Three-dimensional numerical modeling of vertical ground heat exchangers: Domain decomposition and state model reduction

Abstract

Modeling of vertical ground heat exchangers is relatively complex because of the three-dimensional transient nature of the problem inside the borehole and in the surrounding ground. Furthermore, the system is characterized by various time scales with rapid changes inside the borehole and slow variations of ground temperature far away from the borehole. Most existing numerical models require important computational resources to adequately represent the short time-scale heat transfer occurring in the immediate vicinity of the borehole, which warrant their use for annual energy simulations. In this article, a three-dimensional reduced model (3D-RM), based on domain decomposition and state model reduction techniques, is proposed to reduce computation time and computer memory. Domain decomposition is used to sub-structure the domain and to vary the time-step values in each sub-domain, and state model reduction is applied to each resulting sub-zone. A comparison with a complete three-dimensional dynamic model indicates that the proposed 3D-RM model reduces computational time by a factor of about 30 without loss of accuracy. A comparison with experimental results shows that the relatively fast transients occurring in the borehole are well predicted by the 3D-RM model not only for the outlet fluid temperature but also for the tube wall temperatures at different depths.

Acknowledgments

The authors want to thank EDF (Electricity of France) R & D for its financial, scientific, and technical support in the framework of the French CIFRE support program for graduate students.

Eui-Jong Kim, PhD, is Post-Doctoral Researcher. Jean-Jacques Roux, PhD, is Professor. Michel A. Bernier, PhD, PE, Member ASHRAE, is Professor. Odile Cauret, PhD, is Researcher.