## 2 Methods
### Constraints on the Design of Large-Diameter EAHXs for Room Load Removal  
To guarantee a specific room setpoint temperature, load removal can be adjusted by changing the airflow rate and/or the supply air temperature. Refrigeration machines allow the precise regulation of supply air temperature, and the removal of large room loads can be achieved by increasing the airflow rate. The behavior of the EAHX is, however, quite distinct. For the EAHX, there is a dependence between the airflow rate \(\dot{V}\) and outflow temperature \(T_{\text{aL}}\), with outflow temperatures increasing from the undisturbed soil temperature \(T_{\text{sso}}\) to the outdoor air temperature \(T_{\text{a0}}\) as \(\dot{V}\) increases from 0 and \(\infty\). For design conditions and during the cooling season, the room setpoint temperature satisfies \(T_{\text{sso}}<T_{\text{ar}}<T_{\text{a0}}\); therefore, airflow rates above a certain threshold reverse the EAHX's operation mode from cooling (\(T_{\text{aL}}\approx T_{\text{sso}}<T_{\text{ar}}\)) to heating (\(T_{\text{aL}}\approx T_{\text{a0}}>T_{\text{ar}}\)), turning the choice of room setpoint temperature into a major EAHX design constraint.  
HVAC design with refrigeration machines typically considers maximum room setpoint temperatures of 27 \({}^{\circ}\)C [28]. However, for naturally ventilated rooms, whose temperatures vary according to outdoor conditions, adaptive models of indoor thermal comfort allow larger setpoints [28]. Since temperatures in rooms cooled with EAHX also vary according to outdoor conditions, papers researching EAHX cooling use the adaptive comfort model [12; 29], allowing indoor temperature setpoints exceeding 27 \({}^{\circ}\)C for hot summer conditions.  
Another major constraint to EAHX design is the undisturbed soil temperature, which, for burial depths larger than 7 m, becomes approximately constant and equal to the annual average outdoor air temperature [30]. Given the large difference in time constants for heat transfer in the air and in the soil, despite being influenced by the temperature of the air flowing inside the EAHX, the EAHX's inner surface temperature remains identical to the undisturbed soil temperature. If, during the daily cycle, the outdoor air temperature drops below the soil temperature, the EAHX reverses operation from cooling to heating (\(T_{\text{aL}}\approx T_{\text{sso}}>T_{\text{a0}}\)). As depicted in Figure 1, to prevent unwanted heating, a bypass to the large-diameter EAHX was implemented, allowing conventional free-cooling with outdoor air. For effective EAHX operation, a careful analysis of the EAHX burial depth and of the year-long outdoor temperatures becomes mandatory.  
Understanding the limitations imposed by soil temperature and room setpoint temperature and recognizing that the airflow rate has an upper threshold are essential aspects in the design of large-diameter EHAXs capable of standalone room cooling, especially since these limitations (except for soil temperature) do not apply to the design of EAHXs that pre-cool outdoor air. Indeed, for EAHXs used for pre-cooling, the supply air temperature is not determined by the EAHX but in a downwind refrigeration machine.