Performance evaluation of multi-stage, multi-bed adsorption chiller employing re-heat scheme

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Renewable Energy 33 (2008) 88–98 www.elsevier.com/locate/renene

Performance evaluation of multi-stage, multi-bed adsorption chiller employing re-heat scheme M.Z.I. Khana,,1, K.C.A. Alamb, B.B. Sahac, A. Akisawaa, T. Kashiwagia a

Graduate School of Bio-Applications and Systems Engineering, Tokyo University of A & T, 2-24-16, Naka-machi, Koganei, Tokyo 184-8588, Japan b Department of Mathematics, COMSATS Institute of Information Technology, Islamabad, Pakistan c Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, 6-1 Kasuga-koen, Kasuga-shi, Fukuoka 816-8580, Japan Received 26 September 2006; accepted 21 January 2007 Available online 26 March 2007

Abstract This paper deals with the performance investigation of a silica gel/water-based multi-stage, multi-bed, six-bed adsorption chiller employing re-heat scheme. The innovative chiller is powered by waste heat or renewable energy sources of temperature between 50 and 70 1C along with a coolant of inlet temperature at 30 1C for air-conditioning purpose. The performance of the six-bed adsorption chiller using re-heat scheme is compared with that of the six-bed chiller without re-heat. With the same operating conditions, such as the heat transfer fluid inlet (HTF) temperatures, HTF flow rates, adsorption/desorption cycle time and same chiller physical dimension, it is found that both the cooling capacity (CC) and the coefficient of performance (COP) of the three-stage chiller with re-heat scheme are superior than those of the three-stage chiller without re-heat scheme. r 2007 Elsevier Ltd. All rights reserved. Keywords: Re-heat scheme; Renewable energy utilization; Silica gel/water; Three-stage chiller; Thermal capacitance ratio

1. Introduction The environment-friendly adsorption cooling system is an attractive alternative to the traditional CFC or HCFCbased vapor-compression cooling system as it employs safe and natural refrigerants. Another advantage of such adsorption cooling systems is that they can be driven by low-grade energy such as waste heat or solar energy. As a result, adsorption cooling systems have attracted considerable attentions in recent years. Adsorption cooling system is a noiseless, non-corrosive and environment-friendly energy conversion system. So, many researchers around the world have made significant efforts to study such a cooling system in order to commercialize it. Following are some representative examples. The silica gel/water adsorption chiller driven by the waste heat source has been successfully commercialized in Corresponding author. Tel./fax: +81 42 388 7282.

E-mail address: [email protected] (M.Z.I. Khan). On leave of absence from Mathematics Department, Bangladesh University of Engineering and Technology, Dhaka 1000, Bangladesh. 1

0960-1481/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2007.01.012

Japan, as reported by Saha et al. [1]. Waste heat at the temperature between 50 and 90 1C abounds in industry. It is seldom utilized, but usually discharged into the environment at present. Compared with the single-stage LiBr– water absorption chiller, the silica gel/water adsorption chiller can effectively use such low waste heat without corrosion or crystallization. Moreover, it need not consume electric energy to drive the solution pump. Multi-bed, multi-stage or dual-mode adsorption chillers have been successfully developed in order to utilize low-grade waste heat. Saha et al. [2] designed a three-bed silica gel/water adsorption chiller and developed a cycle simulation computer program to predict its performance. For the three-bed chiller, waste heat recovery efficiency is about 35% higher than that of the two-bed system, and the coefficient of performance (COP) value is 0.38 with a driving source temperature at 80 1C and the coolant and chilled water inlet temperatures at 30 and 14 1C, respectively. A similar study has been carried out by Khan et al. [3] applying mass recovery scheme in the three-bed silica gel/water adsorption chiller. The mass recovery scheme yields higher performance. In the three-bed mass recovery

ARTICLE IN PRESS M.Z.I. Khan et al. / Renewable Energy 33 (2008) 88–98

Nomenclature A C Dso Ea L _ m Ps q q* Qst R Rp T t U

area (m2) specific heat (J kg1 K1) surface specific heat (m2 s1) activation energy (J kg1) latent heat of vaporization (J kg1) mass flow rate (kg s1) saturated vapor pressure (Pa) concentration, kg refrigerant/kg adsorbent concentration equilibrium, kg refrigerant/kg adsorbent isosteric heat of adsorption (J kg1) gas constant (J kg1 K1) average radius of a particle (m) temperature (K) time (s) heat transfer coefficient (W m2 K1)

chiller, first two beds are in mass recovery process isolating from both evaporator and condenser, and at the same time third bed is connected with evaporator to enhance cooling effect. In another endeavor, Saha et al. [4] developed a three-stage adsorption chiller which utilized about 50 1C waste heat as the driving source and 30 1C cooling water as the cooling source. In Ref. [5], a multi-bed regenerative adsorption chiller design has been proposed. The simulation results have showed that, using the same waste heat source, a four-bed chiller generated 70% refrigerating capacity improvement compared with a typical two-bed chiller, and a six-bed chiller generated 40% refrigerating capacity improvement compared with a four-bed chiller. Alam et al. [6] proposed and analyzed re-heat two-stage adsorption chiller which can be operated with driving heat source temperature range between 50 and 90 1C along with a heat sink at 30 1C. COP of the re-heat two-stage chiller is higher than that of two-stage chiller and also found, the reheat two-stage chiller produces effective cooling even though heat source temperature fluctuated between 50 and 90 1C. Saha et al. [7] analyzed experimentally a twostage adsorption chiller without reheat scheme. Khan et al. [8] analyzed parametrically the two-stage adsorption chiller using re-heat scheme. In his paper, the influence of overall thermal conductance values of adsorption elements and evaporator as well as adsorbent mass on the chiller performance is discussed. To improve the performance, many researchers proposed various simulation models. Chua et al. [9,10] presented analytical studies of a two-bed silica gel/water adsorption chiller with a lump parameter model (a distributed-parameter model). Recently, Critoph and Metcalf [11] presented a one-dimensional transient model to study the effect of operating conditions on a carbon–ammonia system. The initial adsorption temperature effect is not considered in their investigation and micro-

W

89

weight (kg)

Subscripts ads cond chill cw des eva hex hw in out s w wv

adsorber, adsorption condenser chilled water cooling water desorber, desorption evaporator heat exchanger hot water inlet outlet silica gel water water vapor

mass transfer limitations are neglected. The performance of an adsorption cooling system is affected mainly by adsorption/adsorbate properties, configuration parameters and operating conditions. Various heat and mass transfer models have been proposed to study the thermal performance in terms of the COP and specific cooling power (SCP) of adsorptive cooling systems [12–17]. However, the effects of operating conditions on the thermal performance of such systems are scarcely reported in the literature. Llobet and Goetz [18] proposed a thermodynamic model on such rotary system for the continuous operation using the concept of heat regeneration in steady state. The energy performance of the continuous system is measured in terms of COP and cold production capacity. It is reported that the number of transfer units (NTU) of the heat exchanger is the main parameter. A similar study has been carried out by Critoph [19] who developed a one-dimensional radial conduction model to simulate a continuous multiple-bed regenerative adsorption cycle. By using simple governing equations, the performance of the system consisting of 32 tubular adsorption modules has been predicted. The effect of key parameters such as thermal capacity ratio, number of modules, generator heat transfer coefficient, and evaporator air inlet temperature on the system performance has been also studied. However, some assumptions on which their model is based are so ideal that cannot reflect quantitatively the realistic situation. Another problem is that though NTU is used as a characteristic parameter in analyzing adsorbent bed [18,20], it is an indicative parameter of the size of the heat exchanger, which includes the combined influence of heat transfer coefficient and the velocity of heat transfer fluid, and cannot be varied independently. Hence, NTU cannot be considered as independent value which influences the performance of the system in terms of individual parameters.

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The present paper investigates the utilization of unexploited, near ambient temperature waste heat between 50 and 70 1C as the driving heat source with a cooling source at 30 1C using a lump parameter model. The influences of heat transfer fluid inlet (HTF) temperatures on cooling capacity (CC), COP and chilled water outlet temperature, silica gel mass on thermal capacitance ratio as well as cycle time and mass recovery time effect on CC and COP are determined. Performances are also compared with that of a conventional three-stage chiller without re-heat scheme. 2. Working principle 2.1. Three-stage chiller without re-heat scheme Most of the advanced cycles in adsorption refrigeration/ heat pump are proposed to achieve high COP and/or SCP values. Few cycles, however, are proposed to utilize relatively low-temperature waste heat sources. Multi-stage advanced adsoprtion cycle is the cycle that can use lowtemperature (45–60 1C) heat source with a fixed nearenvironmental temperature heat sinks (30 1C). If chilled water at 7 1C is to be obtained with conventional adsorbent/refrigerant pair such as silica gel/water, a conventional single-stage cycle will not be operational with such a low-temperature waste heat (Fig. 1(b)). The reason is that the regenerating temperature lift of 15–30 K is too small for an evaporating temperature lift of 23 K to be spanned by raising the pressure in one single stage. In order to overcome the technical difficulty intrinsic in operating a refrigeration cycle, with such a small regenerating temperature lift, a three-stage adsorption cycle without re-heat scheme is proposed and designed by Saha et al. [4]. In the three-stage adsorption cycle without re-heat scheme, the regenerating temperature lift of the adsorbent can be small because the refrigerant evaporating temperature (or pressure) lift is split into three smaller temperature lifts (Fig. 1(b)). Pressure thus rises into three progressive steps from evaporation to condensation level. To achieve this, the introduction of two additional pairs of adsorbent beds is necessary (Fig. 1(a)). Although the operating pressure levels are different, adsorption/desorption temperatures are kept equal for the three beds. Hence, each of three pairs of beds must be cooled and heated in parallel, which in principle triplicates the heat input required to drive the chiller. The increased need for driving heat input, however, is less pronounced for temperatures such as 50 1C heat source with a heat sink at 30 1C, since the heat losses inherent in batched cycle operation decrease with smaller temperature lifts. To describe the cycle of the system, it is assumed that Hex1, Hex4 and Hex5 are in cooling position at temperature Tc while Hex2, Hex3 and Hex6 are in heating position at temperature Th (Fig. 1(a)). At the beginning of the cycle all valves are closed. The desorbers (Hex2, Hex3 and Hex6) are heated by hot water while adsorbers (Hex1, Hex4 and Hex5) are cooled by cooling water. During a

short intermediate process (30 s for the present system) no adsorption/ desorption occurs. After this short period, valves 1, 3, 6 and 8 are opened to allow refrigerant to flow from Hex2 to condenser, Hex6 to Hex4, Hex3 to Hex1 and from evaporator to Hex5. When refrigerant concentrations in the adsorbers and desorbers are near their equilibrium level, the flows of hot and cooling water are redirected by switching the valves so that the desorber can change its mode into adsorber, and adsorber into desorber. The adsorption/desorption process can be continued by changing the direction of hot and cooling water flow. The standard operational strategy (without re-heat scheme) is shown in Table 1. Saha et al. [4] studied the three stages without re-heat scheme analytically and experimentically and showed that both CC and COP can be improved significantly by setting the operating and design conditions optimally. The simulation and experiment were performed of the three-stage chiller without re-heat scheme by some of the author [4] and satisfactory qualitative agreement was obtained. The calculated and experimental results differ by only 5% for the evaporator and condenser. Experimental heat balances exceeded the calculated values by 7% for the adsorber and 15% for the desorber. 2.2. Three-stage chiller with re-heat scheme The design criteria of the three-stage chiller using re-heat scheme is almost similar to that of a three-stage chiller without re-heat scheme developed by Saha et al. [4]. Operational strategy of the three-stage chiller with re-heat scheme (Table 2), however, is completely different from the operational strategy of the three-stage chiller without reheat scheme (Table 1). In the three-stage adsorption chiller without re-heat scheme, the evaporating pressure lift is divided into three consecutive pressure lifts to exploit low heat source temperature by introducing three pairs of adsorbent bed (Fig. 1(a, b)). In the three-stage chiller using re-heat scheme (Fig. 2(b)), the evaporating pressure (temperature) lift, however, can be divided into different ways compared to that in the conventional three-stage chiller without re-heat scheme (Fig. 1(b)). To complete one full cycle, all beds pass through six consecutive steps: (i) desorption, (ii) mass recovery process with heating, (iii) pre-cooling, (iv) adsorption, (v) mass recovery process with cooling, and (vi) pre-heating. The adsorbent is packed in the adsorber/desorber heat exchanger, which undergo alternate cooling and heating to allow refrigerant adsorption and desorption. In the adsorption–evaporation process, refrigerant (water) in evaporator is evaporated at evaporation temperature, Teva, and seized heat, Qeva, from the chilled water. The evaporated vapor is adsorbed by adsorbent (silica gel), at which cooling water removes the adsorption heat, Qads. The desorption–condensation process takes place at pressure Pcond. The desorber is heated up to temperature Tdes by heat input Qdes provided by the driving heat source.

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91

a Qcond

Refrigerant Vapor

Condenser

V1

V5 Liquid Refrig Hex2

Hex1

Qads

Qdes V6

V2 Hex4

Hex3

Qdes

Qads V3

V7 Hex6

Hex5 Qads

Qdes

Evaporator V4

V8

Hex: heat exchanger V: valve Qeva Concentration 40

7.37

Condenser pressure 100%

30% 30%

20% 20%

1010% %

2.5% 2.5%

Saturated Vapor Pressure [kPa]

4.24

30 III

2.34

20

II

Single-stage Evaporator r Evaporato pressure pressure

1.23

I

Saturated vapor Temperature [0C]

b

10 Three–stage

Coo lin gwater Cooling watertemp. temp .

Hot water temp. 0

0 0

10

20

30

40

50

60

70

80

90

Silica Gel Temperature [0C] Fig. 1. (a) Schematic of the three-stage chiller without re-heat scheme. (b) Conceptual PTX diagram for single-stage and three stage schemes without reheat scheme.

The resulting refrigerant is cooled down by temperature Tcond in the condenser by the cooling water, which removes condensation heat Qcond. The resulting condensate

flows back to the evaporator via a capillary tube connecting the condenser and the evaporator, to complete the cycle.

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Table 1 Operational strategy of three-stage chiller without re-heat scheme

Table 2 Operational strategy of three-stage chiller with re-heat scheme

The three-stage chiller using re-heat scheme comprises three pairs of adsorbent beds, one condenser, one evaporator, and metalic tubes for hot, cooling and chilled water flows as shown in Fig. 2(a). In the conventional three-stage chiller without re-heat scheme, lower four beds never interact with the condenser and upper four beds never interact with the evaporator, and the middle two beds never interact with either evaporator or condenser. However, in the three-stage chiller using re-heat scheme, all beds go through all processes and also interact with the condenser and evaporator one by one. The chiller operational strategy using re-heat scheme is presented in Table 2. The baseline parameter values adapted in simulation and standard operating conditions are presented in Tables 3 and 4, respectively.

water upon adsorption, and hot water inlet and outlet upon desorption. T denotes adsorbent bed temperature. The adsorbent bed temperature, pressure and concentration are assumed to be uniform throughout the adsorbent bed. The heat transfer and energy balance equations for the adsorbent bed are as follows:   U hex Ahex , (1) T out ¼ T þ ðT in  TÞ exp  _ w cw m d fðW s C s þ W s C w q þ W hex C hex ÞTg dt dq ¼ W s Qst  d:W s C w fgðT  T eva Þ dt dq _ w C w ðT in  T out Þ, ð2Þ þ ð1  gÞðT  T wv Þg þ m dt where d is either 0 or 1 depending on whether bed is working as desorber or adsorber and g is either 1 or 0 depending on whether bed is connected with evaporator or another bed. Eq. (1) expresses the importance of heat transfer parameters, namely heat transfer area Ahex and heat transfer coefficient Uhex. The left-hand side of the adsorber/desorber energy balance equations (Eq. (2)) provides the amount of sensible heat required to cool or heat the silica-gel (s), the water (w) as well as metallic (hex) parts of the heat exchanger during adsorption or desorption. This term accounts for the input/output of sensible heat required by the batched cycle operation. The first term on the right-hand side of Eq. (2) represents the release of adsorption heat or the input of desorption heat, the second and third terms represent the sensible heat of the adsorbed vapor. The last term on the right-hand side of Eq. (2) indicates the total amount of heat released to the cooling water upon adsorption or provided by the hot water for desorption. Eq. (2) does not account for external heat losses to the environment. 3.2. Energy balance for the evaporator In the present analysis, it is assumed that the tube bank surface is able to hold a certain amount of condensate and the condensate would flow into the evaporator easily. The heat transfer and energy balance equations for evaporator can be expressed as   U eva Aeva T chill;out ¼ T eva þ ðT chill;in  T eva Þ exp  , (3) _ chill cchill m

3.1. Energy balance for the adsorber/desorber

d fðW eva;w C w þ W eva;hex C eva;hex ÞT eva g dt dq dq ¼ LW s ads  W s C w ðT cond  T eva Þ des dt dt _ chill C chill ðT chill;in  T chill;out Þ, þm

Adsorption and desorption heat balances are described by identical equations, where HTF (water) temperature terms Tin and Tout denote the inlet and outlet of cooling

where the suffixes ‘‘chill’’ and ‘‘eva’’ indicate chilled water and evaporator, respectively. Left-hand side of Eq. (4) represents the sensible heat required by the liquid refrigerant (w) and the metal of heat exchanger tubes in

3. Formulation of the problem

ð4Þ

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93

Fig. 2. (a) Schematic of the three-stage chiller with re-heat scheme. (b) Conceptual PTX diagram of three-stage chiller with re-heat scheme.

the evaporator. On the right hand side, the first term gives the latent heat of evaporation (L) for the amount of refrigerant adsorbed (dqads/dt), the second term shows the sensible heat required to cool down the incoming condensate from the condensation temperature Tcond to evaporation temperature Teva, and the last term represents the total amount of heat given away by the chilled water. 3.3. Energy balance for the condenser The heat transfer and energy balance equations for condenser can be expressed as   U cond Acond T cond;out ¼ T cond þ ðT cw;in  T cond Þ exp  . _ cw cw m (5)

d fðW cw;w C w þ W cond;hex C cond;hex ÞT cond g dt dq dq ¼ LW s des  W s C w ðT des  T cond Þ des dt dt _ cw C w ðT cw;in  T cw;out Þ, þm

ð6Þ

where the suffixes ‘‘cw’’ and ‘‘cond’’ indicate cooling water and condenser, respectively. The left hand side of Eq. (6) represents the sensible heat required by the metallic parts of heat exchanger tubes due to the temperature variations in the condenser. On the right hand side, the first term gives the latent heat of vaporization (L) for the amount of refrigerant desorbed (dqdes/dt), the second term accounts for the amount of heat that the liquid condensate carries away when it leaves the condenser to the evaporator, and

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3.5. Adsorption rate

Table 3 Baseline parameters

The adsorption rate is expressed as

Values adopted in simulation Symbol

Value

Unit

Ahex Acond Aeva Cs Cw Cchill L Dso Ea R Rp Uads Udes Ucond Ueva Qst Ws Wcw Weva,w

0.061 (m2 kg1)  Ws (kg) 2.0 6.0 924 4.18E+3 4.20E+3 2.50E+6 2.54E–4 2.33E+3 4.62E+2 0.30E–3 1000 750 3900 5800 2.80E+6 16 5 25

m2 m2 m2 J kg1 K1 J kg1 K1 J kg1 K1 J kg1 m2 s1 J kg1 J kg1 K1 m W m2 K1 W m2 K1 W m2 K1 W m2 K1 J kg1 kg kg kg

Table 4 Standard operating condition Temperature (1C) Hot water Cooling water Chilled water Cycle time

Flow rate (kg/s)

60 0.4 30 0.74( ¼ 0.4 ads+0.34 cond) 14 0.11 ads/des ¼ 810s, mr ¼ 600s, ph/pc ¼ 30 s

ads/des ¼ adsorption/desorption; mr ¼ mass recovery; ph/pc ¼ pre-heat/ pre-cool.

the last term represents the total amount of heat released to the cooling water.

dq ¼ ks ap  ðq  qÞ, (8) dt where the overall mass transfer coefficient (ksap) for adsorption is given by ks ap ¼ ð15Ds Þ=ðRp Þ2 .

(9)

The adsorption rate is considered to be controlled by surface diffusion inside a gel particle and surface diffusivity (Ds) is expressed as a function of temperature and can be expressed as [21] Ds ¼ Dso  exp½ðE a Þ=ðRTÞ,

(10)

*

where q is the amount adsorbed in equilibrium with pressure Ps(Tw) and is derived from the manufacturer property data by the following equation: q ¼

0:8  ½Ps ðT w Þ=Ps ðT s Þ 1 þ 0:5  ½Ps ðT w Þ=Ps ðT s Þ

(11)

where Ps(Tw) and Ps(Ts) are the saturation vapor pressure at temperatures Tw (water vapor) and Ts (silica gel), respectively. The saturation vapor pressure and temperature are correlated by Antoine’s equation, which can be written as   3820 Ps ¼ 133:32  exp 18:3  . ð12Þ T  46:1

3.6. Measurement of the system performance The performance of the three-stage chiller using re-heat mainly characterized by CC, and COP and can be measured by the following equations: Cooling capacity Z tcycle _ chill C w ¼m ðT chill;in  T chill;out Þdt=tcycle , 0

3.4. Mass balance Mass and heat balances are based on the assumption that both the temperature and the amount of refrigerant adsorbed are uniform in the adsorbent beds. Since the temperatures in an adsorption cycle are in an unsteady state, the energy balance equations (Eqs. (2), (4), (6)) must account for sensible heat input and/or output during the cyclic operation periods. The mass balance for the refrigerant can be expressed by neglecting the gas phase as   dW eva;w dqdescond dqevaads ¼ W s þ , (7) dt dt dt where subscripts ‘‘des-cond’’ and ‘‘eva-ads’’ stand for the vapor flow from desorber to condenser and evaporator to adsorber, respectively.

Coefficient of performance ðCOPÞ Rt _ chill C w 0cycle ðT chill;in  T chill;out Þdt m ¼ . Rt _ hot C w 0 cycle ðT hot;in  T hot;out Þdt m

4. Simulation procedure The systems of differential Equations (1)–(8) are solved by finite difference approximation with a time step of 1 s. The temperature is assumed to be uniform along the adsorber/desorber heat exchangers. A real chiller starts its operation from un-steady conditions. However, it reaches steady-state conditions after a few cycles. Therefore, an iteration technique is employed in the solution procedure to fix the initial conditions for the cyclic steady state. In the

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5. Results and discussion

Cooling Capacity [kW]

5 4 3 2 RH3S-C4400 3S-C4400 3S-C2200 3S-C1100

1 0 45

75

0.3

0.2 RH3S-C4400 3S-C4400 3S-C2200 3S-C1100

0.1

The three-stage adsorption chiller using re-heat scheme is designed to utilize the low temperature thermal heat from the industries or from renewable energy sources. The simulation techniques are applied to determine the effect of driving heat source temperature on chiller performance and the results are also compared with those of the conventional three-stage chiller without re-heat scheme. Cycle time and mass recovery time and important parameters for re-heat scheme. Due to fixed design of the chiller, all design parameters for each adsorbent bed are considered equal. In Figs. 3 and 4, numerical values of CC and COP are depicted against the driving heat source inlet temperatures which vary from 50 to 70 1C. Three lines are depicted for different cycle times for the three-stage chiller without reheat scheme (3S), 1100, 2200 and 4400 s. In the three-stage adsorption chiller using re-heat scheme (RH3S), cycle time is considered to be 4400 s only for comparison. From Fig. 3, it is seen that the CC increases with the increase of heat source temperature from 50 to 70 1C in all cases. However, CC decreases when cycle time increases from 1100 to 4400 s for the three-stage chiller without re-heat scheme, but opposite tendency is observed for COP (Fig. 4). Because of an excessively long cycle time, the outlet temperature of hot water approaches its inlet temperature value: However, there is still some cold production. Hence, COP increases as cycle time increases for all heat source temperatures. At the same cycle time of 4400 s, one interesting observation is that the CC for the three-stage adsorption chiller using re-heat scheme is higher than that of the conventional three-stage adsorption chiller without re-heat when the heat source inlet temperature is greater than 52 1C. This is caused because of the suitability of relatively longer cycle time for the re-heat scheme [6]. With the variation of heat source inlet temperature in Fig. 4, COP for the three-stage chiller without re-heat scheme is

55 65 Heat Source Temperature [°C]

Fig. 3. Effect of heat source temperature on cooling capacity.

COP [-]

beginning of the solution process, the initial conditions are assumed; however, those are adjusted for the cyclic steady conditions by the iteration process. Refrigerant mass flows between evaporator and adsorber, condenser and desorber, adsorber and desorber are taken equivalent to overcome computational torpidity. When two beds are connected to each other, the vapor pressure is unknown which is essential for the calculation of adsorption/desorption rate inside the adsorbent beds. Therefore, the vapor pressure is assumed and the amounts of vapor adsorbed/desorbed by the beds are calculated. Conceptually, the desorbed vapor from one bed should be equal to the amount of vapor adsorbed by the other bed. If these amounts are not equal then vapor pressure are adjusted for next iteration. Once the satisfactory convergence criterion is achieved, then the process goes for the next time step. The output results have almost no dependency (less than 5%) on the assumed initial conditions. The convergence factor is taken as 103 for all parameters.

95

0 45

55 65 Heat Source Temperature [°C]

75

Fig. 4. Effect of heat source temperature on COP.

almost same but, for the three-stage adsorption chiller using re-heat scheme, COP is increased. COP of the proposed cycle exceeds that of the three-stage cycle without re-heat scheme when heat source inlet temperature is greater than 59 1C (when cycle time 1100 s), 62 1C (when cycle time 2200 s) and 64 1C (when cycle time 4400 s). In an adsorption chiller, the chilled water for airconditioning purposes is obtained from the delivered chilled water. Generally, less chilled water outlet temperature is expected, while the requirement of CC is relatively higher. The chilled water outlet temperature, however, affects the cooling demand of the demand side. Therefore, the requirement of chilled water outlet temperature is very important. Fig. 5 shows the average chilled water outlet temperature with the variation of the driving heat source inlet temperature. It may be seen that at the same cycle time of 4400 s, the chilled water outlet temperature for the three-stage adsorption chiller using re-heat scheme is less compared to that of the conventional three-stage adsorption chiller without reheat scheme when heat source temperature is greater than 52 1C. Also the proposed re-heat scheme gives lower chilled water outlet temperature than that of conventional threestage adsorption chiller without re-heat scheme for cycle times 2200 and 1100 s when driving heat source inlet temperature is greater than 57 1C. The outlet temperature of the chilled water, however, can be controlled by adjusting the chilled water mass flow rate. In Fig. 5 mass flow rate is kept fixed for all cases.

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96

RH3S-C4400 3S-C4400 3S-C2200 3S-1100

12

4.5 Cooling Capacity [kW]

Chilled water outlet [C]

14

10 8 6 4 55 65 Heat Source Temperature [°C]

Fig. 5. Effect of heat source temperature on chilled water outlet temperature.

In the absorption heat pump/refrigeration system, the amount of absorbent mass in the heat exchanger is the most influential parameter. Therefore, the influence of silica gel mass on the system performance with variation in heat exchanger thermal capacitance ratio (Cs/Cm) is discussed in the following subsection: In Figs. 6 and 7 the numerical values of the CC and COP are depicted against the silica gel mass which varies from 4 to 48 kg. In both Figs. 6 and 7 three lines are drawn for the three-stage adsorption chiller using re-heat scheme (RH3S) for different values of adsorbent-to-metal thermal capacitance ratios, Cs/Cm ¼ 1.0, 2.75 (standard in the present case), 5.0. Another three lines are drawn for the conventional three-stage adsorption chiller without re-heat scheme (3S) for different values of adsorbent-to-metal thermal capacitance ratio namely, Cs/Cm ¼ 1.0, 2.75 (standard in the present case), 5.0. Standard operation conditions (Table 4) are applied in the present simulation. It is seen from Fig. 6 that CC increases substantially in the range of silica gel mass from 4 to 36 kg. In this range, CC for the three-stage adsorption chiller using re-heat scheme is higher than that of the conventional three-stage adsorption chiller without re-heat scheme. The reason is that thermal conductance values of the adsorber/desorber heat exchanger, condenser and evaporator are relatively high in comparison to that of silica gel mass, since thermal conductance values of all heat exchanger components are kept constant in the whole region. On the other hand, for adsorbent mass higher than 36 kg, it is seen that CC increases slowly with the increase of silica gel mass for the three-stage adsorption chiller using re-heat scheme but the CC values are less than those of the conventional threestage adsorption chiller without re-heat scheme. This tendency is attributed mainly to the fact that the base line values are applied for the thermal conductance values of heat exchanger components and they become relatively low when the silica gel mass is increased. From Fig. 7, it is observed that COP increases owing to the decrease of silica gel mass because of lower heat input requirement for the three-stage adsorption chiller using re-heat scheme, but COP of the conventional three-stage adsorption chiller without re-heat scheme is almost the same. It is natural that

RH3S(Cs/Cm=1.0) RH3S(Cs/Cm=2.75) RH3S(Cs/Cm=5.0) 3S(Cs/Cm=1.0) 3S(Cs/Cm=2.75) 3S(Cs/Cm=5.0)

2.5 1.5 0.5

75

0

8

16 24 32 40 Silica Gel Mass [kg]

48

Fig. 6. Effect of silica gel mass on cooling capacity for different Cs/Cm.

0.3

COP [-]

45

3.5

0.2 RH3S(Cs/Cm=1.0) RH3S(Cs/Cm=2.75) RH3S(Cs/Cm=5.0) 3S(Cs/Cm=1.0) 3S(Cs/Cm=2.75) 3S(Cs/Cm=5.0)

0.1

0 0

8

16 24 32 40 Silica Gel Mass [kg]

48

Fig. 7. Effect of silica gel mass on COP for different Cs/Cm.

higher amount of adsorbent mass in the adsorbent bed adsorbs more refrigerant, and results in higher CC. At the same time, the larger amount of adsorbent mass in the bed, the more heat input is required, which is responsible for lowering COP. Figs. 6 and 7 also show the effect of silica gel mass on CC and COP corresponding to different absorbent-to-metal thermal capacitance ratio (Cs/Cm) values, 1.0, 2.75 (standard in the present case), and 5.0. The values in each of the three lines are obtained by varying both the metal and absorbent masses in the same proportion so that the thermal capacitance is kept constant for each plot. From Fig. 6, it is observed that the CC becomes sensitive to adsorbent-to-metal thermal capacitance ratio for higher amount of silica gel. It is also observed that CC for the three-stage adsorption chiller using re-heat scheme increases with higher value of Cs/Cm but there is all most no effect for the conventional three-stage adsorption chiller without re-heat scheme. In Fig. 7, COP of both systems increases with higher values of Cs/Cm. CC and COP variation with adsorption/desorption cycle time are depicted in Fig. 8 only for the proposed re-heat scheme. The pre-heating/pre-cooling time is kept constant at 30 s. The highest CC values are obtained for cycle times between 4000 and 4600 s. When cycle times are less than 3000 s, there is not enough time for adsorption or desorption, so CC decreases abruptly. On the other hand,

ARTICLE IN PRESS M.Z.I. Khan et al. / Renewable Energy 33 (2008) 88–98

0.3

3 0.2 2

0 2000

0.1

Cooling Capacity COP

1

3000

4000 5000 6000 Cycle Time [s]

COP [-]

Cooling Capacity [kW]

4

0 7000

Fig. 8. Effect of cycle time on cooling capacity and COP.

driving heat source temperature 60 1C with cooling source 30 1C, and cycle time of 4400 s. Fig. 9 shows the effect of mass recovery process time on CC and COP. It is shown that both CC and COP values are improved with the increase of mass recovery time up to 700 s. Both CC and COP values are maximized when mass recovery time is increased from 500 to 700 s. In the proposed re-heat scheme, during mass recovery process time, the hot water and cooling water are supplied to the system that is, the cycle uses more heat. Moreover, the hot water outlet temperature decreases at the beginning of the mass recovery process; therefore, more heat was used in the mass recovery process.

6. Conclusions

3 0.2 COP [-]

Cooling Capacity [kW]

0.3

97

2

1

0 100

Cooling Capacity COP

0.1

0 300 500 700 900 Mass Recovery Time [s]

Fig. 9. Effect of mass recovery time on cooling capacity and COP.

when cycle time are greater than 4800 s, CC decreases gradually as the adsorbent mass approaches to its equilibrium condition. From the same Figure, it can also be observed that COP increases uniformly with longer cycle time. This is because of the lower consumption of driving heat with longer cycle time. For the proposed chiller, standard cycle time was taken as 4400 s with 600 s mass recovery time. If one operates the chiller with excessively long cycle time, there will be a marginal gain in COP value, whereas CC will decline significantly. Mass recovery cycle is very simple but effective to operate. For operating conditions such as high-condensing temperatures, low-evaporation temperatures, or low-generation temperatures, mass recovery operation is strongly recommended by Wang [22]. Akahira et al. [23] by investing the effect of mass recovery process time states the mass recovery cycle with heating and cooling has the advantage of conventional mass recovery cycle at low heat source temperature investigating the effect of mass recovery process time. Saha et al. [24] showed that the adsorption/ desorption cycle time has significant effect on system performance. Mass recovery between the adsorbent beds after the end of adsorption/desorption process in an adsorption refrigeration cycle is helpful for enhancing the cycle sorption capacity that is enhancing the CC of a cycle, and is presented by Wang et al. [25]. In the present analysis, effect of mass recovery process time is investigated without fixing chilled water outlet temperature, providing the

There is an increasing need for energy efficiency and there is also a need for the system driven with low temperature heat source. For realizing this, the three-stage adsorption chiller using re-heat scheme with silica gel/water pair is presented and the effects of operating conditions are investigated. On the same operating and physical conditions, the re-heat scheme has clear advantage over the conventional three-stage chiller without re-heat scheme at low heat source temperature. CC of the three-stage adsorption chiller using re-heat scheme increases with increase heat source inlet temperature from 50 to 70 1C. Another observation is that the CC of the proposed re-heat scheme is greater than that of the conventional three-stage adsorption chiller without re-heat scheme when the heat source inlet temperature is higher than 52 1C. Chilled water outlet temperature of the proposed scheme is less than that of the three-stage chiller without re-heat scheme when the heat source inlet temperature is greater than 52 1C. The maximum system performances are obtained for cycle time between 4000 and 4600 s with mass recovery cycle time 600 s in the present case. So cycle time as well as mass recovery process time is an influential parameter for the proposed re-heat scheme. The simulated value of the threestage chiller without re-heat scheme have been compared with experimental data by [4] and satisfactory agreement has been obtained. In order to improve the performance of the three-stage chiller without re-heat scheme, the present paper proposed the re-heat scheme in the three-stage adsorption chiller and its performances were investigated numerically. We believe that the present numerical analysis will provide a guideline in designing multi-stage chillers employing re-heat scheme.

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