Results & Discussion

The results obtained will be presented in comparison with a three-dimensional transient analysis using advanced CFD tools [20], aiming at both the simplified model validation and the support for the above referred assumptions.

In order to be able to answer to issues concerning: the relative influence of the air flow inside the soil and therefore the soil ability to dissipate the stored heat; the influence of the entrance flow region and the validity of the proposed correlation (Eq. 7); the influence of tube length on the heat transfer coefficient and the influence of seasonally thermal amplitudes on the system thermal performance; a transient process was modelled for a period of three years, with a time step of a week.

Two different soil types were analysed, a sand based soil and a standard soil characterized by [21]. A sinusoidal boundary condition describing both inlet air temperature and surface ground temperature was imposed (Eq. 1). The seasonal thermal amplitude between 301K and 279K (Summer and Winter average temperatures for Aveiro-Portugal was considered [23].

In order to analyse the soil capacity for heat dissipation and the influence of the air flow on the soil thermal stability, a study is presented in Figs. 5-8 (results referring to the 3D transient analysis). From the results it can clearly be seen, how the presence of the tube affects the soil thermal stability, mainly during Summer (Fig. 5) and Winter (Fig. 7). This study therefore justifies the introduction of a transient heat flux term from the interface soil/tube along the tube air flow (q3) on the simplified model energy balance.

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Fig. 5. Soil/tube system cross-section during Summer.

As far as the influence of the entrance flow region is concerned, it can clearly be depicted from Fig. 9 that the heat transfer coefficient (h) is highly influenced by the tube length.

Is it therefore postulated that the air flow thermal analysis could incur inaccuracies if an entrance region was not taken into account. The latter was therefore considered for tube characteristic dimensions corresponding to approximately ^ < 10, in terms of air

flow exit temperature calculation through Eq. 8.

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Fig. 6. Soil/tube system cross-section during Autumn.

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Fig. 7. Soil/tube system cross-section during Winter.

Figs. 10-11 highlight, for a chosen tube buried depth of 2m and for the two soils type studied, the air flow exit temperature acquired with both ID and 3D models with the same boundary conditions, for the same duration period of 3 years. From these results a few conclusions can be withdrawn: the ID model can compute the air flow temperature value with an error of approximately 1%. It should also be noted that the 3D analysis implied a computational time of over than 3 hours whereas the ID model required only a few minutes. The ID model due to its simplicity is able of becoming a module in a pre­feasibility tool, not requiring a great deal of expertise, whereas the 3D model implied specific knowledge and training in computational fluid dynamics physical and mathematical modelling.

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Fig. 8. Soil/tube system cross-section during Spring.

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Fig. 9. Heat transfer coefficient variation with tube length.

Fig. 12 represents the variation of the air temperature difference between the exit and inlet ports (Tout-Ti„) for the ETVS, again for a 3 years period and two different soil types. The influence of the soil characteristics and the climatic conditions is quite notorious; both factors infer a heavy dependence on site location upon the system thermal effectiveness. Perhaps a better understanding of these factors could be acquired if the model would include a consideration of daily thermal amplitudes. The latter can easily be implemented on a revised tool version. From the analysis can also be postulated that the greatest thermal effectiveness correspond to Summer (where cooling is required) and Winter (where heating is concerned). As expected, the system does not appear to be effective on Spring and Autumn, due to the small thermal amplitudes observed during these periods.

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Fig. 10. Air flow exit temperature for a sand based soil (tube depth of 2m).

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Fig. 11. Air flow exit temperature for a standard soil (tube depth of 2m).

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Fig. 12. ETVS thermal effectiveness for two different soil types.

Once the time variation of the ventilation air temperature difference between the ETVS inlet port and outlet port is know, it is possible to determine the energy gain during a defined period, typically one year. As different technologies are many time used to produce heating and cooling, specific energy gains have to be determined separately as follows:

Z7 —

heating

1 Kir-CPairiToUt-Tin)-dt

(9)

Winter

^cooling

f ™air-Cpair-{Tin-T0Ul)-dt

(10)

Summer

Winter and Summer periods are respectively defined as those when (Tout – тіп)>ьттіп and {Tin-Tout) >b. Tmin.

Theoretical value for tTmm is zero, however, for practical purposes it may be considered a slightly higher value, e. g., 0.5 °С, to take into account only relevant thermal effectiveness (i. e. neglecting minimal local effects).

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