## 2 Materials and Methods
### EAHX Performance Assessment
* **Region C**: Start of the afternoon with EAHX exit air temperature lower than the room upper setpoint temperature and both of these lower than outdoor air temperature, \(T_{\rm AL}<T_{\rm rs}^{\rm U}<T_{\rm a0}\). In this region, outdoor air makes no contribution to room cooling; still, it is customary to distinguish two components in the EAHX outdoor air load removal, \[\dot{Q}_{\rmoa}^{\rm EAHX}=\dot{Q}_{r}^{\rm EAHX}+\dot{Q}_{\rm Rn}^{\rm EAHX}= \dot{m}_{\rm a}c_{\rm a}\Delta T_{\rm al,rs}+\dot{m}_{\rm a}c_{\rm a}\Delta T _{\rm rs,a0},\] (8) namely, the EAHX room load removal component, \(Q_{r}^{\rm EAHX}\), and a component for the EAHX outdoor air load removal to the \"neutral\" state, \(\dot{Q}_{\rm Rn}^{\rm EAHX}\), with \[\Delta T_{\rm rs,a0}= \begin{cases}T_{\rm rs}^{\rm U}-T_{\rm a0}&\text{ if }\ T_{\rm rs}^{\rm U}<T_{\rm a0};\\ 0&\text{otherwise};\end{cases} \] (9) being the temperature gradient that brings outdoor air to the room upper setpoint temperature, i.e., the condition for which outdoor air neither heats nor cools the room (\"neutral\" state). In region C, the following inequation applies: \(Q_{r}^{\rm EAHX}\leq Q_{\rmoa}^{\rm EAHX}\). * **Region D**: During the afternoon, with room upper setpoint temperature lower than EAHX exit air temperature and both of these lower than outdoor air temperature, \(T_{\rm rs}^{\rm U}<T_{\rm aL}<T_{\rm a0}\). In this region, since EAHX exit air temperature exceeds the room upper setpoint, the EAHX is incapable of removing room loads, \(Q_{r}^{\rm EAHX}=0\). The EAHX operates for outdoor air load removal only. The analysis presented for the distinct regions--A, B, C and D--highlights the following conclusions:
* In region B, the EAHX complements free cooling with outdoor air, increasing room load removal. * In region C, the EAHX replaces free cooling with outdoor air, increasing the duration of room load removal. * A prime sizing requirement for standalone EAHX cooling is to avoid region D, i.e., for cooling design conditions, inequations \(T_{\rm aL}<T_{\rm a0}\) and \(T_{\rm aL}<T_{\rm rs}^{\rm U}\) should stand. A final aspect relevant for standalone EAHX cooling performance is the definition of room upper setpoint temperature. When room cooling relies on refrigeration machines (including the case of EAHX designed solely for outdoor air precooling with a downwind refrigeration machine), \"close control\" of indoor air temperatures is possible; hence, a constant room setpoint is defined for the whole summer period. With standalone EAHX cooling, constant indoor air temperature can not be guaranteed. Indeed, standalone EAHX cooling resembles much more closely natural ventilation with window opening, with room temperature varying according to outdoor conditions. For naturally ventilated
rooms, standard EN 15251:2007 [29] specifies free-floating room setpoint temperatures in accordance with adaptive comfort principles [30; 31; 32]. Given the resemblance to natural ventilation, previous researchers applied standard EN 15251:2007 and the adaptive comfort viewpoint to the study of EAHX [5; 33]. This viewpoint is also used in this paper with free-floating room upper (U) setpoint temperatures defined as,  
\[\left\{ \begin{aligned} & T^{\text{U}}_{\text{sIII}}=0.33\theta_{ \text{rm}}+18.8+4&\Leftarrow\text{Category III};\\ & T^{\text{U}}_{\text{rSI}}=0.33\theta_{\text{rm}}+18.8+2& \Leftarrow\text{Category I};\end{aligned} \right. \tag{10}\]  
free-floating room lower (L) setpoint temperatures defined as,  
\[\left\{ \begin{aligned} & T^{\text{L}}_{\text{rSI}}=0.33\theta_{ \text{rm}}+18.8-2&\Leftarrow\text{Category I};\\ & T^{\text{L}}_{\text{rSI}}=0.33\theta_{\text{rm}}+18.8-4& \Leftarrow\text{Category III};\end{aligned} \right. \tag{11}\]  
and with subscripts III and I denoting acceptable and high comfort expectancy levels, respectively [29].