Buried pipe systems with sensible and latent heat exchanges : validation of numerical simulation against analytical solution and long-term monitoring

A finite differences numerical model for buried pipe systems is presented, accounting for sensible as well as for latent heat exchanges, so as for fully three dimensional heat diffusion in soil and flexible border conditions. After description of the algorithm, extensive validation against an analytical solution as well as against several long-term monitored real scale installations will be discussed. INTRODUCTION Lacking better tools, most authors (Athienitis et al. 2000; Bansal et al. 1983; Chen et al. 1983; Elmer and Schiller 1981; Levit et al. 1989; Rodriguez et al. 1988; Santamouris and Lefas 1986; Schiller 1982; Seroa da Motta and Young 1985; Serres et al. 1997; Tiwari et al. 1993; Tzaferis et al. 1992) are dimensioning air/soil heat exchangers by way of simple static exchange models, simple to handle but for which estimation of the fundamental parameters (air/soil heat exchange coefficient and effective soil temperature) isn't evident at all, especially in transient regime. As an alternative, some analytical models explicitly treat heat diffusion in the soil. One of them (Claesson and Dunand 1983) concerns periodic heat diffusion from a cylindrical pipe embedded in a semi-infinite medium (with constant temperature at upper free surface). The induced effect on the longitudinal temperature of the airflow has been treated apart (Sawhney and Mahajan 1994), appropriate physical interpretation and operational presentation of the results unfortunately not being carried out. A similar problem includes the interference of neighboring pipes (Kabashnikov et al. 2002) but concerns deeply buried pipes, without interference of upper border conditions. As a last case, a cylindrical model (Hollmuller 2003) treats the case of a pipe subject to isothermal or adiabatic boundary condition at finite radial distance (limitation of available soil layer). Apart from yielding explicit understanding of the heat diffusion phenomenon (in terms of the natural temperature penetration depth) latter model also puts forward the theoretical possibility, under certain conditions, to completely phase-shift the periodic input while barely dampening its amplitude, a phenomenon apparently unexploited up to now. Although they might give important insight in the physical heat exchange and storage phenomenon which are at work, preceding analytical models are obviously limited to constant airflow rates and rather simple geometries and border conditions. As an alternative, several numerical simulation models based on finite differences have also contributed to characterize diffusive heat exchangers. Some of them are limited to description of one only typical pipe (Bojic et al. 1997; Huber and Remund 1996; Mihalakakou et al. 1994). Other ones allow for the description of several parallel running pipes, with or without possibility to treat more complicated cases than steady flow rate, homogenous and laterally adiabatic soils, or sole sensible heat exchange (Boulard et al. 1989; De Paepe 2002; Gauthier et al. 1997; Gygli and Fort 1994). However, when validation against monitoring is ever carried out, latter in all cases remains limited to a few hours or days and does generally not concern real scale installations, thereby not providing necessary proof of robustness one would expect. Corroboration against an analytical solution is furthermore never given, except for the last one of these models and for the trivial case of one-dimensional heat diffusion without airflow. As a response to preceding state of the art, we will present a flexible, finite differences numerical model, allowing for description of sensible as well as latent heat exchanges. After description of the algorithm, extensive validation against an analytical solution as well as against several long-term monitored real scale installations will be discussed. NUMERICAL MODEL The simulation tool developed here bases on a previously developed finite element model, which already accounted for simultaneous sensible and latent heat exchange between air and tubes, as well as fully tree dimensional heat diffusion in soil (Boulard et al. 1989). The original model has been completely revised, so as to allow for various geometries, soil properties and border conditions, as well as to include frictional losses, possible water Ninth International IBPSA Conference Montreal, Canada August 15-18, 2005

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