Comparison of Single- and Multipipe Earth-to-Air Heat Exchangers in Terms of Energy Gains and Electricity Consumption: A Case Study for the Temperate Climate of Central Europe

Abstract

Earth-to-air heat exchangers (EAHEs) can be used in the ventilation systems of various types of buildings. Multipipe structures can be found in large-volume buildings, yet scientific analysis of such systems is rare. Annual energy gains and electricity consumption for equivalent single-pipe and multipipe systems are typically not available. This paper bridges this gap, presenting the results of experimental studies on pressure losses in three-, five- and seven-pipe EAHEs and analysis for the annual energy gains and electric energy consumption as compared to a single-pipe exchanger. The results showed that the multipipe EAHE can be successfully replaced by a single-pipe structure with the same thermal performance and similar pressure losses if a tube with the appropriate diameter is used. However, multipipe heat exchangers can also use pipes of larger diameter (manifolds and/or branches), which improves their energy efficiency and may then make them more advantageous than single-pipe structures. From this reason, ultimately, the final selection of exchanger geometry should take into account economic and environmental issues and also user preferences and their importance in the hierarchy.

1. Introduction

This study belongs to the category of energy efficiency improvement, which is currently one of the world’s priorities. As the building sector is responsible for approximately 40% of global energy consumption, in recent decades, much attention has been paid to increasing the efficiency of heating, ventilation and air conditioning (HVAC) and domestic hot water (DHW) preparation systems. All over the world, more stringent legal requirements regarding the thermal insulation of building partitions are being introduced. This procedure is easy to perform and brings the most significant reduction in energy consumption by buildings. At the same time, however, requirements are being introduced to reduce the demand for nonrenewable primary energy (i.e., energy that comes from the processing of fossil fuels). This promotes the use of renewable energy sources (RESs). Meeting the legal requirements in this area (e.g., in the European Union countries) requires much more effort from building designers than just caring for the appropriate thermal insulation of building partitions. Only the application of energy-efficient HVAC and DHW systems and the use of RESs help in achieving the limit value of the PE (primary energy input coefficient).

Analysis of energy consumption in buildings (e.g., [1]) has shown that aside from good-quality thermal insulation of partitions, other components of significant energy demand include ventilation and hot water preparation. This has been supported by several studies, for example, by the results of experimental studies of hot water consumption in single-family houses [2], by the analysis of hybrid hot water preparation systems for an industrial hall [3] and by the analysis of the possibility of using renewable energy sources for heating hot water [4]. In the case of ventilation systems, reduction in energy demand can be achieved by using heat recovery systems from the exhaust air [5]. Especially favorable are decentralized systems, in which the low flow resistance of the installation combined with better adaptation to the current needs of users result in significant energy and primary energy savings for residential buildings [6,7,8] but also for swimming pools [9] or for kindergartens [10].

Another way to reduce energy consumption in ventilation is to use earth-to-air heat exchangers (EAHEs) as a way to heat ventilation air in winter in a cold or moderate climate [11]. EAHEs are devices located at the inlet of the ventilation air that make use of the energy stored in the ground. These can be diaphragm-less exchangers, most often gravel-type or plate-type heat exchangers [12], the efficiency of which was experimentally verified in [13]. There are also pipe-type exchangers, made of pipes with a rectangular cross-section [14] or, more commonly, with a circular cross-section [15,16,17]. Pipe-type earth-to-air heat exchangers can be further divided into single-pipe and multipipe. Single-pipe configurations tend to have longer lengths and can change direction, creating a coil system, which may be suitable when space is lacking. Multipipe configurations consist of many pipes connected in parallel by means of separating and collecting manifolds. A simplified diagram for both types of exchangers is shown in Figure 1. Although other possible designs exist [18], the parallel system shown in the figure below seems to be the most popular.

Despite many articles on EAHEs, no papers were found in the available literature in which analysis comparing the single- and multipipe configurations in terms of energy gains and electricity consumption was carried out. In one paper, [19], experimental measurements of full-scale single-pipe EAHEs were taken to investigate the effects of depth and pipe diameter on the cooling capacity. However, total pressure losses were not investigated as a cost of using EAHE, and multipipe structures were not taken into account. Modeling of heat flow taking into account moisture transport in single-pipe EAHEs has been explored [20,21], although neither pressure losses nor multipipe systems were investigated or compared. The subject of the experimental research presented in [22] was an exchanger made of a single PVC pipe, 66 m long and 110 mm in diameter, buried at a depth of 1.5 m and working without any mechanical devices forcing the air through the exchanger. The study did not take into account the possibility of using multipipe structures and did not compare their performance with analogous single-pipe structures. Ref. [23] analyzed a single-pipe heat exchanger coupled with a solar chimney, which was responsible for passively driving the airflow without the use of fans and electricity. Compared to [23], in the present paper, the annual electricity consumption was analyzed for the case in which the air movement of the exchanger was forced by the fan, which in the case of using mechanical ventilation systems is the more common, active solution that guarantees the independence of fresh air supply from weather conditions. A similar solution with a domed roof was analyzed numerically in [24], yet neither pressure losses nor multipipe structures were analyzed. In [25], a multiple-criteria decision-making method was used to optimize a single-pipe EAHE cooperating with a residential building. The study did not consider the possibility of using a multipipe EAHE, which would replace the analyzed single-pipe structures, in consideration of thermal terms. Single-pipe heat exchangers made of PVC pipes and steel pipes were compared in terms of heat [26]. The results suggested that the material was of negligible importance for energy efficiency and that the length of the exchanger branch was the dominant parameter. However, multipipe heat exchangers were not analyzed, and pressure losses, which constitute the energy and financial cost of EAHEs’ work, were ignored. EAHEs buried in multilayered soils were analyzed in [27]. However, only single-pipe exchangers were analyzed, without comparing their performance to analogous multipipe structures. The use of multipipe EAHEs for ventilation of a hospital building was analyzed in the article [28], however, single-pipe structures were not taken into account, and their performance and pressure losses were not compared with those of multipipe systems.

A thermal resistance capacity model was used for transient simulation of earth-to-air heat exchangers [29]. Only a single-pipe structure was analyzed. The transient effect may be important for the results of the analysis of many years of EAHE work, which was also shown in [30,31,32,33,34], but in the current article, it was not taken into account, because the aim was to compare single-pipe and multipipe structures operating under similar conditions—scheduled variable use. Transient analysis should be used especially when the analysis covers the use of phase-change materials to increase the energy efficiency of EAHEs [35,36,37,38].

Using an EAHE for a residential building in a warm climate was analyzed in [39]. In such a situation, the cooling gains caused by the operation of the heat exchanger were more important and desirable than the short-term heat demand for the building. In the present case study, the heat exchanger was used in a temperate climate, where, similarly as in a cold climate, the demand for heat is dominant. Ref. [40] focused on the optimization of the geometry of a single-pipe heat exchanger installed in the Italian climate. The study did not analyze the possibility of using other, equivalent single- or multipipe systems. The EAHE was treated as a theoretic device not cooperating with the natural ventilation system of the building and working according to its own schedule in an annual work cycle. In the present article, the calculations took into account the schedules of using the exchanger for the imposed stream of ventilation air. Ref. [41] presented a case study of the use of a multipipe heat exchanger for greenhouses, in which moisture is a significant load for the ventilation and air conditioning system. For this reason, the focus was on the dehumidifying potential of the exchanger. The results of the analyses presented in [42] showed different EAHEs design strategies, which resulted in different geometries of exchangers depending on which selection criterion was adopted. The authors pointed out that most scientific works do not analyze pressure losses and costs of air pumping through the heat exchanger, so exchangers can be optimized in terms of energy yield but at the same time economically ineffective. For this reason, in the present work, in addition to the thermal properties of exchangers, electricity consumption was also analyzed. This has an impact on the primary energy consumption for pumping ventilation air. It may also be taken into account in the future for further economic analysis when choosing between single-pipe and multipipe heat exchangers.

The above review shows that current research lacks comparisons of single-pipe and multipipe EAHEs in terms of energy gains and that electricity consumption was not addressed in any of the studies. To bridge this gap, this case study presents a comparison in terms of energy gains, pressure loss and hence energy consumption for driving fans in single-pipe and multipipe earth-to-air heat exchangers. The novelty introduced in this analysis was the inclusion in the calculations the following aspects: (i) using the results of experimental studies on pressure losses in multipipe exchangers, (ii) taking into account reduction in thermal efficiency in multipipe exchangers due to uneven air distribution by using the results of analyses carried out in previous works [43,44], (iii) taking into consideration variable (scheduled) airflow through the system, which is usually neglected in theoretical analyses focused on the mathematical modeling of heat transfer in earth-to-air heat exchangers, and (iv) taking into account not only the energy gains but also the costs of using the system (energy for driving the fan), which are usually neglected. This paper is organized as follows:

• the paper presents the results of experimental studies on pressure losses in multipipe heat exchangers made of 3, 5 and 7 parallel branches;
• these results were then used to compare pressure losses in these exchangers and analogous single-pipe exchangers (with the same total length of pipes used in their construction) for different airflows;
• then, analyses of the annual heat and cool gains and the annual electricity consumption by the EAHE supporting fan were conducted;
• finally, an analysis was carried out involving the search for the equivalent length of a single-pipe heat exchanger that would replace a given multipipe heat exchanger in terms of heat gains (the same heating capacity instead of the same length of the pipes)—analyses were performed for two boundary branch lengths and two selected airflows.

2. Materials and Methods

2.1. Experimental Setup for Pressure Loss Measurements

Both total pressure loss and total airflow had to be measured to achieve the goal of this study. Pressure losses of the EAHE vs. airflow rate constituted the function representing the flow characteristic of this device depending on its geometry and airflow. The greater the airflow value, the greater the pressure loss. It is a nonlinear relationship. For this reason, a single-point measurement could not be used for a single given air stream flowing through the exchanger. Rather, it was necessary to perform multiple measurements for different air streams to obtain an accurate relationship over the exchanger’s operating range. Earth-to-air heat exchangers are typically quite large, with lengths ranging from 10 to 60 m and pipe diameters around DN110 to DN315 (O.D. 110–315 mm). Therefore, 1:4 scale models of exchangers were used to carry out the research.

A detailed description of the procedures used and analysis of the validity of the current assumptions were presented in previous articles about the experimental flow characteristics of EAHEs [45,46,47,48]. The details about the experiment are presented in Appendix A and Appendix B. The Reynolds number was used as the aerodynamic criterion of the similarity of flows in terms of the flow characteristics (pressure losses as a function of the air stream). To obtain the value of the Reynolds number as in the full-scale exchanger, the exchangers made in the scale of 1:4 used flow velocities 4 times higher than in the real exchangers, which resulted directly from the relationship used to calculate the Reynolds number:

$$Re=\frac{w·d}{\nu }$$

(1)

where:

• w—velocity of the flowing air (m/s);
• d—internal diameter of the pipe (m);
• ν—kinematic viscosity of fluid (in this case: air) (m²/s).

The schema of the experimental setup is presented in Figure 2, and a photo of the setup is presented in Figure 3.

Table 1. Experimental apparatus and its precision [49].

Measured Value	Apparatus	Precision
T (°C)	Laboratory thermometer	±0.5 °C
p (Pa)	Laboratory barometer	±100 Pa
Δpi, ΔpC–D, ΔpA–D (Pa)	Micromanometer with range 0–50 Pa	±0.05 Pa
	Micromanometer with range 50–500 Pa	±0.5 Pa
	Micromanometer with range 500–1990 Pa	±3.0 Pa
L (m), Li (m), ΔL (m)	Measuring tape	±1.0 mm

presents the precision for each experimental apparatus.

The internal diameter of the branch pipe d was chosen as the characteristic geometry of the full-scale heat exchanger. The diameter of the full-scale exchanger was assumed to be PP DN200 = 0.1844 m. Therefore, the pipes used in the models had internal diameter PP DN50 = 0.0461 m. For the investigations, three exchanger models were constructed and tested:

• 3 branch-pipes, L = 76d, d = PP DN50, d_main = PP DN50;
• 5 branch-pipes, L = 76d, d = PP DN50, d_main = PP DN50;
• 7 branch-pipes, L = 76d, d = PP DN50, d_main = PP DN50.

2.2. Calculations of Annual Energy Gains

2.2.1. General Assumptions and Equations

The procedure for calculating the annual heating and cooling gains due to the earth-to-air heat exchanger came from previous articles [43,44,50,51], in which it was described in detail. The main assumptions and most important formulas used in calculations are presented briefly here.

Energy performance, ${\dot{Q}}_{i,j}$ (in W), of a single parallel branch of the EAHE was calculated for every hour during the whole year. ${\dot{Q}}_{i,j}$ was divided by 1000 to obtain a result in kW and multiplied by the time (1 h) to obtain the energy in kWh in a given hour:

$$Q_i={\sum }_{\mathrm{j}=1}^{8760}{\dot{Q}}_{i,j}/1000·\Delta t$$

(2)

where:

• j−hour number of the year = 1 to 8760;
• $\Delta t-$time step, 1 h.

Summation over one year provided the total amount of energy obtained from the exchanger’s operation for the annual cycle of operation (values for heating and cooling were calculated separately). Heating and cooling gains were calculated for each single branch-pipe of multipipe exchanger and then added:

$$Q={\sum }_{i=1}^n{Q}_i$$

(3)

where:

• n—number of branches in multipipe EAHE (3, 5 or 7), or 1 in the case of a single-pipe structure.

$${\dot{Q}}_{i,j}={\dot{m}}_{i,j}·c_j·\left(t_{i,j}-t_{e,j}\right)$$

(4)

where:

• ${\dot{m}}_{i,j}$—mass flowrate of air in the i branch of the multipipe exchanger, or total mass flowrate in the case of a single-pipe structure (kg/s);
• $c_j$—specific heat of air in j hour of the year (J/(kgK));
• $t_{i,j}$—temperature at the outlet of i branch of the exchanger (°C);
• $t_{e,j}$—temperature at the inlet to the exchanger (external air temperature) in the j hour of the year (°C).

Temperature at the outlet of an exchanger was calculated as follows:

$$t_{i,j}=t_{g,k}-\left(t_{g,k}-t_{e,j}\right)·\exp \left(-\frac{U_{i,j} · L}{{\dot{m}}_{i,j} · c_j}\right)$$

(5)

where:

• $t_{g,k}$—temperature of the ground at a given depth on day k of the year (°C);
• $t_{e,j}$—external air temperature in j hour of the year (°C);
• $U_{i,j}$—total heat transfer coefficient (W/(mK));

$$U_{i,j}=\frac{1}{R_{w,i,j}+R_d+R_g}$$

(6)

$$R_{w,i,j}=\frac{1}{\pi ·d·{\alpha }_{i,j}}$$

(7)

$$R_d=\frac{1}{2\pi ·{\lambda }_w·\ln \left(D/d\right)}$$

(8)

where:

• D—external diameter of a pipe (m);
• d—internal diameter of the pipe (m);
• ${\lambda }_w$—thermal conductivity of the material constituting the pipe’s wall (W/(mK)).

The thermal resistance of heat conduction in the ground, Rg, was calculated using the procedure described in [52]. The convective heat transfer coefficient at the internal wall of pipe was calculated as:

$${\alpha }_{i,j}=\frac{N{u}_{i,j}·{\lambda }_{a,j}}{d}$$

(9)

where:

• ${\lambda }_{a,j}$—thermal conductivity of air in j hour of the year, calculated as the average of the ground temperature at given depth and external air temperature (W/(mK)).

The Nusselt number at the internal wall of the pipes was calculated using the following equation taken from a handbook of convective heat transfer [53]:

$$N{u}_{i,j}=0.024·R{e}_{i,j}^{0.786}·P{r}_j^{0.45}·\left[1+\frac{2.42454}{{\left(\frac{L}{d}\right)}^{0.676}}\right]$$

(10)

where:

• $R{e}_{i,j}^{}$—Reynolds number for i branch and at j hour of the year,
• $P{r}_j^{}$—Prandtl number of air at j hour of the year.

The additional amount of energy from the condensation of water vapor on the cold wall of the pipe during the summer period (see Figure 4) was calculated in a simplified manner from the following equation and added to the cooling capacity of the EAHE:

$$Q_{w,i}={\sum }_{j=1}^{8760}{\dot{m}}_{i,j}·\left(X_{\mathrm{e},j}-X_{\mathrm{N},i,j}\right)/1000·r·\Delta t$$

(11)

$$Q_{w }={\sum }_{i=1}^n{Q}_{w,i}$$

(12)

where:

• $X_{\mathrm{e},j}$—humidity content in the external air at j hour of the year, taken from climatic data (g/kg);
• $X_{\mathrm{N},i,j}$—humidity content at the i branch outlet and in j hour of the year (g/kg);
• $r-$heat of condensation of water vapor (J/kg).

$$X_{\mathrm{N},i,j}=0.622·\frac{p_{\mathrm{s},i,j}}{p-p_{\mathrm{s},i,j}}·1000$$

(13)

where:

• $p_{\mathrm{s},i,j}$—water vapor saturation pressure calculated at t_i,j with Equation (14) from [54] (Pa);
• $p$—actual pressure of air (Pa).

$$p_{\mathrm{s},i,j}=610.7·{10}^{\frac{t_{i,j}}{a_0+a_1{t}_{i,j}+a_2{t}_{i,j}^2}}$$

(14)

where:

• a₀ = 31.6885;
• a₁ = 0.130986;
• a₂ = 2.52493·10⁻⁵.

2.2.2. Soil Temperature at a Given Depth throughout the Year

The calculations used a formula that allowed for calculating the soil temperature at a given depth on a given day of the year and took into account the thermophysical parameters of the ground and climatic data—Equation (15). This formula was suitable for the present calculations because it was calibrated on the basis of the results of experimental studies presented in [55,56] that were carried out in the locality for which the calculations were performed (Poznan, Poland, Central Europe, temperate climate).

$$\begin{gathered} t_{g,k}=\left(T_m+\Delta T_m\right)-1.07·k_v·A_s·\exp \left(-0.0003155·H·a_g^{-0.5}\right) \\ \cos \left[\frac{2\mathsf{\pi }}{365}·\left(k-T_o-0.01834·H·a_g^{-0.5}\right)\right] \end{gathered}$$

(15)

where:

• k—number of the day in the year, range: 1–365;
• H—depth of the exchanger placement, assumed as 2 m;
• a_g—thermal diffusivity of the ground (m²/s);
• k_v—vegetation coefficient, assumed 0.85;
• A_s—annual amplitude of the average monthly temperature of the dry thermometer, assumed for Poznan as 10.1 K;
• T_m—average annual temperature of the outside air, assumed for Poznan as 8.26 °C;
• ΔT_m—difference between the temperature, T_m, and the average temperature of the ground at depth H = 10 m, assumed for Poznan as 2.24 K;
• T_o—phase shift, assumed for Poznan as 21 days.

Thermal diffusivity of the ground was assumed as a_g = 4.40 · 10⁻⁷ m²/s (for dry sand, [44]), which resulted from the following thermal parameters:

• density: ρ_g = 1600 kg/m³;
• specific heat: c_g = 753 J/(kgK);
• thermal conductivity: λ_g = 0.53 W/(mK).

Figure 5 presents a calculation of ground temperature at a depth of 2 m below the surface that was taken into consideration during calculation in every single day. External air temperature was taken into account with 1 h step and is also presented in the figure.

2.2.3. Electric Energy and Primary Energy for Driving the Fan

Electricity consumption by the fan supporting the operation of the EAHE was calculated for each hour in which the ventilation system cooperated with the EAHE. The following formula was used (results given in kWh with the period of 1 h taken into account):

$$E_{\mathrm{fan}}={\sum }_{j=1}^{8760}\frac{V_j·\Delta p_j}{1000·{\eta }_{\mathrm{fan}}}$$

(16)

where:

• $V_j$—total airflow through the EAHE in j hour during the year (m³/s);
• $\Delta p_j$—pressure drop at EAHE in j hour during the year (Pa);
• ${\eta }_{\mathrm{fan}}$—total efficiency of the fan (−).

Primary energy consumption to drive the fan was calculated assuming that the fan was driven by electricity generated and distributed in such a way that the input coefficient w was equal to 3:

$$PE=E_{\mathrm{fan}}·w$$

(17)

3. Results

3.1. Experimental Flow Characteristics of Multipipe EAHEs

To determine the flow characteristics of multipipe EAHEs, tests were carried out for the measurements described in Section 2.1. The value of an EAHE’s total pressure losses as a function of the volume flow of the air was determined. The measurements were repeated for many different values of airflows typical for these systems when used in practice, as indicated by the information contained, for example, in [40,41,42,43]. In this way, the flow characteristics of exchangers built of 3, 5 and 7 parallel branches were obtained. Figure 6 shows the measurement results in the form of the relation Δp = f(V).

Figure 7 presents the obtained flow characteristics for exchangers built of 3, 5 and 7 parallel branches, using both axes of the graph on a logarithmic scale. In this way, the measurement results appear in a straight line. The results showed that regardless of the number of branches, the pressure losses were nearly identical for the same volumetric airflow. This was an important observation that allowed for simplifying the considerations presented in this paper. Specifically, the results could be averaged and used for exchangers with different numbers of branches, which was done later in the work.

Using the Reynolds number instead of the volumetric airflow makes the results more versatile. The volumetric air flow through the 1:4 scale model of the heat exchanger was four times smaller than that through the full-scale exchanger. It is worth noting that the pressure losses for a given Reynolds number in full-scale exchangers would be approximately 16 times smaller than those measured in the exchanger models in the 1:4 scale because of the quadratic relationship between flow velocity and pressure losses. Figure 8 shows the test results in a dimensionless form. The volumetric flow of the air was replaced, similarly as in the previous collective diagram, with the value of the Reynolds number and the pressure losses in the form of the pressure loss coefficient, calculated as total pressure losses divided by the dynamic pressure in the exchanger’s manifold:

$$k=\frac{\Delta p}{\frac{\rho ·w_{\mathrm{main}}^2}{2}}$$

(18)

Figure 8 shows that the value of the k-factor for a given number of branches changed slightly in a wide range of Reynolds numbers corresponding to a typical range of airflows in earth-to-air heat exchangers.

For this reason, the measurement results were averaged in

Table 2. Values of total pressure losses coefficient k_m.

3 Pipes	5 Pipes	7 Pipes
1.77	1.83	1.87
Average for 3, 5 and 7 pipes: km = 1.82

. The average value of the coefficient k for an exchanger with i branches was calculated as:

$$k_{m,i}=\frac{k_{max,i}+k_{min,i}}{2}$$

(19)

Then, the average value for all analyzed exchangers was calculated from the following formula:

$$k_m=\frac{k_{m,3}+k_{m,5}+k_{m,7}}{3}$$

(20)

This procedure was established for the needs of engineering analysis, because the percentage difference between the extreme values and the average in this case was only 2.4%. Therefore, the use of the average value of the k factor for exchangers with different numbers of branches did not cause a significant loss of accuracy.

3.2. Total Pressure Losses in Single-Pipe and Multipipe EAHEs

To compare the pressure losses of single-pipe and multipipe earth-to-air heat exchangers, it was assumed that these exchangers would have the same heat exchange surface. Assuming the same pipe diameter, i.e., PP DN200, this meant that a single-pipe exchanger was assumed to be three, five or seven times longer than a multipipe exchanger made of three, five or seven branches, respectively. It was assumed that the pressure losses in the single-pipe heat exchanger would be calculated as a straight section with a fully developed velocity profile. The presence of elbows causing a change in the direction of pipe arrangement would be taken into account by assuming two 90-degree elbows for every 50 m exchanger. Therefore, in the case of an exchanger shorter than 50 m, it was assumed that a change in direction would not be necessary, and in the case of longer exchangers, local pressure losses due to the change in direction of the pipes were added. To summarize the assumptions:

• pipe diameters in single and multipipe EAHE were assumed to be the same and equal to PP DN200 (internal diameter d = 0.1844 m);
• the length of a one-pipe heat exchanger used for calculations resulted from the assumption of the same heat exchange surface between the compared exchangers; i.e., if, for example, a single-pipe exchanger was compared with a five-pipe exchanger with a length for each branch L = 150d, the length of the one-pipe heat exchanger used for calculations was 5 × 150d;
• in a single-pipe heat exchanger, additional pressure losses were assumed when changing the direction of the pipe every 50 m in order to take into account the limited ground surface for the heat exchanger’s construction.

To calculate the total pressure losses in single-pipe structures of EAHEs, the Blasius formulafor calculating the friction pressure losses for turbulent airflow was used (this formula does not take into account additional pressure losses at the entrance sector):

$$\Delta p=\left(\lambda ·\frac{n·L}{d}+\sum \zeta \right)·\frac{\rho ·w^2}{2}$$

(21)

where:

• λ—friction factor calculated from the Blasius formula = 0.3164/Re^0.25, (−);
• n—number of branches of equivalent multipipe EAHE (3, 5 or 7);
• L—length of single branch-pipe of the equivalent multipipe EAHE (m);
• d—internal diameter of pipe (m);
• $\zeta$—local pressure loss coefficient, assumed as 1 for a single elbow, taken from the handbook for engineering application [57], (−);
• $\rho$—air density (kg/m³);
• w—air velocity in pipe (m/s).

To calculate the total pressure losses in multipipe structures of EAHEs, the experimental data presented in Section 3.1 were used. To calculate the pressure losses of exchangers of dimensionless length identical as in the experimental tests, the following formula was used:

$$\Delta p=k_m·\frac{\rho ·w^2}{2}$$

(22)

where:

• k_m—average coefficient of total pressure losses for exchangers constructed of 3, 5 and 7 pipes (−);
• w—air velocity in the manifold (in the main pipe, before division of air streams between branches of the exchanger) (m/s).

For multipipe exchangers with longer branches than those used in the experimental tests, fully developed flow was assumed for the additional length of pipes, and the pressure losses were equal to the average friction pressure losses at the additional sector of a dimensionless length = L/d − 76 (the length of the branches in the experimental tests was equal to 76d). Assuming this simplification, the following formula was used:

$$\Delta p=k_m·\frac{\rho ·w^2}{2}+\lambda ·\left(L/d-76\right)·\frac{\rho ·w_m^2}{2}$$

(23)

where:

• w—air velocity in the manifold (in the main pipe, before separation of air streams between branches of the exchanger) (m/s);
• w_m—average air velocity in a single branch-pipe, assuming the ideal distribution of air among all pipes: $w_m=w/n$, where n is a number of parallel branch-pipes (m/s);
• λ—friction factor in a single branch-pipe calculated for w_m; for laminar airflow, λ = 64/Re; for turbulent air flow, λ was calculated as 0.3164/Re^0.25.

The results of the pressure loss calculations are presented in

Table 3. Comparison of total pressure losses given in Pa in different structures of single-pipe and multipipe EAHEs.

Type of EAHE:		Single-Pipe (Pipes in Series)			Multipipe (Parallel Pipes)
V = 200 m3/h, Re = 26,597
Number of pipes:		3	5	7	3	5	7
Length of a single pipe:	76d	15.0	30.4	40.4	4.8	4.8	4.8
	150d	35.0	60.1	85.2	5.6	5.1	5.0
	300d	75.3	125.5	175.7	7.0	5.7	5.3
V = 600 m3/h, Re = 79,790
Number of pipes:		3	5	7	3	5	7
Length of a single pipe:	76d	102.8	219.3	287.8	43.6	43.6	43.6
	150d	250.8	434.0	617.2	48.5	45.6	44.7
	300d	549.5	915.9	1282.3	58.4	49.6	46.9

for the air streams corresponding to the Reynolds number that occurred during the experimental tests (i.e., from approximately 20,000 to approximately 80,000) and for three exchanger tube lengths (76d, 150d and 300d).

3.3. Energy Consuption for Fan Operation during a Year

Figure 9 and Figure 10 show the results of calculations of additional electrical energy needed in ventilation system for driving the fan to overcome the total pressure losses of earth-to-air heat exchanger. The calculations were done for the two lengths: L = 76d and L = 300d as representative, boundary values (L = 150d was skipped in this and further calculations). The main assumptions included:

• time of operation: one year;
• nominal (maximum) airflow: 600 m³/h;
• air flowrate changes during the single day in two variants: 100% of the time at maximum airflow or scheduled system usage. Schedule is presented in

  Table 4. Daytime ventilation airflow schedule assumed during calculations.

  Hour	Airflow	Hour	Airflow
  0	40%	12	100%
  1	40%	13	100%
  2	40%	14	100%
  3	40%	15	100%
  4	40%	16	100%
  5	40%	17	70%
  6	70%	18	70%
  7	70%	19	40%
  8	100%	20	40%
  9	100%	21	40%
  10	100%	22	40%
  11	100%	23	40%

  (the schedule is representative of a building wherein users are fully staffed from 8 a.m. to 4 p.m. and performance is reduced outside of these hours);
• days of operation during the year: 250 (assuming periods in which the EAHE is not used);
• energy consumption for fan operation calculated for a single day and added day by day, taking into consideration the number of days on which the EAHE is used;
• total efficiency of the fan: 39%.

3.4. Full-Year Heating and Cooling Gains and Energy Cost of Harvesting Geothermal Energy

The calculations were carried out as described in Section 2.2 and took into account a variable ventilation air stream, as opposed to the standard procedures used to calculate the energy performance of a building [58,59,60]. Only those hours of the year were taken into account when the ground temperature was at least 2 K higher than the outside air temperature in winter, and only those summer hours when the outside air temperature was higher than 20 °C. These restrictions were introduced to make the calculated results more realistic, thus taking into account the fact that earth-to-air heat exchangers do not operate all year round. Particularly in transition periods, when the building needs to be heated and the outside air temperature is higher than the ground temperature, using an EAHE results in energy losses, and so EAHEs should not be used. In the following analysis, the variability of the ventilation airflow was assumed according to the schedule presented in Table 4.

In [43,44,45,46,47,48], which focused on multipipe EAHEs, the results of the research revealed uneven air distribution among individual branches. The results of CFD simulations presented in [41,61] confirmed this observation. The results presented in [61] confirmed reduction in the heat efficiency of the exchanger as a result of the uneven distribution of air among the branches, which had been previously reported in [43,44]. The results of both a CFD simulation and experimental tests showed that the air flows in the individual branches were not equal. In [43,44], a quantitative assessment of the impact of this phenomenon on annual heating and cooling consumption through the exchanger was conducted. It was shown that the actual amount of heating and cooling could be significantly lower than that which would have been obtained if the air distribution had been perfectly uniform. For the present study, calculations were made assuming perfectly even air distribution, and the results were then corrected (reduced).

Table 5. Assumed percentage reduction in the thermal efficiency of a multipipe heat exchanger due to uneven air distribution among the branches.

Number of Pipes:		3	5	7
Length of a single pipe:	76d	10%	15%	25%
	300d	5%	10%	20%

summarizes the applied percentages of heating and cooling yield reduction in the annual heat exchanger operation cycle depending on the number and length of the branches of multipipe structures. These assumptions resulted directly from the results of the analysis presented in [43,44]. The calculations presented below were prepared for the climatic data of Poznan (Poland, Central Europe, temperate climate).

The results of the annual energy consumption for the fan drive differed from the results presented in Section 3.3, in which only the pressure losses were compared with simplified assumptions of EAHE operation during the year. Only the hours in which the EAHE actually carries out heating or cooling from the ground were included in this analysis. Moreover, the calculations presented in this chapter were more accurate because they took into account the actual thermophysical parameters of air in every hour of usage during the year. The results of the full-year energy calculation, including the benefits (heating and cooling) and costs (electric energy and primary energy usage PE) related to usage of single-pipe and multipipe earth-to-air heat exchangers, are presented in

Table 6. Results of full-year energy calculation: benefits (heating and cooling) and costs (electric energy and primary energy usage PE) related to usage of single- and multipipe EAHEs, V = 600 m³/h.

Type of EAHE:		Single-Pipe (Pipes in Series)			Multipipe (Parallel Pipes)
Number of Pipes:		3	5	7	3	5	7
EAHE length:		3 × 76d	5 × 76d	7 × 76d	3 × 76d	5 × 76d	7 × 76d
Benefits	Heat (kWh/year)	2179	3059	3668	1654	2027	2066
	Cool (kWh/year)	569	851	1085	436	557	584
Cost	Electric energy (kWh/year)	112	238	313	47	47	47
	PE for driving fan (kWh/year)	336	714	939	141	141	141
EAHE length:		3 × 300d	5 × 300d	7 × 300d	3 × 300d	5 × 300d	7 × 300d
Benefits	Heat (kWh/year)	4511	5037	5207	3972	4221	3937
	Cool (kWh/year)	1504	1858	1991	1272	1469	1430
Cost	Electric energy (kWh/year)	597	994	1391	63	53	50
	PE for driving fan (kWh/year)	1791	2982	4173	189	159	150

.

The results presented in Table 6 showed that using single-pipe structures of EAHEs with the same length of pipes as the sum of the lengths of the pipes in multipipe structures resulted in higher heating and cooling gains during the year. At the same time, the consumption of electric energy was several times greater. From the point of view of primary energy consumption, these differences were even more to the detriment of single-pipe structures, because the analysis assumed that electricity was produced mainly from coal, and the value of the primary nonrenewable energy input factor was 3.

It may be puzzling why the cost of operation of three-, five- or seven-branch exchangers was the same for short-branch exchangers (L = 76d) and different in other cases. This phenomenon resulted from the method of calculating pressure losses adopted in this paper. Experimental tests were carried out for exchangers with short branches (L = 76d) and averaged for exchangers made of three, five and seven branches. To calculate the cost of operation of these exchangers, the same averaged value of the pressure loss coefficient was used. In the case of exchangers with longer branches, it was assumed that the value of pressure losses in an additional straight pipe section was added to the measured value. These losses depend on the number of pipes. For this reason, they were larger in the case of three-pipe exchangers and smaller in the case of seven-pipe heat exchangers, because the same amount of air flowing through the exchanger was distributed over a greater number of branches, and therefore, the average flow velocity in these branches was lower.

Further calculations were carried out to deepen the analysis. This time, by trial and error, an equivalent length of single-pipe EAHE was explored, which would replace a given multipipe exchanger thermally. The equivalent length of the single-pipe heat exchanger was sought such that the annual heat yield was as close as possible to the analogous heat yield of a given multipipe exchanger (less importance was attached to the amount of cold because of the fact that an exchanger located in a temperate climate zone was analyzed—Poland, in Central Europe, where heating needs dominate and air conditioning is seen as a luxury, not a standard). The calculation results are presented in

Table 7. Equivalent length of DN200 single-pipe EAHE replacing a given multipipe exchanger in terms of heat; the results of calculations of annual electricity consumption and primary energy consumption for fan drive, V = 600 m³/h.

Type of EAHE:		Single-Pipe (Pipes in Series)			Multipipe (Parallel Pipes)
EAHE length:		1 × 29 m DN200	1 × 38 m DN200	1 × 39 m DN200	3 × 14 m DN200	5 × 14 m DN200	7 × 14 m DN200
Equivalent multipipe EAHE		3 × 14 m DN200	5 × 14 m DN200	7 × 14 m DN200
Benefits	Heat (kWh/year)	1643	2064	2064	1654	2027	2066
	Cool (kWh/year)	416	535	535	436	557	584
Cost	Electric energy (kWh/year)	78	104	104	47	47	47
	PE for driving fan (kWh/year)	234	312	312	141	141	141
EAHE length:		1 × 117 m DN200	1 × 136 m DN200	1 × 114.5 m DN200	3 × 55.4 m DN200	5 × 55.4 m DN200	7 × 55.4 m DN200
Equivalent multipipe EAHE:		3 × 55.4 m DN200	5 × 55.4 m DN200	7 × 55.4 m DN200
Benefits	Heat (kWh/year)	3973	4218	3937	3972	4221	3937
	Cool (kWh/year)	1221	1342	1204	1272	1469	1430
Cost	Electric energy (kWh/year)	414	465	408	63	53	50
	PE for driving fan (kWh/year)	1242	1395	1224	189	159	150

.

In the above analysis, it was assumed each time that the diameter of the single-pipe exchanger was the same as the diameter of the multipipe branches. Further calculations were performed assuming larger diameters of pipes for the single-pipe heat exchanger: DN250 and DN315.

Table 8. Equivalent length of DN250 single-pipe EAHE replacing a given multipipe exchanger in terms of heat; the results of calculations of annual electricity consumption and primary energy consumption for fan drive, V = 600 m³/h.

Type of EAHE:		Single-Pipe (Pipes in Series)			Multipipe (Parallel Pipes)
EAHE length:		1 × 26.5 m DN250	1 × 35 m DN250	1 × 35.5 m DN250	3 × 14 m DN200	5 × 14 m DN200	7 × 14 m DN200
Equivalent multipipe EAHE:		3 × 14 m DN200	5 × 14 m DN200	7 × 14 m DN200
Benefits	Heat (kWh/year)	1641	2032	2054	1654	2027	2066
	Cool (kWh/year)	420	531	538	436	557	584
Cost	Electric energy (kWh/year)	24	31	32	47	47	47
	PE for driving fan (kWh/year)	72	93	96	141	141	141
EAHE length:		1 × 107 m DN250	1 × 125 m DN250	1 × 105 m DN250	3 × 54.4 m DN200	5 × 54.4 m DN200	7 × 54.4 m DN200
Equivalent multipipe EAHE:		3 × 54.4 m DN200	5 × 54.4 m DN200	7 × 54.4 m DN200
Benefits	Heat (kWh/year)	3975	4229	3942	3972	4221	3937
	Cool (kWh/year)	1228	1353	1213	1272	1469	1430
Cost	Electric energy (kWh/year)	136	152	134	63	53	50
	PE for driving fan (kWh/year)	408	456	402	189	159	150

and

Table 9. Equivalent length of DN315 single-pipe EAHE replacing a given multipipe exchanger in terms of heat; the results of calculations of annual electricity consumption and primary energy consumption for fan drive, V = 600 m³/h.

Type of EAHE:		Single-Pipe (Pipes in Series)			Multipipe (Parallel Pipes)
EAHE Length:		1 × 24.5 m DN315	1 × 32 m DN315	1 × 33 m DN315	3 × 14 m DN200	5 × 14 m DN200	7 × 14 m DN200
Equivalent multipipe EAHE:		3 × 14 m DN200	5 × 14 m DN200	7 × 14 m DN200
Benefits	Heat (kWh/year)	1645	2019	2065	1654	2027	2066
	Cool (kWh/year)	426	534	547	436	557	584
Cost	Electric energy (kWh/year)	7	10	10	47	47	47
	PE for driving fan (kWh/year)	21	30	30	141	141	141
EAHE length:		1 × 98.5 m DN315	1 × 115 m DN315	1 × 96.5 m DN315	3 × 54.4 m DN200	5 × 54.4 m DN200	7 × 54.4 m DN200
Equivalent multipipe EAHE:		3 × 54.4 m DN200	5 × 54.4 m DN200	7 × 54.4 m DN200
Benefits	Heat (kWh/year)	3973	4228	3938	3972	4221	3937
	Cool (kWh/year)	1235	1360	1218	1272	1469	1430
Cost	Electric energy (kWh/year)	37	50	37	63	53	50
	PE for driving fan (kWh/year)	111	150	111	189	159	150

present the results of calculations of the equivalent lengths of single-pipe exchangers with pipe diameters of DN250 or DN315 replacing a given multipipe exchanger with a diameter of DN200 for the branch-pipes. Also provided are the results of calculations of the annual electricity consumption and primary energy used to drive the fan.

The results presented in Table 8 and Table 9 may be puzzling: why was the length of the equivalent single-pipe exchanger shorter when it replaced the seven-pipe than when it replaced the five-pipe heat exchanger? This was the case with multipipe structures with long branches, L = 300 × DN200. The reason is as follows: in the case of a greater number of branches in a multipipe exchanger, when the diameter of the manifolds is equal to the diameter of the branches (DN200), the airflow is distributed unevenly among the branches. This causes a significant reduction in thermal efficiency, which in this calculation was taken into account by the correction factor, the value of which is presented in Table 5. In other words, the greater nonuniformity of the air distribution caused the heat gains of the seven-pipe exchanger to be lower than those of the five-pipe exchanger for the same airflow. Then, for this lower value of heat gains, the equivalent length of the single-pipe exchanger was calculated and was obviously shorter.

A comparison of the full-year energy consumption by fans for the operation of EAHEs is presented in Figure 11 and Figure 12.

The above results were obtained assuming the maximum ventilation airflow of 600 m³/h. This is a relatively small value, which, assuming the hygienic standard of the amount of air per one person at the level of approximately 30 m³/h, is sufficient for the ventilation of rooms used by 20 people. The results of the above analysis showed that in terms of thermal efficiency, single-pipe exchangers could replace multipipe exchangers, but they caused higher pressure losses and thus higher energy and primary energy consumption for the fan drive. However, by using larger pipe diameters, correspondingly lower pressure losses can be obtained. To check whether the same conclusions were valid for larger air flows, analogous calculations of energy consumption were carried out for exchangers that could provide fresh air for a building used by 50 people, i.e., for a nominal air stream of 1500 m³/h. The results are presented in Figure 13 and Figure 14, in which energy demand for fan operation during a year is presented. The equivalent lengths of the single-pipe heat exchangers that replace multipipe heat exchangers with given numbers of branches in the context of thermal performance (heat gained during the year) are also shown in Figure 13 and Figure 14.

4. Discussion

The present study compared single-pipe and multipipe earth-to-air heat exchangers. A comparison was made in terms of the annual amount of heating and cooling obtained from the ground, as well as in terms of energy and primary energy consumption to drive the fan forcing the air flow through the exchanger.

The calculations were performed using a simple mathematical model describing the heat exchange between the air flowing in the exchanger pipes and the ground in steady state. The effect of EAHE operation on the ground temperature distribution was neglected. The thermophysical parameters of air were calculated assuming the design temperature as the average of the outside air temperature and the ground temperature. As a result, it was not necessary to use iterative calculations to obtain the result. The simplifications seem to be justified and should not affect the conclusions drawn on the basis of the calculation results. The accuracy of modeling the thermal efficiency appear to be sufficient for the purposes of the analysis in the annual work cycle of the exchanger, in which the assumption of the air flow schedule (building use schedule) during a single day may be more important for the results. Moreover, the results of experimental studies on pressure losses were used to calculate the pressure losses in multipipe exchangers. This procedure significantly and positively influenced the credibility of the obtained results; as shown in previous analysis, computational determination of pressure loss value is not easy because of the uneven distribution of air between the individual branches of the exchangers. This was confirmed by the results of studies carried out by the authors, e.g., [45,46,47,48], but also by results obtained independently by a research group from China [61]. Another circumstance that increased the credibility of the obtained results was taking into account the correction of the exchanger’s efficiency due to the aforementioned uneven air distribution in multipipe exchangers, based on the results of previous works [43,44]. However, it should be remembered that the long-term operation of the system has a significant impact on the effectiveness of an EAHE. This is emphasized by the authors of works on modeling of transient heat transfer, e.g., [30,31,32,33,34]. Nevertheless, according to the authors, taking into account the influence of the exchanger on the ground temperature field in the transient calculations would not significantly affect the conclusions drawn from the present analysis. This is because both single-pipe and multipipe exchangers would operate in the same soil environment when compared.

The results of the calculations did not conclusively decide whether it is better to use single-pipe and multipipe heat exchangers or in what situations. However, they showed that in the analyzed cases, multipipe heat exchangers can be replaced with one-pipe heat exchangers, but with larger air flows, their diameter should be appropriately larger. This is an important observation, since from a technical point of view, it is much easier to make a one-pipe heat exchanger. However, it should be remembered that in multipipe exchangers it is also possible to use larger diameters. This is true not only for the branches themselves, but also for the collectors, which significantly affects their flow characteristics (both the value of pressure loss and the uniformity of air distribution) [45]. It should also be remembered that the best results when it comes to making decisions bring the use of multicriteria decision support methods, where appropriate weighting is assigned to various criteria and preferences of the user/investor. Consideration should be given to economic aspects, environmental aspects (the analysis of annual electricity consumption presented in this article, but also the analysis of material consumption—plastics for the construction of the exchanger) and the available technical limitations (i.e., available ground surface). It is a complex problem that requires a detailed approach and the development of a separate methodology/design procedure. This paper did not undertake this work, which can be treated as a challenge for the future work. It is also worth emphasizing that this study compared the structures of single- and multipipe heat exchangers in terms of energy. The structures adopted for comparison were not optimal from the point of view of the adopted objective functions, which were not defined in this work. In the literature, one can find many works that deal with the topic of the optimal selection of heat exchanger geometry in terms of heat exchange, which, in a multicriteria analysis, could become a starting point for further comparisons.

The results presented in this study indicate the need to take into account many aspects related to the construction of earth-to-air heat exchangers in order to choose the best or optimal geometry. It was shown that it is impossible to predict in advance which type of exchanger is more energy-efficient: single-pipe or multipipe. Therefore, the decision should always be supported by calculations and an in-depth analysis of the results. The results of this analysis showed that, e.g., in the case of a ventilation airflow of 600 m³/h, a seven-pipe EAHE with a single branch length of 14 m DN200 (a total of 7 × 14 = 98 m of DN200 pipe) could be replaced in terms of heat exchange with a single-pipe heat exchanger with a diameter of DN250 and a length of 35.5 m (35.5 m of DN250 pipe), with the annual electricity consumption lower by approximately 35%. In the case of a ventilation airflow of 1500 m³/h, a seven-pipe EAHE with a single branch length of 54.4 m DN200 (total 7 × 55.4 = 388 m of DN200 pipe) could be replaced in terms of heat exchanged with a single-pipe heat exchanger with a diameter of DN315 and a length of 139 m (139 m of DN315 pipe), with almost the same annual electricity consumption. Of course, the results would be different if larger diameters of branches and/or collectors were also used in the multipipe exchanger. For this reason, the results of this work represent a case study for a limited number of variants and may inspire a more complex earth-to-air heat exchanger design methodology taking into account thermal, energy, environmental, economic and technical aspects as well as user preferences and their importance in the hierarchy.

It may be interesting to compare the costs of installing single- and multipipe EAHEs. Assuming a situation in which the sum of the pipe lengths of both types of exchangers is the same, the costs should be similar, because a comparable amount of material is used for construction and a similar number of earthworks are required. In the event that we would like to compare a single-pipe heat exchanger with a thermally equivalent branch length with a multipipe heat exchanger, which provide the same annual heating gains, it can be expected that the costs of a shorter heat exchanger would not be proportionally lower than the cost of making an exchanger with a greater total length of the branches. This is because some fixed costs, such as the arrival of an excavator, transport of materials or the connection of the exchanger to the ventilation system, are independent of the length of the pipes used, and therefore, a simple cost ratio cannot be used. For this reason, no attempt was made to conduct an economic analysis in this study. Economic analysis is even more difficult because it depends on the specific situation of a given investment, e.g., whether the excavation has already been made, because there was a need to level the ground anyway; whether it must be paid for separately; or whether the machines would be on the construction site anyway or they would have to come specially. This paper is a voice in the discussion on earth-to-air heat exchangers that indicates that the choice between a single- or multipipe structure should be analyzed each time, as it was verified that it is not possible to provide a universal answer in energy terms or in terms of economy. Moreover, the energy-only or economic-only choice is now being abandoned. Preference is given to using multicriteria decision support methods based on the investor’s profile that assign appropriate weights to many of the possible criteria. Such an assessment should be a separate task and from the perspective of this paper can be seen as an interesting idea for the future work.

5. Conclusions

The findings from this study can be summarized as follows:

• multipipe EAHEs could be replaced by single-pipe structures of with greater diameter with similar energy performance and electricity consumption during the year;
• for airflow of 600 m³/h, a seven-pipe EAHE of L = 14 m DN200 (a total of 7 × 14 = 98 m of DN200 pipe) could be replaced with a single-pipe DN250 of L = 35.5 m (35.5 m of DN250 pipe), with the annual electricity consumption lower by approximately 35%;
• for airflow of 1500 m³/h, a seven-pipe EAHE of L = 54.4 m DN200 (total 7 × 55.4 = 388 m of DN200 pipe) could be replaced with a single-pipe DN315 of L = 139 m (139 m of DN315 pipe), with almost the same annual electricity consumption;
• taking into account other designs of multipipe EAHEs (larger diameters of branches and/or manifolds) would change the heat yield and electricity consumption in favor of multipipe structures compared to single-pipe structures. However, such heat exchangers were not tested in this study and therefore were not analyzed in the calculations, which is an inspiration for future work born on the basis of the results of this article.

The results showed that there is no unambiguous and universal answer to the question of whether to use single-pipe or multipipe earth-to-air heat exchangers and that the decision should be based on a comparison of calculations taking into account thermal, energy, environmental, economic and technical aspects as well as user preferences and their importance in the hierarchy.