Numerical modeling of slinky-coil horizontal ground heat exchangers

doi:10.1016/j.geothermics.2011.09.002

Geothermics

Volume 41, January 2012, Pages 55-62

https://doi.org/10.1016/j.geothermics.2011.09.002 Get rights and content

Abstract

Horizontal ground heat exchangers have been widely used in many countries as the heat source for ground-source heat pump systems. When abundant land space is available for the installation of ground heat exchangers, the horizontal ground heat exchangers provide a cost-effective choice because the installation costs of horizontal ground heat exchangers are much lower than those of vertical ground heat exchangers. Slinky-coil horizontal ground heat exchangers, which are basically coiled ground heat exchangers, require less land space than conventional straight horizontal ground heat exchangers because of the higher installation density of heat exchange pipes per given area. However, at present, the slinky-coil horizontal ground heat exchangers tend to be over- or undersized because of the lack of an appropriate design method for them. In this research on the optimum design of slinky-coil horizontal ground heat exchangers, a commercial finite-element simulator, FEFLOW, was used to simulate the performance of slinky-coil horizontal ground heat exchangers taking into account the energy balance at the land surface. The accuracy of the developed simulation model was validated through history-matching calculations on the basis of the results of thermal response tests and a long-term air-conditioning test under various test conditions. In history matching, reasonable agreement was obtained between the measured and simulated values of the heat medium and ground temperatures, demonstrating the reliability of the developed numerical simulation model using FEFLOW.

Highlights

► Performance of slinky-coil ground heat exchangers (GHEs) is not well understood. ► We develop numerical simulation models of slinky-coil GHE for its optimum design. ► Spiral shape of slinky-coils is simplified to a plate-like GHE. ► Consideration of surface heat flux is important for modeling ground temperatures. ► Validity of numerical models is shown through matching with field test results.

Introduction

Horizontal ground heat exchangers (HGHEs) have been widely used as the heat source for ground-source heat pump (GSHP) systems in several regions of the world. In cases where there are few limitations on land space usage, the HGHE can provide a cost-effective choice for ground heat exchangers (GHEs) because the excavation costs of horizontal trenches are significantly lower than the drilling costs for vertical boreholes. In densely populated countries such as Japan, however, HGHEs are rarely used because the available land space is usually limited in residential or commercial areas. To minimize the installation costs and promote GSHP systems with HGHEs, the minimum necessary length of GHEs needs to be accurately predicted by means of numerical or analytical simulations.

In GSHP systems using conventional HGHEs, straight polyethylene pipes are laid in the bottom of 1–2-m-deep horizontal trenches, as shown in Fig. 1(a) (Kavanaugh and Rafferty, 1995). The heat exchange rates per unit length of the straight horizontal heat exchange pipes are significantly lower than those obtained from vertical GHEs because the temperatures in the shallow ground show large seasonal changes, and the dry soils near land surface show low thermal conductivity. Slinky-coil HGHEs use coil-like heat exchange pipes instead of straight pipes, as shown in Fig. 1(b). Slinky-coil HGHEs can collect more energy per unit trench length because of the greater pipe length per trench length. Hence, the application of slinky coils could reduce the land space requirement, which would facilitate the application of GSHP systems with HGHEs, even in cases of limited land availability.

Several research studies have been carried out to predict the performance of conventional straight HGHEs. Piechowski (1998) carried out thermal response tests (TRTs) using straight HGHEs at 1.6-m and 2.0-m depths with a length of 12 m. He developed a numerical simulation model using the 2D finite difference method (Piechowski, 1999) and validated the model with TRT results. Inalli and Esen (2004) performed long-term air-conditioning (A/C) tests on two sets of straight HGHEs, each of which were connected with a water source heat pump. The pipes were 1.0 m and 2.0 m deep and 50 m long in each case. On the basis of these field test results, Esen et al. (2007) constructed a 2D finite difference numerical model and history-matched the ground temperatures to validate the numerical model. Philippe et al. (2010) carried out TRTs on four sets of straight HGHEs with two types of sunshine strength (sunny or shaded) and two types of surface coverage (grassed or paved). They measured the ground temperature behaviors during the TRTs using a distributed temperature sensor (DTS) 0.5 m, 1.0 m (depth of the HGHEs), and 1.5 m deep to investigate the influence of surface conditions on ground temperature behavior.

Research studies on slinky-coil HGHEs are quite limited because of the limited number of installations compared with straight HGHEs. Fujii et al. (2010) presented the results of TRTs and long-term A/C tests on two sets of slinky-coil HGHEs with different loop angles (vertical and horizontal in the trenches) and compared their heat exchange capabilities. They also proposed a performance prediction method of HGHEs using simple linear correlation. On the practical side, the procedures for the installation of slinky-coils were well documented by Jones (1995). However, because of the complex configuration of slinky coils, mathematical models have never been developed using numerical simulation for the prediction of the long-term performance of slinky-coil HGHEs.

Because of the lack of proper prediction tools, the design of slinky-coil HGHEs has to be empirically based, which can lead to the improper design of GSHP systems. In this study, to establish a performance prediction method for slinky-coil HGHEs, a simulation model of slinky-coil HGHEs was developed using a finite-element simulator, FEFLOW, taking into account the energy balance at the land surface. The model was validated using the results of TRTs and a long-term A/C test, which were carried out under various test conditions in Fukuoka City, Japan.

Section snippets

Field tests of slinky-coil ground heat exchangers

In 2008 and 2009, we conducted a series of field tests on slinky-coil HGHEs, i.e., short-term TRTs and a long-term A/C test in Fukuoka City, Japan. In this section, the information on the field test site and the field test conditions are presented.

The field test site was located in the Ito Campus of Kyushu University, in the western part of Fukuoka City. The local annual temperature used the 10-year average (2000–2009) for the annual average temperature (16.5 °C) and for the monthly average

Description of the numerical model

In this study, we developed a 3D numerical model including the slinky-coils and the surrounding ground using a finite-element numerical simulator, FEFLOW Ver. 5.4 (Diersch, 2005), for the groundwater and heat transport. FEFLOW uses the following equations to model the mass and heat transport in the ground:

Mass conservation $\frac{\partial}{\partial t} (ε_{α} ρ^{α}) + \frac{\partial}{\partial x_{i}} (ε_{α} ρ^{α} v_{i}^{α}) = ε_{α} ρ^{α} Q_{ρ}^{α}$

Momentum conservation equation $v_{i}^{α} + \frac{k_{i j}^{α}}{ε_{α} μ_{α}} (\frac{\partial p^{α}}{\partial x_{j}} - ρ^{α} g_{j}) = 0$

Energy conservation equation $\frac{\partial}{\partial t} (ε_{α} ρ^{α} E^{α}) + \frac{\partial}{\partial x_{i}} (ε_{α} ρ^{α} v_{i}^{α} E^{α}) + \frac{\partial}{\partial x_{i}} (j_{i T}^{α}) = ε_{α} ρ^{α} Q_{T}^{α}$

A 3D view of

Model validation

In this section, the 3D simulation model developed in Section 3 is validated based on the results of TRTs and the long-term A/C test. In all simulation runs, the inlet temperatures and circulation rates of the heat medium are input every minute, and the calculated outlet and ground temperatures are compared with the measured temperatures. Weather conditions observed at the test field are also input using Eqs. (3), (4), (5), (6), (7), (8), (9), (10) every hour as the surface boundary conditions.

Conclusions

In this research, numerical simulations of a field test were carried out using a finite-element simulator, FEFLOW, taking into consideration the energy balance at the land surface. The spiral shape of the coils was simplified to a plate-like heat exchanger, and low thermal conductivities were applied in the surrounding pipes to model the heat exchange performance between the heat exchanger and the surrounding soil.

Representation of the slinky coil by a pipe of a different thermal conductivity

References (10)

H. Esen et al.
Numerical and experimental analysis of a horizontal ground-coupled heat pump system
Building and Environment
(2007)
M. Inalli et al.
Experimental thermal performance evaluation of a horizontal ground-source heat pump system
Applied Thermal Engineering
(2004)
Y. Nam et al.
Development of a numerical model to predict heat exchange rates for a ground-source heat pump system
Energy and Buildings
(2008)
H.J.G. Diersch
FEFLOW Reference Manual
(2005)
H. Fujii et al.
Field tests of horizontal ground heat exchangers

There are more references available in the full text version of this article.

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Numerical modeling of slinky-coil horizontal ground heat exchangers

Abstract

Highlights

Introduction

Section snippets

Field tests of slinky-coil ground heat exchangers

Description of the numerical model

Model validation

Conclusions

Building and Environment

Applied Thermal Engineering

Energy and Buildings

FEFLOW Reference Manual

Field tests of horizontal ground heat exchangers