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Dynamic behaviors of adsorption chiller: Effects of the silica gel grain size and layers
Energy 78 (2014) 304e312
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Dynamic behaviors of adsorption chiller: Effects of the silica gel grain size and layers Anutosh Chakraborty a, Bidyut Baran Saha b, c, *, Yuri I. Aristov d, e a
School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Republic of Singapore Kyushu University Program for Leading Graduate School, Green Asia Education Center, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, 6-1 Kasuga-Koen, Kasuga Shi, Fukuoka 816-8580, Japan c International Institute for Carbon-Neutral Energy Research (WPI-I2CNER), Kyushu University, Japan d Boreskov Institute of Catalysis, Siberian Division, Russian Academy of Sciences, pr. Akademika Lavrent'eva 5, Novosibirsk 630090, Russia e Novosibirsk State University, Pirogova Str., 2, Novosibirsk 630090, Russia b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 25 June 2014 Received in revised form 3 October 2014 Accepted 4 October 2014 Available online 6 November 2014
This article presents the dynamic behaviour of a single effect two bed adsorption chiller employing adsorbent beds with various layers of loose grain configurations and silica gel particle sizes, which is based on the experimentally confirmed adsorption isotherms and kinetics data. Compared with the experimental data of conventional adsorption chiller based on RD silica gel-water pair, we found that the silica gel configuration in terms of layers and sizes provides an interesting result, that is, the “grain size sensitive” regime is realized for large adsorbent grains with more layers. From numerical simulation, it is found that the specific cooling power and the coefficient of performance are reduced and the peak chilled water temperatures are increased with increasing the grain size and grain layers. We also demonstrate here that the sizes and layers of adsorbents should be considered for the design of adsorption heat exchanger for adsorption cooling applications. © 2014 Elsevier Ltd. All rights reserved.
Keywords: Adsorption Adsorbent layers Cooling Grain size Waste heat recovery
1. Introduction The advancement of adsorption chiller is based on the thermal compression of natural working refrigerants such as water and depends on the nature of porous adsorbents in terms of water vapour uptakes and offtakes and the appropriate kinetics rates. The widespread acceptance of the adsorption chiller is hindered by its relatively poor performances and bulky size due to limited properties of solid adsorbents even though it is amenable to regenerative use of adsorption heat, incorporates no mechanical moving parts and generates no noise or vibration. The performances of adsorption chiller depend mainly on the nature of adsorption isotherms, kinetics and the isosteric heat of adsorption of adsorbentadsorbate pairs. Up to now, numerous investigations are reported on various adsorption system configurations, experimental investigations and mathematical modelling of adsorption cycles [1e10], and the isotherms and kinetics of various adsorbent-
* Corresponding author. Kyushu University Program for Leading Graduate School, Green Asia Education Center, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, 6-1 Kasuga-Koen, Kasuga Shi, Fukuoka 816-8580, Japan. Tel.: þ81 92 583 7903; fax: þ81 92 583 8909. E-mail address: [email protected] (B.B. Saha). http://dx.doi.org/10.1016/j.energy.2014.10.015 0360-5442/© 2014 Elsevier Ltd. All rights reserved.
adsorbate pairs such as silica gel-water, zeolite-water, silica gelmethanol, activated carbon-methanol, activated charcoal-NH3, zeolite-CO2, MOFs-water etc. [11e22], from which it is understood th and DubinineAstakhov equations are that (i) the Freundlich, To mainly used for describing the amount of adsorbate uptakes for various pressures and temperatures, (ii) the enthalpy of adsorption derived from the isosteric chart of adsorbent-adsorbate pair in the ClausiuseClapeyron coordinates is used to calculate the theoretical maximum COP (coefficient of performance) and (iii) adsorption kinetics approximated by the LDF (linear driving force) model are used to calculated the dynamic behaviour of adsorption chiller [23e25]. All these information are needed to model and simulate an adsorption chiller. Silica gels and zeolites are mainly used as adsorbents for adsorption chiller purposes. However recently a new family of composite sorbents called SWSs (selective water sorbents) based on a porous host matrix (silica, alumina, etc.) and an inorganic salt (CaCl2, LiBr, MgCl2, MgSO4, Ca(NO3)2, etc.) impregnated inside pores [26e29] has been presented for sorption cooling and heat pumping [2,26]. Among the different SWSs, the SWS-1L (“CaCl2 confined to KSK silica gel”) shows very high water sorption capacity (up to 0.7 g of water per 1 g of dry adsorbent) [26]. It is found experimentally that very simple monolayer configuration of loose adsorbent grains results in a quite fast adsorption
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dynamics and large specific cooling power [30,31]. Experimental desorption rate is also found to be faster than appropriate adsorption rate by a factor of 2.2e3.5. The size (dp) of silica gel grains was found to be a powerful tool to manage the dynamics of isobaric water ad-/desorption [31]. For large grains (>0.5 mm), the characteristic time for adsorption and desorption was strongly dependent on the adsorbent grain size and is found to be proportional to d2p that is in accordance with the LDF model. For smaller silica grains, the maximum specific cooling power can exceed 5 kW/kg, which is very attractive for designing compact adsorption chiller as a monolayer configuration of loose silica gel grains provides quite fast adsorption dynamics. However, it is expected that employing the present configuration of adsorption chiller as displayed in Table 1, the COP (coefficient of performance) is not optimal as the mass of adsorbent housed in the monolayer is small as compared with the inert masses of adsorption bed unit. Because of this, the design with more than one layer is more realistic. So, the investigation of adsorption dynamics in a thin bed containing a small number n of loose grain layers (1 < n < 10) is of high practical interest [31e33]. Experimental tests confirmed the promising properties of loose grains configurations of silica gel [31,32]. It can be shown that the use of various loose grains silica gel designs in the sorption bed allows significant effects on COP and cooling capacity of adsorption chiller even though the gross COP is affected by heat losses, the heat capacity of the inert masses and the heat exchangers efficiency which are not optimised in the unit tested. The authors mentioned that both the COP and cooling power are expected to be further improved in the multi-bed system with internal heat recovery and well-designed heat-exchanger with optimised silica gel grains configuration including particle sizes and layers. The aim of this study is to analyse the performances of adsorption chiller employing the dynamic behaviours of various silica gel grains arrangements with respect to the silica gel sizes and layers in more optimized configuration similar to that used in commercial adsorption chillers. Building from the previous works, this article
Table 1 The characteristic sorption times during adsorption/desorption periods for the two boundary conditions (50 ¼ >30 C and 58 ¼ >80 C) with various silica gel grain sizes and layers. Grain size, mm
Adsorption/Desorption ( C)
Layers
t
t0.5
0.2e0.25
50 ¼ >30
1 2 4 8 1 2 4 8 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4
13.3 17.0 26.0 38.0 6.20 6.20 12.0 21.0 18.0 30.0 86.0 6.70 13.5 42.1 47.3 100 200 16.5 45.0 115 182 316 588 64.0 169 310
8.00 11.0 22.7 45.1 4.20 4.40 9.10 20.5 11.5 20.1 58.7 4.70 9.10 29.1 31.2 65.1 145 11.1 13.3 79.0 112 225 380 42.8 116 216
58 ¼ >80
0.4e0.5
50 ¼ >30
58 ¼ >80
0.8e0.9
50 ¼ >30
58 ¼ >80
1.6e1.8
50 ¼ >30
58 ¼ >80
305
presents both the steady-state and dynamic behaviours of various configurations of silica gel in a two-bed solid sorption cooling system using a transient distributed model. These results are compared with those of commercial adsorption cooler based on silica gel Fuji RD such that a device with various adsorbent sizes and layers for new generation of cooling can be enlightened commercially. Both the heat and mass transfer resistances of the adsorption heat exchanger as well as the temporal energetic behaviour in the evaporator and condenser are also taken into account in a distributed manner in the present model. In this paper, we also compare the present simulation results with the experimental data.
2. Mathematical modelling of adsorption chiller It is well known that the adsorption chiller utilizes the adsorbent-adsorbate characteristics to produce the useful cooling effects at the evaporator by the union of “adsorption-triggeredevaporation” and “desorption-activated-condensation” and these are described elsewhere [14e16]. Fig. 1 shows the schematic layout of the adsorption chiller that comprises the evaporator, the condenser and the reactors or adsorbent beds. For continuous cooling operation, firstly a low-pressure refrigerant (hence water) is evaporated at the evaporator due to external cooling load (or chilled water) and is adsorbed into the solid adsorbent located in the adsorber, and these phenomena as shown in Fig. 2(a) with respect to control volume approach are represented mathematically in the following way. At the evaporator, the chilled water is supplied through the heat exchanging tubes in the evaporator. The energy balance equation on the chilled water control volume is written as
rchill cchill f p;f
vT chill vT chill v2 T chill ¼ uchill þ lchill rchill cchill f f p;f f vt vz vz2 4hi chill T T evap dm;i
(1)
The boundary conditions of the chilled water tube are Tchill(z ¼ 0,t) ¼ Tchill,in and vTchill/vz(z¼ Ltube,t) ¼ 0. The heat of chilled water, which activates the enthalpy of evaporation, is absorbed at the refrigerant of the evaporator through the heat exchanger metal tubes. So the energy balance of the metal tube should be taken into account, and the energy balance equation is written as:
evap
vT rm cp;m m vt
d2m;o d2m;i 4
evap
v2 Tm ¼ lm vz2
d2m;o d2m;i
4
evap Tm þ dm;i hi T evap dm;o ho Tm T evap chill
(2)
Pool boiling is affected on the water refrigerant outside the heat exchanging tube in the evaporator by the vapour uptake at the adsorber. In that case, the mass and energy balance equations become
dmevap _ evap ¼ m_ cond vap mvap ; and dt rVevap cevap p
vT evap dmcond cond evap m_ evap ¼ hf T Þ vap hfg ðT vt dt evap pdm;o L ho Tm T evap ; evap
(3)
(4)
where ðrVevap cp Þ is the sum of all mass capacities of the evaporator and the first term of the right hand side of Equation (4) indicates the amount of condensate (refrigerant) that is refluxed back
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Fig. 1. Schematic layout of a two-bed adsorption chiller.
to the evaporator via a pressure reducing valve for maintaining the pressure difference between the condenser and the evaporator. The process of adsorption results in the liberation of heat due to the enthalpy of adsorption at the adsorption reactor and this amount of heat is removed by the supply of cooling water to the adsorber through the heat exchanging tubes. Secondly, the adsorbed bed is heated by the external heat source and the refrigerant is desorbed from the adsorbent and goes to the condenser. These phenomena as shown in Fig. 2(b) are expressed mathematically using the mass and energy balances of the adsorption reactor. During adsorption period, the cooling fluid at ambient conditions is supplied to the bed through the heat exchanging tube to accelerate the amount of water vapour uptakes and during desorption period, the desorbed refrigerant is dissociated from the solid adsorbent by the flow of heating fluid to the bed. The heat energy is exchanged between cooling/heating fluid and the adsorption bed. The energy balance for the heat transfer fluid is given by
j j
rf cp;f
j j j vT j v2 Tf hf m Af j f j j j j j T ; ¼ rf cp;f uf þ lf 2 T m f j vt vz vz V
j vTf
(5)
f
where u defines the flow rate of cooling/heating fluid, j indicates heating or cooling for desorption or adsorption, hjf m represents the heat transfer coefficient and is calculated from the DittuseBoelter correlation [2]. The boundary conditions for fluid flow become during adsorption: Tfj ðz ¼ 0; tÞ ¼ Tfcool;in and vTfj =vzðz ¼ Ltube ; tÞ ¼ 0, during desorption: Tfj ðz ¼ 0; tÞ ¼ Tfhot;in and vTfj =vzðz ¼ Ltube ; tÞ ¼ 0. The energy balance of the metal tube that contains heat transfer fluid is written as
rtube ctube p
j tube vT tube v2 T tube hf m A j T tube Tf ¼ ltube 2 tube vt vz V hms Atube tube Atube vT fin T T sg z tube lfin tube vr V V (6)
Here the value of 2 is equal to 1 when any fin is attached with the tube, otherwise 2 ¼ 0. The boundary conditions of the heat exchanger tube inside the adsorber are vTtube/vz(z ¼ 0,t) ¼ 0 and vTtube/vz(z ¼ Ltube,t) ¼ 0, respectively. The fin thickness is very small and the heat transfer in the fin is assumed to be one dimensional in
the radial direction. The energy balance equation of the fin is given by.
! rfin cfin p
vT fin ¼ lfin vt
v
vT fin vr
rvr
r
hfins Afin fin sg T : T Vfin
(7)
The boundary conditions are Tfin(r ¼ ro) ¼ Ttube and vTfin/ vr(r ¼ rfin) ¼ 0. The energy balance of the adsorbent control volume can be written as (heat flow is considered both in r- and z-directions)
vT sg dx sg rsg cp þ rg xcap ¼ V$ leff VT sg þ rsg fDHads g dt vt hfins Afin fin sg T T Vfin hms Atube tube T T sg ; tube V
(8)
where the specific heat capacity of the adsorbed phase is given by Ref. [34] cap ¼ cgp þ DHads f1=T sg 1=vg vvg =vT sg g vðDHads Þ=vT sg . The first term in the right hand side indicates the specific heat capacity at gaseous phase, and the other terms occur due to a non ideality of gaseous phase, which incorporate two additional inputs from the properties of adsorbent þ adsorbate system, namely the heat DHads and the isotherms (P-T-x) data [35]. On the other hand, the effective thermal conductivity of the adsorbed phase is leff ¼ lg =ðf þ 2=3lg =lsg Þ[24], where f indicates the porosity of bed. Here leff is defined as the total thermal conductivity of adsorbent particles stacked together in the adsorber. The boundary condition at radial direction becomes leff vT sg =vrjr¼ro ¼ hms ðT tube T sg Þ and vT sg =vrjr¼rfin ¼ 0. The overall mass conservation in the porous bed is described as
Z vr vx dV ¼ m_ kvap ; εt v þ ð1 εt Þrsg vt vt V
where k indicates ‘evap’ or ‘cond’ depending on adsorption and desorption phase. The authors have measured the isotherms of water adsorption on silica gel Fuji Davison type RD and type A [36]. These experimentally measured data are fitted using the following equation [36,37], i.e.
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307
Fig. 2. Schematic of the control-volume selections of (a) an evaporator heat exchanger, (b) an adsorption bed and (c) a condenser.
*
x ¼
xm Ko $expfDHads =ðR$TÞg$P ½1 þ fK0 $expðDHads =ðR$TÞÞ$Pgt1 1=t1
;
(9)
where x* is the adsorbed adsorbate at equilibrium conditions, xm denotes the monolayer capacity, DHads the isosteric enthalpies of adsorption, Ko the pre-exponential constant, and t1 is the dimen th’s constant, and these isotherm parameters are fursionless To nished in Table 2. The mathematical models of non-isothermal adsorption dynamics are mainly focused on a single adsorbent grain or on a porous adsorbent bed that consists of a high number of loose grain layers. It should be noted that the dynamic parameters of silica gel adsorbents were investigated in another studies by an Isothermal Differential Step method [24], and the kinetics of water adsorption on loose silica grains was measured over temperature range of 30e65 C. The experimental study of loose grain silica gel layers is the only efficient way for their optimization. One of the authors has experimentally measured the adsorption
kinetics of silica gel-water system for the temperature drop (from 50 C to 30 C) and the temperature rise (from 58 C to 80 C) [32] which is typically valid for the adsorption and desorption processes of adsorption cooling cycles. In these experiments, the size of silica gel grains is varied from 0.2 to 1.8 mm. Employing the experimental data of various silica gel grain sizes and their configuration in layers, the adsorption/desorption uptake as a function of time is calculated by the following equation [32]
x t ¼ x* f1 expðt=tÞg þ expðt=tÞxi ;
(10)
where xi defines the amount of adsorbate uptake at time t ¼ 0 and (1/t) is the rate constant. x* is the uptake at equilibrium conditions. Here the values of characteristic sorption time,t, depend on the silica gel sizes and layers number in different ways for adsorption and desorption rates. These parameters are furnished in Table 1. After desorption, the desorbed refrigerant is delivered to the condenser as latent heat and this amount of heat is pumped to the
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Table 2 Values adopted for adsorption chiller simulation used in the present model. 2.54 104 m2/s for RD silica gel 4.2 104 J/mol for RD silica gel 0.2 103 m, 0.4 103 m, 0.8 103 m, 1.6 103 m 924 J(/kg K)
Dso Ea Rp sg
cp hms hfins ri Atube ¼ 2pro Ltube
36 W/(m2 K) [16] 36 W/(m2 K) [16] 7.94 mm ro ¼ 8.64 mm, Ltube ¼ 1 m
Vfchill ¼ pro2 Levap
Levap ¼ 2.1 m
Vfcool ¼ pro2 Lcond
Lcond ¼ 2.34 m
and the last term denotes the sensible cooling through condenser heat exchanger. The roles of the beds (containing the adsorbent) are refreshed by switching which is performed by reversing the direction of the cooling and the heating fluids to the designated sorption beds and similarly, the evaporator and condenser are also switched to the respective adsorber and desorber. It is noted that during switching interval, no mass transfers occur between the hot bed and the condenser or the cold bed and the evaporator. The cycle average cooling capacity Qchill, heating capacity heating Q and COP are, respectively calculated as.
2 r 2 Þ N ¼ 100, h ¼ 0.1 mm, rfin ¼ 22 mm V fin ¼ pNhðrfin o 0.18 m/s uchill f
ucool f
0.198 m/s
uheating f
0.14 m/s
M sg
Q
chill
¼
ðruAcP Þchill f
Tfhot;in
85 C
Tfchill;in
14.8 C
f
Q heating ¼ ðruAcP Þheating f
rcool ccool f p;f
vT cool vT cool v2 T cool ¼ ucool þ lcool rcool ccool f f p;f f vt vz vz2 4hi cool T T cond dm;i
(11)
The boundary conditions of the cooling water tube are Tcool(z ¼ 0,t) ¼ Tcool,in and vTcool/vz(z ¼ Ltube,t) ¼ 0. The supply of cooling water activates the enthalpy of condensation in the condenser and the heat is rejected through the heat exchanger metal tubes. hi is calculated from the well known Dittus Boelter correlation. So the energy balance of the metal tube should be taken into account, and is given by:
vT cond rm cp;m m vt
d2m;o d2m;i 4
2 cond d2 m;o dm;i v2 Tm ¼ lm 4 vz2 cool cond Tm þ dm;i hi T cond dm;o ho T cond Tm
COP ¼
dt;
tcycle heating;in Z T T heating;out f
0
environment by the flow of external cooling fluid. In the modelling, we assume that the condenser tube bank surface is able to hold a certain maximum amount of condensate. Beyond this the condensate would flow into the evaporator via a U-tube. This ensures that the condenser and the desorber are always maintained at the saturated pressure of the refrigerant. At the condenser, the cooling water is supplied through the heat exchanging tubes to remove heat. The energy balance equation on the cooling water control volume as shown in Fig. 2(c) is written as
f
tcycle
0
20 kg 31 C
Tfcool;in
tcycle chill;in Z T T chill;out
f
tcycle
dt; and
Q chill : Q heating
The set of partial differential equations is solved numerically using finite difference method. The whole computational domain is discredited into a number of equal step discrete elements in the r (radial) and the axial (z) directions. Since the fin thickness and the spacing between fins are very small, silica gel particles between fins are separately treated as two interacting control volumes, each having its own temperature and mass distribution as a function of space and time. Finally all equations are solved employing fifth order Gear's differentiation formulae method. Double precision is carried out and the tolerance is set to 1 106. Once the initial condition is provided, the program computes from transient to cyclic steady state conditions.
(12)
The value of ho is calculated from condensation correlation. The energy balance inside the condenser space is expressed as
dmcond vT cond cond ¼ m_ cond hf T cond Vcond rcp vap vap hfg T vt dt cond pdm;o L ho T cond Tm (13) Vcond
where is the volume of empty space in the condenser. The first term on the right hand side defines the latent heat of condensation, the second term is the enthalpy of liquid condensate
Fig. 3. Temporal histories for the various components of two beds adsorption chiller. Here (—) indicates adsorption chiller with single layer silica gel size of 0.2e0.25 mm, and (e) defines adsorption chiller with double layer silica gel size of 1.6e1.8 mm. The red lines indicate the experimental data. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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3. Results and discussion The adsorption bed design incorporates finned tube heat exchanger. The values for the parameters used in the present model are furnished in Tables 1 and 2. Fig. 3 features the temporal histories of beds, and heat exchanging fluid temperatures of the adsorption chiller system and these are compared with experimental data of RD silica gel and water based adsorption chiller. Due to the positioning of the temperature sensors, the experimentally measured outlet temperatures are affected by the time constant of downstream mixing valves in the pipeline. It is evident that our present simulation results exhibit a sufficiently good agreement with the experimental data stemming from a distributed parameter model. Fig. 3 also shows the temperature histories at the outlets of the condenser and chilled water. It should be noted here that the delivered chilled water temperature depends on various silica gel grain sizes and layers. Fig. 4 presents the simulated Dühring diagram of the cyclic steady state condition of an entire bed comprising 4 layers with two different grain sizes such as 0.2 mm and 0.8 mm, from which one observes that during cold-to-hot thermal swing of the adsorption bed, the temperature and pressure of the bed increases and pressure remains constant during the change in isosteres. During desorption process, the momentary adsorption takes place in the bed. The entire bed is observed to be essentially following an isosteric path (constant x) during switching. In contrast, the local spatial points in the bed are not evolving in an isosteric manner, which is confirmed by the present analysis. This shows that while some parts of the bed may continue to adsorb, other parts desorb, resulting in the entire bed following an isosteric path. At the end of hot-to-cold thermal swing, there is a pressure drop in the bed. This causes the adsorbate in the cool bed to desorb momentarily and condense into the evaporator. Fig. 5 shows the effects of silica gel grain sizes and layers on COP for type RD based adsorption chiller systems. It is clearly seen that the COP increases monotonically with the reduction of adsorbent grain sizes and layers. The reason is that with larger grain sizes and layers, the relative time frame occupied by the sorption beds for adsorption and desorption is higher due to slower sensible heat exchange in the sorption beds. This will lead to unfavorable effects on the specific cooling power and COP. The variations of cooling
Fig. 4. Dühring diagram of the cyclic steady state condition of an adsorption bed comprising 8, 4 and 1 layers with the silica gel grain sizes of (a) 0.2e0.25 mm, (b) 0.4e0.5 mm and (c) 0.8e0.9 mm.
Fig. 5. Effects of silica gel sizes and layers on COP.
capacity for various silica gel grain sizes and layers are also shown in Fig. 6. For understanding the cycle time effects on adsorption chiller, a plot of COP and specific cooling capacity against cycle times for different silica gel grain sizes and layers are shown in Fig. 7(aec). It is observed that the cooling power increases steeply up to 500 s, and it begins to decrease with a similar slope at the cycle time of over 500 s. Lower cooling capacity is caused by a reduced extent of adsorption, which is also related to a reduced extent of desorption due to the insufficient heating of the desorber. At a certain cycle time, the maximum adsorption/desorption capacity is achieved at the prevailing heating and cooling source temperatures. Extending the cycle time further brings forth unfavourable effect on useful cooling as the cycle average cooling capacity decreases. For the higher layer and large grain size based silica gel-water pair as shown in Fig. 7(c), cycle times longer than 500 s can be realized with the lower cooling power and higher COP as compared to the adsorption cooling system based on single layer and smaller grain size silica gel-water pair. When the adsorber or desorber is saturated, the adsorber must be switched to the desorber for regeneration and the desorber must be switched to the adsorber to provide cooling. The switching
Fig. 6. Effects of silica gel sizes and layers on cooling capacity.
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The system performances at different driving heat source temperatures in case of optimum conditions for various grain sizes and layers are shown in Fig. 9 (aed) for the same heat sink temperature and chilled water inlet temperatures of 31 C and 14.8 C, respectively. As can be observed from Fig. 9(a), the COP reaches the maximum value of 0.36 at 80 C with 0.2 mm grain size and single layer bed configurations. From the present simulation (Fig. 9(aed)) it is observed that the COP of a single layer silica gel - water system is higher than that of higher layer RD type silica gel - water system because of high cooling and less driving heat generation powers, which may occur due to larger kinetics rates of adsorption and desorption for the same heat source and heat sink temperatures. This much larger COP shows significant advantage of the new working pair as compared with the conventional unit. 4. Conclusions We have successfully modelled and predicted the performances of various particle sizes and layers of silica gel and water based adsorption chiller using a simplified distributed approach such that both the transient and steady state behaviours of adsorption chiller can be captured. It is found that the performances of adsorption chiller incorporating adsorbents with smaller grain size and layers, in terms of cooling capacity, coefficient of performance and average chilled water temperature, are better than those of larger grain size and layer based silica gel-water adsorption chiller. The results may provide important clue in developing high efficient solar and/or
Fig. 7. Effect of cycle times on COP and cycle average cooling capacity for various layers with (a) 0.2e0.25 mm, (b) 0.8e0.9 mm and (c) 1.6e1.8 mm silica gel grains.
phase plays an important role on the chiller's performances and may be indispensable. Fig. 8(a) and (b) present the effects of switching time on cycle average cooling capacity and COP for various sizes and layers of RD type silica gel-water systems, respectively. The cycle average cooling capacity and COP vary slightly with switching time and reach an optimum value at 30 s. However the COP and cooling capacity differ significantly with various silica gel grain sizes and layers for various switching times. One can observe that (i) 30 s is the best value for the switching time of smaller silica gel grains with single layer - water system, and (ii) 30 s is also the optimum switching time for type RD silica gel-water system with higher layers.
Fig. 8. Effect of switching times on cycle average cooling capacity and COP for (a) single and (b) 4 layers silica gels arrangements and various grain sizes.
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Fig. 9. Influence of driving heat source temperature on cyclic average cooling capacity and COP for single, 4 and 8 layers bed configurations with (a) 0.2e0.25 mm, (b) 0.4e0.5 mm, (c) 0.8e0.9 mm and (d) 1.6e1.8 mm grain sizes.
YIA thanks the Russian Foundation for Basic Researches (project 14-08-01186) for partial financial support of this study. AC acknowledges the financial support from National Research Foundation, Singapore (grant number NRF-CRP8-2011-3).
P R Rp r T Tm T t u U V v x x* Dx
Nomenclature
z
thermally powered adsorption chillers. However, reducing the grain size and number of layer reduces the amount of silica gel that can be used per unit volume of the adsorber bed and hence increase the overall size of the system leading to the increase in the capital cost. The design of adsorption bed with higher effective thermal conductivity, high packing density of adsorbents in the adsorbent beds and the multiple channels in the adsorption bed could solve these issues and may favor the commercialization of the chiller. Acknowledgements
Symbol A cp d hfg h hi ho Ko L M
f t
area, m2 specific heat capacity, J/kg K tube diameter, m latent heat of evaporation, J/kg enthalpy, J/kg convective heat transfer coefficient at inner surface, W/ m2 K convective heat transfer coefficient at outer surface, W/ m2 K pre-exponential coefficient, 1/Pa length, m mass, kg
ε
r l DHads
pressure, Pa universal gas constant, J/mol. K adsorbent radius, m radial direction, m or mm temperature, C temperature of metal, C average temperature, C time, s fluid velocity, m/s overall heat transfer coefficient, W/m2 K volume, m3 specific volume, m3/kg uptake, kg/kg uptake at equilibrium conditions, kg/kg the difference between uptake and off-take during adsorption desorption processes, kg/kg axial direction, m or mm adsorbent bed porosity, e inverse of rate constant, e adsorbent porosity, e density, Kg/m3 thermal conductivity, W/m K isosteric heat of adsorption, J/kg
Subscripts ads adsorption des desorption chill chilled water fin fin ref refrigerant cycle cycle time
312
f m m, i m, o f-m m-s fin-s eff s vap
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fluid maximum value inner part outer part fluid-metal metal-silica gel fin-silica gel effective value saturation vaporization
Superscripts Sg silica gel evap evaporator cond condenser bed sorption bed chill chill water f liquid phase g gaseous phase in inlet tube heat exchanger tube a adsorbate cool cooling fluid heating heating fluid References [1] Meunier F. Solid sorption: an alternative to CFCs. Heat recovery Syst CHP 1993;13:289e95. [2] Saha BB, Chakraborty A, Koyama S, Aristov YI. A new generation cooling device employing CaCl2-in-silica gelewater system. Int J Heat Mass Transfer 2009;52:516e24. [3] Chakraborty A, Leong KC, Thu K, Saha BB, Ng KC. Theoretical insight of adsorption cooling. Appl Phy Lett 2011;98:221910. [4] Sakoda A, Suzuki M. Fundamental study on solar powered adsorption cooling system. J Chem Eng Jpn 1984;17(1):52e7. [5] Cho SH, Kim JN. Modeling of a silica gel/water adsorption-cooling system. Energy 1992;17(9):829e39. [6] Boelman EC, Saha BB, Kashiwagi T. Experimental investigation of a silica gelwater adsorption refrigeration cycle - the influence of operating conditions on cooling output and COP. ASHRAE Trans 1995;101(2):358e66. [7] Saha BB, Boelman EC, Kashiwagi T. Computer simulation of a silica gel-water adsorption refrigeration cycle - the influence of operating conditions on cooling output and COP. ASHRAE Trans 1995;101(2):348e57. [8] Saha BB, Chakraborty A, Koyama S, Srinivasan K, Ng KC, Kashiwagi T, Dutta P. Thermodynamic formalism of minimum heat source temperature for driving advanced adsorption cooling device. Appl Phy Lett 2007;91:111902. [9] Saha BB, Chakraborty A, Koyama S, Ng KC, Sai MA. Performance modelling of an electro-adsorption chiller. Philos Mag 2006;86(23):3613e32. [10] Liu YL, Wang RZ, Xia ZZ. Experimental performance of a silica gel-water adsorption chiller. Appl Therm Eng 2005;25:359e75. [11] Aristov YI. Novel materials for adsorptive heat pumping and storage: screening and nanotailoring of sorption properties (review). J Chem Eng Jpn 2007;40(13):1241e51. [12] Lozan FJV, Henninger SK, Janiak C. Programming MOFs for water sorption: amino-functionalized MIL-125 and UiO-66 for heat transformation and heat storage applications. Dalton Trans 2013;42:15967.
[13] Zhang LZ, Wang L. Effects of coupled heat and mass transfers in adsorbent on the performance of a waste heat adsorption cooling unit. Appl Therm Eng 1999;19(2):195e215. [14] Critoph RE. Performance limitations of adsorption cycles for solar cooling. Sol Energy 1988;41(1):21e31. [15] Banker ND, Prasad M, Dutta P, Srinivasan K. Development and transient performance results of a single stage activated carbon e HFC 134a closed cycle adsorption cooling system. Appl Therm Eng 2010;30:1126e32. [16] Freni A, Bonaccorsi L, Proverbio E, Maggio G, Restuccia G. Zeolite synthesised on copper foam for adsorption chillers: a mathematical model. Microporous Mesoporous Mater 2009;120:402e9. [17] Saha BB, El-Sharkawy II, Chakraborty A, Koyama. S. Study on an activated carbon fiber-ethanol adsorption chiller: Part I e system description and modelling. Int J Refrig 2007;30(1):86e95. [18] Sun LM, Feng Y, Pons M. Numerical investigation of adsorptive heat pump systems with thermal wave heat regeneration under uniform-pressure conditions. Int J Heat Mass Transfer 1997;40(2):281e92. [19] Henninger SK, Schicktanz M, Hugenell PPC, Sievers H, Henning HM. Evaluation of methanol adsorption on activated carbons for thermally driven chillers part I: thermophysical characterization. Int J Refrig 2012;35:543e53. [20] Dawoud B, Sohel MI, Freni A, Vasta S, Restuccia G. On the effective thermal conductivity of wetted zeolite under the working conditions of an adsorption chiller. Appl Therm Eng 2011;31:2241e6. [21] Gong LX, Wang RZ, Xia ZZ, Chen CJ. Design and performance prediction of a new generation adsorption chiller using composite adsorbent. Energy Convers Manage 2011;52:2345e50. [22] Okunev BN, Gromov AP, Heifets LI, Aristov YI. Dynamics of water sorption on a single adsorbent grain caused by a large pressure jump: modelling of coupled heat and mass transfer. Int J Heat Mass Transfer 2008;51(25e26):5872e6. [23] Aristov YI. Adsorptive transformation of heat: principles of construction of adsorbents database. Appl Therm Eng 2012;42:18e24. [24] Ruthven DM. Principles of adsorption and adsorption processes. London: J. Wiley & Sons; 1984. [25] El-Sharkawy II. On the linear driving force approximation for adsorption cooling applications. Int J Refrig 2011;34:667e73. [26] Aristov YI, Restuccia G, Cacciola G, Parmon VN. A family of new working materials for solid sorption air conditioning systems. Appl Therm Eng 2002;22(2):191e204. [27] Aristov YI. New family of materials for adsorption cooling: material scientist approach. J Eng Thermophys 2007;16(2):63e72. [28] Mrowiec-Bialon J, Jarzebskii AB, Lachowski A, Malinovski J, Aristov YI. Effective inorganic hybrid adsorbents of water vapor by the sol-gel method. Chem Mater 1997;9(11):2486e90. [29] Ponomarenko IV, Glaznev IS, Gubar AV, Aristov YI, Kirik SD. Synthesis and water sorption properties of a new composite “CaCl2 confined to SBA-15 pores”. Microporous Mesoporous Mater 2010;129(1e2):243e50. [30] Glaznev IS, Aristov YI. The effect of cycle boundary conditions and adsorbent grain size on dynamics of adsorption chillers. Int J Heat Mass Transfer 2010;53:1893e8. [31] Aristov YI. Experimental and numerical study of adsorptive chiller dynamics: a loose grains configuration. Appl Therm Eng 2013;61:841e7. [32] Aristov YI, Glaznev IS, Girnik IS. Optimization of adsorption dynamics in adsorptive chillers: loose grains configuration. Energy 2012;46:484e92. [33] Gordeeva LG, Aristov YI. Dynamic study of methanol adsorption on activated carbon ACM-35.4 for enhancing the specific cooling power of adsorptive chillers. Appl Energy 2014;117:127e33. [34] Chakraborty A, Saha BB, Koyama S, Ng KC. The specific heat capacity of a single component adsorbent-adsorbate system. Appl Phy Lett 2007;90:171902. [35] Chakraborty A, Saha BB, Koyama S, Ng KC. On the thermodynamic modeling of isosteric heat of adsorption and comparison with experiments. Appl Phys Lett 2006;89:171901. [36] Chua HT, Ng KC, Chakraborty A, Oo NM, Othman MA. Adsorption characteristics of silica gel þ water systems. J Chem Eng Data 2002;47(5):1177e81. [37] Sun B, Chakraborty A. Thermodynamic formalism of water uptakes on solid porous adsorbents for adsorption cooling applications. Appl Phy Lett 2014;104:201901.
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Dynamic behaviors of adsorption chiller: Effects of the silica gel grain size and layers Anutosh Chakraborty a, Bidyut Baran Saha b, c, *, Yuri I. Aristov d, e a
School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Republic of Singapore Kyushu University Program for Leading Graduate School, Green Asia Education Center, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, 6-1 Kasuga-Koen, Kasuga Shi, Fukuoka 816-8580, Japan c International Institute for Carbon-Neutral Energy Research (WPI-I2CNER), Kyushu University, Japan d Boreskov Institute of Catalysis, Siberian Division, Russian Academy of Sciences, pr. Akademika Lavrent'eva 5, Novosibirsk 630090, Russia e Novosibirsk State University, Pirogova Str., 2, Novosibirsk 630090, Russia b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 25 June 2014 Received in revised form 3 October 2014 Accepted 4 October 2014 Available online 6 November 2014
This article presents the dynamic behaviour of a single effect two bed adsorption chiller employing adsorbent beds with various layers of loose grain configurations and silica gel particle sizes, which is based on the experimentally confirmed adsorption isotherms and kinetics data. Compared with the experimental data of conventional adsorption chiller based on RD silica gel-water pair, we found that the silica gel configuration in terms of layers and sizes provides an interesting result, that is, the “grain size sensitive” regime is realized for large adsorbent grains with more layers. From numerical simulation, it is found that the specific cooling power and the coefficient of performance are reduced and the peak chilled water temperatures are increased with increasing the grain size and grain layers. We also demonstrate here that the sizes and layers of adsorbents should be considered for the design of adsorption heat exchanger for adsorption cooling applications. © 2014 Elsevier Ltd. All rights reserved.
Keywords: Adsorption Adsorbent layers Cooling Grain size Waste heat recovery
1. Introduction The advancement of adsorption chiller is based on the thermal compression of natural working refrigerants such as water and depends on the nature of porous adsorbents in terms of water vapour uptakes and offtakes and the appropriate kinetics rates. The widespread acceptance of the adsorption chiller is hindered by its relatively poor performances and bulky size due to limited properties of solid adsorbents even though it is amenable to regenerative use of adsorption heat, incorporates no mechanical moving parts and generates no noise or vibration. The performances of adsorption chiller depend mainly on the nature of adsorption isotherms, kinetics and the isosteric heat of adsorption of adsorbentadsorbate pairs. Up to now, numerous investigations are reported on various adsorption system configurations, experimental investigations and mathematical modelling of adsorption cycles [1e10], and the isotherms and kinetics of various adsorbent-
* Corresponding author. Kyushu University Program for Leading Graduate School, Green Asia Education Center, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, 6-1 Kasuga-Koen, Kasuga Shi, Fukuoka 816-8580, Japan. Tel.: þ81 92 583 7903; fax: þ81 92 583 8909. E-mail address: [email protected] (B.B. Saha). http://dx.doi.org/10.1016/j.energy.2014.10.015 0360-5442/© 2014 Elsevier Ltd. All rights reserved.
adsorbate pairs such as silica gel-water, zeolite-water, silica gelmethanol, activated carbon-methanol, activated charcoal-NH3, zeolite-CO2, MOFs-water etc. [11e22], from which it is understood th and DubinineAstakhov equations are that (i) the Freundlich, To mainly used for describing the amount of adsorbate uptakes for various pressures and temperatures, (ii) the enthalpy of adsorption derived from the isosteric chart of adsorbent-adsorbate pair in the ClausiuseClapeyron coordinates is used to calculate the theoretical maximum COP (coefficient of performance) and (iii) adsorption kinetics approximated by the LDF (linear driving force) model are used to calculated the dynamic behaviour of adsorption chiller [23e25]. All these information are needed to model and simulate an adsorption chiller. Silica gels and zeolites are mainly used as adsorbents for adsorption chiller purposes. However recently a new family of composite sorbents called SWSs (selective water sorbents) based on a porous host matrix (silica, alumina, etc.) and an inorganic salt (CaCl2, LiBr, MgCl2, MgSO4, Ca(NO3)2, etc.) impregnated inside pores [26e29] has been presented for sorption cooling and heat pumping [2,26]. Among the different SWSs, the SWS-1L (“CaCl2 confined to KSK silica gel”) shows very high water sorption capacity (up to 0.7 g of water per 1 g of dry adsorbent) [26]. It is found experimentally that very simple monolayer configuration of loose adsorbent grains results in a quite fast adsorption
A. Chakraborty et al. / Energy 78 (2014) 304e312
dynamics and large specific cooling power [30,31]. Experimental desorption rate is also found to be faster than appropriate adsorption rate by a factor of 2.2e3.5. The size (dp) of silica gel grains was found to be a powerful tool to manage the dynamics of isobaric water ad-/desorption [31]. For large grains (>0.5 mm), the characteristic time for adsorption and desorption was strongly dependent on the adsorbent grain size and is found to be proportional to d2p that is in accordance with the LDF model. For smaller silica grains, the maximum specific cooling power can exceed 5 kW/kg, which is very attractive for designing compact adsorption chiller as a monolayer configuration of loose silica gel grains provides quite fast adsorption dynamics. However, it is expected that employing the present configuration of adsorption chiller as displayed in Table 1, the COP (coefficient of performance) is not optimal as the mass of adsorbent housed in the monolayer is small as compared with the inert masses of adsorption bed unit. Because of this, the design with more than one layer is more realistic. So, the investigation of adsorption dynamics in a thin bed containing a small number n of loose grain layers (1 < n < 10) is of high practical interest [31e33]. Experimental tests confirmed the promising properties of loose grains configurations of silica gel [31,32]. It can be shown that the use of various loose grains silica gel designs in the sorption bed allows significant effects on COP and cooling capacity of adsorption chiller even though the gross COP is affected by heat losses, the heat capacity of the inert masses and the heat exchangers efficiency which are not optimised in the unit tested. The authors mentioned that both the COP and cooling power are expected to be further improved in the multi-bed system with internal heat recovery and well-designed heat-exchanger with optimised silica gel grains configuration including particle sizes and layers. The aim of this study is to analyse the performances of adsorption chiller employing the dynamic behaviours of various silica gel grains arrangements with respect to the silica gel sizes and layers in more optimized configuration similar to that used in commercial adsorption chillers. Building from the previous works, this article
Table 1 The characteristic sorption times during adsorption/desorption periods for the two boundary conditions (50 ¼ >30 C and 58 ¼ >80 C) with various silica gel grain sizes and layers. Grain size, mm
Adsorption/Desorption ( C)
Layers
t
t0.5
0.2e0.25
50 ¼ >30
1 2 4 8 1 2 4 8 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4
13.3 17.0 26.0 38.0 6.20 6.20 12.0 21.0 18.0 30.0 86.0 6.70 13.5 42.1 47.3 100 200 16.5 45.0 115 182 316 588 64.0 169 310
8.00 11.0 22.7 45.1 4.20 4.40 9.10 20.5 11.5 20.1 58.7 4.70 9.10 29.1 31.2 65.1 145 11.1 13.3 79.0 112 225 380 42.8 116 216
58 ¼ >80
0.4e0.5
50 ¼ >30
58 ¼ >80
0.8e0.9
50 ¼ >30
58 ¼ >80
1.6e1.8
50 ¼ >30
58 ¼ >80
305
presents both the steady-state and dynamic behaviours of various configurations of silica gel in a two-bed solid sorption cooling system using a transient distributed model. These results are compared with those of commercial adsorption cooler based on silica gel Fuji RD such that a device with various adsorbent sizes and layers for new generation of cooling can be enlightened commercially. Both the heat and mass transfer resistances of the adsorption heat exchanger as well as the temporal energetic behaviour in the evaporator and condenser are also taken into account in a distributed manner in the present model. In this paper, we also compare the present simulation results with the experimental data.
2. Mathematical modelling of adsorption chiller It is well known that the adsorption chiller utilizes the adsorbent-adsorbate characteristics to produce the useful cooling effects at the evaporator by the union of “adsorption-triggeredevaporation” and “desorption-activated-condensation” and these are described elsewhere [14e16]. Fig. 1 shows the schematic layout of the adsorption chiller that comprises the evaporator, the condenser and the reactors or adsorbent beds. For continuous cooling operation, firstly a low-pressure refrigerant (hence water) is evaporated at the evaporator due to external cooling load (or chilled water) and is adsorbed into the solid adsorbent located in the adsorber, and these phenomena as shown in Fig. 2(a) with respect to control volume approach are represented mathematically in the following way. At the evaporator, the chilled water is supplied through the heat exchanging tubes in the evaporator. The energy balance equation on the chilled water control volume is written as
rchill cchill f p;f
vT chill vT chill v2 T chill ¼ uchill þ lchill rchill cchill f f p;f f vt vz vz2 4hi chill T T evap dm;i
(1)
The boundary conditions of the chilled water tube are Tchill(z ¼ 0,t) ¼ Tchill,in and vTchill/vz(z¼ Ltube,t) ¼ 0. The heat of chilled water, which activates the enthalpy of evaporation, is absorbed at the refrigerant of the evaporator through the heat exchanger metal tubes. So the energy balance of the metal tube should be taken into account, and the energy balance equation is written as:
evap
vT rm cp;m m vt
d2m;o d2m;i 4
evap
v2 Tm ¼ lm vz2
d2m;o d2m;i
4
evap Tm þ dm;i hi T evap dm;o ho Tm T evap chill
(2)
Pool boiling is affected on the water refrigerant outside the heat exchanging tube in the evaporator by the vapour uptake at the adsorber. In that case, the mass and energy balance equations become
dmevap _ evap ¼ m_ cond vap mvap ; and dt rVevap cevap p
vT evap dmcond cond evap m_ evap ¼ hf T Þ vap hfg ðT vt dt evap pdm;o L ho Tm T evap ; evap
(3)
(4)
where ðrVevap cp Þ is the sum of all mass capacities of the evaporator and the first term of the right hand side of Equation (4) indicates the amount of condensate (refrigerant) that is refluxed back
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Fig. 1. Schematic layout of a two-bed adsorption chiller.
to the evaporator via a pressure reducing valve for maintaining the pressure difference between the condenser and the evaporator. The process of adsorption results in the liberation of heat due to the enthalpy of adsorption at the adsorption reactor and this amount of heat is removed by the supply of cooling water to the adsorber through the heat exchanging tubes. Secondly, the adsorbed bed is heated by the external heat source and the refrigerant is desorbed from the adsorbent and goes to the condenser. These phenomena as shown in Fig. 2(b) are expressed mathematically using the mass and energy balances of the adsorption reactor. During adsorption period, the cooling fluid at ambient conditions is supplied to the bed through the heat exchanging tube to accelerate the amount of water vapour uptakes and during desorption period, the desorbed refrigerant is dissociated from the solid adsorbent by the flow of heating fluid to the bed. The heat energy is exchanged between cooling/heating fluid and the adsorption bed. The energy balance for the heat transfer fluid is given by
j j
rf cp;f
j j j vT j v2 Tf hf m Af j f j j j j j T ; ¼ rf cp;f uf þ lf 2 T m f j vt vz vz V
j vTf
(5)
f
where u defines the flow rate of cooling/heating fluid, j indicates heating or cooling for desorption or adsorption, hjf m represents the heat transfer coefficient and is calculated from the DittuseBoelter correlation [2]. The boundary conditions for fluid flow become during adsorption: Tfj ðz ¼ 0; tÞ ¼ Tfcool;in and vTfj =vzðz ¼ Ltube ; tÞ ¼ 0, during desorption: Tfj ðz ¼ 0; tÞ ¼ Tfhot;in and vTfj =vzðz ¼ Ltube ; tÞ ¼ 0. The energy balance of the metal tube that contains heat transfer fluid is written as
rtube ctube p
j tube vT tube v2 T tube hf m A j T tube Tf ¼ ltube 2 tube vt vz V hms Atube tube Atube vT fin T T sg z tube lfin tube vr V V (6)
Here the value of 2 is equal to 1 when any fin is attached with the tube, otherwise 2 ¼ 0. The boundary conditions of the heat exchanger tube inside the adsorber are vTtube/vz(z ¼ 0,t) ¼ 0 and vTtube/vz(z ¼ Ltube,t) ¼ 0, respectively. The fin thickness is very small and the heat transfer in the fin is assumed to be one dimensional in
the radial direction. The energy balance equation of the fin is given by.
! rfin cfin p
vT fin ¼ lfin vt
v
vT fin vr
rvr
r
hfins Afin fin sg T : T Vfin
(7)
The boundary conditions are Tfin(r ¼ ro) ¼ Ttube and vTfin/ vr(r ¼ rfin) ¼ 0. The energy balance of the adsorbent control volume can be written as (heat flow is considered both in r- and z-directions)
vT sg dx sg rsg cp þ rg xcap ¼ V$ leff VT sg þ rsg fDHads g dt vt hfins Afin fin sg T T Vfin hms Atube tube T T sg ; tube V
(8)
where the specific heat capacity of the adsorbed phase is given by Ref. [34] cap ¼ cgp þ DHads f1=T sg 1=vg vvg =vT sg g vðDHads Þ=vT sg . The first term in the right hand side indicates the specific heat capacity at gaseous phase, and the other terms occur due to a non ideality of gaseous phase, which incorporate two additional inputs from the properties of adsorbent þ adsorbate system, namely the heat DHads and the isotherms (P-T-x) data [35]. On the other hand, the effective thermal conductivity of the adsorbed phase is leff ¼ lg =ðf þ 2=3lg =lsg Þ[24], where f indicates the porosity of bed. Here leff is defined as the total thermal conductivity of adsorbent particles stacked together in the adsorber. The boundary condition at radial direction becomes leff vT sg =vrjr¼ro ¼ hms ðT tube T sg Þ and vT sg =vrjr¼rfin ¼ 0. The overall mass conservation in the porous bed is described as
Z vr vx dV ¼ m_ kvap ; εt v þ ð1 εt Þrsg vt vt V
where k indicates ‘evap’ or ‘cond’ depending on adsorption and desorption phase. The authors have measured the isotherms of water adsorption on silica gel Fuji Davison type RD and type A [36]. These experimentally measured data are fitted using the following equation [36,37], i.e.
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307
Fig. 2. Schematic of the control-volume selections of (a) an evaporator heat exchanger, (b) an adsorption bed and (c) a condenser.
*
x ¼
xm Ko $expfDHads =ðR$TÞg$P ½1 þ fK0 $expðDHads =ðR$TÞÞ$Pgt1 1=t1
;
(9)
where x* is the adsorbed adsorbate at equilibrium conditions, xm denotes the monolayer capacity, DHads the isosteric enthalpies of adsorption, Ko the pre-exponential constant, and t1 is the dimen th’s constant, and these isotherm parameters are fursionless To nished in Table 2. The mathematical models of non-isothermal adsorption dynamics are mainly focused on a single adsorbent grain or on a porous adsorbent bed that consists of a high number of loose grain layers. It should be noted that the dynamic parameters of silica gel adsorbents were investigated in another studies by an Isothermal Differential Step method [24], and the kinetics of water adsorption on loose silica grains was measured over temperature range of 30e65 C. The experimental study of loose grain silica gel layers is the only efficient way for their optimization. One of the authors has experimentally measured the adsorption
kinetics of silica gel-water system for the temperature drop (from 50 C to 30 C) and the temperature rise (from 58 C to 80 C) [32] which is typically valid for the adsorption and desorption processes of adsorption cooling cycles. In these experiments, the size of silica gel grains is varied from 0.2 to 1.8 mm. Employing the experimental data of various silica gel grain sizes and their configuration in layers, the adsorption/desorption uptake as a function of time is calculated by the following equation [32]
x t ¼ x* f1 expðt=tÞg þ expðt=tÞxi ;
(10)
where xi defines the amount of adsorbate uptake at time t ¼ 0 and (1/t) is the rate constant. x* is the uptake at equilibrium conditions. Here the values of characteristic sorption time,t, depend on the silica gel sizes and layers number in different ways for adsorption and desorption rates. These parameters are furnished in Table 1. After desorption, the desorbed refrigerant is delivered to the condenser as latent heat and this amount of heat is pumped to the
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Table 2 Values adopted for adsorption chiller simulation used in the present model. 2.54 104 m2/s for RD silica gel 4.2 104 J/mol for RD silica gel 0.2 103 m, 0.4 103 m, 0.8 103 m, 1.6 103 m 924 J(/kg K)
Dso Ea Rp sg
cp hms hfins ri Atube ¼ 2pro Ltube
36 W/(m2 K) [16] 36 W/(m2 K) [16] 7.94 mm ro ¼ 8.64 mm, Ltube ¼ 1 m
Vfchill ¼ pro2 Levap
Levap ¼ 2.1 m
Vfcool ¼ pro2 Lcond
Lcond ¼ 2.34 m
and the last term denotes the sensible cooling through condenser heat exchanger. The roles of the beds (containing the adsorbent) are refreshed by switching which is performed by reversing the direction of the cooling and the heating fluids to the designated sorption beds and similarly, the evaporator and condenser are also switched to the respective adsorber and desorber. It is noted that during switching interval, no mass transfers occur between the hot bed and the condenser or the cold bed and the evaporator. The cycle average cooling capacity Qchill, heating capacity heating Q and COP are, respectively calculated as.
2 r 2 Þ N ¼ 100, h ¼ 0.1 mm, rfin ¼ 22 mm V fin ¼ pNhðrfin o 0.18 m/s uchill f
ucool f
0.198 m/s
uheating f
0.14 m/s
M sg
Q
chill
¼
ðruAcP Þchill f
Tfhot;in
85 C
Tfchill;in
14.8 C
f
Q heating ¼ ðruAcP Þheating f
rcool ccool f p;f
vT cool vT cool v2 T cool ¼ ucool þ lcool rcool ccool f f p;f f vt vz vz2 4hi cool T T cond dm;i
(11)
The boundary conditions of the cooling water tube are Tcool(z ¼ 0,t) ¼ Tcool,in and vTcool/vz(z ¼ Ltube,t) ¼ 0. The supply of cooling water activates the enthalpy of condensation in the condenser and the heat is rejected through the heat exchanger metal tubes. hi is calculated from the well known Dittus Boelter correlation. So the energy balance of the metal tube should be taken into account, and is given by:
vT cond rm cp;m m vt
d2m;o d2m;i 4
2 cond d2 m;o dm;i v2 Tm ¼ lm 4 vz2 cool cond Tm þ dm;i hi T cond dm;o ho T cond Tm
COP ¼
dt;
tcycle heating;in Z T T heating;out f
0
environment by the flow of external cooling fluid. In the modelling, we assume that the condenser tube bank surface is able to hold a certain maximum amount of condensate. Beyond this the condensate would flow into the evaporator via a U-tube. This ensures that the condenser and the desorber are always maintained at the saturated pressure of the refrigerant. At the condenser, the cooling water is supplied through the heat exchanging tubes to remove heat. The energy balance equation on the cooling water control volume as shown in Fig. 2(c) is written as
f
tcycle
0
20 kg 31 C
Tfcool;in
tcycle chill;in Z T T chill;out
f
tcycle
dt; and
Q chill : Q heating
The set of partial differential equations is solved numerically using finite difference method. The whole computational domain is discredited into a number of equal step discrete elements in the r (radial) and the axial (z) directions. Since the fin thickness and the spacing between fins are very small, silica gel particles between fins are separately treated as two interacting control volumes, each having its own temperature and mass distribution as a function of space and time. Finally all equations are solved employing fifth order Gear's differentiation formulae method. Double precision is carried out and the tolerance is set to 1 106. Once the initial condition is provided, the program computes from transient to cyclic steady state conditions.
(12)
The value of ho is calculated from condensation correlation. The energy balance inside the condenser space is expressed as
dmcond vT cond cond ¼ m_ cond hf T cond Vcond rcp vap vap hfg T vt dt cond pdm;o L ho T cond Tm (13) Vcond
where is the volume of empty space in the condenser. The first term on the right hand side defines the latent heat of condensation, the second term is the enthalpy of liquid condensate
Fig. 3. Temporal histories for the various components of two beds adsorption chiller. Here (—) indicates adsorption chiller with single layer silica gel size of 0.2e0.25 mm, and (e) defines adsorption chiller with double layer silica gel size of 1.6e1.8 mm. The red lines indicate the experimental data. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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309
3. Results and discussion The adsorption bed design incorporates finned tube heat exchanger. The values for the parameters used in the present model are furnished in Tables 1 and 2. Fig. 3 features the temporal histories of beds, and heat exchanging fluid temperatures of the adsorption chiller system and these are compared with experimental data of RD silica gel and water based adsorption chiller. Due to the positioning of the temperature sensors, the experimentally measured outlet temperatures are affected by the time constant of downstream mixing valves in the pipeline. It is evident that our present simulation results exhibit a sufficiently good agreement with the experimental data stemming from a distributed parameter model. Fig. 3 also shows the temperature histories at the outlets of the condenser and chilled water. It should be noted here that the delivered chilled water temperature depends on various silica gel grain sizes and layers. Fig. 4 presents the simulated Dühring diagram of the cyclic steady state condition of an entire bed comprising 4 layers with two different grain sizes such as 0.2 mm and 0.8 mm, from which one observes that during cold-to-hot thermal swing of the adsorption bed, the temperature and pressure of the bed increases and pressure remains constant during the change in isosteres. During desorption process, the momentary adsorption takes place in the bed. The entire bed is observed to be essentially following an isosteric path (constant x) during switching. In contrast, the local spatial points in the bed are not evolving in an isosteric manner, which is confirmed by the present analysis. This shows that while some parts of the bed may continue to adsorb, other parts desorb, resulting in the entire bed following an isosteric path. At the end of hot-to-cold thermal swing, there is a pressure drop in the bed. This causes the adsorbate in the cool bed to desorb momentarily and condense into the evaporator. Fig. 5 shows the effects of silica gel grain sizes and layers on COP for type RD based adsorption chiller systems. It is clearly seen that the COP increases monotonically with the reduction of adsorbent grain sizes and layers. The reason is that with larger grain sizes and layers, the relative time frame occupied by the sorption beds for adsorption and desorption is higher due to slower sensible heat exchange in the sorption beds. This will lead to unfavorable effects on the specific cooling power and COP. The variations of cooling
Fig. 4. Dühring diagram of the cyclic steady state condition of an adsorption bed comprising 8, 4 and 1 layers with the silica gel grain sizes of (a) 0.2e0.25 mm, (b) 0.4e0.5 mm and (c) 0.8e0.9 mm.
Fig. 5. Effects of silica gel sizes and layers on COP.
capacity for various silica gel grain sizes and layers are also shown in Fig. 6. For understanding the cycle time effects on adsorption chiller, a plot of COP and specific cooling capacity against cycle times for different silica gel grain sizes and layers are shown in Fig. 7(aec). It is observed that the cooling power increases steeply up to 500 s, and it begins to decrease with a similar slope at the cycle time of over 500 s. Lower cooling capacity is caused by a reduced extent of adsorption, which is also related to a reduced extent of desorption due to the insufficient heating of the desorber. At a certain cycle time, the maximum adsorption/desorption capacity is achieved at the prevailing heating and cooling source temperatures. Extending the cycle time further brings forth unfavourable effect on useful cooling as the cycle average cooling capacity decreases. For the higher layer and large grain size based silica gel-water pair as shown in Fig. 7(c), cycle times longer than 500 s can be realized with the lower cooling power and higher COP as compared to the adsorption cooling system based on single layer and smaller grain size silica gel-water pair. When the adsorber or desorber is saturated, the adsorber must be switched to the desorber for regeneration and the desorber must be switched to the adsorber to provide cooling. The switching
Fig. 6. Effects of silica gel sizes and layers on cooling capacity.
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The system performances at different driving heat source temperatures in case of optimum conditions for various grain sizes and layers are shown in Fig. 9 (aed) for the same heat sink temperature and chilled water inlet temperatures of 31 C and 14.8 C, respectively. As can be observed from Fig. 9(a), the COP reaches the maximum value of 0.36 at 80 C with 0.2 mm grain size and single layer bed configurations. From the present simulation (Fig. 9(aed)) it is observed that the COP of a single layer silica gel - water system is higher than that of higher layer RD type silica gel - water system because of high cooling and less driving heat generation powers, which may occur due to larger kinetics rates of adsorption and desorption for the same heat source and heat sink temperatures. This much larger COP shows significant advantage of the new working pair as compared with the conventional unit. 4. Conclusions We have successfully modelled and predicted the performances of various particle sizes and layers of silica gel and water based adsorption chiller using a simplified distributed approach such that both the transient and steady state behaviours of adsorption chiller can be captured. It is found that the performances of adsorption chiller incorporating adsorbents with smaller grain size and layers, in terms of cooling capacity, coefficient of performance and average chilled water temperature, are better than those of larger grain size and layer based silica gel-water adsorption chiller. The results may provide important clue in developing high efficient solar and/or
Fig. 7. Effect of cycle times on COP and cycle average cooling capacity for various layers with (a) 0.2e0.25 mm, (b) 0.8e0.9 mm and (c) 1.6e1.8 mm silica gel grains.
phase plays an important role on the chiller's performances and may be indispensable. Fig. 8(a) and (b) present the effects of switching time on cycle average cooling capacity and COP for various sizes and layers of RD type silica gel-water systems, respectively. The cycle average cooling capacity and COP vary slightly with switching time and reach an optimum value at 30 s. However the COP and cooling capacity differ significantly with various silica gel grain sizes and layers for various switching times. One can observe that (i) 30 s is the best value for the switching time of smaller silica gel grains with single layer - water system, and (ii) 30 s is also the optimum switching time for type RD silica gel-water system with higher layers.
Fig. 8. Effect of switching times on cycle average cooling capacity and COP for (a) single and (b) 4 layers silica gels arrangements and various grain sizes.
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Fig. 9. Influence of driving heat source temperature on cyclic average cooling capacity and COP for single, 4 and 8 layers bed configurations with (a) 0.2e0.25 mm, (b) 0.4e0.5 mm, (c) 0.8e0.9 mm and (d) 1.6e1.8 mm grain sizes.
YIA thanks the Russian Foundation for Basic Researches (project 14-08-01186) for partial financial support of this study. AC acknowledges the financial support from National Research Foundation, Singapore (grant number NRF-CRP8-2011-3).
P R Rp r T Tm T t u U V v x x* Dx
Nomenclature
z
thermally powered adsorption chillers. However, reducing the grain size and number of layer reduces the amount of silica gel that can be used per unit volume of the adsorber bed and hence increase the overall size of the system leading to the increase in the capital cost. The design of adsorption bed with higher effective thermal conductivity, high packing density of adsorbents in the adsorbent beds and the multiple channels in the adsorption bed could solve these issues and may favor the commercialization of the chiller. Acknowledgements
Symbol A cp d hfg h hi ho Ko L M
f t
area, m2 specific heat capacity, J/kg K tube diameter, m latent heat of evaporation, J/kg enthalpy, J/kg convective heat transfer coefficient at inner surface, W/ m2 K convective heat transfer coefficient at outer surface, W/ m2 K pre-exponential coefficient, 1/Pa length, m mass, kg
ε
r l DHads
pressure, Pa universal gas constant, J/mol. K adsorbent radius, m radial direction, m or mm temperature, C temperature of metal, C average temperature, C time, s fluid velocity, m/s overall heat transfer coefficient, W/m2 K volume, m3 specific volume, m3/kg uptake, kg/kg uptake at equilibrium conditions, kg/kg the difference between uptake and off-take during adsorption desorption processes, kg/kg axial direction, m or mm adsorbent bed porosity, e inverse of rate constant, e adsorbent porosity, e density, Kg/m3 thermal conductivity, W/m K isosteric heat of adsorption, J/kg
Subscripts ads adsorption des desorption chill chilled water fin fin ref refrigerant cycle cycle time
312
f m m, i m, o f-m m-s fin-s eff s vap
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fluid maximum value inner part outer part fluid-metal metal-silica gel fin-silica gel effective value saturation vaporization
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