![The validation of the COPs of both ADS and VCS models against their counterparts; (a) ADS validation reference [12], and (b) VCS validation reference [31].](https://www.researchgate.net/profile/Mahmoud-Elsheniti/publication/380178638/figure/fig4/AS:11431281389657669@1745224152544/The-validation-of-the-COPs-of-both-ADS-and-VCS-models-against-their-counterparts-a-ADS_Q320.jpg)
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Citation: Elsheniti, M.B.; Al-Ansary,
H.; Orfi, J.; El-Leathy, A. Performance
Evaluation and Cycle Time
Optimization of Vapor-Compression/
Adsorption Cascade Refrigeration
Systems. Sustainability 2024,16, 3669.
https://doi.org/10.3390/su16093669
Academic Editor: Zisheng Lu
Received: 25 March 2024
Revised: 16 April 2024
Accepted: 25 April 2024
Published: 27 April 2024
Copyright: © 2024 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
sustainability
Article
Performance Evaluation and Cycle Time Optimization of
Vapor-Compression/Adsorption Cascade Refrigeration Systems
Mahmoud Badawy Elsheniti 1, 2, * , Hany Al-Ansary 1, Jamel Orfi 1and Abdelrahman El-Leathy 1
1Mechanical Engineering Department, College of Engineering, King Saud University,
Riyadh 11451, Saudi Arabia; hansary@ksu.edu.sa (H.A.-A.); orfij@ksu.edu.sa (J.O.);
aelleathy@ksu.edu.sa (A.E.-L.)
2
Mechanical Engineering Department, Faculty of Engineering, Alexandria University, Alexandria 21544, Egypt
*Correspondence: mbadawy.c@ksu.edu.sa
Abstract: The reliance on more sustainable refrigeration systems with less electricity consumption
attracts a lot of attention as the demand for refrigeration increases due to population growth and
global warming threats. This study examines the use of a cascade vapor-compression/adsorption
refrigeration system in hot weather, focusing on condensing temperatures of 50, 55, and 60
◦
C,
whereas an air-cooled condenser is in use due to practical considerations. A fully coupled transient
model is developed using COMSOL Multiphysics to simulate the integrated system, considering
the practical limitations of the vapor compression system (VCS) and the dynamic nature of the
adsorption system (ADS). The model combines a lumped model for the ADS with the manufacturer’s
data for a VCS compressor at different condensing and evaporating temperatures. It was found
that the VCS is more sensitive to the change in the ADS’s condensing temperature, since when the
temperature is raised from 50
◦
C to 60
◦
C, the VCS’s COP decreases by 29.5%, while the ADS’s COP
decreases by 7.55%. Furthermore, the cycle time of ADS plays an important role in providing the
cooling requirements for the bottoming cycle (VCS), and it can be optimized to maximize the energy
conversion efficiency of the VCS. At optimum cycle time and compared to the conventional VCS, the
cascade system can boost the cooling capacity of the VCS by 18.2%, lower the compressor power
by 63.2%, and greatly enhance the COP by 221%. These results indicate that the application of the
cascade VCS/ADS in such severe conditions is a more sustainable and energy-efficient solution to
meet the growing need for refrigeration.
Keywords: sustainable refrigeration system; energy conversion efficiency; dynamic modeling;
adsorption system; high ambient temperature; optimum cycle time
1. Introduction
Many sectors depend on the refrigeration process as a necessary means for human
comfort and industrial production, and it is crucial in hot weather conditions. In Saudi
Arabia, summertime temperatures are 2.5 times higher than wintertime averages. In the
past 45 years, the hottest temperature observed in KSA has been 53
◦
C [
1
], and warming
trends for the summer and winter seasons in Riyadh are 0.058
◦
C and 0.042
◦
C annually,
respectively [
2
]. Approximately 20% of the electricity used globally is consumed by the
refrigeration industry, and it is expected to grow in the next years as a result of global
warming and the growing cooling needs across many different industries [
3
]. According to
Lelieveld et al. [
4
], KSA’s summertime temperatures will rise by 6
◦
C by 2081–2100 relative
to the period of 1986–2005. The conventional vapor compression refrigeration system (VCS)
is a commonly utilized technique in the refrigeration industry due to its superior efficiency,
in contrast to alternative refrigeration systems that are currently in use [5,6].
However, the VCS uses a lot of electricity, generated mostly from fossil fuels, and
represents one of the challenges in controlling the emissions of greenhouse gases [
7
]. Statis-
tically, about 60% of the energy used in buildings is accounted for by air conditioning [
8
].
Sustainability 2024,16, 3669. https://doi.org/10.3390/su16093669 https://www.mdpi.com/journal/sustainability
Sustainability 2024,16, 3669 2 of 18
Unfavorably, the high temperature of the heat sink greatly reduces the coefficient of per-
formance (COP) of the VCS. For each degree Celsius that the condenser temperature rises,
the COP of a VCS drops by 2–4% [
9
]. On the other hand, the development of alternative
refrigeration technologies, including the adsorption refrigeration system (ADS), is there-
fore gaining excessive attention [
10
,
11
]. The ADS is a thermally driven cooling method
that generates cooling by using a refrigerant’s adsorption/desorption process on a solid
adsorbent material [
12
]. Two main benefits of this technique are its low electricity use
and the utilization of natural refrigerants. However, the operating circumstances, such
as the temperatures of the heating and cooling sources and the temperature of chilling or
ice production in their evaporators, have a significant impact on the performance of the
ADS [
13
]. The studies on the ADS for ice production reported COP ranged from 0.452 to
0.086 [
14
]. A recent strategy to increase the benefits of both systems (the VCS and ADS) and
lessen their drawbacks has been offered in the literature by integrating the two systems
using different approaches [15–17].
The effectiveness of integrating an adsorption system as a topping cycle to cool the con-
denser of a compression refrigeration system was theoretically examined by
Gado et al. [18]
.
They utilized a generalized thermodynamic model for a VCS combined with a lumped
model for the ADS. Given the ambient circumstances in Alexandria, Egypt (latitude
31.2◦N
and longitude 29.92
◦
E), the PVT collector system was proposed to power the integrated
system. In order to produce brine at
−
20
◦
C from the VCS evaporator, the AD cycle time of
900 s was chosen, and the cooling water for the ADS condenser and beds was set at 30
◦
C,
assuming a cooling application with chilled water temperature of 12
◦
C, as in reference [
19
].
They concluded that the suggested solution might save
24.8% of
energy annually. Addition-
ally, they suggested that lowering the cooling temperature and compressor capacity might
significantly improve energy savings and the overall coefficient of performance. Using
the same approach and two different sources of driving power, Gado et al. [
20
] assessed
the performance of coupling ADS and VCS in a cascade arrangement, with the maximum
condensing temperature of the upper cycle being close to 31
◦
C. They found that the COP
of the integrated system increased by 41.6% compared to the conventional VCS.
Koushaeian et al. [
21
] evaluated an integrated cascade ADS and VCS using a lumped
model for the ADS and a sample thermodynamic model for the VCS for cooling purposes
at a chilled water temperature of 12
◦
C. They highlighted that when the temperature
of the cooling water was raised from 26 to 34
◦
C, a 34.33% drop in energy savings and
a 20.99%
loss in overall COP were reported. Kilic and Anjrini [
22
] theoretically investigated
the combined cascade ADS and VCS when the ambient temperature changed from 25 to
40 ◦C, using a cycle time of 1100 s. The highest COP of the VCS was 8.8 at an evaporating
temperature of 0 ◦C when the R152A refrigerant was used.
To fully utilize the electrical and thermal energy produced by a CPVT system operating
in the hot climate of Riyadh city, Elsheniti et al. [
23
] investigated the parallel integration
of the VCS and ADS. They suggested a coupled ice-production system attained a solar
COP of 0.875 on average over the year. According to their findings, adjusting the ADS
cycle duration can be a useful strategy for getting the best use out of the heating power
produced by the CPVT system. Because the VCS has a greater COP than the ADS, it was
able to contribute 84.5% of the total ice production over the year. According to Albaik
et al. [
24
], ADS was also effectively used to cool down the condenser of an organic Rank-
ine cycle (ORC), and the ORC’s thermodynamic efficiency jumped to 11.6% from 6.95%.
Calise et al. [
25
] simulated a polygeneration system including parallel arrangement for
the ADS and solar-assisted heat pump for space cooling and heating, respectively, and
using component-based thermodynamic models in TRNSYS software. They revealed that
the suggested approach may save 20% on electricity by using the meteorological data of
a Mediterranean city, at a moderately warm heat sink. Roumpedakis et al. [
26
] experimen-
tally evaluated the performance of a solar driven adsorption system while a conventional
VCS was used in parallel operation to cover the peak load at higher ambient temperatures.
They concluded that the combined operation improved overall performance, and the ADS’s
Sustainability 2024,16, 3669 3 of 18
maximum COP was 0.575. To improve the ADS performance, Xu et al. [
27
] proposed and
examined a hybrid ADS with desiccant-coated heat exchangers to treat the conditioned air
latent load. The hybrid system increased the cooling capacity from 3 kW to 3.95 kW and
increased the COP to 0.539. Activated carbon and silica gel are the most recommended
adsorbates in the previous research relevant to hybrid ADS and VCS, as summarized by
Kılıç [
11
]. He also reported that the use of such hybrid systems makes it possible to use
a wide range of heating sources with low grades and can enhance the performance of the
VCS by up to 100%,reducing the electrical power consumption by 50%.
Vasta et al. [
28
] conducted experimental tests to evaluate the performance of a cascade
adsorption unit and vapor compression chiller using condenser cooling temperatures up
to 40
◦
C. They reported that the electrical COP of the integrated system increased in the
range from 25% to 50%, obtaining an ultimate COP of 8. They also extended the study
theoretically to optimize the cascade system using thermodynamic models for both cycles
while setting the ADS cycle time to 1000 s. They revealed that an increase of 110% in
the efficiency of the VCS can be attained in refrigeration applications while applying the
cascade system. Gibelhaus et al. [
29
] investigated the application of ADS to improve the
performance of a CO
2
-based VCS as a cascade refrigeration system. They showed that
when considering the ambient temperatures of 35
◦
C and 25
◦
C, respectively, annual energy
savings of 22% and 16% can be achieved. For both cycles, thermodynamic models were
utilized, and the ADS cycle periods were adjusted to account for the varying size ratios
between the two cycles. Palomba et al. [
30
] investigated critical control strategies for the
hybrid VC/AD chillers. They emphasized that the ADS’s cycle duration can be adjusted to
correspond with changes in the hybrid system’s cooling power.
Previous studies focused on condensing temperatures in the range of 25–30
◦
C, except
for a few papers extending the range to 40
◦
C. This range will not be applicable in severe
conditions where ambient temperatures reach 47
◦
C and are expected to be higher due to
global warming, according to the statistics discussed earlier. In this introductory section,
it can be highlighted that the modeling of such systems was mainly based on a simple or
general thermodynamic model for the VCS. In some studies, the compressor’s isentropic
efficiency was fixed. Furthermore, the cycle time of the adsorption system was set to
a fixed value during most of the studies. To the best of the author’s knowledge, no single
study has discussed the ADS’s cycle time limitation and optimization in order to enhance
the electrical energy conversion efficiency of the VCS, as expressed by the COP, particularly
at higher ambient temperatures.
To support the effective integration of the cascade chillers in practice, further informa-
tion, and findings about the variation limits of the ADS cycle time are required, particularly
under harsh operating conditions. Previous studies make it clear that integrating the
ADS as a topping cycle for the conventional VCS is a very promising strategy for raising
the VCS’s energy efficiency and lowering its electricity consumption. Given that VCS
is an established technology, this study aims to fill the gap between the theoretical and
experimental studies in which the manufacturer datasheet of a VCS has been utilized in
modeling the cascaded adsorption-compression refrigeration system. The direct impact
of the VCS’s practical limitations and component sizes has been used to determine the
operational conditions of the coupled ADS, mainly the range and the optimum cycle time,
along with the intermediate condenser/evaporator temperatures. Unlike the previous
studies with generalized thermodynamic models for the VCS, the investigation in this
study will focus on how the defined compressor of the VCS responds to the dynamic
nature of the ADS. Additionally, the use of an air-cooled condenser to deal with the heat
sink of the upper cycle comes with many benefits, particularly in terms of small-scale
refrigeration systems and limited cooling water sources; however, it limits the condensing
temperatures to the ambient conditions. Therefore, this study will investigate the effect of
condensing temperatures in the range of 50
◦
C to 60
◦
C, which are expected when applying
such a system in Riyadh city. The integrated VCS/ADS could help mitigate excessive
Sustainability 2024,16, 3669 4 of 18
energy consumption and the associated indirect emissions from the refrigeration system
that produce ice for continuous cooling.
2. Methodology
Figure 1shows the schematic diagram of the proposed cascade refrigeration system,
which shows the adsorption system (ADS) as a topping cycle and the vapor compression
system (VCS) as a bottoming cycle. The use of water-cooled condensing units can be
limited in some applications, particularly in arid climates, where the availability of water
represents a great challenge. Therefore, in this study, the ADS condenser is an air-cooled
unit that can be used with medium- and small-scale refrigeration equipment to lessen
reliance on the cooling water circuit and associated complications. The proposed system
is used to produce ice using a conventional ice maker. The ice can be used directly for
freezing purposes, or it can be used to overcome the solar heating system’s intermittent
operation, which can be used to power the ADS, and provide constant chilling over the
day and night.
Sustainability2024,16,36694of19
withtheheatsinkoftheuppercyclecomeswithmanybenefits,particularlyintermsof
small-scalerefrigerationsystemsandlimitedcoolingwatersources;however,itlimitsthe
condensingtemperaturestotheambientconditions.Therefore,thisstudywillinvestigate
theeffectofcondensingtemperaturesintherangeof50°Cto60°C,whichareexpected
whenapplyingsuchasysteminRiyadhcity.TheintegratedVCS/ADScouldhelpmitigate
excessiveenergyconsumptionandtheassociatedindirectemissionsfromthe
refrigerationsystemthatproduceiceforcontinuouscooling.
2.Methodology
Figure1showstheschematicdiagramoftheproposedcascaderefrigerationsystem,
whichshowstheadsorptionsystem(ADS)asatoppingcycleandthevaporcompression
system(VCS)asaboomingcycle.Theuseofwater-cooledcondensingunitscanbe
limitedinsomeapplications,particularlyinaridclimates,wheretheavailabilityofwater
representsagreatchallenge.Therefore,inthisstudy,theADScondenserisanair-cooled
unitthatcanbeusedwithmedium-andsmall-scalerefrigerationequipmenttolessen
relianceonthecoolingwatercircuitandassociatedcomplications.Theproposedsystem
isusedtoproduceiceusingaconventionalicemaker.Theicecanbeuseddirectlyfor
freezingpurposes,oritcanbeusedtoovercomethesolarheatingsystem’sintermient
operation,whichcanbeusedtopowertheADS,andprovideconstantchillingoverthe
dayandnight.
Figure1.Schematicdiagramoftheintegratedvapor-compression/adsorptionrefrigerationsystem.
Asextensivelystudiedintheliterature,theheatingsourcecanbesolarorwasteheat
thatcanproducearegenerationtemperatureof90°C[18,23,25].Thedesignoftheadsorbent
bedsisbasedonMaxsorbIIIadsorbentfilledinapromisingstructuredaluminum-foambed
andusesethanolasarefrigerant.Thisdesignprovidedremarkableperformancecompared
toatypicalfinned-tubeconfiguration,asreportedinreference[12].
Figure 1. Schematic diagram of the integrated vapor-compression/adsorption refrigeration system.
As extensively studied in the literature, the heating source can be solar or waste heat
that can produce a regeneration temperature of 90
◦
C [
18
,
23
,
25
]. The design of the adsorbent
beds is based on Maxsorb III adsorbent filled in a promising structured aluminum-foam bed
and uses ethanol as a refrigerant. This design provided remarkable performance compared
to a typical finned-tube configuration, as reported in reference [12].
The VCS uses an off-the-shelf compressor, type Copeland ZP42K5E-PFV [
31
], with
known performance under a range of condensing and evaporating temperatures, from
26.6
◦
C to 65.6
◦
C and from
−
23.3
◦
C to 12.78
◦
C, respectively. The nominal cooling
capacity and compressor power are 12.29 kW and 4.07 kW at condensing and evaporating
temperatures of 54.44
◦
C and 7.22
◦
C, respectively. To produce ice in the freezer unit, the
VCS’s evaporating temperature is set to
−
5
◦
C, and VCS’s condensing temperature is set
to 5
◦
C above the ADS’s evaporating temperature. By using this approach, the developed
Sustainability 2024,16, 3669 5 of 18
model in this study can calculate the temperatures of the circulated refrigerants in the
condenser/evaporator unit, which is an intermediate heat exchanger (HEX), based on
the energy balances between the two cycles and under any specific circumstance. In this
study, a datasheet-based thermodynamic model for the VCS is simultaneously solved with
a transient lumped-parameter model for the two-bed ADS. As a result, both the condensing
and evaporating temperatures of the bottoming cycle and the topping cycle, respectively, as
well as the instantaneous amount of heat transfer from the bottoming cycle to the topping
cycle, fluctuate over time.
Through control valves, the intermediate heat exchanger is connected to the beds and
functions as the ADS’s evaporator of a conventional two-bed system. The valves allow
for the switching between the four ADS modes because they only open while a bed is
undergoing the adsorption process. Conversely, only during the desorption process will
the valves connecting the two beds to the condenser of the ADS be turned on.
3. Mathematical Modeling
3.1. Adsorbent Beds
The transient natural operation of the ADS involves repeated cycles, each of which
being represented by four sequential processes, namely, preheating/precooling, des-
orption/adsorption, precooling/preheating, and adsorption/desorption, applied to
beds A and B, respectively. This operation can be replicated using the energy balance
Equations (1) and (2), as follows [32]:
MCb1
dTb1
dt =(1−αb).
mcCcεc(Tc,i−Tb1)]−αb.
mhChεh(Th,i−Tb1)] + HsMsdwb1
dt (1)
MCb2
dTb2
dt =αb.
mcCcεc(Tc,i−Tb2)]−(1−αb).
mhChεh(Th,i−Tb2)] + HsMsdwb2
dt (2)
The thermal masses,
MCb1
and
MCb2
, represent all the components of beds A and B,
respectively, and can be written as follows:
MCb1=MsCs+MsCrl wb1+MbCb+MfCf(3)
MCb2=MsCs+MsCrl wb2+MbCb+MfCf(4)
The thermal masses of the solid sorbent, adsorbate, bed metal heat exchanger, and
foam are represented by the RHS term in Equations (3) and (4), respectively. Except for the
mass of adsorbate, which varies with time, the masses of the two beds are the same. The
water mass flow rates for cooling and regeneration are denoted by
.
mc
and
.
mh
, respectively,
and
Hs
is the isosteric heat of adsorption. The heat transfer effectiveness of the foam bed
during cooling and heating is represented by
εc
and
εh
. These parameters rely on the heat
transfer resistances within the bed heat exchanger, which are influenced by factors such as
the fluid flow scheme, foam thickness, and thermophysical characteristics of both the foam
structure and adsorbent material.
The present zero-dimensional lumped model necessitates simplification. Therefore,
the values of
εc
and
εh
were calculated from the more intricate CFD model developed in
reference [
12
] to be 0.802 and 0.853, respectively. The obtained results were validated for
the specific situation under investigation. The operator
αb
is used in the program coding to
alternate between the cooling and heating modes in the equations, delivering either the
cooling or heating effect for each bed, and switching between them every half cycle.
In an adsorption system, the isotherms and kinetics equations are typically integrated
with the bed energy equation to determine the amount of adsorbate in both equilibrium
(
weq
) and instantaneous (
w
) states. For the Maxsorb III/ethanol system, the following
equations were utilized [33,34]:
weq =wmaxexp−RTb
ElnPs
pn(5)
Sustainability 2024,16, 3669 6 of 18
Ps=0.1333 ×108.1122−1592.864
Tb+226.184 (6)
∂w
∂t=KLDFweq −w(7)
KLDF =Aexp−Ea
RuTb(8)
where the maximum uptake, ethanol-gas constant, characteristic energy, and heterogeneity
parameter are defined, respectively, by
wmax =
1.2
kg·kg−1
,
R=
0.1805
kJ·kg−1·K−1
,
E=
139.5
kJ·kg−1
, and n= 1.8 [
26
].
Ps
is the saturation pressure at the bed temperature,
and
p
is the pressure of the associated evaporator/condenser module. The adsorption
kinetics were defined by the linear-driving-force model, Equation (7), where
KLD F
de-
notes for the overall intra-particle mass-transfer coefficient. The pre-exponential con-
stant, activation energy, and universal gas constant are given as
A=
132.89
s−1
,
Ea=22.97 kJ·mol−1, andRu=8.314 kJ·kmol−1·K−1, respectively [33].
3.2. Intermediate Condenser/Evaporator Heat Exchanger
The energy balance equation of the intermediate heat exchanger between the two
cycles should consider the instantaneous heat released from the VCS,
.
Qcond,v(Tcond,v,t)
,
which in turn is relevant to the condensing temperature,
Tcond,v
, of the VCS. It should also
consider the intermittent connections between the two beds during the adsorption process.
Therefore, it can be written as follows:
MCHEX d Teva ,a
dt =.
Qcond,v(Tcond,v,t)−(1−βeva,a)hhf g (Teva,a,t)−Crl,aTcond,a−Teva,aiMsdwb1
dt
−(1−γeva,a)hhf g (Teva,a,t)−Crl,aTcond,a−Teva,aiMsdwb2
dt
(9)
MCHEX
denotes the thermal mass of the heat exchanger, and
Teva,a
and
Tcond,a
are the
evaporating and condensing temperatures of the ADS, respectively. The
Tcond,a
is also ab-
breviated as
Tc
. The
hf g
is the latent heat of evaporation as a function of
Teva,a
. The amount
of ethanol vapor generated during the throttling process in the ADS is eliminated from
the latent heat in the evaporator by the term (
Crl,aTcond,a−Teva,a
).
βeva,a
and
γeva,a
are
programing operators used to mimic the alternating connections between the two beds.
The simulation parameters for the adsorption system are displayed in Table 1.
Table 1. Adsorption system parameters.
Parameter Symbol Value Unit
Cooling water mass flow rate .
mc0.7628 kg·s−1
Heating water mass flow rate .
mh0.5394 kg·s−1
Bed effectiveness during cooling εc0.802 -
Bed effectiveness during heating εh0.853 -
Adsorbent mass per bed Ms9.512 kg
Foam mass per bed Mf9.509 kg
Mass of copper heat exchanger per bed Mb54 kg
Thermal mass of the intermediate HEX MCHEX 366 kJ·k−1
Isosteric heat of adsorption Hs1002 kJ·kg−1
Activated carbon specific heat Cs1370 J·kg−1·k−1
Aluminum-foam specific heat Cf895 J·kg−1·k−1
Cupper specific heat Cb385 J·kg−1·k−1
Specific heat of ethanol (liquid) Crl 2570 J·kg−1·k−1
Bed inlet cooling water temperature Tc,i30 °C
Regeneration temperature Th,i90 °C
ADS’s condensing temperature Tcond,aor Tc50, 55, and 60 °C
Sustainability 2024,16, 3669 7 of 18
3.3. Vapor Compression System
The datasheet of the compressor unit provided by the manufacturer can be used to
determine the refrigerant mass flow rate, compressor isentropic efficiency, and the second-
law efficiency of the cycle at different condensing and evaporating temperatures [
31
].
Figure 2shows the changes in the previous parameters when the evaporating temperature
is set to
−
5
◦
C, as calculated from the manufacturer’s confirmed results based on a 72 h
run-in period, with maximum
±
5% deviations [
31
]. It is evident that at higher condensing
temperatures, the VCS’s performance is significantly reduced in terms of compressor
isentropic efficiency (
ηis
) and second-law efficiency (
ηII
). This emphasizes how crucial
it is to research the suggested method in severe conditions in order to lower the VCS
condensing temperature. In addition, setting some of the main compressor parameters
to fixed values can lead to misleading results, which was avoided in the present study.
The figure also shows that, as the condensing temperature rises, the mass flow rate of the
refrigerant (
.
mre f ,v
) experiences a modest increase, resulting from the increased volumetric
capacity of the compressor at a high discharge pressure. These results consider the physical
parameters of the compressor, as well as the changes in the thermophysical properties of
the refrigerant at different condensing temperatures.
Sustainability2024,16,36697of19
Massofcopperheatexchangerperbed 𝑀54
kg
ThermalmassoftheintermediateHEX𝑀𝐶366
kJ
∙
k
1
Isostericheatofadsorption 𝐻1002
kJ·kg
1
Activatedcarbonspecificheat 𝐶1370
J
·kg
1
∙
k
1
Aluminum-foamspecificheat 𝐶895
J
·kg
1
∙
k
1
Cupperspecificheat𝐶385
J
·kg
1
∙
k
1
Specificheatofethanol(liquid)𝐶2570
J
·kg
1
∙
k
1
Bedinletcoolingwatertemperature𝑇,30℃
Regenerationtemperature𝑇,90℃
ADS’scondensingtemperature 𝑇,or 𝑇50,55,and60℃
3.3.Vapor CompressionSystem
Thedatasheetofthecompressorunitprovidedbythemanufacturercanbeusedto
determinetherefrigerantmassflowrate,compressorisentropicefficiency,andthe
second-lawefficiencyofthecycleatdifferentcondensingandevaporatingtemperatures
[31].Figure2showsthechangesinthepreviousparameterswhentheevaporating
temperatureissetto−5°C,ascalculatedfromthemanufacturer’sconfirmedresultsbased
ona72hrun-inperiod,withmaximum±5%deviations[31].Itisevidentthatathigher
condensingtemperatures,theVCS’sperformanceissignificantlyreducedintermsof
compressorisentropicefficiency(𝜂)andsecond-lawefficiency(𝜂).Thisemphasizes
howcrucialitistoresearchthesuggestedmethodinsevereconditionsinordertolower
theVCScondensingtemperature.Inaddition,seingsomeofthemaincompressor
parameterstofixedvaluescanleadtomisleadingresults,whichwasavoidedinthe
presentstudy.Thefigurealsoshowsthat,asthecondensingtemperaturerises,themass
flowrateoftherefrigerant(𝑚,)experiencesamodestincrease,resultingfromthe
increasedvolumetriccapacityofthecompressoratahighdischargepressure.These
resultsconsiderthephysicalparametersofthecompressor,aswellasthechangesinthe
thermophysicalpropertiesoftherefrigerantatdifferentcondensingtemperatures.
Figure2.ThedatasheetparametersoftheVCSat−5°Cevaporatingtemperatureanddifferent
condensingtemperatures.
Thethermodynamicpropertiesoftherefrigerant[35],whichisHFC-410A,are
integratedwiththedatasheetinterpolationfunctions,developedinCOMSOL
MultiphysicstomodeltheperformanceoftheVCSunderdifferentoperatingconditions.
Figure3showstherefrigerantstatusonthep-hgraphforacompleterefrigerationcycle.
Inpractice,certainamountsofsuperheatandsubcoolingshouldbeconsideredbeforethe
compressorandafterthecondenser,respectively,tosaveoperationandincreasethe
coolingeffect.Theamountsofsuperheatandsubcoolingusedinthesimulationarebased
0.049
0.050
0.051
0.052
0.053
0.054
0.055
0.3
0.4
0.5
0.6
0.7
0.8
295 300 305 310 315 320 325 330
Refrigerant mass flow rate
(kg∙s−1)
Isentropic efficiency or
second-law efficiency (-)
Tcond,v (K)
η_is η_II m_ref
Figure 2. The datasheet parameters of the VCS at
−
5
◦
C evaporating temperature and different
condensing temperatures.
The thermodynamic properties of the refrigerant [
35
], which is HFC-410A, are inte-
grated with the datasheet interpolation functions, developed in COMSOL Multiphysics to
model the performance of the VCS under different operating conditions. Figure 3shows
the refrigerant status on the p-h graph for a complete refrigeration cycle. In practice, certain
amounts of superheat and subcooling should be considered before the compressor and after
the condenser, respectively, to save operation and increase the cooling effect. The amounts
of superheat and subcooling used in the simulation are based on the recommendations in
the compressor datasheet. The main specifications and parameters of the VCS used in the
simulation are shown in Table 2.
Sustainability 2024,16, 3669 8 of 18
Sustainability2024,16,36698of19
ontherecommendationsinthecompressordatasheet.Themainspecificationsand
parametersoftheVCSusedinthesimulationareshowninTabl e 2.
Figure3.Therepresentationofthevaporcompressioncycleonapressure–enthalpygraph.
Tab l e2.TheparametersusedinthesimulationoftheVCS.
ParameterValueUnit
Compressortype CopelandZP42K5E-PFV
RefrigerantHFC-410A
Coolingcapacity
@𝑇,=54.44°C
and𝑇,=7.22°C
12.29kW
Compressorpower
@𝑇,=54.44°C
and𝑇,=7.22°C
4.07kW
Degreeofsuperheating11℃
Degreeofsubcooling8.3℃
Evaporatingtemperature−5℃
Enthalpyatcompressorinlet
ℎ432kJ·kg1
Enthalpyatevaporatoroutlet
ℎ,@
,
°421kJ·kg1
TheVCSperformanceissimulatedusingthefollowingsetofequations,which
considerthatallparametersaretime-dependentandmustbesimultaneouslysolvedina
fullycoupledschemewiththesystemofequationsofADS.
𝑇, 𝑇
, 5(10)
ℎℎℎ, ℎ
𝜂 (11)
𝑄, 𝑚,ℎℎ,(12)
𝑄, 𝑚,ℎ, ℎ(13)
Figure 3. The representation of the vapor compression cycle on a pressure–enthalpy graph.
Table 2. The parameters used in the simulation of the VCS.
Parameter Value Unit
Compressor type Copeland ZP42K5E-PFV
Refrigerant HFC-410A
Cooling capacity
@Tcond,v= 54.44 ◦C
and Teva,v= 7.22 ◦C
12.29 kW
Compressor power
@Tcond,v= 54.44 ◦C
and Teva,v= 7.22 ◦C
4.07 kW
Degree of superheating 11 °C
Degree of subcooling 8.3 °C
Evaporating temperature −5 °C
Enthalpy at compressor inlet h1432 kJ·kg−1
Enthalpy at evaporator outlet h1,sat@Teva,v=−5◦C421 kJ·kg−1
The VCS performance is simulated using the following set of equations, which consider
that all parameters are time-dependent and must be simultaneously solved in a fully
coupled scheme with the system of equations of ADS.
Tcond,v=Teva,a+5 (10)
h2=h1+h2,is −h1
ηis
(11)
.
Qcond,v=.
mre f ,v(h2−h3,sat)(12)
.
Qeva,v=.
mre f ,v(h1,sat −h4)(13)
COPv=Teva,v
Tcond,v−Teva,v
×ηII (14)
.
Wv=
.
Qeva,v
COPv(15)
At any given time, both
.
Qcond,v
and
Tcond,v
relate the VCS to the ADS to find out the
instant compressor power (
.
Wv
), which, in turn, enables the set of equations of both cycles
to be solved.
Sustainability 2024,16, 3669 9 of 18
3.4. Performance Indicators
Once cyclic steady state is reached, the cascade VCS/ADS’s performance is assessed
using the data of the last cycle as follows:
CCads =Rtcycl e
0
.
Qcond,vdt
tcycle
(16)
.
Qheat,ads =Rtcycle
0
.
mhCh(Th,in −Th,out )dt
tcycle
(17)
COPthermal,ads =CCads
.
Qheat,ads
(18)
Powerelect,vcs =Rtcycle
0
.
Wvdt
tcycle
(19)
CCvcs =Rtcycl e
0
.
Qeva,vdt
tcycle
(20)
COPelect,vcs =CCev a,vcs
Powerelect,vcs
(21)
DIPVCS =CCeva,vcs ∗3600 ∗Working hours
Cp,wTw,in −Tf reez ing +hf g,ice +Cp,iceTf re ezing −Tice,out (22)
where
CC
and
DIP
denote the cooling capacity and the daily ice production. The working
hours of the system are 24 h, as the adsorption system can be driven by either industrial
waste heat or solar collectors assisted with heat storage.
COPelect,vcs
is the coefficient of the
performance of the VCS, which represents the electrical energy conversion efficiency of
the system.
3.5. Mathematical Model Validation
The adsorbent bed design and working pair used in this study are identical to those
identified in the reference [
12
]. As seen in Figure 4a, the published data corresponding to
a foam thickness of 2 mm are therefore used for validation. The COPs determined from the
lumped model in this study for the ADS at different cycle times exhibit adequate agreement
with the published ones, with a maximum deviation of 6.2%. On the other hand, as can
be shown in Figure 4b, the COPs of the VCS model at various condensing temperatures
demonstrate an accurate match with those specified in the manufacturer’s datasheet [
31
].
As mentioned earlier, the test case reported in the datasheet had a deviation of
±
5% based
on a 72 h run-in period.
Sustainability2024,16,366910of19
(a)(b)
Figure4.ThevalidationoftheCOPsofbothADSandVCSmodelsagainsttheircounterparts;(a)
ADSvalidationreference[12],and(b)VCSvalidationreference[31].
4.ResultsandDiscussions
First,thestudywillclarifyhowthemajorcharacteristicsoftheboomingcycle(VCS)
varyovertimeandhowthedynamicnatureofthetoppingcycle(ADS)affectsthese
variations.Next,adetailedinvestigationwillbeconductedatvariouscondensing
temperaturesforthetoppingcyclebasedontheuseoftheADS’scycletimeastheprimary
controllingparametertofitthecoolingrequirementsoftheVCS.
4.1.CyclicPerfo rman ceoftheIntegratedSystem
Inthissection,theresultsareobtainedbyseingthecondensingtemperatureofthe
toppingcycleto50°CandtheADScycletimeto760s.Thesimulationlasts10complete
cycles(7600s)toreachacyclicsteadystate,whichisrequiredintheevaluationand
comparisonofthedifferentcyclesinthenextsection,asshowninFigures5–7.
Figure5.Thetimevariationoftherefrigerantflowratesinbothcycleswithanadsorptioncycletime
of760s.
0.18
0.2
0.22
0.24
0.26
0.28
0.3
200 700 1200 1700
COP (-)
Adsorption system cycle time (s)
COP_ads_model
COP_ads _ref
0
1
2
3
4
5
6
20 30 40 50 60
COP (-)
Tcond,v
COP_vcs_model
COP_vcs_datasheet
0
0.01
0.02
0.03
0.04
0.05
0.06
0 1000 2000 3000 4000 5000 6000 7000 8000
Refrigerant flow rate
(kg/s)
Time (s)
ADS VCS
Figure 4. The validation of the COPs of both ADS and VCS models against their counterparts;
(a) ADS validation reference [12], and (b) VCS validation reference [31].
Sustainability 2024,16, 3669 10 of 18
4. Results and Discussions
First, the study will clarify how the major characteristics of the bottoming cycle
(VCS) vary over time and how the dynamic nature of the topping cycle (ADS) affects
these variations. Next, a detailed investigation will be conducted at various condensing
temperatures for the topping cycle based on the use of the ADS’s cycle time as the primary
controlling parameter to fit the cooling requirements of the VCS.
4.1. Cyclic Performance of the Integrated System
In this section, the results are obtained by setting the condensing temperature of the
topping cycle to 50
◦
C and the ADS cycle time to 760 s. The simulation lasts 10 complete
cycles (7600 s) to reach a cyclic steady state, which is required in the evaluation and
comparison of the different cycles in the next section, as shown in Figures 5–7.
Sustainability2024,16,366910of19
(a)(b)
Figure4.ThevalidationoftheCOPsofbothADSandVCSmodelsagainsttheircounterparts;(a)
ADSvalidationreference[12],and(b)VCSvalidationreference[31].
4.ResultsandDiscussions
First,thestudywillclarifyhowthemajorcharacteristicsoftheboomingcycle(VCS)
varyovertimeandhowthedynamicnatureofthetoppingcycle(ADS)affectsthese
variations.Next,adetailedinvestigationwillbeconductedatvariouscondensing
temperaturesforthetoppingcyclebasedontheuseoftheADS’scycletimeastheprimary
controllingparametertofitthecoolingrequirementsoftheVCS.
4.1.CyclicPerformanceoftheIntegratedSystem
Inthissection,theresultsareobtainedbyseingthecondensingtemperatureofthe
toppingcycleto50°CandtheADScycletimeto760s.Thesimulationlasts10complete
cycles(7600s)toreachacyclicsteadystate,whichisrequiredintheevaluationand
comparisonofthedifferentcyclesinthenextsection,asshowninFigures5–7.
Figure5.Thetimevariationoftherefrigerantflowratesinbothcycleswithanadsorptioncycletime
of760s.
0.18
0.2
0.22
0.24
0.26
0.28
0.3
200 700 1200 1700
COP (-)
Adsorption system cycle time (s)
COP_ads_model
COP_ads _ref
0
1
2
3
4
5
6
20 30 40 50 60
COP (-)
Tcond,v
COP_vcs_model
COP_vcs_datasheet
0
0.01
0.02
0.03
0.04
0.05
0.06
0 1000 2000 3000 4000 5000 6000 7000 8000
Refrigerant flow rate
(kg/s)
Time (s)
ADS VCS
Figure 5. The time variation of the refrigerant flow rates in both cycles with an adsorption cycle time
of 760 s.
Sustainability2024,16,366911of19
Figure6.Thetimevariationoftemperaturesinbothbeds,VCScondensingtemperature,andADS
evaporatingtemperature.
Figure7.Thevariationofevaporatorcoolingpower,compressorpower,andcondenserheat
rejectionintheVCS.
Figure5showsthehighfluctuationsinthevariationoftheADS’refrigerantmass
flowrateintheintermediateheatexchanger(HEX).Thisisduetothehigheradsorption
kineticsatthestartoftheadsorptionprocesses,whicharesloweddowndramaticallyover
thehalf-cycletimes.Sincethereisnoadsorptionprocessoccurringineitherbedduring
theswitchingperiods,thereisnomassflowrateofrefrigerantfortheADSduringthese
briefintervals.However,thefluctuationsintheVCS’srefrigerantflowratearevery
limitedcomparedtothoseinitscounterpart,theADS.Thisiscontrolledbythescroll-type
compressor’scharacteristics,whichcausethesevariationsintheVCS’srefrigerantflow
rate,relatedtothecompressor’svolumetriccapacityandtemperaturelift,asshownin
Figure2.ThethermalmassoftheHEXabsorbsorreleasesitsenergytomaintainabalance
betweenthetwocyclesandmitigatetheeffectofthehighfluctuationsassociatedwiththe
ADSside.
Figure6showshowtheapproachfollowedinthisstudymaintainedatemperature
differenceof5°CbetweenthetworefrigerantsintheHEXoverthestudyperiods,
reachingacyclicsteadystate.Additionally,thevariationsinthetwobeds’temperatures
arecyclicafterthe10completeADScycles.Thecoolingwatertemperatureforthebedsin
thistestcaseissetto25°C,andtheregenerationtemperatureissetto90°C.Afterreaching
acyclicsteadystate,thecascadesystemsuccessfullymanagedtoreachanaverage
condensingtemperatureoftheVCSof26.42°C,usinganaverageevaporating
temperatureof21.42°CfortheADS.
TheenergybalanceamongtheVCScomponentsisconfirmedduringthesimulation
periods,asexemplifiedinFigure7.Thefigureshowshowtheoperationalconditionsof
thetoppingcycle,whichfeaturedtransientconditions,affectthetimevariationsofthe
capacitiesofthecompressorandevaporatoroftheVCS.Thesevariationsinthetwo
componentsaccumulatetoformtheheatrejectedbythecondenseroftheVCS,whichis
handledbytheHEX.
-10
15
40
65
90
0 1000 2000 3000 4000 5000 6000 7000 8000
Temperature (°C)
Time (s)
Bed-A Bed-B Tcond,vcs Teva,ads Teva,vcs Treg,ads
0
500
1000
1500
2000
2500
3000
8,000
9,000
10,000
11,000
12,000
0 1000 2000 3000 4000 5000 6000 7000 8000
Compressor power (W)
VCS evaporator or
condenser capacity (W)
Time (s)
VCS Evaporator VCS Condenser VCS Compressor
Figure 6. The time variation of temperatures in both beds, VCS condensing temperature, and ADS
evaporating temperature.
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Figure6.Thetimevariationoftemperaturesinbothbeds,VCScondensingtemperature,andADS
evaporatingtemperature.
Figure7.Thevariationofevaporatorcoolingpower,compressorpower,andcondenserheat
rejectionintheVCS.
Figure5showsthehighfluctuationsinthevariationoftheADS’refrigerantmass
flowrateintheintermediateheatexchanger(HEX).Thisisduetothehigheradsorption
kineticsatthestartoftheadsorptionprocesses,whicharesloweddowndramaticallyover
thehalf-cycletimes.Sincethereisnoadsorptionprocessoccurringineitherbedduring
theswitchingperiods,thereisnomassflowrateofrefrigerantfortheADSduringthese
briefintervals.However,thefluctuationsintheVCS’srefrigerantflowratearevery
limitedcomparedtothoseinitscounterpart,theADS.Thisiscontrolledbythescroll-type
compressor’scharacteristics,whichcausethesevariationsintheVCS’srefrigerantflow
rate,relatedtothecompressor’svolumetriccapacityandtemperaturelift,asshownin
Figure2.ThethermalmassoftheHEXabsorbsorreleasesitsenergytomaintainabalance
betweenthetwocyclesandmitigatetheeffectofthehighfluctuationsassociatedwiththe
ADSside.
Figure6showshowtheapproachfollowedinthisstudymaintainedatemperature
differenceof5°CbetweenthetworefrigerantsintheHEXoverthestudyperiods,
reachingacyclicsteadystate.Additionally,thevariationsinthetwobeds’temperatures
arecyclicafterthe10completeADScycles.Thecoolingwatertemperatureforthebedsin
thistestcaseissetto25°C,andtheregenerationtemperatureissetto90°C.Afterreaching
acyclicsteadystate,thecascadesystemsuccessfullymanagedtoreachanaverage
condensingtemperatureoftheVCSof26.42°C,usinganaverageevaporating
temperatureof21.42°CfortheADS.
TheenergybalanceamongtheVCScomponentsisconfirmedduringthesimulation
periods,asexemplifiedinFigure7.Thefigureshowshowtheoperationalconditionsof
thetoppingcycle,whichfeaturedtransientconditions,affectthetimevariationsofthe
capacitiesofthecompressorandevaporatoroftheVCS.Thesevariationsinthetwo
componentsaccumulatetoformtheheatrejectedbythecondenseroftheVCS,whichis
handledbytheHEX.
-10
15
40
65
90
0 1000 2000 3000 4000 5000 6000 7000 8000
Temperature (°C)
Time (s)
Bed-A Bed-B Tcond,vcs Teva,ads Teva,vcs Treg,ads
0
500
1000
1500
2000
2500
3000
8,000
9,000
10,000
11,000
12,000
0 1000 2000 3000 4000 5000 6000 7000 8000
Compressor power (W)
VCS evaporator or
condenser capacity (W)
Time (s)
VCS Evaporator VCS Condenser VCS Compressor
Figure 7. The variation of evaporator cooling power, compressor power, and condenser heat rejection
in the VCS.
Sustainability 2024,16, 3669 11 of 18
Figure 5shows the high fluctuations in the variation of the ADS’ refrigerant mass
flow rate in the intermediate heat exchanger (HEX). This is due to the higher adsorption
kinetics at the start of the adsorption processes, which are slowed down dramatically
over the half-cycle times. Since there is no adsorption process occurring in either bed
during the switching periods, there is no mass flow rate of refrigerant for the ADS during
these brief intervals. However, the fluctuations in the VCS’s refrigerant flow rate are very
limited compared to those in its counterpart, the ADS. This is controlled by the scroll-type
compressor’s characteristics, which cause these variations in the VCS’s refrigerant flow
rate, related to the compressor’s volumetric capacity and temperature lift, as shown in
Figure 2. The thermal mass of the HEX absorbs or releases its energy to maintain a balance
between the two cycles and mitigate the effect of the high fluctuations associated with the
ADS side.
Figure 6shows how the approach followed in this study maintained a temperature
difference of 5
◦
C between the two refrigerants in the HEX over the study periods, reaching
a cyclic steady state. Additionally, the variations in the two beds’ temperatures are cyclic
after the 10 complete ADS cycles. The cooling water temperature for the beds in this test
case is set to 25
◦
C, and the regeneration temperature is set to 90
◦
C. After reaching a cyclic
steady state, the cascade system successfully managed to reach an average condensing
temperature of the VCS of 26.42
◦
C, using an average evaporating temperature of 21.42
◦
C
for the ADS.
The energy balance among the VCS components is confirmed during the simulation
periods, as exemplified in Figure 7. The figure shows how the operational conditions
of the topping cycle, which featured transient conditions, affect the time variations of
the capacities of the compressor and evaporator of the VCS. These variations in the two
components accumulate to form the heat rejected by the condenser of the VCS, which is
handled by the HEX.
It is important to highlight that most of the heat generated due to the inefficiencies in
the compression process is absorbed by the refrigerant and then rejected by the condenser;
however, some heat is directly released to the surrounding area from the compressor unit
and connections.
Based on the data presented in Figure 7, the average compressor power during the final
cycle, which lasted from 6840 to 7600 s, is approximately 1870 W. However, the difference
between the average thermal power transferred in the condenser and the evaporator is
1783 W in this cycle. This difference, which is about 87 W, is due to the use of practical
data from the manufacturer to calculate the compressor power, which should be slightly
higher than that calculated from the direct energy balance due to the thermal losses from
the compressor unit and its connections. In this cyclic steady-state cycle, the condenser
heat rejected is 11,383 W, while the evaporator cooling power is about 9600 W.
4.2. The Effect of Adsorption Cycle Time
When the condenser is an air-cooled type, the heat sink temperature in severe weather,
such as that of Riyadh City, causes a high condensing temperature (
Tc
) in the topping
cycle. This section examines the influence of ADS cycle time, which affects the ADS’s
cooling capacity, at various
Tc
values of 50, 55, and 60
◦
C. Contrary to what was frequently
done in earlier studies, the real VCS system data used in the current simulations come
with limitations on modifying the ADS’s cycle time to comply with VCS requirements.
Therefore, the maximum cycle time shown in each line graph in the following figures is
the maximum possible cycle time for the ADS in the case under study that can be used for
balanced operation in the integrated system. Increasing the cycle time over that period
decreases the cooling capacity of the ADS to a point where it is not able to absorb the
heat released from the VCS, leading to a cumulative heat and increasing the condensing
temperature of the VCS. In practice, the VCS will go into forced shutdown in such cases
to save the compressor unit. On the other hand, since further cycle time reduction is not
beneficial, the minimum cycle time for each line graph is set when a deterioration in the
Sustainability 2024,16, 3669 12 of 18
performance of both cycles is observed. These limitations on the maximum and minimum
cycle times can be deduced from the results in Figures 8–11.
Figure 8shows how the temperatures of both refrigerants in the HEX change with
respect to the ADS cycle time and its limitations at different
Tc
. The best cycle times are 360,
320, and 320 s, which led to the minimum condensing temperatures of the VCS (
Tcond,v
)
of 18.14, 22.75, and 27.37
◦
C at
Tc
values of 50, 55, and 60
◦
C, respectively. These result
from the minimum evaporating temperature of the ADS (
Teva,a
) attained at these times.
Reducing the cycle duration below the optimal times results in an increase in
Teva,a
, and
subsequently increases
Tcond,v
. In the adsorption system, a very short cycle time can lead to
a decrease in the net amount of adsorbate (circulated refrigerant) during the cycle, due to
insufficient time for the desorption process. This demolishes the benefit gained from the
higher adsorption kinetics at shorter cycle times.
Sustainability2024,16,366912of19
Itisimportanttohighlightthatmostoftheheatgeneratedduetotheinefficienciesin
thecompressionprocessisabsorbedbytherefrigerantandthenrejectedbythecondenser;
however,someheatisdirectlyreleasedtothesurroundingareafromthecompressorunit
andconnections.
BasedonthedatapresentedinFigure7,theaveragecompressorpowerduringthe
finalcycle,whichlastedfrom6840to7600s,isapproximately1870W.However,the
differencebetweentheaveragethermalpowertransferredinthecondenserandthe
evaporatoris1783Winthiscycle.Thisdifference,whichisabout87W,isduetotheuse
ofpracticaldatafromthemanufacturertocalculatethecompressorpower,whichshould
beslightlyhigherthanthatcalculatedfromthedirectenergybalanceduetothethermal
lossesfromthecompressorunitanditsconnections.Inthiscyclicsteady-statecycle,the
condenserheatrejectedis11,383W,whiletheevaporatorcoolingpowerisabout9600W.
4.2.TheeffectofAdsorptionCycleTime
Whenthecondenserisanair-cooledtype,theheatsinktemperatureinsevere
weather,suchasthatofRiyadhCity,causesahighcondensingtemperature(𝑇)inthe
toppingcycle.ThissectionexaminestheinfluenceofADScycletime,whichaffectsthe
ADS’scoolingcapacity,atvarious 𝑇valuesof50,55,and60°C.Contrarytowhatwas
frequentlydoneinearlierstudies,therealVCSsystemdatausedinthecurrent
simulationscomewithlimitationsonmodifyingtheADS’scycletimetocomplywithVCS
requirements.Therefore,themaximumcycletimeshownineachlinegraphinthe
followingfiguresisthemaximumpossiblecycletimefortheADSinthecaseunderstudy
thatcanbeusedforbalancedoperationintheintegratedsystem.Increasingthecycletime
overthatperioddecreasesthecoolingcapacityoftheADStoapointwhereitisnotable
toabsorbtheheatreleasedfromtheVCS,leadingtoacumulativeheatandincreasingthe
condensingtemperatureoftheVCS.Inpractice,theVCSwillgointoforcedshutdownin
suchcasestosavethecompressorunit.Ontheotherhand,sincefurthercycletime
reductionisnotbeneficial,theminimumcycletimeforeachlinegraphissetwhena
deteriorationintheperformanceofbothcyclesisobserved.Theselimitationsonthe
maximumandminimumcycletimescanbededucedfromtheresultsinFigures8–11.
Figure8.TheeffectofADScycletimeontheintermediateHEXtemperaturesatdifferentADS
condensingtemperatures.
10
15
20
25
30
35
10
15
20
25
30
35
200 300 400 500 600 700 800
Evaporating temperature of ADS (°C)
Condensing temperature of VCS (°C)
Adsorption system cycle time (s)
VCS Tc=50 °C VCS Tc=55 °C VCS Tc=60 °C
ADS Tc=50 °C ADS Tc=55 °C ADS Tc=60 °C
Figure 8. The effect of ADS cycle time on the intermediate HEX temperatures at different ADS
condensing temperatures.
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Figure9.TheeffectoftheADScycletimeonthecoolingcapacitiesofbothcyclesatdifferentADS
condensingtemperatures.
Figure10.TheeffectofADScycletimeonthecompressorpowerandDIPatdifferentADS
condensingtemperatures.
9.2
9.5
9.8
10.1
10.4
10.7
11
11.3
11.6
9.2
9.5
9.8
10.1
10.4
10.7
11
11.3
11.6
200 300 400 500 600 700 800
Cooling capacity of ADS (kW)
Cooling capacity of VCS (kW)
Adsorption system cycle time (s)
VCS Tc=50 °C VCS Tc=55 °C VCS Tc=60 °C
ADS Tc=50 °C ADS Tc=55 °C ADS Tc=60 °C
1.6
1.65
1.7
1.75
1.8
1.85
1000
1500
2000
2500
3000
3500
200 300 400 500 600 700 800
Daily ice production (ton/day)
Compressor power (W)
Adsorption system cycle time (s)
Wcomp Tc=50 °C Wcomp Tc=55 °C Wcomp Tc=60 °C
DIP Tc=50 °C DIP Tc=55 °C DIP Tc=60 °C
Figure 9. The effect of the ADS cycle time on the cooling capacities of both cycles at different ADS
condensing temperatures.
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Sustainability2024,16,366913of19
Figure9.TheeffectoftheADScycletimeonthecoolingcapacitiesofbothcyclesatdifferentADS
condensingtemperatures.
Figure10.TheeffectofADScycletimeonthecompressorpowerandDIPatdifferentADS
condensingtemperatures.
9.2
9.5
9.8
10.1
10.4
10.7
11
11.3
11.6
9.2
9.5
9.8
10.1
10.4
10.7
11
11.3
11.6
200 300 400 500 600 700 800
Cooling capacity of ADS (kW)
Cooling capacity of VCS (kW)
Adsorption system cycle time (s)
VCS Tc=50 °C VCS Tc=55 °C VCS Tc=60 °C
ADS Tc=50 °C ADS Tc=55 °C ADS Tc=60 °C
1.6
1.65
1.7
1.75
1.8
1.85
1000
1500
2000
2500
3000
3500
200 300 400 500 600 700 800
Daily ice production (ton/day)
Compressor power (W)
Adsorption system cycle time (s)
Wcomp Tc=50 °C Wcomp Tc=55 °C Wcomp Tc=60 °C
DIP Tc=50 °C DIP Tc=55 °C DIP Tc=60 °C
Figure 10. The effect of ADS cycle time on the compressor power and DIP at different ADS condensing
temperatures.
Sustainability2024,16,366914of19
Figure11.TheeffectofADScycletimeontheCOPofbothcyclesatdifferentADScondensing
temperatures.
Figure8showshowthetemperaturesofbothrefrigerantsintheHEXchangewith
respecttotheADScycletimeanditslimitationsatdifferent 𝑇.Thebestcycletimesare
360,320,and320s,whichledtotheminimumcondensingtemperaturesoftheVCS(𝑇,)
of18.14,22.75,and27.37°Cat 𝑇valuesof50,55,and60°C,respectively.Theseresult
fromtheminimumevaporatingtemperatureoftheADS(𝑇,)aainedatthesetimes.
Reducingthecycledurationbelowtheoptimaltimesresultsinanincreasein𝑇,,and
subsequentlyincreases𝑇,.Intheadsorptionsystem,averyshortcycletimecanlead
toadecreaseinthenetamountofadsorbate(circulatedrefrigerant)duringthecycle,due
toinsufficienttimeforthedesorptionprocess.Thisdemolishesthebenefitgainedfrom
thehigheradsorptionkineticsatshortercycletimes.
ItcanalsobenotedthattheintegratedVCS/ADScanbeoperatedusingawiderange
ofcycletimes,from320sto780satalower 𝑇of50°C;however,thisrangeisreduced
from240stoamaximumof480satahigher 𝑇of60°C.Thisisaributedtothedynamic
balancepointfortheintegratedsystem,whichcanbeachievedindifferentcircumstances.
Forinstance,theelevatedtemperaturesintheHEX(𝑇,,and𝑇,)canenhancethe
adsorptionprocessonthesideoftheADSandadverselyincreasethecompressorpower
consumptionontheotherside.Figure9illustratestheinconsistencybetweentheADS’s
andVCS’scoolingcapacitiesinresponsetothevariationsinthe 𝑇overvariouscycle
times.WhiletheADS’scoolingcapacitygetshighervaluesat 𝑇of60°Catdifferentcycle
times,theVCS’scoolingcapacityhaslowervaluescomparedtothevaluesat 𝑇of50and
55°C.
InconventionalADS,thecoolingcapacitydeclinesathighercycletimes;however,in
theintegratedsystem,the𝑇,alsoincreasesathighercycletimes,which unusually
enhancedtheADS’scoolingcapacity,asshowninFigure9.Conversely,asthecycletime
increases,theVCS’scoolingcapacitydeclines.Thisisbecausetheevaporatorexperiences
lesseffectivecooling,resultingfromtheriseinthecondensingtemperaturesoftheVCS.
TheoptimalcycletimesidentifiedinFigure8correspondtothehighestcoolingcapacity
oftheVCSateach 𝑇.
Figure10showshowthechangeintheADS’scycletimeatdifferent 𝑇affectsthe
compressorpowerandtheDIPoftheVCS.Theminimumcompressorpowerandthe
maximumDIPindicatethattheVCSperformsbestattheidealcycledurationsof360,320,
and320s,with 𝑇of50,55,and60°C.Thisisaributedtotheminimumcompressor
temperatureliftsatthesetimes,resultinginminimum𝑇,,asindicatedinFigure8.
ThecompressorpowercanbesignificantlyincreasedbyprolongingtheADS’scycle
0.35
0.4
0.45
0.5
0.55
2
3
4
5
6
7
8
200 300 400 500 600 700 800
COP of ADS
COP of VCS
Adsorption system cycle time (s)
VCS Tc=50 °C VCS Tc=55 °C VCS Tc=60 °C
ADS Tc=50 °C ADS Tc=55 °C ADS Tc=60 °C
Figure 11. The effect of ADS cycle time on the COP of both cycles at different ADS condensing
temperatures.
It can also be noted that the integrated VCS/ADS can be operated using a wide range
of cycle times, from 320 s to 780 s at a lower
Tc
of 50
◦
C; however, this range is reduced
from 240 s to a maximum of 480 s at a higher
Tc
of 60
◦
C. This is attributed to the dynamic
balance point for the integrated system, which can be achieved in different circumstances.
For instance, the elevated temperatures in the HEX (
Teva,a
, and
Tcond,v
) can enhance the
adsorption process on the side of the ADS and adversely increase the compressor power
consumption on the other side. Figure 9illustrates the inconsistency between the ADS’s
and VCS’s cooling capacities in response to the variations in the
Tc
over various cycle times.
While the ADS’s cooling capacity gets higher values at
Tc
of 60
◦
C at different cycle times,
the VCS’s cooling capacity has lower values compared to the values at Tcof 50 and 55 ◦C.
In conventional ADS, the cooling capacity declines at higher cycle times; however,
in the integrated system, the
Teva,a
also increases at higher cycle times, which unusually
enhanced the ADS’s cooling capacity, as shown in Figure 9. Conversely, as the cycle time
increases, the VCS’s cooling capacity declines. This is because the evaporator experiences
less effective cooling, resulting from the rise in the condensing temperatures of the VCS.
Sustainability 2024,16, 3669 14 of 18
The optimal cycle times identified in Figure 8correspond to the highest cooling capacity of
the VCS at each Tc.
Figure 10 shows how the change in the ADS’s cycle time at different
Tc
affects the
compressor power and the DIP of the VCS. The minimum compressor power and the
maximum DIP indicate that the VCS performs best at the ideal cycle durations of 360, 320,
and 320 s, with
Tc
of 50, 55, and 60
◦
C. This is attributed to the minimum compressor
temperature lifts at these times, resulting in minimum
Tcond,v
, as indicated in Figure 8. The
compressor power can be significantly increased by prolonging the ADS’s cycle duration
beyond what is considered optimal. The compressor power increases by approximately
41.3%, from 1390.6 W to 1964.7 W, when the cycle time is increased from 360 s to 780 s,
with
a Tc
of 50
◦
C. Moreover, raising the
Tc
lowers the DIP and raises the compressor power.
The minimum compressor power at a
Tc
of 60
◦
C is 1922.17 W, which is 38.3% more than
the minimum power at
a Tc
of 50
◦
C. The DIP drops by only 2.57%, from 1.8308 to 1.7837
ton day−1, when Tcis raised from 50 to 60 ◦C.
Figure 11 illustrates how, at various ADS condensing temperatures, the energy conver-
sion efficiency of both DAS and VCS, as represented by the COPs, responds to the cycle
time variations. The ideal cycle times found while examining the prior parameters consis-
tently yield the highest COPs for VCSs. At optimal cycle times of 360, 320, and 320 s, and
with
Tc
of 50, 55, and 60
◦
C, the maximum VCS’ COPs are 7.06, 5.84, and 4.98, respectively.
The VCS’s COPs are significantly decreased when the cycle periods are increased beyond
the optimal ones. For instance, at a
Tc
of 50
◦
C, the VCS’s COP decreases by 31.16%, from
7.06 to 4.86, when the cycle time is increased from 360 s to 780 s.
Conversely, when the cycle time increases, the ADS’s COPs rise dramatically, as seen
in Figure 11. In conventional ADS, this is certainly because the regeneration heat supplied
to the ADS at longer cycle durations is decreased, and in this integrated system, its cooling
capacity is also marginally increased. The reduction in the heat supply, combined with a
fixed or increased cooling capacity of the ADS, leads to these increases in the ADS’s COPs
at higher cycle times.
The ADS’s COP decreases with increasing
Tc
; for example, it is reduced by 7.55%,
from 0.45 to 0.416 at cycle times of 360 s and 320 s, when the
Tc
is increased from 50
◦
C to
60
◦
C. This is less significant than what can be observed for the VCS’s COP under the same
circumstances compared to the above example, where the VCS’s COP has a reduction of
29.5%, from 7.06 to 4.98. Therefore, the VCS is more sensitive to the change in the ADS’s
condensing temperature,
Tc
. This is due to the dynamics of the balancing conditions of the
intermediate heat exchanger, which raises both the evaporating temperature of the ADS
and the condensing temperature of the VCS in response to an increase in Tc.
4.3. Comparison with the Conventional VCS
Finally, the importance of the cascade vapor compression and adsorption refrigeration
system being applied at higher ambient temperatures can be summarized as shown in
Figure 12. The datasheet of the manufacturer for the VCS’s compressor is used to define the
performance of the single conventional VCS, which is also used in this study to simulate
the integrated VCS/ADS. The above findings in this study emphasize how crucial it is to
use the optimal ADS cycle time. As a result, the comparisons in Figure 12 use the optimal
ADS cycle time of 360 s and a condensing temperature of 50 ◦C.
By using the cascade system, the VCS’s cooling capacity can be raised from 8.31 to
9.82 kW
, representing an increase of 18.2%. This is directly related to the evaporator’s
increased ability, with a higher enthalpy difference when the VCS condensing temperature
drops from 50
◦
C to 18.14
◦
C. In such a case, compressor power can be significantly
decreased by 63.2% by taking advantage of the larger condensing temperature drops.
Consequently, the COP of the VCS has a very high potential to be increased by 221%, from
2.2 to 7.06. These findings make the use of such integrated VCS/ADS a promising solution
for refrigeration systems working under high ambient temperature conditions. On the
other hand, using the ADS as a topping cycle for the VCS results in a higher COP for the
Sustainability 2024,16, 3669 15 of 18
ADS compared to operating it individually. The ADS’s COP can be increased by 104.5%
in such challenging circumstances, with a condensing temperature of 50
◦
C, as shown in
Figure 12.
Sustainability2024,16,366916of19
Figure12.TheperformanceofthehybridsystematthebestADScycletimecomparedtothe
conventionalsystem.
TheresultsmatchthosereportedfortheVCS.Whenthecondensingtemperature
increasesby1°C,theCOPdropsby2–4%[9].Inthisstudy,andaccordingtothecase
giveninFigure12,thecondensingtemperatureisincreasedby31.86°C.Thatresultsina
minimumexpecteddropintheCOPof63.72%.Theresultofthepresentstudyshowsthat
thedropintheCOPfrom7.06to2.2representsa68.8%drop,whichalsorepresentsan
increaseof221%whencalculatedbasedonthechangeinCOPfrom2.2to7.06.
5.Conclusions
Thisstudyinvestigatesusingacascadevapor-compression/adsorptionrefrigeration
systeminhotweatherwhenthereisnotasmuchcoolingwateravailable,whichraisesthe
condensingtemperature.Fortheadsorptionsystem(ADS)inthetoppingcycle,50,55,
and60°Careconsideredtobethecondensingtemperatures.Furthermore,thecombined
VCS/ADSsystemisassessedusingchangesintheADS’scycletime.Inthisstudy,
COMSOLMultiphysicsisusedtoconstructafullycoupledtransientmodelthatsimulates
theintegratedsystem.Themanufacturer’sdataforaVCScompressorundervarious
condensingandevaporatingtemperaturesaremergedwithanadsorptionmodel.Taking
intoaccountthepracticallimitationsoftheVCS,theintegratedmodelbuiltinthisstudy
capturesthedynamicnatureoftheADSontheoverallperformanceoftheintegrated
system.IntheeventthattheADSispoweredbyasolarheatingsystem,thecascadesystem
generatesicetooffercontinuouscoolingforairconditioningpurposes.Themainfindings
ofthestudycanbesummarizedasfollows:
TheminimumtemperaturesintheintermediateHEXcanbereachedatanidealADS
cycletime,leadingtothebestperformanceforthevaporcompressionsystem.
Toensureabalancedfunctioningbetweenthetwocycles,thereisalimittohowlong
theADScyclecanbeextended,whichshouldnotbedisregarded.
Whenthecondensingtemperature, 𝑇,israisedfrom50°Cto60°C,theVCS’sCOP
decreasesby29.5%,whiletheADS’sCOPdecreasesby7.55%,indicatingthattheVCS
ismoresusceptibletothechangeinthecondensingtemperatureoftheADS.
ComparedtotheconventionalVCS,thecascadesystemcanincreasetheVCS’s
coolingcapacityby18.2%,reducethecompressorpowerby63.2%,andincreasethe
COPby221%,atahighcondensingtemperature, 𝑇,of50°C.Theseresults
demonstratedthat,inextremeenvironmentalcircumstances,thecascadeVCS/ADS
8.31
9.82
3.78
1.39
2.20
7.06
0.22 0.45
0
2
4
6
8
10
12
VCS Integrated
VCS/ADS
VCS Integrated
VCS/ADS
VCS Integrated
VCS/ADS
ADS ADS
Upper cycle
Cooling capacity (kW) Compressor power (kW) COP Electrical (−) COP Thermal (−)
Figure 12. The performance of the hybrid system at the best ADS cycle time compared to the
conventional system.
The results match those reported for the VCS. When the condensing temperature
increases by 1
◦
C, the COP drops by 2–4% [
9
]. In this study, and according to the case
given in Figure 12, the condensing temperature is increased by 31.86
◦
C. That results in
a minimum expected drop in the COP of 63.72%. The result of the present study shows
that the drop in the COP from 7.06 to 2.2 represents a 68.8% drop, which also represents an
increase of 221% when calculated based on the change in COP from 2.2 to 7.06.
5. Conclusions
This study investigates using a cascade vapor-compression/adsorption refrigeration
system in hot weather when there is not as much cooling water available, which raises
the condensing temperature. For the adsorption system (ADS) in the topping cycle, 50, 55,
and 60
◦
C are considered to be the condensing temperatures. Furthermore, the combined
VCS/ADS system is assessed using changes in the ADS’s cycle time. In this study, COMSOL
Multiphysics is used to construct a fully coupled transient model that simulates the inte-
grated system. The manufacturer’s data for a VCS compressor under various condensing
and evaporating temperatures are merged with an adsorption model. Taking into account
the practical limitations of the VCS, the integrated model built in this study captures the
dynamic nature of the ADS on the overall performance of the integrated system. In the
event that the ADS is powered by a solar heating system, the cascade system generates ice
to offer continuous cooling for air conditioning purposes. The main findings of the study
can be summarized as follows:
•
The minimum temperatures in the intermediate HEX can be reached at an ideal ADS
cycle time, leading to the best performance for the vapor compression system.
•
To ensure a balanced functioning between the two cycles, there is a limit to how long
the ADS cycle can be extended, which should not be disregarded.
Sustainability 2024,16, 3669 16 of 18
•
When the condensing temperature,
Tc
, is raised from 50
◦
C to 60
◦
C, the VCS’s COP
decreases by 29.5%, while the ADS’s COP decreases by 7.55%, indicating that the VCS
is more susceptible to the change in the condensing temperature of the ADS.
•
Compared to the conventional VCS, the cascade system can increase the VCS’s cooling
capacity by 18.2%, reduce the compressor power by 63.2%, and increase the COP by
221%, at a high condensing temperature,
Tc
, of 50
◦
C. These results demonstrated that,
in extreme environmental circumstances, the cascade VCS/ADS refrigeration system
has a tremendous potential to be more sustainable with lower electricity consumption
compared to the typical system.
•
In this study, the selection of the adsorption working pair was based on their higher
adsorption performance along with their lower environmental impact. However, more
investigations need to be carried out to compare different adsorbent/adsorbate pairs,
considering many more aspects, such as conducting a 4E (energy, exergy, economic,
and environment) study.
Author Contributions: Conceptualization, M.B.E.; methodology, M.B.E.; software, M.B.E.; validation,
M.B.E. and J.O.; formal analysis, M.B.E. and A.E.-L.; investigation, M.B.E.; resources, H.A.-A., J.O. and
A.E.-L.; data curation, M.B.E.; writing—original draft, M.B.E.; writing—review and editing, M.B.E.;
visualization, J.O. and A.E.-L.; supervision, H.A.-A.; project administration, J.O. and A.E.-L.; funding
acquisition, H.A.-A. All authors have read and agreed to the published version of the manuscript.
Funding: This project was funded by the National Plan for Science, Technology and Innovation
(MAARIFAH), King Abdulaziz City for Science and Technology, Kingdom of Saudi Arabia, award
number (ll-ENE1845-02).
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: The data that support the findings of this study are available from the
corresponding author, [M.B.E.], upon reasonable request.
Conflicts of Interest: The authors declare no conflict of interest.
Nomenclature
ADS Adsorption system
COP Coefficient of performance (−)
CpSpecific heat capacity J·kg−1·K−1
CC Cooling capacity (W)
DIP Daily ice production kg·day−1
KLDF Mass-transfer coefficient s−1
hf g Ethanol refrigerant latent heat J·kg−1
hEnthalpy J·kg−1
MMass (kg)
MCHEX Thermal mass of the intermediate HEX ( kJ·k−1
.
mMass flow rate (kg·s−1)
pPressure (Pa)
.
QRate of heat transfer (W)
HsIsosteric heat of adsorption J·kg−1
TTemperature (K)
tTime (s)
tcycle Adsorption system cycle time (s)
VCS Vapor compression system
wUptake kgw·kg−1
ad
weq Equilibrium adsorption uptake kgw·kg−1
ad
.
WvInstantaneous compressor work (W)
Sustainability 2024,16, 3669 17 of 18
Greek symbols:
εHeat transfer effectiveness
ηis Compressor isentropic efficiency (−)
ηII Second law efficiency (−)
Subscripts and superscripts:
a,ads Adsorption
bBed
ccooling
cond Condenser
com p Compressor
eva Evaporator
eq Equilibrium
fFoam
hHeating
iInlet
is Isentropic
re f Refrigerant
rl Refrigerant liquid
sSolid adsorbent
sat Saturation
vVapor
wWater
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