Design and Performance of a Large-Diameter Earth–Air Heat Exchanger Used for Standalone Office-Room Cooling

Abstract

Earth–air heat exchangers (EAHXs) use the soil’s thermal capacity to dampen the amplitude of outdoor air temperature oscillations. This effect can be used in hot and dry climates for room cooling with no or very little need for resources other than those used during the EAHX construction, an obvious advantage compared to the significant operational costs of refrigeration machines. Contrary to the streamlined process applied in conventional HVAC design (using refrigeration machines), EAHX design lacks straightforward and well-established rules; moreover, EAHXs struggle to achieve office room design cooling demands determined with conventional indoor thermal environment standards, hindering designers’ confidence and the wider adoption of EAHXs for standalone room cooling. This paper presents a graph-based method to assist in the design of a large-diameter EAHX. One year of post-occupancy monitoring data are used to evaluate this method and to investigate the performance of a large-diameter EAHX with up to 16,000 m³/h design airflow rate. Considering an adaptive standard for thermal comfort, peak EAHX cooling capacity of 28 kW (330 kWh/day, with just 50 kWh/day of fan electricity consumption) and office room load extraction of up to 22 kW (49 W/m²) provided evidence in support of standalone use of EAHX for room cooling. A fair fit between actual EAHX thermal performance and results obtained with the graph-based design method support the use of this method for large-diameter EAHX design.

1. Introduction

The concept of earth–air heat exchangers (EAHXs) for building cooling can be traced back to construction techniques employed by Persians and Greeks in the pre-Christian era [1] and to the more recent and still operating example of the 16th century villas at Costozza, in the hills of Vicenza, Italy [2]. Despite the millennium-old origin, building cooling with EAHXs is a topic of contemporary interest that is being actively researched [3,4,5], this interest is intensified by the Net Zero Emissions by 2050 Scenario [6], which advocates a halt to the current increase in electricity demand and in installed electric capacity for space cooling and promotes the use of technologies complementary or alternative to the prevailing refrigeration machines.

Earth–air heat exchangers are commonly used for pre-cooling, removing outdoor air loads, and leaving room load extraction to refrigeration machines. A typical design consists of pipes with diameters of 0.30 m or lower; for single-family residential applications, a single buried pipe is often the adopted solution. Lee and Strand [7] studied the use of this type of EAHX in four locations in the USA and concluded that, when properly designed, an EAHX could save more than 50% of the total cooling capacity, significantly reducing building cooling loads. For the desert climate conditions of Kuwait, Al-Ajmi et al. [8] showed that a reduction of 30% in seasonal cooling demand was possible with the use of an EAHX, and in a study conducted by Michalak [9], a single-pipe EAHX in Poland allowed an annual reduction in energy consumption for cooling of 43%. For residential and office buildings requiring larger ventilation flowrates, EAHX design favors, typically, an increase in the number of pipes, while the pipe diameter remains smaller than 0.30 m [10,11]. However, using fewer pipes and larger pipe diameters (for commercial buildings, 1 m or more [12,13,14]) remains a viable alternative. Barnard and Jauzens [13], Amanowicz and Wojtkowiak [15], and Duarte et al. [14] balance the reduction in heat transfer for this latter design with non-heat-transfer-related aspects, such as pipe maintenance, ensuring adequate indoor air quality, and economic factors. According to Santamouris (in Mihalakakou et al. [16]) and Duarte et al. [14], for the Mediterranean region, coupling of an EAHX with appropriate building passive cooling techniques can cover up to 100% of a building’s cooling demand, highlighting the extent of the savings that could be achieved from a broader use of large-diameter EAHXs.

Since EAHXs are built with materials produced locally, familiar to local constructors, and since they can operate with no or very little need for resources other than those used during its construction, from a life cycle analysis perspective, EAHXs have an obvious advantage compared to sophisticated refrigeration machines, often imported and with significant operational costs. Moreover, making use of the soil’s thermal capacity to dampen the amplitude of outdoor air oscillations, EAHXs have no use for refrigerant fluids, hence reducing the release to the atmosphere of gases contributing to the greenhouse effect.

In spite of their advantages, large-diameter EAHXs for room cooling make sense only when unobstructed soil is available and when excavation costs represent a small fraction of the total building (being cooled by the EAHX) construction costs. Moreover, a very important challenge facing the adoption of a large-diameter EAHX is winning decision makers’ trust in its room-cooling capability. To achieve this trust, adequate design methods validated with post-occupancy monitoring become essential.

According to both Soares et al. [4] and Mihalakakou et al. [3], EAHX design requires more research and is far from the streamlined process used in conventional HVAC design. The scientific literature on EAHXs focuses on the evaluation of EAHX performance [7,9,17] using monitored outdoor conditions or existing climate data. Typically, estimates of the performance of real-size EAHXs are derived from small-scale models or commercial computational tools [8,18,19,20]. These computational tools may not be available to HVAC designers willing to consider EAHX solutions, and the procedure used in system design/sizing, focusing on the analysis of specific and demanding operating conditions, is distinct from a performance analysis based on climate data or on monitored outdoor conditions for a particular period of time.

Simplified analytical and empirical methods are also available and are sufficiently accurate in predicting the temperature of the air exiting the EAHX, as concluded by Tzaferis and Liparakis [21], who analyzed the sensitivity of different methods to predict EAHX performance. Consequently, simplified methods remain adequate for EAHX design.

Simplified methods available to HVAC designers are presented as analytical expressions [22], as rules derived from parametric studies [1,13,23,24], and as simplified computational tools [25,26,27]. Still, concerning large-diameter EAHXs used for room load removal in hot and dry climates, a research gap persists, and studies dedicated to the design of these EAHXs using post-occupancy monitoring data are rare. This paper contributes to the reduction of this research gap, presenting a graph-based method to assist the design of a large-diameter EAHX. Moreover, with post-occupancy data, the performance of a large-diameter EAHX designed for standalone cooling is assessed, and the challenges facing designers considering using EAHXs to cool office buildings located in hot and dry climates are discussed.

Using the experience gathered from a five-year-long project consisting of the design, construction, and monitoring of a large-diameter EAHX, this paper starts by presenting characteristics and limitations of EAHXs for room load removal and the graph-based method used to determine EAHX performance under design conditions. Next, a detailed description of the built EAHX, relevant specifications of the building (being cooled by the large-diameter EAHX), and climate/soil characteristics are provided. Using post-occupancy monitoring data and considering an adaptive indoor thermal environment standard, the performance of the built EAHX is assessed. Post-occupancy data are also used to evaluate the graph-based design methodology. Useful recommendations for the design of large-diameter EAHX capable of standalone room cooling are, finally, presented.

2. Methods

2.1. Characterization of an EAHX for Standalone Room Cooling

Figure 1 sketches a large-diameter EAHX for office building cooling. In the daytime, hot outdoor air enters the EAHX at temperature $T_{\mathrm{a}0}$ and flows along a horizontal pipe with length L buried at depth z. Since the pipe is in contact with soil at temperature $T_{\mathrm{s}\infty }$ (undisturbed soil temperature), which is lower than outdoor air, cooled air at temperature $T_{\mathrm{aL}}$ leaves the EAHX at an air handling unit (AHU) before being delivered to the building (the AHU allows a bypass to the EAHX).

Figure 1 also sketches the flow of air inside the building. Air from the EAHX enters the building and contacts buried structural elements with large thermal mass that are cooled during the nighttime [23], when outdoor air temperatures are lower; as a result, during the daytime, air is supplied to the room at a temperature $T_{\mathrm{as}}$, which is lower than $T_{\mathrm{aL}}$. The room (air) setpoint temperature is depicted in Figure 1 as $T_{\mathrm{ar}}$.

Using the classification scheme of Soares et al. [4], Figure 1 sketches an open-loop horizontal single-pipe EAHX for cooling. Moreover, the coupling with building thermal mass (TM) and nighttime forced ventilation results in a hybrid EAHX–TM system operating in continuous mode.

The above classification makes no distinction between EAHX for outdoor air load removal—for air pre-cooling—and EAHX for room load removal, i.e., for standalone room cooling. To clarify the meaning given in this paper to an EAHX capable of removing room loads, Figure 2 presents a sketch of the thermo-hygrometric processes with air from the instant air enters the EAHX $\left(T_{\mathrm{a}0}, {\omega }_{\mathrm{a}0}\right)$ until it leaves the office room $\left(T_{\mathrm{ar}}, {\omega }_{\mathrm{ar}}\right)$. Sensible cooling of outdoor air is depicted in Figure 2 by the horizontal line, from right to left, with constant specific humidity ${\omega }_{\mathrm{a}0}={\omega }_{\mathrm{as}}$, a reasonable approximation for EAHXs operating in hot and dry climates [17]. In fact, for these climates, the EAHX inner surface temperature remains larger than the air dew temperature, preventing condensations; moreover, indoor air quality constraints impose the choice of EAHX materials (or coatings) impervious to water, preventing moisture transfer from the soil to the air flowing inside the EAHX.

The line from $T_{\mathrm{a}0}$ to $T_{\mathrm{as}}$ is divided into three subprocesses. The first subprocess occurs in the EAHX and is the sensible cooling of air from outdoor temperature $T_{\mathrm{a}0}$ to temperature $T_{\mathrm{ar}}$, which is equal to the room design setpoint temperature. This subprocess translates into outdoor air load extraction, ${\dot{Q}}_{\mathrm{oa}}^{\mathrm{EAHX}}$. Still occurring inside the EAHX, the next subprocess corresponds to the sensible cooling from temperature $T_{\mathrm{ar}}$ to the EAHX exit temperature, $T_{\mathrm{aL}}$. This subprocess translates into the EAHX room (air) load extraction ${\dot{Q}}_{\mathrm{rm}}^{\mathrm{EAHX}}$. The third subprocess depicted in Figure 2 results from heat transfer between the air and buried building structural elements that are cooled during the nighttime. This sensible cooling from $T_{\mathrm{aL}}$ to supply air temperature $T_{\mathrm{as}}$ also translates into a room (air) load extraction, but occurring in the building, not the EAHX. This building load removal is represented as ${\dot{Q}}_{\mathrm{rm}}^{\mathrm{bldg}}$. A final process corresponding to heating and humidification of room air from $\left(T_{\mathrm{as}}, {\omega }_{\mathrm{as}}\right)$ to $\left(T_{\mathrm{ar}}, {\omega }_{\mathrm{ar}}\right)$ is also represented in Figure 2.

Expressions for sensible cooling load removal by the EAHX and building are as follows:

$$\begin{array}{}\mathrm{(1a)}& {\dot{Q}}_{\mathrm{oa}}^{\mathrm{EAHX}}=\dot{m}{c}_a\left(T_{\mathrm{ar}}-T_{\mathrm{a}0}\right) ,\mathrm{(1b)}& {\dot{Q}}_{\mathrm{rm}}^{\mathrm{EAHX}}=\dot{m}{c}_a\left(T_{\mathrm{aL}}-T_{\mathrm{ar}}\right) ,\mathrm{(1c)}& {\dot{Q}}_{\mathrm{rm}}^{\mathrm{bldg}}=\dot{m}{c}_a\left(T_{\mathrm{as}}-T_{\mathrm{aL}}\right) ,& \mathrm{and},\mathrm{by}\mathrm{the}\mathrm{definition}\mathrm{of}\mathrm{an}\mathrm{EAHX}\mathrm{for}\mathrm{room}\mathrm{load}\mathrm{extraction},\hfill \mathrm{(1d)}& {\dot{Q}}_{\mathrm{rm}}^{\mathrm{EAHX}}+{\dot{Q}}_{\mathrm{rm}}^{\mathrm{bldg}}={\dot{Q}}_{\mathrm{rm}}=\dot{m}{c}_a\left(T_{\mathrm{as}}-T_{\mathrm{ar}}\right) .\end{array}$$

A large-diameter EAHX fit for standalone room cooling, i.e., fit for (sensible) load extraction is, then, one capable of offsetting, on its own or in combination with building passive cooling techniques, the room design cooling demand, i.e., ${\dot{Q}}_{\mathrm{rm}}$ should equal the simultaneous sum of (sensible) room design internal heat gains and gains occurring through the building envelope, warranting the room design setpoint temperature, $T_{\mathrm{ar}}$.

2.2. 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 $T_{\mathrm{aL}}$, with outflow temperatures increasing from the undisturbed soil temperature $T_{\mathrm{s}\infty }$ to the outdoor air temperature $T_{\mathrm{a}0}$ as $\dot{V}$ increases from 0 and ∞. For design conditions and during the cooling season, the room setpoint temperature satisfies $T_{\mathrm{s}\infty }<T_{\mathrm{ar}}<T_{\mathrm{a}0}$; therefore, airflow rates above a certain threshold reverse the EAHX’s operation mode from cooling ($T_{\mathrm{aL}}\approx T_{\mathrm{s}\infty }<T_{\mathrm{ar}}$) to heating ($T_{\mathrm{aL}}\approx T_{\mathrm{a}0}>T_{\mathrm{ar}}$), 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 °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 °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 ($T_{\mathrm{aL}}\approx T_{\mathrm{s}\infty }>T_{\mathrm{a}0}$). 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.

2.3. Simplified Expressions for Large-Diameter EAHX Thermal Design

Sensible heat transfer in the EAHX is modeled with the differential equations for diffusion in the soil, for advection in the air inside the pipe, and initial and boundary conditions [27]. Important boundary conditions are the outdoor air and the undisturbed soil temperatures.

Outdoor air temperatures $T_{\mathrm{a}0}\left(t\right)$, with t denoting time, are often available from national meteorological services; undisturbed soil temperature $T_{\mathrm{s}\infty }(z,t)$ at EAHX depth z can be derived from soil temperatures $T_{\mathrm{s}0}\left(t\right)$ measured at a reference depth $z_0$, as described in Givoni and Katz [30].

For design purposes and depths with small thermal amplitude, Givoni and Katz’s equation for $T_{\mathrm{s}\infty }(z,t)$ is simplified to

$${\widehat{T}}_{\mathrm{s}\infty }\left(z\right)={\overline{T}}_{\mathrm{s}0}+{\theta }_{\mathrm{s}0}{e}^{-K(z-z_0)} ,$$

(2)

with ${\widehat{T}}_{\mathrm{s}\infty }\left(z\right)$ and ${\overline{T}}_{\mathrm{s}0}$ being the annual maximum and annual average values of undisturbed soil temperatures at depths z and $z_0$, respectively, and ${\theta }_{\mathrm{s}0}$ the soil temperature amplitude at depth $z_0$.

Although modeling of the heat transfer in EAHXs using commercial computational models is found in the scientific literature [27], since our design is concerned with the system’s operation under specific and demanding (sizing) conditions, solutions derived from simplified heat transfer expressions remain relevant [21]. Examples of the successful use of simplified expressions validated against monitoring data are described in Al-Ajmi et al. [8], Sodha et al. [31], and Do et al. [32].

In line with the above argument, the advice provided in standard EN 15241:2007 CEN [22] for EAHX design considers the following expression for EAHX outflow air temperature:

$$\begin{array}{c}\hfill T_a\left(x\right)=T_{\mathrm{s}\infty }+(T_{\mathrm{a}0}-T_{\mathrm{s}\infty })exp\left(-{\displaystyle \frac{2\pi r_{0}U}{{\dot{m}}_a{c}_a}}x\right) ,\end{array}$$

(3)

where U is a joint convection–conduction heat transfer coefficient defined as

$$\begin{array}{c}\hfill U={\displaystyle \frac{h_a{h}_s}{h_a+h_s}} ;\end{array}$$

(4)

with

$$\begin{array}{}\mathrm{(5a)}& h_a=\left[4.13+0.23\left({\displaystyle \frac{T_a}{100}}\right)-0.0077{\left({\displaystyle \frac{T_a}{100}}\right)}^2\right]{\displaystyle \frac{v_{STP}^{0.75}}{{\left(2r_0\right)}^{0.25}}}& \mathrm{and}\hfill \mathrm{(5b)}& h_s={\displaystyle \frac{2\pi {\lambda }_s}{ln\left(\frac{R}{r_0}\right)}} \end{array}$$

denoting, respectively, the convective heat transfer coefficient between the air and the inner surface of the EAHX (from Schack’s expression in [33]) and the conduction heat transfer coefficient in the cylindrical soil domain between the inner and outer radii, $r_0$ and R, respectively, the latter being the radial position where the thermal influence of the EAHX in the soil becomes negligible [34].

2.4. Graph-Based Design Method

In a development similar to that of De Paepe and Janssens [35], the following nondimensional quantities are defined: $\overline{T}$, a measure of the EAHX thermal efficiency,

$$\overline{T}={\displaystyle \frac{T_{\mathrm{a}0}-T_{\mathrm{a}}\left(x\right)}{T_{\mathrm{a}0}-T_{\mathrm{s}\infty }}}\left[=\epsilon \right] ,$$

(6)

and $\overline{x}$, a fraction of the EAHX characteristic length,

$$\overline{x}={\displaystyle \frac{x}{L^{*}}} ,$$

(7)

with the characteristic length,

$$\begin{array}{c}\hfill L^{*}={\displaystyle \frac{{\rho }_a\left(\pi r_0^{2}v\right)c_a}{2\pi r_{0}U}} ,\end{array}$$

(8)

defining the distance from the EAHX inlet for which the reduction in temperature difference $T_{\mathrm{a}0}-T_{\mathrm{a}}\left(x\right)$ equals $63\%(\approx 1-1/e)$ of the maximum reduction possible, i.e., $T_{\mathrm{a}0}-T_{\mathrm{s}\infty }$.

Redefining Equation (3) in terms of $\overline{T}$ and $\overline{x}$, the following simplified expression is obtained:

$$\begin{array}{c}\hfill \overline{T}=1-exp\left(-\overline{x}\right) .\end{array}$$

(9)

Taking advantage of the concept of EAHX characteristic length, using Equation (8) together with Equations (2) and (9), and the expression for volumetric flow rate,

$$\begin{array}{c}\hfill \dot{V}=\pi r_o^{2}v ;\end{array}$$

(10)

a set of graphs to assist large-diameter EAHX design is obtained—see Figure 3, Figure 4 and Figure 5.

In deriving these graphs, air and soil properties and temperatures from the case study described in Section 3 were considered.

Using Equation (2), the top graph in Figure 3 relates soil depth z and outdoor air temperature $T_{\mathrm{a}0}$ to EAHX maximum temperature gradient $T_{\mathrm{a}0}-{\widehat{T}}_{\mathrm{s}\infty }\left(z\right)$. The bottom graph in Figure 3 is derived from Equation (9) and presents lines of constant fraction $x/L^{*}$ as a function of temperature differences $T_{\mathrm{a}0}-T_{\mathrm{aL}}$ and $T_{\mathrm{a}0}-{\widehat{T}}_{\mathrm{s}\infty }\left(z\right)$.

Figure 4, obtained from Equation (10), presents lines of constant airflow rate (per pipe), $\dot{V}$, for different diameters and airflow velocities.

The graphs in Figure 5 were derived from Equation (8) and depict lines of constant pipe length L for specific fractions of characteristic length $x/L^{*}$, different diameters, and different airflow velocities.

To understand how Figure 3, Figure 4 and Figure 5 assist in the design of an EAHX, consider the following specifications, which will be referred to as “Case 1”:

• Pipe burial depth $z=5.5$ m;
• EAHX inlet air temperature: $T_{\mathrm{a}0}=37$ °C;
• EAHX airflow rate: $\dot{V}=8000 {\mathrm{m}}^3/\mathrm{h}$.

Moreover, assume that the pipe length L should not exceed 70 m (due to property limits) and the desired EAHX exit air temperature is $T_{\mathrm{aL}}=28 °\mathrm{C}$.

Using the pipe burial depth $z=5.5$ m and $T_{\mathrm{a}0}=37$ °C, from Figure 3, point $\overline{)\mathrm{i}0}$, the maximum temperature gradient $T_{\mathrm{a}0}-{\widehat{T}}_{\mathrm{s}\infty }(z=5.5)$ is 17 K. Since the desired EAHX inlet to outlet temperature difference $T_{\mathrm{a}0}-T_{\mathrm{aL}}$ is 9 K, the minimum fraction $x/L^{*}$ meeting specifications is 0.75, point $\overline{)\mathrm{i}1}$ in Figure 3.

From Figure 4, it can be seen that the specified airflow rate could be met with different pipe layouts. A single pipe with 1.0 m diameter and airflow velocity ∼$2.8$ m/s (point $\overline{)\mathrm{j}0}$) would meet the requirement. Other options are represented in points $\overline{)\mathrm{k}0}$ and $\overline{)\mathrm{l}0}$ for two and four parallel pipes with 1.0 and ∼$0.7$ m diameter, respectively. For these layouts, pipe airflow velocity is equal to ∼$1.4$ m/s.

Switching focus to the $x/L^{*}=0.75$ (bottom) graph in Figure 5, the shaded area depicts the domain meeting the pipe length specification, $L\le 70$ m. Points $\overline{)\mathrm{k}2}$ and $\overline{)\mathrm{l}2}$ represent two (1 m diameter) 70 m and four (0.7 m diameter) 50 m long parallel pipes, respectively. These are the two possible design solutions.

Next, consider the analysis of the solution consisting of two (1 m diameter) 70 m long parallel pipes with specifications similar to “Case 1” but with increased airflow rate, i.e.,

• Pipe burial depth $z=5.5$ m;
• EAHX inlet air temperature: $T_{a0}=37 °$C;
• EAHX airflow rate: $\dot{V}$ = 16,000 ${\mathrm{m}}^3/\mathrm{h}$.

This will be referred to as “Case 2”.

Suppose we wish to determine the change to EAHX exit air temperature for this case. Figure 4 confirms two 1 m diameter pipes can be used to deliver a total of 16,000 m³/h (8000 m³ /h per pipe). Point $\overline{)\mathrm{j}0}$ depicts this case with a corresponding airflow velocity of ∼$2.8$ m/s. Using this velocity and 1 m diameter, point $\overline{)\mathrm{j}1}$ in Figure 5—upper graph, for fraction $x/L^{*}=0.575$—shows that the thermal performance of a (1 m diameter) 70 m long pipe delivering 8000 m³/h is equivalent to approximately 60% (the actual value is 57.5%) of the thermal performance of a pipe with the characteristic length $L^{*}$. From the bottom graph in Figure 3, with $x/L^{*}=0.575$ and $T_{\mathrm{a}0}-{\widehat{T}}_{\mathrm{s}\infty }(z=5.5)=17$ K, it can be seen that the EAHX inlet to outlet air temperature difference is $T_{\mathrm{a}0}-T_{\mathrm{aL}}=7.5$ K, which translates into $T_{\mathrm{aL}}=29.5°C$.

Given the larger air flowrate, it is concluded that outdoor air load removal (Equation (1a)) is higher for “Case 2”; still, with a larger outflow air temperature, the thermal efficiency (Equation (6)) for “Case 2” is lower than for “Case 1,” and the proximity to the room setpoint temperature cancels the effect the larger ventilation rate has on room load removal (Equation (1b)).

These results provide an important insight into large-diameter EAHX performance and, together with fan energy consumption (the largest EAHX operational cost) and other non-heat-transfer constraints (e.g., excavation and pipe costs, ease of maintenance), contribute to narrowing the set of possible solutions to large-diameter EAHX design problems.

3. Case Study

3.1. EAHX Location, Climate and Soil Temperature

The studied EAHX (and the building it serves) is located in the Alentejo region, in Portugal, approximately 40 km east from the district capital, Beja, with climate variety Csa—Mediterranean climate with hot and dry summer [37].

Figure 6 presents box and violin plots obtained from (instantaneous) outdoor air temperature and relative humidity data collected at the EAHX location between June and September.

Figure 6 shows that mean monthly air temperatures exceed 20 °C, reaching 26 °C in July. Maximum temperatures exceeded 40 °C in June and were higher than 35 °C in July and August. The relative humidity interquartile range is defined (approximately) between 30 and 70%, and an increase in monthly mean relative humidity is observed from June to September.

Regarding the soil, rhodo-chromic-Luvisols [38] are typical at the EAHX location. Figure 7 compares instantaneous soil temperature measurements at the EAHX site, at 10 cm depth, with analytic results [30]. A fair agreement between measured and analytical soil temperature at this depth is observed.

Analytical results at 5.5 m are also represented in Figure 7. At this depth, a pronounced reduction in annual thermal amplitude is expected, with temperatures varying approximately 2 K around the average annual value of 18.5 °C. Moreover, a phase shift delaying the lowest soil temperature by approximately 4 months, from January to May, is observed.

Figure 7 also depicts dew point temperatures derived from instantaneous outdoor air temperature and relative humidity measured at the EAHX site. The purpose of including this information is to show that for warm months, between June and September, the dew point seldom exceeded the undisturbed soil temperature, supporting the low probability of condensation in the EAHX and supporting the horizontal sensible cooling line depicted in Figure 2.

Finally, Figure 7 presents upper free-floating setpoints (category I to III of an adaptive thermal comfort model) as defined in standard EN 15251:2007 [28].

Free-floating setpoints were determined from outdoor air temperature running means derived, in turn, from instantaneous outdoor air temperature measurements at the EAHX site. From June to September, upper free-floating setpoints lay above 28 °C (category I upper limit), reaching 32 °C (category III upper limit) for most of July and August. This information is relevant for the definition of the office room design air temperature setpoint used in the next section.

3.2. The Building (Being Cooled by the EAHX)

Relevant for EAHX design are the building design specifications summarized in Table 1. Free-floating room temperatures are assumed, and on hot summer days, adaptive setpoint temperatures are considered as defined in standard EN 15251:2007 [28].

Table 1 emphasizes the extent to which the design of the building and of the large-diameter EAHX are related (similar to the design of naturally ventilated office buildings). Use of building thermal mass and forced nighttime ventilation to extend EAHX cooling capacity has been mentioned and used previously [14,23,39] and is also considered in the present case study. Moreover, complementing this “supply side” increase in room load extraction, careful building design allowed a reduction in sensible cooling demand in the room to approximately 50 W/m². Special care was placed, also, in the selection and location of room air supply diffusers and air extractor grilles, preventing local draft discomfort.

Table 1. Building design specifications relevant to the EAHX design.

Bldg Parameter	Design Value	Comment
1. Floor area †, $A_{\mathrm{rm}}$	450 m2 (EAHX cooled)	1a. Total floor area 750 m2.
2. Room height, ${\overline{h}}_{\mathrm{rm}}$	3 m	2a. Average value.
3. Outdoor air temperature	37 °C (equal to EAHX inlet temperature, $T_{\mathrm{a}0}$)	3a. ASHRAE’s 0.4% annual dry bulb design value for Beja, Portugal [40].
4. Room setpoint temperature †, $T_{\mathrm{ar}}$	32 °C (upper limit according to data in Figure 7)	4a. Ventilation and cooling with EAHX is handled as equivalent to natural ventilation, allowing free-floating indoor air temperatures. 4b. An adaptive comfort model is used with office room upper setpoint temperature defined from outdoor running mean temperature [28].
5. Room (air) cooling load demand †, ${\dot{Q}}_{\mathrm{rm}}^{″}$	∼50 W/m2 (sensible heat; considering the simultaneous sum of internal gains and gains through the building envelope)	5a. Rooms are used for light office work; have low occupancy density; design makes use of structural elements’ thermal mass; an airtight, well-insulated envelope and glazings with appropriate solar control reduce room cooling demand.
6. Room ach †, $n_{\mathrm{rm}}$	∼11 ${\mathrm{h}}^{-1}$ (100% fresh air system as in “Case 2”); $\dot{V}=A·\overline{h}·n_{\mathrm{rm}}\approx$ 16,000 ${\mathrm{m}}^3/\mathrm{h}$ ≈$4.5{\mathrm{m}}^3/\mathrm{s}$	6a. Local draught discomfort is prevented with careful selection and placement of air supply diffusers and air extractor grilles; 6b. During summer, larger (controlled) airflow velocities in the room working area offset larger air temperatures [28].
7. Supply air temperature †, Tas	∼4 K below the design upper free-floating setpoint temperature ($28 °$C when $T_{\mathrm{ar}}=32 °$C)	7a. Use of building’ structural elements (foundations) thermal mass in combination with forced nighttime ventilation allows a design temperature gradient $T_{\mathrm{as}}-T_{\mathrm{aL}}$ between the air supplied to the room and the air as it exits the EAHX between $-1$ and $-2$ K.

^† Design values related by ${\dot{Q}}^{″}{A}_{\mathrm{rm}}={\dot{Q}}_{\mathrm{rm}}\approx {\rho }_a{c}_a\dot{V}\left(T_{\mathrm{as}}-T_{\mathrm{ar}}\right)$.

Table 1. Building design specifications relevant to the EAHX design.

Bldg Parameter	Design Value	Comment
1. Floor area †, $A_{\mathrm{rm}}$	450 m2 (EAHX cooled)	1a. Total floor area 750 m2.
2. Room height, ${\overline{h}}_{\mathrm{rm}}$	3 m	2a. Average value.
3. Outdoor air temperature	37 °C (equal to EAHX inlet temperature, $T_{\mathrm{a}0}$)	3a. ASHRAE’s 0.4% annual dry bulb design value for Beja, Portugal [40].
4. Room setpoint temperature †, $T_{\mathrm{ar}}$	32 °C (upper limit according to data in Figure 7)	4a. Ventilation and cooling with EAHX is handled as equivalent to natural ventilation, allowing free-floating indoor air temperatures. 4b. An adaptive comfort model is used with office room upper setpoint temperature defined from outdoor running mean temperature [28].
5. Room (air) cooling load demand †, ${\dot{Q}}_{\mathrm{rm}}^{″}$	∼50 W/m2 (sensible heat; considering the simultaneous sum of internal gains and gains through the building envelope)	5a. Rooms are used for light office work; have low occupancy density; design makes use of structural elements’ thermal mass; an airtight, well-insulated envelope and glazings with appropriate solar control reduce room cooling demand.
6. Room ach †, $n_{\mathrm{rm}}$	∼11 ${\mathrm{h}}^{-1}$ (100% fresh air system as in “Case 2”); $\dot{V}=A·\overline{h}·n_{\mathrm{rm}}\approx$ 16,000 ${\mathrm{m}}^3/\mathrm{h}$ ≈$4.5{\mathrm{m}}^3/\mathrm{s}$	6a. Local draught discomfort is prevented with careful selection and placement of air supply diffusers and air extractor grilles; 6b. During summer, larger (controlled) airflow velocities in the room working area offset larger air temperatures [28].
7. Supply air temperature †, Tas	∼4 K below the design upper free-floating setpoint temperature ($28 °$C when $T_{\mathrm{ar}}=32 °$C)	7a. Use of building’ structural elements (foundations) thermal mass in combination with forced nighttime ventilation allows a design temperature gradient $T_{\mathrm{as}}-T_{\mathrm{aL}}$ between the air supplied to the room and the air as it exits the EAHX between $-1$ and $-2$ K.

^† Design values related by ${\dot{Q}}^{″}{A}_{\mathrm{rm}}={\dot{Q}}_{\mathrm{rm}}\approx {\rho }_a{c}_a\dot{V}\left(T_{\mathrm{as}}-T_{\mathrm{ar}}\right)$.

3.3. The Built EAHX and Monitoring Equipment Used

A photograph of the EAHX during its construction is presented in Figure 8.

This photograph shows a trench as viewed from the EAHX air intake and two parallel pipes leaving this air intake towards the air handling unit (not yet built). The pipes (concrete) have 1 m diameter, are placed 4 m apart (distance between axes), are 70 m long (with the construction completed), and are buried 5.5 m deep (average depth, since pipes are sloped towards the air intake for water drainage).

Simultaneous with the EAHX construction, a Vaisala weather station [41] was installed onsite to record outdoor data. Dataloggers [42,43] and sensors were also installed to measure: undisturbed soil temperature at 0.1 m depth [44]; air temperature and air relative humidity at the AHU air inlet; and electric current at the AHU switchboard to monitor fan electricity consumption and ventilation rate. Fifteen-minute measurement intervals were selected, except for the weather station, which used one-minute intervals.

4. Results and Discussion

4.1. Monitoring Data

Monitoring data collected between June and September were used to analyze the performance of the built EAHX. During this period, EAHX airflow rate was kept in the 7000 to 9000 m³/h range—nominal 8000 m³/h airflow rate (4000 m³/h per pipe)—24 h a day, 7 days a week.

The timeseries presented in this section serve two purposes. They allow the generic evaluation of the EAHX performance with hot and dry climate conditions. Additionally, they allow the assessment of the EAHX design, namely the assessment of the standalone capability of the large-diameter EAHX.

Figure 9 compares timeseries of outdoor air temperature (equal to EAHX inlet temperature, $T_{\mathrm{a}0}$) and EAHX outflow air temperature ($T_{\mathrm{aL}}$). The amplitude damping promoted by the EAHX on the outdoor air thermal wave is highlighted with contour lines for daily maxima outdoor air and EAHX exit air temperatures. The EAHX airflow rate timeseries ($\dot{V}$) is also depicted close to horizontal time axis.

Figure 9 shows that EAHX exit temperatures lay below 30 °C despite frequent outdoor daily maxima above 35 °C.

Figure 9 includes lines for running mean and upper free-floating setpoint temperatures [28] (category III). Free-floating setpoints exceed 30 °C, showing little variability, with a mean value of 31 °C and maxima of approximately 32 °C during July and most of August.

Using the design free-floating setpoint temperature $T_{\mathrm{ar}}=32 °$C and monitoring data, Figure 10 presents timeseries of daily energy (heat) removed by the EAHX, namely total energy $Q_{\mathrm{t}}^{\mathrm{EAHX}}\left(=Q_{\mathrm{rm}}^{\mathrm{EAHX}}+Q_{\mathrm{oa}}^{\mathrm{EAHX}}\right)$ and energy removed from room air $Q_{\mathrm{rm}}^{\mathrm{EAHX}}$. Timeseries of daily fan electricity consumption ($W^{\mathrm{EAHX}}$) and EAHX coefficient of performance (COP = $Q_t/W$) are also included in Figure 10.

Figure 10 shows that total loads extracted in the EAHX reached 330 kWh/day. Room maximum and average load extraction were 240 and 112 kWh/day, respectively. Daily fan electricity consumption—50 kWh/day—remained (approximately) constant during the monitoring period. EAHX energy performance measured by the COP shows that with the exception of September, with lower outdoor air temperatures, heat removed in the EAHX exceeded between 2.5 and 5 times the fan electricity consumption.

Using the room design setpoint $T_{\mathrm{ar}}=32 °$C and monitored data, Figure 11 presents outdoor air and room loads removed in the EAHX as a function of outdoor air temperature $T_{\mathrm{a}0}$. These loads are identified as gray crosses (${\dot{Q}}_{\mathrm{oa}}^{\mathrm{meas}.}$) and gray circles (${\dot{Q}}_{\mathrm{rm}}^{\mathrm{meas}.}$), respectively.

As regards the monitored room loads (gray circles), the depicted variability is attributed to changes in the temperatures of air and soil, and to the multiple combinations of these parameters that occurred in the four-month monitoring period. A reduction in this variability is visible as the outdoor air temperature approaches the less frequent (maximum) value of 40 °C.

For the largest recorded outdoor air temperature in Figure 11, 40 °C, it is concluded that a total of 28 kW is removed by the EAHX: 25 kW of outdoor air load and 3 kW of room air load (points $\overline{)\mathrm{n}1}$ and $\overline{)\mathrm{n}2}$, respectively). As the outdoor air temperature decreases to the room setpoint, 32 °C, loads removed from outdoors decline to zero, whereas room load extraction increases to a maximum, 22 kW (point $\overline{)\mathrm{n}3}$). For outdoor temperatures lower than 32 °C, room load extraction becomes progressively smaller, and below 20 °C, the heat transfer from air to soil is less than 1 kW.

Using the room floor area $A_{\mathrm{rm}}=450 {\mathrm{m}}^2$ (see Table 1) to determine room specific load removal, Figure 11 shows that as outdoor temperatures decrease from 40 to 20 °C, the specific load first increases from (3000/450=) 7 W/m² in point $\overline{)\mathrm{n}2}$ to 49 W/m² in point $\overline{)\mathrm{n}3}$, and then decreases to 0 W/m² as outdoor temperatures fall below the room setpoint temperature, 32 °C. Table 1 specifies the room design cooling load demand—50 W/m²—for an outdoor design temperature of 37 °C; naturally, for a lower outdoor air temperature, the cooling demand should decrease, and since room specific load removals of approximately 50 W/m² were obtained for outdoor temperatures below 37°, close to the room setpoint temperature, it is concluded that the studied large-diameter EAHX is capable of standalone cooling for these outdoor temperatures (near point $\overline{)\mathrm{n}3}$). For outdoor temperatures lower than 32 °C, Figure 11 shows that room specific load removal decreases to zero; but the room cooling demand also decreases from the design value to zero as the outdoor temperature drops from 37 °C to the room heating setpoint temperature; therefore, the EAHX’s standalone capability is possible for outdoor temperatures lower than 32 °C. Since the EAHX’s ability to extract room loads decreases for outdoor temperatures above 32 °C—while room cooling demand increases to its design value—it is concluded that the EAHX standalone capability is lost as outdoor temperatures rise above 32 °C.

4.2. Evaluation of the Graph-Based Method

Since the EAHX operating conditions were identical to those described in Case 1 of Section 2.4, monitoring data for periods with outdoor temperature approaching or exceeding ASHRAE’s 0.4% annual dry bulb design temperature (37 °C, see Table 1) are used to evaluate the graph-based design method.

The analysis of the contour lines in Figure 9 (measured data) reveals that when outdoor air temperatures exceed 35 °C, temperature differences (between maxima of the red and blue lines) lay in the 6.5 to 9.2 K range. Using Figure 3 from the graph-based method, a fair estimation is achieved with temperature differences in the 8 to 10 K range when $z=5.5$ m, $35\le T_{\mathrm{a}0}\le 40 °$C and considering Case 1 fraction $x/L^{*}=0.75$.

As regards load extraction results, using the analytical expressions supporting the graph-based method, Figure 11 includes light blue lines ${\dot{Q}}_{\mathrm{rm}}^{\mathrm{analyt}.}$ and ${\dot{Q}}_{\mathrm{oa}}^{\mathrm{analyt}.}$ for room and outdoor air load removal when the ventilation rate is 8000 m³/h. For outdoor temperatures above $35 °$C (and below $39 °$C), the analytical results provide a good fit to monitored outdoor air and to upper room load removal.

Table 2. Comparison of load removal measurements with results determined from analytical expressions when the design outdoor air temperature is considered, $T_{\mathrm{a}0}=37 °$C. Values of specific load removal are obtained using the room floor area $A_{\mathrm{rm}}=450 {\mathrm{m}}^2$.

		Measured	Analytical (Case 1) 8000 m3/h; $\mathit{x}/{\mathit{L}}^{*}=0.75$	Analytical (Case 2) 16,000 m3/h; $\mathit{x}/{\mathit{L}}^{*}=0.575$
${\dot{Q}}_{\mathrm{rm}}$	Point(s) in Figure 11 [kW] [W/m2]	$\overline{)\mathrm{n}4}$∼$\overline{)\mathrm{n}5}$ 7∼11 15.5∼24.4	$\overline{)\mathrm{n}5}$ 11 24.4	$\overline{)\mathrm{n}6}$ 13.75 30.5
${\dot{Q}}_{\mathrm{oa}}$	Point(s) in Figure 11 [kW] [W/m2]	$\overline{)\mathrm{n}6}$ 13.75 30.5	$\overline{)\mathrm{n}6}$ 13.75 30.5	—

highlights the results depicted in Figure 11 for the design outdoor air temperature $T_{\mathrm{a}0}=37 °$C.

Table 2 shows that the EAHX removes ∼9 kW of room air loads (${\dot{Q}}_{\mathrm{rm}}^{\mathrm{meas}.}$), an average value between 7 and 11 kW (points $\overline{)\mathrm{n}4}$ and $\overline{)\mathrm{n}5}$) corresponding to a cooling capacity per room floor area between 15.5 and 24.4 W/m². Outdoor air loads (${\dot{Q}}_{\mathrm{oa}}^{\mathrm{meas}.}$) removed are approximately 13.75 kW (point $\overline{)\mathrm{n}6}$), corresponding to 30.5 kW/m² of cooling capacity.

Considering the analytical results for Case 1, with 8000 m³/h and $x/L^{*}=0.75$ (blue line in Figure 11 and $T_{\mathrm{a}0}=37 °$C), the outdoor air load removal is (as expected) in excellent agreement with measured data; room load extraction, 11 kW (point $\overline{)\mathrm{n}5}$), is a fair fit to the averaged monitoring values of room load extraction (9 kW).

The agreement observed between measured data and analytical results and diminishing variability in data for higher outdoor air temperatures—for design temperatures—supports the applicability of the graph-based method for EAHX design in hot and dry climates.

4.3. EAHX’s Capacity to Meet the Room Design Cooling Load Demand

In Section 4.1, it was concluded that, for the studied EAHX, the ability for standalone cooling (warranting room setpoint temperature) is lost as outdoor temperatures rise above 32 °C. Indeed, Table 1 states a room design cooling load demand of 50 W/m² when outdoor air temperature is 37 °C, whereas Table 2 shows that for Case 1 (as defined in Section 2.4), with 8000 m³/h flowrate, the EAHX’s maximum measured room load removal is 24.4 W/m², half the design value.

Since the design ventilation rate stated in Table 1 is 16,000 m³/h, to study the increase in the EAHX’s airflow rate, Figure 11 includes the line, ${\dot{Q}}_{\mathrm{rm};\dot{V}=16,000{\mathrm{m}}^3/\mathrm{h}}^{\mathrm{analyt}.}$, consisting of orange vertical marks, depicting room air load removal results when analytical expressions are used with two (1 m diameter) 70 m long pipes and 16,000 (=2 × 8000) m³/h ventilation rate.

Table 2 highlights the ${\dot{Q}}_{\mathrm{rm};\dot{V}=16,000{\mathrm{m}}^3/\mathrm{h}}^{\mathrm{analyt}.}$ result in Figure 11, considering the design outdoor air temperature $T_{\mathrm{a}0}=37 °$C, which corresponds to Case 2 (also defined in Section 2.4). For this case, the estimate of room air load extraction is 13.75 kW (point $\overline{)\mathrm{n}6}$), or 30.5 W/m².

This result represents more than 60% of the design room cooling load demand, 50 W/m²; still, it is concluded that despite the increased ventilation rate, the built EAHX is incapable, on its own, of canceling the room design heat gains. Only in the case where building thermal mass and nighttime ventilation allows a temperature difference $T_{\mathrm{as}}-T_{\mathrm{aL}}\approx -1.6$ K, equivalent to room load removal ${\dot{Q}}_{\mathrm{rm}}^{\mathrm{bldg}}\approx 8.75$ kW, is the design cooling demand specification met. If the building cooling capacity ${\dot{Q}}_{\mathrm{rm}}^{\mathrm{bldg}}$ is lower than 8.75 kW (19.5 W/m²), the room air temperature rises above the 32 °C upper free-floating setpoint.

Hence, it is concluded that, for the large-diameter EAHX described in this paper and for the hottest summer days, with outdoor temperatures exceeding $32 °$C, full standalone cooling capability requires that the cooling in the EAHX is supplemented with cooling obtained from the use of the building’s structural elements thermal mass in combination with forced nighttime ventilation, as described in Table 1 and as previously mentioned in the scientific literature [14,23,39].

5. Conclusions

The design of a large-diameter EAHX for standalone use, capable of removing office room loads in hot and dry climates, is a very challenging task. However, using monitoring data from an existing large-diameter EAHX, this paper confirmed that, in spite of the challenge, a graph-based method relying on simplified analytical expressions can assist in this design.

Using monitoring data it was concluded that:

• With adequate sizing, large-diameter EAHX can remove significant room loads without the need for refrigeration machines and with little electrical energy consumption. For the monitored EAHX, a total peak cooling capacity of 28 kW and a total of 330 kWh removed in a day were achieved with just 50 kWh/day of fan electricity consumption. As regards specifically the EAHX’s ability to remove room loads—essential to assess the standalone cooling capability, a maximum value of 22 kW was monitored, i.e., the EAHX is capable of offsetting 49 W/m² of the room cooling demand.
• Still, these results are only possible when an adaptive standard for thermal comfort is considered. Indeed, regarding the choice of the design room setpoint temperature, use of adaptive comfort models allowing setpoints higher than those for conventional HVAC systems is, most likely, mandatory when designing an EAHX for standalone use.
• Moreover, for the hottest summer days, the monitoring data showed that for hours with outdoor temperature equal to $37 °$C (meeting the design condition criteria), room load removal in the EAHX reached, at best, 60% of the design cooling demand. As it happens in the design of naturally ventilated office buildings for hot and dry climates, the adoption of (building-related) passive cooling techniques, such as combining the use of building thermal mass with forced nighttime ventilation, is, most likely, also mandatory when designing an EAHX for standalone room cooling.
• Concerning the graph-based design method, the monitoring results obtained considering the design conditions were fairly matched by those determined from the graphs and from the analytical expressions supporting the graphs. This confirms that simplified analytical expressions and graphical methods can assist designers seeking an EAHE alternative to conventional HVAC solutions based on refrigeration machines.

This paper addressed heat-transfer-related challenges in large-diameter EAHX design; however, a designer has to overcome many non-heat-transfer obstacles to justify the adoption of this type of EAHX for standalone room cooling. From the authors’ experience, winning decision makers’ trust in large-diameter EAHX cooling capabilities is a major challenge, justifying the need for continued research and dissemination of post-occupancy monitoring data.