Numerical Assessment of Earth to Air Heat Exchanger with Variable Humidity Conditions in Greenhouses

Article Numerical Assessment of Earth to Air Heat Exchanger with Variable Humidity Conditions in Greenhouses

Di Qi *, Chuangyao Zhao, Shixiong Li, Ran Chen and Angui Li

School of Building Services Science and Engineering, Xi’an University of Architecture and Technology, Xi’an 710055, China; [email protected] (C.Z.); [email protected] (S.L.); [email protected] (R.C.); [email protected] (A.L.) * Correspondence: [email protected]

Abstract: Earth to air heat exchangers are widely utilized to cool or heat passive buildings for energy savings. They often need to deal with high humidity air conditions, especially in the greenhouse due to plant transpiration, and the condensation phenomenon is frequently observed during the cooling process. To evaluate the effect of humidity and condensation on thermal performance, a three dimensional computational fluid dynamic (3D-CFD) model was developed. The distribution of relative humidity in each pipe was investigated, and the impact of inlet air relative humidity on the integrated performance of the earth to air heat exchanger was discussed. The effects of inlet air temperature and volume flow rate were also analyzed. Moreover, the influence of the heat exchanger configurations on the performance of the air condensation was researched. The results indicated that condensation had few effects on the airflow distribution uniformity of the earth to air heat exchanger,

while it acted observably on the thermal performance. In addition, humid air in a small diameter pipe tended to condense more easily. Humidity and condensation should be taken into consideration

Citation: Qi, D.; Zhao, C.; Li, S.; for the design of earth to air heat exchangers in greenhouses during engineering applications. Chen, R.; Li, A. Numerical Assessment of Earth to Air Heat Keywords: earth to air heat exchanger (EAHE); relative humidity (RH); thermal performance; Exchanger with Variable Humidity condensation; uniformity Conditions in Greenhouses. Energies 2021, 14, 1368. https://doi.org/ 10.3390/en14051368 1. Introduction Academic Editor: John The energy crisis and global warming have been the main concern nowadays all over Kaiser Calautit the world. It is worth mentioning that buildings’ energy consumption nearly takes up 40% of total global energy consumption. Additionally, 60% of the total energy consumption of Received: 20 January 2021 buildings is the energy consumption of heating, ventilation and air conditioning systems [1]. Accepted: 26 February 2021 Published: 3 March 2021 For energy savings, many approaches including system design and operation control optimization [2] for vapor compression systems were investigated, and the utilization of

Publisher’s Note: MDPI stays neutral geothermal energy was also an effective method. with regard to jurisdictional claims in The development and utilization of shallow geothermal energy technology [3] are published maps and institutional affil- relatively convenient and cost-effective. Meanwhile, the ground temperature was usually iations. stable, thus the ground can be used as a heat sink or source. The earth to air heat exchanger (EAHE) is buried under the ground. The air flows in the buried pipes through the inlet, which could absorb heat in winter and release heat in summer. The heated or cooled air from the outlet flows to the buildings and greenhouse to maintain proper indoor temperature. Therefore, it is widely utilized in passive heating and cooling of buildings Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. and greenhouse to reduce power consumption. Dabaieh and Serageldin [4] used the EAHE · −2· −1 · −2· −1 This article is an open access article to reduce heating/cooling demands to 7.9 kWh m annum and 2.8 kWh m annum distributed under the terms and in a passive house. Congedo et al. [5] used EAHE to pre-heat or pre-cool the air in the conditions of the Creative Commons Air-Source Heat Pump (ASHP). They found that the EAHE could improve the system ◦ Attribution (CC BY) license (https:// performance by 10% under 35 C water condition. Bonuso et al. [6] applied horizontal creativecommons.org/licenses/by/ EAHE to cool the indoor air in a greenhouse. They found that the EAHE system could ◦ 4.0/). decrease the temperature by 5 C in summer.

Energies 2021, 14, 1368. https://doi.org/10.3390/en14051368 https://www.mdpi.com/journal/energies Energies 2021, 14, 1368 2 of 18

Although EAHE could reduce power consumption of the heating/cooling, its performance also needs to be enhanced for a better application. Many researchers focused on the parameters optimization of EAHE. Gomat et al. [7] investigated the thermal balance of EAHE via a mathematical model and gave the prediction of the daily and annual air temperature variation. Lekhal et al. [8] optimized the parameters of the EAHEs in the different climatic regions, and the results showed that there are no standard criteria for all climatic regions. Zajch and Gough [9] investigated the effect of the ground surface and air temperature on the EAHE performance and suggested that a higher ground surface temperature could increase the heating potential in Canada. After that, they [10] established linear models using the seasonal air and soil temperature and found that the change of the inlet air temperature of daytime had many contributions to the cooling performance in the summer. Agostino et al. [11,12] investigated the effect of diameter and length on heat transfer performance of EAHE, and they recommended that the optimal tube length was 80 to 100 m. Rosa et al. [13] concluded the influence of the parameters on the overall EAHE heat transfer characterize, which demonstrated that the pipe spacing could be decreased by 0.5 m. Chiesa and Zajch [14] investigated the relationship between climate and EAHE system performance and proposed an evaluation factor of the EHAE possible cooling capacity. Overall, most researchers focused on the sensible heat transfer in EAHE. However, air condensation could occur in the EAHE when the air’s relative humidity (RH) exceeds 100%. In particular, the air in the greenhouse is more easily condensed due to the plant transpiration. Li et al. [15] optimized the thermal environment in the greenhouse based on the computational fluid dynamic (CFD) method, but they ignored the latent heat transfer and water vapor exchanges. Guo et al. [16] developed a 3D-CFD model to investigate the cooling performance of the water-sprinkling roof in the greenhouse. The multiphase flow model was selected. Ghoulem et al. [17] used a passive downdraught evaporative cooling windcatcher in the greenhouse, and relative humidity was considered in the CFD model. Sakhi et al. [18] studied the efficiency of an EAHE without an external device in arid environments and found that EAHE technology was beneficial to enhance building hygrometry. Wei et al. [19] conducted full-scale experiments to investigate the effect of structure parameters on EAHE cooling capacity. The results showed that latent heat transfer acted significantly on EAHE cooling capacity when the earth to air heat exchanger operated under high temperature and humidity conditions. Cucumo et al. [20] developed a model to evaluate the dynamic EAHE performance, and the potential condensation phenomenon was also studied and analyzed. Chardome and Feldheim [21] developed 2D/3D numerical model to study the heat transfer and condensation in an EAHE, and the model could be used to quantify the condensate in one year’s operation. Niu et al. [22] developed a mathematical model to investigate the temperature variation along the pipe and declared that it was less affected by inlet RH. Gan [23] proposed an evaporation and condensation computer program to predict the thermal performance of EAHE. The results presented that the direct heat and moisture interaction among EAHE had a significant influence on heat transfer capacity. Gao et al. [24,25] proposed a new condensation model to simulate the cooling and dehumidification process of buried tunnels, which could obtain the unsaturated condensation process. Moreover, they also found that the air humidity acted significantly on the thermo-hygrometric performance of EAHE system. Estrada et al. [26] proposed a model to deal with latent and sensible heat transfer between soil and pipes. The results showed that the latent heat transfer played a negative effect on EAHE. Liu et al. [27] established a 2D simulation model for EAHE integrated with greenhouse, which considered heat and mass transfer in EAHE. It was found that this model could obtain more accurate thermal performance of soil than the heat conduction model. EAHE often needs to deal with high humidity air conditions, especially in the greenhouse. Greco and Masselli [28] found that EAHE could generate water condensation along the tube. Mongkon et al. [29] evaluated the cooling performance and condensation phenomenon of EAHE in the greenhouse. They also obtained that a small amount of con- Energies 2021, 14, x FOR PEER REVIEW 3 of 20

Energies 2021, 14, 1368 3 of 18

the tube. Mongkon et al. [29] evaluated the cooling performance and condensation phenomenon of EAHE in the greenhouse. They also obtained that a small amount of con- denseddensed waterwater appearedappeared duringduring thethe systemsystem operation.operation. TheThe condensationcondensation hadhad aa considerable considera- influenceble influence on theon the thermal thermal performance performance of heatof heat exchangers. exchangers. Meanwhile, Meanwhile, the the condensation condensa- watertion water in the in pipethe pipe was was suitable suitable for for the the microorganisms microorganisms to to growgrow on, which which might might affect affect humanhuman health. Therefore, the the investigation investigation in intoto air air condensation condensation in in the the EAHE EAHE deserves deserves research.research. However, few studies focused focused on on the the investigation investigation of of the the relationship relationship between between airair condensationcondensation andand thethe integrated integrated performance performance of of EAHE. EAHE. Thus, Thus, this this paper paper focused focused on on the influencethe influence of RH of andRH and condensation condensation on the on integratedthe integrated performance performance of the of EAHE.the EAHE. The simu-The lationsimulation model model of the of EAHE the EAHE was developedwas developed to evaluate to evaluate the integratedthe integrated performance performance at first. at Thenfirst. Then the distribution the distribution of RH of in RH each in each pipe pi waspe investigated.was investigated. After After that, that, the effectthe effect of inlet of airinlet RH air on RH the on thermal the thermal performance performance of the of the EAHE EAHE was was discussed. discussed. Finally, Finally, the the impact impact of structureof structure on on air air condensation condensation in in the the EAHE EAHE was was studied. studied.

2.2. Materials and Methods The multi-pipemulti-pipe EAHEEAHE consistedconsisted ofof mainmain pipespipes andand parallelparallel pipes, pipes, which which are are shown shown in Figurein Figure1. The 1. The dimensions dimensions of the of multi-pipethe multi-pipe EAHE EAHE are also are depictedalso depicted in Figure in Figure1. The 1. EAHE The wasEAHE installed was installed at the depth at the of depth 2 m, andof 2 them, lengthand the of length parallel of pipeparallel L was pipe 19 L m. was The 19 spacing m. The of thespacing parallel of the pipe parallel l was pipe 0.8 m. l was The 0.8 dimensions m. The dimensions of the surrounding of the surrounding soil are length soil are Ls length = 25 m, widthLs = 25 Ws m, =width 16 m Ws and = depth16 m and Hs =depth 15 m. Hs The = 15 material m. The and material thermophysical and thermophysical properties prop- of the EAHEerties of are the shown EAHE in are Table shown1. in Table 1.

dmain

Figure 1. The physical model of the earth to air heat exchanger (EAHE) and the surrounding soil. Figure 1. The physical model of the earth to air heat exchanger (EAHE) and the surrounding soil. Table 1. Thermophysical properties for EAHE [30]. Table 1. Thermophysical properties for EAHE [30]. Thermal Conductivity Density Speciﬁc Heat Absolute Viscosity Material Thermal Conductivity Density Specific Heat Absolute Viscosity Material (W·m−1·K−1) (kg·m−3) (J·kg−1·K−1) (kg·m−1·s−1) (W·m−1·K−1) (kg·m−3) (J·kg−1·K−1) (kg·m−1·s−1) PipePipe (PVC) (PVC) 0.16 0.16 1380 1380 900 900 / / Soil 2.1 1800 1780 / Soil 2.1 1800 1780 / Air 0.0242 1.225 1006.43 1.7894 × 10−5 Air 0.0242 1.225 1006.43 1.7894 × 10−5

The EAHEEAHE meshmesh waswas generatedgenerated by by ANSYS ANSYS Mesh, Mesh, which which is is shown shown in in Figure Figure2. The2. The un- structuredunstructured mesh mesh was was selected. selected. The The mesh mesh density density on theon the pipe pipe inlet inlet and and outlet, outlet, ground ground near thenear pipe, the pipe, the coupled the coupled surface surface between between the pipe the pipe and theand soil the wassoil increased,was increased, and theand mesh the densitymesh density on the on ground the ground far from far pipes from was pipes reduced. was reduced. The total The mesh total number mesh wasnumber 12,911,475, was and12,911,475, the skewness and the ofskewness the mesh of wasthe mesh less than was 0.83.less than Furthermore, 0.83. Furthermore, the mesh the independence mesh inde- analysispendence was analysis conducted was conducted using the outletusing the temperature outlet temperature of air. From of Figureair. From3, the Figure outlet 3, tem-the 7 peratureoutlet temperature of air remained of air almostremained constant almostwhen constant the when mesh the number mesh above number 10 above. It indicated 107. It that simulation results were independent of the mesh number when the mesh number was above 107. Therefore, the model with mesh number 12,911,475 was chosen. Energies 2021Energies, 14, x 2021FOR, PEER14, x FOR REVIEW PEER REVIEW 4 of 20 4 of 20

indicatedindicated that simulation that simulation results were results independent were independent of the mesh of the number mesh numberwhen the when mesh the mesh Energies 2021, 14, 1368 7 4 of 18 number numberwas above was 10 above7. Therefore, 10 . Therefore, the model the with model mesh with number mesh number12,911,475 12,911,475 was chosen. was chosen.

Figure 2.Figure FigureThe mesh 2.2. TheThe model meshmesh of model modelthe earth ofof thetheto air earthearth heat toto exchanger. airair heatheat exchanger.exchanger.

Figure 3. The mesh independence. Figure 3. FigureThe mesh 3. The independence. mesh independence. The boundary condition of the EAHE inlet was velocity inlet, and that of the EAHE The boundaryoutletThe wasboundary condition pressure condition of outlet. the EAHE of The the inlet temperatureEAHE was inlet velocity was of far-ﬁeld velocityinlet, and soil inlet, that was and of assumedthe that EAHE of the as constantEAHE outlet wasoutlet atpressure 291.85 was pressure Koutlet. [31], whileThe outlet. temperature the The convection temperature of far-field thermal of far-fieldsoil condition was soilassumed was was applied assumed as constant to as the constant at surface at soil. 291.85K 291.85K[31],The while contact [31], the while surfaceconvection the betweenconvection thermal the thermalco pipendition and co was thendition soilapplied was to coupled.applied the surface to The the soil.detailedsurface The soil. boundary The contact surfacecontactconditions betweensurface setup between the waspipe shown theand pipe the in soiland Table wasthe2. soilcoupled. was coupled. The detailed The detailedboundary boundary condi- condi- tions setuptions was setup shown was in shown Table in2. Table 2. Table 2. The boundary conditions setup. Table 2. TheTable boundary 2. The boundary conditions conditions setup. setup. Boundary Conditions Setup Values [31] Boundary Conditions Setup Values [31] Boundary ConditionsInlet Setup Velocity-inlet Values [31] / Inlet InletOutlet Velocity-inlet Velocity-inlet Pressure-outlet / / / OutletUpper Outlet surface of soil Pressure-outlet Pressure-outlet Wall / 297.49 / K Far-ﬁeld soil Wall 291.85 K Upper surfaceUpper ofsurface soil of soil Wall Wall 297.49 K 297.49 K Far-fieldFar-field soil soil Wall Wall 291.85 K 291.85 K In the study, the steady performance and the effects of parameters of EAHE were investigated. Thus, the steady-state simulation was conducted. Due to the forced convection in the EAHE, the turbulence model was selected. With respect to the simulation of wall condensation, Zschaeck et al. [32] applied the SST k-ω model to study wall condensation in the presence of non-condensable gases, and the model was validated by experimental data. Energies 2021, 14, 1368 5 of 18

Considering simplicity, robustness, reasonable accuracy and fast convergence, the k-ω model acted a better performance to solve wet air turbulence flow, especially for the air condensation phenomenon. Therefore, the SST k-ω model was used to simulate turbulence flow in this study. The water vapor in wet air was taken into consideration. The wet air was mixed with dry air and water vapor, and a multi-species transport model was used to calculate it. The Eulerian wall film model was utilized to predict the generation of thin liquid films on the inner surface of the EAHE and its flow on the pipe’s surface. The Eulerian wall film model can simultaneously calculate the water film flow under the action of wall pressure gradient, gravity, surface tension, shear force, liquid viscosity force and other external factors. As the thickness of the film was smaller than the radius of curvature of the surface, the films were thin enough. Therefore, the liquid flow in the film can be considered parallel to the wall. The thin film assumption was adopted in the Eulerian wall film model. The following assumptions of the model were made to simplify the calculation. (1) The water film flow in the multi-pipe EAHE was continuous; (2) The condition of the water film forming a small flow was not considered; (3) The breaking and splashing process of the droplet was ignored; (4) The wet air contains air and water vapor, which was assumed as an incompressible ideal gas. It conformed to the ideal gas mixing law. The governing equations [33] for wall film are listed as follows: Mass conservation equation for wall film:

→ . ∂h f ms + ∇s• h f Vl = (1) ∂t ρl

Momentum equations for wall ﬁlm:

→ → → → → ∂h f Vl h f ∆sPL → 3 → 3vl qs + ∆s• h f Vl Vl = − + g τh f + τ f s − Vl + (2) ∂t ρl 2ρl h ρl

Energy equation for wall ﬁlm:

∂(h f Tf ) → 1 Ts − Tf Tf − Tw . . + ∇s•(Vf h f T) = [k f ( − ) + qimp + mevap L(Ts)] (3) ∂t ρcp h f /2 h f /2

The thermal computational model of the EAHE was veriﬁed in the author’s previ- ous work [30]. The numerical outlet temperature was compared with the experimental data in the paper of Rodrigues et al. [31]. The results showed that the average outlet temperature differences between the experimental data and numerical results in each duct were 1.57 K, 1.19 K and 1.21 K. The absolute error was calculated using formula |T − T | (Percentage = sim exp ). Therefore, the average error of outlet temperature in different Texp conditions were 0.5%, 0.4% and 0.4%. The simulation model ﬁtted the experimental data well, and it could be used to analyze the thermal performance of the EAHE.

3. Evaluation Index 3.1. Airflow Division Uniformity Coefficient The airflow uniformity was evaluated by the airflow division uniformity coefficient Ω [34]. It could reflect airflow distribution uniformity in each parallel pipe. It was defined as follows: v . . u n 2 1 u ∑ ( V − Va) Ω= 1− ·t i=1 i (4) . ( − ) Va n n 1 . . ∑n V V = i=1 i (5) a n Energies 2021, 14, 1368 6 of 18

. . where, Va means the average volume ﬂow rate in EAHE, and Vi was the volume ﬂow rate in each pipe of EAHE.

3.2. Temperature Extraction Efficiency The temperature extraction efficiency θ [35] was applied to estimate the thermal performance of the EAHE. It was defined as follows:

T − T θ = out in (6) Tsoil − Tin

where, Tout means the outlet temperature of EAHE, and Tin was the inlet temperature of EAHE. Tsoil was the soil temperature in the far-ﬁeld.

3.3. Integrated Evaluation Factor The integrative performance of the EAHE was estimated by the integrated evaluation factor η [36]. It was composed of the pressure drop and overall heat transfer coefﬁcient. The higher η means better thermal performance and lower pressure drop.

Nu η = (7) f 1/3

hD Nu = (8) λ Q h = (9) πDL(∆Tm)

Q = m(Hin − Hout) (10) ∆p D f = · (11) 1 ρ u2 L 2 f f where, f was the friction factor, which was calculated using Equation (11). ∆p was the pressure drop between the inlet and outlet, uf was the velocity of air. h was the overall heat transfer coefficient of the EAHE, which was not the heat transfer coefficient of the airflow in the pipe. ∆Tm was the logarithmic mean temperature differences between soil and air, ρf was the density of air.

4. Results and Discussion 4.1. Uniformity of RH in EAHE The RH non-uniformity in the multi-pipe EAHE is discussed in this section. To clearly evaluate the influence of RH, the inlet air humidity was selected as an independent variable. Thus, the inlet volume flow rate, inlet temperature and tube diameter were selected as the fixed value. The inlet temperature was 299.54 K, and the volume flow rate of air was 0.32 m3·s−1. The EAHE was the U-type structure, and the diameter of the main pipe and parallel pipe were 110 and 75 mm, respectively. The distribution of the mass flow rate in each pipe is displayed in Figure4. Pipe 1 near the inlet obtained the maximum flow rate, while the flow rate in pipe 8 was the minimum one. The distribution of mass flow rate experienced a decreased trend along the flow direction when the EAHE was the U-type structure. As Figure5 shows, when the inlet air RH was 10%, the air RH in each parallel pipe was different. The air RH in parallel pipe 1 was the lowest, which was nearest to the inlet pipe. The relative humidity of air in parallel pipe 8 was 12.6%. The air RH difference between parallel pipe 1 and parallel pipe 8 was 1.5%. It seemed there was no obvious difference of the air RH in each tube under the 10% inlet air RH condition. Energies 2021, 14, x FOR PEER REVIEW 7 of 20

Energies 2021, 14, x FOR PEER REVIEW 7 of 20

4. Results and Discussion 4.1. Uniformity of RH in EAHE 4. ResultsThe and RH Discussionnon-uniformity in the multi-pipe EAHE is discussed in this section. To clearly evaluate the influence of RH, the inlet air humidity was selected as an independent 4.1. variable.Uniformity Thus, of theRH inlet in EAHE volume flow rate, inlet temperature and tube diameter were se- lectedThe asRH the non-uniformityfixed value. The inlet in temperaturthe multi-pipee was 299.54 EAHE K, and is thediscussed volume flowin thisrate ofsection. To 3 −1 clearlyair was evaluate 0.32 m ·sthe. Theinfluence EAHE was of RH, the U-type the inlet structure, air humidity and the diameter was selected of the mainas an pipe independent and parallel pipe were 110 and 75 mm, respectively. variable. Thus, the inlet volume flow rate, inlet temperature and tube diameter were se- The distribution of the mass flow rate in each pipe is displayed in Figure 4. Pipe 1 lectednear as the the inlet fixed obtained value. the The maximum inlet temperatur flow rate, whilee was the 299.54flow rate K, in and pipe the 8 was volume the min- flow rate of air wasimum 0.32 one. m The3·s− 1distribution. The EAHE of was mass the flow U-type rate experienced structure, a and decreased the diameter trend along of the the main pipe andflow parallel direction pipe when were the 110 EAHE and was 75 themm, U-type respectively. structure. The distribution of the mass flow rate in each pipe is displayed in Figure 4. Pipe 1 near the inlet obtained the maximum flow rate, while the flow rate in pipe 8 was the minimum one. The distribution of mass flow rate experienced a decreased trend along the Energies 2021, 14, 1368 flow direction when the EAHE was the U-type structure. 7 of 18

Figure 4. The mass flow rate of air in each pipe.

As Figure 5 shows, when the inlet air RH was 10%, the air RH in each parallel pipe was different. The air RH in parallel pipe 1 was the lowest, which was nearest to the inlet pipe. The relative humidity of air in parallel pipe 8 was 12.6%. The air RH difference between parallel pipe 1 and parallel pipe 8 was 1.5%. It seemed there was no obvious difference of the air RH in each tube under the 10% inlet air RH condition. Figure 4. The mass ﬂow rate of air in each pipe. Figure 4. The mass flow rate of air in each pipe.

Figure 5. Figure 5. AirAir relative humidityhumidity (RH) (RH) in in each each pipe pipe when when inlet inlet air RH air was RH 10%. was 10%. When the inlet air RH was 40%, the air RH in pipe 8 was the highest (see Figure6). The parallel pipe 8 was situated in the farthest pipe from the perspective of flow direction. The mass flow rate in this pipe was the lowest, seen in Figure4. It meant that the air RH experienced the opposite trend with mass flow rate. The air RH in parallel pipe 1 was 44.3%, and that of outlet air in pipe 8 was 50.4%. Therefore, the difference between parallel pipe 1 (minimum RH) and parallel pipe 8 (maximum RH) was 6.1%. As the inlet air RH increased to 80%, the RH distribution in each parallel pipe was similar to that in the condition of 40% (see Figure7). The RH of the pipe far from the inlet was the highest, which reached 100%. That was to say, the air inside pipe 8 began to condense under this condition. Meanwhile, the air RH maximum difference among the tubes was increased to 11.9%. As presented in Figure8, the standard deviation of air relative humidity in each Figureparallel 5. Air pipe relative increased humidity as inlet (RH) air RH in each increased. pipe when In other inlet words, air RH as the was inlet 10%. air RH increased, the uniformity of air RH in each parallel pipe deteriorated. Compared to the standard deviation of air RH in different diameters of parallel pipe, the parallel pipe with the larger diameter led to the better uniformity air RH. Energies 2021, 14, x FOR PEER REVIEW 8 of 20

When the inlet air RH was 40%, the air RH in pipe 8 was the highest (see Figure 6). The parallel pipe 8 was situated in the farthest pipe from the perspective of flow direction. The mass flow rate in this pipe was the lowest, seen in Figure 4. It meant that the air RH experienced the opposite trend with mass flow rate. The air RH in parallel pipe 1 was 44.3%, and that of outlet air in pipe 8 was 50.4%. Therefore, the difference between parallel Energies 2021, 14, x FOR PEER REVIEW 8 of 20 pipe 1 (minimum RH) and parallel pipe 8 (maximum RH) was 6.1%.

When the inlet air RH was 40%, the air RH in pipe 8 was the highest (see Figure 6). The parallel pipe 8 was situated in the farthest pipe from the perspective of flow direction. The mass flow rate in this pipe was the lowest, seen in Figure 4. It meant that the air RH experienced the opposite trend with mass flow rate. The air RH in parallel pipe 1 was 44.3%, and that of outlet air in pipe 8 was 50.4%. Therefore, the difference between parallel Energies 2021, 14, 1368 pipe 1 (minimum RH) and parallel pipe 8 (maximum RH) was 6.1%. 8 of 18

Figure 6. Air RH in each pipe when inlet air RH was 40%.

As the inlet air RH increased to 80%, the RH distribution in each parallel pipe was similar to that in the condition of 40% (see Figure 7). The RH of the pipe far from the inlet was the highest, which reached 100%. That was to say, the air inside pipe 8 began to condense under this condition. Meanwhile, the air RH maximum difference among the tubes was increased to 11.9%. Figure 6. Air RH in each pipe when inlet air RH was 40%. Figure 6. Air RH in each pipe when inlet air RH was 40%.

Energies 2021, 14, x FOR PEER REVIEW 9 of 20

Figure 7. Air RH in each pipe when inlet air RH was 80%. Figure 7. Air RH in each pipe when inlet air RH was 80%.

As presented in Figure 8, the standard deviation of air relative humidity in each parallel pipe increased as inlet air RH increased. In other words, as the inlet air RH increased, the uniformity of air RH in each parallel pipe deteriorated. Compared to the standard deviation of air RH in different diameters of parallel pipe, the parallel pipe with the larger diameter led to the better uniformity air RH.

Figure 7. Air RH in each pipe when inlet air RH was 80%.

Figure 8. The standard deviation of air RH in each parallel pipe under different inlet air RH. Figure 8. The standard deviation of air RH in each parallel pipe under different inlet air RH. In conclusion, the larger inlet air RH caused the worse uniformity of air RH in each parallelIn conclusion, pipe. The the non-uniformitylarger inlet air RH RH caused distribution the worse resulted uniformity in theof air non-uniformity RH in each air parallel pipe. The non-uniformity RH distribution resulted in the non-uniformity air condensation phenomenon. In particular, the air inside pipe 8 was much easy to condense for U-type structure EAHE, which was located in the farthest pipe from the inlet.

4.2. The Effect of Inlet Air RH on the Thermal Performance of EAHE The effect of inlet air RH on the thermal performance of EAHE is investigated in this part. The diameter of the pipe and supply type were 110 mm and U type structure, respectively. The inlet temperature was 299.54 K, and the volume flow rate of air was 0.32 m3·s−1. The other dimensions and configuration were the same as aforementioned. As depicted in Figure 9, the inlet air RH has a minimal impact on the airflow distribution uniformity. The Ω of wet air was slightly higher than that of dry air. After that, the Ω remained stable at 0.74. Those results meant that the airflow division uniformity of wet air was superior to that of dry air. However, increasing the inlet air RH had few effects on the airflow division uniformity. In other words, the airflow division uniformity was independent of inlet air RH. The diameter of the parallel pipe had a significant influence on the coefficient Ω. Increasing the diameter of the parallel pipe could improve the airflow division uniformity, rather than increasing the inlet air RH. Energies 2021, 14, 1368 9 of 18

condensation phenomenon. In particular, the air inside pipe 8 was much easy to condense for U-type structure EAHE, which was located in the farthest pipe from the inlet.

4.2. The Effect of Inlet Air RH on the Thermal Performance of EAHE The effect of inlet air RH on the thermal performance of EAHE is investigated in this part. The diameter of the pipe and supply type were 110 mm and U type structure, respectively. The inlet temperature was 299.54 K, and the volume flow rate of air was 0.32 m3·s−1. The other dimensions and configuration were the same as aforementioned. As depicted in Figure9, the inlet air RH has a minimal impact on the airflow distribution uniformity. The Ω of wet air was slightly higher than that of dry air. After that, the Ω remained stable at 0.74. Those results meant that the airflow division uniformity of wet air was superior to that of dry air. However, increasing the inlet air RH had few effects on the airflow division uniformity. In other words, the airflow division uniformity was Energies 2021, 14, x FOR PEER REVIEW 10 of 20 independent of inlet air RH. The diameter of the parallel pipe had a significant influence on the coefficient Ω. Increasing the diameter of the parallel pipe could improve the airflow division uniformity, rather than increasing the inlet air RH.

FigureFigure 9. The 9. The Ω withΩ with inlet inlet air RH. air RH.

TheThe θ couldθ could reflect reflect the the thermal thermal performance performance of the of the EAHE. EAHE. The The higher higher temperature temperature extractionextraction efficiency efficiency θ θcausedcaused better better thermal performanceperformance of of the the EAHE. EAHE. As As Figure Figure 10 shows, 10 shows,the temperaturethe temperature extraction extraction efficiency efficiencyθ of wetθ of airwet was air slightlywas slightly higher higher than than that ofthat dry of air. dryFor air. the For wet the air, wet the air, increasing the increasing inlet air inlet RH air had RH few had effects few oneffects the temperatureon the temperature extraction extractionefficiency efficiencyθ. When θ. theWhen inlet the air inlet RH air was RH 90%, was the 90%, water the vaporwater vapor of wet of air wet inside air inside the pipe thecondensed pipe condensed to water to liquid.water Theliquid. temperature The temperature extraction extraction efficiency efficiencyθ declined θ sharply declined from sharply0.187 from and 0.1940.187 to and 0.173 0.194 and to 0.192, 0.173 respectively. and 0.192, respectively. Moreover, increasing Moreover, the increasing diameter the of the diameterparallel of pipe the parallel was beneficial pipe was to improvebeneficial the to temperatureimprove the extractiontemperature efficiency, extraction when effi- the diameter of the main pipe was 110 mm. ciency, when the diameter of the main pipe was 110 mm. The EAHE heat transfer rate experienced a slight rise as the inlet air RH increased from 10% to 80% (see Figure 11). The heat transfer rate of wet air was a little higher than that of dry air. When the inlet air RH increased to 90%, the heat transfer rate of the EAHE dropped to 512.8 W and 568.2 W, respectively. From Figure 12, the integrated evaluation factor η saw a slight increase as the inlet air RH increased from 10% to 80%. This meant that variation of inlet air RH has no significant impact on the integrated performance of the EAHE under the condition of no condensation. Interestingly, when the wet air inside the pipe showed the condensation phenomenon, the integrated evaluation factor declined by 7.9%. This meant that the integrated performance of the EAHE deteriorated under condensation conditions. The integrated evaluation

Figure 10. The θ with inlet air RH.

The EAHE heat transfer rate experienced a slight rise as the inlet air RH increased from 10% to 80% (see Figure 11). The heat transfer rate of wet air was a little higher than that of dry air. When the inlet air RH increased to 90%, the heat transfer rate of the EAHE dropped to 512.8 W and 568.2 W, respectively. Energies 2021, 14, x FOR PEER REVIEW 10 of 20

Figure 9. The Ω with inlet air RH.

The θ could reflect the thermal performance of the EAHE. The higher temperature Energies 2021, 14, 1368 10 of 18 extraction efficiency θ caused better thermal performance of the EAHE. As Figure 10 shows, the temperature extraction efficiency θ of wet air was slightly higher than that of dry air. For the wet air, the increasing inlet air RH had few effects on the temperature extractionfactor efficiencyη has rather θ. When a slight the inlet variation air RH comparedwas 90%, the with water heat vapor transfer of wet variation air inside at RH = 90%. the pipe condensed to water liquid. The temperature extraction efficiency θ declined This was because η was directly proportional to heat transfer performance, while it was in- sharply from 0.187 and 0.194 to 0.173 and 0.192, respectively. Moreover, increasing the versely proportional to pressure drop. Although the heat transfer rate experienced a drastic diameter of the parallel pipe was beneficial to improve the temperature extraction effi- Energies 2021, 14, x FOR PEER REVIEWciency,drop when when the diameter RH reached of the 80%, main the pipe pressure was 110 dropmm. declined. The heat transfer11 of performance 20 was a dominating factor in the EAHE integrated performance under this condition.

Energies 2021, 14, x FOR PEER REVIEW 11 of 20

FigureFigure 10. The 10. θ withThe θinletwith airinlet RH. air RH.

The EAHE heat transfer rate experienced a slight rise as the inlet air RH increased from 10% to 80% (see Figure 11). The heat transfer rate of wet air was a little higher than

that of dry air. When the inlet air RH increased to 90%, the heat transfer rate of the EAHE droppedFigure to11. 512.8 The heat W andtransfer 568.2 rate W, with respectively. inlet air RH.

From Figure 12, the integrated evaluation factor η saw a slight increase as the inlet air RH increased from 10% to 80%. This meant that variation of inlet air RH has no significant impact on the integrated performance of the EAHE under the condition of no condensation. Interestingly, when the wet air inside the pipe showed the condensation phenomenon, the integrated evaluation factor declined by 7.9%. This meant that the integrated performance of the EAHE deteriorated under condensation conditions. The integrated evaluation factor η has rather a slight variation compared with heat transfer variation at RH = 90%. This was because η was directly proportional to heat transfer performance, while it was inversely proportional to pressure drop. Although the heat transfer rate experienced a drastic drop when RH reached 80%, the pressure drop declined. The heat transfer performance was a dominating factor in the EAHE integrated performance under this condition.

Figure 11. The heat transfer rate with inlet air RH. Figure 11. The heat transfer rate with inlet air RH.

Figure 12. The integrated evaluation factor η with inlet air RH. Figure 12. The integrated evaluation factor η with inlet air RH.

Figure 12. The integrated evaluation factor η with inlet air RH. Energies 2021, 14, x FOR PEER REVIEW 12 of 20

Energies 2021, 14, 1368 11 of 18 Overall, the airflow distribution uniformity was independent of inlet air RH. Con- densation of wet air could cause a degradation in thermal performance. Therefore, the integrated performance of EAHE deteriorated when the wet air condensed in the pipes. Overall, the airflow distribution uniformity was independent of inlet air RH. Conden- sation of wet air could cause a degradation in thermal performance. Therefore, the inte- 4.3. The Effect of Inlet Air Temperature and Volume Flow Rate on the Thermal Performance of grated performance of EAHE deteriorated when the wet air condensed in the pipes. EAHE 4.3.The The inlet Effect air oftemperature Inlet Air Temperature and volume and flow Volume rate Flow had Rate a significant on the Thermal effect Performance on the distri- butionof EAHE of RH in pipes. In this section, the effect of inlet air temperature and volume flow rate on theThe RH inlet uniformity air temperature and thermal and volumeperformance flow rateof the had EAHE a significant were investigated. effect on theThe dis- configurationtribution of of RH the in EAHE pipes. was In U-type. this section, the effect of inlet air temperature and volume flowFigure rate 13 on presents the RH uniformityair RH uniformity and thermal in ea performancech parallel pipe of the under EAHE different were investigated. inlet air temperatureThe configuration conditions. of the As EAHEbeforewas mentioned, U-type. the standard deviation of air RH in each parallel Figurepipe increased 13 presents as inlet air RHair uniformityRH increased. in eachIt meant parallel that pipethe uniformity under different of RH inlet dis- air tributiontemperature in each conditions. pipe became As worse before as mentioned, the inlet air the RH standard increased. deviation Obviously, of air when RH in the each inletparallel air temperature pipe increased rose, asthe inlet standard air RH deviation increased. of air It meantRH in thateach the parallel uniformity pipe rose of RH sharply.distribution As the ininlet each temperature pipe became varied worse from as the 294.54 inlet K air to RH 299.54 increased. K and Obviously,from 299.54 when K tothe 304.54inlet K, air the temperature air RH standard rose, the deviation standard increased deviation ofby air44% RH and in each34%, parallel respectively. pipe rose It indi- sharply. catedAs that the inletthe air temperature RH uniformity varied in fromeach parallel 294.54 K pipe to 299.54 was closely K and related from 299.54 to inlet K toair 304.54 tem- K, perature.the air The RH standardair in EAHE deviation condensed increased much by more 44% easily and 34%, under respectively. high temperature It indicated and that hu- the midityair RH conditions. uniformity in each parallel pipe was closely related to inlet air temperature. The air in EAHE condensed much more easily under high temperature and humidity conditions.

FigureFigure 13. 13.TheThe standard standard deviation deviation of ofair air RH RH in in each each pa parallelrallel pipe pipe under under different different inlet airair temperatures.temperatures. As Figure 14 shows, the impact of inlet volume flow rate on the standard deviation of airAs RH Figure in each 14 parallelshows, pipethe impact was massive. of inlet Asvolume the inlet flow air rate volume on the flow standard rate increased deviation from 3 −1 3 −1 of air0.13 RH m in·s eachto 0.32parallel m · spipe, thewas air massive. RH standard As the deviation inlet air volume increased flow by 49%.rate increased That was to fromsay, 0.13 the m air3·s RH−1 to uniformity 0.32 m3·s−1, in the each air parallelRH standard pipe became deviation worse. increased Therefore, by 49%. the possibilityThat was of to say,part the condensation air RH uniformity under lowerin each flow parallel rate conditionspipe became was worse. low. Therefore, the possibility of part condensationThe integrated under evaluation lower flow factor rateη underconditions different was low. inlet air temperature conditions is depicted in Figure 15. It was found that the variation of inlet air RH has no significant impact on the integrated performance of the EAHE under the condition of no condensation. However, the inlet air temperature had a remarkable influence on the integrated performance of the EAHE. Similarly, the inlet volume flow rate had a great effect on the integrated evaluation factor η (see Figure 16). As the inlet volume flow rate increased from 0.13 m3·s−1 to 0.32 m3·s−1, the integrated evaluation factor η increased by 39%. This finding was understandable because the overall heat transfer coefficient rose and the pressure drop increased, when the inlet volume flow rate increased. The overall heat transfer coefficient was a dominating factor in the EAHE integrated performance in the same configuration. Energies 2021, 14, x FOR PEER REVIEW 13 of 20

Energies 2021, 14, x FOR PEER REVIEW 13 of 20 Energies 2021, 14, 1368 12 of 18

Figure 14. The standard deviation of air RH in each parallel pipe under different inlet volume flow rates.

The integrated evaluation factor η under different inlet air temperature conditions is depicted in Figure 15. It was found that the variation of inlet air RH has no significant impact on the integrated performance of the EAHE under the condition of no condensation. However, the inlet air temperature had a remarkable influence on the integrated per- FigureformanceFigure 14. The 14.of thestandardThe EAHE. standard deviation deviation of air RH of in air each RH parallel in each pipe parallel under pipe different under inlet different volume inletflow volume rates.ﬂow rates.

Energies 2021, 14, x FOR PEER REVIEW 14 of 20

FigureFigure 15. 15.TheThe integrated integrated evaluation evaluation factor factor η underη under different different inlet air inlet temperatures. air temperatures.

Similarly, the inlet volume flow rate had a great effect on the integrated evaluation factor η (see Figure 16). As the inlet volume flow rate increased from 0.13 m3·s−1 to 0.32 m3·s−1, the integrated evaluation factor η increased by 39%. This finding was understandable because the overall heat transfer coefficient rose and the pressure drop increased, when the inlet volume flow rate increased. The overall heat transfer coefficient was a dom- Figureinating 15. factor The integrated in the EAHE evaluation integrated factor performanceη under different in theinlet same air temperatures. configuration.

Similarly, the inlet volume flow rate had a great effect on the integrated evaluation factor η (see Figure 16). As the inlet volume flow rate increased from 0.13 m3·s−1 to 0.32 m3·s−1, the integrated evaluation factor η increased by 39%. This finding was understandable because the overall heat transfer coefficient rose and the pressure drop increased, when the inlet volume flow rate increased. The overall heat transfer coefficient was a dominating factor in the EAHE integrated performance in the same configuration.

FigureFigure 16. 16.TheThe integrated integrated evaluation evaluation factor factor η underη under different different inlet volume inlet volume flow rates. ﬂow rates.

In summary, the inlet air temperature and volume flow rate affected the air RH distribution in parallel pipes. Moreover, they also influenced the integrated evaluation factor η significantly.

4.4. The Effect of Structure on Condensation in EAHE The influence of parallel pipe diameter and supply type on the condensation phenomenon inside the EAHE was studied. The humidity ratio of inlet air of the EAHE was the same in the section. That was to say, the mass fraction of H2O in inlet air was the same under those conditions. Table 3 shows the variation of the EAHE integrated performance under the different parallel pipe diameters. With the increasing diameter of parallel pipes, the heat transfer capacity increased while the pressure drop decreased. Therefore, a larger parallel pipe contributed to the larger integrated evaluation factor η, and the EAHE integrated performance was enhanced.

Table 3. Thermal and pressure performance with different parallel pipe diameters.

Diameter of Parallel Heat Transfer Rate The Integrated Pressure Drop (Pa) Pipes (mm) (W) Evaluation Factor η 75 512.8 6842.7 19.9 90 549.7 2875.1 27.0 110 568.2 1128.9 35.8

As shown in Figure 17, the mass fraction of H2O in the inlet air was the same, while the mass fraction of H2O in the outlet air was different under the different diameters of parallel pipes. It was understandable that the water vapor in wet air was condensed to water liquid. In other words, the phase change (condensation) appeared in the parallel pipes. Therefore, the mass fraction of H2O in the outlet air decreased compared with that in the inlet air. Meanwhile, the mass fraction of H2O in the outlet air decreased as the diameter of the parallel pipes decreased. This meant that the condensation water increased as the diameter of the parallel pipes decreased. In other words, the wet air was likely to condense in a narrower parallel pipe. Energies 2021, 14, 1368 13 of 18

In summary, the inlet air temperature and volume flow rate affected the air RH distribution in parallel pipes. Moreover, they also influenced the integrated evaluation factor η significantly.

4.4. The Effect of Structure on Condensation in EAHE The inﬂuence of parallel pipe diameter and supply type on the condensation phenomenon inside the EAHE was studied. The humidity ratio of inlet air of the EAHE was the same in the section. That was to say, the mass fraction of H2O in inlet air was the same under those conditions. Table3 shows the variation of the EAHE integrated performance under the different parallel pipe diameters. With the increasing diameter of parallel pipes, the heat transfer capacity increased while the pressure drop decreased. Therefore, a larger parallel pipe contributed to the larger integrated evaluation factor η, and the EAHE integrated performance was enhanced.

Table 3. Thermal and pressure performance with different parallel pipe diameters.

Diameter of Parallel Heat Transfer Rate The Integrated Pressure Drop (Pa) Pipes (mm) (W) Evaluation Factor η 75 512.8 6842.7 19.9 90 549.7 2875.1 27.0 110 568.2 1128.9 35.8

As shown in Figure 17, the mass fraction of H2O in the inlet air was the same, while the mass fraction of H2O in the outlet air was different under the different diameters of parallel pipes. It was understandable that the water vapor in wet air was condensed to water liquid. In other words, the phase change (condensation) appeared in the parallel pipes. Therefore, the mass fraction of H2O in the outlet air decreased compared with that Energies 2021, 14, x FOR PEER REVIEW in the inlet air. Meanwhile, the mass fraction of H2O in the outlet air decreased15 of as 20 the

diameter of the parallel pipes decreased. This meant that the condensation water increased as the diameter of the parallel pipes decreased. In other words, the wet air was likely to condense in a narrower parallel pipe.

Figure 17. Mass fraction of H2O at the outlet vent with different diameters of parallel pipes. Figure 17. Mass fraction of H2O at the outlet vent with different diameters of parallel pipes. The integrated performance of the EAHE with different supply types is listed in TableThe 4integrated. The heat performance transfer rate of of the the EAHE Z-type with structure different was supply 542.6 W, types which is listed was the in Ta- lowest ble under4. The theheat three transfer supply rate type of the conditions. Z-type structure Moreover, was the 542.6 pressure W, which drop was between the lowest inlet and underoutlet the wasthree the supply highest type in theconditions. three supply Moreover, type conditions.the pressure The drop lowest between heat transferinlet and rate outletand was highest the highest pressure in dropthe three resulted supply in the type lowest conditions. integrated Theevaluation lowest heat factor transferη of rate Z-type and highest pressure drop resulted in the lowest integrated evaluation factor η of Z-type structure. However, L-type structure EAHE obtained the best integrated performance among the three supply type conditions. The integrated evaluation factor η of the L-type structure was 2.47 times as much as that of the Z-type structure. The integrated evaluation factor η of the U-type structure increased by 15%.

Table 4. Thermal and pressure performance with different supply types of EAHE.

Type Z-Type U-Type L-Type

Structure

Heat transfer rate (W) 542.6 568.2 576.7 Pressure drop (Pa) 1474.9 1128.9 123.5 η 31.1 35.8 77.2

The condensation rate in parallel pipes was diverse, as Figure 18 shows. When the supply type of the EAHE was the L-type, pipe 1 near the inlet obtained more condensation water. The mass fraction of H2O in each pipe with the Z- type EAHE had a similar distribution to that of the L-type EAHE. However, the condensate water of the L-type structure was more evenly distributed. When the supply type of the EAHE was the U-type, the condensation water in pipe 8 (far from the inlet) was the largest. The mass fraction of H2O in each pipe with the U- type EAHE had an inverse distribution with that of the Z-type EAHE. EnergiesEnergiesEnergies 2021 20212021, ,,14 1414, ,,x xx FOR FORFOR PEER PEERPEER REVIEW REVIEWREVIEW 151515 of of 20 2020

FigureFigureFigure 17. 17.17. Mass MassMass fraction fractionfraction of ofof H HH22O2OO at atat the thethe outlet outletoutlet vent ventvent with withwith different differentdifferent diameters diametersdiameters of ofof parallel parallelparallel pipes. pipes.pipes.

TheTheThe integrated integratedintegrated performance performance of of the the EAHEEAHE EAHE withwith with different different different supply supply supply types types types is is islisted listed listed in in inTable Ta- Ta- Energies 2021, 14, 1368 ble4.ble The 4. 4. The Theheat heat heattransfer transfer transfer rate rate ofrate the of of Zthe the‐type Z-type Z-type structure structure structure was 542.6was was 542.6 W,542.6 which W, W, which whichwas the was was lowest the the lowest14 lowestunder of 18 undertheunder three the the supplythree three supply supplytype conditions. type type conditions. conditions. Moreover, Moreover, Moreover, the pressure the the pressure pressure drop betweendrop drop between between inlet and inlet inlet outlet and and outletwasoutlet the was was highest the the highest highest in the in inthree the the three supplythree supply supply type type conditions.type conditions. conditions. The lowestThe The lowest lowest heat heat transferheat transfer transfer rate rate andrate andhighestand highest highest pressure pressure pressure drop drop drop resulted resulted resulted in in thein th th eloweste lowest lowest integrated integrated integrated evaluation evaluation evaluation factorfactor factor η η η of of Z-type ZZ-type‐type structure. However, L-type structure EAHE obtained the best integrated performance structure.structure.structure. However,However,However, L-typeLL-type‐type structurestructurestructure EAHEEAHEEAHE obtainedobtainedobtained thethethe bestbestbest integratedintegratedintegrated performanceperformanceperformance among the three supply type conditions. The integrated evaluation factor η of the L-type amongamongamong the thethe three threethree supply supplysupply type typetype conditions conditions.conditions. . The TheThe integrated integratedintegrated evaluation evaluationevaluation factor factorfactor η η η of ofof the thethe L-type LL-type‐type structure was 2.47 times as much as that of the Z-type structure. The integrated evaluation structurestructurestructure was waswas 2.47 2.472.47 times timestimes as asas much muchmuch as asas that thatthat of ofof the thethe Z-type ZZ-type‐type structure. structure.structure. The TheThe integrated integratedintegrated evaluation evaluationevaluation factor η of the U-type structure increased by 15%. factorfactorfactor η η η of ofof the thethe U-type UU-type‐type structure structurestructure increased increasedincreased by byby 15%. 15%.15%. Table 4. Thermal and pressure performance with different supply types of EAHE. TableTableTable 4. 4.4. Thermal ThermalThermal and andand pressure pressurepressure performance performanceperformance wi withwithth different differentdifferent supply supplysupply types typestypes of ofof EAHE. EAHE.EAHE. Type Z-Type U-Type L-Type TypeTypeType Z-TypeZZ-Type‐Type U-TypeUU-Type‐Type L-TypeLL-Type‐Type

StructureStructureStructure

HeatHeatHeat transfer transfertransfer rate rate raterate (W) (W) (W)(W) 542.6542.6 542.6 568.2568.2 568.2 568.2 576.7 576.7576.7 576.7 PressurePressurePressure drop drop dropdrop (Pa) (Pa) (Pa)(Pa) 1474.91474.9 1474.9 1128.91128.9 1128.9 1128.9 123.5 123.5123.5 123.5 ηηηη 31.131.131.1 35.835.835.8 35.8 77.2 77.277.2 77.2

TheTheTheThe condensation condensation condensationcondensation rate rate raterate in in inin parallel parallel parallelparallel pipes pipes pipespipes was was waswas diverse, diverse, diverse,diverse, as as asas Figure Figure FigureFigure 18 18 1818 shows. shows. shows.shows. When When WhenWhen the the thethe supplysupplysupplysupply typetype typetype ofof ofof thethe thethe EAHE EAHEEAHE waswas waswas theth thethee L-type, LL-type,‐type, pipe pipepipe 1 11 near nearnear the thethe inlet inletinlet obtained obtainedobtained more moremore condensation condensationcondensation water.water.water.water. The TheThe mass mass mass fraction fraction fractionfraction of of of ofH H 2 HOH2O2 2Oin Oin each inineach eacheach pipe pipe pipepipe with with withwith the the Z- theZ-the ty ty Z-peZpe‐ typeEAHE typeEAHE EAHEEAHE had had a a hadsimilarhad similar aa similar similardistri- distri- distributionbutiondistributionbution to to that that toto of of that thatthe the ofL-type ofL-type the the L-type EAHE. LEAHE.‐type EAHE. However, EAHE.However, However, However, the the condensate condensate the the condensate condensate water water of of water the waterthe L-type L-type of of the the structure structure L-type L‐type Energies 2021, 14, x FOR PEER REVIEW structurewasstructurewas moremore was was evenlyevenly more more distributed. evenlydistributed. evenly distributed. distributed. WhenWhen the Whenthe When susupply thepply the supply typetype supply of of type thethe type of EAHEEAHE the of EAHEthe waswas EAHE wasthethe U-type, theU-type,was U-type, the the theU‐ 16 of 20 thecondensationtype,condensation condensation the condensation water water water in in pipe pipe inwater pipe8 8 (far (far in 8 from (farfrompipe fromthe the8 (farinlet) inlet) the from inlet)was was thethe the was largest.inlet) largest. the largest.was The The the mass mass The largest. fraction fraction mass The fraction of of massH H2O2O ofinfractionin Heach each2O inpipe pipeof each H with 2withO pipe in the eachthe with U- U- pipe type thetype with U- EAHE EAHE type the had EAHEUhad‐ type an an had inverse EAHEinverse an inverse haddistribution distribution an inverse distribution with with distribution that that with of of thatthe the with Z-type ofZ-type thethat Z-typeEAHE.ofEAHE. the Z EAHE. ‐type EAHE.

Figure 18. Mass fraction of H2O in each pipe with different supply types. Figure 18. Mass fraction of H2O in each pipe with different supply types. Meanwhile, Figure 19 shows the mass fraction of H2O in the outlet vent with differ- entMeanwhile, supply types. Figure The mass 19 shows fraction the of Hmass2O decreased fraction when of H2 aO phase in the change outlet appeared. vent with different Compared to the three supply types, the mass fraction of H2O in the outlet vent was not supply types. The mass fraction of H2O decreased when a phase change appeared. Com- signiﬁcantly different. pared toConsequently, the three supply the integrated types, performancethe mass fraction increased of as H the2O diameter in the outlet of the parallelvent was not sig- nificantlypipes increased, different. and the amount of condensation water decreased as the diameter of the parallel pipes increased. It was better to choose the larger diameter of parallel pipes when the diameter of the main pipe was constant. Due to the difference in supply type, the mass

Figure 19. Mass fraction of H2O in the outlet vent with different supply types.

Consequently, the integrated performance increased as the diameter of the parallel pipes increased, and the amount of condensation water decreased as the diameter of the parallel pipes increased. It was better to choose the larger diameter of parallel pipes when the diameter of the main pipe was constant. Due to the difference in supply type, the mass fraction of H2O in each pipe distribution had a significant difference. The L-type structure EAHE obtained the best integrated performance and relatively uniform distribution. The Z-type structure EAHE was not recommended, considering the integrated performance and the distribution of condensate water.

5. Conclusions Energies 2021, 14, x FOR PEER REVIEW 16 of 20

Energies 2021, 14, 1368 15 of 18 Figure 18. Mass fraction of H2O in each pipe with different supply types.

Meanwhile, Figure 19 shows the mass fraction of H2O in the outlet vent with different supply types. The mass fraction of H2O decreased when a phase change appeared. Com- fraction of H2O in each pipe distribution had a signiﬁcant difference. The L-type structure paredEAHE to the obtained three supply the best types, integrated the mass performance fraction of and H relatively2O in the uniformoutlet vent distribution. was not sig- The Z- nificantlytype structure different. EAHE was not recommended, considering the integrated performance and the distribution of condensate water.

Figure 19. Mass fraction of H2O in the outlet vent with different supply types. Figure 19. Mass fraction of H2O in the outlet vent with different supply types. 5. Conclusions Consequently,To reduce energy the integrated consumption, performance the earth increased to air heat as exchangerthe diameter (EAHE) of the wasparallel widely pipesutilized increased, to heat and or the cool amount passive of buildings condensa andtion greenhouses. water decreased However, as the condensation diameter of may the ap- parallelpear pipes in the increased. EAHE when It was the relativebetter to humanity choose the (RH) larger of airdiameter is high. of In parallel this paper, pipes the when conden- the diametersation phenomenon of the main in pipe the EAHEwas constant. was displayed. Due to the Meanwhile, difference the in supply influence type, of condensation the mass fractionon the of integratedH2O in each performance pipe distribution of EAHE had was a sign studied.ificant Itdifference. was shown The that: L-type structure EAHE1. obtainedThe uniformity the best integrated performance performanc of the RHe and in each relatively parallel uniform pipe deteriorated distribution. with The the Z-type structureincrease EAHE in the RHwas inlet not air.recommended, The condensation considering phenomenon the integrated occurred performance easily in the last and the distributionpipe from the of perspectivecondensate ofwater. the flow direction, when the earth to air heat exchanger was the U-type structure. 5. Conclusions2. The condensation had few effects on the airflow distribution uniformity of the EAHE. However, it had a significant effect on the thermal performance of the EAHE. The integrated performance of the EAHE declined by 7.9% when the wet air condensed in the pipes. 3. The higher inlet air temperature and volume flow rate resulted in more non-uniform distributions of RH. Thus, the possibility of condensation increased. 4. When the diameter of the main pipe was constant, decreasing the diameter of the parallel pipe would decrease the integrated performance of the EAHE by 44% and increase the amount of condensation water. Considering the integrated performance and the distribution of condensation water, the performance of the Z-type structure EAHE was worst. The integrated performance of the L-type structure EAHE was optimal. These results may have certain guidance functions for the design of earth to air heat exchangers. Moreover, they could help avoid condensation in the EAHE in greenhouses. In future works, the greenhouse model will be established, and then the results of this paper would be considered as the boundary conditions for the greenhouse model. Based on the greenhouse model, the effect of EAHE performance on the temperature and humidity distribution in greenhouses would be investigated.

Author Contributions: Writing—original draft preparation, D.Q.; writing—review and editing, D.Q. and C.Z.; investigation, D.Q., S.L. and R.C.; supervision, D.Q. and A.L. All authors have read and agreed to the published version of the manuscript. Energies 2021, 14, 1368 16 of 18

Funding: This research was funded by “National Natural Science Foundation of China, grant number 51908444” and “Scientific Research Program funded by the Shaanxi Provincial Education Department, grant number 19JK0473” and “National Natural Science Foundation of China, grant number 51976144”. Conflicts of Interest: The authors declare no conflict of interest.

Abbreviations

EAHE Earth to air heat exchanger RH Relativity humidity hf Film height → Vl Mean film velocity ρl Liquid density ∇s The surface gradient operator . ms The mass source per unit wall area PL Pressure of air on the wall → g The component of gravity parallel to the wall →τ τ f s Shear stress at gas-liquid interface vl The kinematic viscosity of the water film → qs Pressure change caused by the water droplets or the separation of water film cp Specific heat capacity . qimp Source term due to liquid impingement from the bulk flow to the wall Tf Average film temperature Ts Film surface temperature Tw Wall temperature k f Thermal conductivity of wall film L(Ts) Latent heat associated with the phase change . mevap Mass vaporization or condensation rate Ω Airflow division uniformity coefficient . Vi The volume flow rate in each pipe of EAHE . Va The average volume flow rate n Number of parallel pipes θ The temperature extraction efficiency Tout The outlet temperature of EAHE Tin The inlet temperature of EAHE Tsoil The soil temperature in the far-field η The integrated evaluation factor f Friction factor ∆p The pressure drop between the inlet and outlet ρf The density of air uf Velocity of air h Overall heat transfer coefficient of EAHE Q Heat transfer rate m Mass flow rate Hin The enthalpy of the inlet air Hout The enthalpy of the outlet air ∆Tm Logarithmic mean temperature differences between soil and air

References 1. Akeiber, H.; Nejat, P.; Majid, M.Z.A.; Wahid, M.A.; Jomehzadeh, F.; Famileh, I.Z.; Calautit, J.K.; Hughes, B.R.; Zaki, S.A. A review on phase change material (PCM) for sustainable passive cooling in building envelopes. Renew. Sustain. Energy Rev. 2016, 60, 1470–1497. [CrossRef] 2. Yin, X.; Cao, F.; Wang, J.; Li, M.; Wang, X. Investigations on optimal discharge pressure in CO2 heat pumps using the GMDH and PSO-BP type neural network—Part A: Theoretical modeling. Int. J. Refrig. 2019, 106, 549–557. [CrossRef] 3. Qi, D.; Pu, L.; Ma, Z.; Xia, L.; Li, Y. Effects of ground heat exchangers with different connection conﬁgurations on the heating performance of GSHP systems. Geothermics 2019, 80, 20–30. [CrossRef] Energies 2021, 14, 1368 17 of 18

4. Dabaieh, M.; Serageldin, A.A. Earth air heat exchanger, Trombe wall and green wall for passive heating and cooling in premium passive refugee house in Sweden. Energy Convers. Manag. 2020, 209, 112555. [CrossRef] 5. Congedo, P.M.; Baglivo, C.; Bonuso, S.; D’Agostino, D. Numerical and experimental analysis of the energy performance of an air-source heat pump (ASHP) coupled with a horizontal earth-to-air heat exchanger (EAHX) in different climates. Geothermics 2020, 87, 101845. [CrossRef] 6. Bonuso, S.; Panico, S.; Baglivo, C.; Mazzeo, D.; Matera, N.; Congedo, P.M.; Oliveti, G. Dynamic analysis of the natural and mechanical ventilation of a solar greenhouse by coupling Controlled Mechanical Ventilation (CMV) with an Earth-to-Air Heat Exchanger (EAHX). Energies 2020, 13, 3676. [CrossRef] 7. Gomat, L.J.P.; Motoula, S.M.E.; M’Passi-Mabiala, B. An analytical method to evaluate the impact of vertical part of an earth-air heat exchanger on the whole system. Renew. Energy 2020, 162, 1005–1016. [CrossRef] 8. Lekhal, M.C.; Benzaama, M.H.; Kindinis, A.; Mokhtari, A.M.; Belarbi, R. Effect of geo-climatic conditions and pipe material on heating performance of earth-air heat exchangers. Renew. Energy 2021, 163, 22–40. [CrossRef] 9. Zajch, A.; Gough, W.A. Seasonal sensitivity to atmospheric and ground surface temperature changes of an open earth-air heat exchanger in Canadian climates. Geothermics 2021, 89, 101914. [CrossRef] 10. Zajch, A.; Gough, W.A.; Yoon, G. Influence of daily temperature behavior on earth-air heat exchangers: A case study from Aichi, Japan. City Environ. Interact. 2020, 8, 100054. [CrossRef] 11. D’Agostino, D.; Esposito, F.; Greco, A.; Masselli, C.; Minichiello, F. Parametric analysis on an Earth-to-Air Heat exchanger employed in an air conditioning system. Energies 2020, 13, 2925. [CrossRef] 12. D’Agostino, D.; Greco, A.; Masselli, C.; Minichiello, F. The employment of an earth-to-air heat exchanger as pre-treating unit of an air conditioning system for energy saving: A comparison among different worldwide climatic zones. Energy Build. 2020, 229, 110517. [CrossRef][PubMed] 13. Rosa, N.; Soares, N.; Costa, J.; Santos, P.; Gervásio, H. Assessment of an earth-air heat exchanger (EAHE) system for residential buildings in warm-summer Mediterranean climate. Sustain. Energy Technol. Assess. 2020, 38, 100649. [CrossRef] 14. Chiesa, G.; Zajch, A. Contrasting climate-based approaches and building simulations for the investigation of Earth-to-air Heat Exchanger (EAHE) cooling sensitivity to building dimensions and future climate scenarios in North America. Energy Build. 2020, 227, 110410. [CrossRef] 15. Li, K.; Xue, W.; Mao, H.; Chen, X.; Jiang, H.; Tan, G. Optimizing the 3d distributed climate inside greenhouses using multi-objective optimization algorithms and computer fluid dynamics. Energies 2019, 12, 2873. [CrossRef] 16. Guo, J.; Liu, Y.; Lü, E. Numerical simulation of temperature decrease in greenhouses with summer water-sprinkling roof. Energies 2019, 12, 2435. [CrossRef] 17. Ghoulem, M.; El Moueddeb, K.; Nehdi, E.; Zhong, F.; Calautit, J. Design of a Passive Downdraught Evaporative Cooling Windcatcher (PDEC-WC) system for greenhouses in hot climates. Energies 2020, 13, 2934. [CrossRef] 18. Sakhri, N.; Menni, Y.; Ameur, H. Experimental investigation of the performance of earth-to-air heat exchangers in arid environments. J. Arid Environ. 2020, 180, 104215. [CrossRef] 19. Wei, H.; Yang, D.; Wang, J.; Du, J. Field experiments on the cooling capability of earth-to-air heat exchangers in hot and humid climate. Appl. Energy 2020, 276, 115493. [CrossRef] 20. Cucumo, M.; Cucumo, S.; Montoro, L.; Vulcano, A. A one-dimensional transient analytical model for earth-to-air heat exchangers, taking into account condensation phenomena and thermal perturbation from the upper free surface as well as around the buried pipes. Int. J. Heat Mass Transf. 2008, 51, 506–516. [CrossRef] 21. Chardome, G.; Feldheim, V. Heat transfer and condensation in an earth-air heat exchanger: 2D/3D numerical modeling validated by experimental measurements. Energy Build. 2019, 205, 109532. [CrossRef] 22. Niu, F.; Yu, Y.; Yu, D.; Li, H. Heat and mass transfer performance analysis and cooling capacity prediction of earth to air heat exchanger. Appl. Energy 2015, 137, 211–221. [CrossRef] 23. Gan, G. Dynamic interactions between the ground heat exchanger and environments in earth–air tunnel ventilation of buildings. Energy Build. 2014, 85, 12–22. [CrossRef] 24. Gao, X.; Zhang, Z.; Xiao, Y. Modelling and thermo-hygrometric performance study of an underground chamber with a long vertical earth-air heat exchanger system. Appl. Therm. Eng. 2020, 180, 115773. [CrossRef] 25. Gao, X.; Qu, Y.; Xiao, Y.; Xiangkui, G.; Yongtong, Q.; Yimin, X. A numerical method for cooling and dehumidifying process of air flowing through a deeply buried underground tunnel with unsaturated condensation model. Appl. Therm. Eng. 2019, 159, 113891. [CrossRef] 26. Estrada, E.; Labat, M.; Lorente, S.; Rocha, L.A. The impact of latent heat exchanges on the design of earth air heat exchangers. Appl. Therm. Eng. 2018, 129, 306–317. [CrossRef] 27. Liu, Q.; Du, Z.; Fan, Y. Heat and mass transfer behavior prediction and thermal performance analysis of Earth-to-Air Heat Exchanger by finite volume method. Energies 2018, 11, 1542. [CrossRef] 28. Greco, A.; Masselli, C. The optimization of the thermal performances of an Earth to Air Heat Exchanger for an air condi-tioning system: A numerical study. Energies 2020, 13, 6414. [CrossRef] 29. Mongkon, S.; Thepa, S.; Namprakai, P.; Pratinthong, N. Cooling performance assessment of horizontal earth tube system and effect on planting in tropical greenhouse. Energy Convers. Manag. 2014, 78, 225–236. [CrossRef] Energies 2021, 14, 1368 18 of 18

30. Qi, D.; Li, A.; Li, S.; Zhao, C. Comparative analysis of earth to air heat exchanger configurations based on uniformity and thermal performance. Appl. Therm. Eng. 2021, 183, 116152. [CrossRef] 31. Kepes Rodrigues, M.; da Silva Brum, R.; Vaz, J.; Oliveira Rocha, LA.; Domingues dos Santos, E.; Isoldi, LA. Numerical investigation about the improvement of the thermal potential of an Earth-Air Heat Exchanger (EAHE) employing the Constructal Design method. Renew. Energy 2015, 80, 538–551. [CrossRef] 32. Zschaeck, G.; Frank, T.; Burns, A. CFD modelling and validation of wall condensation in the presence of non-condensable gases. Nucl. Eng. Des. 2014, 279, 137–146. [CrossRef] 33. Li, Y.; Guo, T.; Chang, H. Numerical simulation of 3D hot-air anti-icing chamber based on Eulerian wall film model. J. Beijing Univ. Aeronaut. Astronaut. 2018, 44, 959–966. 34. Amanowicz, L. Influence of geometrical parameters on the flow characteristics of multi-pipe earth-to-air heat exchangers— experimental and CFD investigations. Appl. Energy 2018, 226, 849–861. [CrossRef] 35. Zhao, Y.; Li, R.; Ji, C.; Huan, C.; Zhang, B.; Liu, L. Parametric study and design of an earth-air heat exchanger using model experiment for memorial heating and cooling. Appl. Therm. Eng. 2019, 148, 838–845. [CrossRef] 36. Pu, L.; Qi, D.; Li, K.; Tan, H.; Li, Y. Simulation study on the thermal performance of vertical U-tube heat exchangers for ground source heat pump system. Appl. Therm. Eng. 2015, 79, 202–213. [CrossRef]