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Reallocation of adsorption and desorption times for optimisation of cooling cycles
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 5 ( 2 0 1 2 ) 5 2 5 e5 3 1
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Reallocation of adsorption and desorption times for optimisation of cooling cycles Yu.I. Aristov a,*, A. Sapienza b, D.S. Ovoshchnikov a, A. Freni b, G. Restuccia b a b
Boreskov Institute of Catalysis, Pr. Lavrentieva 5, 630090 Novosibirsk, Russia CNR e Istituto di Tecnologie Avanzate per l’Energia “Nicola Giordano”, S. Lucia sopra Contesse 5, 98126 Messina, Italy
article info
abstract
Article history:
In an adsorption cycle it is common to have an equal duration of the adsorption and
Received 24 November 2009
desorption phases. In this paper, we investigated an intermittent cooling cycle with vari-
Received in revised form
able adsorption/desorption duration at fixed total cycle time. A new composite, LiNO3/silica
13 July 2010
KSK (SWS-9L), was used as a water sorbent. It was specifically synthesised for adsorptive
Accepted 20 July 2010
chilling units driven by low temperature heat (65e75 C). The sorption equilibrium and
Available online 24 July 2010
dynamics of SWS-9L were studied under conditions close to those realized in a typical cooling cycle. The actual performance of SWS-9L was tested in a single bed adsorption
Keywords:
chiller with special emphasis on the optimisation of the relative duration of isobaric
Adsorption system
adsorption and desorption stages to maximize the Coefficient Of Performance and the
Variation
Specific Cooling Power of the cycle. The tests resulted in being able to make practical
Duration
recommendations to rationally optimise the relative duration of adsorption and desorption
Cycle-adsorption
phases. ª 2010 Elsevier Ltd and IIR. All rights reserved.
Desorption Optimisation COP Water
Optimisation des cycles de refroidissement par modification des dure´es d’adsorption et de de´sorption Mots cle´s : Syste`me a` adsorption ; Variation ; Dure´e ; Cycle-adsorption ; De´sorption ; Optimisation ; COP ; Eau
1.
Introduction
Adsorptive heat transformation (AHT) allows re-use of enormous heat fluxes with low temperature potential that are commonly wasted (Meunier, 1993; Critoph and Zhong, 2005; Wang and Oliveira, 2006). To be more competitive with
conventional compression chilling units, both the Coefficient Of Performance (COP) and the Specific Cooling Power (SCP) have to be improved. One way is an improvement of the adsorbent used to ensure its harmonization with the AHT cycle: thermodynamic requirements imposed on an optimal adsorbent are formulated in (Aristov, 2007; Critoph, 1988),
* Corresponding author. E-mail address: [email protected] (Yu.I. Aristov). 0140-7007/$ e see front matter ª 2010 Elsevier Ltd and IIR. All rights reserved. doi:10.1016/j.ijrefrig.2010.07.019
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while the optimal dynamic behaviour is discussed in (Aristov, 2009). Improvement of the cycle, taking into account both thermodynamic and dynamic features, gives another independent opportunity. In fact, the total cycle duration tc was selected as an important parameter: commonly, the COP increases monotonically with the cycle time, while the SCP reaches the maximum at a certain tc (Boelman et al., 1995; Saha et al., 2009). New cooling cycles with heat and mass recovery were considered as well (see Wang, 2001; Pons and Poyelle, 1999; Ziegler and Satzger, 2005; Khan et al., 2007 and literature therein). Unlike the majority of studies with equal durations of the isobaric adsorption and desorption stages (tdes ¼ tads) (Boelman et al., 1995; Saha et al., 2009; Wang, 2001; Chua et al., 2004; Cerkvenik and Ziegler, 2006), here we pay special attention to the optimisation of these durations in order to improve the cycle COP and SCP and also to make a comparison with the common case of equal duration. To gain a preliminary idea about the relative durations, the water sorption dynamics was studied by a new Large Temperature Jump (LTJ) method (Aristov et al., 2008) which nearly reproduces conditions of the isobaric stages of an adsorptive cooling cycle. To plot this cycle, we experimentally measured appropriate isobars of water sorption of a new composite LiNO3/silica KSK (SWS-9L) which was specifically synthesised for adsorptive cooling cycles driven by low temperature heat (65e75 C) (Simonova and Aristov, 2008). The actual performance of SWS-9L was tested in a single bed adsorption chiller.
2.
Experimental
2.1.
Sample synthesis
Composite SWS-9L was synthesised by impregnation of a dry commercial silica KSK (the specific pore volume 1.0 cm3/g, the specific surface area 350 m3/g, the average pore size 15 nm) with a saturated aqueous solution of LiNO3. The synthesis procedure consisted of a drying of the pure silica at 200 C during 2 h, the impregnation of the dried silica with the saturated aqueous solution at 25 C, and again drying of the impregnated material at 200 C until its weight remained constant. The volume of the impregnating solution was equal to the pore volume of the silica. The salt content in the dry composite was determined by weighting the dry silica before impregnation and composite after drying, and amounted to 34.5 wt. %. The size of the silica grains was 0.25e0.5 mm.
2.2.
Isobars of water sorption
Sorption equilibrium of water vapour on SWS-9L was measured at T ¼ 30e120 C and PH2 O ¼ 12.6e42 mbar using a CAHN 2000 thermo-balance. Before measurements, the sample was heated up to 120 C under vacuum until reaching a dry weight m0 ¼ 27.1 mg. The amount of water adsorbed Dm was measured as a function of T at constant PH2 O ¼ 12.6 mbar (adsorption run) and 42.0 mbar (desorption run). To maintain these vapour pressures constant, the internal volume of the balance was connected with an evaporator at T ¼ 10 and 30 C respectively. The water uptake w was calculated as w ¼ Dm/m0.
2.3.
Kinetics of water sorption
The kinetics of water sorption on SWS-9L were studied by the Large Temperature Jump method whose description can be found elsewhere (Aristov et al., 2008). The simplest configuration of the adsorber-heat exchanger (A-HEX) unit was chosen for these measurements; namely, one layer of loose adsorbent grains placed on a metal plate which imitates a HEX fin. The temperature of the plate was changed as takes place in real sorption heat pumps, while the vapour pressure over the sorbent maintained almost constant. The experimental set-up used was described in (Glaznev and Aristov, 2008). Boundary conditions, namely the initial and final temperatures, the water vapour pressure at adsorption/desorption stages were set as described below. Typical time of cooling/heating of the metal support was 6e8 s.
2.4.
Tests in the single bed chiller
The real performance of SWS-9L was tested in a single bed adsorption chiller installed at CNR-ITAE laboratory (1 kW cooling power). With this aim, 350 g of sorbent grains 0.25e0.50 mm in size were embedded inside a compact heat exchanger of a finned flat-tube type. This adsorption bed configuration has the following advantages: a) compactness and low weight, as the heat exchanger is made of aluminium; b) good heat transfer properties due to the high heat transfer area and a high thermal conductivity of aluminium; c) high vapour permeability as provided by granular packing. Fig. 1 shows the overall and the detailed view of the heat exchanger of the adsorbent bed tested, while Table 1 reports its main parameters. The distance between the fins was about 1 mm, so that 2e4 grains could be housed in this gap. It is interesting to point out that this configuration allows a rather low “mass metal/mass adsorbent” ratio as well as good heat transfer between the metal finned tubes and adsorbent grains. The single bed chiller (Fig. 2a) consists of a vacuum chamber containing the above described adsorbent bed, a single evaporator and condenser. The vacuum chamber has been specifically designed to test different types of adsorbent beds and has various flanges that allow the connection with the other components of the prototype and the installation of the measurement devices (pressure gauges, temperature sensors), necessary to control and manage the system during testing. The external heat sources/sinks are interfaced with the adsorption chiller by using a test bench that allows management and control of the system (Fig. 2b). The test bench controls the different phases of the cooling cycle and measures the relevant physical parameters. Components installed (plate-type heat exchangers, temperature and pressure sensors, flow meters, electro-valves and hydraulic pumps) are electronically controlled. In fact, a data acquisition and control system were realized by a specific software implemented by the LABVIEW language to automatically operate the system. The external heating/cooling energy is provided by an electrically heated thermal oil boiler and an
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Fig. 1 e Overall (right side) and detailed (left side) view of the A-HEX tested.
electric water chiller installed in a service room close to the laboratory. The test facility is able to work in different operating conditions. In particular, Table 2 reports the range of possible temperatures and flow rates for the heating source (Tdes, Fdes), the evaporator (Tev, Fev) and the condenser (Tcon, Fcon). The cooling COP was calculated as ratio between the cooling effect generated in the evaporator and the amount of thermal energy supplied for isosteric heating and desorption phases: P P
ads
COP ¼
_ p ðTin Tout ÞDtjev mc
ishþdes
3.2.
_ p ðTin Tout ÞDtjbed mc
The Specific Cooling Power was calculated as ratio between the useful cooling effect and the total cycle time: P PS ¼
ads
_ p ðTin Tout ÞDtjev mc ms scycle
3.
Results and discussion
3.1.
Sorption equilibrium
Measuring isobars of water adsorption/desorption is needed for plotting a tentative cycle of adsorptive chiller and determining its boundary temperatures. Isobars of water adsorption at PH2 O ¼ 12.6 mbar and desorption at PH2 O ¼ 42.0 mbar measured for the sorbent SWS-9L represent the isobaric stages of a typical chiller cycle (Fig. 3). Maximum desorption
Table 1 e Main properties of the adsorber module. Dimension [mm] Weight [g] Overall volume [l] Adsorbent mass [g] Mass metal/mass adsorbent Heat transfer surface [m2]
temperature Tdes was fixed at 64 C, that determined the water uptake at the weak isoster, w ¼ 6 wt. % ¼ 0.06 g/g. Desorption of water started at 54 C and finished at 64 C (isobaric line 3e4). Minimal adsorption temperature Ta of 35 C resulted in the maximal uptake w ¼ 22 wt. % ¼ 0.22 g/g at the rich isoster. This demonstrates advanced properties of the new adsorbent which is able to exchange 0.16 g/g at such low temperatures. Water adsorption process occurred between 43 and 35 C (isobaric line 1e2 on Fig. 3) that recovers water released during the isobaric desorption.
257 170 27 636 1.1 350 1.81 1.66
Sorption dynamics
The LTJ dynamic experiments were carried out by performing temperature jumps which correspond to the isobaric stages of the selected heat transformation cycle. The initial and final temperatures of the kinetic experiments were taken from Fig. 3: during desorption run the temperature jumped from 54 C to 64 C at the initial pressure of 42.0 mbar, while during adsorption run the temperature dropped from 43 C to 35 C at the initial pressure of 12.6 mbar. It was found that under these boundary conditions, the experimental uptake curve could be described by an exponential function q(t) ¼ q(0) Dq exp(t/s) both for the adsorption and desorption runs. Fig. 4a demonstrates that up to 78% of the equilibrium uptake, the adsorption kinetic curve can be properly described with a single characteristic time s. The evolution of the residual 22% was slower than exponential, and the ratio of the characteristic times s0.85/s0.75 was as much as 1.66. This gives a hint that the duration of isobaric adsorption stages should be restricted by the time s0.8 (that is app. 73 s for the monolayer of SWS-9L grains under testing) or less. This would allow avoiding a dramatic drop of the specific cooling power at longer times with just a little decrease of the cycle COP and permits the compromise between reasonable values of COP and SCP. The desorption run followed an exponential law up to complete conversion (Fig. 4b). This run was much faster than the adsorption run, and 80% of conversion was reached in 26 s, so that the ratio s0.8(ads)/s0.8(des) is equal to 2.8. This may be due to the higher temperature and vapour pressure during the desorption stage.
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Fig. 2 e The CNR-ITAE test facility: the single bed chiller (left side) and the chilling unit connected to the test bench (right side).
Results achieved teach us that the duration of the desorption phase of AHT cycle should be accordingly shorter than that of the adsorption one. Quite similar ratio was found in (Glaznev and Aristov, 2009) for one, two and four layers of silica Fuji RD loose grains at various boundary conditions, and appropriate recommendations were made. Hence, the equal duration of adsorption and desorption phases is hardly to be an optimal case, and appropriate reallocation is necessary to give more time for adsorption at the expense of desorption duration. Effect of the relative duration of the two isobaric cycle stages was tested in the single bed adsorption chiller.
3.3.
Testing the AHT prototype
The experimental activity on the AHT prototype was focused on assessing the influence of the relative duration of the two isobaric steps on system performance (in terms of cooling COP and delivered Cooling Power). As a consequence, all experiments were carried out by fixing the same inlet temperatures of the external heating/cooling fluids (Tdes ¼ 95 C, Tev ¼ 10 C, Tcon ¼ 30 C). The adsorption/desorption times were changed at fixed total cycle time. In particular, Fig. 5 shows the temporal evolution of the three temperatures related to the adsorbent bed during three consecutive adsorption/desorption cycles at steady state regime for the following operating conditions: Tev ¼ 10 C, Tcon ¼ Tads ¼ 30 C, Tdes ¼ 95 C, tcycle ¼ (tiso-heat þ tdes þ tiso-cool þ tads) ¼ (10 s þ 100 s þ 20 s þ 255 s). Performance achieved under these boundary conditions are COP ¼ 0.176 and SCP ¼ 318 W/kg of dry sorbent that
are noticeably higher than the values (COP ¼ 0.086 and SCP ¼ 144 W/kg) obtained in the same thermodynamic conditions with equal duration of the isobaric steps tcycle ¼ (tisoheat þ tdes þ tiso-cool þ tads) ¼ (10 s þ 177 s þ 20 s þ 178 s). In fact, as shown in Fig. 6 for both cases the heat released to the medium temperature sink (the condenser) strongly decreases after 110e120 s, so that there is no sense to continue desorption phase longer that this time. Furthermore, it is important to note that, due to peculiarities of the set-up flow diagram, the actual temperature of the heating fluid at the inlet of the adsorber Tinmax was lower than the boiler temperature for all the tests. It depended on the working conditions and varied between 78 and 88 C (Table 3, Fig. 5). For short desorption times which appear to be the most optimal for efficient cycle operation, this temperature is close to 79 C, while the maximum temperature inside the adsorbent bed Tbedmax is just 70 C or lower. Nevertheless, the new adsorbent exchanges sufficient amount of water even under these very unfavorable conditions. Moreover, when we had reduced the boiler temperature down to 75 C, so that the maximum inlet temperature was 69 C and the maximum bed temperature was only 64.5 C, both the COP and SCP still remained quite reasonable, 0.155 and 193 W/kg, respectively (Table 3).
Table 2 e Range of possible operating conditions. Tdes [ C] Tev [ C] Tcon [ C]
up to 110 5e25 C 20e45 C
Fdes Fev Fcon
up to 25 up to 12 up to 12
Fig. 3 e Heat transformation cycle (Tev [ 10 C, Tcon [ 30 C, Tads [ 35 C and Tdes [ 64 C) plotted over the SWS-9L adsorption/desorption isobars.
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Fig. 6 e Dynamic behaviour of the inlet/outlet temperature of the external heat transfer fluid at the inlet and outlet of the condenser at Tev [ 10 C, Tcon [ Tads [ 30 C, Tdes [ 95 C, tcycle [ (10 s D 100 s D 20 s D 255 s) and tcycle [ (10 s D 177 s D 20 s D 178 s).
Fig. 4 e Experimental kinetic curves of isobaric stages measured by the LTJ method: (a) adsorption stage, (b) desorption stage. Symbols e experimental data, lines e approximation by the function q(t) [ q(0) ± Dq exp(Lt/s).
Table 3 reports the COP and SCP values for the two fixed cycle times (385 and 600 s), measured for the above described adsorber. Important finding of these experiments is that for the short cycles the COP is much more sensitive to the choice of durations of the adsorption and desorption stages than the SCP (Figs. 7 and 8).
Hence, a proper choice of desorption time tdes is of supreme importance. The prototype tests confirmed that the optimal desorption duration should indeed be 2e3 times shorter that the adsorption one, and for the optimal ratio tdes/tads both the COP and SCP may increase almost twice as compared with the common case tdes ¼ tads (Table 3). The sharp dependence COP(tdes) is due to the fact that at too short desorption time (tdes < 80e90 s) the optimal desorption degree (app. 80%) can not be reached that reduces both the COP and SCP. If this time is longer than the optimal one, the duration of the adsorption phase is reduced accordingly, and there is not enough time for the water uptake to recover. The part of the COP(tdes)-curve at longer time is smoother. For the tested adsorber, the optimal adsorption time can be estimated as 250e280 s. It is longer than that obtained from the LTJ measurements (70e80 s) because the configuration of the real A-HEX module differed from that realized in the LTJ setup. In particular, the real SWS layer was thicker than single layer of loose grains, and the time necessary for its cooling/
Table 3 e The values of Tin-max, Tbed-max, COP and SCP at various durations of the four phases of cooling cycle presented as (tiso-heat D tdes D tiso-cool D tads). Duration of phases, [s]
Fig. 5 e Dynamic behaviour of the temperature of the external heat transfer fluid at the inlet and outlet of the A-HEX and the mean temperature of the bed during three continuous cycles.
tsum ¼ 495 s, Tdes ¼ 75 C 15 þ 200 þ 20 þ 260 tsum ¼ 385 s, Tdes ¼ 95 C 10 þ 80 þ 20 þ 275 10 þ 100 þ 20 þ 255 10 þ 127 þ 20 þ 228 10 þ 154 þ 20 þ 251 10 þ 177 þ 20 þ 178 tsum ¼ 600 s, Tdes ¼ 95 C 10 þ 100 þ 20 þ 470 10 þ 150 þ 20 þ 420 10 þ 200 þ 20 þ 370 10 þ 240 þ 20 þ 330 10 þ 285 þ 20 þ 285
Tin-max, [ C]
Tbed-max, [ C]
COP
SCP, [W/kg]
69.0
64.5
0.155
193
79.0 78.8 82.4 84.8 86.4
71.6 70.8 74.9 77.8 80.0
0.137 0.176 0.128 0.113 0.086
241 318 256 217 144
77.9 82.1 86.0 88.6 89.6
65.0 70.2 75.0 74.9 78.7
0.186 0.19 0.164 0.143 0.13
230 257 224 200 180
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0,2
1/3 t CYCLE
1/3 t CYCLE
1/3 t CYCLE
NEXT CYCLE
0,18 BED 1
ADSORPTION
ADSORPTION
DESORPTION
ADSORPTION
BED 2
ADSORPTION
DESORPTION
ADSORPTION
ADSORPTION
CONDENSER
CONDENSER
CONDENSER
CONDENSER
COP
0,16 0,14 0,12 0,1
1
0,08 50
100
150
200
250
Fig. 7 e COP as a function of the desorption stage duration. The total cycle time was 385 (lower curve) and 600 s (upper curve). Tdes [ 95 C. heating of the A-HEX unit was much longer (Fig. 5) than for the LTJ metal support (6e8 s). Hence, the total cycle time should be about 350e400 s. At proper durations tdes and tads the adsorption and desorption are consistent and both occur satisfactorily. This allows reaching both the high COP and SCP that is confirmed by the experimental results (Table 3). If the cycle time increases, it is possible to slightly improve the cooling load and the COP at the expense of SCP (Table 3). The dependences of both these values on tdes become more smooth (Figs. 7 and 8) although, as before, shortened desorption time results in better performance. It is interesting to note that at short cycle times the maximum values of COP and SCP are reached at the same tdes (Table 3), and there is no need to search for a compromise between these values.
4. Practical recommendations to manage cooling cycles with nonequal durations of adsorption and desorption phases
1
EVAPORATOR
300
Duration of desorption [s]
2
2
1
EVAPORATOR
2
1
EVAPORATOR
an evaporator longer than the half-cycle time. Let, for instance, the time (tdes þ tpc þ tph) be twice as short than tads. In this case, one of the following cycle rearrangements can be done: e for a two bed configuration the two modes are possible (Fig. 9): one bed is connected with the evaporator where cold is produced. At the same time, another bed is under regeneration and is connected with the condenser where heat is rejected; both the beds are linked with the evaporator and generate a double chilling effect. Thus, cold is continuously generated so that each bed is linked with the evaporator two thirds of the cycle time tcycle and with the condenser only one third. In this case, to smooth the cooling effect produced, the chiller could be equipped with an intermediate cold storage unit. To allow the use of a continuous driving heat input an intermediate heat store or a buffer may also need;
1/3 t CYCLE
1/3 t CYCLE
1/3 t CYCLE
350
SCP [W/kg K]
EVAPORATOR
Fig. 9 e Management of a 2-beds adsorption cooling system with reallocated duration of adsorption and desorption steps.
The reallocation of adsorption/desorption durations proposed in this paper causes a subsequent change in cooling cycle organization, because each adsorber now is connected with
300
2
NEXT CYCLE
BED 1
ADSORPTION
ADSORPTION
DESORPTION
ADSORPTION
BED 2
ADSORPTION
DESORPTION
ADSORPTION
ADSORPTION
BED 3
DESORPTION
ADSORPTION
ADSORPTION
DESORPTION
CONDENSER
CONDENSER
250 200 150
1
100 50
100
150
200
250
2
3
1
2
3
CONDENSER
1
2
3
300
Duration of desorption [s]
Fig. 8 e SCP as a function of the desorption stage duration. Total cycle time was 385 (left curve) and 600 s (right curve). Tdes [ 95 C.
EVAPORATOR
EVAPORATOR
EVAPORATOR
Fig. 10 e Management of a 3-beds adsorption cooling system with reallocated duration of adsorption and desorption steps.
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 5 ( 2 0 1 2 ) 5 2 5 e5 3 1
e the AHT unit consists of three adsorbent beds which operate with the time lag equal to (tdes þ tpc þ tph). At any time, two beds are connected with the evaporator and generate a nearly constant cooling power while the third bed is releasing heat to the condenser (Fig. 10). No intermediate cold storage is necessary in this case.
5.
Conclusions
Equal duration of adsorption and desorption phases as is commonly used in adsorptive cooling cycle is reexamined in this paper. It was found that the desorption phase is faster than the adsorption one and this should be considered as a routine case for AHT cycles, probably, because desorption occurs at higher temperature and pressure. The testing of a new composite LiNO3/silica (SWS-9L) in an intermittent lab-scale prototype of AHT unit demonstrated that the duration of desorption phase is a very efficient parameter for optimizing the cycle COP and SCP which can be significantly improved as compared with the common case tdes ¼ tads. This is likely to mean that numerous results reported before for the latter case can be improved by a proper reallocation of adsorption and desorption phases. A modest attempt of such allocation was made in (Miyazaki et al., 2009). The authors extended the cold production phase or the adsorption duration (tads ¼ 300e600 s) up to a half-cycle time s0.5 and accordingly shortened the desorption phase so that tdes ¼ s0.5 tiso-heat tiso-cool, where the durations of pre-cooling and pre-heating phases tiso-cool ¼ tisoheat ¼ 30 s. Even this slight time allocation resulted in the increase of the calculated cooling capacity as much as by 6% for both RD type silica gel e water and SWS-1L e water pairs. Finally, this study suggested practical recommendations to rationally reallocate the duration of adsorption and desorption phases.
Acknowledgments This work was partially supported by the CNR e RAS bilateral agreement and the Russian Foundation for Basic Researches (grant 08-08-00808). YIA thanks the CNR “Short-Term Mobility Program” e 2009. Composite SWS-9L was synthesised by Dr. I.A. Simonova.
references
Aristov, Yu.I., 2007. Novel materials for adsorptive heat pumping and storage: screening and nanotailoring of sorption properties (review). J. Chem. Engn. Jpn. 40 (13), 1241e1251.
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Aristov, Yu.I., Dawoud, B., Glaznev, I.S., Elyas, A., 2008. A new methodology of studying the dynamics of water sorption/ desorption under real operating conditions of adsorption heat pumps: experiment. Int. J. Heat Mass Transfer 51 (19e20), 4966e4972. Aristov, Yu.I., 2009. Optimal adsorbent for adsorptive heat transformers: dynamic considerations. Int. J. Refrigeration 32, 675e686. Boelman, E.C., Saha, B.B., Kashiwagi, T., 1995. Experimental investigation of a silica gelewater adsorption refrigeration cycle e the influence of operating conditions on cooling output and COP. ASHRAE Trans. 101 (2), 358e366. Cerkvenik, B., Ziegler, F., 2006. The influence of periodic operation on the characteristics of adsorption devices. Energ. Convers. Manag. 47, 2020e2033. Chua, H.T., Ng, K.C., Wang, W., Yap, C., Wang, X.L., 2004. Transient modeling of a two bed silica gelewater adsorption chiller. Int. J. Heat Mass Transf. 47 (4), 659e669. Critoph, R.E., 1988. Performance limitation of adsorption cycles for solar cooling. Sol. Energy 41, 21e33. Critoph, R.E., Zhong, Y., 2005. Review of trends in solid sorption refrigeration and heat pumping technology. J. Process Mech. Eng. E 219, 285e300. Glaznev, I.S., Aristov, Yu.I., 2008. Kinetics of water adsorption on loose grains of SWS-1L under isobaric stages of adsorption heat pumps: the effect of residual air. Int. J. Heat Mass Transfer 51 (25e26), 5823e5827. Glaznev, I.S., Aristov, Yu.I., 2009. The effect of cycle boundary conditions and adsorbent grain size on the water sorption dynamics in adsorption heat pumps, Proc. Int. Conference on Heat Powered Cycles (HPC-09), Berlin, Germany, Sept. 7e9. Khan, M.Z.I., Saha, B.B., Alam, K.C.A., Akisawa, A., Kashiwagi, T., 2007. Study on solar/waste heat driven multi-bed adsorption chiller with mass recovery. Renew. Energ. 32 (3), 365e381. Meunier, F., 1993. Solid sorption: an alternative to CFCs. Heat Recov. Syst. CHP 13, 289e295. Miyazaki, T., Akisawa, A., Saha, B.B., El-Sharkawy, I.I., Chakraborty, A., 2009. A new cycle time allocation for enhancing the performance of two-bed adsorption chillers. Int. J. Refrigeration 32, 846e853. Pons, M., Poyelle, F., 1999. Adsorptive machines with advanced cycles for heat pumping or cooling applications. Int. J. Refrigeration 22 (1), 27e38. Saha, B.B., Chakraborty, A., Koyama, S., Aristov, Yu.I., 2009. A new generation cooling device employing CaCl2-in-silica gel-water system. Int. J. Heat Mass Transfer 52 (1e2), 516e524. Simonova, I.A., Aristov, Yu.I., 2008. Composite sorbents “lithium nitrate in silica” for transformation of low temperature heat. Altern. Energy Ecol. 11, 95e99. Wang, R.Z., 2001. Performance improvement of adsorption cooling by heat and mass recovery operation. Int. J. Refrigeration v. 24, 602e611. Wang, R.Z., Oliveira, R.G., 2006. Adsorption refrigeration e an efficient way to make good use of waste heat and solar energy. Prog. Energy Combust. Sci. 32, 424e458. Ziegler, F., Satzger, P., 2005. Increase of the efficiency of the heat transfer phase in solid sorption or reaction systems. Int. J. Thermal Sci. v. 44, 1115e1122.
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journal homepage: www.elsevier.com/locate/ijrefrig
Reallocation of adsorption and desorption times for optimisation of cooling cycles Yu.I. Aristov a,*, A. Sapienza b, D.S. Ovoshchnikov a, A. Freni b, G. Restuccia b a b
Boreskov Institute of Catalysis, Pr. Lavrentieva 5, 630090 Novosibirsk, Russia CNR e Istituto di Tecnologie Avanzate per l’Energia “Nicola Giordano”, S. Lucia sopra Contesse 5, 98126 Messina, Italy
article info
abstract
Article history:
In an adsorption cycle it is common to have an equal duration of the adsorption and
Received 24 November 2009
desorption phases. In this paper, we investigated an intermittent cooling cycle with vari-
Received in revised form
able adsorption/desorption duration at fixed total cycle time. A new composite, LiNO3/silica
13 July 2010
KSK (SWS-9L), was used as a water sorbent. It was specifically synthesised for adsorptive
Accepted 20 July 2010
chilling units driven by low temperature heat (65e75 C). The sorption equilibrium and
Available online 24 July 2010
dynamics of SWS-9L were studied under conditions close to those realized in a typical cooling cycle. The actual performance of SWS-9L was tested in a single bed adsorption
Keywords:
chiller with special emphasis on the optimisation of the relative duration of isobaric
Adsorption system
adsorption and desorption stages to maximize the Coefficient Of Performance and the
Variation
Specific Cooling Power of the cycle. The tests resulted in being able to make practical
Duration
recommendations to rationally optimise the relative duration of adsorption and desorption
Cycle-adsorption
phases. ª 2010 Elsevier Ltd and IIR. All rights reserved.
Desorption Optimisation COP Water
Optimisation des cycles de refroidissement par modification des dure´es d’adsorption et de de´sorption Mots cle´s : Syste`me a` adsorption ; Variation ; Dure´e ; Cycle-adsorption ; De´sorption ; Optimisation ; COP ; Eau
1.
Introduction
Adsorptive heat transformation (AHT) allows re-use of enormous heat fluxes with low temperature potential that are commonly wasted (Meunier, 1993; Critoph and Zhong, 2005; Wang and Oliveira, 2006). To be more competitive with
conventional compression chilling units, both the Coefficient Of Performance (COP) and the Specific Cooling Power (SCP) have to be improved. One way is an improvement of the adsorbent used to ensure its harmonization with the AHT cycle: thermodynamic requirements imposed on an optimal adsorbent are formulated in (Aristov, 2007; Critoph, 1988),
* Corresponding author. E-mail address: [email protected] (Yu.I. Aristov). 0140-7007/$ e see front matter ª 2010 Elsevier Ltd and IIR. All rights reserved. doi:10.1016/j.ijrefrig.2010.07.019
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while the optimal dynamic behaviour is discussed in (Aristov, 2009). Improvement of the cycle, taking into account both thermodynamic and dynamic features, gives another independent opportunity. In fact, the total cycle duration tc was selected as an important parameter: commonly, the COP increases monotonically with the cycle time, while the SCP reaches the maximum at a certain tc (Boelman et al., 1995; Saha et al., 2009). New cooling cycles with heat and mass recovery were considered as well (see Wang, 2001; Pons and Poyelle, 1999; Ziegler and Satzger, 2005; Khan et al., 2007 and literature therein). Unlike the majority of studies with equal durations of the isobaric adsorption and desorption stages (tdes ¼ tads) (Boelman et al., 1995; Saha et al., 2009; Wang, 2001; Chua et al., 2004; Cerkvenik and Ziegler, 2006), here we pay special attention to the optimisation of these durations in order to improve the cycle COP and SCP and also to make a comparison with the common case of equal duration. To gain a preliminary idea about the relative durations, the water sorption dynamics was studied by a new Large Temperature Jump (LTJ) method (Aristov et al., 2008) which nearly reproduces conditions of the isobaric stages of an adsorptive cooling cycle. To plot this cycle, we experimentally measured appropriate isobars of water sorption of a new composite LiNO3/silica KSK (SWS-9L) which was specifically synthesised for adsorptive cooling cycles driven by low temperature heat (65e75 C) (Simonova and Aristov, 2008). The actual performance of SWS-9L was tested in a single bed adsorption chiller.
2.
Experimental
2.1.
Sample synthesis
Composite SWS-9L was synthesised by impregnation of a dry commercial silica KSK (the specific pore volume 1.0 cm3/g, the specific surface area 350 m3/g, the average pore size 15 nm) with a saturated aqueous solution of LiNO3. The synthesis procedure consisted of a drying of the pure silica at 200 C during 2 h, the impregnation of the dried silica with the saturated aqueous solution at 25 C, and again drying of the impregnated material at 200 C until its weight remained constant. The volume of the impregnating solution was equal to the pore volume of the silica. The salt content in the dry composite was determined by weighting the dry silica before impregnation and composite after drying, and amounted to 34.5 wt. %. The size of the silica grains was 0.25e0.5 mm.
2.2.
Isobars of water sorption
Sorption equilibrium of water vapour on SWS-9L was measured at T ¼ 30e120 C and PH2 O ¼ 12.6e42 mbar using a CAHN 2000 thermo-balance. Before measurements, the sample was heated up to 120 C under vacuum until reaching a dry weight m0 ¼ 27.1 mg. The amount of water adsorbed Dm was measured as a function of T at constant PH2 O ¼ 12.6 mbar (adsorption run) and 42.0 mbar (desorption run). To maintain these vapour pressures constant, the internal volume of the balance was connected with an evaporator at T ¼ 10 and 30 C respectively. The water uptake w was calculated as w ¼ Dm/m0.
2.3.
Kinetics of water sorption
The kinetics of water sorption on SWS-9L were studied by the Large Temperature Jump method whose description can be found elsewhere (Aristov et al., 2008). The simplest configuration of the adsorber-heat exchanger (A-HEX) unit was chosen for these measurements; namely, one layer of loose adsorbent grains placed on a metal plate which imitates a HEX fin. The temperature of the plate was changed as takes place in real sorption heat pumps, while the vapour pressure over the sorbent maintained almost constant. The experimental set-up used was described in (Glaznev and Aristov, 2008). Boundary conditions, namely the initial and final temperatures, the water vapour pressure at adsorption/desorption stages were set as described below. Typical time of cooling/heating of the metal support was 6e8 s.
2.4.
Tests in the single bed chiller
The real performance of SWS-9L was tested in a single bed adsorption chiller installed at CNR-ITAE laboratory (1 kW cooling power). With this aim, 350 g of sorbent grains 0.25e0.50 mm in size were embedded inside a compact heat exchanger of a finned flat-tube type. This adsorption bed configuration has the following advantages: a) compactness and low weight, as the heat exchanger is made of aluminium; b) good heat transfer properties due to the high heat transfer area and a high thermal conductivity of aluminium; c) high vapour permeability as provided by granular packing. Fig. 1 shows the overall and the detailed view of the heat exchanger of the adsorbent bed tested, while Table 1 reports its main parameters. The distance between the fins was about 1 mm, so that 2e4 grains could be housed in this gap. It is interesting to point out that this configuration allows a rather low “mass metal/mass adsorbent” ratio as well as good heat transfer between the metal finned tubes and adsorbent grains. The single bed chiller (Fig. 2a) consists of a vacuum chamber containing the above described adsorbent bed, a single evaporator and condenser. The vacuum chamber has been specifically designed to test different types of adsorbent beds and has various flanges that allow the connection with the other components of the prototype and the installation of the measurement devices (pressure gauges, temperature sensors), necessary to control and manage the system during testing. The external heat sources/sinks are interfaced with the adsorption chiller by using a test bench that allows management and control of the system (Fig. 2b). The test bench controls the different phases of the cooling cycle and measures the relevant physical parameters. Components installed (plate-type heat exchangers, temperature and pressure sensors, flow meters, electro-valves and hydraulic pumps) are electronically controlled. In fact, a data acquisition and control system were realized by a specific software implemented by the LABVIEW language to automatically operate the system. The external heating/cooling energy is provided by an electrically heated thermal oil boiler and an
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Fig. 1 e Overall (right side) and detailed (left side) view of the A-HEX tested.
electric water chiller installed in a service room close to the laboratory. The test facility is able to work in different operating conditions. In particular, Table 2 reports the range of possible temperatures and flow rates for the heating source (Tdes, Fdes), the evaporator (Tev, Fev) and the condenser (Tcon, Fcon). The cooling COP was calculated as ratio between the cooling effect generated in the evaporator and the amount of thermal energy supplied for isosteric heating and desorption phases: P P
ads
COP ¼
_ p ðTin Tout ÞDtjev mc
ishþdes
3.2.
_ p ðTin Tout ÞDtjbed mc
The Specific Cooling Power was calculated as ratio between the useful cooling effect and the total cycle time: P PS ¼
ads
_ p ðTin Tout ÞDtjev mc ms scycle
3.
Results and discussion
3.1.
Sorption equilibrium
Measuring isobars of water adsorption/desorption is needed for plotting a tentative cycle of adsorptive chiller and determining its boundary temperatures. Isobars of water adsorption at PH2 O ¼ 12.6 mbar and desorption at PH2 O ¼ 42.0 mbar measured for the sorbent SWS-9L represent the isobaric stages of a typical chiller cycle (Fig. 3). Maximum desorption
Table 1 e Main properties of the adsorber module. Dimension [mm] Weight [g] Overall volume [l] Adsorbent mass [g] Mass metal/mass adsorbent Heat transfer surface [m2]
temperature Tdes was fixed at 64 C, that determined the water uptake at the weak isoster, w ¼ 6 wt. % ¼ 0.06 g/g. Desorption of water started at 54 C and finished at 64 C (isobaric line 3e4). Minimal adsorption temperature Ta of 35 C resulted in the maximal uptake w ¼ 22 wt. % ¼ 0.22 g/g at the rich isoster. This demonstrates advanced properties of the new adsorbent which is able to exchange 0.16 g/g at such low temperatures. Water adsorption process occurred between 43 and 35 C (isobaric line 1e2 on Fig. 3) that recovers water released during the isobaric desorption.
257 170 27 636 1.1 350 1.81 1.66
Sorption dynamics
The LTJ dynamic experiments were carried out by performing temperature jumps which correspond to the isobaric stages of the selected heat transformation cycle. The initial and final temperatures of the kinetic experiments were taken from Fig. 3: during desorption run the temperature jumped from 54 C to 64 C at the initial pressure of 42.0 mbar, while during adsorption run the temperature dropped from 43 C to 35 C at the initial pressure of 12.6 mbar. It was found that under these boundary conditions, the experimental uptake curve could be described by an exponential function q(t) ¼ q(0) Dq exp(t/s) both for the adsorption and desorption runs. Fig. 4a demonstrates that up to 78% of the equilibrium uptake, the adsorption kinetic curve can be properly described with a single characteristic time s. The evolution of the residual 22% was slower than exponential, and the ratio of the characteristic times s0.85/s0.75 was as much as 1.66. This gives a hint that the duration of isobaric adsorption stages should be restricted by the time s0.8 (that is app. 73 s for the monolayer of SWS-9L grains under testing) or less. This would allow avoiding a dramatic drop of the specific cooling power at longer times with just a little decrease of the cycle COP and permits the compromise between reasonable values of COP and SCP. The desorption run followed an exponential law up to complete conversion (Fig. 4b). This run was much faster than the adsorption run, and 80% of conversion was reached in 26 s, so that the ratio s0.8(ads)/s0.8(des) is equal to 2.8. This may be due to the higher temperature and vapour pressure during the desorption stage.
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Fig. 2 e The CNR-ITAE test facility: the single bed chiller (left side) and the chilling unit connected to the test bench (right side).
Results achieved teach us that the duration of the desorption phase of AHT cycle should be accordingly shorter than that of the adsorption one. Quite similar ratio was found in (Glaznev and Aristov, 2009) for one, two and four layers of silica Fuji RD loose grains at various boundary conditions, and appropriate recommendations were made. Hence, the equal duration of adsorption and desorption phases is hardly to be an optimal case, and appropriate reallocation is necessary to give more time for adsorption at the expense of desorption duration. Effect of the relative duration of the two isobaric cycle stages was tested in the single bed adsorption chiller.
3.3.
Testing the AHT prototype
The experimental activity on the AHT prototype was focused on assessing the influence of the relative duration of the two isobaric steps on system performance (in terms of cooling COP and delivered Cooling Power). As a consequence, all experiments were carried out by fixing the same inlet temperatures of the external heating/cooling fluids (Tdes ¼ 95 C, Tev ¼ 10 C, Tcon ¼ 30 C). The adsorption/desorption times were changed at fixed total cycle time. In particular, Fig. 5 shows the temporal evolution of the three temperatures related to the adsorbent bed during three consecutive adsorption/desorption cycles at steady state regime for the following operating conditions: Tev ¼ 10 C, Tcon ¼ Tads ¼ 30 C, Tdes ¼ 95 C, tcycle ¼ (tiso-heat þ tdes þ tiso-cool þ tads) ¼ (10 s þ 100 s þ 20 s þ 255 s). Performance achieved under these boundary conditions are COP ¼ 0.176 and SCP ¼ 318 W/kg of dry sorbent that
are noticeably higher than the values (COP ¼ 0.086 and SCP ¼ 144 W/kg) obtained in the same thermodynamic conditions with equal duration of the isobaric steps tcycle ¼ (tisoheat þ tdes þ tiso-cool þ tads) ¼ (10 s þ 177 s þ 20 s þ 178 s). In fact, as shown in Fig. 6 for both cases the heat released to the medium temperature sink (the condenser) strongly decreases after 110e120 s, so that there is no sense to continue desorption phase longer that this time. Furthermore, it is important to note that, due to peculiarities of the set-up flow diagram, the actual temperature of the heating fluid at the inlet of the adsorber Tinmax was lower than the boiler temperature for all the tests. It depended on the working conditions and varied between 78 and 88 C (Table 3, Fig. 5). For short desorption times which appear to be the most optimal for efficient cycle operation, this temperature is close to 79 C, while the maximum temperature inside the adsorbent bed Tbedmax is just 70 C or lower. Nevertheless, the new adsorbent exchanges sufficient amount of water even under these very unfavorable conditions. Moreover, when we had reduced the boiler temperature down to 75 C, so that the maximum inlet temperature was 69 C and the maximum bed temperature was only 64.5 C, both the COP and SCP still remained quite reasonable, 0.155 and 193 W/kg, respectively (Table 3).
Table 2 e Range of possible operating conditions. Tdes [ C] Tev [ C] Tcon [ C]
up to 110 5e25 C 20e45 C
Fdes Fev Fcon
up to 25 up to 12 up to 12
Fig. 3 e Heat transformation cycle (Tev [ 10 C, Tcon [ 30 C, Tads [ 35 C and Tdes [ 64 C) plotted over the SWS-9L adsorption/desorption isobars.
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Fig. 6 e Dynamic behaviour of the inlet/outlet temperature of the external heat transfer fluid at the inlet and outlet of the condenser at Tev [ 10 C, Tcon [ Tads [ 30 C, Tdes [ 95 C, tcycle [ (10 s D 100 s D 20 s D 255 s) and tcycle [ (10 s D 177 s D 20 s D 178 s).
Fig. 4 e Experimental kinetic curves of isobaric stages measured by the LTJ method: (a) adsorption stage, (b) desorption stage. Symbols e experimental data, lines e approximation by the function q(t) [ q(0) ± Dq exp(Lt/s).
Table 3 reports the COP and SCP values for the two fixed cycle times (385 and 600 s), measured for the above described adsorber. Important finding of these experiments is that for the short cycles the COP is much more sensitive to the choice of durations of the adsorption and desorption stages than the SCP (Figs. 7 and 8).
Hence, a proper choice of desorption time tdes is of supreme importance. The prototype tests confirmed that the optimal desorption duration should indeed be 2e3 times shorter that the adsorption one, and for the optimal ratio tdes/tads both the COP and SCP may increase almost twice as compared with the common case tdes ¼ tads (Table 3). The sharp dependence COP(tdes) is due to the fact that at too short desorption time (tdes < 80e90 s) the optimal desorption degree (app. 80%) can not be reached that reduces both the COP and SCP. If this time is longer than the optimal one, the duration of the adsorption phase is reduced accordingly, and there is not enough time for the water uptake to recover. The part of the COP(tdes)-curve at longer time is smoother. For the tested adsorber, the optimal adsorption time can be estimated as 250e280 s. It is longer than that obtained from the LTJ measurements (70e80 s) because the configuration of the real A-HEX module differed from that realized in the LTJ setup. In particular, the real SWS layer was thicker than single layer of loose grains, and the time necessary for its cooling/
Table 3 e The values of Tin-max, Tbed-max, COP and SCP at various durations of the four phases of cooling cycle presented as (tiso-heat D tdes D tiso-cool D tads). Duration of phases, [s]
Fig. 5 e Dynamic behaviour of the temperature of the external heat transfer fluid at the inlet and outlet of the A-HEX and the mean temperature of the bed during three continuous cycles.
tsum ¼ 495 s, Tdes ¼ 75 C 15 þ 200 þ 20 þ 260 tsum ¼ 385 s, Tdes ¼ 95 C 10 þ 80 þ 20 þ 275 10 þ 100 þ 20 þ 255 10 þ 127 þ 20 þ 228 10 þ 154 þ 20 þ 251 10 þ 177 þ 20 þ 178 tsum ¼ 600 s, Tdes ¼ 95 C 10 þ 100 þ 20 þ 470 10 þ 150 þ 20 þ 420 10 þ 200 þ 20 þ 370 10 þ 240 þ 20 þ 330 10 þ 285 þ 20 þ 285
Tin-max, [ C]
Tbed-max, [ C]
COP
SCP, [W/kg]
69.0
64.5
0.155
193
79.0 78.8 82.4 84.8 86.4
71.6 70.8 74.9 77.8 80.0
0.137 0.176 0.128 0.113 0.086
241 318 256 217 144
77.9 82.1 86.0 88.6 89.6
65.0 70.2 75.0 74.9 78.7
0.186 0.19 0.164 0.143 0.13
230 257 224 200 180
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0,2
1/3 t CYCLE
1/3 t CYCLE
1/3 t CYCLE
NEXT CYCLE
0,18 BED 1
ADSORPTION
ADSORPTION
DESORPTION
ADSORPTION
BED 2
ADSORPTION
DESORPTION
ADSORPTION
ADSORPTION
CONDENSER
CONDENSER
CONDENSER
CONDENSER
COP
0,16 0,14 0,12 0,1
1
0,08 50
100
150
200
250
Fig. 7 e COP as a function of the desorption stage duration. The total cycle time was 385 (lower curve) and 600 s (upper curve). Tdes [ 95 C. heating of the A-HEX unit was much longer (Fig. 5) than for the LTJ metal support (6e8 s). Hence, the total cycle time should be about 350e400 s. At proper durations tdes and tads the adsorption and desorption are consistent and both occur satisfactorily. This allows reaching both the high COP and SCP that is confirmed by the experimental results (Table 3). If the cycle time increases, it is possible to slightly improve the cooling load and the COP at the expense of SCP (Table 3). The dependences of both these values on tdes become more smooth (Figs. 7 and 8) although, as before, shortened desorption time results in better performance. It is interesting to note that at short cycle times the maximum values of COP and SCP are reached at the same tdes (Table 3), and there is no need to search for a compromise between these values.
4. Practical recommendations to manage cooling cycles with nonequal durations of adsorption and desorption phases
1
EVAPORATOR
300
Duration of desorption [s]
2
2
1
EVAPORATOR
2
1
EVAPORATOR
an evaporator longer than the half-cycle time. Let, for instance, the time (tdes þ tpc þ tph) be twice as short than tads. In this case, one of the following cycle rearrangements can be done: e for a two bed configuration the two modes are possible (Fig. 9): one bed is connected with the evaporator where cold is produced. At the same time, another bed is under regeneration and is connected with the condenser where heat is rejected; both the beds are linked with the evaporator and generate a double chilling effect. Thus, cold is continuously generated so that each bed is linked with the evaporator two thirds of the cycle time tcycle and with the condenser only one third. In this case, to smooth the cooling effect produced, the chiller could be equipped with an intermediate cold storage unit. To allow the use of a continuous driving heat input an intermediate heat store or a buffer may also need;
1/3 t CYCLE
1/3 t CYCLE
1/3 t CYCLE
350
SCP [W/kg K]
EVAPORATOR
Fig. 9 e Management of a 2-beds adsorption cooling system with reallocated duration of adsorption and desorption steps.
The reallocation of adsorption/desorption durations proposed in this paper causes a subsequent change in cooling cycle organization, because each adsorber now is connected with
300
2
NEXT CYCLE
BED 1
ADSORPTION
ADSORPTION
DESORPTION
ADSORPTION
BED 2
ADSORPTION
DESORPTION
ADSORPTION
ADSORPTION
BED 3
DESORPTION
ADSORPTION
ADSORPTION
DESORPTION
CONDENSER
CONDENSER
250 200 150
1
100 50
100
150
200
250
2
3
1
2
3
CONDENSER
1
2
3
300
Duration of desorption [s]
Fig. 8 e SCP as a function of the desorption stage duration. Total cycle time was 385 (left curve) and 600 s (right curve). Tdes [ 95 C.
EVAPORATOR
EVAPORATOR
EVAPORATOR
Fig. 10 e Management of a 3-beds adsorption cooling system with reallocated duration of adsorption and desorption steps.
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e the AHT unit consists of three adsorbent beds which operate with the time lag equal to (tdes þ tpc þ tph). At any time, two beds are connected with the evaporator and generate a nearly constant cooling power while the third bed is releasing heat to the condenser (Fig. 10). No intermediate cold storage is necessary in this case.
5.
Conclusions
Equal duration of adsorption and desorption phases as is commonly used in adsorptive cooling cycle is reexamined in this paper. It was found that the desorption phase is faster than the adsorption one and this should be considered as a routine case for AHT cycles, probably, because desorption occurs at higher temperature and pressure. The testing of a new composite LiNO3/silica (SWS-9L) in an intermittent lab-scale prototype of AHT unit demonstrated that the duration of desorption phase is a very efficient parameter for optimizing the cycle COP and SCP which can be significantly improved as compared with the common case tdes ¼ tads. This is likely to mean that numerous results reported before for the latter case can be improved by a proper reallocation of adsorption and desorption phases. A modest attempt of such allocation was made in (Miyazaki et al., 2009). The authors extended the cold production phase or the adsorption duration (tads ¼ 300e600 s) up to a half-cycle time s0.5 and accordingly shortened the desorption phase so that tdes ¼ s0.5 tiso-heat tiso-cool, where the durations of pre-cooling and pre-heating phases tiso-cool ¼ tisoheat ¼ 30 s. Even this slight time allocation resulted in the increase of the calculated cooling capacity as much as by 6% for both RD type silica gel e water and SWS-1L e water pairs. Finally, this study suggested practical recommendations to rationally reallocate the duration of adsorption and desorption phases.
Acknowledgments This work was partially supported by the CNR e RAS bilateral agreement and the Russian Foundation for Basic Researches (grant 08-08-00808). YIA thanks the CNR “Short-Term Mobility Program” e 2009. Composite SWS-9L was synthesised by Dr. I.A. Simonova.
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