An experimental and a numerical study of horizontal earth-air heat exchanger in a hot climate

Abstract

Earth-air heat exchangers (EAHE) are devices used in the geothermal technique in order to reduce energy consumption in buildings. In this study, a simulation was conducted through the computational fluid dynamics platform FLUENT 6.3 for the prediction of thermal performance of the EAHE that describes the variation of the air temperature inside the tube. For this, it was necessary to design the heat exchanger while respecting the design and the actual dimensions of the experimental set-up, and stating that the temperature of the wall of the horizontal tube of the exchanger is equal to that of ground at 3 m depth. It should be noted that in assessing the temperature along the two sections vertical (input and output) of the exchanger, opting for a function (UDF) the user define function. Finally, noting a good agreement between both experimental and numerical study, and showing that a significant reduction in temperature at the outlet of the exchanger to a difference of 20 °C, confirming the effectiveness of the heat exchanger.

Keywords:

• Earth-air heat exchangers (EAHE)
• geothermal
• numerical study
• experimental study

1. Introduction

This article deals with the behaviour thermal of an Earth-air heat exchanger (EAHE) which consists of an underground tubular conduit made of metal or plastic material. The buried heat exchangers are made by passive methods to reduce energy consumption. In our case, the system used is a circular pipe inner of diameter110 mm buried horizontally. This model allows the heat exchange fluid with the ground to cool in summer and warm in winter. The experimental device is installed at the University of Biskra (Algeria), located in a hot climate zone, which is used to provide experimental data and to study its effectiveness.

In the literature, several studies of theoretical and experimental research on buried heat exchangers were conducted in several research laboratories. Explaining various types of heat exchangers and studying the effectiveness of heating and cooling. Sehli, Hasni, and Tamali (2012), developed a one-dimensional steady numerical model to estimate the effectiveness of EAHE, installed in the south of Algeria at different depths. The authors concluded that the EAHE system cannot maintain thermal comfort inside the premises, but it could be used to reduce the energy demand in the domestic building in the same area. This system can be used simultaneously as an air conditioning device. Misra et al. (2013a, 2013b) developed a model in computational fluid dynamics (CFD) software FLUENT 6.3. The analysis based on CFD has been used to solve the temperature field around the line of EAHE, using an unstructured grid, and used it to study and analyse the ground thermal conductivity effects of the continuous operation duration and the flow pipe diameter on the thermal performance of the undercut EAHE speed conditions. Among the considered conditions is that the pipes wall temperature is constant (300.2) K all along EAHE. A numerical model of heat transfer in the ground has been developed by Esen, Inalli, and Esen (2007) to determine the temperature distribution near the pipe.

The finite difference approximation is used for numerical analysis. It should be noted that the numerical results obtained are in agreement with experimental measurements. To reduce the load of cooling of the buildings in summer Bansal et al.(2010) realised several studies on EAHE one of these studies a model that was developed by the CFD software FLUENT (version 6.3), for a warm and dry climate there’s the city of Ajmer (India). Bansal et al. (2012) have developed an EATHE and integrated it into an evaporative cooler of the output EATHE. The use of TRNSYS environment facilitate the coupling heat exchanger air-ground buildings or greenhouses to reduce the building cooling load and to predict the thermal performance of EAHE (Mihalakakou, Santamouris, and Asimakopoulos 1994; Santamouris et al. 1995). A work done by Thiers and Peuportier (2008) provided technical solutions to reduce energy consumption in buildings and shout thermal comfort. Among these solutions the design of the building and the ventilation system (heat recovery unit and a heat exchanger air-ground). A model developed ‘COMFIE’ for passive buildings and coupling with an EAHE. A performance evaluation of an EAHE by different designs, and determine the most important design to achieve a high specific energy performance (Pfafferott 2003). A work done by Amara, Nordell, and Benyoucef (2011) to use the old Fouggara system for heating and cooling of buildings in the desert of Algeria. A numerical study predicts the thermal behaviour of an EAHE for different climates (cold weather, mild and hot) (Ramírez-Dávila et al. 2014; Xamán et al. 2015). It is concluded that the EAHE is effective in extreme climates and moderate temperatures.

The analysis time of one year of the integrated system was made for mainly hot and dry climatic conditions using the model (CFD) modelling with the CFD software FLUENT (version 6.3).

2. Description of the model CFD

A numerical study of EAHE was developed using the CFD software FLUENT 6.3. Assessing the evolution of the temperature along the exchanger tubes; it was necessary to create the geometry of the mesh using Gambit 2.3 software while respecting the dimensions (length, diameter of the tubes, the shape of elbows, thickness and spacing of the tubes).

2.1. The geometry and mesh

In this step, the heat exchanger geometry was discretised with real dimensions (length, diameter …), using a three-dimensional geometry adapted to the grid structure (Figures 1, and 2).

Figure 1. Schematic diagram of the system of EAHE.

Figure 2. Symmetrical Geometry of the exchanger under Gambit.

By using various types of grid and a fine grid very near to the wall of the tube (Figure 3). The volume mesh that affects the entire surface of the heat exchanger can be controlled by using ‘examined mesh’ Figure 4.

Figure 3. Various types of grid used for simulation.

Figure 4. Grid controls.

2.2. The solver FLUENT 6.3

Once the geometry of the exchanger is completed, it is saved with the extension mesh. The solver FLUENT 6.3 was used for numerical simulation, with which the geometry was imported previously, designed with the Gambit software and documentation necessary for the simulation data and defined the conditions limits (stating that the temperature of the wall of the horizontal tube of the exchanger is equal to the soil at a certain depth). The energy model was used to set parameters related to energy or thermal, and define the thermal conductivity of the pipe. The discretisation schemes used in this work for the first-order momentum, turbulent kinetic energy and dissipation rate on the velocity-pressure coupling was chosen for the standard SIMPLE algorithm. As regards the convergence criterion, an estimated 1e-6 for energy was chosen and all variables to ensure convergence.

2.3. The iso-surfaces

The iso-surfaces are a FLUENT method for selecting points of temperature throughout the pipe. The Figure 5 has the air temperature (red line) and the temperature of the wall (Figure 5).

Figure 5. Iso-surfaces.

2.4. Governing equations

The governing equations in 3D Cartesian coordinates for compressible and steady flow, heat and mass transfer are given below:

The continuity equation:(1)

The momentum equations:(2) (3) (4)

The energy conservation equation, for a steady flow, without internal source and viscous dissipation.(5)

Various methods exist for solving these equations such as.

•	The Direct Numerical Simulation (DNS).
•	Large Eddy Simulation (LES).
•	Statistical modelling of Navier–Stokes(Reynolds-Averaged Navier–Stokesequations or RANS equations).

The flow modelling should be able to take into account the flow and turbulence fields in the tubes while allowing relatively short calculations. Approaches to DNS and LES type theoretically odd if they can provide better resolutions of Navier–Stokes equations are too time consuming.

Consequently, the RANS was opted as a method of decomposing each variable into a mean value and a fluctuation around this average value. The resulting averaged equations contain additional terms that reflect the fluctuations in production speeds. These new terms are called the Reynolds stresses that require the closure equations by turbulence models. There is a very wide range of turbulence models including the k − ε model which is certainly the most widespread in the literature. Despite its inability to detail the characteristics of turbulence, statistical modelling it is a good tool to characterise mean fields.

The continuity equation:(6)

The momentum conservation equations:(7)

The energy conservation equation:(8)

The RANS equations ‘Equations 6(6) –8(8) ’ introduce some higher order unknowns:, which are called the Reynolds-stresses and turbulent heat-flux components, respectively. Attempts to derive accurate transport equations for these unknowns give rise to some higher order unknowns. To solve this closure problem, Boussi-nesq (1877) introduced an approximation for the modelling of the Reynolds stresses and turbulent heat flux components. (Khalajzadeh, Farmahini-Farahani, and Heidarinejad 2012), The Boussi-nesq approximation is:(9) (10)

The eddy viscosity is calculated from:

2.4.1. Standard k − ε model

The turbulence kinetic energy, k and its rate of dissipation, ε is obtained from the following transport equations: (11) (12)

G_k: Represents the generation of turbulence kinetic energy due to the mean velocity gradients, calculated as:(13)

G_b: Is the generation of turbulence kinetic energy due to buoyancy, calculated as:(14)

P_rt: Is the turbulent Prandtl number for energy and is the component of the gravitational vector in the ith direction

: The coefficient of thermal expansion.

Y_M: Represents the contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate, calculated as:

, M nombre mach

The model constants , are the turbulent Prandtl numbers for k and ɛ.

are user-defined source terms

Modelling of turbulent viscosity:(15)

By regarding the conditions of the variable limits along vertical tubes depending on the soil depth, a defined function (UDF) was opted for assigning the function of the temperature as a function of vertical tubes depth. The temperature of the surface can be estimated by using a sine function (Equation (11(11) )).(16)

The temperature of the depth of the soil can be shown as follows:(17)

With T (z, t) the soil temperature at time (t) and depth (z), Tm is the annual average soil temperature, T₀ is the amplitude of the temperature on the surface (Z = 0) and ω is the frequency of the annual temperature wave. As seen in Figure 6, the undisturbed ground temperature is changing in shallow regions (until 10 m in depth) and after that the ground temperature becomes constant. Physical as well as the parameters for calculating characteristics are shown respectively, in Tables 1, and 2 (Moummi et al. 2010).

Figure 6. Profile of temperature of the ground for various depths (Khalajzadeh, Heidarinejad, and Srebric 2011).

Table 1. Physical properties (Moummi et al. 2010).

Properties	Values
Thermal conductivity of the ground (W/m. °C)	2.01
Specific heat of the ground (J/kg. °C)	1380
Density of the ground (kg/m^3)	2300
Thermal diffusivity of the ground (m^2/s)	6.33 × 10^−7
Thermal conductivity of the PVC (W/m. °C)	1.17
Specific heat of the PVC (J/kg. °C)	900
Density of the PVC (kg/m^3)	1380

Table 2. Parameters of input for the comparative validation (Moummi et al. 2010).

Properties	Values
Pipe length (m)	50
Pipe diameter (m)	0.11
Depth of pipe (m)	3
Air velocity (m/s)	4.5; 3.5
Inlet temperature (°c)	37,48
Soil temperature (z = 3 m) in summer (°C)	24; 28

3. The experimental study

This part is developed with the aim of studying the efficiency of the EAHE in too hot, arid regions. The exchanger was installed in Biskra, (see Figures 7, 8, and 9 realised the LGM lab of Biskra University). This principle is applied for the renewal of a residential air to achieve energy savings. Pipes, in which air required for renewal circulates, are buried at a depth of 3 m at a slope of 2%. The tubes are arranged and spaced at a very central distance of 2 m.

Figure 7. Location of sensors along the heat exchanger.

Figure 8. Image of the horizontal heat exchanger for various depths.

Figure 9. Detailed site of the sensors of the air inside the sheath.

A receiving tank is built in concrete at the outlet of the exchanger. A variable flow air extractor is placed in the inlet of the exchanger. Series of temperature sensors are positioned along the heat exchanger from the inlet to the outlet. The sensors are connected to a data logger (Moummi et al. 2010).

During the months of July and August, the two hottest months of the year, the behaviour of the exchanger and its effectiveness was studied, the Figure 10 shows the difference of temperature between the inlet and the outlet of the EAHE for three successive days for each month (Figure 10(a) in July, Figure 10(b) in August).

Figure 10. Comparison of inlet and the outlet temperature of the exchanger, for each month (a) July (b) August.

4. Validation of simulation model

In order to validate our model, it was necessary to confront the values of the simulated results with the values from our company measures, this company began in June 2013, until September 2013 during which collected 288 measurements, after finishing, Figure 10 can be constructed.

The Figure 11 and the Table 3 that follows present a comparison between the calculated results and those obtained experimentally (temperature of the ambient air 37 °C, and Soil temperature (Z = 3 m) 24 °C).

Figure 11. Variation in the temperature for different types of grids.

Table 3. Validation of the model of simulation (Temperature of the ambient air 37 °C, and Soil temperature (Z = 3 m) 24 °C).

Position of sensors (m)	Measured temperatures (°C)	Simulated temperatures (°C)
2.65	35.24	35.66
6.9	32.28	31.44
10.81	29.83	29.00
18	26.74	26.70
23.44	25.95	25.44
30.21	25.00	25.02
45.3	24.21	24.26

The Figures 12, and 13 present a distribution of the temperature on the wall of the conduits.

Figure 12. Distribution of the temperature of the air with the length of the conduits.

Figure 13. Distribution of the temperature on the wall of the conduits.

Figure 14 presents a comparison between the results calculated and measured for various hours of measurements. As regards the results obtained with the use of function UDF, they are shown in Figure 15 (Soil temperature (Z = 3 m) 28 °C).

Figure 14. Validation of CFD results with experimental results.

Figure 15. Comparison of the results obtained by the use of the UDF with the experimental ones.

Simulated results agree with the measured Figure 15 and Table 4, while the simulated values with the defined function UDF user still agree to advantage with the values measured.

Table 4. Comparison enters the results simulated and the results obtaining by the UDF (Temperature of the ambient air 37 °C, and soil temperature (Z = 3 m) 24 °C).

Position of sensors (m)	Measured temperature (°C)	Simulated temperatures (°C)	Corrected and simulated temperatures (°C)	Absolute error of the simulated temperature	Absolute error of the simulated temperature corrected	Relative error ‘simulated temperature’	Relative error « simulated temperature corrected »
6.900	32.283	31.440	32.503	0.843	0.220	2.86%	1.12%
10.810	29.830	29.000	29.500	0.83	0.330
14.140	27.974	28.400	28.000	0.426	0.026
18.000	26.745	26.700	26.982	0.045	0.237
22.030	26.356	26.127	26.127	0.229	0.229
23.440	25.954	25.440	25.844	0.514	0.110
26.170	25.327	25.130	25.427	0.197	0.100
34.100	24.809	24.400	24.654	0.409	0.155

5. Conclusions

In this paper it was presented that the EAHE modelling, which allowed us to obtain simulations is consistent with our company of measures.

The model of EAHE was improved acting on limits conditions that are more realistic, using the user-defined function (UDF) which consists in writing limit conditions for variable depending on the depth, achieving a significant improvement of results closest to the experimental values.

A sufficiently fine mesh was opted so that the results of the sought variables are not affected by a further refinement.

In-situ measurements that indicate a substantial reduction in the temperature of the air that can enter some days at 49 °C and after crossing the EAHE it exits at 29 °C, which is a difference of 20 °C. This temperature reduction can be a cooling which may cause a consequent saving of cooling energy.

It is therefore clear that when the exchanger is used as a method of passive system, it contributes effectively in the comfort of buildings in hot and arid regions.

In-situ measurements that indicate a substantial reduction in the temperature of the air that can enter some days at 49 °C and after crossing the EAHE it exits at 29 °C, which is a difference of 20 °C. This temperature reduction can be cooling which may cause a consequent saving of cooling energy.

It is therefore clear that when the exchanger is used as a method of passive system contributes effectively in the comfort of buildings in hot and arid regions.

Nomenclature
EAHE:	=	Earth-air heat exchanger
u:	=	X velocity, m/s
v:	=	Y velocity, m/s
w:	=	Z velocity, m/s
μt:	=	Turbulent viscosity m2/s
ϑ:	=	kinematic viscosity (m2/s)
ρ:	=	Air density (kg / m3)
T:	=	Air temperature (°C)
P:	=	Air pressure (Pascal)
μ:	=	Air dynamic viscosity (kg/ms)
ε:	=	Rate of dissipation (m2/s3)
k:	=	Turbulent kinetic energy (m2/s2)
γ:	=	Air kinematic viscosity (m2/s)
α:	=	Average thermal diffusivity (m2/s)

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes on contributors

Mohamed El Ghazali Benhamza is a PhD student at University of Biskra, Department of mechanical engineering, Algeria. His research centered essentially on geothermal, thermal insulation systems. Previous conferences paper have presented in national congress and seminaries.

Abdelhafid Brima, PhD, is a professor of mechanical engineering in mechanical department at the University of Biskra, Algiers. His research and professional experience centred on fluid mechanics, heat and mass transfer and renewable energy. Previous publications have appeared in European. Phys. Journal and also in International Journal of Green Energy and Frontiers in energy journal.

Sadok Houda, PhD, is a teacher in architectural department at the University of Biskra, Algiers. His research and professional experience centred on thermal insulation systems and studies of mass housing development, multidisciplinary design practices and sustainable design. Previous conference papers have been presented and a publication has also appeared in Journal of Science and Technology.

Noureddine Moummi, PhD, is a professor of mechanical engineering in mechanical department at the University of Biskra, Algiers. His research and professional experience essentially centred on solar energy, geothermal and heat and mass transfer. Previous publications have appeared in European. Phys. Journal as well as in International Journal of Green Energy, Frontiers in energy journal, Sustainable energy journal, progress in clean energy, and International Journal of Advanced Renewable Energy Research.

Acknowledgements

The authors are grateful for the support provided for the project by Mechanical Engineering Laboratory (LGM), and Mr. T.Bouhitm from department of English, Mohamed Khider University Biskra.