obstacles, such as unstable solar intensity and solar radiation as a result of sunlight being blocked by neighboring tall buildings. To overcome this problem, air-source heat pumps have gained attention for their ability to supply heat to outdoor swimming pools. Considering the subtropical weather conditions (the average outdoor temperature in the winter season varies from 15°C to 20°C), Lam et al. [13, 14] used air-source heat pumps to provide heat for the outdoor pool of a four-star Hong Kong hotel. The swimming pool had a surface area of 35 m2 and a volume of 52 m3. The heat pump’s coefficient of performance (COP) was used to calculate the system’s economic index. Their work showed that the use of a heat pump system with a COP of 3.5 would lead to annual savings of about 75% over a traditional electric boiler. Lopez et al. [15] experimentally investigated an air-source heat pump to heat the swimming pool of the Aquatic Center of Azcapotzalco; they focused on an analysis of the COP curve of the air-source heat pump in different weather conditions.
Following the work of Lam et al. [13], this study proposes a new heating system for outdoor
3
swimming pools for cold season application in subtropical weather conditions. The proposed system integrates an air-source heat pump (for heat supply), a phase change material (PCM) storage tank (for heat storage), and a thermal insulation cover (for heat maintenance). The configuration, operation and control of the proposed heating system is illustrated below in detail. Its technical and economic feasibility is analyzed for control performance, energy performance, thermal comfort, and economic performance by comparing it with a traditional heating system that uses electrical boilers for its heat supply.
This study is not the first to use PCM for thermal comfort in outdoor swimming pools. Zsembinszki et al. [16] previously considered its use. In their work, PCM was used to reduce the temperature variation of an outdoor pool in Spain. Compared with their work, the novelty of the proposed heating system is that a PCM thermal storage tank is used to completely shift the electrical demand of the air-source heat pumps from on-peak to off-peak periods. Combined with an insulation layer, the proposed system can reduce operation costs and make outdoor swimming pools in subtropical districts economically viable. In addition, this study establishes a general method and platform to analyze the technical and economic feasibility of the proposed heating system, which in turn provide guidelines for the design and use of the proposed heating system for outdoor swimming pools.
The remainder of this paper is organized as follows. Section 2 describes the proposed heating system. Section 3 shows the method used to analyze the technical and economic feasibility of the proposed system. Section 4 provides a case study, and concluding remarks are presented in Section 5.
2. System description 2.1 System configuration The proposed heating system consists mainly of air-source heat pumps, a PCM storage tank, heat exchangers, a thermal insulation cover, pumps, and valves. Fig. 1 is a schematic diagram of the system. The functions of the key components are listed below.
4
Air-source heat pumps are used to collect heat from the ambient air. Considering the load variation, multiple heat pumps should be adopted to guarantee the efficient operation of the heat pumps at partial load conditions and to increase operating flexibility.
A PCM storage tank is used to store the heat collected from the air-source heat pumps and to discharge heat into the swimming pool as necessary. The PCM storage tank aims to shift the energy consumed during on-peak electrical periods to off-peak periods when the price of electricity is lower, thereby reducing utility costs.
A thermal insulation cover covers the swimming pool when it is not in use to reduce heat loss.
Fig. 1. Schematic of the proposed heating system for outdoor swimming pools
Tables 1 and 2 summarize the important time frames and rated operations, respectively, of the main components over a 24-hour operation cycle. The swimming pool is open from
5
to
and is covered with an insulation layer from
to
and from
to
(the start of the
next period). The PCM storage tank is charged by the air-source heat pumps to the rated maximum temperature (
) from
discharged into the swimming pool from
to
. The heat stored in the storage tank is
to
to maintain the water temperature at the
desired comfort level. The air source heat pumps are switched on from , when they are used to heat the thermal storage tank, and from
to to
: from
to
, when they are
used to preheat the swimming pool.
Table 1 Important time frames within a 24-hour period PCM charging starts
Swimming pool preheating starts
On-peak electrical use starts
Swimming pool open starts
Swimming pool close starts
Off-peak electrical use starts
Table 2 Rated operations of the main components within a 24-hour period →
→
→
→
→
→ (next)
cover with insulation Swimming pool
cover with insulation layer
open layer
PCM storage tank
charge
Air-source heat pump
on
idle
discharge
on
idle off
Fig. 2 shows the rated temperature profile of the swimming pool. temperature of the swimming pool water (for example, 28°C).
is the design
indicates the temperature
decrease from heat loss when the swimming pool is not in use.
is the increase in
temperature once the pool is preheated, and it is expected that the set of temperature reach a design point when the swimming pool reopens.
6
can help the
Fig. 2. Rated temperature profile of the swimming pool 2.2 Sizing of main components The sizing procedure of the main components is explained below. First, the thermodynamic model of an outdoor swimming pool is identified and validated, which is then used to predict the hourly heating load during the open period ( → ) when the water temperature is maintained at the design point (
). Because the heat loss that occurs during the open
period is affected significantly by the weather conditions, the worst-case scenario for the weather conditions should be considered. Thus, design days should be introduced into the sizing procedure.
The hourly heating loads during the open period ( → ) on the design days are used to calculate the maximum heat energy needed for the thermal comfort of the swimming pool. The maximum heat energy is the amount of heat energy that should be stored in the PCM storage tank, and thus it can be used to determine the size of the tank. The heat energy stored in the PCM storage tank should be calculated according to the temperature difference between the swimming pool’s design temperature
(indicating that the tank is fully
discharged) and the rated maximum temperature that can be provided by the air-source heat pumps
(indicating that the tank is fully charged), shown in Eq. (1). (1)
where and
and
are the specific heat of the PCM and water, respectively;
are the mass of PCM and water in the PCM storage tank, respectively; and
7
is the specific enthalpy of the PCM.
Because air-source heat pumps are used to charge the PCM storage tank during the charging period ( → ) and to provide the heat necessary to the swimming pool during the preheating period ( → ), they should be sized according to the power requirements from these two processes. For the PCM storage tank charging process, it is assumed that the temperature will be raised from
during this period ( → ), based on the minimum
to
power requirements for the heat pumps that can be estimated, denoted as
and
calculated by (2) For the swimming pool preheating process, it is assumed that the pool’s water temperature will be raised from
during this period ( → ), based on
to
the minimum power requirements for the heat pumps that can be estimated, denoted as and calculated by (3) where
and
are the specific heat and density of water, respectively;
volume of the swimming pool; and
is the
is the maximum heat energy loss of the
swimming pool during the preheating period ( → ). The larger value of
and
is used to size the total capacity of the heat pumps. By using the thermodynamic model of the swimming pool and the insulation property of the insulation cover layer, both the maximum heat energy lost during the pool’s preheating period ( → ) and the drop and rise in its temperature (
and
) can be predicted.
2.3 Thermal properties of thermal insulation cover The thermal insulation cover used in this study is inflatable (Fig. 3). The thicknesses of the upper layer, air layer, and lower layer are 5 mm, 10 mm, and 5 mm, respectively. The insulation material is a type of low-density polyethylene, and its thermal properties are shown in Table 3.
8
Fig. 3. Schematic diagram of the inflatable thermal insulation cover
Table 3 Thermal properties of low-density polyethylene Properties
Value
Thermal conductivity ( Density (
)
0.36 920
)
Specific heat (
)
Emissivity coefficient
2.3 0.93
Effective solar absorptance coefficient 0.92
2.4 Control strategy Three basic controls are used in the proposed system: (i) the PCM storage charging control; (ii) the swimming pool preheating control; and (iii) the swimming pool water temperature control used during the open period.
An on/off controller is used for the PCM storage charging control. At time
, the air-source
heat pumps and their associated pumps are switched on to charge the PCM storage tank. The temperature of the tank is monitored. When the temperature reaches its design value (i.e., the rated maximum temperature that can be provided by the air-source heat pumps), the air-source heat pumps are switched off.
Another on/off controller is used for the swimming pool preheating control. At time
, the
air-source heat pumps and their associated pumps are switched on to preheat the swimming pool, and the temperature of the pool is measured. When the temperature reaches , the air-source heat pumps are switched off.
9
A PI controller is used for the swimming pool water temperature control during its open period. The PI controller adjusts the water flow rate through the PCM storage tank to collect and deliver heat to the swimming pool so that the water temperature is maintained at its design value
. The water temperature is continuously measured and compared with
the design value, and the error between them is inputted into the PI controller to calculate the required water flow rate through the PCM storage tank.
3. Methodology used for the feasibility analysis Fig. 4 shows the methodology used to analyze the technical and economic feasibility of the proposed heating system. First, a simulation platform is constructed that integrates the weather data, swimming pool thermodynamic model, heating system models (including heat pumps, PCM thermal storage tank, heat exchangers, and pumps), and system control strategy. Models of the main components are then validated using the available experimental data. Next, the heating system’s control performance is tested to determine which control parameters must be adjusted until the control performance is satisfactory. When the simulation platform is ready, simulations are carried out to generate data for the analysis of the system’s energy performance and its technical and economic feasibility. It should be noted that in system modelling, the time delay and thermal inertia in the heating processes, including the processes of heat collection/supply and charging/discharging, were not considered as they were in the work of [17] because their influence as transients might be insignificant when long-time scale analysis is performed.
10
Fig. 4. Method used to study the proposed heating system
3.1 Models of the main components Given that the models of pumps, valves, heat exchangers, and air-source heat pumps have been well studied [18, 19], only the thermodynamic models of the outdoor swimming pool and the PCM thermal storage tank are illustrated.
3.1.1 Outdoor swimming pool thermodynamic model The temperature of an outdoor swimming pool can be calculated with the following equations [6, 11]: (4) where
represents the swimming pool’s temperature, and
represents the
swimming pool’s total heat transfer rate calculated in two cases (shown in Fig. 5): during the open period (without thermal insulation cover) and during the thermal-insulation period (with thermal insulation cover).
11
Fig. 5. Heat transfer of the swimming pool: (a) open period; and (b) thermal-insulation period
During the open period, the total heat transfer rate of the swimming pool is determined as: (5) where
and
are the heat gain and heat loss of the swimming pool, respectively.
The heat gain
is calculated by: (6)
where
and
are the heat flow rate from the heat exchanger connected to the PCM
storage tank and solar heat, respectively. The heat gain from solar heat is calculated by: (7) where
is the surface area of the swimming pool, and
absorptance coefficient, set at 0.85 [14];
is the effective solar
is the solar radiation use efficiency
considering the blockage of solar radiation by neighboring tall buildings; and
is the
solar irradiance.
The total heat loss of the swimming pool is calculated by: (8) where
,
,
,
, and
are the heat loss from evaporation, radiation,
refilling with fresh water, convection and conduction, respectively. Heat loss resulting from refilling with fresh water is calculated by: (9) where
is the mass flow rate of the refilled fresh water; and
12
is the temperature of
the fresh water. The evaporative heat loss is determined by: (10) where
is the evaporation heat transfer coefficient;
is the air saturated vapor
pressure of the swimming pool surface temperature; and
is the air partial vapor
pressure of the ambient temperature. The evaporative heat transfer coefficient is determined by [11]: (11) where
is the wind velocity. The radiation heat loss is calculated by the Stefan-
Boltzmann equation, shown below: (12) where
is the water emissivity coefficient set at 0.95 [16, 20];
constant equal to 5.67×10-8W/(m2·K4) [21]; and
is the Stefan-Boltzmann
is the equivalent sky temperature,
calculated by [22, 23]: (13) where Ta is the ambient temperature. The convective heat loss is determined by: (14) where
is the convection heat transfer coefficient between the swimming pool surface and
the ambient environment, calculated by [14]: (15) The conductive heat loss is [24]: (16) where
is the characteristic length of the swimming pool;
conduction heat transfer rate; 0.52
[24].
is the dimensionless
is the thermal conductivity of the soil, assumed to be
is the conductive heat transfer area; and
is the soil temperature.
During the thermal-insulation period, the total heat transfer rate is calculated by: (17) where pumps; and
is the heat flow rate from the heat exchanger connected to the air-source heat is the heat loss from the lower surface of the thermal insulation cover.
13
The heat transfer process in the upper or lower layer of the cover is [25]: (18) where
,
,
, and
are the density, specific heat, temperature, and
thermal conductivity of the cover, respectively. The heat transfer process in the air layer between the upper and lower layer of the cover is calculated by: (19) where
,
,
, and
are the density, specific heat, temperature, and thermal
conductivity of the air, respectively.
The boundary conditions of these thermodynamic models are shown as follows. The lower surface temperature of the lower layer satisfies: (20) For the contacting surface between the upper or lower layer and air layer, it is calculated by (21) For the upper surface of the upper layer, it satisfies (22) where
,
, and
are the heat gain from solar, radiative heat loss, and
convective heat loss in the upper surface, respectively. The heat gain from solar in the upper surface is: (23) where
is the effective solar absorptance coefficient of the thermal insulation cover. is the solar radiation use efficiency during thermal-insulation.
The radiative heat loss from the upper surface is: (24) where
is the emissivity coefficient of the thermal insulation cover;
temperature of the upper surface.
14
is the
The convective heat loss in the upper surface is: (25) where
is the convection heat transfer coefficient between the upper surface and the
ambient environment, which is [26]: (26) (27) (28) where
,
,
, and
are the Nussle Reynolds, Rayleigh, Grashof, and Prandtl
numbers of the air, respectively; and
is the characteristic length of the upper surface; and
are the constants determined by the status of the air flow.
3.1.2 PCM storage tank thermodynamic model To simplify the mathematical model, the following assumptions are proposed: (1) the temperature of the PCM remains constant during the phase change process; (2) there is no heat loss from the storage tank; (3) no internal heat is generated inside the PCM tubes; (4) only variations in the PCM and water temperature along the water flow direction are considered; (5) the thermophysical properties of PCM and water are not affected by the temperature.
Based on the above assumptions, the governing energy balance equation for the heat transfer process between the PCM and the HTF is [27]: (29) where
is the density of the HTF;
velocity of the HTF;
is the specific heat of the HTF;
is the temperature of the HTF;
is the time;
is the mean
is the water fraction
in the energy storage tank;
is the effective convective heat transfer coefficient between
the HTF and the PCM;
is the heat transfer area of the tube wall;
temperature of the PCM;
is the volume of one element; and x is the distance.
The heat transfer process of the PCM is determined by:
15
is the
(30) where
is the density of the PCM, and
is the enthalpy of the PCM. The effective
convective heat transfer coefficient between the HTF and the PCM is: (31) where
,
, and
are the thermal resistance of the HTF, the tube walls, and the PCM,
respectively. The thermal resistance of the PCM is determined by [28]:
(32)
where
and
respectively;
are the solid and liquid thermal conductivities of the PCM, and
are the solid diameters during the solidification process and the
liquid diameters during the melting process, respectively; and
is the inner diameter of the
tube walls.
The convective heat transfer coefficient of the HTF is calculated by [29]: (33) (34) where
,
, and
respectively; and
are the Nussle, Reynolds, and Prandtl numbers of the HTF, is the outer diameter of the tube walls. The finite difference method
can be used to discretize the governing equations [27]; and the discretized algebraic equations can be solved by MATLAB codes.
3.2 Performance indices To study the performance and feasibility of the proposed heating system, the following indices are adopted.
Indices for energy performance The annual energy consumption
is used to evaluate the energy performance of the
proposed system, calculated by:
16
(35) where
and
are the annual energy consumption of the air-source heat pumps
and pumps, respectively. To compare with the energy use of a traditional heating system, the energy saving ratio (ESR) is adopted and defined as: (36) where
is the annual energy consumption of the traditional heating system.
Index for technical feasibility The index of total thermal comfort unmet time percentage is adopted to analyze the technical feasibility, defined as the total thermal comfort unmet time divided by the total time of the open period throughout the entire winter. This index indicates the degree to which a system is unable to cater to the thermal comfort demand. The index is expressed as: (37) where
is the total time of the open period.
, either 0 or 1, is the thermal comfort
failure of the system. It is 0 if the thermal comfort is satisfied; otherwise it is 1.
Index for economic performance To analyze the economic performance of the proposed system, its annual operating cost is calculated according to local utility prices. To compare it with the annual operating cost of a traditional heating system, the operating cost saving ratio (OCSR) is used and defined as: (38) where and are the operating costs of the proposed and traditional heating systems, respectively. Based on the annual operating cost savings, the simple payback period ( ) is also calculated, defined as: (39) where
is the initial total investment of the proposed system.
4. Case studies 4.1 Simulation platform
17
The outdoor swimming pool considered in this study is located at the City University of Hong Kong. It is 50 m long and 22 m wide with a total volume of 1963.5
. Along its length, for
the first 10 m at both ends, the depth is 1.2 m, and in the middle the depth is 2.5 m, with the transition spread over 15 m. Along its width, the depth changes from 1.2 m to 2.5 m at 7.5 m from both sides. The swimming pool is always closed from the middle of November until the following April due to cold weather.
Table 4 shows the important time frames within the 24-hour operating schedule. The charging start time for the PCM storage tank was set at 21:00 ( ); the swimming pool preheating start time was set at 05:00 (
; the swimming pool open period was set between 12:00 ( ) and
20:00 ( ); and the electrical on-peak start and end times were 09:00 ( ) and 21:00 ( ), respectively.
Table 4 Important time frames in this case study 21:00
05:00
09:00
12:00
20:00
21:00
Table 5 lists the structural parameters of the PCM storage tank. The PCM of sodium acetate trihydrate was selected due to its high latent heat value. The thermophysical properties of sodium acetate trihydrate are given in Table 6 [30].
Table 5 Structural parameters of the PCM storage tank Parameters
Value
Number of PCM tubes
3000
Tube length (m)
2.5
Tube inner diameter (m) 0.098 Tube outer diameter (m) 0.1 Water fraction
0.25
18
Table 6 Thermophysical properties of sodium acetate trihydrate [30] Parameters
Value 58
( ) (
)
266
(
)
1450
(
)
1.68
(
)
2.37
(
)
0.43
(
)
0.34
Table 7 Main specification/characteristics of the air-source heat pump unit Item
Unit
Value
Refrigerant
-
R410A
Heating capacity (
)
450
Input power
(
)
81.7
COP
-
Power supply
(
5.5 ) 380-400/50
Table 8 Global configuration table of the heating system Item
Number Rated capacity Rated power
PCM storage tank
1
78.5m3
-
Air-source heat pump
3
450kW
81.7kW
Thermal insulation cover
1
1100m2
-
Pump-I
3
213.9L/s
10kW
Pump-II
3
71.3L/s
4kW
Valve
4
-
-
Controller
2
-
-
19
Table 7 gives the main specifications and characteristics of the air-source heat pump unit, and Table 8 shows the heating system’s global configuration table. Hong Kong meteorological data, collected by the Hong Kong Observatory from 2003 to 2012, were used in this study. The meteorological data contains dry-bulb temperatures, wet-bulb temperatures, wind speeds, and solar irradiance.
The simulation platform was established using TRNSYS 17 software as shown in Fig. 6, where Type 941 was used for air-source heat pumps, and Type 741 was adopted for variable speed pumps. The rated flow rate of the discharging pump and the preheating pump were set at 213.9 L/s, and the rated flow rate of the other pumps was set at 71.3 L/s. The heat exchanger was simulated using Type 91, in which the effectiveness of the heat exchanger was assumed to be 0.95. Type 647 and Type 649 were used to model the diverting and mixing valves, respectively. The PID controller for the swimming pool’s water temperature control was simulated using Type 23. The thermodynamic models of the PCM storage tank and the outdoor swimming pool were solved using MATLAB programs, linked into TRNSYS 17 using Type 155, the MATLAB interface.
Fig. 6. Simulation platform constructed in TRNSYS 17
4.2 Model validation The experimental data of Watanabe et al. [29] and Ruiz et al. [20] were used to validate the
20
swimming pool and PCM storage tank models, respectively. The values of the parameters and work conditions used in the simulation were the same as those used by Watanabe et al. and Ruiz et al. To describe the accuracy of the adopted models for the outdoor swimming pool and the PCM storage tank, the average relative error (
) between the numerical and
experimental results was used, as defined by: (40) where
is the number of experimental samples;
and
are the experimental and
simulated temperatures, respectively. Fig. 7 gives a temperature comparison in the outdoor swimming pool model. The average relative error (
) was 0.50%, indicating that the
swimming pool model was reliable and accurate.
Fig. 8 shows a comparison of the numerical and experimental results for the PCM storage tank during the charging and discharging processes, where x is the distance from the top of the tank. The calculated
for the thermodynamic model of the PCM storage tank was 3.59%,
indicating that this model was reliable and accurate.
Fig. 7. Comparison between the temperature measured and predicted by the adopted model
21
Fig. 8. Comparison between the temperatures measured and predicted by the adopted model: (a) charging process and (b) discharging process
4.2 Control performance analysis After the swimming pool and the PCM storage tank models were validated, the control performance of the proposed heating system was analyzed. The design temperature of the swimming pool was set at 28°C and
, the temperature increase necessary for preheating
was calculated at 0.2°C. Analysis of the pool’s water temperature variation show that the adopted operation and control methods could achieve the water temperature required for the open period.
As an example, Fig. 9 shows the water temperature variation for 1 week (from 05/1, 2012, to 11/1, 2012). Within a 24-hour operating period, starting at 05:00 ( , the moment preheating started), the temperature of the swimming pool rose until it reached 28.2°C (
).
This preheating process normally required 1 to 2 hours. Before the swimming pool opened to swimmers (at 12:00), the pool’s temperature was likely to first decrease from heat loss (although the insulation cover was on the pool) and then increase slightly when the heat gain from solar radiation became greater than the heat loss (05/1 to 08/1, 11/1) or to constantly decrease because the solar heat gain could not cover the heat loss (09/1, 10/1). After the swimming pool opened, the temperature dropped significantly due to evaporation (10/1). Thereafter, the water temperature was maintained at approximately 28°C by the PI controller. During the thermal-insulation period (from 20:00 until 05:00 the next morning), the
22
temperature experienced an average drop of 0.5°C before preheating due to the insulation cover
Fig. 9. Water temperature variation of the swimming pool within a week
The corresponding heat flow rates are shown in Fig. 10, where
is the heat flow rate
inside the heat exchanger connecting the air-source heat pumps and the swimming pool, and is the heat flow rate inside the heat exchanger connecting the PCM storage tank and the swimming pool. The heat flow rate of the swimming pool
was positive (heat gain)
when preheating, slightly negative (heat loss) during the thermal-insulation period, and maintained at approximately 0 (heat balanced) when the swimming pool was open.
Fig. 10. Variations in the heat flow rate during a week
23
Fig. 11 shows the corresponding PCM liquid fraction. The liquid fraction decreased when the PCM storage tank was discharging and increased when the tank was charging. Because the PCM tank was sized using the worst-case scenario, the PCM tank did not fully discharge every day (but it was fully charged every day due to the control methods adopted). In this example, the PCM tank was fully discharged on only 2 days (06/1 and 07/1), and on other days it was partially discharged.
Fig. 11. Variation in PCM liquid fraction in the PCM storage tank in a week
4.3 Energy performance analysis Fig. 12 shows the annual energy use of the traditional and the proposed systems, where the traditional system used an electrical boiler to provide heat and a thermal insulation cover when the swimming pool was closed. The maximum annual energy use of the proposed system
was 8.76×108 kJ (occurring in 2010); the minimum was 8.18×109 kJ (occurring
in 2008); and the average was 8.42×108 kJ. The maximum annual energy use of the traditional system
was 3.65×109 kJ (in 2004); the minimum was 3.49×109 kJ (in 2009); and the
average was 3.57×109 kJ. Fig. 12 also shows the energy saving ratio ( for each year. The maximum
, defined by Eqn. 36)
was 77.03% (in 2007); the minimum was 75.66% (in
2010); and the average was 76.40%. Thus, the proposed system achieved significant energy savings.
24
Fig. 12. Annual energy use comparison between the traditional and proposed systems (numbers in brackets are energy saving ratios)
4.4 Technical feasibility analysis Fig. 13 shows the total thermal comfort unmet time percentage ( for the years 2003 to 2012. All
, defined by Eqn. 37)
values during these years were lower than 1%, which
means that the capacity of the proposed system could satisfy the requirements for thermal comfort. The maximum
was 0.40% (in 2010); the minimum was 0.00% (in 2006 and
2012); and the average was 0.10%.
25
Fig. 13. Total thermal comfort unmet time percentage (
) of the proposed system
4.5 Economic feasibility analysis The initial cost of the proposed system was estimated at around HK$2,016,348 according to the price quoted in the Chinese market for the major components, shown in Table 9. The majority of funds were allocated to the air-source heat pumps and the PCM storage tank, and the price of the selected PCM was HK$2250.8
, referring to [30].
Table 9 Costs of the main components of the proposed system Item
Value
PCM storage tank (
)
Air-source heat pump ( Thermal insulation cover ( Pump ( Controller (
)
190,498 )
1,709,000 )
35,000 30,600
)
Total investment (
51,250 )
2,016,348
To calculate the annual operating cost, the electricity price was referred to the bulk tariff of a local power company (CLP Hong Kong), which consisted of demand and energy charges [31], shown in Table 9. Fig. 14 shows the operating costs of the traditional and the proposed systems. The maximum operating cost for the traditional system
26
was HK$1,440,096 (in
2010); the minimum was HK$1,336,354 (in 2008); and the average was HK$1,381,543. The maximum operating cost for the proposed system
was HK$218,774 (in 2010); the
minimum was HK$204,253 (in 2008); and the average was HK$210,842. The daily average for the proposed and traditional systems was HK$1,396 and HK$9,149 respectively. Fig. 14 also shows the yearly operating cost saving ratios (
, defined by Eqn. 38). The maximum
was 84.98% (in 2012); the minimum was 84.49% (in 2004); and the average was 84.74%. The calculated simple payback period (
) was 1.72 years, suggesting that the
investment could be paid back over a short period of time. Thus, considerable economic benefits were derived from the proposed heating system.
Fig. 14. Annual cost comparison between the traditional and proposed systems (numbers in brackets are operational cost saving ratios)
Table 8 Electricity price referred to the bulk tariff in the CLP [31] On-peak period Demand charge
Range (
)
Off-peak period
Charge (
)
Range (
)
Charge (
)
[0, 650)
68.4
[0, don-peak)
0
[650, ∞)
65.4
[don-peak, ∞)
26.8
27
Energy charge
Range (
)
Charge (
)
Range (
)
Charge (
)
[0, 200000)
0.738
-
0.661
[200000, ∞)
0.722
-
-
don-peak: on-peak billing demand
5. Conclusions In this study, a heating system for outdoor swimming pools with winter application for subtropical weather conditions was proposed. The proposed system integrates a PCM thermal storage tank, air-source heat pumps and a thermal insulation cover and aims to completely shift the electrical demand from on-peak to off-peak periods, thereby rendering outdoor swimming pools economically viable during the winter season. Case studies have shown that the proposed system, with its sizing and control method, can guarantee the thermal comfort of outdoor swimming pools during winter because the total unmet thermal comfort time percentage can be maintained, on average, at around 0.10%. Compared with a traditional heating system that uses an electrical boiler, the average energy saving ratio can reach 76.40%, and the average operating cost saving ratio can reach 84.74%. Therefore, the proposed outdoor swimming pool heating system is feasible in both technical and economic aspects for winter application in subtropical weather conditions.
Acknowledgement The work described in this paper was supported by the Campus Sustainability Fund of the City University of Hong Kong (No. 6986039) and the Guangdong Basic and Applied Basic Research Fund (No. 2015A030313814).
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CLP
tariff
structure,
available
at
/business-and-other-customers/bulk-tariff, in.
30
https://www.clp.com.hk/en/customer-service/tariff
Highlights
PCM integrated heating system for outdoor swimming pool for winter use is studied The electrical load is shifted from on-peak period to off-peak period The technical and economic feasibility analysis of the proposed system is conducted Compared with traditional heating system energy can be saved by 76.40% Compared with traditional heating system operational cost can be saved by 84.74%
31