Compact buried pipes system analysis for indoor air conditioning Alexandre de Jesus Freire a , José Luís Coelho Alexandre a , Valter Bruno Silva b, * , Nuno Dinis Couto b , Abel Rouboa b, c a Mechanical Engineering Department, Faculty of Engineering, University of Porto, Porto, Portugal b CITAB/Engineering Department, School of Science and Technology of University of U TAD, Quinta dos Prados, Vila Real, Portugal c Mechanical Engineering and Applied Mechanics Department, University of Pennsylvania, Philadelphia, PA, United States highlights < The use of a compact buried pipe system for indoor air conditioning is studied. < The compact buried pipe system is compared with the single layer configuration. < The performance of the buried pipe system is simulated by a 1-D discrete model. < The system is also studied performing a parametric analysis. < The physical layout of the heat exchanger is described. article info Article history: Received 14 February 2012 Accepted 16 September 2012 Available online 29 October 2012 Keywords: Passive cooling Ground cooling Earth-to-air heat exchanger abstract Given the international state of affairs in what concerns the heating of buildings and the necessary reduction of costs in the heating and cooling energy consumption, it is imperative to study and develop passive methods of heat transfer including heat exchange through buried pipes. Common configurations of a heat exchanger usually consider one single layer of pipes requiring a large installation area. This major drawback can be overcome using a multiple layer configuration. This paper presents a study considering the use of a heat exchanger with a multiple layer configuration, namely, comparing it with a single layer of pipes and describing the major performance differences. A parametric analysis was also performed to better understand the effect of the main input parameters on the heat exchanger power output. It was concluded that the heat exchanger power increases with the layers depth until 3 m and that the more efficient distance between layers should be kept at 1.5 m. The heat exchanger layout is also described as well as the implementation of the numerical model and the corresponding application to a real case study. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction About 40% of the energy consumption in Europe is delivered to the building sector [1]. Current trend on building design and European legislations, like the EPBD recast of 2010 [2], are pushing buildings to low energy designs with the creation of the “near zero energy buildings” concept. More than 50% of this consumption could be reduced through energy efficiency measures, leading to a possible annual reduction of 400 millions of tons of CO 2 e nearly the total commitment of the EU to the Kyoto Protocol target. In light of this, it is clear that a major potential for the implementation of low energy consumption systems like earth-to-air heat exchangers (buried pipes) can be found in the household and service sectors. A wide diversity of ground cooling/heating systems has been already used and applied [3], from closed to open system, and both analytical and discrete models have been studied and compared to predict the performance of buried pipe systems. For example, Santamouris et al. [4] compared eight different models to study their sensitivity to change the main operation parameters of an open horizontal earth-to-air heat exchanger. The analysis of buried pipe systems must consider the study of the soil’s thermal behaviour. It includes formulating the proper energy balance equations at the soil surface level [5] and devel- oping the temperature profiles of the soil due such energy balance [6]. It was noted that the soil energy balance is affected by the type of cover, for example, grass covered or bare, and the humidity ratio [7,8]. A sophisticated model describing the complex mechanisms of * Corresponding author. Tel.: þ351 913413196. E-mail addresses: [email protected](V. Bruno Silva), [email protected], rouboa@ seas.upenn.edu (A. Rouboa). Contents lists available at SciVerse ScienceDirect Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng 1359-4311/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.applthermaleng.2012.09.045 Applied Thermal Engineering 51 (2013) 1124e1134
Compact buried pipes system analysis for indoor air conditioning
Alexandre de Jesus Freire a, José Luís Coelho Alexandre a, Valter Bruno Silva b,*,Nuno Dinis Couto b, Abel Rouboa b,c
aMechanical Engineering Department, Faculty of Engineering, University of Porto, Porto, PortugalbCITAB/Engineering Department, School of Science and Technology of University of U TAD, Quinta dos Prados, Vila Real, PortugalcMechanical Engineering and Applied Mechanics Department, University of Pennsylvania, Philadelphia, PA, United States
h i g h l i g h t s
< The use of a compact buried pipe system for indoor air conditioning is studied.< The compact buried pipe system is compared with the single layer configuration.< The performance of the buried pipe system is simulated by a 1-D discrete model.< The system is also studied performing a parametric analysis.< The physical layout of the heat exchanger is described.
a r t i c l e i n f o
Article history:Received 14 February 2012Accepted 16 September 2012Available online 29 October 2012
1359-4311/$ e see front matter � 2012 Elsevier Ltd.http://dx.doi.org/10.1016/j.applthermaleng.2012.09.04
a b s t r a c t
Given the international state of affairs in what concerns the heating of buildings and the necessaryreduction of costs in the heating and cooling energy consumption, it is imperative to study and developpassive methods of heat transfer including heat exchange through buried pipes. Common configurationsof a heat exchanger usually consider one single layer of pipes requiring a large installation area. Thismajor drawback can be overcome using a multiple layer configuration. This paper presents a studyconsidering the use of a heat exchanger with a multiple layer configuration, namely, comparing it witha single layer of pipes and describing the major performance differences. A parametric analysis was alsoperformed to better understand the effect of the main input parameters on the heat exchanger poweroutput. It was concluded that the heat exchanger power increases with the layers depth until 3 m andthat the more efficient distance between layers should be kept at 1.5 m. The heat exchanger layout is alsodescribed as well as the implementation of the numerical model and the corresponding application toa real case study.
� 2012 Elsevier Ltd. All rights reserved.
1. Introduction
About 40% of the energy consumption in Europe is delivered tothe building sector [1]. Current trend on building design andEuropean legislations, like the EPBD recast of 2010 [2], are pushingbuildings to low energy designs with the creation of the “near zeroenergy buildings” concept. More than 50% of this consumptioncould be reduced through energy efficiency measures, leading toa possible annual reduction of 400 millions of tons of CO2 e nearlythe total commitment of the EU to the Kyoto Protocol target. In lightof this, it is clear that a major potential for the implementation of
low energy consumption systems like earth-to-air heat exchangers(buried pipes) can be found in the household and service sectors.
A wide diversity of ground cooling/heating systems has beenalready used and applied [3], from closed to open system, and bothanalytical and discrete models have been studied and compared topredict the performance of buried pipe systems. For example,Santamouris et al. [4] compared eight different models to studytheir sensitivity to change the main operation parameters of anopen horizontal earth-to-air heat exchanger.
The analysis of buried pipe systems must consider the study ofthe soil’s thermal behaviour. It includes formulating the properenergy balance equations at the soil surface level [5] and devel-oping the temperature profiles of the soil due such energy balance[6]. It was noted that the soil energy balance is affected by the typeof cover, for example, grass covered or bare, and the humidity ratio[7,8]. A sophisticated model describing the complex mechanisms of
Roman symbolsA area of heat transfer, soil surface (m2)Cp thermal capacity (J kg�1 �C�1)f factor of moistness of the ground surface (%)Isol total incident radiation on the horizontal (W m�2)mar mass flow rate of environment air through pipe
(kg s�1)Nu Nusselt numberPr Prandtl numberQ circulating air volume (m3)Qarm heat stored in the node (J)Qcd heat for conduction in the surface of the ground (J)Qcv heat for convection (J)Qev heat for evaporation (J)Qre heat for incident radiation (J)Qri heat for incident radiation (J)Re Reynolds numberTamb exterior temperature (�C)Tin interior temperature (�C)
Tout exterior temperature (�C)Tsolo soil surface temperature (�C)X element size on the direction xY element size on the direction yZ element size on the direction zWe power of the fan (W)COP coefficient of performanceEER energy efficiency ratioIAQ interior air qualityLNEC Civil Engineer National Lab e Laboratório Nacional de
Greek symbolsfar relative air humidity (%)asolo coefficient of absorption of the groundasup coefficient of convection in the surface of the ground
(W m�1 �C�1)rar density of the air (kg m�3)rsolo density of the ground (kg m�3)l mineral conductivity (W m�1 �C�1)
A. de Jesus Freire et al. / Applied Thermal Engineering 51 (2013) 1124e1134 1125
simultaneous heat and mass transfer occurring around an earthtube has also been developed and integrated into TRNSYS byMihalakakou et al. [9].
In order to describe the performance of the buried pipes systemtheoretical and numerical models were developed. Frequent casesfound on literature are discrete numerical models applied to earth-to-air heat exchangers with a single layer of pipes [3,10e12].Another approach not so frequent is the analytical modelling of theheat exchanger [13,14]. Other features of this technology havealready been studied, such as economic feasibility and integrationinto a building [15e17]. In the Middle Eastern Europe a similartechnology on buried ducts cooling air into buildings is also beingcarried out. However, the major limitation for the implementationof this kind of ground-coupled heat exchanger is the area restric-tions particularly in dense urban areas, where large buildings leavefew spaces in the surroundings to install these systems. The majoradvance of the model described in this article is its capacity toconsiderably reduce the installation area of the system, whilemaintaining the high performance characteristics of this tech-nology. The system under study consists of a compact multi-layerearth-to-air heat exchanger.
The exchanger consists of layers of horizontal tubes buriedunderground next to each other in each layer, in which air will flowfrom the outside into the building and will be cooled or heatedwhile it crosses along the buried pipes in an open circuit. Thesystemwill be installed in a green area besides the building insteadof beneath the building. However, horizontal exchangers havea serious disadvantage of requiring large horizontal area to installthe pipes, thus, in this paper the effectiveness of a horizontalexchanger on two and three levels without saturating the soil’s heatexchange capacity was explored. This system can be thought forretrofit and new buildings. However, for retrofit buildings someproblems can arise up affecting the foundations. The imple-mentation should take into account safety, economical and tech-nical issues.
For performance analysis of the multiple layer heat exchangersit is important to bear in mind that the gap from the surface andbetween layers both need to be dimensioned, otherwise the pipescan saturate quickly the soil’s thermal capacity, thereby reducing
the overall system performance. Multiple layer horizontal heatexchangers have an advantage when compared to single layer heatexchangers because of the considerably reduced horizontal areaneeded for the system installation. However, the decreased areashould not sacrifice significantly the heat exchanger performance.The analysis of both configurations performance will be studied inthe present paper.
The approach followed in this paper starts with a description ofthe Portuguese soil as well as climatic factors, in order to establishtheir characteristics regarding the heat transfer capacity. Then,a physical model of a heat exchanger with two and three levels wasdeveloped with the corresponding boundary conditions andassumptions. Next, the most promising numerical models wereanalysed, namely, analytical and discrete (one and two-dimensional)with the corresponding validation. The one-dimensional model wasselected as the best option to model this heat exchanger, under anaccuracy and computational effort perspective. A parametric studywas also carried out to check all the variables of the heat exchangersystem and the corresponding optimal values for each parameterwere obtained. Finally, the developed model was applied to a heatexchanger in a real case study in Portugal.
The systems were designed for cooling purposes where thetarget indoor temperature was 25 �C defined by the nationalPortuguese regulation, RCCTE [18]. During the winter season thesoil is able to gather about 260 kWh of useful energy and deliverabout 870 kWh during the summer season.
2. Main considerations
The soil properties are crucial to ease the heat transfer betweenthe ground and the conditioned air supplied to the building, eitherfor cooling or heating purposes. Both the internal and externalcharacteristics of the ground, which have a part in the calculation ofits thermal properties, were defined in the following sections. Themineral classification of the soil is addressed at a national Portu-guese level and considered as the basis for the calculation ofthermal conductivity and thermal capacity. The effect of porosityand soil moisture was studied, as well as other external factors(described below) that can influence the temperature along time.
A. de Jesus Freire et al. / Applied Thermal Engineering 51 (2013) 1124e11341126
2.1. Soil surface properties
Soil reaction to solar heat gains is quite bounded to the type ofground. Two options were available for the soil surface. It could beeither grass covered or be bare ground (without any vegetation).These options affect soil humidity and evaporative heat transferaccording to the humidity conditions at the surface level (f). Drybare surfaces present a value of f ¼ 0.4 and humid grass coveredsurfaces a value of f ¼ 0.7.
Regarding the mining-geological settings, a wide range ofmineral combinations on the earth’s crust and especially in thePortuguese territory is found. Thus, all the elements and mineralswere put into groups of predominant rock formations. Thesegroups have been given thermal and conductivity values, whichresult from the research studies previously done. The value rangesfor the mineral thermal conductivity and mineral thermal capacityused for the numerical simulation are listed in Table 1 [15,16,19].
2.3. Physical classification
Besides the type of mineral constitution of the soil, thermalconductivity and capacity are also dependent on the porosity. Thisfeature allows us to assess the amount of air or water that the soilcan hold. Very compact soils should present similar thermalbehaviour to their predominant mineral, while soils with higherporosity should be more affected by water or air depending on itshumidity. This means that a dry soil will show lower thermalconductivity while a saturated soil will have a higher thermalconductivity. The thermal capacity shows an opposite trend. Afrequent combination of porosity and relative humidity, found onprevious studies, indicates soils with a porosity of 40% anda humidity level of 50%. Taking into account these values, theoverall soil’s thermal conductivity and capacity were calculated fordifferent mineral compositions and the results are shown in Table 2[15,16,19].
2.4. Density
In the literature the density of the ground varies slightly, from2.55 kg dm�3 to 2.94 kg dm�3 [20]. In this study, the density of theground is considered as constant with an average value of 2.6. Thisassumption is usually made in these studies because of the impacton the calculation effort of the discrete energy equations, also it haslow influence on the output results.
2.5. Wind speed
Wind speed at ground level is one of the variables when theconvection coefficient of the surface (asup) is computed. This coef-ficient affects the convective and evaporative heat transfer at thesurface level. Since the average values for rugged areas (urban)range within 4 m s�1e5 m s�1, and as this study is devoted to theseareas, the value of 5 m s�1was adopted, in agreement with the
Table 1Maximum intervals for the soil conductivity and thermal capacity.
Mineral thermal conductivity(W m�1 �C�1)
Mineral thermal capacity(J kg1 �C�1)
3.5 < l < 8.2 760 < C < 916
national legislation for thermal behaviour of buildings in Portugal,RCCTE [18].
2.6. Environmental temperature
The environmental air temperature value is required asa boundary condition to develop the numerical model, namely, todefine the temperature profile of the soil. It can be obtained byexperimental data (direct measurement) on the climatic conditionsin situ. It can also be obtained applying the Fourier transform toapproximate the fluctuation of climatic conditions in a trigono-metric series. In this study, the data for Porto, Lisbon and Faro(extreme weather conditions of Portugal) were collected from theexperimental data contained in METEONORM [21]. A set of avail-able values from direct measurement was used, which gives moreaccuracy to the numerical simulationwithout the necessity of usinga more robust program.
2.7. Relative air humidity
The relative air humidity varies with exchanges of latent heat.The intensity of the heat flow increases with the difference inhumidity between the ground and the air. Equations to describe theevaporative heat transfer are described below on the boundaryconditions and they are related to latent heat exchanged betweenthe soil surface and the nearby outside air [21].
2.8. Solar radiation
The solar radiation mentioned throughout this paper is under-stood as the total radiation (direct and diffuse) reaching a hori-zontal surface. The total horizontal radiation is available directly inthe weather databases. Therefore, it is not necessary to make anyadaption to the weather data used for the purposes of this study. Ingeneral, the selected areas (Porto, Lisbon and Faro) have quitedifferent insolation values, therefore they can be considered goodcase studies to evaluate the influence of this variable.
3. Model and methods
3.1. Heat exchanger design
The heat exchanger design is of crucial importance to increasethe heat exchange with the soil. The studied heat exchangerincludes a set of pipes that are distributed uniformly in a horizontallayer at a certain depth on the soil. A multiple layer configuration iseasily obtained by adding new parallel pipe layers in the soil. Fig. 1shows the physical layout of the buried pipe exchanger. The heatexchanger removes part of the cooling from the building by
Fig. 1. Physical layout of the buried pipe exchanger.
A. de Jesus Freire et al. / Applied Thermal Engineering 51 (2013) 1124e1134 1127
supplying cooled air to the conditioned room as described in Fig. 2.A multiple layer horizontal configuration is particularly advanta-geous because it uses less land area, which is one of the key issueswhen the installation of this type of equipment is considered. Acompact configuration has the disadvantage of possible heatsaturation of the soil, which compromises the efficiency of thesystem. So, special attention should be given to the use of thiscompact configuration to prevent excessive heat congested in thesoil. The comparison between single layer and multiple layerconfigurations will be discussed in Section 3.6.
3.1.1. Number of layersAfter determining the geometric configuration of the exchanger,
it was necessary to select the number of layers for the simulation.Here, the decisive element was the maximum coverage of borderconditions. A heat exchanger with two layers allows studying thebehaviour of soil between them e when it becomes saturated andat what temperature. However, two layers do not cover all possibleconditions resulting from the use of a multiple layer solution. Toovercome this issuewas selected amodel with three layers of pipes,namely, the upper layer interaction to the surface, the interactionbetween isolated layers of pipes and the layer facing infinite groundboundary.
3.1.2. Depth, and space between layersTo study the depth of the pipes as an analysis parameter, the
variables of “first pipe depth” and “space between layers” havebeen assessed separately by fixing one and varying the other. So,
Fig. 2. Scheme of heat transfer on the heat exchanger/building coupling.
a set of numerical calculations was performed considering a fixedvalue for the depth and varying the spacing. Results were ana-lysed and it was found that distance between layers should bekept around the 1.5 m and for the depth of the first layer close tothe 2 m. These values allow maximizing the efficiency of thesystem.
3.1.3. Diameter of pipesTo determine this parameter were considered two essential
conditions, the mechanical stability of the buried material and itsefficiency. From the materials available in the market, the selectedpipes were of HDPE (High Density Polyethylene) pipe and vitrifiedstoneware (which are typical in twentieth century Portuguesesewage pipe systems). 100 mm diameter pipes were selected andthis value was included in the numerical simulations.
3.1.4. Length of pipesThe length of the tubes can be conditioned by the available area.
Thus, and because this is a compact system to be used in placeswith a small available area, use of all the area available for theplacement of pipes must be assumed. The value of 35 m wasdefined according to the availability of the case study where thissystem was simulated.
3.1.5. Velocity of flowSince the flow under laminar conditions is less effective in
transferring heat to the air, the resonance that the velocity of flowcan bring to the pipes should be taken into account. By replacingthe Reynolds number of a small turbulent flow (3000) in the actualexpression of the Reynolds number, we can easily determine thevelocity of the flow. Thus, it was concluded that with the initialconditions, flow rates between 5m s�1 and 10m s�1 are satisfactoryto transfer heat, without making the supply system too noisy.
3.2. Model simplifications
The soil is considered as a continuous and homogeneousmedium. However, real systems consist of heterogeneous compo-nents where the properties of materials change in space and time.In such cases, three-dimensional arrays are constructed to describethe variability of such properties in the directions X, Y, Z at eachinstant. To simplify the computational weight for the simulation, itwas considered that the soil is a homogenous mixture of air, waterand minerals. Neither the porosity nor the soil moisture has anyspatial distribution, the whole system is dry, damp or totallysaturated with uniform porosity. Thermal capacity and conduc-tivity as well as the density parameters are considered constant intime and space. Therefore, the only factor that influences thedirection of heat flow is the temperature gradient. The pipesdiameter is limited by the width of the mesh and the side surfacesof the soil are considered as isolated. For reasons of IAQ (Indoor AirQuality) the collectors are coated with low conductivity materialswhich also act as insulators. Due to this fact, the side walls of thesoil are represented as isolated and themesh is only confined to theground. Moreover, if the pipes were extended directly to thesurface, there would be a heat flow between the air, in the verticalpart of the tubes heeding to the surface, and the soil, which couldbe accounted for in the model as an additional column of nodeswhich represent the air in those places. However, given the rela-tionship between the size of the vertical plots and the length of thesystem, heat exchange in the vertical parts of tubes can be dis-regarded and the mesh is simplified to the horizontal layers only.The arrangement of pipes allows the consideration of a geometricapproximation of the system. Thus, it is not necessary to createa mesh that is adapted to curve pipe surfaces. Even so, the details of
A. de Jesus Freire et al. / Applied Thermal Engineering 51 (2013) 1124e11341128
the curves are not at all ignored; they are included to providea correct description of the operation of the exchanger in theequations of heat pipe transfer. Fig. 3a represents the cross sectionof one layer of the exchanger using the simplification describedabove. This simplification is also assumed for the other layers of theexchanger. It was also assumed that all the pipes are coupled andthe calculations performed for one pipe could be extended to thesame layer pipes just multiplying the effect for the number of thepipes in each layer (Fig. 3b). Finally, the area related to the end ofthe pipes was assumed as an enlarged rectangle instead of a circle(Fig. 3c).
3.3. Selection of the numerical model for the simulation
Given all the considerations made so far, it is necessary to selectthe model that best meets the needs of the case study. Such anapplication requires a model that accurately approaches the realityof the problem over time. Regarding analytical models, it must beremembered that the temperature is approximated by a simple“sine” function which issues a simple harmonic function. Whenannual, monthly or even weekly data are used, the dispersion andrandomness of typical weather data produces a striking departurefrom the analytical model results, which can have temperaturedifferences of up to 10 �C. Therefore, it was concluded from theresults obtained that discrete models are more suitable for thesestudies, thus discarding the hypothesis of the analytical model
Fig. 3. Steps of model simplification: cross section of th
applied to the present case study. In these circumstances a decisionmust be made between one or two-dimensional discrete models.The two-dimensional discrete model shows the climate changesmore accurately and has a more realistic approximation regardingthe behaviour of the soil surface when compared to the onedimensionmodel. However, the computing time related to the one-dimensional model is six times lower than the two-dimensionalone, which allows faster answers in practical cases. Comparingthe results of a day simulation with one and two-dimensionalmodels, there are variations of 6.5% in the average exit tempera-ture of the exchanger, which in absolute terms represents differ-ences of about 1 �C. Under more extreme temperatures, thevariation of results increase without significant error, recordinga maximum difference of 2.5 �C. Based on previous studiesconsidering the comparison between different models, it wasconcluded that the model that has the best features to apply inpractical cases is the distributed one-dimensional model. Thus, theone-dimensional model was selected to be applied for this casestudy.
3.4. Mathematical model (alterar equaçoes)
The numerical model deals with the discrete equations ofconductive transient heat transfer. For the general 3D case, thediscretization of the diffusion equation assumes the shape ofequation (1).
e heat exchanger a) x axis; b) y axis and c) z axis.
A. de Jesus Freire et al. / Applied Thermal Engineering 51 (2013) 1124e1134 1129
lsolodx
DYDZ�T½iþ1;j;k� þ T½i�1;j;k� � 2T½i;j;k�
�
þ lsolody
DXDZ�T½i;jþ1;k� þ T½i;j�1;k� � 2T½i;j;k�
�
þ lsolodz
DXDY�T½i;j;kþ1� þ T½i;j;k�1� � 2T½i;j;k�
�
þ Fonte ¼ r$DV$CpT½i;j;k� � T0½i;j;k�
Dt
(1)
where directions X, Y and Z will be respectively the horizontal axisalong the pipes edge, the vertical axis along the pipes’ depth andthe pipes’ cross section on the horizontal. Also the indexes “i”, “j”and “k” are the node counters on each direction. “Fonte” will applyfor any heat source in the node.
The heat transfer inside the pipes is described by the convectiveheat transfer equation where the Nusselt number is obtained fora turbulent flow inside a pipe in the equation (2).
Nu ¼ 0:023$Re0:8
$Prn (2)�Ttubo < Tar/n ¼ 0:3Ttubo > Tar/n ¼ 0:4
aar ¼ Nu� lardin
(3)
rar$cpar$var$Nt$p$
d2in4
ðTin � ToutÞ ¼ aar$X$Nt$p$din�Tar � Ttubo
�(4)
The convection coefficient will be given by the equation (3) andthe heat balance that will couple the flow to buried pipes system iscorrelated in the equation (4). For the calculation procedure thesefunctions were computed for hourly data in conjunction with theweather data files used for the simulations.
3.5. Mesh generation for more complex case (3 layers)
After defining the system’s geometric configuration, the gener-ation of an appropriate mesh becomes the core of a satisfactoryresolution. A well-defined mesh can significantly reduce thecomputing time, and may increase the processing capacity ofinformation in areas where it is very dense. Fig. 4 shows the meshgenerated for the 3-layers configuration. The mesh design appliedis a vertical plane coincident with the axis of the pipe; this choiceallows the use of the existing symmetry. In the model developedaccording to these conditions, it is only necessary to simulatea single pipe and then multiply the result by the total number ofpipes. The mesh boundaries are limited by the surface, by the pipewalls and by the selected depth of the soil. The mesh length (x) isdefined by the length of the pipes and the sides of the tube on bothsides, coincident with the boundaries of the mesh. The spacebetween nodes is, in both cases, considered uniform. The mesh isa one-dimensional column of nodes that subdivides the earth into“N” levels in the same “y” direction. The layers on the boundariesare the only finite elements which have half the thickness and thisfeature is common to all elements that form the boundary of thesystem. There are also exclusive nodes for the tubewalls and the airthat circulates inside the tube. The height of the associated layersmatches the thickness of the tube and its inner diameter.
3.5.1. Boundary conditionThe boundary conditions are specific conditions of a given
problem which allow a specific solution for the set of general
equations that result from general principles of conservation ofmass and energy. In the earth-to-air heat exchanger model theboundaries are located in several places, namely, at the top by thesoil surface, at the bottom by the depth limit of the soil section, atthe middle of the soil section by the pipe walls, and finally, at thesides of the soil section by the ground and the pipe thickness.
� The soil surface
On the soil surface the conditions of the border are representedby an energy balance that includes heat exchanged by radiation,convection and evaporation. As a result of the energy balance theheat transmitted is stored in the soil spread to the internal nodes byconduction. The energy balance at the surface can be displayed bythe following equations:
Qarm ¼ Qri þ Qre þ Qev þ Qcv þ Qcd (5)
Qarm ¼ r$DV$CpTsup � T0
sup
Dt(6)
Qri ¼ asoloX$Z$Isol (7)
Qre ¼ �εsolo$s$X$Z$�T4sup � T4amb
�(8)
Qev ¼ �0:0168$f $X$Z$asup$P�103$Tsup þ 609
�� far$ð103$Tamb þ 609ÞR (9)
Qcv ¼ asup$X$Z$�Tamb � Tsup
�(10)
asup ¼ 0:5þ 1:2$ffiffiffiffiffiffiffiffiffiffiffiffiffijvambj
p(11)
Here X and Z represent the element size on the horizontaldirections.
� Adiabatic surfaces
In the heat exchanger model, the side walls of the mesh wereconsidered adiabatic borders. Thus, the nodes that make up themesh only exchange heat with the neighbouring nodes but notwith the exterior. This can be expressed by the equation (12).
vTvx
¼ 0 (12)
The lateral boundaries can be considered adiabatic for severalreasons, namely because the intensity of heat fluxes in horizontal isquite low, due to gradients of temperature. Consequently, heat fluxcan be assumed only on the vertical direction, the ends of the pipesare also adiabatics. This explains why many researchers have onlystudied the earth-air exchanger as a one-dimensional problem. Oneshould also consider that the side surfaces of the mesh are incontact with the walls of the input and output collectors, andconsidering the physical problem they can be considered isolateddue to several factors. To ensure the conditions of IAQ in the wholesystem, the collectors are coated by inner layers of EPOXY whichtypically have low thermal conductivity, acting as insulation of theside walls of the ground. The epoxy resin has a relatively lowconductivity, 0.20Wm�1 �C�1 when compared with the propertiesof the soil, which is ten times higher. Therefore, it can be assumedthat the heat flow through the lateral limits of the soil is so low thatit can be disregarded. This is the main reason why the change intemperature along each of the input and output collectors wasn’t
Fig. 4. Mesh generated for the three layers configuration.
A. de Jesus Freire et al. / Applied Thermal Engineering 51 (2013) 1124e11341130
considered. Finally, another important asset for the insulated wallfocuses on the relationship between the depth and length of thetubes, showing that the total amount of energy transferred in theseareas can be ignored. A typical system 4 m deep and 40 m in lengthrequires a ratio of 1e10 regarding heat exchanges.
� Isothermal
From a given depth, the diffusion of the heat resulting from theaction of an air-ground exchanger is no longer present. For thisreason, it can be considered that the temperature is constant overtime. Since there is no significant variation on the gradient oftemperature this can be mistreated with a zero heat flow, which issimilar to an adiabatic surface.
For modelling purposes, it was considered sufficient to use thesame depth on the first and last layers of pipes. This means that thedistance between the soil surface and the first layer is the same asthe distance between the last layer and the bottom of the mesh. Aconstant temperature was assigned, equal to the annual averagesoil temperature (15 �C) for all nodes belonging to the lower limit ofthe mesh.
3.5.2. Power of the fanEnergy use of the system is determined by the pressure drop
(DP) during the passage through the air circulating fan. This ismeasured from the exchanger tube entry to the areas of inflation.The entry and exit of the exchanger are not counted since thesespaces are very wide, with probable reduced DP, and settings weremade according to the needs of each case. However, the valueassigned to the building losses is oversized to compensate the
pressure drop on collectors. It was assumed 220 Pa for the build-ing’s pressure drop. The route takes into account the losses due tothe hydraulic characteristics of the pipes (roughness) and thepossible losses located in the system. The roughness of the pipesdepends on the material used. In this work, two cases were studiedfor the earth-air heat exchanger tubes; high density polyethylenetubes (HDPE), and vitrified stoneware pipes. The HDPE pipes havea surface roughness of about 0.0015 mm and 0.04 mm for thevitrified stoneware. These values were used to compute the pres-sure drop along the pipes.
3.5.3. Duty of exchange and COPTo obtain the duty of the heat exchanger, it is only necessary to
compute the heat transferred by air according to the equation (13):
Q,
¼ mar,
$cparðTout � TinÞ (13)
The referred temperatures are the air temperatures at the outletand inlet of the exchanger. The heat transfer duty is zero when thesystem chooses to bypass the heat exchanger and allows air tocome directly from the outside. Finally, the COP and EER of the heatexchanger are given by equations (14) and (15), respectively:
COP ¼ Q :
We, (14)
EER ¼ 3:412Q :
We, (15)
Fig. 5. Soil temperature profile in a three-layer heat exchanger.
A. de Jesus Freire et al. / Applied Thermal Engineering 51 (2013) 1124e1134 1131
3.6. Parametric analysis
In this study, the effect of the number of layers, depth and spacebetween layers, diameter of pipes, length of pipes and velocity floware considered in regard to the heat exchanger duty output. Severalsimulations were performed with progressive variations of eachparameter independently. However, it was not considered thecombined effect due to changing more than one parameter at thesame time.
When a multiple layer configuration is adopted, it was verifiedthat maintaining similar transfer areas and velocity flows incursa decrease of 3e6% in the duty delivered by the heat exchangerwith two and three layers, respectively. The reason behind thisdecrease is a temperature increment in the soil between the layers,which leads to a reduction in the gradient temperature betweenthe soil and the air that flows through the pipes. Nevertheless, thedecrease of 3% and 6% in heat exchanger duty corresponds toa decrease of 50% and 67% in the area needed, respectively. Fig. 5
Fig. 6. Floor layout o
depicts the soil temperature profile in a three-layer heatexchanger. The pipes of each layer are located at 4 m, 6 m and 8 mfor the first, second and third layer. With a three-layer configura-tion, the soil temperature at the second and third layer depth ishigher than if the heat exchanger consists of only one pipe.
The soil temperature determines the available heat to betransferred along the heat exchanger, and when it becomes similarto the room temperature the heat exchanger duty tends to zero. Theheat exchange potential increases with the layers depth until 3 m.On the other hand, the space between the layers is crucial for theheat exchanger design. When the space between layers is reducedthe temperature increases sharply and the soil achieves its satu-ration point. Under these circumstances the soil is not able toabsorb more heat and the heat exchanger duty drops considerably.The ideal space between layers was computed as 1.5 m butdistances up to 2 m can also be considered reasonable.
The heat exchanger duty increases with the pipe length. A valuenear 500 W was obtained for a pipe length of 100 m. However, due
Fig. 7. Transferred power of the heat exchanger during one year.
A. de Jesus Freire et al. / Applied Thermal Engineering 51 (2013) 1124e11341132
to local restrictions the pipe length has to be in lower ranges. On theother hand, it was also verified that the heat exchanger dutydecreases inversely to the pipe diameter. Increasing the pipediameter leads to decreased velocities and also decreased heatconvection transfer coefficients. Therefore, the ideal diameter valueshould consider reasonable heat exchanger duty but also shouldallow for reasonable flow rates. Regarding the two formerrequirements, an ideal value of 100 mm was obtained.
Heat exchanger duty output increases as a function of thevelocity flow. However, this effect tends to be zero because highervelocities also lead to decreased heat transfer efficiencies and thetemperature gradient becomes zero. This trend starts to occur after10 m s�1. For practical purposes flow velocities higher than 5 m s�1
should not be used due to noise issues.
4. Practical application of the case
The practical application of this study aims at determining theimpact of the presented solution on the acclimatization of a realbuilding with real characteristics and needs imposed on it,including minimum flow rates and profiles of occupation. TRNSYSsoftware was used to simulate the thermal behaviour of thebuilding as a function of time [22], in which all conditions of thebuilding as well as data on the buried pipe heat exchanger wereintroduced. According to the building needs, the required charac-teristics of the exchanger have been specified to obtain comfortabletemperatures inside air-conditioned spaces. The TRNSYS simula-tions consider the temperatures of air-conditioned spaces as anoutput, which allows to follow the result of coupling the heatexchanger to the building according to the inside conditions. Theheat exchanger was integrated as a single system for cooling thebuilding. In this sectionwe studied whether the systemwas able tomaintain thermal comfort. The results of the temperatures pre-sented in this work match a single flat of the building, with similarestimates for other areas of the building.
4.1. The building
The studied building is a partially buried residential buildingwith the layout shown in Fig. 6. The residential storeys have 2 flatsof 3 rooms each. The buried floors are the basement parking area.The minimum flow rates imposed by IAQ requirements are155m3 h�1. The nominal flow is 1.2 air changes per hour in the flats.Considering the total number of flats, a required minimum flow of960 m3 h�1 is estimated for the building.
The apartments have a ground floor area about 85 m2 anda ceiling height of 2.5 m. They consist of three bedrooms, a livingroom, a kitchen and two bathrooms. They have two fronts and theroom is oriented to the south. The roof of the building is horizontaland the envelope is complies with the national regulation, RCCTE.
4.2. The soil and pipes
The heat exchanger is located SW of the building, and theadmission from the collector to the exchanger output is madethrough the lift box. The heat exchanger is buried in the groundwithbare soil cover and occupies a horizontal area of 64.4 m2, approxi-mately 7 m in depth. Their characteristics are shown in Table 3.
5. The final results
The simulations found that although the conductivity of the soilcould have strong variations, the soil type is not a key factor in theperformance of the exchanger. It was also concluded that thethermal capacity is the main element to take into account in the
selection of the soil, materials with higher values being preferablewhere possible. It should bementioned that a numerical simulationcomparing the performance of the single layer heat exchanger vsthe multiple layer heat exchanger was also performed, and it wasverified that the latter provides similar results with the majoradvantage of using smaller areas for installation. Regarding thevalidation of the developed model, the simulation covers a periodof one year, during which the achieved temperatures in the accli-matized space as well as the near to comfort temperatures wereanalysed. All the other aspects that influence the functioning andperformance of the exchanger were also analysed. From Fig. 7, it canbe seen that the heat exchanger worked for about a third of the yearsupplying heat to the ground. In the remaining time, it removedheat from the ground. The duty of the heat exchanger is, on average,1 kW throughout the whole year. During the cooling period, thesystem stored 266 kW h in the soil and in the heating season thesystem provided 871 kW h, a difference of 605 kW h was removedfrom the ground. A crude analysis compares the temperature of theroom with the outside temperature. In the first analysis, incorpo-rating the heat exchange system allows a reduction in thetemperature range inside the building, which by itself brings somethermal comfort. In Fig. 8 (taken from the cooling period of the heatexchanger) can be seen a reasonably lower average temperature atthe exchanger output when related with the outside temperature.It is observed that the sector can reach temperatures below 25 �Cthroughout the cooling season helped by the weather conditionsthat do not reach temperatures above the reference value duringthe same period. During the heating period, the effect of the heatexchanger is to keep the housing above the outside temperature,but as expected, this system alone cannot sustain comfortabletemperatures. There were no occurrences of overheating in anypart of this simulation, or even temperatures equal to or above26 �C. In contrast, the results deviate from the reference
9085
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Fig. 10. Frequency of occurrence of temperatures below those indicated in the heatingperiod.
Fig. 8. Example of the heat exchanger work during a cooling week.
A. de Jesus Freire et al. / Applied Thermal Engineering 51 (2013) 1124e1134 1133
temperature for lower values. The occurrence frequency of suchdeviations, in which the temperature remains below 25 �C andabove the temperature indicated, is shown in Fig. 9. It was foundthat a deviation of 3 �C below the reference temperature (25 �C)occurs with a frequency of 65%. This value is quite high and may bedue to heat exchanger over dimensioning. Thus, it can be concludedthat the airflow or the length of the tubes should be reduced.However, this correction could make the temperature in thehousing exceed the reference temperature. In 107 days of thecooling period, it is shown that the room temperature was kept inan acceptable range of temperatures of comfort, from 20 �C to 25 �Cwhich corresponds to 88% of the considered time. Considering theheating season, temperatures above 20 �C were registered, but atlow frequency e 3% for an increase of 1 �C.
It can be concluded from Fig. 10 that the frequencies areconsiderably high, indicating that the exchanger is unable tomaintain a comfortable temperature alone, so it only acts assupport for a conventional system.
For an overall pressure drop of 325 Pa and a total airflow of960 m3 h�1, the fan power required is about 145 W. This type ofsystems does not imply high pressure drops as they usually havea very straight forward configuration.
Based on the studies made so far, it can be stated that thistechnology is effective for densely occupied multifamily buildingswhere the use of compact spaces is a strong handicap.
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Fig. 9. Occurrence of temperatures below those indicated in the cooling period.
6. Conclusions
Thework reported here aimed to expand the applications of thistechnology to residential buildings where available space is limited,considering the feasibility of compact exchangers that canmeet therequirements of such buildings.
The thermal behaviour of the soil is the basic principle ofoperation considering the heat exchanger. This behaviour iscontrolled by the corresponding thermal properties, namely,thermal conductivity and thermal capacity but also by soil density.In turn, the characteristics mentioned above are strongly influ-enced by soil porosity and moisture.
It was found that a one-dimensional discrete model can respondsatisfactorily to a performance analysis of compact buried pipessystems, producing results significantly faster than the bi-dimensional model, within a good accuracy. When the multiplelayer configuration is adopted, it was verified that maintainingsimilar transfer areas and velocity flows incurs a decrease of 3e6%in the duty delivered by heat exchangers with two and three layersrespectively, when compared to heat exchangers with a singlelayer. However, this corresponds to a decrease of 50% and 67% in thearea needed, respectively. This factor is very attractive given thecurrent limitations in urban spaces.
Analysed parameters showed that the heat exchanger dutyincreases with the floor depth until 3 m and that the optimumspace between layers is 1.5 m, but distances up to 2 m are alsoefficient. This value allowsmaking a good compromise between theinstallation area and the intensity of the usage. Economic aspects ofthe installation are the constraints to the total depth of the system.
To maximize the duty of this system, high speeds should bemaintained to ensure a turbulent flow, but given the noise issues itis recommended to limit the maximum speed up to 5 m s�1.However, this value could be adapted to each case study.
The creation of high speeds requires a selection of appropriatediameters and numbers of tubes. Small diameters and high numbersof tubes should be aimed for, instead of fewer tubes and bigger pipes.This fact makes it possible to consider the installation of compactsystems in limited urban residential and office building areas.
Acknowledgements
We would like to express our gratitude to the PortugueseFoundation for Science and Technology (FCT) for the supportgiven by grant SFRH/BPD/71686 and to the National PTDC/AAC-AMB/103119/2008 Project.
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