Simulative Investigation of Ground-Coupled Heat Pump System with Spiral Coil Energy Piles

Abstract

Combining the heat exchanger and building foundation pile as the energy pile can eliminate the drilling expense and land area requirement of the conventional borehole heat exchanger. For the spiral coil energy pile, the circulation coil pipe is intertwined tightly in spiral shape against the reinforcing steel of a pile. The distinct advantage of spiral coil energy pile is it can offer higher heat transfer efficiency, reduce pipe connection complexity, prevent air chocking and decrease the thermal short-circuit between circulating pipes compared with other configurations. In order to investigate the operation performance of ground-coupled heat pump system with spiral coil energy piles, analytical simulation models of spiral coil energy piles and the entire heat pump system are established. Temperature responses of the circulating water entering/effusing the spiral coil energy piles and the heat pump unit to the short time step building heating/cooling loads are simulated based on the established analytical models. Then, the heat exchange capacity of the spiral coil energy piles is investigated, and the operation performance of the entire system is analysed. The economic superiority of the ground-coupled heat pump system with spiral coil energy piles is found to be obvious compared with traditional air conditioning modes.

1 Introduction

It is well known that, the high initial cost and land area requirement to install the borehole ground heat exchanger (GHE) remain the major obstacles of the ground-coupled heat pump technology [1]. Based on previous research, the energy pile which combining the heat exchanger and building foundation pile can eliminate the deficiencies of borehole GHE [2,3,4,5]. In order to enlarge the inside heat transfer area as well as heat transfer efficiency, and to reduce pipe connection complexity as well as prevent the air chocking of energy pile, this study utilizes the spiral coil energy pile, which intertwined the circulation coil pipe tightly in spiral shape against the reinforcing steel of a pile, as shown in Fig. 1.

Fig. 1

Schematic diagram of the spiral coil energy pile

For the ground-coupled heat pump system with spiral coil energy piles, heat is extracted from or injected into the ground by circulating water between the heat pump unit and the energy piles, as shown in Fig. 2. It is crucial to calculate the heat transfer of the energy piles and the heat pump unit for simulating the performance of the whole ground-coupled heat pump system.

Fig. 2

Ground-coupled heat pump system with spiral coil energy pile

2 Model Establishment of Energy Pile

Compared with borehole GHE, the proposed spiral coil energy pile possesses thicker diameter and shorter depth. As shown in Fig. 3, the buried coil inside spiral coil energy pile can be simplified into spiral heat source. Then, the spiral heat source model can be established by taking the three-dimensional geometrical characteristic of the spiral pile into account.

Fig. 3

Spiral coil energy pile, finite spiral heat source model and the virtual heat source model

2.1 Temperature Response to the Spiral Heat Source

According to the Green’s function theory, the temperature response at point $\left( {r,\varphi ,z} \right)$ to an instantaneous point heat source with intensity of $\rho {\kern 1pt} c$, located at $\left( {r^{'} ,\varphi^{'} ,z^{'} } \right)$ and activated at the instant $\tau^{'}$ can be expressed as:

$$G\left( {r,\varphi ,z,\tau ;r^{\prime},\varphi^{\prime},z^{\prime},\tau^{\prime}} \right) = \frac{1}{{8\left[ {\pi a\left( {\tau - \tau^{\prime}} \right)} \right]^{3/2} }} \cdot \;\exp \left[ { - \frac{{\left( {r\cos \varphi - r^{\prime}\cos \varphi^{\prime}} \right)^{2} + \left( {r\sin \varphi - r^{\prime}\sin \varphi^{\prime}} \right)^{2} + \left( {z - z^{\prime}} \right)^{2} }}{{4a\left( {\tau - \tau^{\prime}} \right)}}} \right]$$

(1)

As shown in Fig. 2. The spiral heat source and heat sink can be approximated as the sum of numerous point heat sources and heat sinks. Then, the temperature response of the medium around energy pile can be deduced based on the Green’s function theory and the superposition method:

$$\begin{aligned} \theta_{{f,{\text{spiral}}}} & = \frac{{q_{l} b}}{2\pi \rho c}\int\limits_{0}^{\tau } {{\text{d}}\tau^{\prime}\left[ {\int\limits_{2\pi h1/b}^{2\pi h2/b} {G\left( {z^{\prime} = b\varphi^{\prime}/2\pi } \right){\text{d}}\varphi^{\prime} - \int\limits_{2\pi h1/b}^{2\pi h2/b} {G\left( {z^{\prime} = - b\varphi^{\prime}/2\pi } \right){\text{d}}\varphi^{\prime}{\text{d}}\varphi^{\prime}} } } \right]} \\ & = \frac{{q_{l} b}}{16\pi \rho c}\int\limits_{0}^{\tau } {\frac{{d\tau^{\prime}}}{{\left[ {\pi a(\tau - \tau ')} \right]^{3/2} }} \cdot \;\exp \left[ { - \frac{{r^{2} + r_{0}^{2} }}{4a(\tau - \tau ')}} \right]} \\ & \cdot \int\limits_{2\pi h1/b}^{2\pi h2/b} {\exp \left[ {\frac{{2rr_{0} \cos (\varphi - \varphi ')}}{4a(\tau - \tau ')}} \right]\left\{ {\exp \left[ { - \frac{{\left( {z - b\varphi^{\prime}/2\pi } \right)^{2} }}{4a(\tau - \tau ')}} \right]} \right.} - \left. {\exp \left[ { - \frac{{\left( {z + b\varphi^{\prime}/2\pi } \right)^{2} }}{4a(\tau - \tau ')}} \right]} \right\}{\text{d}}\varphi^{\prime} \\ \end{aligned}$$

(2)

2.2 Temperature Response of Pipe Wall

The spiral heat source can be approximated as located at the centre of coil pipe, and the pipe wall located at r_p away from the spiral heat source, as shown in Fig. 4. Then, the temperature response of pipe wall at moment $\tau$ can be deduced in Eq. (3) based on the short time step pulse heat currents $q_{{l_{i} }}$.

Fig. 4

Spiral coil pipe buried in pile GHE

$$\begin{aligned} \theta_{\text{ring,pile}} & = \frac{1}{k}\sum\limits_{i = 1}^{\infty } {\left( {q_{{l_{i} }} - q_{{l_{i - 1} }} } \right) \cdot p\left( {\tau - \tau_{i - 1} } \right)} \\ & = \frac{1}{k}\left[ {\sum\limits_{i = 1}^{\infty } {q_{{l_{i} }} \cdot p\left( {\tau - \tau_{i - 1} } \right)} - \sum\limits_{i = 1}^{\infty } {q_{{l_{i - 1} }} \cdot p\left( {\tau - \tau_{i - 1} } \right)} } \right] = \frac{1}{k}\left[ {\sum\limits_{i = 1}^{\infty } {q_{{l_{i} }} \cdot p\left( {\tau - \tau_{i - 1} } \right)} - q_{{l_{0} }} \cdot p\left( {\tau - \tau_{0} } \right) - \sum\limits_{j = 1}^{\infty } {q_{{l_{j} }} \cdot p\left( {\tau - \tau_{j} } \right)} } \right] \\ & = \frac{1}{k}\sum\limits_{i = 1}^{\infty } {q_{{l_{i} }} } \cdot \left[ {p\left( {\tau - \tau_{i - 1} } \right) - p\left( {\tau - \tau_{i} } \right)} \right] = \frac{1}{k}\sum\limits_{i = 1}^{\infty } {q_{{l_{i} }} } \cdot q\left( {\tau - \tau_{i - 1} } \right) \\ \end{aligned}$$

(3)

2.3 Temperature Response of Circulating Water

Compared with the heat transfer characteristics of ground outside the pile, the heat transfer of circulating water inside the spiral coil energy pile can be approximated as a steady-state process. Then, the entering and effusing fluid temperatures of the spiral coil energy pile can be determined by heat currents and heat transfer resistances:

$$\left\{ {\begin{array}{*{20}l} {T_{f}^{{\prime }} = T_{\text{p}} + \frac{{q_{l} \cdot b \cdot R_{\text{rp}} }}{{\sqrt {\left( {2\pi \cdot r_{0} } \right)^{2} + b^{2} } }} + \frac{{q_{l} \left( {h_{2} - h_{1} } \right)}}{{2 \, M \cdot C_{\text{p}} }}} \hfill \\ {T_{f}^{{\prime \prime }} = T_{\text{p}} + \frac{{q_{l} \cdot b \cdot R_{\text{rp}} }}{{\sqrt {\left( {2\pi \cdot r_{0} } \right)^{2} + b^{2} } }} - \frac{{q_{l} \left( {h_{2} - h_{1} } \right)}}{{2 \, M \cdot C_{\text{p}} }}} \hfill \\ \end{array} } \right.$$

(4)

3 Model Establishment of Heat Pump Unit

Energy consumption of the ground-coupled heat pump system is major affected by the operation performance of the heat pump unit. For simulating the heat pump’s performance based on variable building air conditioning loads, it is more feasible to fit the functions of its COP and effusing fluid temperature versus entering fluid temperature by utilizing the least square method and the 2th power polynomial curves. Operation parameters of the selected heat pump unit in this study are plotted in Fig. 5.

Fig. 5

Operation parameters of the selected heat pump unit

4 Results

4.1 Field Temperature Response to the Sample Spiral Coil Energy Pile

According to the normal pile configurations in the practical engineering, a sample spiral coil energy pile with r₀ = 0.4 m, h₁ = 2 m, h₂ = 22 m, b = 0.4 m, r_pi = 20 mm and r_p = 32 mm buried in the soil with undisturbed temperature of 12.5 °C is selected in this study. The fluid flow velocity inside coil pipe is set to be 0.5 m/s. By simulation, the temperature fields covering the sample energy pile and its surrounding soil at different operation times are described in Fig. 6. As shown, the temperature rise fluctuates considerably in the vicinity to the spiral coil. The axial heat conduction influence is limited to the two ends of energy pile in relatively short time periods, and penetrate deeper for longer-term operation.

Fig. 6

Temperature response to the spiral coil energy pile

4.2 Operation Parameters of the Sample Spiral Coil Energy Pile

The hourly heat transfer loads afforded by the sample spiral coil energy pile is shown in Fig. 7, and its hourly operation parameters are simulated and plotted in Fig. 8. Based on simulation results, the sample energy pile possesses heat exchange capacity of about 212 W/m. For the sample energy pile with depth of 20 m, it can afford about 100 m² building air conditioning areas.

Fig. 7

Hourly heat transfer loads afforded by the sample spiral coil energy pile

Fig. 8

Hourly operation parameters of sample spiral coil energy pile

4.3 Performances of the Heat Pump Unit

As shown in Fig. 8, the highest outlet water temperature of the spiral coil energy pile in the ground-coupled heat pump system with spiral coil energy piles for cooling provision during summer is 28.4 °C, and the lowest outlet water temperature of the spiral coil energy pile in the ground-coupled heat pump system for heating provision during winter is 3.8 °C. Compared with the building ambient air, the spiral coil energy pile can provide the heat pump with the heat sink in lower temperature for cooling provision and the heat source in higher temperature for heating provision. Therefore, the heat pump unit of the ground-coupled heat pump system with spiral coil energy piles can obtain high COP value and low operation energy consumption. The operation COP value of the heat pump unit during one year operation is simulated and plotted in Fig. 9.

Fig. 9

COP and energy consumption of the heat pump unit

According to the operation simulation results of the ground-coupled heat pump system with spiral coil energy piles, the average COP of the heat pump unit during one year operation is 4.2, and the total energy consumption of the heat pump unit for heating and cooling provision during the whole year’s operation is about 27.2 kWh/m². Taking the energy consumption of the circulating water pumps and the fan coil units into account, total cost of the ground-coupled heat pump system with spiral coil energy piles for the whole year’s heating and cooling provision to building is as low as 22.5 RMB Yuan/m². The economic superiority of the ground-coupled heat pump system with spiral coil energy piles is obvious compared with traditional air conditioning modes.

5 Conclusions

In order to investigate the operation performance of the ground-coupled heat pump system with spiral coils energy piles, this study simulated the temperature responses of the spiral heat source, the coil pipe wall and the circulating water entering/effusing the spiral coil energy pile to the hourly heat transfer loads based on the established analytical model. Then, the operation performance of the spiral coil energy pile and the whole ground-coupled heat pump system is investigated.

According to the simulative operation parameters of the ground-coupled heat pump system with spiral coil energy piles, the highest outlet water temperature of the spiral coil energy pile for cooling provision during summer is 28.4 °C, and the lowest outlet water temperature of the spiral coil energy pile for heating provision during winter is 3.8 °C. The heat exchange capacity of the sample spiral coil energy pile is about 212 W/m. The average COP of the heat pump unit in one year’s operation is 4.2, and the total energy consumption of the heat pump unit for heating and cooling provision during the whole year’s operation is about 27.2 kWh/m².

The economic superiority of the ground-coupled heat pump system with spiral coil energy piles compared with traditional air conditioning modes is found to be obvious in this study. For further research, the optimal design parameters of the ground-coupled heat pump system with spiral coil energy piles should be discussed.