Heat and mass transfer performance analysis and cooling capacity prediction of earth to air heat exchanger Fuxin Niu a , Yuebin Yu a,⇑ , Daihong Yu b,⇑ , Haorong Li a a Durham School of Architectural Engineering and Construction College of Engineering, University of Nebraska-Lincoln, Omaha, NE, USA b Architectural Engineering Department, Lawrence Technological University, Southfield, MI, USA highlights We investigated the performance and deduced a regression model for an EAHE. A one-dimensional steady-state control volume model was developed and applied. The model considered both heat and mass transfer in the tube and was calibrated. Six structural and operation factors were analyzed with the validated model. A polynomial regression model with high accuracy was developed. article info Article history: Received 21 March 2014 Received in revised form 21 September 2014 Accepted 1 October 2014 Available online 24 October 2014 Keywords: Earth to air heat exchanger Sensible cooling capacity Latent cooling capacity Fast regression model abstract A great portion of the primary energy is consumed by space heating and cooling in buildings. The need for utilizing more renewable energy in the building sector remains critical for ensuring the energy and environment sustainability. Geothermal energy is one of the renewable energy sources that we have an easy access to for supplying low-grade thermal energy with a low impact on the environment. The methods of utilizing geothermal energy for buildings include such as ground source heat pumps and earth to air heat exchangers (EAHEs). In this paper we presented the comprehensive performance anal- ysis and deduced an easy-to-apply regression model for predicting the cooling capacity of an EAHE. A one-dimensional steady-state control volume model was developed and applied to simulate the perfor- mance of the EAHE. It couples both heat and mass transfer between the air and the tube. The model was calibrated by comparing against the experimental data from an existing renewable energy testing facility. After the calibration, six factors, namely the air temperature, the air relative humidity, the air velocity at the inlet of EAHE, the tube surface temperature, and the tube length and diameter on the performance were analyzed using the calibrated model. The polynomial regression models for predicting the cooling capacities including total, sensible and latent cooling capacity with high accuracy were obtained. The easy-to-apply formulas can be of great use in the design and application of EAHEs. Ó 2014 Elsevier Ltd. All rights reserved. 1. Introduction Geothermal energy is a huge renewable energy source that can be easily accessed for space heating and cooling purposes. The utilizing styles and exploring methods are various. Geothermal electricity, ground source heat pump, earth to air heat exchanger (EAHE), etc. are the main application measures. Among them, an EAHE has the advantages of simple system, easy implementation and low operation cost [1]. An EAHE system is a thermal system with tubes buried in the ground which can extract the thermal energy from the soil into the air for heating and cooling the space in winter and summer, respectively. The performance of an EAHE has been researched by many researchers [2–6]. To understand the heat and mass transfer between the air and the soil of an EAHE, analytical methods such as using Green’s func- tion and through a simplified superposition analysis and numerical models by differencing the control equations were generally applied. For instance, Cucumo et al. proposed a one-dimensional transient model and obtained the analytical solutions after simpli- fication for an EAHE [7]. Both mass transfer and thermal distur- bance from the ground surface were considered. The results could be used to predict the temperature of the fluid in the tube and of the soil near the tube. The solution was also evaluated by http://dx.doi.org/10.1016/j.apenergy.2014.10.008 0306-2619/Ó 2014 Elsevier Ltd. All rights reserved. ⇑ Corresponding authors. Tel.: +1 402 554 2082. E-mail addresses: [email protected](Y. Yu), [email protected](D. Yu). Applied Energy 137 (2015) 211–221 Contents lists available at ScienceDirect Applied Energy journal homepage: www.elsevier.com/locate/apenergy
Fuxin Niu a, Yuebin Yu a,⇑, Daihong Yu b,⇑, Haorong Li a
a Durham School of Architectural Engineering and Construction College of Engineering, University of Nebraska-Lincoln, Omaha, NE, USAb Architectural Engineering Department, Lawrence Technological University, Southfield, MI, USA
h i g h l i g h t s
�We investigated the performance and deduced a regression model for an EAHE.� A one-dimensional steady-state control volume model was developed and applied.� The model considered both heat and mass transfer in the tube and was calibrated.� Six structural and operation factors were analyzed with the validated model.� A polynomial regression model with high accuracy was developed.
a r t i c l e i n f o
Article history:Received 21 March 2014Received in revised form 21 September2014Accepted 1 October 2014Available online 24 October 2014
Keywords:Earth to air heat exchangerSensible cooling capacityLatent cooling capacityFast regression model
a b s t r a c t
A great portion of the primary energy is consumed by space heating and cooling in buildings. The need forutilizing more renewable energy in the building sector remains critical for ensuring the energy andenvironment sustainability. Geothermal energy is one of the renewable energy sources that we havean easy access to for supplying low-grade thermal energy with a low impact on the environment. Themethods of utilizing geothermal energy for buildings include such as ground source heat pumps andearth to air heat exchangers (EAHEs). In this paper we presented the comprehensive performance anal-ysis and deduced an easy-to-apply regression model for predicting the cooling capacity of an EAHE. Aone-dimensional steady-state control volume model was developed and applied to simulate the perfor-mance of the EAHE. It couples both heat and mass transfer between the air and the tube. The model wascalibrated by comparing against the experimental data from an existing renewable energy testing facility.After the calibration, six factors, namely the air temperature, the air relative humidity, the air velocity atthe inlet of EAHE, the tube surface temperature, and the tube length and diameter on the performancewere analyzed using the calibrated model. The polynomial regression models for predicting the coolingcapacities including total, sensible and latent cooling capacity with high accuracy were obtained. Theeasy-to-apply formulas can be of great use in the design and application of EAHEs.
� 2014 Elsevier Ltd. All rights reserved.
1. Introduction
Geothermal energy is a huge renewable energy source that canbe easily accessed for space heating and cooling purposes. Theutilizing styles and exploring methods are various. Geothermalelectricity, ground source heat pump, earth to air heat exchanger(EAHE), etc. are the main application measures. Among them, anEAHE has the advantages of simple system, easy implementationand low operation cost [1]. An EAHE system is a thermal systemwith tubes buried in the ground which can extract the thermal
energy from the soil into the air for heating and cooling the spacein winter and summer, respectively. The performance of an EAHEhas been researched by many researchers [2–6].
To understand the heat and mass transfer between the air andthe soil of an EAHE, analytical methods such as using Green’s func-tion and through a simplified superposition analysis and numericalmodels by differencing the control equations were generallyapplied. For instance, Cucumo et al. proposed a one-dimensionaltransient model and obtained the analytical solutions after simpli-fication for an EAHE [7]. Both mass transfer and thermal distur-bance from the ground surface were considered. The resultscould be used to predict the temperature of the fluid in the tubeand of the soil near the tube. The solution was also evaluated by
Roman letter symbolsa coefficientf enhancement coefficienth enthalpy (kJ/kg)hc convectional heat transfer coefficient (W/m2 K)m mass flow rate of air flow (kg/s)t time (h)u coefficientw humidity ratio (kg/kg)z depth (m)A area (m2)B amplitude (�C)C specific heat (J/kg K)D diameter (m)L length of tube (m)N node numberP perimeter (m)Q cooling capacity (kW)T temperature (�C)
Subscripts/acronymsa airi, n counter
l latents soil, sensiblesat saturationt totalEAHE earth to air heat exchangerMRE mean relative errorNu Nusselt numberPr Prandtl numberRe Reynolds numberRH relative humiditySh Sherwood number
Greek lettersa thermal diffusivity (m2/s)b convective mass transfer coefficient (m/s)k heat conductivity (W/m K)d residualx diffusion coefficient (m2/s)h temperature (�C)q specific density (kg/m3)
212 F. Niu et al. / Applied Energy 137 (2015) 211–221
using reference experimental data from the literature. Hollmullerpresented an analytical solution for the heat diffusion of a cylindri-cal EAHE with adiabatic or isothermal boundary conditions [8]. Theairflow with harmonic temperature signal at input was assumedconstant. The analytical results were validated by numerical vali-dation on hourly data over one year. Based on that model, it hasbeen shown that depending on its thickness, the soil layer couldinduce either an amplitude-dampening or phase-shifting regimes.Paepe and Janssens used a simplified one-dimensional analyticalmethod to evaluate the various design parameters including tubelength, tube diameter and number of tubes in parallel of an EAHEsystem. The study was to support the selection of the characteristicdimensions of an EAHE during the design period, thereforeoptimize the hydraulic and thermal effectiveness [9].
In addition to the analytical solution on just an EAHE, manyresearchers carried out the numerical model research of an EAHEcoupled with either a building or mechanical devices. Kumaret al. built a numerical model to predict the energy conservationpotential of an EAHE system and passive thermal performance ofbuildings [10]. The model was improved upon previous studiesby incorporating effects of ground temperature gradient, surfaceconditions, moisture content and various design aspects of anearth–air–tunnel. The model was validated against experimentaldata of a similar tunnel in Mathura (India), and was then used topredict the tunnel outlet temperature for various parameters suchas humidity variations of circulating air, airflow rate and ambientair temperature. Using a numerical model, M. Bojic evaluated thetechnical and economic performance of an EAHE coupled to abuilding that uses 100% fresh air as heating or cooling mediumduring winter and summer [11]. It was found that the use of theEAHE covered a portion of the daily building needs for space ther-mal conditioning. A computation fluid dynamic simulation of anEAHE applied to a hybrid ventilation building in Grong (Norway)was conducted and the results were then evaluated by using fieldmeasurements [12]. The convective heat transfer coefficient,obtained from the simulation, showed that the correlations signif-icantly underestimated the heat convection in the EAHE.
Besides modeling and simulation, field experiments are still ofgreat importance in order to evaluate the thermal and mass trans-fer performance of EAHEs. For example, Ghosal carried out anexperimental research on an EAHE [13]. The experiment was con-ducted for many typical clear sunny days in a year for an EAHE 1 munder the ground surface. The room air temperature was mainlymeasured and compared for the operation with and without theEAHE. About 3–4 �C lower in summer and 6–7 �C degree higherin winter were found when the EAHE is in operation. Recently, Liet al. [6] and Yu et al. [14] conducted a series of tests on an EAHEsystem coupled with a building and a solar chimney. The soil tem-perature at different levels under the ground, the air temperaturesand humidity in the EAHE, and the outdoor air temperature andhumidity were continuously measured for years. The coolingcapacity in both passive driven mode and active driven model wereanalyzed in terms of the air flow rates and outdoor air conditions. Itwas found that the enhanced EAHE system could maintain theindoor thermal conditions in a comfortable range without a fan.However, a performance drop of the EAHE system due to soilsaturation in both modes was also identified.
From the literature review, we found that the majority ofsimulation and modeling research focus on only very limited EAHEconfigurations. Few efforts were paid to the comprehensive evalu-ation of an EAHE with different design and operation parameters.In addition, most research ignored the latent heat transfer whichaffects the humidity load of buildings. Above all, a practical ques-tion of how to easily and accurately apply the simulation researchresults to real applications for EAHE generalization remainsunsolved. In this paper a numerical model considered both sensibleand latent heat transfer was used. The effect of main parameters ofair temperature, relative humidity, air velocity at the inlet of EAHE,surface temperature, length and diameter of EAHE on the perfor-mance were analyzed. The model was calibrated by comparingthe simulated results against the experimental data trended froman existing facility. With the calibrated model, general formulasfor accurately predicting the sensible, latent and total coolingcapacity of EAHEs were achieved. The identified formulas are
F. Niu et al. / Applied Energy 137 (2015) 211–221 213
easy-to-apply and deemed to provide great helps to engineers forEAHE optimal design considering both sensible and latent heattransfer.
2. Mathematic modeling of EAHE
2.1. Underground soil temperature model
The underground soil temperature was one of main parametersin the process of EAHE design. The determinant parameter for theevaluation of the ground cooling and heating potential is theunderground soil temperature at various depths. Ideally, this valueshould be measured onsite. However, only a few weather stationsperform measurements of ground surface temperature, while thenumber of the stations where measurements at various depthswere performed was even smaller. This is why algorithms for thecalculation of the underground soil temperature at various depthshave been developed. For homogeneous soil of constant thermaldiffusivity, the underground soil temperature at any depth z andtime t is shown as follows [15]:
Tðz;tÞ¼ Tm�Bs
� exp �zp
365as
� �1=2" #
cos2p365
� �t� t0�
z2
365pas
� �1=2 !" #
ð1Þ
where Tm is the average soil temperature, Bs is the amplitude of thesoil surface temperature variation, t0 is the phase constant of thesoil surface, and as is the soil thermal diffusivity.
2.2. Earth to air heat exchanger model
Following assumptions were made during the development ofthe mathematical model:
(1) The EAHE is of uniform cross-section area and thermalcharacteristics.
(2) The soil properties are isotropic.(3) There exists a perfect contact between the tube and the soil.(4) Thermal resistance due to tube thickness is negligible.(5) Air is incompressible and its thermal propertied are
constant.(6) Air is well mixed in the tube with no temperature
stratification.
Fig. 1. Control volume method and energy balance in each volume.
Control volume method was used to establish an energybalance for each micro-volume. Similar model was developed forheat transfer of an EAHE tube in [16]. Fig. 1 shows the EAHE tubemesh along the length and the energy balance existing within indi-vidual small control volume. In order to comprehensively analyzethe performance of EAHE mass transfer was also considered.Therefore, the progress of heat transfer between air and earthwas divided into two parts including sensible heat transfer andlatent heat transfer.
2.2.1. Heat transferFor each control volume, the energy governing equation with no
condensation is shown as follows [9]:
m � CadTa ¼ P � hcðTs � TaÞdx ð2Þ
As a homogeneous ordinary differential equation, the air tem-perature in each small control volume can be solved analytically.After reorganizing the terms, it becomes:
adhdxþ h ¼ 0 ð3Þ
where h ¼ Ta � Ts; a ¼ m�CaP�hc
The heat transfer coefficient, hc, between the air and the surfaceof the tube depends on flow properties, dimensions of the tube andthermal conductivity of the air.
hc ¼Nu � ka
Dð4Þ
Within the equation, Nu is Nusselt number; ka is thermal con-ductivity of air; they can be calculated as follows [17,18],respectively:
Nu ¼ 0:023Re0:8Pr0:4ðheatingÞNu ¼ 0:023Re0:8Pr0:3ðcoolingÞ
ð5Þ
ka ¼ 0:02442þ ð10�4ð0:6992TaÞÞ ð6Þ
With the key parameters, the above ordinary differential Eq. (3)can be solved as follows for each control volume:
TaðxÞ ¼ Ts � ðTs � T0Þ expð�x=aÞ ð7Þ
With the air temperature within each control volume, Eq (1)can be differenced as:
m � CaðTn�1 � TnÞ ¼ A � f � hcðTa � TsÞ ð8Þ
To ensure the simulation accuracy, in this study, each elementwas further divided into i sub-elements. Therefore, the representa-tive air temperature in each element can be obtained by theaveraging the air temperatures in the included i sub-elements:
Ta ¼P
iðTs � ðTs � Tn�1Þ expð�xi=aÞÞi
ð9Þ
The air temperature at the various locations along the meshedtube, from the inlet to the outlet, is numerically achieved:
Tn ¼ Tn�1 � uP
i Ts � ðTs � Tn�1Þ expð�xi=aÞð Þi
� Ts
� �ð10Þ
where u ¼ A�f �hcm�Ca
is a combined coefficient of the model.
2.2.2. Integrated heat and mass transferWhen the air temperature in a control volume drops to the cor-
responding dew point, condensation could happen. The masstransfer governing equation can be established as follows wherethe driving force for mass transfer between the air and EAHEsurface is the air humidity ratio and the saturated humidity ratiocorresponding to the EAHE surface temperature [19]:
Start
Input structure and initial parameters
Divide the tube into control volumes
x=0
Calculate convective heat and mass transfer coefficient
Calculate the average air temperature in each control volume
Condensation
Apply both heat and mass balance
Apply only heat balance
x=L
Output the result
x=x+Δx
No
Yes
Yes No
Adjust unknown parameters
Comparing experimental and simulated result
Error >δYes
The end
No
(For
cal
ibra
tion)
Fig. 2. The simulation and calibration flowchart.
Table 1Coefficients of the underground soil temperature.
Fig. 3. The underground soil temperature of experiment and prediction withdifferent depths.
214 F. Niu et al. / Applied Energy 137 (2015) 211–221
mðwn�1 �wnÞ ¼ A � b � qaðwa �wsat;sÞ ð11Þ
where b ¼ Sh�xD : Sh is Sherwood number; x is diffusion coefficient.
Coupling the heat and mass transfer balance for each controlvolume, the total governing equation is achieved:
m � CaðTn�1 � TnÞ þmðwn�1 �wnÞhfg ¼ A � f � hcðTa � TsÞ ð12Þ
Eqs. (2)–(12) constitute the model for the heat and mass transferwith the EAHE.
2.3. Simulation program and calibration of EAHE
The simulation program was developed in Matlab 8. Fig. 2shows the simulation and calibration flowchart. In the process ofsimulation, the calculation proceeds along with length step fromthe inlet to the outlet of tube. The surface temperature of the EAHEtube is considered constant for a given short period by using theundisturbed soil temperature at the depth of the buried tube. Bycomparing the air temperature and the corresponding dew pointtemperature of the air in each control volume, the programdetermines whether condensation should be concluded or not.Accordingly, different calculation models for sensible heat transferonly and both mass and heat transfer would be selected by the pro-gram. In the real testing based on the existing facility, the param-eters in Eqs. (2), (7) and (12) including the dimensions of EAHE, theair temperature and relative humidity at the inlet, the air flow ratecould be measured or obtained directly. The only unknown param-eters needed in the model are the real heat transfer coefficient andinner surface temperature of the tube. Two-step calibration wasused in this study. First, the soil model was validated in Section 3.1to accurately predict the soil temperature; second, the EAHE modelwas calibrated with an optimal method to obtain the heat transferenhancement coefficient and the surface temperature of the EAHE.The tube surface temperature was adjusted in the small range of
the predicted soil temperature. The simulated supply air tempera-ture was compared against the measured data to evaluate theaccuracy of the model and calibrate it. The mean relative error(MRE) between the predicted supply air temperature and the mea-sured supply air temperature was employed as the indicator of themodel accuracy. MRE equal and less than 0.09 was selected as theacceptable threshold for this calibration.
3. Model calibration and validation
Based on the existing facility, the field testing data was used toverify the model. An existing test facility is located in Omaha inU.S. for the coupled EAHE and solar chimney thermal system. Aculvert steel EAHE with 57 m in length and 0.45 m in diameterwas buried at a depth of about 3 m underground. The test facilitybuilding is a one-story building with external dimensions of19.4 m long, 4.9 m wide, and 3 m high. It includes a main testingroom about 15.2 m long, 4.52 m wide and 2.4 m high.
3.1. Validation of underground soil temperature model
Based on the meteorological data and field test the under-ground soil temperature model in the location of facility wasobtained with parameters as shown in Table 1. The average annualtemperature of the soil surface was 11.42 �C, amplitude of surfacetemperature variation was 12.42 �C and a phase constant was 15 h.Underground soil temperatures of two depths with 1.53 m and2.90 m were measured and simulated. The comparison betweenthe experimental value and simulated value is presented inFig. 3. As seen from the figure the tested and simulated valuematched very well. It indicates that the equation of undergroundsoil temperature can be used to design EAHE in the location ofOmaha.
3.2. Calibration of EAHE model
A long term experiment testing was carried out throughout thewhole year of 2008 and 2009 using the mentioned existing facility.
F. Niu et al. / Applied Energy 137 (2015) 211–221 215
The comprehensive performance of EAHE including winter modeand summer mode, condensation condition and non-condensationcondition, natural ventilation and forced ventilation were obtainedand analyzed clearly [6,14]. Based on the measurement data andthe simulated results in the cooling season, the EAHE model canbe calibrated. In order to clearly compare the experimental andsimulated data from the calibrated model, only one day’s collecteddata of September 10, 2008 was used, as shown in Figs. 4(a) and5(a). The error analysis of model prediction based on data of thesummer season was presented in Figs. 4(b) and 5(b). Fig. 4(a)shows the experimental and simulated supply air temperature
Experimental air humidity ratio (kg/kg) Simulated air humidity ratio (kg/kg) Outdoor air humidity ratio (kg/kg)
Time
Supp
ly a
ir h
umid
ity ra
tio (k
g/kg
)
0.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0.016
Out
door
air
hum
idity
ratio
(kg/
kg)
(a)
Fig. 5. Comparison of the supply air humidity ratio
0 1284 16 20 24 28 32 36 40 4410
12
14
16
18
20
22
24
26
28
30
Air
tem
pera
ture
(o C
)
EAHE length (m)
Experimental air temperature Simulated air temperature
(a)
Fig. 6. Comparison of the air temperature along
profile of the EAHE. The two supply air temperature curves matchvery well. The supply air temperature was kept at about 15 �C atthe beginning and then began to rise with the increasing of theoutdoor air temperature. Fig. 4(b) indicates the matching level ofsimulated and experimental results. The relative and absolute errorindexes of mean relative error (MRE) and mean square error (MSE)were introduced to analyze the reliability of the mathematic modeland program. The MRE of the supply air temperature during thesummer season is only 4.6% and the MSE is 0.63 �C. Fig. 5(a) showsthe supply air humidity ratio for the calibration between experi-ment and simulation results. The relative error index of the MRE
10 12 14 16 18 20 2210
12
14
16
18
20
22
MSE=0.63 oC
MRE=4.6%
Sim
ulat
ed su
pply
air
tem
pera
ture
(o C
) o Experimental supply air temperature ( C)
(b)
of EAHE (a) one day and (b) summer season.
0.006 0.008 0.010 0.012 0.014 0.016 0.010.004
0.006
0.008
0.010
0.012
0.014
0.016
0.018
MSE=0.000003 kg/kgMRE=8.7%
Sim
ulat
ed su
pply
air
hum
idity
ratio
(kg/
kg)
Experimental supply air humidity ratio (kg/kg)
(b)
of EAHE (a) one day and (b) summer season.
10 12 14 16 18 20 22 24 26 28 3010
12
14
16
18
20
22
24
26
28
30
MSE=0.45 oCMRE=3.3%
Sim
ulat
ed a
ir te
mpe
ratu
re (o C
)
oExperimental air temperature ( C)
(b)
with the length of EAHE (existing facility).
0 510
12
14
16
18
20
22
24
26
28
Experimental air temperature (reference) Simulated air temperature
Fig. 7. Comparison of the air temperature along with the length of EAHE (reference).
216 F. Niu et al. / Applied Energy 137 (2015) 211–221
of supply air humidity ratio between experiment and simulationresults is 8.7%. The absolute error index of MSE is just only0.000003 kg/kg.
The above comparison is only about the supply air condition atthe outlet of this EAHE. Further, the calibrated model was used tocompare the predicted air temperature along with the length ofEAHE against the experiment and reference results. Fig. 6 showsthe air temperature along with the length of EAHE between thesimulated and experiment data. Fig. 7 shows the comparisonbetween Benkert’s testing results and our simulation [13]. As seenfrom both figures the air temperature fell quickly along with thelength of EAHE due to the larger temperature difference at the for-mer segment. The air temperature dropped slowly close to the out-let of the EAHE. The trend is clearly shown for the experiment,reference and simulation data. Fig. 6(a) indicates that the simu-lated air temperature and the measured air temperature has a littlebig error in the front part of the tube. The possible reason is that, inthe experiment, there was no well air mixing especially for theentry part of the EAHE. In addition, the entry part was greatlyaffected by the outdoor environment, which could result in theimprecise measurement data. Therefore, the experimental data atthe entry part were ignored in the process of the error analysis.The MRE of air temperature along the length of tube is 3.3%, andthe MSE is 0.45 �C. The MRE between the reference data from[13] and simulation results is 3.2%, and the MSE is 0.37 �C. Theerror is acceptable for engineering applications. According to theabove comparison and error analysis of simulated and experimen-tal results (existing facility testing and reference data), the mathe-matic model and simulation program were validated credibly andaccurately.
4. Parametric performance analysis
A comprehensive performance analysis of an EAHE could supplygreat help for the design and application of EAHE. With thecalibrated EAHE model considering the sensible and latent heat
Table 2Simulation conditions of all influence factors.
Conditions
Mode 1: Tin (�C) 34 32 30
Mode 2: RHin (%) 20 40 60
Mode 3: Vin (m/s) 0.5 1 1.5
Mode 4: Ts (�C) 8 10 12
Mode 5: D (m) 0.3 0.4 0.5
transfer, the effect of structural factors including the length anddiameter, operational factors including the air temperature andrelative humidity at the inlet of an EAHE, air velocity and surfacetemperature of tube on the performance were studied. Table 2shows the simulation conditions of all influencing factors. Thereare five calculation modes to analyze the effect of each factor onthe performance of EAHE. Five conditions of each mode wereselected to cover as much as possible the full range of all influenc-ing factors. The air temperature at the inlet of EAHE was selected inthe range of 26–34 �C. The air relative humidity at the inlet of EAHEwas selected from 20% to 90%, the air velocity from 0.5 m/s to2.5 m/s, the tube surface temperature from 8 �C to 16 �C and thetube diameter from 0.3 m to 0.7 m. The influence from the lengthof the EAHE is naturally included since the simulation providesthe results along the length.
4.1. Effect of the inlet air temperature
In Mode 1, the effect of the inlet air temperature on the perfor-mance of EAHE was analyzed. Fig. 8 shows the air temperature andhumidity ratio along with the length of EAHE under the differentinlet air temperature conditions. It can be seen from Fig. 8(a) thatthe air temperature in the forepart of the tube dropped faster thanthat of the end. At the inlet side, there was a big different betweenair temperature and the surface temperature of the tube. Therefore,the heat transfer is much stronger. When the inlet air temperaturewas 34 �C, the air temperature decline rate was the biggest. Therate decline with the inlet temperature of 26 �C was the lowest.Almost all of outlet air temperatures were near 15 �C when thetube surface temperature is 12 �C. If the length of tube was longenough, the air temperature at the outlet will get very close tothe surface temperature of tube. As seen from Fig. 8(b) the airhumidity ratio kept a constant value first and then began to reduce.When air humidity ratio began to decline, it meant that the airachieved the saturated state at that point, and water vapor beganto condense. The condensation points under the inlet air
Notes
28 26 RHin = 60; Vin = 1.5; Ts = 12; L = 70; D = 0.5
80 90 Tin = 30; Vin = 1.5; Ts = 12; L = 70; D = 0.5
2 2.5 Tin = 30; RHin = 60; Ts = 12; L = 70; D = 0.5
14 16 Tin = 30; RHin = 60; Vin = 1.5; L = 70; D = 0.5
0.6 0.7 Tin = 30; RHin = 60; Vin = 1.5; Ts = 12; L = 70
0 10 20 30 40 50 60 70
15
20
25
30
35
Tem
pera
ture
(o C
)
Length of EAHE (m)
Tin=34oCTin=32oCTin=30oCTin=28oCTin=26oC
0 10 20 30 40 50 60 700.008
0.010
0.012
0.014
0.016
0.018
0.020
0.022
Hum
idity
ratio
(kg/kg
)
Length of EAHE (m)
Tin=34 oCTin=32 oCTin=30 oCTin=28 oCTin=26 oC
(a) (b)
Fig. 8. Performance of EAHE under different inlet air temperature conditions.
F. Niu et al. / Applied Energy 137 (2015) 211–221 217
temperature of 34 �C, 32 �C, 30 �C, 28 �C and 26 �C with 60% rela-tive humidity ratio were 10 m, 11 m, 13 m, 15 m and 17.5 mrespectively. The air with high temperature had a high humidityratio, and declined faster than that of low temperature.
4.2. Effect of the inlet air relative humidity
In Mode 2, the effect of the inlet air relative humidity on theperformance of EAHE was analyzed. Fig. 9 shows the air tempera-ture and the humidity ratio along with the length of EAHE underthe different inlet air relative humidity conditions. As seen fromFig. 9(a), the air temperatures along with the length of EAHE underdifferent inlet air relative humidity conditions were almost thesame. All outlet air temperatures were about 14 �C. In fact, theair temperature was affected by the air relative humidity but onlyin a very little magnitude. In other word, the second term in Eq.(12) standing for the latent heat transfer process was much smallerthan the third term, which stands for the sensible heat transferprocess. It can be seen from Fig. 9(b) when the inlet air relativehumidity was 20%, the humidity ratio along with length of tubekept a constant value. There was no vapor condensation duringthe whole process. The results indicated that when the inlet airrelative humidity was low enough, no condensation along withthe length of tube occurred. In our case, the air relative humiditylimit was about 30%.
4.3. Effect of the air velocity
In Mode 3, the effect of the air velocity on the performance ofEAHE was investigated. Fig. 10 shows the air temperature and
0
15
20
25
30
Tem
pera
ture
(oC
)
Length of EAHE (m)
RHin=20% RHin=40% RHin=60% RHin=80% RHin=90%
10 20 30 40 50 60 70
(a)
Fig. 9. Performance of EAHE under differen
humidity ratio along with the length of EAHE under the differentair velocity conditions. When the air velocity was 0.5 m/s the airtemperature decreasing rate was the fastest. The smaller the airvelocity was, the faster the air temperature decreasing rate was,and the lower the outlet air temperature was. When the airvelocity was low, the time of air staying in the tube was long.Therefore, the heat transfer amount was also more than that ofhigh air velocity. As seen from Fig. 10(b) the air humidity ratio kepta same constant value first and then began to reduce. Condensationpoint under the low air velocity came out earlier than that of thehigh air velocity. The condensation points under the air velocityof 0.5, 1.0, 1.5, 2.0 and 2.5 m/s were 11, 12, 13, 13.5 and 14 m,respectively.
4.4. Effect of the tube surface temperature
In Mode 4, the effect of the tube surface temperature on theperformance of EAHE was analyzed. Fig. 11 shows the air temper-ature and humidity ratio along with the length of EAHE under thedifferent tube surface temperature conditions. As seen fromFig. 11(a), when the surface temperature of tube was much loweras 8 �C, the air temperature along with the length of EAHE reducedmore quickly. And the outlet air temperature under the low tubesurface temperature was lower than that of the high tube surfacetemperature. When the tube surface temperature was 8 �C, theoutlet air temperature was 11 �C. When the tube surface tempera-ture was 16 �C the outlet air temperature was 18 �C. As seen fromFig. 11(b), the air humidity ratio under the low surface tempera-ture of tube reached the saturated state earlier than that of highsurface temperature. In addition, the humidity ratio under the
Fig. 10. Performance of EAHE under the different air velocity conditions.
0
Length of EAHE (m)10 20 30 40 50 60 70
(a)
0
Length of EAHE (m)10 20 30 40 50 60 70
(b)
9
12
15
18
21
24
27
30
Tem
pera
ture
(o C)
Ts=8 oC Ts=10 oC Ts=12 oC Ts=14 oC Ts=16 oC
0.008
0.010
0.012
0.014
0.016
Ts=8 oC Ts=10 oC Ts=12 oC Ts=14 oC Ts=16 oC
Hum
idity
ratio
(kg/
kg)
Fig. 11. Performance of EAHE under the different tube surface temperature conditions.
218 F. Niu et al. / Applied Energy 137 (2015) 211–221
low surface temperature of tube declined faster than that of highsurface temperature.
4.5. Effect of the tube diameter
In Mode 5, the effect of the tube diameter on the performance ofEAHE was simulated. Fig. 12 shows the air temperature andhumidity ratio along with the length of EAHE under the differenttube diameter conditions. When the tube diameter was 0.3 m,the air temperature reduced the most quickly at the former seg-ment of EAHE. The air temperature under the large tube diametercondition reduced more slowly than that of the small tube diame-ter. The outlet air temperature under the tube diameter of 0.3 m
0
Length of EAHE (m)10 20 30 40 50 60 70
(a)
12
15
18
21
24
27
30
Tem
pera
ture
(o C
)
D=0.3 mD=0.4 mD=0.5 mD=0.6 mD=0.7 m
Fig. 12. Performance of EAHE under the
was 17 �C, and 13 �C under the tube diameter of 0.7 m. The humid-ity ratio had a similar trend with the air temperature in the phaseof saturated status. As seen from Fig. 12(b), the air humidity ratiowith the small tube diameter reached the saturated state earlierthan that of large diameter. And the humidity ratio under the smalltube diameter declined faster than that of a large diameter.
4.6. The cooling capacity of EAHE
Both the heat and mass transfer were considered in the mathe-matic modeling and simulation during the whole process. There-fore, the cooling capacity of EAHE including the sensible coolingcapacity, the latent cooling capacity and the total cooling capacity
0
Length of EAHE (m)10 20 30 40 50 60 70
(b)
0.008
0.010
0.012
0.014
0.016
0.018
D=0.3 mD=0.4 mD=0.5 mD=0.6 mD=0.7 m
Hum
idity
ratio
(kg/
kg)
different tube diameter conditions.
F. Niu et al. / Applied Energy 137 (2015) 211–221 219
is presented in the following figures. Fig. 13 shows the coolingcapacities of EAHE under the influences of six structural and oper-ational factors. As seen from Fig. 13(a), the cooling capacityincreased along with the increase of the inlet air temperature.However, the increase of latent cooling capacity was faster thansensible cooling capacity along with the inlet air temperatureincrease. The change rate of sensible cooling capacity was0.31 kW/�C and 0.79 kW/�C of latent cooling capacity. The totalcooling capacity’s change rate was 1.1 kW/�C. Fig. 13(b) showsthe three cooling capacities along with the inlet air relative humid-ity change. It can be seen from the figure that the sensible coolingcapacity of EAHE which was not affected by air relative humiditykept a constant value. And the latent cooling capacity was alsoalmost constant value when the inlet air relative humidity was
2
4
6
8
10
12
14
16
18
Coo
ling
capa
city
(kW
)
Tin (oC)
QsQlQt
26 28 30 32 34
(a)
2
4
6
8
10
12
14
16
18
Coo
ling
capa
city
(kW
)
Vin (m/s)
QsQlQt
0.5 1.0 1.5 2.0 2.5
(c)
0
2
4
6
8
10
12
14
Coo
ling
capa
city
(kW
)
L (m)
QsQlQt
50 60 70 80 90
(e)
Fig. 13. The cooling capacity of EAHE unde
below 40%. After then the latent cooling capacity began to increasequickly. The change rate was 0.26 kW/%. Fig. 13(c) shows the cool-ing capacity along with the change of air velocity. As seen from thefigure the sensible and latent cooling capacities had the samechange rate of 3.55 kW/(m/s) and were linear. The change rate ofthe total cooling capacity was 7.1 kW/(m/s). It can be seen fromFig. 13(d) the sensible and latent cooling capacities reduced alongwith the increase of the tube surface temperature. The sensiblecooling capacity was linear with the change rate value of0.33 kW/�C. The latent cooling capacity was parabolic. The higherthe tube surface temperature was, the faster the latent coolingcapacity reduced. Fig. 13(e) presents the cooling capacity alongwith the length of tube. It can be seen from the figure the sensibleand latent cooling capacities were parabolic. However the latent
10 20 30 40 50 60 70 80 90 100-202468
101214161820
Coo
ling
capa
city
(kW
)
RH (%)
QsQlQt
(b)
8 10 12 14 162
4
6
8
10
12
14
16
Coo
ling
capa
city
(kW
)
Ts (oC)
QsQlQt
(d)
0.3 0.4 0.5 0.6 0.7
2
4
6
8
10
12
14
16
18
Coo
ling
capa
city
(kW
)
D (m)
QsQlQt
(f)
r the influence from different factors.
Table 4R-value of regression function.
Qs Ql Qt
R-square 0.999 0.992 0.996
220 F. Niu et al. / Applied Energy 137 (2015) 211–221
cooling capacity was affected by the tube length more drasticallythan the sensible cooling capacity. Fig. 13(f) shows the coolingcapacity along with the change of the tube diameter. The sensiblecooling capacity was linear. The latent cooling capacity was para-bolic. So the total cooling capacity was also parabolic. The changerate of sensible cooling capacity was 18.25 kW/m. The wider thetube diameter was, the faster the latent cooling capacity reduced.
5. Regression of cooling capacity
Models are useful for predicting the performance of a systemacross a range of operating conditions. These predictions are usedin energy consumption simulation, system design, advanced con-trol techniques or fault detection and diagnosis. The heat transferof EAHE was a complex process especial considering both heatand mass heat transfer. It is very costly to calculate the perfor-mance using a sophisticated program before designing an EAHE,which could retard the generalization of EAHE. In order to realizethe quick and optimal design for the application of EAHE, the gen-eral formulas of sensible cooling capacity, latent cooling capacityand total cooling capacity will be achieved. From the previousparametric analysis, we deduced that the regression function insecond-order polynomial form including the cross-terms couldgive a high accurate prediction.
According to the above analysis the cooling capacity was relatedto structural factors including the tube length and diameter, andoperational factors including the air temperature and relativehumidity at the inlet of EAHE, the air velocity and the tube surfacetemperature. Eq. (13) was proposed as the regression function forthe prediction of the cooling capacities. All the simulation resultsobtained in Section 4 were utilized to obtain the model by usingMatlab 8 regression toolbox. The regression coefficients of sensible,latent and total cooling capacity are collected in Table 3. The R-value was calculated as shown in Table 4 to analyze the accuracyof regression function. Because the comprehensive structure ofthe second-order polynomial equation included the cross-terms,the R-value were high, which indicated a great regression. It can
accurately predict the cooling capacities of an EAHE. The predictionformulas can be easily applied for the different design and opera-tion conditions. In the real application, the soil temperature canbe predicted by using the soil model for approximating the tubesurface temperature in the regression formulas. The regressionfunction will significantly contribute to the design and applicationof EAHE.
� RHin þ A14 � T in � V in þ A15 � T in � Ts þ A16
� T in � Lþ A17 � T in � Dþ A18 � RHin � V in þ A19
� RHin � Ts þ A20 � RHin � Lþ A21 � RHin � D
þ A22 � V in � Ts þ A23 � V in � Lþ A24 � V in � D
þ A25 � Ts � Lþ A26 � Ts � Dþ A27 � L � D ð13Þ
6. Conclusions
A one-dimensional steady-state control volume model consid-ering both sensible and latent heat transfer was developed forpredicting the performance of an EAHE. The model was calibratedby using the experimental data based on an existing testing facil-ity. Using the calibrated model the comprehensive performanceof EAHE with different structural and operation conditions wassimulated. The effects of main parameters including the air tem-perature and relative humidity, the air velocity at the inlet of EAHE,the tube surface temperature, the tube length and diameter ofEAHE on the performance were analyzed.
According to the analysis on the simulation results, the follow-ing conclusions can be obtained. The lower the inlet air tempera-ture was, the smaller the air temperature decreasing rate alongwith the length of EAHE was. The air relative humidity under thehigh inlet air temperature condition increased faster than that ofthe low air temperature condition. The air temperature along withlength of EAHE under the different inlet air relative humidity con-ditions were the same and it was not affected by the air relativehumidity. The smaller the air velocity was, the faster the air tem-perature decreasing rate was, and the lower the outlet air temper-ature was. When the tube surface temperature was much lower,the air temperature along with the length of EAHE reduced morequickly. The air temperature under the big tube diameter conditionreduced more slowly than that of small tube diameter. In addition,the cooling capacities including the total, sensible and latent cool-ing capacity under the influences of six structural and operationalfactors were developed.
The heat transfer of EAHE was a complex process especial con-sidering both heat and mass heat transfer. It is costly to calculatethe performance using a sophisticated program before designingan EAHE. In order to realize the quick and optimal design for theapplication of EAHE, the general formulas with second-order poly-nomial equation including the cross-terms for sensible coolingcapacity, latent cooling capacity and total cooling capacity wereachieved. High R-values were found for all the predictions. It willsignificantly contribute to the design and application of EAHE.
F. Niu et al. / Applied Energy 137 (2015) 211–221 221
Future work will include investigation on the dynamic perfor-mance of an EAHE system coupling the soil temperature andcontrol for improved technical and economic performance.
Acknowledgements
The authors gratefully acknowledge the support of this studyfrom University of Nebraska-Lincoln Faculty Start-up Fund andNational High Technology Research and Development Program ofChina (863 Program) (2012AA052503).
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