key: cord-1003682-ngez3hwb
authors: D'Agostino, D.; Greco, A.; Masselli, C.; Minichiello, F.
title: The employment of an earth-to-air heat exchanger as pre-treating unit of an air conditioning system for energy saving: a comparison among different worldwide climatic zones
date: 2020-10-03
journal: Energy Build
DOI: 10.1016/j.enbuild.2020.110517
sha: ff4deb9f3009a2fec15ec2d0e6287358d90f78a4
doc_id: 1003682
cord_uid: ngez3hwb

A great fraction (20-40%) of primary energy is required for building air conditioning, so the use of renewable energy sources is increasing. The geothermal energy for Heating, Ventilating and Air Conditioning (HVAC) systems can be used considering an Earth-to-Air Heat eXchanger (EAHX). This work analyses the performance of an EAHX through a mathematical model (2D), as a function of diameter and length of the air ducts. The problem is solved with finite element method. A case study office building is analyzed. The air conditioning plant is characterized by fan-coil units and primary air; the EAHX is positioned upstream the Air Handling Unit (AHU) to pre-cool/pre-heat the air. The building is virtually placed initially in six Italian cities (different climatic zones according to Italian regulation DPR 412/93) and subsequently in eight worldwide cities according to Köppen climate classification. The following parameters are calculated: air temperature variation and thermal efficiency of the EAHX; the decreasing of cooling and heating capacity of the coils into the AHU. The best results refer to a duct length of 100 m for Ottawa (warm-summer humid continental climate, 65% capacity reduction), the worst ones for Rio de Janeiro (tropical wet and dry climate, maximum 24% reduction).

Buildings are attributed the responsibility of accounting for 20% -40% in the global energy consumption of developed countries, often overcoming the industry and transport fields. Within the building sector, Heating Ventilation & Air Conditioning (HVAC) systems represent the greatest source of energy demand (50% of the total energy consumption of the sector) that represents 10-20% of global energy consumption [1] .

Indeed, the energy policies prescribe as primary goal to adopt energetically optimized solutions, also with reference to ventilating and air conditioning systems. Thus, restrictive standards are fixed to keep these prescriptions such providing energy certificates for buildings that incorporate all the aspects concerning with them (materials, the standardization of the checks for the regular maintenance, etc...). In most of the cases, the vapor compression systems could not overcome certain energy limits; consequently, the adoption of HVAC systems exclusively based on vapor compression would not satisfy the energy efficiency guidelines prescribed by these policies. Therefore, many worldwide directives push towards a spread utilization of energy from renewable sources to satisfy the energy constraints, and this also applies to buildings. As a matter of fact, to encourage these aspects, the European Directives on renewable sources issued the "green-building" standards.

Nowadays 14% of the worldwide energy demand is addressed by means of renewable energy sources [2, 3] and the global goal is to bring this figure to grow significantly in the next decade. The research for solutions that could supply or integrate vapor compression systems for refrigeration and HVAC, constitutes a spur in the development of renewable energy-based systems for exploiting green energy and, thus, for counteracting the enormous energy demand connected to these fields. Among the most used renewable energy sources (wind, solar, biomass, waves, tides, …), geothermal energy is very useful for air conditioning systems of buildings. In fact, beginning from certain depths, the soil temperature is almost constant during all the year; moreover, it is frequently higher than the temperature of the outside air in winter, lower in summer.

Clearly, the specific value of the temperature is a dependent variable of the geographic location, but the common denominator is the possibility of taking advantage from this property for projecting geothermal systems with the capability of air cooling during the summer and air heating during the winter [4] .

Consequently, the ground assumes a double role: a sink when the system operates in cooling mode; a source when it works in heating mode. The results are that a part of the primary energy could be preserved and the environmental impact [5] [6] [7] of the systems could be mitigated [8, 9] . Specifically, the use of geothermal energy for improving the thermal indoor environment is typically addressed by means of the following three solutions [10] :

 earth homes;

 Ground-Source Heat Pumps (GSHPs);

 Earth-to-Air Heat eXchangers (EAHXs).

The first solution refers to buried buildings, so the contact with the soil reduces their heating and cooling loads. Ground source heat pumps are systems where the secondary fluid (typically water or antifreeze glycolwater mixtures) circulates throughout banks of underground ducts, in closed loop circuits, to exchange heat with the soil.

Earth-to-air heat exchangers are systems formed by a number of ducts, horizontally or vertically placed and buried in the ground at a depth useful to exploit the ground property of exhibiting, under undisturbed conditions, constant temperature during the whole year. The heat transfer fluid to be used in EAHXs is typically air: in the most common configurations the EAHX is inserted in a mechanical ventilation system, more rarely in a primary air circuit. As the ground temperature, below about 10 m depth, is often higher in winter and lower in summer than air temperature [11] , the EAHX gives rise to a pre-heating of the external ventilation air in winter and pre-cooling in summer.

The EAHXs should be adequately projected to let the air, during the ducts blowing, brings its temperature (heated or cooled). Subsequently the air is either sent directly to the building that has to be ventilated/airconditioned or carried in a conventional air handling unit (inside a HVAC system) to be further heated or cooled and then sent to the building. The open loop system provides that the air, after has completed its "conditioning" task, would be expelled directly from the building into the atmosphere. In the closed loop systems, at the end of the air conditioning process (heat exchange with the ground through flowing in the ducts and heat transfer with the building to be conditioned) the air is fed back at inlet of the EAHX ducts to be recirculated. Therefore, in a closed loop EAHX system, after several circulations, the air needs to exchange a relatively lower amount of heat with the ground compared to an open loop system. In general, the closed loop configuration is energetically more efficient than the open loop one, also allowing to reduce the problem of undesired water condensation in the ducts due to the humidity rate of the external air introduced in the EAHX (a typically summer problem). However, the open loop system is often preferable because it also allows the air exchange in the building, which is not possible for the full air recirculation systems; moreover, the air recirculation can carry to the contamination of the HVAC systems by Coronavirus or other viruses.

EAHX systems can be characterized by vertical or horizontal air ducts. The arrangement of the pipes plays a fundamental role since the portion of the ground required for the installation of the EAHX systems in order to satisfy the heating/cooling demand depends on the design and layout of the pipes; indeed the air conditioning potential of an EAHX system is strongly linked to its geometric configuration. Horizontally oriented pipes are generally used in EAHX systems, mainly because they present a simpler and cheaper type of installation than the vertical ducts, since the former requires a shallower excavation. A further classification in the EAHX system with horizontal ducts can be made between single-layer configuration, with all the ducts buried at a single depth level, and multi-layer configuration where the ducts, horizontally oriented, are buried one on the other at various depths in the ground and separated by vertical drops. Single layer configurations are by far the most used among the solutions proposed in literature [10, 12] . At the best of our knowledge, very few are the investigations performed on multilayer EAHX systems but worthy of attention is the work proposed by de Jesus Freire et al. [13] . They made a comparison in an EAHX between multilayer pipes and single layer configurations, on equal number of tubes and distance between one each other, as well as the same were the duct design parameters (diameter, length, air velocity) [13] . On equal amount of heat transfer surface, number of tubes and air velocity, they detected 3% and 6% decreasing in temperature span, respectively considering the two-and three-layer configurations with respect to the single layer one. On the other side, the two-and three-layer configurations analyzed required a reduction of the available flat surface for installation estimated, respectively, on 50% and 67%, if compared to the single-layer one. Indeed, despite of slight energy performances decreasing, the multi-layer configuration could prove very promising in urban contexts with limited installation surfaces.

Earth-to-air heat exchanger is a very promising technology but mandatory is the optimization of the system to the purpose of appropriately setting the design parameters (such as diameter, length and number of tubes, displacements of the tubes, air velocity), according to the installations specifics and limits as well as to the geographical zone, in order to let the EAHX system showing the highest energy performances [14] . To pursuit this goal, before the installation of the system, it is important to widely test the projected EAHX system.

This crucial point could be addressed by means of the development of an accurate numerical model able to predict the energy performances under a wide number of working conditions.

A lot of mathematical models are present in the scientific literature: many models are commented in the next paragraph (State-of-the art).

Based on the literature analyses, it is therefore possible to briefly summarize the main advantages in using and investigating EAHX systems: i) the working fluid is air (unlimited and free available); ii) the energy consumptions of stand-alone EAHX or EAHX/HVAC-coupled systems are lower than the traditional HVAC systems, as well as higher are the coefficients of performances too; iii) the EAHX system is simple, therefore it requires few maintenance and operating costs; iv) the environmental impact deriving from the operation of the EAHX systems is reduced with respect to the traditional ones, since the former is supplied by a renewable energy source and, furthermore, it requires less use of compressors and high-GWP (Global Warming Potential) refrigerants. However, it must be pointed out that the use of the EAHX is not yet widespread. This is due to both the space problems related to the installation of buried pipes, which can be problematic in widely urbanized contexts, and the excavation costs necessary for burying the pipes.

In this section many of the numerical models or computational methods reported in the scientific literature for the analysis of the EAHX are reviewed and summarized.

Bordoloi et al. [15] in their review paper classified and compared the energy performances of the main EAHX systems describing the most relevant analytical and experimental studies on the different combinations of EAHXs, up to the year 2018. Another very appropriate classification was proposed by Bisoniya et al. [16] in their review where, specifically, the numerical models of EAHX were categorized based on the method they are solved through and the dimensions of the geometry investigated. Anyhow, the common denominator of both the reviews is to propose an overview of the worldwide research scenario on this type of geothermal system; the emerging data is the really huge number of EAHX systems and models proposed. An accurate numerical model should be able of evaluating punctually both the conductive (from/to duct/ground) and the convective (related to the air flowing in the duct) heat transfer mechanisms acting in the EAHXs. Even if a number of commercial software like TRNSYS or Energy Plus allows to easily model geothermal systems, providing qualitative data on their performances ("black-box approach"), they are not able to provide punctual (in space and time) indications on the heat transfer and temperature fields in the whole systems. Indeed, to perform accurate heat transfer investigations on the operation of earth-to-air heat exchangers, the most appropriate solution is represented by Computational Fluid Dynamics (CFD)-based models, founded on the discretization of the domain in finite differences/volume/elements despite of the method adopted for solving the differential equations that govern the heat transfer problem.

In open literature, various 1-D, 2-D, and 3-D models of earth-to-air heat exchangers were presented and described.

Over the years, the beginning investigations on EAHXs founded on the development of one-dimensional models with simple balances made to derive the inlet-outlet relations for the air parameters. In 2002

Kabashnikov et al. [17] introduced one of the first one-dimensional models of an earth-to-air heat exchanger;

the mathematical model was very simple as well as few were the results collected: based on Fourier integral for evaluating the temperature in the system, a mathematical investigation was carried out, by varying length, diameter and depth of the ducts. As main result the model can provide an analytical expression giving the mathematical value of the length and the diameter that optimizes the heat exchange between the air and the ground. Subsequently, in 2003 Kumar et al. [18] presented a parametric analysis carried out through a 1-D finite differences numerical model of an earth-to-air heat exchanger that couples simultaneously the heat and mass transfer equations. The tool was developed through a MATLAB code and validated with experimental data, coming from a system placed in India, and a good agreement (±1.6% relative error) was found. The peculiarity is that the model of Kumar et al. has been one of the first to investigate the transient behaviour of the EAHX for a whole day in summer and in winter, as well as the humidity of the air flowing was considered.

In the same year, De Paepe and Janssens [19] shared with the scientific community their one-dimensional analytical model where the convective heat exchange is accounted through the calculation of the convective coefficients by means of dimensionless numbers approach. They evaluated the influence of pressure drop as function of volumetric flow rate, of diameter and length of the duct. They noticed that smaller diameters provide higher thermal performance, but greater pressure drops. The solutions they suggested is to project EAHX with more ducts placed in parallel to counteract these contrasting trends. Through the one-dimensional mathematical model proposed in 2008 by Cucumo et al. [20] the effect of burial depth of the tubes on the energy performances of earth-to-air heat exchanger systems was evaluated. The model is able to provide the results following two methods: superposition principle, Green functions. They performed the investigation in a sandy soil, and they asserted that optimal deepness belongs to the range 3-6 m. The effect of burial depth was also investigated by Sehli et al. [21] by means of a finite volume CFD model. The convective heat exchange of the fluid flowing under turbulent motions was evaluated through the k-ε method. They identified 4 m as optimal depth and they noticed that, as soon as Reynolds number increases, the inlet-outlet temperature span decreases due to the less time spent by the air in tube and, consequently, for the heat exchange with the ground.

Among the 1-D models that are worthy of mention, there is the one developed by Su et al. [22] since the approach is very unconventional: the EAHX was modelled through a sequential computing algorithm An intense study is the one of Serageldin et al. [23] that, with their one dimensional CFD transient model of EAHX experimentally validated, asserted that with reference to Egyptian weather: i) the larger are duct diameter, length and distance, the higher is the inlet-outlet temperature span; ii) greater air flow velocities reduce the inlet-outlet temperature span; iii) the duct material does not affect significantly the heat exchange between the air and the ground. Another interesting contribution was given in 2015 by Niu et al. [24] where, through a regression algorithm applied to a 1-D steady state model, the cooling capacity of an earth-to-air heat exchanger was predicted with extreme accuracy. The polynomial regression model bases on six calibration parameters: temperature, relative humidity and inlet velocity of the air, surface temperature, length, and diameter of the tube. The obtained formula could be of wide usage in designing the EAHX systems. Among the latest 1-D models proposed, worthy of note is the one of Cuny et al. [25] published in 2020, where, following the multi-criteria optimization based on genetic algorithms, the Pareto front for an EAHX systems was determined. Three were the criteria selected, two energy and one economic, and they were applied to the operation of an EAHX with reference to French climates. The optimum combination suggests large duct length (97 m), whereas small should be duct diameter (0.15 m) and air flow velocity (0.7 m s -1 ). A good compromise between performances and cost for burial depth could be 3.2 m. Furthermore, in 2020, a one-dimensional model was used by Lin et al. [26] to quantify the correlation between the moisture of the ground and the logterm energy performances of an earth-to-air heat exchanger. Three different cases were considered: partially and fully saturated, fully dry. The results show that the EAHX energy performance is not affected by the soil moisture when the air velocity is low (up to 1 m s -1 ) but for higher velocity the effect of the moisture in the soil affects significantly the energy performances, since also basing on their operative condition the flow evolves in turbulent. The performances are higher the more is the soil saturation and a 40% difference in energy performances between the fully dry and fully saturated grounds was appreciated. Moreover, they asserted that the maximum air flow velocity in the tube should not overcome 4.0 m s −1 .

One-dimensional models show some limits: they cannot calculate the field of speed and temperature of the air into a transversal section of the duct, neither the temperature field of the soil when the depth varies. the Keller shooting method was employed for solving the model. It was detected that the saturation of the ground is mostly sensitive to its initial temperature, the air inlet temperature and flow rate.

A two-dimensional model of an earth-to-air heat exchanger was also approached through the concept of artificial neural network by Kumar et al. [31] in 2006. They developed two models, a deterministic and an intelligent one: the former was needed to concurrently study the heat and mass transfer of the EAHX; the latter is the employment of data driven model founded on artificial neural network. The most salient parameters of the ground to air heat exchanger were considered as influencing meters of the energy performances and the investigation revealed that the intelligent model predicted the outlet temperature of the air from the duct with a ±2.6% error with respect to the ±5.3% proper of the deterministic one. In 2015, Bisoniya et al. [35] , through the development of a quasi-steady state CFD 3-D model, focused on the energy payback period, the annual thermal performances and the seasonal efficiency ratio of an experimental EAHX system installed in Bhopal (Central India). They asserted that considering 50 years as lifetime, the EAHX system allows the reduction of 101.3 tons of CO 2 whereas the total carbon credit has estimated being around $ 2838. Always about considering the operation of the EAHX for many years of system life, interesting is the concept of "derating factor" introduced by Bansal et al. [36] , that accounts the degradation of the thermal performances over the time. It is defined as instantaneous inlet-outlet temperature span detected on the corresponding steady state one. Indeed, due to the saturation of the soil, the smaller is the ratio, the greater is the degradation of the thermal performances.

The study on the effect of different displacements of the ducts in an earth-to-air heat exchanger is a crucial concept that has been deepened through 3-D models in various works. In 2012, Congedo et al. [37] performed a comparative investigation for evaluating the thermal and energy performances of three different duct configurations: linear, helical and slinky and the effect of the variation of geometrical and functional parameters were studied for each one. The investigation was made by means of a 3-D CFD tool developed in Fluent ambient and the EAHX was supposed to be placed in South Italy. For all the geometrical configuration, the optimal buried depth in terms of costs and performance is 1.5 m. In terms of energy performance, the better design resulted to be the helical one but, on the contrary, the installation costs are higher that the linear one.

In 2017 Mathur et al. [38] investigated about the straight and spiral configurations for a ground to air heat exchanger. The performances of the system were analysed over a year while it operates in cooling and heating modes. The comparison was made also in terms of COP and, on equal design and operative parameters, they observed that the cooling/heating mode COP are 6. As for 1-D and 2-D, the artificial neural network approach was applied also to a 3-D model, through a deterministic model developed by Mihalakakou [40] where the author found that this approach could accurately estimate the outlet temperature of the tubes.

A well-designed EAHX system can be used independently but it can also be coupled to a traditional HVAC system to meet the heating/cooling requirements of the buildings. In the inherent scientific literature, a number of interesting works investigated the energy performances of HVAC plants coupled to/integrated with earth-to-air heat exchangers systems. In 2012, Bansal et al. [41] analysed the energy saving and economic impact deriving from integrating the earth-to-air heat exchanger technology into an evaporative cooling system. Specifically, by means of a CFD tool, they considered four base cases of air-conditioning and electric heater systems characterized by three diverse blowers: energy efficient blower, standard blower, and inefficient blower. With reference to these cases, the energy saving and the payback period related to the use of the EAHX were evaluated. They found that a 2 years payback period for integrating EAHX with an efficient blower evaporative system is very convenient. On the other side, for inefficient blowers the integration of an earth-to-air heat exchanger would result in a financially unviable choice. The authors showed that the energy saving was hardly affected by the electricity tariff and the blower efficiency. In 2016 Ascione et al. [42] analysed the effects on energy efficiency and environmental impact of employing an earth-to-air heat exchanger in the air conditioning system enslaving a Nearly Zero Energy Building (NZEB) through the software Energy Plus.

The HVAC plant based on an air-to-water heat pump supplying fan-coil units plus mechanical ventilation: the EAHX was employed as pre-treating unit (pre-heating in winter and pre-cooling in summer). They observed that the EAHX integration carried up to a 29% energy saving in winter and 36-46% in summer, for a global yearly saving rate of 24-38%.

In 2020, Li et al. [43] analysed, from energy, environmental and economic point of view the integration of EAHX in an air-to-air heat recovery unit based on mechanical ventilation with respect to the case of coupling a heat pump to a primary air handling unit. The EAHX was tested in a parametric analysis with two parallel horizontal ducts buried at 2.5 m and 5 m with 2 m and 5 m as space between the tubes. The results showed that for severe cold climates, the EAHX-based solution carries to remarkable benefits with respect to all the three above aspects. The static and dynamic payback periods for the EAHX-based system were about 2.1 and 2.4 years (with return rate of 8%); a reduction of 17% in equivalent emissions of CO 2 was also calculated. The most promising results were obtained with 5 m distance between the two ducts. D'Agostino et al. [44, 45] evaluated the thermal performances of EAHX compared to air-to-air heat exchangers providing promising energy savings also for this configuration but with higher economic costs.

Indeed, the above state-of-the art on numerical models of earth-to-air heat exchanger systems revealed the limits shown by one-dimensional models, especially in the impossibility of drawing the temperature and velocity profiles of the air flowing in the pipes, as well as the temperature range established around the pipes.

As a matter of fact, even if these limits could be overcome through the development of both two-or threedimensional models, currently, the vast majority of the numerical EAHX tools is 2D because the latter represents a good compromise in accuracy and computational costs. Anyhow, for complex geometries or particular placements of the pipes, where is needed, the 3D model is used.

At the best of our knowledge, the state-of-the-art lacks a worldwide comparison on the performances of a hybrid HVAC system where an EAHX is installed upstream the Air Handling Unit (AHU). Specifically, the present paper aims to fill this gap. At this aim, a case study office building is analyzed and virtually collocated in various climatic zones around the world. -the EAHX has been commonly investigated as a component added to a usual mechanical ventilation system, while this paper analyses a hybrid air conditioning system in which the EAHX is inserted upstream the air handling unit to minimize the energy requirements;

-for various climatic zones around the world, the thermal efficiency of the EAHX is evaluated, and also the decreasing of cooling and heating capacity of the coils into the AHU.

The methodology of this paper is based on a 2D mathematical model of an EAHX to obtain the system performances under different outdoor air temperatures. The EAHX is considered not only as an air pretreatment device placed inside a mechanical ventilation system, but as a component to pre-treat the air to be conditioned into an air handling unit inside a HVAC system. In this way it can ensure a relevant energy saving.

The investigation is conducted on a HVAC system for an office building. The building is spread over two floors for a total area equal to 260 m 2 and a volume equal to 910 m 3 . In Figure 1a and The climatic conditions of the localities where the system is installed, affect the EAHX thermal performance.

Therefore, to make a comparison, the office building is virtually placed in six different cities of Italy, chosen to belong to six different climatic zones identified by D.P.R. 412/93 [48] . For a further comparison, the building is subsequently placed in eight cities of the world following the Köppen climate classification [49] (the Italian cities are also included).

During the analysis on the EAHX, the diameter of the air ducts is varied to optimize the system, but the airflow rate necessary for the building must remain constant, so the speed of the air varies consequently. The temperature of the air at the exit of the EAHX is evaluated; this air is then sent to the air handling unit before it is supplied to the building. The following parameters are evaluated: the variation of air temperature in the EAHX; its thermal efficiency; the decreasing of cooling and heating capacity of the coils into the AHU when comparing with the solution without EAHX. The analysis on the coils of the AHU is performed for winter, summer and for the whole year.

According to D.P.R n. 412 of 1993 [48] , as shown in Figure 2 , the Italian territory is divided into six To make a comparison, six Italian localities have been considered in this analysis (Lampedusa, Catania, Naples, Rome, Milan, Pian Rosa) belonging to the different six climatic zones. The weather data considered were identified through ASHRAE climatic data [50] . Table 1 shows, for each of the six localities, the design values of the outside air temperature, the relative humidity and the solar incident radiation in winter and summer. 

The Köppen climate classification [49] is based on the evaluation of the local vegetation in each zone, since it was known, from the first publication in 19th century, that in a certain region the concentration of the vegetation depends on both the temperature and precipitation. The Köppen classification subdivides the Earth area into five main climatic zones based on temperature criteria, apart from the second zone (B) in which it is assumed that the dryness of the zone is the main key factor for vegetation's concentration.

The principal zones are identified with a capital letter as follows [49] :

Zone A: equatorial or tropical climates (the minimum monthly temperature value during the year is equal to or greater than 18 °C). This zone includes the warmest climates.

Zone B: dry climates (annual mean value of precipitation is less than a specific limit). This zone includes deserts and steppes.

Zone C: mild temperate climates (monthly average temperature of the warmest month is equal or greater than 10°C, monthly average temperature of the coldest month ranging from -3°C to 18°C).

Zone D: continental climates (monthly average temperature of the warmest month is equal or greater than 10°C, monthly average temperature of the coldest month is equal or lower than -3°C).

Zone E: polar climates (monthly average temperature of the warmest month is less than 10°C).

Each climatic area can be also divided in subareas by means of a second letter to take into account precipitations; in some cases, also another sub-criterion (based on temperature) is considered, by adding a third letter. Table 2 . Pian Rosa was omitted since it is characterized by extreme and not very generalizable climatic conditions. Furthermore, in the summer season it does not require a cooling system. and D zones, respectively, based on the classification proposed by Köppen, whereas zone E (polar area) is not considered. Table 3 shows, for these three towns, the design values of outside air temperature, relative humidity and solar incident radiation in winter and summer. According to this classification, Rio de Janeiro belongs to Aw (tropical wet and dry climate) climate zone;

Dubai to Bwh (hot desert climate) and Ottawa to Dfb (warm-summer humid continental climate).

The air conditioning system is characterized by fan coils and primary air. A reversible (invertible) heat pump provides hot and cold water for both the coils of an air handling unit, in order to treat the primary air, and the fan-coil units located in each room of the building. The design external (or outdoor) air flow has been set at 11 10 -3 m 3 s -1 per person, for a total of 1300 m 3 h -1 . The design thermo-hygrometric conditions to be • guaranteed inside each room are:

-indoor air: temperature of 20 °C for winter and 26 °C for summer, relative humidity (ϕ) of 50% for both winter and summer;

-supply primary air: temperature of 20°C and ϕ of 50% for winter, 15°C and ϕ of 85.2 % for summer (this value of ϕ is calculated after evaluating the specific humidity ω by means of a mass balance for each room, referred to water).

Two air conditioning systems are analyzed: Figure 4 shows the traditional one characterized by only the AHU for primary air (without EAHX), whereas Figure 5 shows the system where the EAHX is placed upstream the AHU. The first one is a usual HVAC system with only the AHU (without EAHX) and fan-coil units: the air treated in the AHU is outdoor air. The second air conditioning system is instead characterized by the EAHX which pre-heats or pre-cools the outside air before being handled into the AHU. The AHU is composed of the following main components:  filters;

 pre-heating water coil;

 cooling and dehumidifying water coil;

 humidifying section;

 re-heating coil;

 supply fan.

(a) (b) In the Figures 6(a) for summer and 6(b) for winter the transformation in the AHU on the psychometric chart are reported. During the summer (Fig. 6(a) ) the processes that the humid air undergoes are: cooling and dehumidification from point "o" (outdoor air conditions) to point "A" and subsequent re-heating from point "A" to point "s" (supply air conditions). The cooling coil is supposed to be ideal with a by-pass factor equal to 0% (i.e., ϕ A =100%). During the winter (Fig. 6(b) ) the processes are: pre-heating from point "o" to point "A", humidification with liquid water from point "A" to point "B" and re-heating from point "B" to point "s" which coincides with the thermohygrometric conditions to be maintained in the room (point "r"). The humidifier is supposed to be ideal (with saturation efficiency of 100%). When the EAHX is used for pre-cooling/pre-heating the air flow, the point "o" (outside air) is substituted with the point EAHX (air conditions at the exit of the EAHX, individuated through the 2D model below described). To evaluate the coils capacity, the mass and energy balances are carried out on the control volumes shown in Figure 7 (a) and Figure 7 (b). During the summer (Fig. 7(a) ) the running components of the AHU are: the cooling coil and the re-heating coil. The energy balance equation for calculating the cooling capacity (with reference to control volume 1 of Fig. 7 (a)) is:

The re-heating coil power (control volume 2 of Figure 7 a) can be evaluated as:

During the winter, as shown in Figure 7 (b), the active components are: the pre-heating coil, the humidifier with liquid water and the re-heating coil. The pre-heating coil capacity (control volume 3 of Figure 7 (b)) can be evaluated as:

The mass flowrate of humidification water (control volume 4 of Figure 7 (b)) can be evaluated as:

The re-heating coil capacity (control volume 5 of Figure 7 (b)) is obtained from the equation:

When the EAHX is in use, the reduced capacity of the AHU coils both for summer and winter has been evaluated. Consequently, the reduction of the coils' capacity obtained by the introduction of the EAHX technology compared to the AHU without this heat exchanger is calculated, considering the coils operating in winter season, summer season and all over the year.

In this research, the open-loop earth-to-air heat exchanger was 2D modeled through a finite element method software. The EAHX was made of five horizontal ducts. The horizontal disposition was chosen since vertical one usually involves with higher installation and maintenance costs. The number of tubes has been chosen to obtain, at fixed air volumetric flowrate, a range of air velocity between 0.4 and 2.5 m s -1 that is a good compromise between effectiveness of heat transfer and pressure drops. 2.5 m is the distance d stemming between two adjacent ducts: this value is chosen to avoid thermal interaction between the two air ducts. The computational domain of the model consists of one circular buried duct (for air flowing) surrounded by a ground volume of 20 m deep. This value of deepness was chosen to consider the ground as undisturbed [51, 52] .

The buried duct is installed at 2.5 m deep from the soil surface because, in agreement with other studies [11] , for deepness more than 2 m, the soil temperature is about undisturbed and close to the annual mean values of the outdoor air. Burying the pipe between 2 m and 3 m is a good compromise [27, 53] between yearly temperature excursion and excavation costs.

The mass flowrate of the air entering each pipe is evaluated as: 

,

The outside airflow of 1300 m 3 h -1 must be provided to the building, so the modification of the duct diameter leads to a modification in the air speed. In Table 4 for each diameter the air velocity and the Reynolds number are reported. The table clearly shows that the airflow rate can be always considered in fully turbulent developed regime.  the soil considered as an isotropic medium.

The air entering the ducts is humid air. The thermodynamic properties of humid air (dry bulb temperature; relative and specific humidity) can be punctually evaluated, in time and space, through the model. Therefore, the condensed water flow rate can be also evaluated. For the fluid domain the following differential equations can be numerically solved:

 the mass conservation of the humid air:

where is a negative term that represents the mass of water vapor condensed;  the conservation momentum of the air flow is guaranteed by the Navier-Stokes equations for turbulent flow: (10) where is the turbulent viscosity defined as:

with , that is one of the constants of the K-model for turbulent flow [29] ;

 the energy equation for the air flow:

where is the effective conductivity defined as the sum of the conventional thermal conductivity of the fluid ( ) and the thermal conductivity of the turbulent flow ( ) and thus modeled as:

, (13) = +  Using the K-model for turbulent flow, the turbulence kinetic energy equation is:

can be evaluated as:

The specific dissipation rate equation is:

The experimental constants of the K-model are reported in Table 5 . The differential equation of conduction in solid domain numerically solved is:

The soil humidity is considered balancing water and solid properties throughout the porosity ( with the following equation:

For each locality of the analysis the thermal properties of the soil are evaluated and reported in Table 6 . Table 7 reports the weather data used in equation (19) and the resulting undisturbed ground temperature for each locality of the present analysis: 

A time dependent solver is used to solve the mathematical model, while the implicit BDF (Backward Differentiation Formula) is used as time step procedure. The implicit BDF procedure utilizes backward differentiation equations that present accuracy from one (named as the backward Euler method, too) to five. BDF procedures were often utilized due to their stability characteristics. On the other hand, they could show some damping effects, mainly when considering the lowest order methods (some high frequencies are often damped). Although one could expect a solution with sharp gradient, a frequently smooth solution is obtained due to the above-mentioned damping effects. The use of BDF could be characterized by high order if possible, and lower order when it is indispensable to reach stability. The strategy of the solver selected for the model used in this work is BDF with "Free time stepping": in this way, the solver can set greater or smaller time steps to satisfy the required tolerances. In fact, the solver tries to calculate with the largest possible time step, but, when the solution starts to rapidly vary and therefore the (relative and absolute) tolerances are not verified, it As clearly visible from the figure we found a substantial overlapping between the temperature profiles with 15827 and 70625 elements and a good agreement between the solution with 11124 elements (maximum difference lower than 0.04K). Since the computational time for elaborating the solution does not differ appreciably if we simulate with 15827 and 70625 elements, we opted for the finer meshing (70625 elements).

To ensure the reliability of the results obtained with the numerical code, the model is validated by In Table 8 is reported the absolute and relative error on the outlet air temperature: the maximum relative deviation between the experimental and the numerical data is 3.5% (at 17 m of tube length). That is, the maximum difference between the predicted and the experimental air temperature at the outlet of the EAHX is 1°C. In addition, the EAHX model has also been validated by means of some of the experimental results provided by Khabbaz et al. [59] , related to an Earth-to-Air Heat Exchanger system located in Marrakech Table 9 is reported the absolute and relative error on the outlet air temperature. It can be noted that the maximum relative deviation between the experimental and the numerical data is 1.2% (at 63 m of tube length).

The maximum difference between the predicted and the experimental air temperature at the outlet of the EAHX is 0.3 °C (lower than the experimental uncertainty on the measured temperature). Reynolds number follows in the transition between laminar and turbulent flow. In this range the numerical model uses the laminar solution. The experimental temperature was detected with T-type calibrated thermocouples, with an error following in the normal range with deviations between the thermocouples reading and that of a standard one (beta Calibrator TC-100) of + 0.1-0.5 °C. In Figure 12 is reported a comparison between experimental and numerical air temperature as a function of the tube length: the figure clearly shows that the numerical model always overpredicts the experimental data.

Figure12.Experimental and numerical air temperature alongside the pipe of the earth-to-air heat exchanger.

In Table 10 the absolute and relative error on the outlet air temperature is reported. It can be noted that the maximum relative deviation between the experimental and the numerical data is 2.55 % (at 4.67 m of tube length). The maximum difference between the predicted and the experimental air temperature at the outlet of the EAHX is 0.70°C.

From all these analyses we can conclude that the presented model is able to predict the thermal performance on a horizontal EAHX not only in fully developed turbulent flow but also in laminar or transition regime. 

In this paper the thermal and energy performances of an EAHX pre-treating unit coupled to an AHU are evaluated. The thermal behaviour of an EAHX is not the same on the globe but depends on the climatic context, the soil temperature, and the configuration of the EAHX. The soil temperature is very similar to the annual mean temperature of the place in which EAHX is installed; therefore, it is often higher than air temperature in winter and lower in summer. The aim of this paper is to compare the performances of an EAHX in: i) six localities of Italy belonging to different climatic zones according to the Italian D.P.R. 412/93 classification; ii) nine cities with different climatic conditions based on the classification proposed by Köppen. The described EAHX is tested by means of a mathematical model; each simulation is carried out until the steady state regime is obtained. At this point, all the parameters are calculated.

In Figure 13 the temperature variation along the tube length in winter and in summer varying the inner tube diameter for the six localities is reported. Figure 13 The Figure clearly shows that temperature variation is more marked for Milan, a city characterized by cold winter and hot summer (with a maximum value greater than 17 K). The lowest values are those pertaining to Lampedusa, a locality characterized by very mild climate (maximum value lower than 10 K).

In Figure 15 is reported the variation between the outlet and the inlet temperature of the EAHX for the six localities in winter season. It could be noted that the greatest temperature variation can be obtained for Pian Rosa, a locality characterized by very cold winters (maximum value of 14.7 K), whereas the lowest is for Lampedusa (maximum value of 8.9 K).

From the data plotted in Figures 14 and 15 the following considerations can be drawn:  the temperature variation that can be obtained with an EAHX at fixed tube length is always greater in the summer than in the winter season. This is due to the greater temperature difference between the external air and the soil during the summer for each of the tested localities;  the temperature of the undisturbed ground is almost constant and very similar to the yearly average value for the outside air. So, the lowest temperature of the ground is for zone F, while the highest occurs for the zone A. The temperature difference between the ground and the outside air represents the principal driving force in the heat exchange process. Where the difference between the air temperature at the inlet of the heat exchanger (corresponding at L=0 in Figures 13) and the undisturbed soil is more marked, the more efficient is the heat transfer process. The greatest values of driving force can be obtained in the localities with greater temperature excursions between summer and winter (Pian Rosa, Milan).  Lampedusa shows the lowest temperature span because it has very mild winters with moderate rainfall and hot, dry summers. So, the temperature span along the EAHX is minor than 10 °C, although a relevant length of 100 m is considered for the air duct (ΔT belongs to 3.7÷9.5 K in summer and to 3.5÷8.9 K in winter). Figure 16 is reported the efficiency of the EAHX as a function of the tube length for the six localities for an inner tube diameter of 0.2 m. From the results obtained, the efficiency in winter and summer is almost the same, this is the reason why there is only one graph that can be used for both seasons. The graph also shows that at fixed tube length the efficiency is independent on the climatic zone where the EAHX is installed. Indeed, the effectiveness of the heat exchange mainly depends on the convective heat transfer coefficient that at fixed inner tube diameter is almost constant for the different localities (because constant is the air flow velocity too). Furthermore, the Figure 16 clearly shows that the increase of the efficiency is very pronounced up to about 80 m: for longer lengths, the increase becomes moderate. An optimal efficiency value of about 86% is ensured with a length duct of 100 m. This result is also relevant in the possible comparison between the analyzed EAHX and an air-to-air heat recovery unit. In fact, the latter is characterized by a mean efficiency of about 65%-80% [61] [62] [63] . Moreover, air-to-air heat exchangers are usually more dangerous due to the risk of spreading SARS-CoV-2 or other viruses.

The efficiency is a strong function of the inner tube diameter (and of the consequent fluid velocity). As an example, in Fig.17 is reported the efficiency for the different tube diameter for the city of Milan during summer. Similar results can be obtained in winter and for the other examined Italian localities. The EAHX also implies a relevant decreasing of the heating and cooling capacity of the coils inside the air handling unit. Figure 18 reports the heating and cooling capacity of the operating coils during winter (i.e.

preheating coil and reheating coil) (a), during summer (i.e. cooling coil and reheating coil) (b), all over the year (c), as a function of the tube length for an inner tube diameter of 0.5 m for the different localities. Figure 18 also shows the heating and cooling capacity values for the system without the EAHX. Finally, the figure also reports the decreasing (in percentage) of these capacity values when the EAHX is considered, for various lengths of the air ducts. From the Figure 18 the following considerations can be drawn:  increasing the tube length carries to an augmentation of the capacity reduction, too. Therefore, the best results can be obtained with the duct 100 m long;  during the winter (Fig. 18(a) ) the capacity reduction using the EAHX to pre-heat the air flow is more marked in zone A (maximum value of 40%) than in zone F (maximum value of 19%).

Indeed, in Lampedusa, the southernmost point of Italy with a very mild winter and hot, dry summer, the capacity reduction is greater than in Pian Rosa (with a short and cool summer and a long, freezing, and snowy winter);  an opposite trend is observed during the summer (Fig. 18(b) ): the capacity reduction using the EAHX to pre-cool air flow is more marked in zone E (maximum value of 48%) than in zone A (maximum value of 21%);  with reference to winter and summer (Fig. 18(c) ), the highest total decrease in capacity of the coils occurs for zone E (Milan -decrease of 38% for a duct length of 100 m), while the lowest value occurs for zone A (Lampedusa -maximum decrease of capacity equal to 27%). So, in Italy the annual utilization of the EAHX linked to an air handling unit is useful in all the national territory, even if preferable in zone E (i.e. in the climatic areas showing a high temperature excursion between winter and summer) compared to zone A. From a comparison among Figures 18, 19 and 20, the emerging data is the greatest coils capacity reduction that can be achieved considering the smallest diameter of 0.2 m (maximum global power reduction of 55% in Milano).

The previous analysis has shown that the best results can be obtained with the smaller inner tube diameter considered (0.2 m). Therefore, in this analysis the tube diameter is fixed at 0.2 m.

In Figures 21 is reported the temperature variation in EAHX as a function of the tube length in summer (a) and in winter (b) season.

According to the Köppen classification, the analyzed Italian localities belong to the zone C (mild temperature climates) except Lampedusa that belongs to the zone B (dry climates).

 the temperature span between the inlet and the exit of the EAHX, in the Italian localities, is lower in winter than in summer, while an opposite result is obtained for Ottawa, Dubai and Rio de Janeiro. This depends on the temperature span between the soil and the outside air. This difference in Italy is not so dissimilar between summer and winter and slightly greater in summer. Instead, the contrary is found for Dubai, Rio de Janeiro and Ottawa (in this last case there is a strong variation between summer (14.5 K) and winter (27.4 K);  in summer conditions, the maximum EAHX temperature difference between the inlet and the exit is obtained for Milan (higher than 17 °C), while the minimum temperature difference is obtained for Rio de Janeiro (maximum value lower than 7 °C);  during summer, the best results can be obtained in Milan (maximum value greater than 17 K), whereas the worst results are registered in Rio de Janeiro (maximum value lower than 7 K);  during winter Ottawa shows the greatest temperature variation in the EAHX (maximum value of 27.4 K), on the contrary Rio shows the lowest (maximum value 6.8 K);  the temperature of the undisturbed ground is almost constant and very similar to the yearly average temperature of the outside air, in all the considered climatic areas. The temperature difference between ground and outside air is the principal driving force in the heat transfer process related to the EAHX: its highest values occur in the climatic areas with higher temperature excursion between winter and summer. So, the most relevant results occur for zones C and D (mild temperate climatic areas and continental climatic areas, respectively), while the less relevant results occur for equatorial or tropical climatic areas (zone A). Figure 22 shows the EAHX efficiency in summer, when varying the air duct length, for the eight analyzed towns. Indeed, in winter the results are almost the same. It can be shown that the efficiency depends slightly on the climatic and soil characteristics of the area in which the exchanger is installed. For all the climatic areas the efficiency exceeds 80% at 100 m tube length.  in Dubai and Rio de Janeiro, the temperature of the air at the exit of the air duct is higher than 20 °C, even when the duct length is only 20 m. Moreover, the couple dry bulb temperature -specific humidity of the air at the exit of the air duct is very similar to those required for comfort conditions in winter.

So, the air exiting the EAHX can be supplied to the building without any HVAC system (only a suitable filtration of the air is obviously required). Therefore, in these cases the decreasing of the heating capacity of the coils rises 100 % for the air handling unit working in heating operating conditions;  the heating capacity reduction using the EAHX to pre-heat the air flow is more marked in A and B zones (maximum value of 100%) than in C or D zones (maximum value of 47%).

From Figure 23 (b), referred to summer, one can notice that:  the air temperature in the duct decreases below the dew point temperature (17.6 °C) in Ottawa, for duct lengths higher than 50 m; it means that the air has been dehumidified. length;  in Ottawa, with a tube length of 100 m the air flow reaches temperature and relative humidity values such that the air can be directly conveyed in the building without using the air conditioning plant. Therefore, the percentage cooling capacity reduction in cooling mode is 100%;  the capacity reduction using the EAHX to pre-cooling the air is more marked in D and C zones (maximum value 100% for Ottawa) than for A and B zones (maximum value of 18% for Rio de Janeiro).

From Figure 23 (c) it can be seen that the highest decreasing of cooling plus heating capacity for the coils occurs for Dubai while low values of the length of the air duct are considered (up to 60 m), whereas for higher lengths of the air ducts the best results occur for Ottawa. Therefore, one can conclude that the best results can be obtained for tube length of 100 m in the city of Ottawa (reduction of 65% of heating + cooling capacity using the EAHX) that belongs to the Dfb zone according to the Köppen classification. This city is characterized by the greatest temperature span between winter and summer season, with a very cold winter (with frequent snowfalls) and a hot-humid summer.

In this paper the thermal and energy performance of an earth-to-air heat exchanger are investigated.

A two-dimensional unsteady numerical model of a horizontal EAHX has been developed. The EAHX is formed by 5 horizontal circular ducts, displaced in parallel at 2.5 m depth. Two adjacent ducts are 2.5 m spaced apart. The 2D model represents one of the five circular horizontal buried ducts of the EAHX surrounded by a ground volume 20 m deep; the problem is solved through finite element method. The model has been validated with experimental results found in literature: the maximum relative deviation between the experimental and the numerical data is 3.5 %, the absolute deviation is always lower than 1°C.

The EAHX is considered as a component of an air conditioning system for an office building. The air preheated or pre-cooled in the EAHX is not directly supplied to the building, but it is successively treated into the air handling unit. Since the thermal performance of the EAHX depends on the climatic conditions of the place where it is installed, the office building was firstly virtually placed in six different localities of Italy (Lampedusa, Catania, Naples, Rome, Milan, Pian Rosa), which belong to different climatic zones according to the Italian law D.P.R. 412/93, based on heating degree-days. For a further comparison, the building was subsequently placed in eight cities of the world according to Köppen climate classification (Dubai, Rio de Janeiro, Ottawa, plus five of the abovementioned Italian localities).

The EAHX is simulated and optimized as a function of the diameter and length of the air ducts. The following parameters are calculated: the variation of air temperature in the EAHX; its thermal efficiency; the decreasing of cooling and heating capacity of the coils into the AHU when comparing with the solution without EAHX. The analysis on the coils of the AHU is performed for winter, summer and for all the year.

The following main conclusions are obtained.

 At the EAHX outlet, a temperature of the air close to the undisturbed ground temperature (Knee point)

is obtained for tube length of about 80 m for all the localities. Therefore, a duct length of 80 m represents an acceptable compromise considering thermal performances, pressure drops and EAHX costs.  Decreasing the tube diameter, the air velocity increases enhancing the convection heat transfer coefficient and, as a result, the heat exchange becomes more efficient. Therefore, with the lowest value of the inner tube diameter (0.2 m) a greater air temperature variation can be obtained in the EAHX.  For all the analyzed climatic zones the undisturbed soil temperature is about constant and close to the annual mean values of the external air. Temperature gradient between ambient air and soil is the main driving force for the heat transfer in the EAHX. The greatest values of driving force can be obtained in the locality with the greatest temperature excursions between summer and winter. Therefore, the worst results in terms of temperature variation in the EAHX can be obtained in the zone A (according to Köppen climate classification, it refers to tropical or equatorial climates) and the best in zones D (continental climates) and C (mild temperate climates).  Among the Italian localities, Lampedusa shows the lowest temperature span between the inlet and outlet of the EAHX, always smaller than 10 K even with a tube length of 100 m (ΔT belongs to 3.7÷9.5 K in summer and to 3.5÷8.9 K in winter). Milan (with a maximum value greater than 17 K) and Pian Rosa in winter (whose maximum temperature span is 14.7 K) show the highest temperature spans.

 According to the climate classification of Köppen, during summer the best results can be obtained in Milan (maximum value greater than 17 K), whereas the worst results are registered in Rio de Janeiro (maximum value lower than 7 K). During winter Ottawa shows the greatest temperature variation in the EAHX (maximum value of 27.4 K), on the contrary Rio de Janeiro shows the lowest (maximum value of 6.8 K).  The efficiency of the EAHX is almost independent on the climatic zone where the EAHX is installed and its increase is very pronounced up to about 80 m: for longer lengths, the increase becomes moderate. Indeed, 100 m as length of each duct ensures the achievement of an optimal efficiency value, around 86%.  Considering the reduction of heating and cooling capacity of the coils inside the AHU (deriving from the placement of EAHX upstream the AHU) for the whole year, the best case is Milan (zone E) with a heating + cooling capacity reduction of 55% for a tube length of 100 m, whereas the worst case is Lampedusa (zone A) with a maximum value of reduction equal to 39%. Therefore, when the yearly operation period of the AHU coupled to an EAHX is considered, in Italy the use of an EAHX is recommended in all the climatic zones, but more in E than in A zone. The best results can be obtained in the localities with a great temperature excursion between summer and winter.  Considering the reduction of heating and cooling capacity of the coils inside the AHU based on Köppen climatic zones, one can conclude that the best results can be obtained for tube length of 100 m in the city of Ottawa (reduction of 65% when using the EAHX) that belongs to the Dfb zone. This city is characterized by the greatest temperature excursion between winter and summer season, with a very cold winter (with frequent snowfalls) and a hot-humid summer. On the contrary, the worst results can be obtained in Rio de Janeiro (Aw zone) with a maximum value of reduction of 24%.

The map of energy flow in HVAC systems

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Author Contributions: All the authors have contributed in the same manner to the various aspects of the research activity described in the paper All authors have read and agreed to the published version of the manuscript

[64]

☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:[65]

 Earth-to-Air Heat eXchanger uses geothermal energy for air conditioning systems  A 2D mathematical model of the EAHX is developed to obtain the system performance  A case study office building is analysed for eight worldwide localities  Air temperature variation along the EAHX and EAHX efficiency are calculated  Reduction of thermal capacity of the coils inside air handling unit is evaluated [66]