![A comparison of cooling capacity per 24.5 kg of sorbent mass from three numerical models, and experimental results (Chang et al. [23]).](https://www.researchgate.net/publication/340624942/figure/fig5/AS:11431281397352338@1745502459426/A-comparison-of-cooling-capacity-per-245-kg-of-sorbent-mass-from-three-numerical-models_Q320.jpg)
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energies
Article
Effects of Evaporator and Condenser in the Analysis
of Adsorption Chillers
Woo Su Lee, Moon Yong Park, Xuan Quang Duong , Ngoc Vi Cao and Jae Dong Chung *
Department of Mechanical Engineering, Sejong University, Seoul 05006, Korea; kanzest@gmail.com (W.S.L.);
cavalier94@naver.com (M.Y.P.); duongquang.mt@gmail.com (X.Q.D.); caongocvi@gmail.com (N.V.C.)
*Correspondence: jdchung@sejong.ac.kr; Tel.: +82-2-3408-3776; Fax: +82-2-3408-4333
Received: 11 March 2020; Accepted: 11 April 2020; Published: 13 April 2020
Abstract:
In a survey of the literature from the last 20 years, 20% of the numerical models used to
analyze the performance of adsorption chillers assumed the evaporator and condenser were ideal,
with a fixed evaporation temperature and condenser temperature, and ignored interactions between
the adsorption bed and evaporator/condenser. Even when the interaction with the evaporator and
condenser was included, the other 80% of studies modeled the adsorption bed based on the LPM
(lumped parameter method), which ignores the geometry effect and contact resistance of the bed,
and thus reduces the accuracy of the analysis. As a consequence, these earlier numerical studies
overestimated the system performance of the adsorption chiller. In this study, we conducted a refined
numerical approach which avoids these limitations, producing estimates in close agreement with
experimental results. Compared with our approach, the models with ideal treatment of evaporator
and condenser overestimated COP (coefficient of performance) and SCP (specific cooling power) by
as much as 16.12% and 24.64%, respectively. The models based on LPM overestimated COP and SCP
by 22.82% and 11.28%, compared to our approach.
Keywords: adsorption chiller; numerical analysis; evaporator; condenser
1. Introduction
Demand for cooling has rapidly increased due to global warming and economic development.
There are many types of refrigerator systems that can be employed to address this demand. Among
them, the vapor compression refrigerator has been most commonly used. However, its operation
negatively impacts the environment and consumes an excessive amount of electric power. As a result,
many researchers have focused on the development of eco-friendly refrigeration systems. Among
these, heat-driven refrigerators, such as absorption, desiccant, and adsorption cooling system, have
been highly attractive.
The adsorption chiller operates using reversible adsorption and desorption processes, in a cycle
of preheating, heating, pre-cooling, and cooling. During the pre-heating process, the sorption bed
is isolated from both the condenser and the evaporator by closing the connecting valves. Because
desorption is an endothermic process, heat must be supplied to maintain the desorption process.
When the pressure of the sorption bed reaches that of the condenser, the valve connecting the sorption
bed and the condenser is opened and the desorbed refrigerant flows to the condenser. During the
pre-cooling process, the sorption bed is again isolated by closing the connecting valves. Because of
the exothermic nature of adsorption, the heat needs to be removed by the cold heat source. When the
pressure of the sorption bed reaches that of the evaporator, the valve connecting to the evaporator is
opened and the evaporated refrigerant vapor moves towards the sorption bed.
Energies 2020,13, 1901; doi:10.3390/en13081901 www.mdpi.com/journal/energies
Energies 2020,13, 1901 2 of 14
To understand the adsorption chiller process in more detail, a number of researchers have been
conducting studies, investigating adsorbents [
1
–
3
], the geometry of the heat exchanger [
4
–
6
], advanced
cycle [7–10], and operating conditions [11–13].
From the literature survey, the research target of numerical analyses was confined to the adsorption
bed due to the limitation in numerical analysis. From a literature survey of the last 20 years, 20% of
the published papers were found to belong to this category. Although they rigorously modeled the
adsorption bed, they did not include modeling of the evaporator or condenser.
Adsorption beds have the same role as the compressor in a conventional refrigerator. Due
to the reversibility of adsorption and desorption processes, outlet temperature is unstable and
fluctuates [
14
,
15
]. For accurate prediction of coefficient of performance (COP), the change of chilled-out
temperature of the evaporator should be included in the modeling, and the analysis of evaporators
and condensers is important.
Previous numerical studies [
1
,
3
,
5
,
6
] covered many interesting issues and practical improvement
of adsorption cooling systems. However, there has been no report on the impact of assumption on the
evaporator and condenser. The isotherm of the sorbent is a function of pressure and temperature [
3
].
Thus, the idealized evaporator temperature distorts the evaluation of the system performance.
The other 80% of published papers included modeling of the evaporator or condenser. However,
modeling of the adsorption bed, which is the most crucial component in the adsorption chiller, was
based on the lumped parameter method (LPM), i.e., the adsorption bed, and the evaporator and
condenser were modeled by assuming there was no spatial variation. Thus, the LPM-based analyses
cannot include the effects of geometric features and the interaction between the sorbent material and
the metallic finned tube. Note that geometric factors such as fin height, fin spacing, tube diameter,
and thickness, are highly influential on the system performance, thus plenty of previous studies
have conducted the optimization of geometric factors. The LPM, which assumes no special variation,
affirmatively deteriorates the accuracy of the analysis.
Most of LPM-based analyses were for macrosystems such as recovery cycles and multi-stages.
They have advantages in understanding system arrangement and the effect of each composition.
However, essentially, LPM-based analyses suffer from low accuracy due to the excessive simplification
of the adsorption bed, which is the most important part of adsorption cooling system.
In this study, we numerically analyzed an adsorption chiller with a SWS-1 L +water working pair
based (1) on a rigorous CFD simulation for the adsorption bed, and (2) also including the evaporator
and condenser. Model validity was checked by the comparison with experiments. For the present
approach and the previous approaches, a close examination on the accuracy of system performance
prediction was conducted. This approach provided detailed information over time and space and also
enabled a much closer estimate of system performance.
2. Numerical Method
2.1. Mathematical Model
Figures 1and 2show the schematics of the 2-bed adsorption chiller, and the current numerical
model, respectively. The numerical model includes the following assumptions.
(1)
The particles in the adsorption bed are all spherical with a uniform size and porosity.
(2)
Thermal equilibrium between the adsorbed and vapor phases is assumed.
(3)
A two-dimensional (2D) axisymmetric model is assumed.
(4)
Refrigerant vapor is an ideal gas and the adsorbed phase is liquid.
(5)
There is no heat loss through the chamber wall and the effect of radiation is negligible.
(6)
The thermo-physical properties of the thermal fluid, tube, fins, dry adsorbent, adsorbate liquid,
and gas are constant, except for the density of the adsorbate gas.
Energies 2020,13, 1901 3 of 14
Energies 2020, 13, x FOR PEER REVIEW 3 of 14
Figure 1. The schematic of the 2-bed adsorption chiller with two adsorption beds, evaporator, and
condenser.
Figure 2. Current numerical model of adsorption bed with a circular fin-tube heat exchanger.
2.2. Energy and Mass Balance Equations
2.2.1. Adsorption Bed
Our recent research showed that inter- and intra-particle mass transfer kinetics have a large
influence on system performance, and therefore it is highly recommended that models be chosen
considering a valid diffusion ratio range (Hong et al. [16]). Given a sufficiently large value of Deq/rp,
the non-isobaric model and linear driving force (LDF) model were used for the inter- and intra-
particle mass transfer models, respectively.
Non-isobaric model (Hong et al. [3], Niazmand et al. [4], Hong et al. [13]):
v
t v v 0
ads
q
u
tt
(1)
Figure 1.
The schematic of the 2-bed adsorption chiller with two adsorption beds, evaporator,
and condenser.
Energies 2020, 13, x FOR PEER REVIEW 3 of 14
Figure 1. The schematic of the 2-bed adsorption chiller with two adsorption beds, evaporator, and
condenser.
Figure 2. Current numerical model of adsorption bed with a circular fin-tube heat exchanger.
2.2. Energy and Mass Balance Equations
2.2.1. Adsorption Bed
Our recent research showed that inter- and intra-particle mass transfer kinetics have a large
influence on system performance, and therefore it is highly recommended that models be chosen
considering a valid diffusion ratio range (Hong et al. [16]). Given a sufficiently large value of Deq/rp,
the non-isobaric model and linear driving force (LDF) model were used for the inter- and intra-
particle mass transfer models, respectively.
Non-isobaric model (Hong et al. [3], Niazmand et al. [4], Hong et al. [13]):
v
t v v 0
ads
q
u
tt
(1)
Figure 2. Current numerical model of adsorption bed with a circular fin-tube heat exchanger.
2.2. Energy and Mass Balance Equations
2.2.1. Adsorption Bed
Our recent research showed that inter- and intra-particle mass transfer kinetics have a large
influence on system performance, and therefore it is highly recommended that models be chosen
considering a valid diffusion ratio range (Hong et al. [
16
]). Given a sufficiently large value of D
eq
/r
p
,
the non-isobaric model and linear driving force (LDF) model were used for the inter- and intra-particle
mass transfer models, respectively.
Non-isobaric model (Hong et al. [3], Niazmand et al. [4], Hong et al. [13]):
εt∂ρv
∂t+∇·ρv→
uv+ρads
∂q
∂t=0 (1)
Energies 2020,13, 1901 4 of 14
The distribution of the velocity of water vapor (
*
uv
) in the adsorption bed follows the porous
model, expressed as Darcy’s law:
*
uv=−Kapp
µv∇P(2)
The apparent permeability, K
app
, was obtained using the following equations. (Bird et al. [
17
], Lee
and Thodos [18], Ruthven [19]):
Kapp =Kd+εbµv
τPDeq (3)
Kd=εb3dp2
150(1−εb)2(4)
Deq =
1
0.02628 √T3/MV
Pσ2Ω
+1
48.5dpore pTb/Mv
−1
(5)
τ=εb−0.4 (6)
dpore =0.6166dp(7)
where σand Ωare σ=2.641Å and Ω=2.236.
When substituting Equation (2) into Equation (1), the following equation can be obtained:
εt
∂P
RvT
∂t+∇· ρvKapp
µ∇P!+ρads ∂q
∂t=0 (8)
LDF model (Hong et al. [16]):
∂q
∂t=15Dso
rp2exp −Ea
RuTb!(q∗−q)(9)
The pre-exponent constant, D
so
, and the activation energy of diffusion, E
a
, were 0.000254 m/s
2
and 42,000 J/s, respectively. The adsorption amount is expressed in isotherms and the isotherm of
SWS-1 L from Saha et al. [20] was used:
q∗=1.6 ×10−12Cq∗
1+2×10−12Cq∗1.11/1.1 (10)
Cq∗=Pexp ∆H
RvTb!(11)
The heat transfer equation in the adsorption bed is expressed as:
ρCp∂Tb
∂t+∇·ρvCp,v *
uvTb=∇·(kb∇Tb)+ρads∆H∂q
∂t(12)
where ρCpis the heat capacity of the entire bed, including the adsorbent and the refrigerant.
ρCp=εtρvCp,v+ρads Cp,ads +qCp,b(13)
εt=εb+ (1−εb)εp(14)
The second term on the right-hand side in Equation (12),
ρads∆H∂q
∂t
, is the heat generated by
adsorption and desorption.
Energies 2020,13, 1901 5 of 14
The energy equation for the heat transfer fluid is as follows:
ρCp∂Tf
∂t+∂
∂ZρfCp,fufTf=∂
∂Z kf∂Tf
∂Z!+4
dihTc,R=Ri−Tf(15)
The last term is a heat exchange term. The convective heat transfer coefficient, h, is obtained from
the following correlations:
Nu =0.023Re0.8Prnn=0.3 forcoolingphase
n=0.4 forheatingphase (16)
The energy equation for the copper fin-tube is as follows:
ρCp,c ∂Tc
∂t=∇(kc∇Tc)(17)
2.2.2. Evaporator
The evaporator is connected to the adsorption bed during the adsorption process and allows the
evaporated refrigerant vapor to move towards the adsorption bed. Therefore, the energy equilibrium
equation of the evaporator is expressed as (Miyazaki et al. [21]):
mCpeva
dTeva
dt =−θhfg mads
dqads
dt !+.
mCpchill(Tchill,in −Tchill,out )−Cp(Tcon −Teva)mads
dqdes
dt (18)
Note that the evaporator was modeled by LPM, like in most previous research. The novelty in
this work was to model the sorption bed from the refined CFD simulation, and simultaneously include
the effect of the evaporator and condenser.
The term on the left-hand side in Equation (18) is the heat capacity, showing the internal energy
of the entire evaporator. The first term on the right-hand side shows the cooling energy generated
by the latent heat of evaporation.
θ
is equal to 1 or 0 during adsorption (or desorption) and the
switching period, respectively. The second term on the right-hand side is the heat exchange between
the evaporator and chilled water, and the last term is the heat needed to lower the temperature of the
regenerated refrigerant from Tcon to Teva.
2.2.3. Condenser
The condenser is connected to the adsorption bed during the desorption process to condense the
desorbed vapor. The regenerated fluid is sent to the evaporator through the U-tube. The condenser
energy equilibrium equation is as follows (Miyazaki et al. [21]):
mCpcon
dTcon
dt =−θhfg mads
dqdes
dt !+.
mCpcon(Tcool,in −Tcool,out )−Cp(Tdes −Tcon)mads
dqdes
dt (19)
The term on the left-hand side is heat capacity reflecting the internal energy of the entire condenser.
The first term on the right-hand side is the latent heat of evaporation. The second term is the heat
exchange between condenser and cooling water, and the last term is the heat needed to lower the
refrigerant temperature from Tdes to Tcon.
Energies 2020,13, 1901 6 of 14
2.2.4. Outlet temperature
The log mean temperature difference (LMTD) determines the outlet temperature of the evaporator
and condenser (Miyazaki et al. [21]):
Tchill,out =Teva + (Tchill,in −Teva)exp
−(UA)eva
.
mCpchill
(20)
Tcool,out =Tcon + (Tcool,in −Tcon)exp
−(UA)con
.
mCpcool
(21)
where Uis the overall heat transfer coefficient and Ais the heat transfer area.
2.2.5. Mass balance equation
The mass balance equations are expressed as follows (Miyazaki et al. [21]):
dmeva
dt =−mads"dqads
dt +dqdes
dt #(22)
2.3. Initial and Boundary Conditions
Initial condition for adsorption process:
Tinitial =Tads =303.15K
Pinitial =Pads =1633Pa
qinitial =qads =0.13kg/kg
(23)
Initial condition for desorption process:
Tinitial =Tdes =353.15K
Pinitial =Pdes =4144Pa
qinitial =qdes =0.13kg/kg
(24)
Boundary condition:
R=Ri, 0 ≤Z≤Zo:h(Tc−Tf)=kc∂Tc
∂R(25)
R=Rm, 0 ≤Z≤Zo:kc∂Tc
∂R=∆T
1/hCR =kb∂Tb
∂R,∂P
∂R=0 (26)
R=Ro, 0 ≤Z≤Zo:∂Tb
∂R=0, "∂P
∂R=0 forthepre-heatingandpre-coolingphase
P=PevaorPcon fortheheatingandcoolingphase (27)
Rm≤R≤Roatfin-absorbentboundary : kc∂Tc
∂Z=∆T
1/hCR =kb∂Tb
∂Z,∂P
∂Z=0 (28)
"Tf=Tads at Z =0(cooling phase)
Tf=Tdes at Z =0(heating phase)(29)
where 1/h
CR
is the contact resistance between the adsorption bed and the tube (or fin), empirically
obtained by Zhu and Wang [22] as follows:
1
hCR =0.00122T2−0.1699T+8.15×10−3(30)
Energies 2020,13, 1901 7 of 14
2.4. Performance Index
The coefficient of performance (COP) and specific cooling power (SCP) were selected as
performance indicators, and were defined as the following:
COP =Qeva
Qin (31)
SCP =Qeva
madstcycle (32)
where Q
eva
denotes the input heat energy supplied to the sorption bed during the desorption process,
mb is the total mass of the solid sorbent, and t
cycle
means cycle time. When the evaporator and the
condenser were assumed to be ideal, as in most previous studies, the cooling energy, Q
eva
, was obtained
as the amount of adsorbed vapor (Equation (33)). However, when the evaporator and the condenser
are included in the modeled analysis, the cooling energy should be obtained by using the temperature
difference between the inlet chilled water and the outlet chilled water of the evaporator (Equation (34)).
Qeva =LvZtads
tdes Zinterface ρv*
uv·d*
Adt (33)
Qeva =Ztads
tdes n.
mCpchill(Tchill,in −Tchill,out )odt (34)
Qin =Ztdes
tads n.
mCpcool(Tcool,in −Tcool,out )odt (35)
where Lvis the latent heat and is expressed as follows:
Lv=L(Teva)−CP,ads (Teva −Tcon)(36)
2.5. Numerical Procedure
The detailed numerical procedures used in the two models, i.e., the previous studies which
assumed an ideal evaporator and condenser and the newly proposed model, are shown in Figures 3
and 4. The separate analysis of each adsorption bed and its integration with an evaporator and
condenser avoids the over-simplified assumptions in the previous model and enables an accurate
estimation of bed behavior and evaporator outlet temperature, which results in a more accurate
estimation of system performance.
Energies 2020, 13, x FOR PEER REVIEW 7 of 14
2.4. Performance Index
The coefficient of performance (COP) and specific cooling power (SCP) were selected as
performance indicators, and were defined as the following:
eva
in
COP Q
Q
(31)
eva
cycle
SCP
ads
Q
mt
(32)
where Qeva denotes the input heat energy supplied to the sorption bed during the desorption process,
mb is the total mass of the solid sorbent, and tcycle means cycle time. When the evaporator and the
condenser were assumed to be ideal, as in most previous studies, the cooling energy, Qeva, was
obtained as the amount of adsorbed vapor (Equation (33)). However, when the evaporator and the
condenser are included in the modeled analysis, the cooling energy should be obtained by using the
temperature difference between the inlet chilled water and the outlet chilled water of the evaporator
(Equation (34)).
ads
des
eva v v v
interface
t
t
Q L u d Adt
(33)
ads
des
eva p chill,in chill,out
chill
t
t
Q mC T T dt
(34)
des
ads
in p cool,in cool,out
t
cool
t
Q mC T T dt
(35)
where Lv is the latent heat and is expressed as follows:
P,ads eva con
( ) ( )
v eva
L L T C T T
(36)
2.5. Numerical Procedure
The detailed numerical procedures used in the two models, i.e., the previous studies which
assumed an ideal evaporator and condenser and the newly proposed model, are shown in Figures 3
and 4. The separate analysis of each adsorption bed and its integration with an evaporator and
condenser avoids the over-simplified assumptions in the previous model and enables an accurate
estimation of bed behavior and evaporator outlet temperature, which results in a more accurate
estimation of system performance.
Figure 3. Flowchart of performance evaluation strategy based on the numerical method with an ideal
evaporator and condenser.
Figure 3.
Flowchart of performance evaluation strategy based on the numerical method with an ideal
evaporator and condenser.
Energies 2020,13, 1901 8 of 14
Energies 2020, 13, x FOR PEER REVIEW 8 of 14
Figure 4. Flowchart of performance evaluation strategy based on the present model including realistic
evaporator and condenser.
3. Results and Discussion
The governing equations subject to the given boundary conditions were solved using STAR-
CCM+v12, a commercial computational fluid dynamics (CFD) program, and additional user-
supplied codes. The grid dependence was thoroughly tested for 2000~9600 hexagonal grids, and the
test results indicated that 4400 grids were sufficient to obtain grid-independent results. The first-
order temporal discretization was used to solve the implicit unsteady problem. A hybrid-scheme and
a central difference scheme were used for the convection and diffusion terms, respectively. The
resulting discretized equations were solved using a Gauss–Seidel algorithm for every time step. Time
steps of 0.01 s were used for the isosteric phase and 0.5 s was used for the isobaric phase. The
computation time was approximately 24 h for a typical model running on an Intel Core i7-8700 CPU
@3.20Ghz, which was two times longer than the earlier model with an ideal evaporator and condenser
because two beds were simultaneously analyzed, as described in Figure 4.
All results were obtained after an initial couple of cycles, which ensured that the system had
reached a quasi-equilibrium state.
The parameters and operating conditions required for the analysis are summarized in Table 1.
The properties of the evaporator and condenser such as overall heat transfer coefficient are given in
Miyazaki et al. [21].
Table 1. Parameter values and operating conditions of the adsorption chiller.
Parameter
Values
Fin pitch
1.68 mm
Fin thickness
0.06 mm
Fin height
6.82 mm
Inner diameter of tube
9.6 mm
Outer diameter of tube
8.8 mm
Fluid velocity
1 m/s
Heating temperature
80 ℃
Cooling temperature
30 ℃
Cycle time
900 s
Density
700 kg/m3
Specific heat
900 J/kgK
Thermal conductivity
0.2 W/mK
Heat of adsorption
2760 kJ/kg
Total porosity
0.6352
Figure 4.
Flowchart of performance evaluation strategy based on the present model including realistic
evaporator and condenser.
3. Results and Discussion
The governing equations subject to the given boundary conditions were solved using
STAR-CCM+v12, a commercial computational fluid dynamics (CFD) program, and additional
user-supplied codes. The grid dependence was thoroughly tested for 2000~9600 hexagonal grids,
and the test results indicated that 4400 grids were sufficient to obtain grid-independent results. The
first-order temporal discretization was used to solve the implicit unsteady problem. A hybrid-scheme
and a central difference scheme were used for the convection and diffusion terms, respectively. The
resulting discretized equations were solved using a Gauss–Seidel algorithm for every time step. Time
steps of 0.01 s were used for the isosteric phase and 0.5 s was used for the isobaric phase. The
computation time was approximately 24 h for a typical model running on an Intel Core i7-8700 CPU
@3.20Ghz, which was two times longer than the earlier model with an ideal evaporator and condenser
because two beds were simultaneously analyzed, as described in Figure 4.
All results were obtained after an initial couple of cycles, which ensured that the system had
reached a quasi-equilibrium state.
The parameters and operating conditions required for the analysis are summarized in Table 1.
The properties of the evaporator and condenser such as overall heat transfer coefficient are given in
Miyazaki et al. [21].
Table 1. Parameter values and operating conditions of the adsorption chiller.
Parameter Values
Fin pitch 1.68 mm
Fin thickness 0.06 mm
Fin height 6.82 mm
Inner diameter of tube 9.6 mm
Outer diameter of tube 8.8 mm
Fluid velocity 1 m/s
Heating temperature 80 °C
Cooling temperature 30 °C
Cycle time 900 s
Density 700 kg/m3
Specific heat 900 J/kgK
Thermal conductivity 0.2 W/mK
Heat of adsorption 2760 kJ/kg
Total porosity 0.6352
Energies 2020,13, 1901 9 of 14
3.1. Validation
The cooling capacity of the present model was compared to the results of an experiment
by
Chang et al. [23]
. The numerical analysis was conducted under the operating conditions of
Theat =60–90 °C
,T
cool
=30
°C
,T
chill
=14
°C
,T
eva
=15
°C
,t
cycle
=12 min,
.
mcool
=0.6 kg/s,
.
mheat=0.48 kg/s.
The details of the geometrical shapes of the adsorber, evaporator, and condenser are given in
Chang et al. [23].
Figure 5shows that there is close agreement between the present numerical model and the prior
experiment, however, the predictions by LPM or with ideal treatment of the evaporator and condenser
are considerably different than the experiment. Most of the earlier studies, about 80%, are based on
LPM. The assumption that there is no spatial variation in the adsorption bed, a component which is
highly influential on the performance of the adsorption chiller, inherently limits the accuracy of the
model. Also, detailed analyses of the effects of geometric features (fin height, fin spacing, tube diameter,
and thickness) and the interaction between sorbent material and metallic finned tube, are not feasible
in the LPM. The remaining 20% of the studies treat the evaporator and condenser as ideal, even though
the adsorption bed was rigorously modeled. In those models, the evaporator and condenser did not
interact with the adsorption bed and it is assumed that the evaporator temperature and condenser
temperature were fixed, i.e., they assumed an ideal evaporator and condenser. As a consequence, these
models inherently overestimated performance, which is the reason most previous numerical results
showed higher system performance than the experiment.
Energies 2020, 13, x FOR PEER REVIEW 9 of 14
3.1. Validation
The cooling capacity of the present model was compared to the results of an experiment by
Chang et al. [23]. The numerical analysis was conducted under the operating conditions of Theat = 60–
90 ℃, Tcool = 30 ℃, Tchill = 14 ℃, Teva = 15 ℃, tcycle = 12 min,
cool
m
= 0.6 kg/s,
heat
m
= 0.48 kg/s. The details
of the geometrical shapes of the adsorber, evaporator, and condenser are given in Chang et al. [23].
Figure 5 shows that there is close agreement between the present numerical model and the prior
experiment, however, the predictions by LPM or with ideal treatment of the evaporator and
condenser are considerably different than the experiment. Most of the earlier studies, about 80%, are
based on LPM. The assumption that there is no spatial variation in the adsorption bed, a component
which is highly influential on the performance of the adsorption chiller, inherently limits the accuracy
of the model. Also, detailed analyses of the effects of geometric features (fin height, fin spacing, tube
diameter, and thickness) and the interaction between sorbent material and metallic finned tube, are
not feasible in the LPM. The remaining 20% of the studies treat the evaporator and condenser as ideal,
even though the adsorption bed was rigorously modeled. In those models, the evaporator and
condenser did not interact with the adsorption bed and it is assumed that the evaporator temperature
and condenser temperature were fixed, i.e., they assumed an ideal evaporator and condenser. As a
consequence, these models inherently overestimated performance, which is the reason most previous
numerical results showed higher system performance than the experiment.
Figure 5. A comparison of cooling capacity per 24.5 kg of sorbent mass from three numerical models,
and experimental results (Chang et al. [23]).
3.2. Effect of Evaporator/Condenser Model
Figure 6 compares the Clapeyron diagram of the present model and the model of an ideal
evaporator and condenser, i.e., with a fixed evaporation temperature (15 ℃) and condenser
temperature (30 ℃). During the isosteric phase in processes (A) and (C), the valves are disconnected
from the evaporator and condenser and the adsorption bed is isolated. Thus, except for the starting
(4 and 4’) and end points (1 and 1’), there is no difference between the models.
The processes (B) and (D) are the heating and cooling phases, which are desorbing or adsorbing
the vapor. In contrast to the real pressure behavior, which was properly estimated in the present
model, the pressure in the idealized model is assumed to be constant at the saturation pressure
corresponding to the temperature of the evaporator, 15 ℃, or the condenser, 30 ℃.
Figure 7 shows the isotherm of the adsorbent SWS-1 L and compares the adsorption and
desorption amounts corresponding to the ideal and real pressures of the condenser and evaporator.
Figure 5.
A comparison of cooling capacity per 24.5 kg of sorbent mass from three numerical models,
and experimental results (Chang et al. [23]).
3.2. Effect of Evaporator/Condenser Model
Figure 6compares the Clapeyron diagram of the present model and the model of an ideal evaporator
and condenser, i.e., with a fixed evaporation temperature (15
°C
) and condenser temperature (30
°C
).
During the isosteric phase in processes (A) and (C), the valves are disconnected from the evaporator
and condenser and the adsorption bed is isolated. Thus, except for the starting (4 and 4’) and end
points (1 and 1’), there is no difference between the models.
Energies 2020,13, 1901 10 of 14
Energies 2020, 13, x FOR PEER REVIEW 10 of 14
In the model with ideal treatment of the evaporator and condenser, the pressure during the
adsorption and desorption process is constant, shown in the bold dashed line in Figure 7, which
causes constant q*. On the other hand, in the present model, relative pressure varies from 0.09 to 0.11
during the desorption process and varies from 0.31 to 0.4 during the adsorption process, as described
in the hatched region in Figure 7. A larger variation is observed during the adsorption process, which
results in 4.2% less adsorption and 1.8% less desorption compared to the ideal evaporator and
condenser. This difference is the reason that most previous numerical results overestimated system
performance. In the model based on an ideal evaporator and condenser, COP was estimated to be
0.523, which is an overestimate of 16.12%, and SCP was 637 W/kg, which is an overestimate of 24.64%,
compared to the present model.
Figure 6. Clapeyron diagram of the present model and the model based on ideal treatment of the
evaporator and condenser.
Figure 7. Comparison of adsorption and desorption interval for the two models in Figure 6.
Figure 6.
Clapeyron diagram of the present model and the model based on ideal treatment of the
evaporator and condenser.
The processes (B) and (D) are the heating and cooling phases, which are desorbing or adsorbing
the vapor. In contrast to the real pressure behavior, which was properly estimated in the present model,
the pressure in the idealized model is assumed to be constant at the saturation pressure corresponding
to the temperature of the evaporator, 15 °C, or the condenser, 30 °C.
Figure 7shows the isotherm of the adsorbent SWS-1 L and compares the adsorption and desorption
amounts corresponding to the ideal and real pressures of the condenser and evaporator. In the model
with ideal treatment of the evaporator and condenser, the pressure during the adsorption and desorption
process is constant, shown in the bold dashed line in Figure 7, which causes constant q*. On the other
hand, in the present model, relative pressure varies from 0.09 to 0.11 during the desorption process and
varies from 0.31 to 0.4 during the adsorption process, as described in the hatched region in Figure 7.
A larger variation is observed during the adsorption process, which results in 4.2% less adsorption and
1.8% less desorption compared to the ideal evaporator and condenser. This difference is the reason that
most previous numerical results overestimated system performance. In the model based on an ideal
evaporator and condenser, COP was estimated to be 0.523, which is an overestimate of 16.12%, and
SCP was 637 W/kg, which is an overestimate of 24.64%, compared to the present model.
Energies 2020, 13, x FOR PEER REVIEW 10 of 14
In the model with ideal treatment of the evaporator and condenser, the pressure during the
adsorption and desorption process is constant, shown in the bold dashed line in Figure 7, which
causes constant q*. On the other hand, in the present model, relative pressure varies from 0.09 to 0.11
during the desorption process and varies from 0.31 to 0.4 during the adsorption process, as described
in the hatched region in Figure 7. A larger variation is observed during the adsorption process, which
results in 4.2% less adsorption and 1.8% less desorption compared to the ideal evaporator and
condenser. This difference is the reason that most previous numerical results overestimated system
performance. In the model based on an ideal evaporator and condenser, COP was estimated to be
0.523, which is an overestimate of 16.12%, and SCP was 637 W/kg, which is an overestimate of 24.64%,
compared to the present model.
Figure 6. Clapeyron diagram of the present model and the model based on ideal treatment of the
evaporator and condenser.
Figure 7. Comparison of adsorption and desorption interval for the two models in Figure 6.
Figure 7. Comparison of adsorption and desorption interval for the two models in Figure 6.
Energies 2020,13, 1901 11 of 14
3.3. Effect of Bed Model
For the rough design purpose in system scale analysis, LPM has an advantage because the refined
model in beds requires special treatment and much longer computation time (Duong et al. [
24
]).
However, LPM is not enough when higher accuracy or detailed information in beds is required during
the process. Figure 8shows a Clapeyron diagram of the present model and the model based on LPM.
The result of LPM was obtained for the same device geometry and operating condition in the present
model. The only difference is the treatment of the bed simulation. The processes (A) and (C) are the
isosteric phase and the processes (B) and (D) are the heating and cooling phase of the desorbing or
adsorbing vapor. Both models allow variable pressure, based on the temperature of evaporation or
condensation. However, because the adsorption bed behaviors are different depending on the bed
model, processes (B) and (D) in Figure 8are significantly different. The resulting COP in the model
based on LPM for all components was 0.553, which was 22.82% higher than the present model, and
SCP was 568 W/kg, which was 11.28% higher than the present model.
Energies 2020, 13, x FOR PEER REVIEW 11 of 14
3.3. Effect of Bed Model
For the rough design purpose in system scale analysis, LPM has an advantage because the
refined model in beds requires special treatment and much longer computation time (Duong et al.
[24]). However, LPM is not enough when higher accuracy or detailed information in beds is required
during the process. Figure 8 shows a Clapeyron diagram of the present model and the model based
on LPM. The result of LPM was obtained for the same device geometry and operating condition in
the present model. The only difference is the treatment of the bed simulation. The processes (A) and
(C) are the isosteric phase and the processes (B) and (D) are the heating and cooling phase of the
desorbing or adsorbing vapor. Both models allow variable pressure, based on the temperature of
evaporation or condensation. However, because the adsorption bed behaviors are different
depending on the bed model, processes (B) and (D) in Figure 8 are significantly different. The
resulting COP in the model based on LPM for all components was 0.553, which was 22.82% higher
than the present model, and SCP was 568 W/kg, which was 11.28% higher than the present model.
Figure 8. Clapeyron diagram of the present model and the model based on the lumped parameter
method (LPM) for all components of the bed, evaporator, and condenser.
In contrast to the LPM, the present model includes the effects of geometric features (fin height,
fin spacing, tube diameter, and thickness) and considers the contact resistance between the sorbent
material and metallic finned tube, which affirmatively enhances the accuracy of the analysis. There
were a lot of studies on geometric optimization in adsorption beds [4,13,25–27]. Also, recent coating
technology has made it possible to reduce contact resistance and tremendously enhance performance
(Rezk [28], Girnik and Aristov [29]). The LPM cannot accommodate all these effects, thus has to limit
to estimate the real system performance.
In summary, Figure 9 shows how much the accuracy of COP improved as the model became
more precise.
Figure 8.
Clapeyron diagram of the present model and the model based on the lumped parameter
method (LPM) for all components of the bed, evaporator, and condenser.
In contrast to the LPM, the present model includes the effects of geometric features (fin height,
fin spacing, tube diameter, and thickness) and considers the contact resistance between the sorbent
material and metallic finned tube, which affirmatively enhances the accuracy of the analysis. There
were a lot of studies on geometric optimization in adsorption beds [
4
,
13
,
25
–
27
]. Also, recent coating
technology has made it possible to reduce contact resistance and tremendously enhance performance
(Rezk [
28
], Girnik and Aristov [
29
]). The LPM cannot accommodate all these effects, thus has to limit
to estimate the real system performance.
In summary, Figure 9shows how much the accuracy of COP improved as the model became
more precise.
Energies 2020,13, 1901 12 of 14
Energies 2020, 13, x FOR PEER REVIEW 12 of 14
Figure 9. Accuracy improvement in coefficient of performance (COP) and specific cooling power
(SCP).
4. Conclusions
In this study, we proposed a novel numerical model for an adsorption chiller including (1) the
proper interaction with the evaporator and condenser, and also (2) a rigorous treatment of the
adsorption bed. The proposed numerical model was compared with results from experiments and
showed close agreement.
Properly accounting for the interaction between the adsorption bed and the evaporator and
condenser enhanced the model’s accuracy. Previous models have used a fixed evaporation
temperature and condenser temperature, which did not interact with the adsorption bed, which is
why the earlier numerical models have normally overestimated system performance.
The model based on an ideal evaporator and condenser resulted in a COP of 0.523, which led to
an overestimate of 16.12%, and a SCP of 637 W/kg, which was an overestimate of 24.64%, compared
to the present model.
Even when the interaction with the evaporator and condenser was included, excessive
simplification of the adsorption bed in previous LPM analyses distorted the actual performance. This
is because LPM failed to reflect the geometry effect and contact resistance of the bed, the component
which is most influential on adsorption chiller system performance. As a result, the estimated COP
was 0.553, and the SCP was 568 W/kg, which were 22.82% and 11.28% higher respectively, than the
present model.
Considering the many studies on the geometric optimization of the adsorption bed, and recent
coating technology to enhance system performance, producing an accurate estimation of adsorption
chiller performance requires not only proper interaction with the evaporator and condenser, but also
rigorous modeling of the adsorption bed.
Author Contributions: Conceptualization, writing—review and editing, J.D.C.; validation, X.Q.D.
and N.V.C.; formal analysis, investigation and writing—original draft preparation, W.S.L. and M.Y.P.
All authors have read and agreed to the published version of the manuscript.
Funding: This research was supported by Basic Science Research Program through the National Research
Foundation of Korea (NRF) funded by the Ministry of Education (No. 2017R1D1A1B05030422)
Conflicts of Interest: The authors declare no conflict of interest.
Figure 9.
Accuracy improvement in coefficient of performance (COP) and specific cooling power (SCP).
4. Conclusions
In this study, we proposed a novel numerical model for an adsorption chiller including (1) the
proper interaction with the evaporator and condenser, and also (2) a rigorous treatment of the
adsorption bed. The proposed numerical model was compared with results from experiments and
showed close agreement.
Properly accounting for the interaction between the adsorption bed and the evaporator and
condenser enhanced the model’s accuracy. Previous models have used a fixed evaporation temperature
and condenser temperature, which did not interact with the adsorption bed, which is why the earlier
numerical models have normally overestimated system performance.
The model based on an ideal evaporator and condenser resulted in a COP of 0.523, which led to
an overestimate of 16.12%, and a SCP of 637 W/kg, which was an overestimate of 24.64%, compared to
the present model.
Even when the interaction with the evaporator and condenser was included, excessive
simplification of the adsorption bed in previous LPM analyses distorted the actual performance. This
is because LPM failed to reflect the geometry effect and contact resistance of the bed, the component
which is most influential on adsorption chiller system performance. As a result, the estimated COP
was 0.553, and the SCP was 568 W/kg, which were 22.82% and 11.28% higher respectively, than the
present model.
Considering the many studies on the geometric optimization of the adsorption bed, and recent
coating technology to enhance system performance, producing an accurate estimation of adsorption
chiller performance requires not only proper interaction with the evaporator and condenser, but also
rigorous modeling of the adsorption bed.
Author Contributions:
Conceptualization, writing—review and editing, J.D.C.; validation, X.Q.D. and N.V.C.;
formal analysis, investigation and writing—original draft preparation, W.S.L. and M.Y.P. All authors have read
and agreed to the published version of the manuscript.
Funding:
This research was supported by Basic Science Research Program through the National Research
Foundation of Korea (NRF) funded by the Ministry of Education (No. 2017R1D1A1B05030422)
Conflicts of Interest: The authors declare no conflict of interest.
Energies 2020,13, 1901 13 of 14
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