Renewable Energy 173 (2021) 401e414
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Renewable Energy
journal homepage: www.elsevier.com/locate/renene
Multivariant optimization and sensitivity analysis of an experimental
vertical earth-to-air heat exchanger system integrating phase change
material with Taguchi method
Zhengxuan Liu a, Pengchen Sun b, Mingjing Xie c, Yuekuan Zhou a, *, Yingdong He a, d,
Guoqiang Zhang a, Dachuan Chen a, Shuisheng Li e, Zhongjun Yan a, Di Qin a
a
College of Civil Engineering, National Center for International Research Collaboration in Building Safety and Environment, Hunan University, Changsha,
Hunan, 410082, China
b
China Construction Design Group Co.LTD Engineering Technology Research Institute, Beijing, 100037, China
c
School of Architecture and Art, Central South University, Changsha, Hunan, 410012, China
d
Center for the Built Environment, University of California, Berkeley, Berkeley, CA, USA
e
China Construction Fifth Engineering Division Corporation Limited, Changsha, Hunan, 410004, China
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 12 January 2021
Received in revised form
1 March 2021
Accepted 22 March 2021
Available online 27 March 2021
Shallow subterranean ventilation of earth-to-air heat exchanger (EAHE) system can improve renewable
utilisation, decrease CO2 emission and promote carbon-neutral transition. However, the conventional
EAHE system has drawbacks, e.g., large occupied land area, low energy-usage efficiency, small falling
gradient for buried pipe and fluctuated outlet air temperature. This study proposes a vertical EAHE integrated with annular PCM with advantages, including less occupied floor space, higher energy efficiency, better centralised discharge of air condensate water and more stable outlet air temperature. An
experimental test-rig was established for online testing and the real-time monitored data was for
modelling calibration to characterise the sophisticated heat transfer in phase change process. Afterwards,
multivariant analysis on thermo-physical PCM parameters was conducted on cooling capacity and outlet
air temperature fluctuation. A dimensionality reduction approach from redundant experiments was
adopted for multivariant optimization and sensitivity analysis. Results show that PCM fusion temperature and latent heat of PCM dominate the cooling capacity with percentage contribution of 37.61% and
28.91%, respectively. PCM thickness and melting temperature dominate the temperature fluctuation with
percentage contribution of 31.27% and 26.18%, respectively. This study provides benchmark and guidelines on PCM thermo-physical parameters’ selection with an efficient dimensionality reduction approach,
paving path for application of the vertical EAHE integrated with PCMs in buildings.
© 2021 Elsevier Ltd. All rights reserved.
Keywords:
Geothermal energy
Vertical earth-to-air heat exchanger
Multivariant optimization
Taguchi method
Dimensionality reduction
Phase change material
1. Introduction
Dependence on traditional fossil fuels [1] to cover the daily
increased energy demands will lead to energy shortage crisis, carbon emission, environmental pollution, deterioration of air quality
and global warming [2,3]. Air pollution issues have attracted
widespread attention and arouse caution worldwide. A report from
World Health Organization (WHO) in 2018 showed that more than
90% of people worldwide breathe the polluted air [4,5], leading to
lung-related health problems, such as pneumonia, lung cancer and
so on. Development, exploration and utilisation of renewable energy to partially or completely replace traditional fossil fuels have
become a mainstream world [6]. The common forms of renewable
energy technologies mainly include the energy, solar, wind energy,
geothermal energy, ocean and biomass energy [7,8]. Compared to
other technologies, the geothermal energy has some intrinsic advantages due to the stability characteristic of the heat source and
the independence on spatiotemporal intermittence of ambient
conditions. The geothermal energy system has been applied widely
to decrease the energy consumption of buildings [9,10]. As one of
* Corresponding author. College of Civil Engineering, National Center for International Research Collaboration in Building Safety and Environment, Hunan University,
Changsha, China.
E-mail address: yuekuan.zhou@outlook.com (Y. Zhou).
https://doi.org/10.1016/j.renene.2021.03.106
0960-1481/© 2021 Elsevier Ltd. All rights reserved.
Z. Liu, P. Sun, M. Xie et al.
Renewable Energy 173 (2021) 401e414
lead to serious quality issues of the supplied flowing air [26].
To solve above problems, a vertical earth-to-air heat exchanger
(VEAHE) system integrating annular PCM was explored in the study
[27], and it can be abbreviated as a VEAHE-APCM system. Compared
with the traditional system, the covered area of the VEAHE-APCM
system is less than 1 m2, extending its application in high-density
building areas, and the buried tube depth is more than 15 m,
providing a more stable soil temperature for air pre-handling.
Moreover, the proposed system has a falling gradient of buried pipe
of 90 , enabling the discharge of the air condensate water in time and
avoid the growth of bacteria. In addition, due to the considerable
energy density for geothermal energy storage, the used PCM
component can decrease the temperature fluctuation. This paper also
studied parametrical analysis on PCM parameters, in respect to the
system performance. The findings showed that, the cooling capacity
and pre-handled outlet air temperature are highly dependent on
thermo-physical parameters of PCMs. However, the optimal multivariant combinations on PCM parameters of the VEAHE-APCM system were still indeterminacy in the study. In addition, only limited
parameters are studied, such as length, thickness and thermal conductivity of PCM, without considerations on other critical parameters,
such as latent heat, phase change temperature and density of PCM.
Furthermore, the parametrical analysis focused on separate single
PCM parameter with control variable method (i.e., each case focuses
on one variable, while other variables are kept constant), without
simultaneous and comprehensive considerations on all combined
parameters due to the complexity in experimental designs and
expensive cost for experiment implementation. According to research
results in the previous study [28], an inappropriate design on annular
PCM component will lead to higher initial investment cost compared
to other PCM macro-encapsulation components. Therefore, the
multivariable optimization and sensitivity analysis on multivariant
PCM parameters are necessary to improve the economic feasibility
with benchmark and guidelines on thermo-physical parameters’ selection for successful applications.
In the past few years, the Taguchi method, due to its distinguishing
characteristics of user-friendly and computational-efficient, has been
widely used in various domains of scientific researches (e.g., ground
coupled heat pump system [29], film cooling technology [30], solar
photovoltaic [31] and other fields [32]) for multi-dimensional optimization analysis of relevant critical parameters. The Taguchi method
the most promising geothermal techniques, the earth-to-air heat
exchanger (EAHE) system is mainly used to pre-heat or pre-cool the
fresh ambient air and then the pre-handled air is blown into the
buildings to decrease the cooling/heating load [11e13]. The operational principle of a conventional EAHE system for building cooling in summer is represented in Fig. 1.
In recent years, the EAHE system has attracted increasing global
interests, due to the simple design structure, low operational cost and
large cooling potentiality [15,16]. Various studies have been conducted through the numerical and experimental method to explore
the effectiveness of EAHE systems on indoor thermal environment
and energy consumption [17,18]. For example, Li et al. [19] investigated the potential of an EAHE system for preheating air in winter. For
an EAHE system with the total length of 32 m, tube diameter of
250 mm and buried depth of 2.05 m, an average temperature rising of
12.4 C and heating capacity of 4665 W can be noticed with a fan
energy use of 130 W. Pakari et al. [20] analyzed the feasibility performance of a near-surface EAHE system with short-grass ground
cover. They concluded that, when the air velocity reached 9.24 m/s,
the air temperature drop was 6.5 C (from 40.6 C at the inlet to 34.1 C
at the outlet), and the system’s coefficient of performance (COP) was
13.4. Compared to conventional air conditioning systems, the energy
saving rate of the EAHE system can reach 76.5% in summer.
An overwhelming majority of studies show that the EAHE systems have an enormous potential to ameliorate indoor temperature
and reduce building energy consumption [21,22]. However, the
conventional EAHE system is almost buried with a series of horizontal tubes, thereby leading to considerable spatially occupied
land area, which is impractical in highly densified building areas
[23]. Moreover, the depth of buried tube for the conventional EAHE
system is typically less than 4 m, at which the soil temperature is
dependent on rainfall, leading to the system reliance and dependence with possible unsatisfactory outlet temperature in some
areas [24]. For a given EAHE system, it possibly has a larger daily
oscillation for outlet air temperature and this temperature oscillation has exceeded 3 C in some studies at a definite inlet air temperature, air velocity and tube length [25]. However, the large
fluctuation of outlet temperature proposes challenges on indoor
thermal comfort. In addition, the air condensate adheres to the pipe
wall over a long period of time under the cooling mode due to a low
falling gradient of buried pipes, which will cultivate bacteria, and
Fig. 1. Operational principle of an EAHE system for building cooling [14].
402
Z. Liu, P. Sun, M. Xie et al.
Renewable Energy 173 (2021) 401e414
implementation in multivariant nonlinear systems, a dimensionality reduction approach from redundant experiments and simulations was adopted for multivariant optimization and sensitivity
analysis. The Taguchi method was firstly adopted for experimental
design and the identification of the best combinatorial factor
within different PCM parameters of the VEAHE-APCM system, e.g.,
PCM thickness, length, latent heat, density, melting temperature,
thermal conductivity and etc. 3) Sensitivity analysis on multivariant
thermo-physical parameters of PCM was conducted with quantitative contribution of each factor to the ultimate objectives, i.e., the
daily cooling capacity and temperature fluctuation at the outlet.
The most optimal multivariant combination was determined for
the improvement of overall system performance. This study reveals
mechanism on parameter design of a novel VEAHE-APCM system,
together with benchmark and guidelines on thermo-physical parameters’ selection of PCM, so as to promote geothermal energy
practical applications for building cooling and heating.
applies the mixed-level fractional factorial designs trial experiments
for guaranteeing better performance in system design stage by
identifying the optimal parameters. Zhou et al. [33] comprehensively
studied performance of a PCM coupled system of a photovoltaic/
thermal panel and Trombe wall, based on the Taguchi method for
multivariable optimization. They indicated that, energy performance
was dominated by the PV/TPCM component, and the contribution
ratio for the water mass flow is higher than 90%. Sivasakthivel et al.
[34] used the Taguchi method to optimize the operation parameters
for building heating/cooling operation. In the study, the Taguchi
method was employed for three different levels of the considered
parameters (i.e., the inlet and outlet temperature of condenser, dryness fraction of evaporator temperature at inlet and outlet) following
an L9 (34) orthogonal array, and then the results were analyzed based
on the optimum conditions using Analysis of Variance (ANOVA) and
Signal-to-Noise (SN) ratio method. According to the analysis results,
the obtained maximum COP for space heating and cooling was 4.25
and 3.32, respectively. Besides, the Taguchi method is also commonly
used to decrease the initial investment through instructing the
experimental design. For example, Xie et al. [34] found the optimal
combination of different parameters of thin layer ring used in an ice
thermal storage tank based on the Taguchi method. In this study, the
used Taguchi method can decrease the cases of experimental testing
from 27 to 2 times. The results showed that, the ice formation is highly
dependent on the arrangement and material of thin layer ring.
According to the above-mentioned analysis, several main
shortages or scientific gaps still exist in previous studies and will
covered in this study. Firstly, compared with the conventional EAHE
system, the VEAHE-APCM system as a newly-proposed geothermal
ventilation technology has several apparent advantages of less
occupied floor space, higher energy efficiency for geothermal energy utilisation, better discharge of air condensate water and
smaller temperature fluctuation. However, the previous studies
only explore the geometrical design parameters of PCM, and some
critical parameters (e.g., the latent heat, phase change temperature
and density of PCM) are not considered, which are entirely possible
to cause significant influence on system’s energy performance.
Secondly, only separate single variable was considered with control
variable method in previous studies, whereas the simultaneous and
comprehensive considerations on multivariant parameters are
inadequately studied in experimental designs, due to complexity in
experimental designs and expensive cost for experiment implementation. In addition, as a novel promising system, the VEAHEAPCM system typically has a relatively high construction cost
especially the deep hole drilling cost. However, studies on the
multivariant optimization of the VEAHE-APCM system have not
been well conducted to improve the application and economic
feasibility. Last but not the least, considering the multivariant
optimization analysis on the VEAHE-APCM system, the Taguchi
method is hardly ever applied to determine the optimum combination of all influencing factors on PCM parameters, despite it has
some obvious advantages of user-friendly, easy accessibility and
computational-efficient characteristics, together with dimensionality reduction from redundant experiments and simulations.
This study will be conducted based on the above-mentioned
scientific gaps and existing issues in previous studies. The novelty
can be described as follows: 1) An energy-efficient coupled system
with annular PCM integrating shallow subterranean heat ventilation of a VEAHE system was proposed, and an experimental test-rig
was established for the online testing to validate an enthalpy-based
numerical model, which was adopted for performance prediction
under multivariant combinations. Sensitivity analysis on several
critical PCM parameters was conducted to explore the energy efficiency improvement potentials; 2) Considering the complexity in
experimental designs and expensive cost for experiment
2. Methods
The detailed overall framework of research methods in this
study can be seen in Fig. 2. The experimental test-rig of the VEAHEAPCM system was firstly built to explore the system performance
feasibility. Then, the enthalpy-based model was developed and
validated by the monitored results. The developed numerical
model was used to explore the impacts of different PCM parameters
(i.e., PCM thickness, length, latent heat, density, melting temperature and thermal conductivity, etc.) on the system performance,
and concurrently to calculate the system assessment criteria
including the outlet air temperature fluctuation and daily cooling
capacity under the different conditions. Furthermore, the parameter analyses and sensitivity analyses were conducted to quantitatively study the influences of different PCM design parameters on
system evaluation criteria. To determine the optimal combination
of PCM design parameters with the maximum daily cooling capacity and minimum temperature fluctuation at the outlet the
Orthogonal matrix method based trial experiments was used to
analyze the contribution rate of each PCM parameter to the daily
cooling capacity and temperature fluctuation at the outlet.
2.1. System configuration and experimental set-up
Dynamic heat transfer of the buried U-tube in the soil was
mathematically modelled. The configuration and detailed
geometrical dimensions of U-tube are shown in Fig. 3. The used
PCM was organic paraffin due to its steady thermo-chemical,
environment-friendly and low cost [35]. An air cavity with a
thickness of 2.5 mm was reserved between the PCM containers and
tube for the convenience of construction. The construction site
pictures of the proposed system are shown in Fig. 4. The test site
located at Changsha (N28 120 /E112 590 ), China, with a subtropical
monsoon climate. The city experiences the highest temperature
above 30 C in summer and the lowest temperature below 5 C in
winter [36]. The practical test was conducted from the 8th to 9th,
September 2017. The temperatures of air and PCM inside EAHE
system were monitored and recorded by a data logger (Agilent
34972A) and corresponding sensors (PT100 thermocouples with a
precision error of ±0.15 C).
2.2. Numerical model and system assessment criteria
The numerical model of proposed system can be separated into
four parts along the air flow direction based on the designed
structure (see in Fig. 3). In this study, only the heat transfer model
in the Part IV with PCMs is developed, while heat transfer models of
403
Z. Liu, P. Sun, M. Xie et al.
Renewable Energy 173 (2021) 401e414
Fig. 2. Overall framework of research methods in this study.
other parts are based on our previous studies [37]. The nodal discretization of different mediums in the Part IV are shown in Fig. 5.
The mathematical equations of the divided Part IV model can be
built based on energy balance principle, as listed in Table 1. Heat
transfer equations are solved in the MATLAB/SIMULINK environment and the detailed solution procedure is highly recommended
to refer to our previous studies [27].
For the parametrical analysis on different thermo-physical parameters of PCM, the maximum daily cooling capacity for regulating the indoor temperature and the minimum outlet air
temperature fluctuation for improving the thermal comfort of
supply-air outlet, as two assessment criteria of the proposed system, are used for achieving the goal of multivariant optimization.
The daily cooling capacity of the proposed system can be calculated
as follows:
ðt
Qdaily ¼
t
t
Cair pri2 v ra Ta;
inlet Ta; outlet dt
(12)
0
where Qdaily is the daily cooling capacity; Cair , v and ra are the air
specific heat capacity, velocity and density, respectively; ri is the
t
t
inner radius; Ta;
and Ta;
are the air temperature at the inlet
inlet
outlet
and outlet at time t, respectively.
The temperature fluctuation at the outlet can be calculated as:
Toutlet; flucation ¼ max Toutlet min Toutlet
0/t
0/t
(13)
where Toutlet; flucation is the outlet air temperature fluctuation;
max Toutlet and min Toutlet represent the maximum and minimum
0/t
0/t
outlet air temperature during the system operation period.
2.3. Multivariants, levels and orthogonal matrix-based trial
experiments
The comprehensive performance of PCM related systems is
mainly dependent on the thickness, length, latent heat, density,
Fig. 3. The system configuration and its detailed dimensions.
404
Z. Liu, P. Sun, M. Xie et al.
Renewable Energy 173 (2021) 401e414
Fig. 4. Construction site pictures of the system.
Fig. 5. Nodal representation of different mediums in the Part IV with an annular PCM component.
VEAHE system without PCM component varied from about 22.1 to
24.7 C, under the working condition of outdoor air temperature
(from 27.4 to 38.6 C for a continuous operation of 96 h [37]), the
PCM fusion temperature was selected to be between 18 and 26 C,
enabling that PCM can completely store and discharge energy
within the range of phase transition temperature. Furthermore, the
value range of thermal conductivity of PCM can be chosen from 0.5
to 10 W/(m$K) according to reference [27]. To specifically analyze
the optimal combination of different parameters, each PCM
parameter can be divided into five levels based on the ascertained
value range, as shown in Table 2.
In this study, the Taguchi method, also known as the orthogonal
experimental design method, has been adopted for the investigation of multivariant parameters of the proposed system, forming
the matrix for experiments. This matrix can contribute to obtaining
most information with the minimum simulation efforts and also
seeking out the optimal level of each parameter. The Taguchi
melting temperature and thermal conductivity of the integrated
PCM [38]. Appropriate PCM design parameters can effectively
improve the applied potential of the PCM coupled system. In this
study, all above-mentioned PCM parameters are considered as independent multi-variables of the VEAHE-APCM system. Based on
previous studies of the above-mentioned parameters, different
levels for each PCM parameter are explored, as illustrated in Table 2.
Based on research results from our previous studies [27], marginal
improvement in the system performance can be noticed, when the
thickness and length of PCM exceeded 30 mm and 15 m, but a
further increase in thickness and length of PCM will lead to
increased investment cost. Therefore, the ranges of PCM thickness
and length are from 1 to 30 mm and from 1 to 15 m in this study.
The most commonly used PCM for cooling is paraffin wax and
inorganic salt hydrate, and the latent heat and density of the PCM
can be chosen from 130 to 260 kJ/kg and from 500 to 2500 kg/m3 in
this study. As the temperature fluctuation at the outlet of the
405
Layers
Air
Heat transfer equations
ra Ca Va tDt Þ
2ðTa;j Ta;j
Dt
"
Supplementary
¼ Ca m_ ðTa;j1
Ta;j Þþ
ðTP;1;j Ta;j Þ
#
(1)
RP;1;j
_
Dt
Ca m_ Dt
Dt
tDt ¼ 1 þ Ca mDt
þ
Ta;j1 Tp;1;j (2)
Ta;j
Ta;j 2 ra Ca Va 2 ra Ca Va Rp;1;j
2 ra Ca Va
2 ra Ca Va Rp;1;j
ha ¼
vP ¼
tDt ¼
TP;1;j
Dt
1
Dt
1
1þ
þ
2 rp CP;1 VP;1;j RP;1;j 2 rp CP;1 VP;1;j RP;2;j
!
TP;1;j Dt
1
Dt
1
Ta;j TP;2;j (3)
2 rp CP;1 VP;1;j
RP;1;j
2 rp CP;1 VP;1;j RP;2;j
5
ri da dP
1
1
6
ln
þ
ha Sa 2p lpcm Dz
ri da dP
RP;1;j ¼
Re ¼
PCM 1
CP;1
0:023Re0:8 Pr n la
2 ðri da dp Þ
ra vP 2 ðri da dp Þ
m
ri 2 v
ðri da dp Þ2
8
>
tDt
>
CP;s TP;1;j
< Ts ðsoildÞ
>
>
<
tDt
¼ CP ðTÞ Ts < TP;1;j
< Tl ðphase changeÞ
>
>
>
t
D
t
>
: CP;l TP;1;j < Tl ðliquidÞ
1
RP;2;j ¼
PCM 2
tDt ¼
TP;2;j
Dt
1
Dt
1
1þ
þ
2 rp CP;2 VP;2;j RP;2;j 2 rp CP;2 VP;2;j RP;3;j
!
TP;2;j Dt
1
Dt
1
TP;1;j TP;3;j (4)
2 rp CP;2 VP;2;j RP;2;j
2 rp CP;2 VP;2;j RP;3;j
CP;2
2p lpcm Dz
406
tDt ¼
TP;3;j
Dt
1
Dt
1
1þ
þ
2 rp CP;3 VP;3;j RP;3;j 2 rp CP;3 VP;3;j RPa;j
!
TP;3;j Dt
1
Dt
1
TP;2;j TPa;j (5)
2 rp CP;3 VP;3;j RP;3;j
2 rp CP;3 VP;3;j RPa;j
CP;3
Tube
1
Soil
tDt ¼
TPt;j
tDt ¼
TPI;j
Dt
1
Dt
1
1þ
þ
2 ra Ca VPa;j RPa;j 2 ra Ca VPa;j RPt;j
Dt
1
Dt
1
1þ
þ
2 rt Ct VPt;j RPt;j 2 rt Ct VPt;j RPI;j
Dt
1
Dt
1
1þ
2 rI CI VI RI;j 2 rI CI VI RPs;1;j
tDt ¼
Soil 1: TPs;1;j
tDt ¼
Soil i: TPs;i;j
Soil m:
2p lpcm Dz
ln
1
dP
6
3
ri da dP
6
ri da 1
ln
2p lpcm Dz
ri da
þ
1
ri da dP
6
da
ri 1
2
ln
2p la Dz ri da
!
TPa;j !
TPt;j !
TPI;j Dt
1
Dt
1
TP;3;j TPt;j (6)
2 ra Ca VPa;j RPa;j
2 ra Ca VPa;j RPt;j
Dt
1
Dt
1
TPa;j TPI;j (7)
2 rt Ct VPt;j RPt;j
2 rt Ct VPt;j RPI;j
Dt
1
Dt
1
TPt;j TPs;1;j (8)
2 rI CI VI RPI;j
2 rI CI VI RPs;1;j
RPt;j ¼
RPI;j ¼
1
ln
2p la Dz
1
2p lt Dz
da
ri 2
r
ln
r
d
2
þ
þ
d
ri þ
1
2
ln
2p lt Dz
ri
1
2p lI Dz
ln
rþ
dI
2
r
Dr
r þ dI þ
r þ dI
1
2
ln
þ
d
2p lI Dz
2p ls;j Dz
r þ dI
rþ I
2
3Dr
r
þ
dI þ
1
2
ln
¼
Dr
2p ls;j Dz
r þ dI þ
2
RPs;1;j ¼
!
Dt
1
Dt
1
Dt
1
Dt
1
1þ
þ
TPI;j TPs;2;j (9)
TPs;1;j 2 rs Cs Vs;1;j RPs;1;j 2 rs Cs Vs;1;j RPs;2;j
2 rs Cs Vs;1;j
RPs;1;j
2 rs Cs Vs;1;j RPs;2;j
RPs;2;j
!
Dt
1
Dt
1
Dt
1
Dt
1
1þ
þ
TPs;i1;j TPs;iþ1;j (10)
TPs;i;j 2 rs Cs Vs;i;j RPs;i;j 2 rs Cs Vs;i;j RPs;iþ1;j
2 rs Cs Vs;i;j RPs;i;j
2 rs Cs Vs;i;j RPs;iþ1;j
ri
1
ln
Renewable Energy 173 (2021) 401e414
Insulation
(INS)
tDt ¼
TPa;j
3
dP
6
5
ri da dP
6
ri da 8
>
tDt
>
> CP;s TP;3;j < Ts ðsoildÞ
>
<
tDt
¼ CP ðTÞ Ts < TP;3;j
< Tl ðphase changeÞ
>
>
>
tDt
>C
:
T
<
T
ðliquidÞ
P;l
l
P;3;j
RPa;j ¼
Air cavity
(Air*)
ln
8
>
tDt
>
CP;s TP;2;j
< Ts ðsoildÞ
>
>
<
tDt
¼ CP ðTÞ Ts < TP;2;j
< Tl ðphase changeÞ
>
>
>
t
D
t
>
: CP;l TP;2;j < Tl ðliquidÞ
RP;3;j ¼
PCM 3
Z. Liu, P. Sun, M. Xie et al.
Table 1
The mathematical equations of Portion IV model.
method has been widely employed in applications of the multiobjective optimization design of a given system due to its superiority characteristics of less design test cases, more coverage
paths and more straightforward manipulation when comparing
with other multi-objective research methods [37]. The specific
principle and computational process of the Taguchi method can
be referred to Ref. [39]. Based on the Taguchi method, the standard orthogonal array L25 (56) of multivariant parameters of PCM
and corresponding levels, as listed in Table 3, can be calculated
through the IBM SPSS Statistics software, which is commonly
used in statistical analysis, data mining and prediction analysis.
The corresponding experimental plan can be calculated as shown
in Table 4.
and soil m at time t- Dt; TPs;1;j , TPs;2;j , TPs;i1;j , TPs;i;j , TPs;iþ1;j , TPs;m1;j , TPs;m;j and TPg;j is the mean temperature of soil 1, soil 2, soil (i-1), soil i, soil (iþ1), soil (m-1), soil m and outermost layer soil, respectively; RPs;1;j , RPs;2;j , RPs;i;j and
RPs;m;j is thermal resistance of the soil 1, soil 2, soil i and soil m with the adjacent medium, respectively; Vs;1;j , Vs;i;j and Vs;m;j is the divided volume of soil 1, soil i and soil m, respectively; Dr the distance of each divided block radius.
tDt and T tDt is tube and insulation temperature at time t- Dt, respectively; T
tDt
tDt
tDt
conductivity and thickness of insulation, respectively; TPt;j
PI;j is mean temperature of insulation; TPs;1;j , TPs;i;j and TPs;m;j is the temperature of soil 1, soil i
PI;j
air cavity; lt is the tube coefficient of heat conductivity; VPt;j is the divided volume of tube; RPI;j is the thermal resistance between tube and insulation; TPI;j is the mean temperature of insulation; lI and dI is the coefficient of heat
VPa;j is the divided volume of air cavity; RPa;j is the thermal resistance between PCM 3 and air cavity; TPt;j is the mean temperature of tube; RPt;j is the thermal resistance between air cavity and tube; VPa;j is the divided volume of
tDt , T tDt and T tDt is the temperature of PCM 1, PCM 2 and PCM 3 at time t- Dt, respectively; r is the PCM density; C
viscosity of air; TP;1;j
P;1 , CP;2 and CP;3 is specific heat capacity of PCM 1, PCM 2 and PCM 3, respectively; VP;1;j , VP;2;j
p
P;2;j
P;3;j
tDt is the air cavity temperature at time t- Dt;
and VP;3;j is the divided volume of PCM 1, PCM 2 and PCM 3, respectively; RPa;j is the thermal resistance between the PCM 3 and air cavity; TPa;j is the mean temperature of air cavity; TPa;j
the mean temperature of PCM 1, PCM 2 and PCM 3, respectively; RP;1;j , RP;2;j and RP;3;j is the thermal resistance of the PCM 1, PCM 2 and PCM 3 with the adjacent medium, respectively; Sa is heat exchange area of flowing air; lpcm
is thermal conductivity of PCM; Dz is the divided height; ri is the tube inner radius; da the wall thickness of tube; dP is the thickness of PCM; v is the air velocity at the inlet; vP is the air velocity in the Portion IV; m is the dynamic
Renewable Energy 173 (2021) 401e414
tDt is the air temperature at time t- Dt; Dt is the time step; m
_ is the mass flow rate; TP;1;j , TP;2;j and TP;3;j is
Note: Ta;j and Ta;j1 is the mean temperature of air at the j-th and (j-1)-th layer between time t- Dt and t, respectively; Ta;j
(11)
tDt ¼
TPs;m;j
Dt
1
Dt
1
1þ
þ
2 rs Cs Vs;m;j RPs;m;j 2 rs Cs Vs;m;j RPs;mþ1;j
!
TPs;m;j Dt
2 rs Cs Vs;m;j
1
RPs;m;j
TPs;m1;j Dt
2 rs Cs VPs;m;j
1
RPs;mþ1;j
TPg;j
1
1
r þ dI þ i Dr
2
ln
RPs;i;j ¼
3
2p ls;j Dz
Dr
r þ dI þ i 2
1
r þ dI þ m Dr
1
2
ln
RPs;m;j ¼
3
2p ls;j Dz
Dr
r þ dI þ m 2
Z. Liu, P. Sun, M. Xie et al.
3. Results and discussion
3.1. Model validation
The numerical model validation of the VEAHE-APCM system is
conducted, as shown in Fig. 6 (a) and (b). Fig. 6 (a) shows the inlet
air temperature of this proposed system. The comparisons between the measured and simulated values are shown in Fig. 6 (b),
under a given air velocity and inlet air temperature. In the
experimental test, the recording time of the test instrument is set
to 3 min each time. In Fig. 6 (b), the left coordinate represents the
values of outlet air and PCM temperature, and the right coordinate represents the values of temperature difference between the
simulated and measured data for outlet air and PCM temperature,
respectively.
As shown in Fig. 6, the maximum temperature differences
between the measured and simulated values for the outlet air
temperature and the PCM temperature are 0.37 C and 0.30 C,
respectively. The corresponding maximum absolute relative errors for them are 1.59% and 1.34%, respectively. Meanwhile, the
average differences between measured and simulated values for
them are less than 0.03 C and 0.14 C, respectively. In addition,
the root mean square error of between measured and simulated
values for them can be calculated as 0.17 C and 0.21 C, respectively. Therefore, it can be concluded that the simulated values
are in good agreement with the monitored values for this VEAHEAPCM system, which also indicates the feasibility of the developed model.
3.2. Parametric and sensitivity analysis of multivariable
parameters on PCM temperature, latent heat and density
The effects of PCM thickness, length and thermal conductivity
on the outlet air temperature of the VEAHE-APCM system have
been discussed in our previous study [27]. As a continuation and
promotion study based on our previous research work, specific
focus was given on the thermo-physical parameters of PCMs (e.g.,
PCM temperature, latent heat and density), to provide benchmark
and guidelines on thermo-physical parameters’ selection, so as to
stabilise outlet air temperature and improve the cooling capacity
of system. The simulation scenarios were carried out under the
air flow velocity of 1 m/s and the system operating continuously
time of 24 h. The input inlet air temperature from the monitored
results varied with a temperature amplitude of between 24.32 C
and 38.17 C, as shown in Fig. 6.
3.2.1. Impacts of PCM temperature
The outlet air temperature and cooling capacity of the VEAHEAPCM system under different PCM temperatures are investigated.
The selected PCM temperatures as the model inputs are 18 C,
20 C, 22 C, 24 C and 26 C based on the temperature variation
407
Z. Liu, P. Sun, M. Xie et al.
Renewable Energy 173 (2021) 401e414
Table 2
Geometrical and thermo-physical parameters of PCM with corresponding levels.
No.
Factors
Level 1
Level 2
Level 3
Level 4
Level 5
A
B
C
D
E
F
PCM thickness (mm)
Length of PCM (m)
Latent heat of PCM (kJ/kg)
Density of PCM (kg/m3)
Melting temperature of PCM ( C)
Thermal conductivity of PCM (W/(m$K))
1
1
130
500
18
0.5
8
5
160
1000
20
3
15
9
190
1500
22
6
22
13
220
2000
24
8
30
15
260
2500
26
10
Table 4
The experimental plan of multivariant parameters using the Taguchi method.
Table 3
The standard orthogonal array L25 (56) of multivariant parameters using the Taguchi
method.
Number of test
A
B
C
D
E
F
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
4
4
1
2
4
2
2
1
2
3
3
1
5
3
3
4
2
1
3
5
5
1
5
4
5
2
1
5
2
5
3
4
3
5
3
2
1
2
5
4
4
1
4
1
3
5
2
4
3
1
3
4
2
1
5
5
4
4
3
1
2
1
4
4
5
1
2
3
3
3
1
5
2
2
5
5
4
5
3
3
4
5
3
1
5
4
1
1
2
1
2
2
4
3
2
4
2
3
1
5
1
5
5
5
4
1
2
3
3
4
3
1
4
1
5
3
4
4
2
5
2
2
1
2
3
5
3
4
2
1
4
1
5
3
3
1
1
4
2
5
4
5
2
4
1
5
3
3
2
2
Number of test
A
B
C
D
E
F
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
22
22
1
8
22
8
8
1
8
15
15
1
30
15
15
22
8
1
15
30
30
1
30
22
30
5
1
15
5
15
9
13
9
15
9
5
1
5
15
13
13
1
13
1
9
15
5
13
9
1
190
220
160
130
260
260
220
220
190
130
160
130
220
220
260
130
160
190
190
190
130
260
160
160
260
2500
2000
2500
1500
1500
2000
2500
1500
500
2500
2000
500
500
1000
500
1000
1000
2000
1500
1000
2000
1000
1500
500
2500
18
26
26
26
24
18
20
22
22
24
22
18
24
18
26
22
24
24
20
26
20
20
18
20
22
10
6
8
3
0.5
8
0.5
10
6
6
0.5
0.5
8
3
10
8
10
3
8
0.5
10
6
6
3
3
the air temperature range at the outlet from the VEAHE system (i.e.,
from 21.4 C to 24.0 C [10]). In addition, when the PCM temperatures are 20 C and 22 C, the VEAHE-APCM system shows a lower
cooling capacity compared to other cases (PCM fusion temperatures are 18 C, 20 C and 26 C). The main reason is that the PCM
can effectively decrease the temperature amplitude at the outlet
through the charging/discharging process.
of outlet air of the VEAHE system. Other input parameters, i.e., PCM
length, PCM thickness, thermal conductivity of PCM, latent heat of
PCM and density of PCM, are regarded as constant values, as shown
in Table 5. Fig. 7 (a) and (b) show the impacts of the PCM temperatures on the outlet air temperature and cooling capacity. The
average temperature and temperature fluctuation of outlet air, and
average cooling capacity of the proposed system under different
PCM temperatures are presented in Table 6.
As shown in Fig. 7 (a) and 7(b), the outlet air temperature and
cooling capacity have no obvious change with the increase of PCM
temperature. Based on Fig. 7 (a) and Table 6, it is easy to find that,
when the used PCM temperature is 22 C, the VEAHE-APCM system
has the minimum temperature fluctuation of outlet air. This result
indicates that, compared to other selected temperatures, the PCM
temperature of 22 C shows a more stable outlet air temperature,
which can effectively improve the requirements of comfortableness
indoors. Furthermore, when the selected PCM temperatures are
18 C, 20 C and 26 C, the VEAHE-APCM system has almost the
same variation curve of outlet air temperature and cooling capacity.
This results also can be seen from Table 6, in which the average
temperature, temperature fluctuation at the outlet and the average
cooling capacity are the same for the PCM temperatures of 18 C,
20 C and 26 C, which shows that the PCM has no effect on the
outlet air temperature and cooling capacity of the VEAHE-APCM
system. The primary reason is that, as the selected PCM fusion
temperatures are 18 C, 20 C and 26 C, the PCM fails to regulate
the outlet air temperature, as the PCM fusion temperature is out of
3.2.2. Impacts of PCM density
The impacts of the PCM density on system performance is
explored under different densities of PCM. The selected densities of
PCM in the model inputs are 500, 1000, 1500, 2000 and 2500 kg/m3
based on the thermophysical properties of the common organic
and inorganic PCM. Other inputs parameters of PCM, i.e., PCM
length, PCM thickness, thermal conductivity of PCM, PCM temperature and latent heat of PCM, are considered as constant to
exclusively analyze the impacts of the PCM density on system
performance, as listed in Table 7. Fig. 8 (a) and (b) show the effects
of the PCM density on the outlet air temperature and cooling capacity. Table 8 lists the average temperature, temperature fluctuation of outlet air, and average cooling capacity under different PCM
densities.
As shown in Fig. 8 (a) and Table 8, the temperature fluctuation of
outlet air decreases along with the increasing of the PCM density.
However, the decreasing magnitude gradually slows down. Specifically, as the density of PCM increases from 500 to 1000 kg/m3,
the temperature fluctuation of outlet air decreases from 2.11 to
2.02 C. When the density of PCM increases from 2000 to 2500 kg/
408
Z. Liu, P. Sun, M. Xie et al.
Renewable Energy 173 (2021) 401e414
Fig. 7a. The impacts of PCM temperature on the outlet air temperature.
Fig. 6. (a) The inlet air temperature; (b) Comparison between the simulated and
measured results and temperature difference, in respect to outlet air temperature and
PCM temperature.
m3, the temperature fluctuation of outlet air is kept almost constant. This result shows that, as the density of PCM increases to a
certain extent, increasing the PCM density is not a very effective
way to reduce the temperature fluctuation of outlet air. From Fig. 8
(b) and Table 8, with the increase of the density of PCM, the average
cooling capacity decreases and the average temperature of outlet
air increases with a relatively small magnitude. The possible reason
is that the used annular PCM component has a relatively low
thickness and length, leading to a little impact of PCM density on
the system performance.
Fig. 7b. The impacts of PCM temperature on the cooling capacity.
As shown in Fig. 9 (a) and 9(b), with the increasing of the latent
heat of PCM, the temperature fluctuation of air at the outlet and
average cooling capacity decreases gradually, and however this
change is relatively small. To be specific, as the latent heats of PCM
are 130, 160, 190, 220 and 260 kJ/kg, the outlet air temperatures
range from 21.67 to 23.73 C, 21.68e23.73 C, 21.70e23.72 C,
21.71e23.72 C and 21.72e23.71 C. The corresponding temperature fluctuation of outlet air can be seen in Table 10. Results showed
that the small-scale change of latent heat of PCM is also not an
efficient way to reduce the air temperature fluctuation and increase
the cooling capacity of the VEAHE-APCM system. The possible
reason is that the used PCM component with a low thermal conductivity and density will have negative impacts on the storage and
release of the selected PCM. In addition, a relatively small PCM
design parameters and small-scale change of latent heat are
3.2.3. Impacts of latent heat of PCM
The outlet air temperature and cooling capacity of the VEAHEAPCM system under different latent heats of PCM are investigated. The selected latent heat is 130, 160, 190, 220 and 260 kJ/kg
based on the common PCM type on the commercial market. For the
parametrical comparison purpose, other input parameters of PCM,
i.e., PCM length, PCM thickness, thermal conductivity of PCM, PCM
temperature and density of PCM, are constant, as listed in Table 9.
The impacts of the PCM latent heat on the outlet air temperature
and cooling capacity is shown in Fig. 9. The average temperature
and temperature fluctuation of air at the outlet, and average cooling
capacity under different PCM latent heats are listed in Table 10.
Table 5
Other input parameters of PCM.
PCM length
PCM thickness
Thermal conductivity of PCM
Latent heat of PCM
Density of PCM
Solid
Liquid
3.6 m
10 mm
0.5 W/(m$K)
160 kJ/kg
870 kg/m3
779 kg/m3
409
Z. Liu, P. Sun, M. Xie et al.
Renewable Energy 173 (2021) 401e414
Table 6
The average temperature and temperature fluctuation of outlet air, and average cooling capacity of proposed system under different PCM temperatures.
PCM temperature
18 C
20 C
22 C
24 C
26 C
Average temperature of outlet air
Temperature fluctuation of outlet air
Average cooling capacity
22.45 C
2.50 C
312.70 W
22.45 C
2.50 C
312.70 W
22.49 C
2.04 C
310.74 W
22.50 C
2.23 C
310.23 W
22.45 C
2.50 C
312.70 W
Table 7
Other input parameters of PCM.
PCM length
PCM thickness
Thermal conductivity of PCM
PCM temperature
Latent heat of PCM
3.6 m
10 mm
0.5 W/(m$K)
22 C
160 kJ/kg
another reasons for the minor impact of PCM latent heat on the
system performance. Actually, from the perspective of system
initial investment, the increasing of the latent heat of PCM is
possible to significantly increase its cost. Thus, the only increasing
of the latent heat is not technically effective, in terms of the temperature fluctuation of outlet air and average cooling capacity.
3.3. Taguchi method-signal to noise ratio analysis
It is noticed that, in Section 3.2, the parametrical analysis only
focused on separate single PCM parameter with control variable
method (i.e., each case focuses on one variable, while other variables are kept constant), without simultaneous and comprehensive
considerations on all combined parameters due to the complexity
in experimental designs and expensive cost for experiment
implementation. In this section, considering the complexity in
experimental designs and expensive cost for experiment implementation in multivariant nonlinear systems, a dimensionality
reduction approach from redundant experiments and simulations
was adopted for multivariant optimization and sensitivity analysis.
According to Table 11, the trial experiments are carried out and the
trial operation results are converted into signal-to-noise (S/N) ratio
by adopting the-higher-the-better concept for the cooling capacity,
as shown in Equation (14), and the-lower-the-better concept for
the temperature fluctuation, as shown in Equation (15).
Fig. 8a. The impacts of the density of PCM on outlet air temperature.
,
S
0
1
n
X
1
1
A the higher the better
N ¼ 10log@
n j¼1 y2T;j
(14)
,
S
0
1
n
X
1
y2 A the lower the better
N ¼ 10log@
n j¼1 T;j
(15)
Afterwards, the response table for the cooling capacity and the
temperature fluctuation are listed in Table 12 (a) and (b), respectively. The influence order of each considered parameter on the
cooling capacity is shown in the rank row from Table 12 (a).
Ranking 1 and ranking 8 represent the most and least influential
Fig. 8b. The impacts of the density of PCM on the cooling capacity.
Table 8
Impact of PCM temperatures on system thermal performance.
Density of PCM
Average temperature of outlet air
Temperature fluctuation of outlet air
Average cooling capacity
500 kg/m3
22.47 C
2.11 C
311.62 W
1000 kg/m3
22.50 C
2.02 C
310.59 W
410
1500 kg/m3
22.51 C
1.98 C
310.12 W
2000 kg/m3
22.51 C
1.97 C
309.85 W
2500 kg/m3
22.52 C
1.97 C
309.67 W
Z. Liu, P. Sun, M. Xie et al.
Renewable Energy 173 (2021) 401e414
Table 9
Other input parameters of PCM.
PCM length
PCM thickness
Thermal conductivity of PCM
PCM temperature
Density of PCM
Solid
3.6 m
10 mm
22 C
0.5 W/(m$K)
Liquid
3
870 kg/m
779 kg/m3
conductivity of PCM at 10 W/(m$K)), D4 (density of PCM at
2000 kg/m3), and A5 (PCM thickness at 30 mm). Meanwhile, from
the perspective of the air temperature fluctuation at the outlet,
optimal levels of the selected parameters are A5 (PCM thickness at
30 mm), E3 (melting temperature of PCM at 22 C), B4 (length of
PCM at 13 m), C1 (latent heat of PCM at 130 kJ/kg), F3 (thermal
conductivity of PCM at 6 W/(m$K)), and D4 (density of PCM at
2000 kg/m3).
It should also be noticed that, the cooling capacity is dominated
by the melting temperature of PCM (factor E), followed by the
latent heat of PCM (factor C). Next come the length of PCM (B),
thermal conductivity of PCM (F), (density of PCM (D), and the
thickness of PCM (A). In other words, the PCM thickness of shows
limited effect on the system cooling capacity. This indicates that,
the melting temperature of PCM can be chosen based on the
principle that more attention could be paid to the storage of natural
cooling energy and the release of stored energy, while little
attention is paid to the thickness design of PCM due to the limited
contribution.
Furthermore, the temperature fluctuation at the outlet is
dominated by the PCM thickness (factor A), followed by the melting
temperature of PCM (factor E). Next come the length of PCM (B),
latent heat of PCM (C), thermal conductivity of PCM (F), and the
density of PCM (D). In other words, the PCM density shows limited
impact on the temperature fluctuation at the outlet. This result
indicates that, the PCM thickness can be designed based on the
principle with focus on the natural cooling energy storage and
release.
Fig. 9a. The impacts of the latent heat of PCM on the outlet air temperature.
3.4. Taguchi methodANOVA analysis
In order to further quantitatively study the impacts of various
factors on the energy performance of the VEAHE-APCM system, the
analysis of variance (ANOVA) is applied to quantify the contribution
rate of each considered parameter to the system criteria. Tables 13
and 14 show the calculation values of the ANOVA analysis of the
VEAHE-APCM system. The sum of squares (SS) and the degree of
freedom (DF) can be calculated based on Equations (16) and (17)
[33], respectively.
Fig. 9b. The impacts of the latent heat of PCM on the cooling capacity.
r Xr
SS ¼
K2
i¼1 i
n
factor, respectively. The best combination of all considered PCM
parameters in the VEAHE-APCM system is thereafter determined
by selecting the level with the largest value of the S/N ratio. Thus,
for the cooling capacity, the optimal levels of the considered parameters are E2 (melting temperature of PCM at 20 C), C1 (latent
heat of PCM at 130 kJ/kg), B3 (length of PCM at 9 m), F5 (thermal
!
1 Xn
y
i¼1 i
n
!2
(16)
DF ¼ level e 1
(17)
As shown in Table 13, the melting temperature and latent heat of
PCM play the dominant role in the cooling capacity, with the
Table 10
The average temperature and temperature fluctuation of outlet air, and average cooling capacity of the proposed system under different PCM latent heat.
Latent heat of PCM (kJ/kg)
Average temperature of outlet air ( C)
Temperature fluctuation of outlet air ( C)
Average cooling capacity (W)
130
160
190
220
260
22.49
2.07
311.01
22.49
2.04
310.74
22.50
2.02
310.53
22.50
2.01
310.37
22.51
1.99
310.21
411
Z. Liu, P. Sun, M. Xie et al.
Renewable Energy 173 (2021) 401e414
Table 11
S/N ratio on cooling capacity and temperature fluctuation.
Number of test
A
B
C
D
E
F
Cooling capacity (W)
S/N ratio
Temperature fluctuation ( C)
S/N ratio
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
22
22
1
8
22
8
8
1
8
15
15
1
30
15
15
22
8
1
15
30
30
1
30
22
30
5
1
15
5
15
9
13
9
15
9
5
1
5
15
13
13
1
13
1
9
15
5
13
9
1
190
220
160
130
260
260
220
220
190
130
160
130
220
220
260
130
160
190
190
190
130
260
160
160
260
2500
2000
2500
1500
1500
2000
2500
1500
500
2500
2000
500
500
1000
500
1000
1000
2000
1500
1000
2000
1000
1500
500
2500
18
26
26
26
24
18
20
22
22
24
22
18
24
18
26
22
24
24
20
26
20
20
18
20
22
10
6
8
3
1
8
1
10
6
6
1
1
8
3
10
8
10
3
8
1
10
6
6
3
3
14830.26
14468.18
14472.84
14596.67
14720.25
15198.93
15477.36
15266.15
15016.81
15278.64
15452.86
15259.14
14100.11
14722.74
14846.46
15587.32
14992.22
14754.87
15184.96
15073.58
16424.42
15328.37
15198.86
15381.23
14956.61
83.42
83.21
83.21
83.29
83.36
83.64
83.79
83.67
83.53
83.68
83.78
83.67
82.98
83.36
83.43
83.86
83.52
83.38
83.63
83.56
84.31
83.71
83.64
83.74
83.50
2.39
2.33
2.84
2.32
1.76
2.12
1.91
1.72
1.52
1.73
1.77
2.55
1.75
2.30
2.50
1.21
2.35
2.30
2.47
1.94
1.22
2.54
1.59
2.17
2.42
7.57
7.34
9.07
7.30
4.93
6.55
5.64
4.70
3.64
4.74
4.95
8.14
4.87
7.22
7.94
1.67
7.42
7.22
7.85
5.78
1.71
8.09
4.04
6.72
7.69
comes the thermal conductivity of PCM with the percentage
contribution of 17.17%. Furthermore, the cooling capacity is less
dependent on the density of PCM and PCM thickness with much
low percentage contribution. In terms of the temperature fluctuation, as shown in Table 14, the PCM thickness and melting temperature of PCM play the dominant role, with the percentage
contribution of 31.27% and 26.18%, respectively. Next comes the
length of PCM with the percentage contribution of 24.17%.
Table 12a
Response table for the cooling capacity.
S/N ratio
D (max-min)
Level
A
B
C
D
E
F
1.00
2.00
3.00
4.00
5.00
1.57
83.52
83.55
83.58
83.52
83.60
0.08
5.19
6.00
83.50
83.44
83.66
83.62
83.55
0.22
14.22
3.00
83.76
83.58
83.51
83.40
83.53
0.36
22.74
2.00
83.47
83.60
83.52
83.66
83.52
0.19
12.18
5.00
83.55
83.84
83.67
83.38
83.34
0.50
31.66
1.00
83.63
83.45
83.55
83.46
83.67
0.22
14.00
4.00
Contribution ratio (%)
Rank
3.5. Research limitations, applications and future prospects
Based on above-mentioned analysis, the VEAHE-APCM system
has been explained to possess great practical application potentials.
Considering the economic feasibility and thermal performance of
the VEAHE-APCM system, this study mainly focuses on the multivariant optimization and sensitivity analysis for different critical
PCM parameters based on the Taguchi method with S/N ratio
analysis and ANOVA analysis. However, the impacts of associated
costs of PCM container construction on the multivariant optimization results is not considered in this study. In reality, the PCM
container construction cost related to the design parameters, such
as the PCM length, is nonlinearly affected by various factors,
including the material cost, processing cost, construction difficulty
and etc. Furthermore, the multivariable optimization and sensitivity analysis are merely conducted under short-term 24 h
continuous operation, whereas the long-time performance analysis
Table 12b
Response table for the temperature fluctuation.
S/N ratio
D (max-min)
Contribution ratio (%)
Rank
Level
A
B
C
D
E
F
1.00
2.00
3.00
4.00
5.00
13.72
7.81
6.11
6.54
5.65
4.82
3.00
21.85
1.00
7.69
6.55
5.70
5.30
5.31
2.38
17.38
3.00
4.71
6.44
6.41
5.95
7.04
2.33
16.98
4.00
6.26
6.04
5.76
5.55
6.94
1.39
10.12
6.00
6.70
6.00
4.53
5.84
7.49
2.96
21.55
2.00
5.89
7.23
5.57
6.00
5.87
1.66
12.11
5.00
percentage contribution of 37.61% and 28.91%, respectively. Next
Table 13
Taguchi methodANOVA analysis of cooling capacity.
Control factors
Degree of freedom (DF)
Sum of squares (SS)
Average of square (AS)
F
P
Percentage contributions
PCM thickness (mm)
Length of PCM (m)
Latent heat of PCM (kJ/kg)
Density of PCM (kg/m3)
Melting temperature of PCM ( C)
Thermal conductivity of PCM (W/m K)
All other/error
Total
4.00
4.00
4.00
4.00
4.00
4.00
8.00
15.00
6.38
0.16
0.34
0.12
0.84
0.19
0.27
4.73
1.60
0.04
0.09
0.03
0.21
0.05
0.03
46.47
1.15
2.50
0.85
6.09
1.41
Pooled
0.43
0.17
0.55
0.04
0.35
1.54
12.10%
28.91%
4.21%
37.61%
17.17%
412
Z. Liu, P. Sun, M. Xie et al.
Renewable Energy 173 (2021) 401e414
Table 14
Taguchi methodANOVA analysis of temperature fluctuation.
PCM thickness (mm)
Length of PCM (m)
Latent heat of PCM (kJ/kg)
Density of PCM (kg/m3)
Melting temperature of PCM ( C)
Thermal conductivity of PCM (W/m K)
All other/error
Total
Degree of freedom (DF)
Sum of squares (SS)
Average of square (AS)
F
P
Percentage contributions
4.00
4.00
4.00
4.00
4.00
4.00
8.00
15.00
47.49
20.71
15.24
5.76
24.15
8.34
14.10
121.69
11.87
5.18
3.81
1.44
6.04
2.09
1.76
6.74
2.94
2.16
0.82
3.43
1.18
0.03
0.13
0.21
0.57
0.10
0.42
1.46
31.27%
24.17%
18.99%
5.32%
26.18%
4.70%
with the increasing of the PCM latent heat. In the case study, as
the latent heat of PCMs increase from 130 to 260 kJ/kg, the
variations of corresponding temperature fluctuation at the
outlet and cooling capacity are 0.08 C and 0.80 W, respectively.
2) By adopting the dimensionality reduction approach from
redundant experiments and simulations, multivariant optimization and sensitivity analysis results indicated that, in terms of
system cooling capacity, the optimal combination of thermophysical parameters are: PCM melting temperature at 20 C,
PCM latent heat at 130 kJ/kg, PCM length at 9 m, thermal conductivity of PCM at 10 W/(m$K), PCM density of at 2000 kg/m3,
and PCM thickness at 30 mm. Meanwhile, from the perspective
of the temperature fluctuation of the outlet air, optimal levels of
the selected parameters are PCM thickness at 30 mm, PCM
melting temperature at 22 C, length of PCM at 13 m, latent heat
of PCM at 130 kJ/kg, thermal conductivity of PCM at 6 W/(m$K),
and density of PCM at 2000 kg/m3.
3) The sensitivity analysis results indicated that, the cooling capacity is dominated by the PCM melting temperature (contribution ratio at 31.66%), followed by the latent heat of PCM
(contribution ratio at 22.74%), the length of PCM (contribution
ratio at 14.22%), thermal conductivity of PCM (contribution ratio
at 14.00%), PCM density (contribution ratio at 12.18%), and the
thickness of PCM (contribution ratio at 5.19%). For the cooling
capacity, the PCM fusion temperature should be given priority
for natural cooling energy storage and release, whereas less
attention should be paid to the PCM thickness due to the limited
contribution. Furthermore, the temperature fluctuation at the
outlet is dominated by the PCM thickness (contribution ratio at
21.85%), followed by the melting temperature of PCM (contribution ratio at 21.55%), length of PCM (contribution ratio at
17.38%), latent heat of PCM (contribution ratio at 16.98%), thermal conductivity of PCM (contribution ratio at 12.11%), and the
density of PCM (contribution ratio at 10.12%). Therefore, the
PCM thickness should be given precedence over other parameters when stabilising the outlet air temperature.
4) The ANOVA analysis of cooling capacity indicates that, the PCM
melting temperature and PCM latent heat of play the dominant
role in the system’s cooling capacity, with the percentage
contribution of 37.61% and 28.91%, respectively. For temperature
fluctuation, the PCM thickness and melting temperature play
the dominant role, with the percentage contribution of 31.27%
and 26.18%, respectively. Above results can provide benchmark
and guidelines on thermo-physical parameters’ selection of
PCM, and promote the application of the VEAHE-APCM systems
in buildings.
is necessary, such as one month or one year. In the following study,
a long-term operating condition (e.g., the hottest month and
coldest month time under typical operating conditions) will be
considered and related research should be explored to comprehensively analyze the system performance in practical application.
Moreover, the analysis and discussion in this study are mainly
focused on air temperature and cooling capacity, whereas the indoor thermal environment has not been considered. Our followingup study will integrate the proposed VEAHE-APCM in the building
model, to quantify the contribution to indoor thermal environment,
indoor temperature fluctuation and building cooling load. In
addition, in respect to spatiotemporal intermittence of renewable
energy, e.g., solar, wind and even geothermal energy, the integration of the VEAHE-APCM systems with other distributed building
systems, such as PCM ventilated Trombe walls [40] and ventilated
PCM-PV systems [41], will be studied to improve the energy supply
reliability and operational stability with synergistic functions of
each subsystem.
4. Conclusions
This study mainly focused on the multivariant optimization and
sensitivity analysis of a novel high energy-efficient coupled system,
i.e., annular PCM integrated VEAHE system, for pre-cooling applications in buildings. Compared with traditional horizontal EAHE
systems, the VEAHE-APCM system shows some obvious advantages, including less occupied floor space, higher energy efficiency
for geothermal energy utilisation, easier discharge of air condensate water to avoid the growth of bacteria and more stable outlet air
temperature. An enthalpy-based numerical model was developed
and was then calibrated through the online monitored values with
a maximum absolute relative error of 1.59%. Afterwards, in terms of
cooling capacity and outlet temperature fluctuation, benchmark
and guidelines on thermo-physical parameters selection of PCM
have been established, through multivariant parametrical analysis
on several critical PCM parameters (i.e., PCM thickness, length,
latent heat, density, melting temperature and thermal conductivity). Last but not the least, considering the complexity in experimental designs and expensive cost for experiment implementation,
a dimensionality reduction approach from redundant experiments
and simulations was adopted for multivariant optimization and
sensitivity analysis, using Taguchi method with S/N ratio analysis
and ANOVA analysis. The main conclusions from the abovementioned analysis can be summarized as:
1) Parametrical analysis indicates that compared to other melting
temperature, PCM fusion temperatures at 20 C and 22 C are
more competitive in cooling capacity regulation and flattened
outlet air temperature. The temperature fluctuation decreases
with the increase of PCM density, and the decreasing magnitude
slows down when the PCM density reaches 1000 kg/m3. In
terms of the latent heat of PCMs, the temperature fluctuation
and average cooling capacity decrease gradually and slightly,
CRediT authorship contribution statement
Zhengxuan Liu: Conceptualization, Data curation, Formal
analysis, Investigation, Methodology, Validation, Visualization.
Pengchen Sun: Project administration, Resources, Writing e
413
Z. Liu, P. Sun, M. Xie et al.
Renewable Energy 173 (2021) 401e414
review & editing. Mingjing Xie: Project administration, Resources,
Writing e review & editing. Yuekuan Zhou: Conceptualization,
Data curation, Formal analysis, Funding acquisition, Investigation,
Methodology, Supervision, Writing e review & editing, Project
administration, Resources, Software, Supervision, Validation,
Visualization. Yingdong He: Writing e review & editing. Guoqiang
Zhang: Funding acquisition, Investigation, Methodology, Supervision, Writing e review & editing. Dachuan Chen: Project administration, Resources, Writing e review & editing. Shuisheng Li:
Project administration, Resources, Writing e review & editing.
Zhongjun Yan: Formal analysis, Methodology. Di Qin: Formal
analysis, Methodology.
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Declaration of competing interest
The authors declare that they have no known competing
financial interests or personal relationships that could have
appeared to influence the work reported in this paper.
Acknowledgements
The authors will be very thankful for the support from the China
Construction Design Group Co.LTD Engineering Technology
Research Institute and China Construction Fifth Engineering Division Corp., Ltd.
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