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water adsorption cooling systems
Applied Thermal Engineering 25 (2005) 1403–1418 www.elsevier.com/locate/apthermeng
The effect of operating conditions on the performance of zeolite/water adsorption cooling systems Y. Liu, K.C. Leong
*
School of Mechanical and Production Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Republic of Singapore Received 28 June 2004; accepted 20 September 2004 Available online 21 November 2004
Abstract A numerical investigation of the effect of operating conditions on the thermal performance (coefficient of performance and specific cooling power) of an adsorption cooling system based on the Zeolite 13X/water working pair is presented in this paper. Both heat and mass transfer limitations are taken into account in the numerical model. DarcyÕs law and the linear driving force (LDF) model are used to describe the mass transfer limitation between the particles and within the particle, respectively. In this study, the effect of operating conditions such as adsorption temperature (Ta), generation temperature (Tg), condensing temperature (Tc), evaporating temperature (Te), the driven temperature of heat exchange fluid (Th,in) and the velocity of heat exchange fluid, on system performance were investigated. The results show that Ta, Tg, Tc and Te have significant effects on the system performance. For a given set of operating conditions, Ta and Tg possess optimal values based on the system performance. The driven temperature, Th,in was found to have negligible effect on the coefficient of performance although the optimal cooling power increases with Th,in. The cycle time decreases with an increase in fluid velocity, but this effect will be reduced for a high value of fluid velocity. The results of the numerical investigation will provide useful inputs to the development of an experimental adsorption cooling facility in the School of Mechanical and Production Engineering at the Nanyang Technological University. 2004 Elsevier Ltd. All rights reserved.
*
Corresponding author. Tel.: +65 6790 5596; fax: +65 6792 2619. E-mail address: [email protected] (K.C. Leong).
1359-4311/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2004.09.013
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Keywords: Adsorption cooling; Operating conditions; Numerical modelling; Coefficient of performance; Specific cooling power
1. Introduction Sorption cooling systems are environment friendly compared with traditional CFC systems as they employ safe and non-polluting refrigerants. Another advantage of sorption cooling systems is that they can be driven by low-grade energy such as waste heat or solar energy. Absorption and adsorption cycles are the two types of sorption cooling systems. Absorption cooling systems such as those using LiBr–H2O or H2O–NH3 pairs present many advantages for specific applications. They give better system efficiency than adsorption cooling systems. However, these systems also possess many limitations in operating conditions [1]. Compared with an absorption system, the adsorption cooling system has the advantages of mechanical simplicity and high reliability. As a result, it has been attracted much research attention in recent years. A big obstacle to the development of adsorption cycle technology is its low coefficient of performance. Research efforts by previous investigators have therefore been focused on improving the performance of the adsorption cooling system [2]. The performance of an adsorption cooling system is affected mainly by adsorption/adsorbate properties, configuration parameters and operating conditions. Recently, various heat and mass transfer models have been proposed to study the thermal performance in terms of the coefficient of performance (COP) and specific cooling power (SCP) of adsorptive cooling systems [3–9]. However, the effects of operating conditions on the thermal performance of such systems especially those pertaining to operating temperature effects are scarcely reported in the literature. The effect of operating conditions on the adsorption cooling cycle based on thermodynamic analyses has been investigated by a number of researchers [10–12]. These studies, however, did not account for the transient heat and mass transfer processes present in the adsorbent bed. Their results were therefore not presented in terms of the SCP. Saha et al. [13] proposed a lumped model and investigated the effects of operating conditions on the thermal performance of a silica gel/ water adsorption cycle. However, they excluded the effect of the adsorption temperature. Recently, Critoph and Metcalf [14] presented a one-dimensional transient model to study the effect of operating conditions on a carbon–ammonia system. The initial adsorption temperature effect was not considered in their investigation and micro-mass transfer limitations were neglected. In this paper, the effect of operating conditions on the thermal performance of a zeolite/water cooling cycle is presented based on a two-dimensional heat and mass transfer model elucidated by the authors [9]. Both heat and mass transfer limitations are considered in this model. The aim is to provide useful guidelines for the selection of operating conditions of an adsorption cooling system.
2. System description The basic adsorption cooling system consists of a solid adsorbent bed, which is alternately connected to a condenser and an evaporator. An adsorption cooling system works on an adsorption–
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Nomenclature Cp COP d D0 De Dek Dk Dm K L Lv _ m M P Ps q r R S Sf SCP t tc tc1/2 T Ta Tc Te Tg u uf u V Z Greek DH e ea ei
specific heat (J/kg K) coefficient of performance particle diameter (m) reference diffusivity (m2/s) equivalent diffusivity in the adsorbent particles (m2/s) equivalent Knudsen diffusivity (m2/s) Knudsen diffusivity (m2/s) molecular diffusivity (m2/s) permeability of adsorbent bed (m2) the length of adsorbent bed latent heat of vaporization (J/kg) total mass flow flux of water vapour (kg/s m2) molar mass (kg/mol) pressure (Pa) saturation pressure (Pa) adsorbed concentration (kg/kg) radial coordinate (m) universal gas constant (J/kmol K); adsorbent bed radius (m) area of adsorbent bed surface (m2) cross-sectional area of heat exchange fluid specific cooling power (W/kg) time (s) cycle time (s) the first half cycle time (s) temperature (K) initial adsorption temperature condensing temperature evaporating temperature generation temperature gaseous velocity in axial direction (m/s) fluid velocity (m/s) gaseous velocity vector (m/s) gaseous velocity in radial direction axial coordinate (m) symbols heat of adsorption (J/kg) total bed porosity macro-porosity of the bed micro-porosity of the particle
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k l r s X
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thermal conductivity (W/m K) viscosity (N/s m) ˚) collision diameter for Lennard-Jones potential (A tortuosity collision integral
Subscripts a adsorbed phase c condensing e evaporating f heat exchange fluid g water vapour h heating in inlet fluid m metal tube out outlet fluid s adsorbent
desorption cycle. This cycle can be represented on a Clapeyron diagram (ln P vs 1/T) as shown in Fig. 1. The entire process consists of four steps. At the beginning of Step 1 (A–B), the adsorbent contains a high concentration of adsorbate (qmax) with an initial ambient temperature of Ta. During this step, the adsorbent bed is heated at a constant concentration of adsorbate. When the vapour pressure in the adsorbent bed is equal to the condensing pressure (Pc), Step 2 (B–C) begins with the opening of a valve between the adsorber and the condenser. The adsorbate gas desorbed from the adsorber is cooled to a temperature Tc until it condenses in either a water or an aircooled condenser. At the end of Step 2, the maximum temperature (Tg) of the adsorbent bed is
lnP Saturation qmax line Pc
qmin B
C
Pe A
Te
Tc Ta
D
Tg
-1/T
Fig. 1. Clapeyron diagram of an adsorption cooling cycle.
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Fig. 2. Schematic diagram of adsorber.
reached and the bed is disconnected from the condenser. During Step 3 (C–D), the adsorber is cooled at a constant adsorbed concentration (qmin). The pressure in the bed decreases from Pc to Pe. Step 4 (D–A) begins with the connection between the adsorbent bed to the evaporator. The adsorbate liquid evaporates from the evaporator and is adsorbed by the cooling bed. The heat exchange fluid (HXF) which flows through the adsorber is used to heat or cool the adsorber. The refrigerant is transferred to the condenser or from the evaporator through the gas path of the adsorber as shown in Fig. 2.
3. Mathematical modelling A schematic of the adsorber is shown in Fig. 2. The modelling of the adsorber involves heat and mass conservation equations for HXF, the metal tube and the adsorbent bed. The following assumptions are made: 1. The adsorbed phase is considered as a liquid, and the adsorbate gas is assumed to be an ideal gas. 2. The adsorbent bed is composed of uniformly sized particles with isotropic properties. 3. The properties of the fluid, the metal tube and adsorbate vapour are constant. 4. There are no heat losses in the adsorption cycle. 5. The thermal resistance between the metal tube and the adsorbent bed is neglected.
3.1. Adsorption equations In most of the previous studies, the equilibrium adsorption model has been assumed and the internal mass transfer resistance between solid and adsorbate gas phases is neglected. The linear driving force (LDF) equation is used to account for mass transfer resistance within the adsorbent particles as proposed by Sakoda and Suzuki [15]. Chahbani et al. [16] pointed out that the LDF
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model could be used to describe internal mass transfer limitations with little error. The terms of the model are given by: o q 15De ¼ 2 ðqeq qÞ ð1Þ ot rp where q is the mean adsorbed concentration within the particle, and qeq is the adsorbed phase concentration in equilibrium with bulk fluid for zeolite NaX/water pair defined by the following equation containing three Langmuir terms [3]: qeq ¼
qs;1 b1 P qs;2 b2 P qs;3 b3 P þ þ 1 þ b1 P 1 þ b2 P 1 þ b3 P
where qs,k and bk (k = 1, 2, and 3) are functions of temperature as follows: a1;k a2;k a3;k þ 2 þ 3 ðk ¼ 1; 2Þ qs;k ¼ a0;k þ T T T qs;3 ¼ 0:267 qs;1 qs;2
ð2Þ
ð3Þ
bk ¼ b0;k expðEk =T Þ The values of the parameters in Eq. (3) are given in the literature [3]. De is the equivalent diffusivity in the adsorbent particles, which can be calculated by the following equation: De ¼ D0 expðED =RT Þ
ð4Þ
where D0 and ED can be obtained from experimental data available in the literature [17]. 3.2. Energy conservation equations The model describes the process which is related to heat transfer between different components of the entire cooling system and mass transfer of refrigerant vapour in the adsorber. The energy equations for different components of the two adsorbers can be developed as follows: The energy balance on the thermal-fluid system yields oðqf C pf T f Þ oðqf C pf uf T f Þ o oT f 1 o oT f þ ¼ kf rkf þ ð5Þ ot oz oz r or oz or The energy balance for the metal tube gives oðqm C pm T m Þ o oT m 1 o oT m ¼ km rkm þ ot oz r or oz or
ð6Þ
The energy balance for the adsorbent can be described by oT s oðqg C pg uT s Þ 1 o ðrqg C pg vT s Þ þ ðqs C ps þ qs qC pa þ eqg C pg Þ þ r or oz ot o oT s 1 o oT s oq ¼ keq rkeq þ þ qs DH oz r or ot oz or
ð7Þ
where subscripts f, m and s denote the heat exchange fluid, metal tube and adsorbent, respectively.
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3.3. Mass conservation equations The overall mass conservation in the adsorber is oeqg o q þ r ðqg uÞ þ qs ¼ 0 ot ot where the water vapour velocity u is defined by the Darcy equation: K ap u¼ rP l
ð8Þ
ð9Þ
The apparent permeability Kap can be obtained by considering viscous flow and diffusion as follows [5]: ea l Dg K ap ¼ K þ ð10Þ sP The inherent permeability of the porous media, K, can be obtained from the semi-empirical Blake–Kozeny equation [18]: K¼
e3a d 2
ð11Þ
150 ð1 ea Þ2
The diffusivity of water vapour, Dg in Eq. (10), can be represented by the following equation [19]: Dg ¼ 1=ð1=Dm þ 1=Dk Þ
ð12Þ
where
and
pffiffiffiffiffiffiffiffiffiffiffiffi T 3 =M Dm ¼ 0:02628 P r2 X
ð13Þ
1=2 1=2 2rp 8RT T ¼ 97rp Dk ¼ M 3 pM
ð14Þ
Substituting Eq. (9) into Eq. (8) for simplicity of calculation, we obtain eM o P o qg K ap oP 1 o rqg K ap oP oq RT ¼ þ qs ot oz r or or ot l oz l
ð15Þ
The initial and boundary conditions are listed below to complete the numerical formulation of the problem. Initial conditions: t¼0
T f ðz; rÞ ¼ T m ðz; rÞ ¼ T s ðz; rÞ ¼ T a ;
P ¼ Pe
ð16Þ
Boundary conditions: T f jz¼0 ¼ T h;in
during the heating process
ð17Þ
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T f jz¼0 ¼ T c;in during the cooling process oT f ¼0 oz z¼L oT m oT m ¼ ¼0 oz z¼0 oz z¼L oT s oT s oT s ¼ ¼ ¼0 oz z¼0 oz z¼L or r¼R oP oP oP ¼ ¼ ¼0 oz z¼0 oz z¼L or r¼R
ð18Þ
P jz¼0 ¼ P jz¼L ¼ P jr¼R ¼ P e
when connected to the evaporator
ð23Þ
P jz¼0 ¼ P jz¼L ¼ P jr¼R ¼ P c
when connected to the condenser
ð24Þ
ð19Þ
ð20Þ
ð21Þ
ð22Þ
3.4. Performance coefficients The heat Qh supplied to the adsorbent bed during the two heating phases can be calculated from Z tc1=2 qf C pf S f ðT h;in T h;out Þ dt ð25Þ Qh ¼ 0
The cooling energy produced in the evaporator can be calculated from Z tc Lv ðT e Þ C pl ðT c T e Þ m_ w dt Qe ¼
ð26Þ
tc1=2
where m_ w is the mass flux of the water vapour entering the adsorber. By neglecting the mass of adsorbate gas in the adsorber, we obtain m_ w ¼ ms
o q ot
Thus, Eq. (26) becomes Z tc o q Qe ¼ Lv ðT e Þ C pl ðT c T e Þ ms dt ¼ ms Dq Lv ðT e Þ C pl ðT c T e Þ ot tc1=2
ð27Þ
ð28Þ
The cooling coefficient of performance is defined as: COP ¼
Qe Qh
ð29Þ
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The specific cooling power is defined as SCP ¼
Qe t c ms
ð30Þ
4. Numerical method The governing equations are solved by using the finite volume method which is described in detail by Patankar [20]. In the computational domain, a two-dimensional, non-uniform and staggered grid is used with a control volume formulation. The convection terms are discretized by using the power law scheme, the diffusion terms are discretized by the central difference scheme and the unsteady terms are discretized by the forward difference scheme. This algorithm provides a remarkably successful implicit method for simulating heat transfer in fluid flow. The discretized equations are solved by the line-by-line procedure, which is the combination of the Tri-Diagonal Matrix Algorithm (TDMA) and the Gauss–Seidel iteration technique. A time step of 0.01 s and 30 · 40 grids are chosen to ensure the reliability of the results. Under-relaxation factors are used to avoid divergence in the iterative solution of strongly non-linear phenomena. The under-relaxation factors for pressure and temperature are set to 0.5 and 0.8, respectively. The convergence criterion used in this method is 106.
5. Results and discussion The parameter values for the base case used in the numerical model are listed in Table 1. The effects of various operating conditions are discussed in the following sections. 5.1. Effect of condensing temperature (Tc) Fig. 3 shows the effect of Tc on the system performance. It can be seen that both COP and SCP decrease linearly with increasing condensing temperature over the range shown. When Tc increases, the condensing pressure also increases. From the Clapeyron diagram of the adsorption cycle (Fig. 1), it can be seen that the cycled adsorbate mass (qmax qmin) decreases for a lower condensing pressure with a fixed generation temperature. Eq. (28) shows that the cooling energy (Qe) is proportional to the cycled adsorbate mass. Thus, an increase in Tc will result in a reduction of COP. The cycle time also decreases with an increase in Tc. However, the decrease rate of cycle time is smaller than that of cooling energy when Tc increases. Hence, SCP also decreases with an increase in condensing temperature. Fig. 3 also suggests that a low condensing temperature would result in better performance. Since the condenser is usually cooled by either atmospheric air or water, the evaporating temperature is normally not lower than the room temperature. 5.2. Effect of evaporating temperature (Te) The effect of Te on system performance is shown in Fig. 4. As can be seen from this figure, both the COP and SCP increases as evaporating temperature increases. The Clapeyron diagram of the
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Table 1 Parameter values and operating conditions used in the model Name
Symbol
Value
Velocity of heat transfer fluid Generation temperature Initial adsorption temperature Fluid inlet temperature during heating Fluid inlet temperature during cooling Evaporator temperature Condenser temperature Density of adsorbent bed Specific heat of adsorbent bed Thermal conductivity of adsorbent bed Heat of adsorption Particle diameter Internal radius of metal tube External radius of metal tube External radius of adsorbent bed Length of adsorbent bed Macro-porosity of adsorbent bed Micro-porosity of adsorbent particle
uf Tg Ta Th,in Tc,in Te Tc qs Cps ks DH d R0 R1 R L ea ei
1 m/s 473 K 318 K 493 K 298 K 279 K 318 K 620 kg/m3 836 J/kg K 0.2 W/m K 3.2 · 106 J/kg 0.2 mm 0.020 m 0.021 m 0.036 m 0.6 m 0.38 0.42
70
0.80 0.75 0.70
COP SCP
COP
0.60
50
0.55 0.50 40
0.45
SCP, W/kg
60
0.65
0.40 30
0.35 0.30 0.25 280
290
300
310
320
330
340
350
20 360
Tc, K
Fig. 3. Variation of performance coefficients with condensing temperature.
adsorption cycle (Fig. 1) also shows that the cycled adsorbate mass will increase as Te is increased. The heat input from the heat exchange fluid (Qh) will also increase with Te. Its increase however is not as large as the increase of cycled adsorbate mass leading to an increase in the COP. Due to the fixed adsorption and generation temperatures, there is very little change in heat input from the heat exchange fluid. The difference in cycle time would be very small (within 3%) resulting in an increase in the SCP.
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60 58
0.46
56
COP
52 50 0.42 48
COP SCP
SCP, W/kg
54
0.44
46
0.40
44 42 40
0.38 265
270
275
280
285
290
Te, K
Fig. 4. Variation of performance coefficients with evaporating temperature.
5.3. Effect of adsorption temperature (Ta) From Fig. 5, it can be seen that the COP decreases with an increase in Ta and that there is a maximum value of SCP over the range of Ta investigated. From Fig. 1, when adsorption temperature decreases, the cycle adsorbate mass will increase and the heat input will need to be increased. The cycle time also increases with the reduction of Ta. The increased mass of cycle adsorbate relative to heat input will be greater contributing to an increase in the COP. Starting from a high value of Ta, the cycled adsorbate mass change proportional to the cycle time will be greater with a reduction of Ta causing SCP to increase. However, when Ta decreases below a certain value, the additional cycled adsorbate mass change proportional to the additional cycle time will decrease causing the SCP to decrease. It can also be seen from this figure that Ta has an optimal value with regards to system performance when other operating conditions are fixed. For the case under
54
0.46
52 0.44
50
46
COP
0.40
44 42
0.38 COP SCP Fitted curves
0.36
SCP, W/kg
48
0.42
40 38 36
0.34
34 0.32 300
320
340
360
380
Ta, K
Fig. 5. Variation of performance coefficients with adsorption temperature.
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COP
0.35 36 0.30 32 0.25
COP
0.20
SCP Fitted curves
SCP, W/kg
0.40
28 24
0.15 20 0.10 296
304
312
320
328
336
344
352
Tc/Ta, K
Fig. 6. Variation of performance coefficients with adsorption temperature in a three-temperature reservoir system.
study, an adsorption temperature in the range of 320–340 K will result in both high COP and SCP values. A suitable operating point in this temperature range will give a COP of about 0.43 and a SCP of about 50 W/kg. The three-heat reservoir system (high temperature reservoir, low temperature reservoir and medium temperature reservoir) is often employed in adsorption cooling systems. In this system, the adsorption and condensing temperatures are assumed to be the same because of the common medium temperature reservoir. Fig. 6 shows the effect of adsorption temperature on the system performance. From this figure, it can be seen that the optimal adsorption temperature and condensing temperature is about 310 K. 5.4. Effect of generation temperature (Tg) and driven temperature (Th,in) The effects of generation temperature on SCP with different driven temperatures (the temperature of heat exchange fluid during the heating process) are shown in Fig. 7. From the figure, it can be seen that SCP has a maximum value for every driven temperature. The reason is that the cycle adsorbate mass proportional to cycle time increases with an increase in generation temperature at low temperature. However, when the generation temperature approaches the driven temperature, the heat transfer rate between HXF and the adsorbent bed decreases. Thus, the cycle adsorbate mass will increase very little and the cycle time becomes longer, resulting in a decrease of SCP. Fig. 8 shows the effects of generation temperature on the COP for different driven temperatures. It can be seen from this figure that the COP is affected directly by the generation temperature and that the driven temperature has a negligible effect on COP. COP values increase asymptotically to a constant value for generation temperature beyond 480 K. The results agree with the findings of Cacciola and Restuccia [12]. The variation of heat input from HXF and cycled adsorbate mass with generation temperature Tg are shown in Fig. 9. From this figure, it can be seen that the heat input increases almost proportionately with cycled adsorbate mass. During Step 1, no cycled adsorbate is generated as the adsorber was disconnected from the condenser and the heat input in this step is about 6 · 104 J. For the large value of Tg the heat input during Step 1 compared
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80 70 60
SCP, W/kg
50 40
T h,in = 393 K
30
T h,in = 423 K 20
T h,in = 493 K T h,in = 523 K
10
T h,in = 573 K
0 360
380
400
420
440
460
480
500
520
540
560
500
Tg, K
Fig. 7. Variation of SCP with generation temperature for different driven temperatures.
0.45 0.40
COP
0.35 0.30
T h,in = 393 K T h,in = 423 K
0.25
T h,in = 493 K T h,in = 523 K
0.20
T h,in = 573 K
0.15 0.10 360
380
400
420
440
460
480
500
520
540
560
580
T g, K
Fig. 8. Variation of COP with generation temperature for different driven temperatures.
to the total heat input is very small. For example, it can be seen from Fig. 9 that the total heat input is more than 10 times that of the heat input in Step 1 when the generation temperature exceeds 480 K. The COP tends to a constant value as the generation temperature exceeds 480 K. The variation of performance coefficients with driven temperature, Tg at maximum SCP, is shown in Fig. 10. It can be seen that COP increases very sharply with driven temperature until approximately 493 K and assumes a constant value of about 0.45 beyond that temperature. The variation of maximum SCP with driven temperature is linear for the range of driven temperature investigated. It appears that using a higher driven temperature would result in a higher SCP. However, when the driven temperature exceeds 493 K, COP values higher than 0.45 cannot be attained.
1.2x10 6
0.30
1.0x10 6
0.25
8.0x10 5
0.20
6.0x10 5
0.15
heat input 4.0x10 5
0.10
cycled mass
2.0x10 5
Cycled mass, kg/kg
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Qh, J
1416
0.05
0.0 350
400
450
500
0.00 600
550
Tg, K
Fig. 9. Variation of heat input and cycled adsorbate mass with generation temperature.
90
0.5
80 0.4
60
0.3
COP
50 40
0.2
COP SCP(max)
0.1
30
SCP(max), W/kg
70
20 10
0.0
0 400
450
500
550
600
Th,in, K
Fig. 10. Variation of performance coefficients with driven temperature, Tg at maximum SCP.
5.5. Effect of velocity of the heat exchange fluid Table 2 shows the effect of the velocity of heat exchange fluid on the performance coefficients. The COP changes very little with the velocity of heat exchange fluid. For fluid velocities smaller than 0.1 m/s, the cycle time will increase very quickly with an increase in fluid velocity. Hence, the SCP increases significantly with an increase in fluid velocity. However, for velocity larger than Table 2 Variation of system performance with velocity of heat exchange fluid (HXF) Velocity of HXF (m/s)
0.01
0.1
0.5
1
2
5
COP SCP (W/kg) tc (s)
0.426 21.5 15,424
0.441 40.6 8448
0.442 47.4 7258
0.441 48.8 7076
0.441 49.2 6984
0.441 49.6 6926
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0.5 m/s, the cycle time does not change with velocity leading to very little change in SCP. To reduce operating energy cost, the optimal velocity of the heat exchange fluid should be in the range of 0.1–0.5 m/s. 6. Conclusions The effects of operating conditions on the system performance of a cooling system based on the Zeolite 13X/water working pair are investigated by using a two-dimensional non-equilibrium numerical model describing the combined heat and mass transfer in a cylindrical adsorbent bed. The following conclusions can be drawn: 1. The system performance in terms of both its COP and SCP varies almost linearly with condensing temperature (Tc) and evaporating temperature (Te). The performance coefficients increase with a reduction in Tc but with an increase in Te. 2. The adsorption temperature, Ta has an optimal value between 320 K and 340 K based on system performance for fixed operating conditions. The optimal Ta for the given case yields a COP of about 0.43 and a SCP of about 50 W/kg. For the three-temperature reservoir system, the optimal adsorption and condensing temperatures are about 310 K. 3. SCP has a maximum value within the range of generation temperature (Tg) investigated for a given driven temperature (Th,in). The maximum value of SCP increases linearly with an increase in Th,in. COP is directly affected by the generation temperature for different driven temperatures. It increases and tends to a constant value with an increase in Tg. 4. The cycle time increases significantly when the velocity of the HXF is smaller than 0.1 m/s but changes very little for velocities of HXF larger than 0.5 m/s. The optimal value of velocity of the heat exchange fluid lies within the range of 0.1–0.5 m/s. References [1] N. Douss, F. Meunier, Experimental study of cascading adsorption cycle, Chemical Engineering Science 44 (1989) 225–235. [2] F. Meunier, Solid sorption heat powered cycles for cooling and heat pumping applications, Applied Thermal Engineering 18 (1998) 715–729. [3] N. Ben Amar, L.M. Sun, F. Meunier, Numerical analysis of adsorptive temperature wave refrigerative heat pump, Applied Thermal Engineering 16 (1996) 405–418. [4] K.C.A. Alam, B.B. Saha, Y.T. Kang, A. Akisawa, T. Kashiwagi, Heat exchanger design effect on the system performance of silica gel adsorption refrigeration systems, International Journal of Heat and Mass Transfer 43 (2000) 4419–4431. [5] L.Z. Zhang, A three-dimensional non-equilibrium model for an intermittent adsorption cooling system, Solar Energy 69 (2000) 27–35. [6] T. Miltkau, B. Dawoud, Dynamic modeling of the combined heat and mass transfer during the adsorption/ desorption of water vapor into/from a zeolite layer of an adsorption heat pump, International Journal of Thermal Sciences 41 (2002) 753–762. [7] L. Marletta, G. Maggio, A. Freni, M. Ingrasciotta, G. Restuccia, A non-uniform temperature non-uniform pressure dynamic model of heat and mass transfer in compact adsorbent beds, International Journal of Heat and Mass Transfer 45 (2002) 3321–3330.
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[8] H.T. Chua, K.C. Ng, W. Wang, C. Yap, X.L. Wang, Transient modelling of a two-bed silica gel–water adsorption chiller, International Journal of Heat and Mass Transfer 47 (2004) 659–669. [9] K.C. Leong, Y. Liu, Numerical modeling of combined heat and mass transfer in the adsorbent bed of a zeolite/ water cooling system, Applied Thermal Engineering 47 (2004) 4761–4770. [10] L. Turner, Improvement of activated charcoal–ammonia adsorption heat pumping/refrigeration cycles— Investigation of porosity and heat/mass transfer characteristics, Ph.D. Thesis, University of Warwick, 1992. [11] L. Luo, M. Feidt, Thermodynamics of adsorption cycles: a theoretical study, Heat Transfer Engineering 13 (1992) 19–31. [12] G. Cacciola, G. Restuccia, Reversible adsorption heat pump: a thermodynamic model, International Journal of Refrigeration 18 (1995) 100–106. [13] B.B. Saha, E. Boelman, T. Kashiwagi, Computer simulation of a silica gel–water adsorption refrigeration cycle— the influence of operating conditions on cooling output and COP, ASHRAE Transactions: Research 101 (2) (1995) 348–357. [14] R.E. Critoph, S.J. Metcalf, Specific cooling power intensification limits in ammonia–carbon adsorption refrigeration systems, Applied Thermal Engineering 24 (2004) 661–678. [15] A. Sakoda, M. Suzuki, Fundamental study on solar power adsorption cooling system, Journal of Chemical Engineering of Japan 17 (1984) 52–57. [16] M.H. Chahbani, J. Labidi, J. Paris, Effect of mass transfer kinetics on the performance of adsorptive heat pump systems, Applied Thermal Engineering 22 (2002) 23–40. [17] Q. Wang, G. Chen, B. Han, The measurement of the equivalent diffusivity of adsorbent/adsorbent pair, Acta Energlae Solaris Sinica 22 (2001) 187–190. [18] R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, Wiley, New York, 1960, pp. 181–207. [19] M. Suzuki, Adsorption Engineering, Kodansha Ltd, Tokyo, 1990, pp. 63–93. [20] S.V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing Corporation, New York, 1980.
The effect of operating conditions on the performance of zeolite/water adsorption cooling systems Y. Liu, K.C. Leong
*
School of Mechanical and Production Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Republic of Singapore Received 28 June 2004; accepted 20 September 2004 Available online 21 November 2004
Abstract A numerical investigation of the effect of operating conditions on the thermal performance (coefficient of performance and specific cooling power) of an adsorption cooling system based on the Zeolite 13X/water working pair is presented in this paper. Both heat and mass transfer limitations are taken into account in the numerical model. DarcyÕs law and the linear driving force (LDF) model are used to describe the mass transfer limitation between the particles and within the particle, respectively. In this study, the effect of operating conditions such as adsorption temperature (Ta), generation temperature (Tg), condensing temperature (Tc), evaporating temperature (Te), the driven temperature of heat exchange fluid (Th,in) and the velocity of heat exchange fluid, on system performance were investigated. The results show that Ta, Tg, Tc and Te have significant effects on the system performance. For a given set of operating conditions, Ta and Tg possess optimal values based on the system performance. The driven temperature, Th,in was found to have negligible effect on the coefficient of performance although the optimal cooling power increases with Th,in. The cycle time decreases with an increase in fluid velocity, but this effect will be reduced for a high value of fluid velocity. The results of the numerical investigation will provide useful inputs to the development of an experimental adsorption cooling facility in the School of Mechanical and Production Engineering at the Nanyang Technological University. 2004 Elsevier Ltd. All rights reserved.
*
Corresponding author. Tel.: +65 6790 5596; fax: +65 6792 2619. E-mail address: [email protected] (K.C. Leong).
1359-4311/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2004.09.013
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Keywords: Adsorption cooling; Operating conditions; Numerical modelling; Coefficient of performance; Specific cooling power
1. Introduction Sorption cooling systems are environment friendly compared with traditional CFC systems as they employ safe and non-polluting refrigerants. Another advantage of sorption cooling systems is that they can be driven by low-grade energy such as waste heat or solar energy. Absorption and adsorption cycles are the two types of sorption cooling systems. Absorption cooling systems such as those using LiBr–H2O or H2O–NH3 pairs present many advantages for specific applications. They give better system efficiency than adsorption cooling systems. However, these systems also possess many limitations in operating conditions [1]. Compared with an absorption system, the adsorption cooling system has the advantages of mechanical simplicity and high reliability. As a result, it has been attracted much research attention in recent years. A big obstacle to the development of adsorption cycle technology is its low coefficient of performance. Research efforts by previous investigators have therefore been focused on improving the performance of the adsorption cooling system [2]. The performance of an adsorption cooling system is affected mainly by adsorption/adsorbate properties, configuration parameters and operating conditions. Recently, various heat and mass transfer models have been proposed to study the thermal performance in terms of the coefficient of performance (COP) and specific cooling power (SCP) of adsorptive cooling systems [3–9]. However, the effects of operating conditions on the thermal performance of such systems especially those pertaining to operating temperature effects are scarcely reported in the literature. The effect of operating conditions on the adsorption cooling cycle based on thermodynamic analyses has been investigated by a number of researchers [10–12]. These studies, however, did not account for the transient heat and mass transfer processes present in the adsorbent bed. Their results were therefore not presented in terms of the SCP. Saha et al. [13] proposed a lumped model and investigated the effects of operating conditions on the thermal performance of a silica gel/ water adsorption cycle. However, they excluded the effect of the adsorption temperature. Recently, Critoph and Metcalf [14] presented a one-dimensional transient model to study the effect of operating conditions on a carbon–ammonia system. The initial adsorption temperature effect was not considered in their investigation and micro-mass transfer limitations were neglected. In this paper, the effect of operating conditions on the thermal performance of a zeolite/water cooling cycle is presented based on a two-dimensional heat and mass transfer model elucidated by the authors [9]. Both heat and mass transfer limitations are considered in this model. The aim is to provide useful guidelines for the selection of operating conditions of an adsorption cooling system.
2. System description The basic adsorption cooling system consists of a solid adsorbent bed, which is alternately connected to a condenser and an evaporator. An adsorption cooling system works on an adsorption–
Y. Liu, K.C. Leong / Applied Thermal Engineering 25 (2005) 1403–1418
Nomenclature Cp COP d D0 De Dek Dk Dm K L Lv _ m M P Ps q r R S Sf SCP t tc tc1/2 T Ta Tc Te Tg u uf u V Z Greek DH e ea ei
specific heat (J/kg K) coefficient of performance particle diameter (m) reference diffusivity (m2/s) equivalent diffusivity in the adsorbent particles (m2/s) equivalent Knudsen diffusivity (m2/s) Knudsen diffusivity (m2/s) molecular diffusivity (m2/s) permeability of adsorbent bed (m2) the length of adsorbent bed latent heat of vaporization (J/kg) total mass flow flux of water vapour (kg/s m2) molar mass (kg/mol) pressure (Pa) saturation pressure (Pa) adsorbed concentration (kg/kg) radial coordinate (m) universal gas constant (J/kmol K); adsorbent bed radius (m) area of adsorbent bed surface (m2) cross-sectional area of heat exchange fluid specific cooling power (W/kg) time (s) cycle time (s) the first half cycle time (s) temperature (K) initial adsorption temperature condensing temperature evaporating temperature generation temperature gaseous velocity in axial direction (m/s) fluid velocity (m/s) gaseous velocity vector (m/s) gaseous velocity in radial direction axial coordinate (m) symbols heat of adsorption (J/kg) total bed porosity macro-porosity of the bed micro-porosity of the particle
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k l r s X
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thermal conductivity (W/m K) viscosity (N/s m) ˚) collision diameter for Lennard-Jones potential (A tortuosity collision integral
Subscripts a adsorbed phase c condensing e evaporating f heat exchange fluid g water vapour h heating in inlet fluid m metal tube out outlet fluid s adsorbent
desorption cycle. This cycle can be represented on a Clapeyron diagram (ln P vs 1/T) as shown in Fig. 1. The entire process consists of four steps. At the beginning of Step 1 (A–B), the adsorbent contains a high concentration of adsorbate (qmax) with an initial ambient temperature of Ta. During this step, the adsorbent bed is heated at a constant concentration of adsorbate. When the vapour pressure in the adsorbent bed is equal to the condensing pressure (Pc), Step 2 (B–C) begins with the opening of a valve between the adsorber and the condenser. The adsorbate gas desorbed from the adsorber is cooled to a temperature Tc until it condenses in either a water or an aircooled condenser. At the end of Step 2, the maximum temperature (Tg) of the adsorbent bed is
lnP Saturation qmax line Pc
qmin B
C
Pe A
Te
Tc Ta
D
Tg
-1/T
Fig. 1. Clapeyron diagram of an adsorption cooling cycle.
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Fig. 2. Schematic diagram of adsorber.
reached and the bed is disconnected from the condenser. During Step 3 (C–D), the adsorber is cooled at a constant adsorbed concentration (qmin). The pressure in the bed decreases from Pc to Pe. Step 4 (D–A) begins with the connection between the adsorbent bed to the evaporator. The adsorbate liquid evaporates from the evaporator and is adsorbed by the cooling bed. The heat exchange fluid (HXF) which flows through the adsorber is used to heat or cool the adsorber. The refrigerant is transferred to the condenser or from the evaporator through the gas path of the adsorber as shown in Fig. 2.
3. Mathematical modelling A schematic of the adsorber is shown in Fig. 2. The modelling of the adsorber involves heat and mass conservation equations for HXF, the metal tube and the adsorbent bed. The following assumptions are made: 1. The adsorbed phase is considered as a liquid, and the adsorbate gas is assumed to be an ideal gas. 2. The adsorbent bed is composed of uniformly sized particles with isotropic properties. 3. The properties of the fluid, the metal tube and adsorbate vapour are constant. 4. There are no heat losses in the adsorption cycle. 5. The thermal resistance between the metal tube and the adsorbent bed is neglected.
3.1. Adsorption equations In most of the previous studies, the equilibrium adsorption model has been assumed and the internal mass transfer resistance between solid and adsorbate gas phases is neglected. The linear driving force (LDF) equation is used to account for mass transfer resistance within the adsorbent particles as proposed by Sakoda and Suzuki [15]. Chahbani et al. [16] pointed out that the LDF
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model could be used to describe internal mass transfer limitations with little error. The terms of the model are given by: o q 15De ¼ 2 ðqeq qÞ ð1Þ ot rp where q is the mean adsorbed concentration within the particle, and qeq is the adsorbed phase concentration in equilibrium with bulk fluid for zeolite NaX/water pair defined by the following equation containing three Langmuir terms [3]: qeq ¼
qs;1 b1 P qs;2 b2 P qs;3 b3 P þ þ 1 þ b1 P 1 þ b2 P 1 þ b3 P
where qs,k and bk (k = 1, 2, and 3) are functions of temperature as follows: a1;k a2;k a3;k þ 2 þ 3 ðk ¼ 1; 2Þ qs;k ¼ a0;k þ T T T qs;3 ¼ 0:267 qs;1 qs;2
ð2Þ
ð3Þ
bk ¼ b0;k expðEk =T Þ The values of the parameters in Eq. (3) are given in the literature [3]. De is the equivalent diffusivity in the adsorbent particles, which can be calculated by the following equation: De ¼ D0 expðED =RT Þ
ð4Þ
where D0 and ED can be obtained from experimental data available in the literature [17]. 3.2. Energy conservation equations The model describes the process which is related to heat transfer between different components of the entire cooling system and mass transfer of refrigerant vapour in the adsorber. The energy equations for different components of the two adsorbers can be developed as follows: The energy balance on the thermal-fluid system yields oðqf C pf T f Þ oðqf C pf uf T f Þ o oT f 1 o oT f þ ¼ kf rkf þ ð5Þ ot oz oz r or oz or The energy balance for the metal tube gives oðqm C pm T m Þ o oT m 1 o oT m ¼ km rkm þ ot oz r or oz or
ð6Þ
The energy balance for the adsorbent can be described by oT s oðqg C pg uT s Þ 1 o ðrqg C pg vT s Þ þ ðqs C ps þ qs qC pa þ eqg C pg Þ þ r or oz ot o oT s 1 o oT s oq ¼ keq rkeq þ þ qs DH oz r or ot oz or
ð7Þ
where subscripts f, m and s denote the heat exchange fluid, metal tube and adsorbent, respectively.
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3.3. Mass conservation equations The overall mass conservation in the adsorber is oeqg o q þ r ðqg uÞ þ qs ¼ 0 ot ot where the water vapour velocity u is defined by the Darcy equation: K ap u¼ rP l
ð8Þ
ð9Þ
The apparent permeability Kap can be obtained by considering viscous flow and diffusion as follows [5]: ea l Dg K ap ¼ K þ ð10Þ sP The inherent permeability of the porous media, K, can be obtained from the semi-empirical Blake–Kozeny equation [18]: K¼
e3a d 2
ð11Þ
150 ð1 ea Þ2
The diffusivity of water vapour, Dg in Eq. (10), can be represented by the following equation [19]: Dg ¼ 1=ð1=Dm þ 1=Dk Þ
ð12Þ
where
and
pffiffiffiffiffiffiffiffiffiffiffiffi T 3 =M Dm ¼ 0:02628 P r2 X
ð13Þ
1=2 1=2 2rp 8RT T ¼ 97rp Dk ¼ M 3 pM
ð14Þ
Substituting Eq. (9) into Eq. (8) for simplicity of calculation, we obtain eM o P o qg K ap oP 1 o rqg K ap oP oq RT ¼ þ qs ot oz r or or ot l oz l
ð15Þ
The initial and boundary conditions are listed below to complete the numerical formulation of the problem. Initial conditions: t¼0
T f ðz; rÞ ¼ T m ðz; rÞ ¼ T s ðz; rÞ ¼ T a ;
P ¼ Pe
ð16Þ
Boundary conditions: T f jz¼0 ¼ T h;in
during the heating process
ð17Þ
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T f jz¼0 ¼ T c;in during the cooling process oT f ¼0 oz z¼L oT m oT m ¼ ¼0 oz z¼0 oz z¼L oT s oT s oT s ¼ ¼ ¼0 oz z¼0 oz z¼L or r¼R oP oP oP ¼ ¼ ¼0 oz z¼0 oz z¼L or r¼R
ð18Þ
P jz¼0 ¼ P jz¼L ¼ P jr¼R ¼ P e
when connected to the evaporator
ð23Þ
P jz¼0 ¼ P jz¼L ¼ P jr¼R ¼ P c
when connected to the condenser
ð24Þ
ð19Þ
ð20Þ
ð21Þ
ð22Þ
3.4. Performance coefficients The heat Qh supplied to the adsorbent bed during the two heating phases can be calculated from Z tc1=2 qf C pf S f ðT h;in T h;out Þ dt ð25Þ Qh ¼ 0
The cooling energy produced in the evaporator can be calculated from Z tc Lv ðT e Þ C pl ðT c T e Þ m_ w dt Qe ¼
ð26Þ
tc1=2
where m_ w is the mass flux of the water vapour entering the adsorber. By neglecting the mass of adsorbate gas in the adsorber, we obtain m_ w ¼ ms
o q ot
Thus, Eq. (26) becomes Z tc o q Qe ¼ Lv ðT e Þ C pl ðT c T e Þ ms dt ¼ ms Dq Lv ðT e Þ C pl ðT c T e Þ ot tc1=2
ð27Þ
ð28Þ
The cooling coefficient of performance is defined as: COP ¼
Qe Qh
ð29Þ
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The specific cooling power is defined as SCP ¼
Qe t c ms
ð30Þ
4. Numerical method The governing equations are solved by using the finite volume method which is described in detail by Patankar [20]. In the computational domain, a two-dimensional, non-uniform and staggered grid is used with a control volume formulation. The convection terms are discretized by using the power law scheme, the diffusion terms are discretized by the central difference scheme and the unsteady terms are discretized by the forward difference scheme. This algorithm provides a remarkably successful implicit method for simulating heat transfer in fluid flow. The discretized equations are solved by the line-by-line procedure, which is the combination of the Tri-Diagonal Matrix Algorithm (TDMA) and the Gauss–Seidel iteration technique. A time step of 0.01 s and 30 · 40 grids are chosen to ensure the reliability of the results. Under-relaxation factors are used to avoid divergence in the iterative solution of strongly non-linear phenomena. The under-relaxation factors for pressure and temperature are set to 0.5 and 0.8, respectively. The convergence criterion used in this method is 106.
5. Results and discussion The parameter values for the base case used in the numerical model are listed in Table 1. The effects of various operating conditions are discussed in the following sections. 5.1. Effect of condensing temperature (Tc) Fig. 3 shows the effect of Tc on the system performance. It can be seen that both COP and SCP decrease linearly with increasing condensing temperature over the range shown. When Tc increases, the condensing pressure also increases. From the Clapeyron diagram of the adsorption cycle (Fig. 1), it can be seen that the cycled adsorbate mass (qmax qmin) decreases for a lower condensing pressure with a fixed generation temperature. Eq. (28) shows that the cooling energy (Qe) is proportional to the cycled adsorbate mass. Thus, an increase in Tc will result in a reduction of COP. The cycle time also decreases with an increase in Tc. However, the decrease rate of cycle time is smaller than that of cooling energy when Tc increases. Hence, SCP also decreases with an increase in condensing temperature. Fig. 3 also suggests that a low condensing temperature would result in better performance. Since the condenser is usually cooled by either atmospheric air or water, the evaporating temperature is normally not lower than the room temperature. 5.2. Effect of evaporating temperature (Te) The effect of Te on system performance is shown in Fig. 4. As can be seen from this figure, both the COP and SCP increases as evaporating temperature increases. The Clapeyron diagram of the
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Table 1 Parameter values and operating conditions used in the model Name
Symbol
Value
Velocity of heat transfer fluid Generation temperature Initial adsorption temperature Fluid inlet temperature during heating Fluid inlet temperature during cooling Evaporator temperature Condenser temperature Density of adsorbent bed Specific heat of adsorbent bed Thermal conductivity of adsorbent bed Heat of adsorption Particle diameter Internal radius of metal tube External radius of metal tube External radius of adsorbent bed Length of adsorbent bed Macro-porosity of adsorbent bed Micro-porosity of adsorbent particle
uf Tg Ta Th,in Tc,in Te Tc qs Cps ks DH d R0 R1 R L ea ei
1 m/s 473 K 318 K 493 K 298 K 279 K 318 K 620 kg/m3 836 J/kg K 0.2 W/m K 3.2 · 106 J/kg 0.2 mm 0.020 m 0.021 m 0.036 m 0.6 m 0.38 0.42
70
0.80 0.75 0.70
COP SCP
COP
0.60
50
0.55 0.50 40
0.45
SCP, W/kg
60
0.65
0.40 30
0.35 0.30 0.25 280
290
300
310
320
330
340
350
20 360
Tc, K
Fig. 3. Variation of performance coefficients with condensing temperature.
adsorption cycle (Fig. 1) also shows that the cycled adsorbate mass will increase as Te is increased. The heat input from the heat exchange fluid (Qh) will also increase with Te. Its increase however is not as large as the increase of cycled adsorbate mass leading to an increase in the COP. Due to the fixed adsorption and generation temperatures, there is very little change in heat input from the heat exchange fluid. The difference in cycle time would be very small (within 3%) resulting in an increase in the SCP.
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60 58
0.46
56
COP
52 50 0.42 48
COP SCP
SCP, W/kg
54
0.44
46
0.40
44 42 40
0.38 265
270
275
280
285
290
Te, K
Fig. 4. Variation of performance coefficients with evaporating temperature.
5.3. Effect of adsorption temperature (Ta) From Fig. 5, it can be seen that the COP decreases with an increase in Ta and that there is a maximum value of SCP over the range of Ta investigated. From Fig. 1, when adsorption temperature decreases, the cycle adsorbate mass will increase and the heat input will need to be increased. The cycle time also increases with the reduction of Ta. The increased mass of cycle adsorbate relative to heat input will be greater contributing to an increase in the COP. Starting from a high value of Ta, the cycled adsorbate mass change proportional to the cycle time will be greater with a reduction of Ta causing SCP to increase. However, when Ta decreases below a certain value, the additional cycled adsorbate mass change proportional to the additional cycle time will decrease causing the SCP to decrease. It can also be seen from this figure that Ta has an optimal value with regards to system performance when other operating conditions are fixed. For the case under
54
0.46
52 0.44
50
46
COP
0.40
44 42
0.38 COP SCP Fitted curves
0.36
SCP, W/kg
48
0.42
40 38 36
0.34
34 0.32 300
320
340
360
380
Ta, K
Fig. 5. Variation of performance coefficients with adsorption temperature.
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Y. Liu, K.C. Leong / Applied Thermal Engineering 25 (2005) 1403–1418 52 0.50 48 0.45 44 40
COP
0.35 36 0.30 32 0.25
COP
0.20
SCP Fitted curves
SCP, W/kg
0.40
28 24
0.15 20 0.10 296
304
312
320
328
336
344
352
Tc/Ta, K
Fig. 6. Variation of performance coefficients with adsorption temperature in a three-temperature reservoir system.
study, an adsorption temperature in the range of 320–340 K will result in both high COP and SCP values. A suitable operating point in this temperature range will give a COP of about 0.43 and a SCP of about 50 W/kg. The three-heat reservoir system (high temperature reservoir, low temperature reservoir and medium temperature reservoir) is often employed in adsorption cooling systems. In this system, the adsorption and condensing temperatures are assumed to be the same because of the common medium temperature reservoir. Fig. 6 shows the effect of adsorption temperature on the system performance. From this figure, it can be seen that the optimal adsorption temperature and condensing temperature is about 310 K. 5.4. Effect of generation temperature (Tg) and driven temperature (Th,in) The effects of generation temperature on SCP with different driven temperatures (the temperature of heat exchange fluid during the heating process) are shown in Fig. 7. From the figure, it can be seen that SCP has a maximum value for every driven temperature. The reason is that the cycle adsorbate mass proportional to cycle time increases with an increase in generation temperature at low temperature. However, when the generation temperature approaches the driven temperature, the heat transfer rate between HXF and the adsorbent bed decreases. Thus, the cycle adsorbate mass will increase very little and the cycle time becomes longer, resulting in a decrease of SCP. Fig. 8 shows the effects of generation temperature on the COP for different driven temperatures. It can be seen from this figure that the COP is affected directly by the generation temperature and that the driven temperature has a negligible effect on COP. COP values increase asymptotically to a constant value for generation temperature beyond 480 K. The results agree with the findings of Cacciola and Restuccia [12]. The variation of heat input from HXF and cycled adsorbate mass with generation temperature Tg are shown in Fig. 9. From this figure, it can be seen that the heat input increases almost proportionately with cycled adsorbate mass. During Step 1, no cycled adsorbate is generated as the adsorber was disconnected from the condenser and the heat input in this step is about 6 · 104 J. For the large value of Tg the heat input during Step 1 compared
Y. Liu, K.C. Leong / Applied Thermal Engineering 25 (2005) 1403–1418
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80 70 60
SCP, W/kg
50 40
T h,in = 393 K
30
T h,in = 423 K 20
T h,in = 493 K T h,in = 523 K
10
T h,in = 573 K
0 360
380
400
420
440
460
480
500
520
540
560
500
Tg, K
Fig. 7. Variation of SCP with generation temperature for different driven temperatures.
0.45 0.40
COP
0.35 0.30
T h,in = 393 K T h,in = 423 K
0.25
T h,in = 493 K T h,in = 523 K
0.20
T h,in = 573 K
0.15 0.10 360
380
400
420
440
460
480
500
520
540
560
580
T g, K
Fig. 8. Variation of COP with generation temperature for different driven temperatures.
to the total heat input is very small. For example, it can be seen from Fig. 9 that the total heat input is more than 10 times that of the heat input in Step 1 when the generation temperature exceeds 480 K. The COP tends to a constant value as the generation temperature exceeds 480 K. The variation of performance coefficients with driven temperature, Tg at maximum SCP, is shown in Fig. 10. It can be seen that COP increases very sharply with driven temperature until approximately 493 K and assumes a constant value of about 0.45 beyond that temperature. The variation of maximum SCP with driven temperature is linear for the range of driven temperature investigated. It appears that using a higher driven temperature would result in a higher SCP. However, when the driven temperature exceeds 493 K, COP values higher than 0.45 cannot be attained.
1.2x10 6
0.30
1.0x10 6
0.25
8.0x10 5
0.20
6.0x10 5
0.15
heat input 4.0x10 5
0.10
cycled mass
2.0x10 5
Cycled mass, kg/kg
Y. Liu, K.C. Leong / Applied Thermal Engineering 25 (2005) 1403–1418
Qh, J
1416
0.05
0.0 350
400
450
500
0.00 600
550
Tg, K
Fig. 9. Variation of heat input and cycled adsorbate mass with generation temperature.
90
0.5
80 0.4
60
0.3
COP
50 40
0.2
COP SCP(max)
0.1
30
SCP(max), W/kg
70
20 10
0.0
0 400
450
500
550
600
Th,in, K
Fig. 10. Variation of performance coefficients with driven temperature, Tg at maximum SCP.
5.5. Effect of velocity of the heat exchange fluid Table 2 shows the effect of the velocity of heat exchange fluid on the performance coefficients. The COP changes very little with the velocity of heat exchange fluid. For fluid velocities smaller than 0.1 m/s, the cycle time will increase very quickly with an increase in fluid velocity. Hence, the SCP increases significantly with an increase in fluid velocity. However, for velocity larger than Table 2 Variation of system performance with velocity of heat exchange fluid (HXF) Velocity of HXF (m/s)
0.01
0.1
0.5
1
2
5
COP SCP (W/kg) tc (s)
0.426 21.5 15,424
0.441 40.6 8448
0.442 47.4 7258
0.441 48.8 7076
0.441 49.2 6984
0.441 49.6 6926
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0.5 m/s, the cycle time does not change with velocity leading to very little change in SCP. To reduce operating energy cost, the optimal velocity of the heat exchange fluid should be in the range of 0.1–0.5 m/s. 6. Conclusions The effects of operating conditions on the system performance of a cooling system based on the Zeolite 13X/water working pair are investigated by using a two-dimensional non-equilibrium numerical model describing the combined heat and mass transfer in a cylindrical adsorbent bed. The following conclusions can be drawn: 1. The system performance in terms of both its COP and SCP varies almost linearly with condensing temperature (Tc) and evaporating temperature (Te). The performance coefficients increase with a reduction in Tc but with an increase in Te. 2. The adsorption temperature, Ta has an optimal value between 320 K and 340 K based on system performance for fixed operating conditions. The optimal Ta for the given case yields a COP of about 0.43 and a SCP of about 50 W/kg. For the three-temperature reservoir system, the optimal adsorption and condensing temperatures are about 310 K. 3. SCP has a maximum value within the range of generation temperature (Tg) investigated for a given driven temperature (Th,in). The maximum value of SCP increases linearly with an increase in Th,in. COP is directly affected by the generation temperature for different driven temperatures. It increases and tends to a constant value with an increase in Tg. 4. The cycle time increases significantly when the velocity of the HXF is smaller than 0.1 m/s but changes very little for velocities of HXF larger than 0.5 m/s. The optimal value of velocity of the heat exchange fluid lies within the range of 0.1–0.5 m/s. References [1] N. Douss, F. Meunier, Experimental study of cascading adsorption cycle, Chemical Engineering Science 44 (1989) 225–235. [2] F. Meunier, Solid sorption heat powered cycles for cooling and heat pumping applications, Applied Thermal Engineering 18 (1998) 715–729. [3] N. Ben Amar, L.M. Sun, F. Meunier, Numerical analysis of adsorptive temperature wave refrigerative heat pump, Applied Thermal Engineering 16 (1996) 405–418. [4] K.C.A. Alam, B.B. Saha, Y.T. Kang, A. Akisawa, T. Kashiwagi, Heat exchanger design effect on the system performance of silica gel adsorption refrigeration systems, International Journal of Heat and Mass Transfer 43 (2000) 4419–4431. [5] L.Z. Zhang, A three-dimensional non-equilibrium model for an intermittent adsorption cooling system, Solar Energy 69 (2000) 27–35. [6] T. Miltkau, B. Dawoud, Dynamic modeling of the combined heat and mass transfer during the adsorption/ desorption of water vapor into/from a zeolite layer of an adsorption heat pump, International Journal of Thermal Sciences 41 (2002) 753–762. [7] L. Marletta, G. Maggio, A. Freni, M. Ingrasciotta, G. Restuccia, A non-uniform temperature non-uniform pressure dynamic model of heat and mass transfer in compact adsorbent beds, International Journal of Heat and Mass Transfer 45 (2002) 3321–3330.
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