4th International Conference On Building Energy, Environment

Effects of Various Parameters on Thermal Performance of a SWHS-LHS System: A Numerical Study

J. Lua, T. Longa, R. Hua，J. Chenb and Y. Lia,*

aKey Laboratory of the Three Gorges Reservoir Region’s Eco-Environment, Ministry of Education Chongqing University, Chongqing, 40045, China

bSchool of architecture and urban planning, Chongqing University, Chongqing, 40045, China

SUMMARY As a prospective energy storage method, latent heat storage (LHS) has been attracting more attentions due to its high-energy storage density and nearly constant phase transition temperature. This paper presented a solar water heater

（SWH）system integrated with LHS unit and numerically

studied the effects of various design and operating parameters on the thermal performance of the novel thermal storage unit. The numerical results showed that the thinner the thickness of the LHS panel, the shorter melting/solidification time, and the higher thermal storage capacity. The higher the inlet water flow velocity, the shorter melting/solidification time. However, once the flow velocity exceeds 0.03m/s during charging period while exceeds 0.01 m/s during discharging period, it has little impact on the thermal performance of the LHS unit. A high latent heat is recommended as it has a significant impact on the thermal performance of the SWH-LHS system.

Table1. Nomenclature, Greek Symbols and Subscript

Nomenclature

𝐴𝑚

the area of liquid or solid PCM occupied in the thickness

direction(m²)

𝐿 air flux (m³·h-1)

𝑝 wetted perimeter (m)

𝑃 power of electric heater (kW)

𝐶𝑝

specific heat capacity at constant pressure (kJ·kg-

1· °C-1)

𝑄 quantity of heat transfer （kJ）

𝑅 thermal

resistance(m²·K·W-1）

𝐺 flow rate of water（kg·h-1）

𝑡 time (s)

ℎ convective heat transfer coefficient (W·m-²·°C-1)

𝑇 temperature (K)

𝑉𝑤 volume of water tank (m³)

𝐻 enthalpy（kJ·kg-1） 𝑥 distance in the thickness direction (m)

𝐾 thermal conductivity (W·m-1·°C-1)

Greek Symbols

𝜌 density (kg·m-3) ∆𝑇 temperature rise (K)

∆𝑡 time interval (s)

Subscript

𝑎 air 𝑤 − 𝑚 water to phase change material

𝑤 water 𝑓 fluid

𝑚 phase change material

INTRODUCTION Thermal storage unit is a key component of solar heating systems, as it can effectively be addressed the issue of mismatch between the energy supply and demand, which is usually happened in solar energy applications. Therefore, the development of effective energy storage units is as important as exploring new sources of energy (Sharma et al. 2009). A good designed energy storage unit would not only reduce the mismatch between the solar energy supply and demand but also improve the efficiency and reliability of the systems (Tay et al. 2012). However, the traditional heat storage unit is facing problems that large occupied place and serious heat loss because the heat stored in the form of sensible heat. Alternatively, the latent heat storage (LHS) with phase change material (PCM) is suggested to be a perfect solution as they possess a high latent heat density and isothermal phase change characteristic (Su et al. 2012).

Several configurations of solar water heater（SWH）system

integrated with PCM have been numerically and experimentally studied (Wu and Fang 2012; Koca et al. 2008; Benli and Durmus 2009; Lopez-Navarro et al. 2014; Haillot et al. 2013; Haillot et al. 2012; Tay et al. 2013). Aydin et al. (2015) designed and evaluated a cylindrical LHS unit for the hot water storage tank. Experimental testing was performed in a four-season climate and results indicated that ultilizing LHS devices is profitable in spring and autumn seasons, resulting in an increase in the fraction of solar energy being used in space heating applications. Canbazoğlu et al. (2005) found that the hot water production capability increased about three fold by integrating cylindrical LHS units into the water storage tank. Kousksou et al. (2011) argued that thermal performance of SWHS-LHS system is highly sensitive to the preliminary design parameters such as the melting temperature of PCM and end-user requirements. There might be an optimum design for such systems. Talmatsky and Kribus (2008) concluded that the performance of a SWH-LHS system might not be substantially beneficial because the system could be very sensitive to the PCM parameters, and it could lead to system failure.

From the above literature review, it is revealed that in most of the studies, the cylindrical or spherical PCM packages were designed for the hot water storage tanks. The review is also shown that thermal performance of SWHS-LHS system is highly sensitive to the system configuration, PCM characteristics and end-user requirements. Actually, rectangular PCM package seems to be more practical due to its simple boundary and easy construction. Therefore, a zigzag plate-type LHS unit for hot water storage tank was designed, and the effects of various operating and design parameters on its thermal performance in terms of phase

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4th International Conference On Building Energy, Environment

change ratio and thermal storage capacity during charging and discharging periods are numerically evaluated. The findings of the current work could provide a guideline of optimizing design such a SWHS-LHS system.

METHODS The LHS system consists of heat source (heating water

tank), zigzag plate-type LHS unit and heating terminal unit

(fan coil), and it is illustrated in Figure.1. The heating water tank with an electric heater is used to replace the function of solar collector. The electric heater heats the water up once the water temperature reaches the set heating temperature and the rooms need heating, the hot water is supplied to the fan coil. Meanwhile, the extra heat is stored in the LHS unit. When the heating water tank could not meet the heating requirements, the LHS unit is used to provide heat to the fan coil as a supplement.

Figure 1. Schematic diagram of SWHS-LHS system

Modeling of LHS system

The heat transfer process within the zigzag plate-type LHS unit during charging and discharging processes is complicated. In order to simplify the numerical modeling, the following assumptions were made:

PCM is packaged by a stainless steel container, and thethermal resistance of the container is negligiblecompared to that of PCM.

Heat transfer within PCM panel is two-dimensional heatconduction, the convective heat transfer ignored.

The water flow rate in the tank is constant, and the watervelocity is uniform anywhere.

The thermal stratification within the water is ignored. The density and volume changes of PCM and water with

temperature changes are ignored. The phase change temperature of the PCM is constant.

Based on the above assumptions, the energy conservation equations for the zigzag plate-type PCM unit are as follows:

Energy conservation equation for PCM panel:

𝐻𝑚 ∙ 𝜌𝑚 ∙𝜕𝐴𝑚(𝑥,𝑡)

𝜕𝑡= 𝐾𝑤−𝑚 ∙ 𝑃 ∙ [𝑇𝑤(𝑥, 𝑡) − 𝑇𝑚] (1)

Energy conservation equation for heat transfer fluid of water：

𝑚𝑤 ∙ 𝐶𝑝𝑓 ∙𝜕𝑇𝑤(𝑥,𝑡)

𝜕𝑥= −𝐾𝑤−𝑚 ∙ 𝑃 ∙ [𝑇𝑤(𝑥, 𝑡) − 𝑇𝑚] (2)

𝐾𝑤−𝑚 = ℎ𝑤 ∙ 𝛽 (3)

𝛽 =𝑅𝑤

𝑅𝑤+𝑅𝑚 (4)

𝑅𝑤 =1

ℎ𝑤(5)

𝑅𝑚 =1

𝐾𝑚(6)

Initial conditions： 𝐴𝑚(𝑥, 𝑡 = 0) = 𝐴𝑚,0(𝑥) , 𝑇𝑤(𝑥, 𝑡 = 0) =

𝑇𝑤,0(𝑥)

Boundary conditions： 𝑇𝑤(𝑥 = 0, 𝑡) = 𝑇𝑤,𝑖𝑛(𝑡)

Where 𝑇𝑤,𝑖𝑛(𝑡) is the temperature of outlet water of heating

water tank at time 𝑡.

Modeling of heating water tank

The heating water tank with an electric heater with the power of 2kW is the heat source for the SWHS-LHS system. The volume of cylindrical heating water tank is 0.2m³ and the dimension is Φ0.25 × 1 (m).

The electric heater is set at the bottom of the water tank. It can convert electricity into heat to increase water temperature. The water enters the tank from the bottom, gets heated in the lower part of the tank, rises to the top and then flows out from the top of the tank. Due to the low height of the tank, the temperature stratification in tank will be ignored.

The thermal equilibrium equation is as follows：

𝑄𝑤 = 𝑃 × ∆𝑡 = 𝑉𝑤 × 𝜌 × 𝐶𝑝,𝑤 × ∆𝑇𝑤 (7)

Where 𝑃 =2kW, 𝑉𝑤 =0.2m³, 𝜌 =1000kg·m-3, 𝐶𝑝,𝑤 =4.2kJ·kg-

1·°C-1.

Modeling of the heating terminal unit (fan coil)

Fan coil is selected as the heating terminal unit which is the most commonly used indoor terminal device. Heat balance equation of fan coil is given as bellow：

𝑄𝑓 = 𝐺𝑓 × 𝐶𝑝,𝑤 × ∆𝑇𝑤 = 𝐿𝑓 × 𝜌𝑎 × 𝐶𝑝,𝑎 × ∆𝑇𝑓 (8)

∆𝑇𝑓 = 𝑇𝑓,𝑜𝑢𝑡 − 𝑇𝑓,𝑖𝑛 (9)

∆𝑇𝑤 = 𝑇𝑤,𝑖𝑛 − 𝑇𝑤,𝑜𝑢𝑡 (10)

Where 𝐶𝑝,𝑤 =4.2kJ·kg-1·°C-1, 𝜌𝑎 =1.29kg·m-3, 𝐶𝑝,𝑎 =1.01kJ·kg-

1·°C-1.

The inlet air temperature of fan coil can be assumed as the room temperature, and the inlet water temperature of fan coil can be derived from the subprogram of the zigzag plate-type LHS unit. So the unknown parameters are 𝑇𝑓,𝑜𝑢𝑡 and 𝑇𝑤,𝑜𝑢𝑡,

and they are mutually constrained. Organic PCM Paraffin wax is chosen as the working PCM in this study due to its suitable thermo-physical properties as listed in Table 2.

Table2. Thermophysical properties of selected PCM

Thermophysical properties Paraffin wax

Melting temperature [°C] 50

Thermal conductivity [W·m-1·°C-1] 0. 4

Heat of fusion [kJ·kg-1] 183

Density [kg·m-3] 870

Specific heat (kJ·kg-1· °C-1) 2.9

MODEL VERIFICATION Charging period

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During charging period, the model was verified by comparing numerical results of outlet water temperature of LHS unit and mean PCM temperature with those of experimental results under the conditions of water flow rate is 1.3m³ / h and distance between PCM panels is 30mm.

Figure.2 Comparison of numerical results and experimental results for charging period: (a) outlet water temperature of LHS unit; (b) mean PCM temperature

Figure.2a presents the errors between the experimental values and simulated values of outlet water temperature of LHS unit during charging period. It is clear that good agreements between the numerical and experimental results are observed. The errors between the errors are within ±5%. Figure.2b presents the errors between experimental values and simulated values of the mean PCM temperature during charging period. It can be seen that the errors are within ±5%. This coherence shows that the developed numerical model is acceptable and reliable to investigate the thermal performance of the zigzag plate-type LHS unit during charging period.

Discharging period

During discharging period, the model was verified by comparing numerical results of outlet water temperature of LHS unit and mean PCM temperature with those of experimental results under the conditions of water flow rate is 0.6 m³ / h and distance between PCM panels is 20 mm.

Figure.3 Comparison of numerical results and experimental results for discharging period: (a) outlet water temperature of LHS unit; (b) mean PCM temperature

Figure.3a presents the errors between the experimental values and simulated values of outlet water temperature of LHS unit during discharging period. The errors are within ±10% and 73% of them are within ±5%. While Figure.3b presents the errors between the experimental values and simulated values of the mean PCM temperature during discharging period. Similarly, the errors are within ±10% and 73% of them are within ±5%. Though the accuracy of the developed model for discharging period is poorer than that for charging period, the numerical model is still acceptable to study the thermal performance of the zigzag plate-type LHS unit during discharging period.

RESULTS AND DISCUSSION With the verified numerical model, the study on the effect of a number of design and operating parameters on the thermal performance of the system is carried out. For a LHS system design, the time taken for the whole PCM to melt or solidify is one crucial factor. Thermal storage capacity indicates how much heat stored in LHS unit after charging period. The inlet water temperature of LHS unit is initially at 55/40 during charging/discharging process. The thickness of the PCM plate is set as 0.02m.

Effect of the thickness of PCM panel

It can be observed that the thinner PCM panel corresponds to a shorter charging/discharging time as shown in Figure 4 (a) and (b). As the melting time of the PCM with thethickness=1, 2, 3 and 4cm are 53.4, 108.6, 196.2, 318minutes, respectively. The melting process of 5cm thicknessis uncompleted. As shown in Figure 4 (c) and (d), during thecharging process, the outlet water temperature rises in astraight line when it is below 53.5℃ within an hour in the firststage. In the second stage, the outlet water temperaturerises slowly until the melting phase completes.

Figure.4 Effect of the thickness of PCM panel on thermal performance of system: (a), (c) charging period; (b), (d)

discharging period

As the initial temperature difference between the outlet water and PCM panel is the largest, the initial thermal storing/releasing rate is the highest as shown in Figure 4 (c) and (d). It can also be seen that the thinner the PCM panel, the larger the initial thermal storing/releasing rate. This can be explained as the larger surface area of the thinner panel lead to more energy transferred. However, the thicker the PCM panel, the faster the thermal storing/releasing rate drops. When the thermal storing rate approaches 0.5~1kW, most of the solid fraction has melted so the storing force diminishes and the phase change process slows down.

Effect of inlet water velocity

As shown in Figure 5 (a) and (b), the phase change ratios within the velocity range of 0.02~0.05m/s are close during the charging/discharging process. The total amounts of thermal storage and thermal release are equal to 22289.4kJ due to the same mass of the PCM. The process of outlet temperature change can be divided into three stages as shown in Figure 5 (c) and (d). It can be seen that at the first stage, the faster the water velocity, the higher/lower initial outlet water temperature during the storing/releasing process.

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4th International Conference On Building Energy, Environment

At the second stage, during the charging/discharging process, the outlet water temperature rises/drops in a straight line until it is equal to the inlet temperature which means the completion of melting/solidification. The outlet water has a constant temperature equal to the inlet water at

Figure.5 Effect of inlet water velocity on thermal performance of system: (a), (c) and (e) charging period; (b), (d) and (f)

discharging period

the last stage. It can be observed that the duration of the lower/higher outlet water temperature can be enhanced by a lower flow velocity, indicating that a slower flow velocity has a better maintenance of the water temperature of the tank.

As shown in Figure 5 (e) and (f), the initial thermal storing/releasing rate at velocity=0.01, 0.02, 0.03, 0.04, 0.05m·s-1 are 2.88, 5.50, 7.67, 6.28, 7.69 kW, respectively, indicating that the increase of the flow velocity can enhance the heat transferred at the beginning stage. The optimum velocity is 0.04 m·s-1 where the maximum thermal storing/releasing rate appears. Then it declines as a result of temperature difference reducing between inlet water and the PCM panel. Moreover, the thermal storing/releasing rates for these 5 flow velocities are equal where the thermal storing/releasing rate drops to 1.5/0.7kW. After this stage, it diminishes quickly, owing to the fact that the mass of the PCM panel in an origin solid/liquid state corresponding to the lower flow velocity is less than it corresponding to the higher flow velocity. It can be concluded that the lower flow velocity allows a more stable thermal storing/releasing rate.

Effect of latent heat of fusion

For a given mass of the PCM, Figure 6 (c) and (d) show that the thermal storage/release capacity is determined by the latent heat of fusion. Moreover, the larger the latent heat, the higher the thermal storing/releasing rate as shown in Figure 6 (a) and (b), and the shorter melting/solidification time as shown in Figure 6 (c) and (d). The increment of the melting/solidification time is equal to 54/39 minutes, suggesting a significant impact of the latent heat of PCM on phase change ratio.

The beginning of melting/solidification process has the same thermal storing/releasing rates and the same outlet water

temperatures as shown in Figure 6 (e) and (f). In the latter stage they both drop in similar trend. It can be seen that the smaller latent heat of PCM, the faster the reducing trend. When the outlet water temperature is higher/lower than 54/42℃, they drop linearly until the phase change complete. Figure 6 also shows that the increase of the latent heat of PCM can prolong the duration of the high thermal storing/releasing capacity.

CONCLUSIONS A 2D numerical model is developed for investigating the thermal performance of a SWHS-LHS system by changing operational and design parameters during charging and discharging processes. The following conclusions are obtained based on findings of the current work:

The thinner PCM panel has a more stable and efficient storing/releasing process than the thicker ones. The thickness of 1-4 cm is recommended.

A larger water flow velocity can shorten the phase change time while a lower flow rate can maintain the water temperature. But once the flow velocity exceeds 0.03 m·s-1 during absorbing period or exceeds 0.01 m·s-1 during releasing period, the enhancement of thermal performance can be ignored. The smallest velocity in the range of the curve-intensive of storing/releasing can be used as a preferred option for pump selection.

Figure.6 Effect of latent heat of fusion on thermal performance of system: (a), (c) and (e) charging period; (b), (d) and (f) discharging period

The higher the latent heat capacity of the PCM, the larger the storage capacity and the phase change rate. But the growth of the latent heat capacity of the PCM can cause the process of the phase change extended. The preferred value of latent heat is the largest value of the overall storing/releasing time.

ACKNOWLEDGEMENT This work is sponsored by National Science Foundation of China (No. 51478058), and the 111 Project (No. B13041).

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4th International Conference On Building Energy, Environment

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