Finite-Element Modeling of Heat Transfer in Ground Source Energy Systems with Heat Exchanger Pipes
Publication: International Journal of Geomechanics
Volume 20, Issue 5
Abstract
Ground source energy systems (GSES) utilize low enthalpy geothermal energy and have been recognized as an efficient means of providing low carbon space heating and cooling. This study focuses on GSES where the exchange of heat between the ground and the building is achieved by circulating a fluid through heat exchanger pipes. Although numerical analysis is a powerful tool for exploring the performance of such systems, simulating the highly advective flows inside the heat exchanger pipes can be problematic. This paper presents an efficient approach for modeling these systems using the finite-element method (FEM). The pipes are discretized with line elements and the conductive–advective heat flux along them is solved using the Petrov–Galerkin FEM instead of the conventional Galerkin FEM. Following extensive numerical studies, a modeling approach for simulating heat exchanger pipes, which employs line elements and a special material with enhanced thermal properties, is developed. The modeling approach is then adopted in three-dimensional simulations of two thermal response tests, with an excellent match between the computed and the measured temperatures being obtained.
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Acknowledgments
The research presented in this paper was funded by the Engineering and Physical Sciences Research Council (EPSRC, grant number 1386304), the Department of Civil and Environmental Engineering, Imperial College London, through a Skempton Scholarship, and the Geotechnical Consulting Group (GCG).
Notation
The following symbols are used in this paper:
- Cpf
- fluid specific heat capacity [J/(kg · K)];
- Cps
- solid specific heat capacity [J/(kg · K)];
- D
- pipe diameter (m);
- dV
- infinitesimal volume (m3);
- h
- convective heat transfer coefficient [W/(m2 · K)];
- kT
- thermal conductivity [W/(m · K)];
- kTEM
- thermal conductivity of TEM [W/(m · K)];
- L
- characteristic length (m);
- l
- pipe length (m);
- Pe
- Péclet number (—);
- Q
- heat pump power (W);
- QT
- heat source or sink (W)
- QT
- total heat flux (W);
- Qa
- advective heat flux (W);
- Qc
- convective heat flux (W);
- Qd
- conductive heat flux (W);
- Qf
- fluid flow rate (m3/s);
- Qf
- fluid source or sink (m3);
- T
- temperature (K);
- Tav
- mean fluid temperature (K);
- Tin
- pipe inlet temperature (K);
- Tout
- pipe outlet temperature (K);
- Tr
- reference temperature (K);
- t
- time (s);
- vf
- fluid velocity (m/s);
- ΔT
- temperature difference (K);
- ρf
- fluid density (kg/m3);
- ρs
- solid density (kg/m3); and
- ΦT
- heat content per unit volume (J/m3).
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Published In
International Journal of Geomechanics
Volume 20 • Issue 5 • May 2020
Copyright
© 2020 American Society of Civil Engineers.
History
Received: Jan 4, 2019
Accepted: Oct 15, 2019
Published online: Mar 16, 2020
Published in print: May 1, 2020
Discussion open until: Aug 17, 2020
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