Thermal characteristics of a seasonal solar assisted heat pump heating system with an underground tank

Thermal characteristics of a seasonal solar assisted heat pump heating system with an underground tank

Journal Pre-proof Thermal characteristics of a seasonal solar assisted heat pump heating system with an underground tank Haotian Huang, Yimin Xiao, Ji...

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Journal Pre-proof Thermal characteristics of a seasonal solar assisted heat pump heating system with an underground tank Haotian Huang, Yimin Xiao, Jianquan Lin, Tiecheng Zhou, Yanan Liu, Qian Zhao

PII:

S2210-6707(19)30981-3

DOI:

https://doi.org/10.1016/j.scs.2019.101910

Reference:

SCS 101910

To appear in:

Sustainable Cities and Society

Received Date:

10 April 2019

Revised Date:

19 October 2019

Accepted Date:

19 October 2019

Please cite this article as: { doi: https://doi.org/ This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. 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. © 2019 Published by Elsevier.

Thermal characteristics of a seasonal solar assisted heat pump heating system with an underground tank

Haotian Huanga,b, Yimin Xiaoa,b,*, Jianquan Lin a,b, Tiecheng Zhoua,b, Yanan Liua,b, Qian Zhaoa,b

a

Key Laboratory of the Three Gorges Reservoir Region’s Eco-Environment, Ministry of Education, Chongqing University, Chongqing 400045, China

b

National Centre for International Research of Low-carbon and Green Buildings, Chongqing University, Chongqing 400045,

*

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China

Corresponding E-mail addresses: [email protected]

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Postal address: School of Civil Engineering, Chongqing University, Chongqing 400045, China

Highlights

Propose a 2D model for seasonal thermal storage system with an underground tank



The model considers the stratification in tanks and the outside temperature field



Discuss the dynamic charge and discharge characteristics of SSTES



Discuss the effect of the tank’s thermal insulation level on the system operation

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Abstract

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Seasonal solar thermal energy storage could be an effective way to relieve energy problems. However, the large storage volume such systems require restricts their practical application. To overcome this problem, this paper proposes a method that increases the heat storage capacity of an underground water tank by coupling it with the soil for heating. In order to consider the stratification of water in a long-term simulation, a two-dimensional computational model was

established based on the plug flow model and the finite difference method to simulate the instantaneous temperature field. Further, the accuracy of the model was verified via a model experiment. The dynamic charge and discharge characteristics were numerically studied, and the effect of the tank’s thermal insulation level was discussed. We simulated the hourly load of a building throughout a year, and the operation of the heat storage system throughout 10 years based on local hourly meteorological data. The results show that the heat storage capacity of the

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Abbreviations AUS auxiliary heat source CFD computational fluid dynamics COP coefficient of performance HTF heat transfer fluid SF solar fraction SSTES seasonal solar thermal energy storage

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system can be effectively improved by insulating only the upper half of the tank.

Keywords: Solar energy; Seasonal solar energy storage; Soil thermal storage; Underground tank

collector area, m2 Archimedes number section area of the tank, m2 specific heat capacity, J/kg·℃ gravity, m2/s Grashof number convective heat transfer coefficient, W/m2·℃ solar radiation intensity, W/m2 solar radiation intensity on the collector plane, W/m2 characteristic length, m mass flow rate through collectors, kg/s

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Ac Ar At c g Gr h I IT l mc

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Nomenclature

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ml mass flow rate in heating system, kg/s Qhp heat supplied to the building through heat pump, W Qload heating load, W Qsupply heat supply from heat storage regenerator, W Qu collect energy by collector, W r radius, m Re Reynolds number S source term t time T temperature, ℃ T0 initial temperature, ℃ Ta ambient temperature, ℃ TA sol-air temperature, ℃ Tco outlet temperature of collector, ℃ Tev evaporation temperature, ℃ Text temperature of extracted hot water from water tank, ℃ Ti average temperature of each layer in the tank, ℃ Tre temperature of return water from building, ℃ Tb designed air temperature inside the building, ℃ Tw temperature of the collector, ℃ u velocity, m/s W power of the heat pump, W z depth, m

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Greek Symbols

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α thermal expansion coefficient, 1/℃ α0 solar-radiation absorptivity of the ground surface ρ density, kg/m3 ε contribution rate of soil, % εs long-wave emissivity of the ground surface ηc collector efficiency, % λ conductivity, W/m℃ ΔR difference between the long-wave radiation emitted by the ground surface and its received long-wave radiation from the sky and surroundings, W/m2 Subscripts and superscripts bot c E lat N P s S

bottom surface of the water tank collector the east element lateral surface of the water tank the north element the element being calculated soil the south element

up w W

upper surface of the water tank water the west element

1 Introduction In China’s northern cities, the energy consumption associated with heating buildings was 191 million tons of standard coal in 2016, accounting for 21% of all building energy consumption. Heating in northern China is generally dominated by coal, which provides more

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than 80% of the total required for this purpose (Building energy conservation research center, 2018). This coal dependency escalates ever-increasing threats of energy shortages and

environmental degradation. However, there are abundant solar energy resources in northern

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China, and thus solar heating could be an effective way to alleviate energy problems.

Randomness and discontinuity are the major factors limiting the development of solar heating,

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and therefore thermal storage technologies must be developed before solar energy can be a

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practical energy source for building heating.

Seasonal solar thermal energy storage (SSTES) has been proposed to eliminate the annual

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time mismatch between supply and demand, and thereby stabilize the solar energy supply (Xu et al., 2014). Schmidt et al. (2004) suggested that more than 50% of the annual heating demand for

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space heating and domestic hot water could be supplied by SSTES. Sameti and Haghighat (2018)

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integrated distributed energy storage into net-zero energy district systems and built an optimization model for the layout of the energy distribution network. Compared to the case with no storage system, the optimal scheme reduced annual CO2 emission by 18%. SSTES systems typically consist of hot water thermal storage, borehole thermal energy storage, aquifer thermal energy storage, and water gravel pit storage (Shah et al., 2018). This paper focuses on a SSTES system that includes an underground tank, and many scholars have

studied this type of storage system. Ucar and Inalli (2008) used the finite element method to compare ground-level and underground placement of the water tank. Their results indicated that the underground tank effectively reduces heat loss: for a given amount of solar irradiation, the underground system reduced the collector area by 9%. Papanicolaou and Belessiotis (2009) also proved experimentally that the ground improves the thermal insulation of the tank. Integrating heat pump technology into a storage system can also improve results. The heat

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storage regenerator can be maintained at a lower temperature, and the temperature reduction reduces the amount of heat loss and improves the collector efficiency (Marx et al., 2014). In

order to eliminate the imbalance between charging and discharging, Banjac (2015) proposed

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installing solar collectors to transmit supplemental heat to the heat storage regenerator, in a

system that guaranteed sustainability in that the ground could be restored to its original state after

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one year of operation. In a system with a heat pump and cylindrical tank, Hesaraki et al. (2015)

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studied the influence of heating temperature on the optimal design parameters of the system, including those of the collector area, tank volume, and tank height-diameter ratio. The simulation

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results from 108 systems showed that for all of the heating temperatures considered, the optimum ratio of tank height to diameter is 1.0.

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However, using water to store heat requires a tremendous volume, which is often

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impractical, and leveraging the ground’s significant heat storage capacity would thus be beneficial for these systems: if the ground could be integrated with the buried tank system, the tank volume could be reduced. Karacavus and Can (2008; 2009) filled sand around the underground tank to increase the heat storage capacity, and the solar fraction of the system improved as a result. The system could meet 69% of space heating and domestic hot water demand and the system's payback period was reduced. They also simulated the system’s

operation, and demonstrated that part of the heat stored in the sand would be transferred back to the tank during the heating season. In previous studies, tanks were usually insulated, and this measure is certainly effective at reducing heat loss. However, the insulation also prevents heat transfer from the soil to the tank, and it is as yet unknown to how much heat would transfer back to the tank during the heating season. If that is sufficient enough, the storage capacity of the tank would thus be expanded. To address this question, this study focuses on the dynamic heat

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transfer characteristics between an uninsulated tank and the soil, and the influence of the insulation on the storage system.

Before this question can be addressed, the question of how to consider tank stratification

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must be addressed. Thermal stratification in the tank can minimize the mixing effect during operations, so that the load side can extract hotter water for heating (Chandra and Matsuka,

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2019). Han, Wang and Dai (2009) noted that for a seasonal storage system, an ideally stratified

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tank will increase the average net energy and exergy efficiencies by 60% compared with a fully mixed tank. In order to predict the tank stratification, Papanicolaou and Belessiotis (2009)

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simulated the temperature field during the charging period using a two-dimensional computational fluid dynamics (CFD) method, and their simulation results agreed well with the

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experiments. In addition, Bouzaher et al. (2019) studied the stratification in a spherical tank in

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dynamic mode using three-dimensional CFD. Further, Sifnaios et al. (2019) evaluated the performance of a heating system consisting of a tank and heat pump using CFD, and optimized the tank’s internal structure to achieve better stratification based on the simulation results. However, all of these methods need to simulate the flow field in the tank, a consideration that adds substantially to the computational burden and is thus not feasible in studies of seasonal storage systems.

At present, there are two kinds of research methods for seasonal storage systems that include a tank. One method only considers the inside of the tank as a one-dimensional temperature field, which can be solved by combining the plug flow model, multi-node model, or plume entrainment model (Chandra and Matuska, 2019). In the plug flow model, the flow inside the tank is considered as piston flow. The tank is divided into several layers in the vertical direction, and the temperature throughout each layer is considered uniform. Each layer’s energy

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inflow and outflow is considered separately, including the heat transfer through the medium and the heat conduction between layers. Based on the one-dimensional energy equation, the

temperature of each layer can be calculated, as in (Hesaraki et al., 2015), and a function for the

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temperature field can also be obtained. Yoo and Pak (1993) also deduced and obtained the

temperature function in space and time via Laplace transform, and the heat dissipation term of

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each layer can be added when considering the energy change (Alizadeh, 1999). In a multi-node

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model, the returning water from the collector or load side must find the node closest to its temperature and enter the tank there. For more detailed explanations of these two models, see

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(Chandra and Matuska, 2019). Based on the multi-node model, Saloux and Candanedo (2019) developed an advanced model of the flow rate distribution of the flow entering the tank. The

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accuracy of the model was validated by test data from a tank with a volume of 240 m3. However,

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the computational domains of these models were limited to the inside of the tank, and the temperature distribution outside the tank was not considered. The other research method for seasonal storage systems that include a tank couples the

internal and external temperatures of the tank. Inalli et al. (1997) and Yumrutaş et al. (2005) considered burying a spherical tank deep in the ground for solar heating systems or earthcoupled cooling systems. The temperature inside the tank was assumed to be uniform to simplify

the model as a one-dimensional problem. They solved the one-dimensional partial differential equation with a complex finite Fourier transform, and obtained a function of the ground temperature in relation to time and spatial coordinates. Yumrutaş and Ünsal (2012) solved the problem of instantaneous heat transfer outside a deeply buried spherical tank via similarity transformation and Duhamel’s superposition principle. The temperature inside the tank was again assumed to be uniform, forming another one-dimensional problem. With monthly mean

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meteorological data as the boundary condition, Inalli (1998) used a finite difference method to solve the two-dimensional temperature field around the cylindrical buried tank, keeping the tank temperature uniform. Thus, methods that couple the internal and external temperatures of the

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tank always assume a uniform temperature inside the tank, and then simplifiy the problem into one- or two-dimensional models.

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The disadvantage of these two methods is that neither considers the water stratification and

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the temperature field outside the tank simulaneously, and both of these conditions are very important for seasonal storage. In addition, the meteorological conditions in the model are

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usually simplified to monthly average parameters (Kandiah and Lightstone, 2016; Ucar and Inalli, 2005; Ucar and Inalli, 2008), and this approach does not account for periods of no sun for

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several consecutive days. These limitations would cause critical differences between the results

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of these approaches and the actual operational efficiency when applied to the system targeted here.

Therefore, this paper proposes a new calculation model for seasonal energy storage systems

with underground tanks. On the basis of the plug flow model, we consider the thermal conduction between each layer and between the water and surrounding soil. The proposed model considers the water stratification and the temperature field outside the tank simultaneously. A

two- dimensional computational model for a cylindrical buried tank was developed using the finite difference method and was verified by a model experiment. We then investigated a standalone house with an area of 100 m2 in Taiyuan, China, as an example, and simulated the operation of the heat storage regenerator. The hourly load demand data were obtained by simulation and set as the boundary conditions of the numerical simulation. The results obtained

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can be used to guide the design and further development of SSTES systems.

2 System Description

The proposed system, shown in Fig. 1, consists of a heat storage regenerator, solar

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collectors, heat load terminal, heat pump, auxiliary heat source (AUS), and heat transfer fluid (HTF). The system comprises two subsystems: a solar collection system and a heating system.

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The collection system collects solar energy and stores it in the heat storage regenerator. The

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heating system supplies heat to the building according to the control strategy in Section 2.1.

Fig. 1. Schematic diagram of solar heating system with seasonal storage.

2.1 Control strategy

In the proposed system, the minimum supply temperature for heating is 35℃, in accordance with the Chinese design code for heating ventilation and air conditioning of civil buildings

(China, 2012). The supply temperature considered suitable for the hot water radiant heating system is in the range 35–45℃. During operation of the heating system, the water supplied to the building is always hotter than 35°C. By mixing this supplied water with backwater, the temperature can be controlled to 35°C. The flow rate of the hot water is related to the heating load and it can be controlled using the bypass pipe. In order to take full advantage of the storage energy, the heat pump is utilized, with a minimum temperature of 15℃ available to it. Depending

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on the tank temperature, the system has three operating modes. The valves and pumps used to implement the control strategy in these three modes are listed in Table 1 and the respective schematic diagrams of the three modes are shown in Fig. 2. In Mode 1, when the tank

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temperature is higher than 35℃, hot water is supplied to the building directly. In Mode 2, when the tank temperature is between 15℃ and 35℃, the energy grade needs to be lifted by the heat

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pump, and then supplied to the building. In Mode 3, when the tank temperature is below 15℃,

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the storage system has no heating capacity, and all of the heat requirement is met by AUS. Table 1. Control strategy for different modes. ON

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Case

Mode 1

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Mode 2

P1

Mode 3

P3, V3, V4

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Storage

P2, P3, V1, V2, V5, V6 P3, V7, V8

Mode 1

Mode 2

Mode 3

Fig. 2. Schematic diagrams of the three modes.

2.2 Physical model

As shown in Fig. 3, the heat storage regenerator includes an underground cylindrical tank

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and the soil, with three operational states of heat transfer. In the heat storage period, solar energy is stored in the tank, causing the tank temperature to increase. Part of the heat is transferred to the soil, resulting in a rise in the soil temperature (Fig. 4a). In the heating season, the heat is

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extracted, and the tank temperature gradually decreases. At first, the tank temperature is still

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higher than that of the soil, and the direction of heat flux is from the tank to the soil (Fig. 4b). When the tank temperature is lower than the surrounding soil, part of the heat in the soil is

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transferred back to the tank and reused (Fig. 4c).

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Unlike classical geothermal systems in which pipes are directly surrounded by the soil, in this study, the heat is primarily stored in a tank rather than in the soil. There are several benefits

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to this method. First, during the heating season, the tank can provide short-term heat storage, and the heat collected in the daytime can be stored for later use. In classical geothermal systems, all

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that can be done is extract the heat from the soil, and a separate tank is often required for shortterm heat storage. Second, heat is directly stored in the water and can be directly supplied to the building without being limited by the heat transfer rate. Further, the classical geothermal system typically uses a vertical borehole with depths between 30 and 100 m to store heat. This implies that drillable ground is required to install a classical geothermal system. Therefore, such a system is more suited to use at the community level than for a single dwelling. In contrast, the system

with a tank can be easily installed at any location. The required burial depth is usually less than

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Fig. 3. Physical model of the heat storage regenerator.

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15 m (Shah et al., 2018).

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a

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Fig. 4. Heat transfer states of storage system. 3 Numerical Model

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3.1 Solar collector

A flat plate collector is used to collect solar energy. The collected energy Qu can be calculated using 𝑄𝑢 (𝑡) = 𝐴𝑐 𝜂𝑐 (𝑡)𝐼𝑇 (𝑡)

(1)

where t is the time, Ac is the collector area, and IT refers to the solar radiation intensity on the

(Yumrutaş and Kaska, 2004): 𝜂𝑐 (𝑡) = 0.72 − 0.64

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collector plane; ηc is the efficiency of the collector, given by the following widely used equation

[𝑇𝑤 (𝑡)−𝑇𝑎 (𝑡)] 𝐼𝑇 (𝑡)

(2)

where Ta is the ambient temperature, and Tw is the temperature of the collector.

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The outlet temperature of the collector (Tco) can be calculated using 𝑄𝑢 (𝑡)

𝑚𝑐 𝑐𝑤

(3)

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𝑇𝑐𝑜 (𝑡) = 𝑇𝑒𝑥𝑡 (𝑡 − 1) +

where Text is the temperature of the hot water extracted from the water tank, mc is the flow rate of

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the collectors, and cw is the specific heat capacity of water. Tco is limited to below 95°C, and

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3.2 Heat pump

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when the temperature exceeds this value, ηc is set to 0%.

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A heat pump is a device that extracts heat from the water tank and supplies it to the building

after improving the quality of the heat. The heat supplied to the building through the heat pump depends on the coefficient of performance (COP) and power: 𝑄ℎ𝑝 (𝑡) = COP × 𝑊(t)

(4)

where Qhp is the heat supplied to the building through the heat pump, and W is the power of the heat pump. The COP can be calculated using the following formula (Banjac, 2015):

COP = 3.5 − 0.125 × (𝑇𝑒𝑣 − 𝑇𝑏 ) { COP𝑚𝑎𝑥 = 4.2

(5)

where Tev is the evaporation temperature, and Tb is the designed air temperature inside the building.

3.3 Heating load

To study the characteristics of the system in a real engineering project, we investigated a

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standalone house with an area of 100 m2 in Taiyuan, Shanxi Province, China (latitude: 37°27′– 38°25′N), as a case study. The heating season in Taiyuan is from November 15th to March 15th. Thus, the time axis for system operation can be determined as shown in Fig. 5. The floor plan of

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the house is shown in Fig. 6a. Designer's Simulation Toolkit (DEST) software (Yan et al., 2008; Zhang et al., 2008) (developed by Tsinghua University) was used to simulate the hourly heating

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load. The software considers the heat transfer through the building fabric element (including the

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external walls, roof, ceiling and floor slabs, and internal partitions), solar radiation transmission, infiltration of outdoor air and air from adjoining rooms, heat and moisture dissipation from the

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lighting and occupants inside the room. Local hourly meteorological data were used as the basis for the simulation and the designed indoor temperature was set at 18℃. The envelope parameters

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of the simulation are shown in Table 2. The hourly heat load profile and hourly local

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meteorological profile are shown in Fig. 6b.

Fig. 5. System operation time axis.

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Fig. 6. Simulation of building load. Table 2. Envelope parameters of the simulation.

Type

Structure

240-mm brick wall

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Exterior wall

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20-mm mixed mortar

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Heat transfer coefficient (W/m2·℃)

0.65

EPS adhesive

Insulated glass window

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Exterior window

2.8

40-mm cement mortar 80-mm concrete

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Roof

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120-mm extruded polystyrene board

Door

Single-layer metal-insulated plywood door

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Because the maximum heat load of the building was approximately 10 kW and the

temperature difference of heating was 5℃, the flow rate for heating ml was calculated to be 0.5 kg/s.

3.4 Heat storage regenerator

The explicit finite difference method was used to model the storage regenerator, and the numerical model is shown in Fig. 7. The following assumptions were used in this study. 

The model is simplified to two dimensions.



Relative to the geometric size of the tank, the flow velocity is very small, and because the value of Gr/Re2 is far greater than 10, the disturbances at the inlet and outlet of the



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tank can be neglected.

Because the hot water enters the tank from above, and the cold water flows out from the bottom, the tank is well-stratified under the influence of natural convection, and the

Heat is transferred between the water and soil through conduction, and the thickness of

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flow in the tank is considered to be perfect piston flow.

the tank wall is negligible.

A position sufficiently distant from the tank is considered as an adiabatic boundary.



The effect of ground-water flow is considered negligible.

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Fig. 7. Numerical model of the heat storage regenerator. In the computational domain, the temperature is governed by a thermal conductivity differential equation in two-dimensional cylindrical coordinates: 𝜌𝑐

𝜕𝑇 𝜕𝑡

1

𝜕

𝑟

𝜕𝑟

= ∙

(𝜆𝑟

𝜕𝑇 𝜕𝑟

)+

𝜕 𝜕𝑧

(𝜆

𝜕𝑇 𝜕𝑧

)+𝑆

(6)

where r is the radius; z is the depth from ground surface; S is the source term, which considers the heat exchange due to plug flow and convective heat transfer, as detailed below; and ρ, c, and λ are the density, specific heat capacity, and thermal conductivity, respectively, determined by the nature of the heat-exchanging materials. For the symmetrical axis: 𝜕𝑇

|

=0

|

=0

|

=0

𝜕𝑟 𝑟=0

(7)

𝜕𝑇

𝜕𝑟 𝑟=𝑅

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For the lateral far boundary:

𝜕𝑇

𝜕𝑧 𝑧=𝐻

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For the far boundary of depth:

(8)

(9)

After the equation is differentiated, for any element P in the computational domain,

𝜆𝑆 𝑟𝑃 ∆𝑟 ∆𝑧

(𝑇𝑊 (𝑡) − 𝑇𝑃 (𝑡)) −

𝜆𝐸 𝑟𝐸 ∆𝑧 ∆𝑟

(𝑇𝑃 (𝑡) − 𝑇𝐸 (𝑡)) +

𝜆𝑁 𝑟𝑃 ∆𝑟 ∆𝑧

(𝑇𝑁 (𝑡) −

(𝑇𝑃 (𝑡) − 𝑇𝑆 (𝑡)) + 𝑟𝑃 ∆𝑟∆𝑧𝑆] · ∆𝑡/(𝜌𝑐𝑟𝑃 ∆𝑟∆𝑧)

(10)

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𝑇𝑃 (𝑡)) −

∆𝑟

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𝜆𝑊 𝑟𝑊 ∆𝑧

𝑇𝑃 (𝑡 + 1) = 𝑇𝑃 (𝑡) + [

For any element P in the tank, 𝑚𝑐 𝑐𝑤

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𝑆=

(𝑇𝑐𝑜 (𝑡) − 𝑇𝑃 (𝑡)) +

𝐴𝑡 ∆𝑧 𝑚𝑐 𝑐𝑤 𝐴𝑡 ∆𝑧 𝑚𝑐 𝑐𝑤

(𝑇𝑁 (𝑡) − 𝑇𝑃 (𝑡)) +

𝐴𝑡 ∆𝑧 𝑚𝑙 𝑐𝑤

𝐴𝑡 ∆𝑧 𝑚𝑙 𝑐𝑤 𝐴𝑡 ∆𝑧

(𝑇𝑆 (𝑡) − 𝑇𝑃 (𝑡)), 𝑖𝑃 < 𝑘 + 1 (𝑇𝑆 (𝑡) − 𝑇𝑃 (𝑡)), 𝑘 + 1 < 𝑖𝑃 < 𝑘 + 𝑛

(11)

(𝑇𝑟𝑒 (𝑡) − 𝑇𝑃 (𝑡)), 𝑖𝑃 = 𝑘 + 𝑛

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{ 𝐴𝑡∆𝑧

(𝑇𝑁 (𝑡) − 𝑇𝑃 (𝑡)) +

𝑚𝑙 𝑐𝑤

where At is the section area of the tank, and Tre is the return temperature from the building. To

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achieve the uniform temperature at each height in the tank, after all the elements of each layer are calculated, we take the average temperature of this layer as the temperature of all the elements of this layer. For the layer i=x, 𝑇𝑖 (𝑥) = ∑𝑚 𝑗=1

2(𝑗−0.5)∆𝑟 2 𝑟2

𝑇(𝑥, 𝑗)

𝑇(𝑥, 𝑗) = 𝑇𝑖 (𝑥) . (𝑗 = 1,2, … … , 𝑚) where Ti is the average temperature of each layer inside the tank, and k+1≤x≤k+n.

(12) (13)

For any element in the soil, 𝑆=0

(14)

Convective heat transfer also occurs between the soil and the air at the ground surface, and the additional source term method (Tao, 2001) is used to integrate this convective heat transfer in Eq. (10). When iP = 1, the source term can be expressed as follow: 𝑆=

ℎ(𝑇𝐴 −𝑇𝑃 )

(15)

∆𝑧

defined as follow (Sodha et al., 1991a): 𝑇𝐴 = 𝑇𝑎 +

𝛼0 𝐼 ℎ



𝜀𝑠 ∆𝑅 ℎ

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where h is the convective heat transfer coefficient and TA is the soil-air temperature, and can be

(16)

Here, α0 and εs are the solar radiation absorptivity and long-wave emissivity of the ground

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surface, respectively; h is the convective heat transfer coefficient; I is the solar radiation

intensity. Sodha et al. (1991b) listed their values for different surface treatments. Thus, α0=0.6,

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εs=1, h=14 W/(m2·k) and I=Idiffuse. Here, Idiffuse indicates the diffuse radiation of the sun that is incident on a surface; ΔR is the difference between the long-wave radiation emitted by the

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ground surface and its received long-wave radiation from the sky and surroundings. For a

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horizontal surface, the value is approximately 63 W/m2 (ASHRAE, 2009).

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4 Model Validation

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4.1 Experimental facility

To verify the accuracy of the numerical model, an experiment was conducted. Because of

the large size of the prototype, we built an experimental model according to the principle of similarity,. The geometric similarity ratio was 1/16, and the Archimedes number (Ar) (Yu, 2005) was equal to that of the prototype. Although previous research on Ar has been based on indoor ventilation, the main characteristics of those applications are very similar to those of the tank

charging process, with the only difference being that the parameters are for a fluid instead of air. Therefore, 𝐴𝑟 =

𝑔𝑙𝛼∆𝑇

(17)

𝑢2

where g is the gravity, l is the characteristic length, α is the thermal expansion coefficient of water, ΔT is the temperature difference between the water at the inlet and that in the tank, and u is the water velocity at the inlet.

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As shown in Fig. 8, sand was packed into a cylindrical container with a height of 0.7 m and diameter 1.4 m. The surface of the container was well-insulated by a thermal insulation layer and a reflective layer. The cylindrical tank was made of stainless steel and had a height of 0.25 m and

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a diameter of 0.25 m. The tank was buried in the sand, with its upper surface 0.25 m below the sand surface. The inlet and outlet pipe were made of stainless steel with an inner diameter of 5

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mm. The inlet was 2 cm below the upper surface of the tank, and the outlet is 2 cm above the

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lower surface of the tank. A hot water bath kept the hot water at the set temperature as a heat source. The pump injected hot water into the tank, and the flow rate could be adjusted by valve

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and read by a rotor flowmeter, the accuracy of which was ±4%. The parameters of the sand used in the experiment are shown in Table 3. The setup included nine K-type thermocouples at the

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positions shown in Fig. 9. Before the test, all K-type thermocouples have been calibrated in the

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water based on a mercury thermometer with accuracy ± 0.1°C.

Table 3. Properties of the sand.

Specific heat capacity 1150 J/kg·℃

Thermal conductivity 1.2 W/m·℃

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1452 kg/m3

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Density

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Fig. 9. Thermocouple positions.

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Fig. 8. Experimental model.

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4.2 Validation result

To ensure the uniformity of the temperature field, the test model was left standing for

several days before the start of the experiment (at approximately 31℃), and the hot water bath was heated to 70℃. In the experiment, the hot water flowed into the tank with a flow rate of 130 mL/min. The temperatures at the measuring points were recorded every five seconds by an

Agilent 3972A data acquisition instrument. The same conditions were simulated, and comparisons between the numerical results (-num) and the experimental results (-exp) are shown

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in Fig. 10 and Fig. 11.

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Fig. 10. Data from measurement points in tank. Fig. 11. Data from measurement points in sand.

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The simulation results can be seen to agree well with the experimental data. However, there is a significant gap between the simulation and experimental results for point 1. This discrepancy

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occurred because this point is close to the inlet and is therefore subject to disturbance. In addition, the gap at point 7 is attributable to the uneven density near the tank caused by the

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backfilling sand, the temperature fluctuation between the 53rd and 70th minutes is a result of the

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pump sucking in some air. In general, the numerical model can be considered reasonable and accurate.

5 Evaluation Index To study the heating capacity of the system, the solar fraction (SF) is defined as the percentage of heat supplied by the heat storage regenerator to the heating load, expressed as SF =

∑ 𝑄𝑠𝑢𝑝𝑝𝑙𝑦 (𝑡) ∑ 𝑄𝑙𝑜𝑎𝑑 (𝑡)

× 100%

(18)

For a given time-step t, the heat supplied by the heat storage regenerator can be calculated using 𝑄𝑠𝑢𝑝𝑝𝑙𝑦 (𝑡) = 𝑐𝑤 𝑚𝑙 ∙ (𝑇𝑒𝑥𝑡 (𝑡) − 𝑇𝑟𝑒 (𝑡))

(19)

To investigate the heat contribution from the soil during the heating season, a soil contribution rate is proposed. It is defined as the percentage of heat transferred from the soil to the tank in relation to the total heat supplied by the heat storage regenerator during the heating

𝜀=

∑[𝑄𝑢𝑝 (t)+𝑄𝑙𝑎𝑡 (t)+𝑄𝑏𝑜𝑡 (t)] ∑ 𝑄𝑠𝑢𝑝𝑝𝑙𝑦 (𝑡)

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season ε: × 100%

(20)

Here, Qup, Qlat, and Qbot are the heat transferred from the soil to the tank through the tank’s

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upper, lateral, and bottom surfaces, respectively. 6 Simulation Parameters

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Based on the control strategy and calculation model described above, the thermal storage system was simulated for 10 years. The main parameters used in the simulation are listed in

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Table 4, and the properties of soil are shown in Table 5. The computational domain’s boundaries were set at a 25-m radius and 33-m depth. Fig. 16 demonstrates that this domain was sufficient

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for the simulation. Prior to the simulation, the model was verified to be independent of grid size and time step. As a result, the grid size was set to 0.1 m, and the time step was 30 s.

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Table 4. Simulation parameters.

Value

Initial temperature

T0=15℃

Simulation time

10 years

Collector area

Ac = 20,25,30,35,40 m2

Heat transfer fluid flow rate in collector

mc = 0.02 kg/s·m2

Heat transfer fluid flow rate on heating side

ml = 0.5 kg/s

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Parameter

Height of tank

4m

Radius of tank

r=2m

Buried depth of tank

4m

Table 5. Properties of the soil (Karacavus and Can, 2008) Density

Specific heat capacity

Thermal conductivity

848 J/kg·℃

1.4 W/m·℃

1500

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kg/m3

7 Results and Discussion

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The functional collecting area of 20 m2 was taken as the research object. Fig. 12 shows the

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hourly tank temperature and the annual SF during the simulation. The annual SF of the system showed little difference from year to year. Affected by the initial temperature field, the SF

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declined slightly and finally stabilized at approximately 49.4%. Nevertheless, the gap between the first year and the stable value was within 0.5%. To prevent the initial temperature field from

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interfering with the analysis, we took the data from the second year to investigate the charging

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and discharging characteristics of the system.

Fig. 12. Simulation data for 10 years.

7.1 Necessity for hourly meteorological data

To illustrate the importance of using hourly meteorological data, we ran a simulation using the monthly average meteorological data and compared the results with those obtained for hourly data. Fig. 13 shows the daily collected energy for one year, which refers to the heat gathered by collectors. It can be seen that the data for the hourly condition fluctuated dramatically, while the data for the monthly condition did not noticeably fluctuate. This is because the latter did not consider the difference in weather between days, or the weather change during a day. However, these changes affect the characteristics of the storage system, which in turn affects the credibility

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of the simulation results. Fig. 14 shows the tank temperature under these two conditions. As can be seen, there is a huge gap between the data from the 100th day to the 250th day, and the

maximum difference is 12.43℃. The simulation results show that the annual SF values of the

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monthly average condition and hourly condition are 46.92% and 49.71% respectively, with a

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relative difference of 5.94%.

Fig. 14. Tank temperature

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Fig. 13. Daily charge energy

7.2 Charge and discharge characteristics of the system

Fig. 15 shows the change in the average tank temperature and the changes in collected

energy, extraction energy, and ambient temperature. During the heat storage period, the tank temperature continued to rise from the initial 17.6℃, reaching a maximum temperature of 62.0℃ on the 186th day. The weather then became cooler, and the soil lost more heat to the

environment. In addition, the heat in the tank transferred to the cooler soil, causing the tank temperature to decrease slowly. From the 244th day, entering the heating period, the heating system extracted heat from the tank, causing the tank temperature to fall sharply. From day 287 to day 346, the temperature was generally maintained at 15℃, which means that the stored heat was exhausted. Thus, reliance was placed mainly on the heat collected during daytime and the heat from the soil for heating. Subsequently, the solar radiation and temperature began to rise,

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distributions at these key moments are illustrated in Fig. 16.

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and the load demand decreased, causing the tank temperature to rise. The temperature field

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Fig. 15. Tank temperature in the second year.

Fig. 16a and Fig. 16b correspond to the first and second heat transfer states identified in Fig.

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4, respectively. It can be seen that during the heat storage period, heat was mainly stored in the water tank and the surrounding soil. Fig. 16c and Fig. 16d depict the third state identified in Fig.

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4, which is the focus of this research. The figures show that at the beginning of the heating period, the tank temperature was still very high and the heat was transferred from the tank to the soil. Because the minimum temperature that can be used by the heat pump investigated here is 15℃, at the beginning of the heating season, the heat pump can use the heat within a range of 14 m from the tank surface. The results also show that the shallow soil is affected by ambient temperature, where most of the stored heat will transfer to the environment, whereas the heat in

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deeper areas can be preserved and returned to the water tank for heating.

b. Day 244

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a. Day 186

c. Day 287

d. Day 345

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Fig. 16. Temperature distributions at different times.

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Because heat conduction occurs in the presence of a temperature gradient, even if the soil temperature is within the usable range of the heat pump, the heat does not necessarily transfer back to the tank and may be transmitted to more distant soil. Therefore, we separately monitored the radial temperature distribution at the center height of the tank and the temperature distribution below the tank axis. Fig. 17 shows the radial temperature distribution change over time during the heating season. In the first 100 days, the soil temperature showed the maximum

value at a certain distance from the tank each day, and the heat stored within this range flowed from the soil to the tank. The location of this maximum temperature value is defined as the available radius of the soil. As the heating season progressed, the temperature of the heat storage regenerator decreased, and the available radius gradually increased from r (the surface of the tank) to r1. Eventually, the heat stored in the soil within the range of 3 meters from the tank’s laterally could be used. As shown in Fig. 18, the vertical direction exhibited a similar trend, and

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the range that could be used was within 4 meters from the tank’s bottom.

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Fig. 17. Temperature distribution in the horizontal direction.

Fig. 18. Temperature distribution in the vertical direction. To illustrate the factors that affect the soil’s capacity to provide energy, the collected energy, extraction energy, meteorological parameters, and tank temperature for five consecutive days of the heating season are shown in Fig. 19. When heat is stored (extracted), the hot water directly

enters (leaves) the tank, and the tank temperature changes rapidly. However, the surrounding soil receives heat through heat conduction. These result in a persistent lag between the change in soil temperature relative to the change in tank temperature. Therefore, heat extraction promotes the soil’s capacity to provide energy, and heat storage suppresses that capacity. To highlight this

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trend, the figure shows a doubling of the true value.

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Fig. 19. Simulation results for five days of the heating season.

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Fig. 20 shows the proportion of heating sources activated during every month of the heating season. In the figure, the tank storage item includes both the heat collected during the daytime,

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which will be quickly used, and the cross-seasonal stored heat. The building load in November was fully satisfied by the tank and the soil. In December, the heat in the heat storage regenerator

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was insufficient, and the heat pump or even AUS was required to meet the load demand. This

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phenomenon was even more pronounced in January, when the SF was only 26.5%. The soil contributed significantly in December, January, and February, with contribution rates of 23.67%, 24.81%, and 9.35%, respectively. Over the entire heating period, the soil contributed 15.29%.

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Fig. 20. Components of supplied heat per month during the heating season.

7.3 Influence of the insulation layer

A large part of the heat stored in the soil is lost to the environment through the ground. Fig.

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16 shows a large temperature gradient above the tank, which means that a lot of heat loss occurs

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there. To explore an adiabatic method that can reduce the heat loss, we simulated several cases of thermal insulation on the tank, as shown in Fig. 21, including no insulation (Group A), insulation

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on the upper surface (Group B), insulation on the upper surface and the upper half of the lateral

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surface (Group C), insulation on the upper surface and the entire lateral surface (Group D), and complete insulation (Group E).

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In practice, the amount of cross-seasonal heat storage is limited by the volume of the tank. For the tank in this study, when the working temperature difference of the heat storage was 80℃,

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the stored heat (16.46 GJ) only reached 33.09% of the annual load (49.74 GJ). For most of the heating season, the collected heat was less than the demand, meaning that the heat stored in the tank was insufficient. Therefore, increasing the tank volume will increase the cross-seasonal heat storage but have little effect on the system during the heating period, and we thus focused on the influence of different collector areas instead of the tank volume. For these five groups, different collector areas (20, 25, 30, 35 and 40 m2) were compared, with the nomenclature used to identify

each condition consisting of the group number plus the collector area (e.g., A20 means that the tank was not insulated and the collector area was 20 m2). The parameters of the thermal insulation layer are shown in Table 6.

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Fig. 21. Different thermal insulation groups applied to the tank model. Table 6. Parameters of thermal insulation layer.

Thickness

50 mm

Density

35 kg/m3

Specific heat

1.38 J/kg·K

Thermal conductivity

0.024 W/m2·K

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Polyurethane

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Material

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Parameters

We then compared the temperature fields at the beginning of the second heating season

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under these different insulation conditions. Fig. 22 shows the cases with 30 m2 collectors, and increasing insulation levels can be seen to increase the tank temperature. However, the amount of

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heat stored in the soil is reduced. As the heat transfer between the tank and the soil is suppressed by the insulation, the tank temperature reaches the upper limit quickly, which limits the work of collectors. From the perspective of an entire year, the weaker the insulation, the more heat is collected and stored in the soil, which is demonstrated by Fig. 23.

b. Group B

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a. Group A

d. Group D

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c. Group C

e. Group E

Fig. 22. Temperature distributions for different insulation conditions.

Fig. 23. Annual collected energy for different conditions.

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The difference in the heat stored in soil has a significant impact on the heat loss from the tank during the heating season. Fig. 24 shows the heat collected by the collectors (-collect) and the lost heat of the tank (-loss) during the heating season where a negative value implies that the

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tank received heat from the soil. It can be seen that the heat collected in the groups was almost

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the same, but the heat loss varied greatly among them. The stronger the thermal insulation was, the greater was the heat lost during the heating season. We took the average temperature of the

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soil within a radius of 3 m around the tank as the soil temperature. Fig. 25 shows the tank and

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soil temperatures for each group during the heating season when the collector area was 30 m2. It can be seen that the tank temperature decreased with decreasing insulation, but the soil

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temperature increased significantly. While the heat transfer resistance between the tank and soil decreased, the temperature difference between them increased, which resulted in the tank

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receiving more heat between the 285th and 345th days. Therefore, over the entire heating season, weakening the insulation can ensure a better storage capacity for heating.

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Fig. 24 Heat collected by the collectors and heat loss from the tanks during the heating season

Fig. 25 Tank and soil temperatures during the heating season.

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To evaluate the contribution of the soil during the heating season, we compared the ε

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values. As shown in Fig. 26, the highest ε was found in A20, where the soil’s contribution was 15.29%. As the collector area increased, more heat was collected during the heating season,

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increasing the tank temperature and reducing the temperature difference between the tank and the soil, thus suppressing the heat transfer from the soil to the tank. On the one hand, the

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insulation enhancement limited heat transfer from the soil to the tank. On the other hand, it reduced the heat loss. These two effects cause opposing results: the heat transfer to the tank is sufficient and results in a higher solar fraction, or the tank loses too much and the SF decreases.

Fig. 26. Annual contribution rate of soil for different conditions.

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Fig. 27 shows the annual SF under each condition. Because the tank is not fully charged when the collector area is small, the stronger the insulation is, the less heat is lost, which is

beneficial to the system. As the collector area increases, the collecting capacity becomes stronger

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and weakening the insulation promotes storing of heat in the soil. Then, part of this heat can be

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reused to improve the SF. From these conditions, Group C can be considered as the most favorable insulation condition. Compared with the complete insulation case (Group E), the

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advantages of Group C increase with the collector area. To further illustrate this result, we

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compared Group C and Group E, as shown in Fig. 28. When the required SF is 76.8%, Group E needs a collector area of 40 m2, whereas Group C requires a collector area of only 36.7 m2,

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which is 8.25% lower. From another point of view, when the collector area is 40 m2, the absolute difference between the SF is 2.6%. This means that Group C can provide 1.29 GJ more heat,

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which is equivalent to 3.94 m3 of a tank with an 80℃ temperature difference, increasing the cross-seasonal heat storage capacity of the tank by 9.85%.

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Fig. 27. Annual solar fractions for different conditions.

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Fig. 28. Annual solar fractions for Group C and Group E.

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8 Conclusions

This paper presented a two-dimensional calculation model of a underground water tank and

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surrounding soil to simulate the dynamic temperature field in a seasonal solar thermal energy

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storage system. In addition, five thermal insulation conditions were considered, and the results were compared for collector areas between 20 m2 and 40 m2. The system characteristics over ten years were dynamically simulated, and a periodic operational condition was obtained from the second year. The results indicate that only the heat within a range of 3 or 4 meters from the surface of the tank will transfer back to the tank during the heating season. With different collector areas, the heat contribution from the soil can reach up to 15.29% of the total heat

supplied by the heat storage regenerator during the heating season. In addition, the storage system was optimized when the tank’s top and the upper parts of its lateral surfaces were insulated. Compared with the case of full insulation, the storage capacity of the tank could be increased by 9.85% when the collector area was 40 m2, and when the required solar fraction was more than 76.8%, the collector area could be reduced by 8.25%. This study did not investigate active measures for extracting heat from the soil. Therefore,

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the system investigated here leaves a huge amount of heat in the soil, which could provide significant potential for energy savings. Future research will focus on how to extract this heat to

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further improve the solar fraction and the soil’s thermal contribution during the heating season.

Acknowledgements

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This work was supported by the Fundamental Research Funds for the Central Universities

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(Project No. 2018CDJDCH0015); the National Natural Science Foundation of China (Project No. 551 51678088); and the Chongqing (China) Science & Technology Commission (Project

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No. cstc2018jcyjAX0072).

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