P. Hollmuller1* and B. Lachal[13]

1 SESUL / IDL, Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal
2 Pole en Sciences de l’Environnement, Universite de Geneve, 1227 Carouge / Geneve, Switzerland
* Corresponding Author, pierre. hollmuller@fc. ul. pt

Abstract

This paper deals with air-soil heat exchangers used for heating or cooling of ambient air used for ventilation of buildings. Basing on a previously published analytical solution concerning heat charge and discharge around an array of buried pipes, it is shown how convective air/pipe and diffusive pipe/soil heat exchange are combining, and how the characteristic exponential amplitude-dampening along the pipe is achieved. The main result consists in dimensioning guidelines, in terms of relations between airflow and pipe length necessary for complete dampening of yearly or daily amplitude. Latter guidelines are finally illustrated and validated with numerical simulation.

Keywords: passive heating and cooling, buried pipes, daily and seasonal heat storage.

1. System description

As considered throughout this article, an air-soil heat exchanger consists of an array of horizontal pipes, possibly a unique pipe, buried underneath or next to a building and situated at the inlet of the ventilation system (fig. 1). Purpose is to take advantage of the soil’s thermal inertia, so as to absorb and dampen the winter/summer or the day/night meteorological oscillation carried by the airflow, hence cutting off the cold or hot thermal peaks which would otherwise be transferred to the building. In principle this technique may be used as well for winter heating as for summer cooling purposes, although it was shown that under Mid-European climates both these modes differ as well in terms of the effect that is to be striven for (yearly versus daily amplitude dampening), as of synergy with the rest of the ventilation system and with the building itself [1].

As is schematically depicted here (fig. 1), and as will be discussed further down in all details, the main working characteristics of an air-soil heat exchanger are, in principle, as follows :

• Winter preheating and summer cooling characterize as well by daily amplitude-dampening (the day/night meteorological extremes contracting around the daily average) as by yearly amplitude-dampening (the daily average approaching the yearly meteorological average).

• While yearly heat storage propagates approximately 3 m around the pipes, daily heat storage does so on approximately 15 cm. Daily amplitude-dampening hence always surpasses yearly amplitude-dampening, which requires a wider storage volume and is limited by more in depth heat diffusion.

*

In the case of a sample soil (conductivity Xs : 1.9 W/K. m ; capacity csps : 1.9 MJ/K. m3), which will be taken as a reference, the daily heat wave hence extends on approximately 15 cm around the pipes, against 3 m for the yearly wave:

8day * 15 cm

8year * 3 m

• Thanks to the diffusive heat storage in the soil, the sinusoidal temperature input carried by the airflow:

Tin = в sm(ot) (2)

dampens exponentially along the pipe exchange surface S:

Strictly speaking, and as for all type of diffusive heat storage, this amplitude-dampening phenomenon actually goes along with delaying or phase-shifting of the input signal. It is however shown that, as long as heat storage may extend over its natural penetration depth, phase-shifting remains secondary, reason why it will here be ignored.

• The amplitude-dampening coefficient h, which will govern the dimensioning guidelines, basically results from serial linking between the convective exchange coefficient ha (air/pipe) and a diffusive exchange coefficient hs (pipe/soil):

The convective exchange coefficient ha can be computed by way of a simplified form of the Gnielinski relation [3], which relates air conductivity Xa and pipe radius r to Reynolds and Prandtl numbers Re and Pr:

The diffusive exchange coefficient hs relates to heat charge and discharge in a soil layer of thickness 8 and can be approximated by the corresponding static conduction coefficient.

Depending whether heat diffusion occurs in radial way around the pipe or in plane way downwards into the ground (as will be discussed further down), it hence writes as: