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Simulation of a continuous multiple-bed regenerative adsorption cycle
International Journal of Refrigeration 24 (2001) 428±437
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Simulation of a continuous multiple-bed regenerative adsorption cycle R.E. Critoph * School of Engineering, University of Warwick, Coventry CV4 7AL, UK Received 22 November 1999; received in revised form 15 March 2000; accepted 16 March 2000
Abstract A refrigeration/heat-pump system based on a number of simple tubular adsorption modules is described. A single module is comprised of a generator and a receiver/condenser/evaporator. A single generator consisting of a 12.7 mm stainless steel tube lined with 3 mm of monolithic active carbon has been manufactured. A complete module has been tested in a simple rig, which subjects it to alternating hot and cold airstreams, desorbing and adsorbing ammonia. A complete system, consisting of 32 modules has been modelled in detail and its predicted performance is presented. Key parameters have been varied and their eect on the performance discussed. # 2001 Elsevier Science Ltd and IIR. All rights reserved. Keywords: Refrigerating system; Adsorption system; Ammonia; Activated charcoal; Prototype; Performance
Simulation d'un cycle aÁ adsorption continu et reÂgeÂneÂrateur aÁ plusieurs lits ReÂsume Un systeÁme frigori®que/pompe aÁ chaleur, base sur des modules tubulaires aÁ absorption, est deÂcrit. Un simple module comprend essentiellement un geÂneÂrateur et un eÂvaporateur-condenseur. Le geÂneÂrateur consiste en un tube en acier (de 0,5 m de long et de 12,7 mm de diameÁtre exteÂrieur) contenant du carbone actif monolithique concentrique au tube et d'une eÂpaisseur de 3 mm. Ledit simple module a eÂte fabrique et teste sur un banc d'essais permettant de soumettre le geÂneÂrateur aÁ des ¯ux d'air alternativement chaud et froid engendrant ainsi la deÂsorption du frigorigeÁne (ammoniac). Un systeÁme complet comprenant 32 modules est modeÂlise et ses performances preÂvues sont preÂsenteÂes. La variation des parameÁtres cleÂs dudit modeÁle a permis d'analyser leurs eets sur les performances du systeÁme # 2001 Elsevier Science Ltd and IIR. All rights reserved. Mots cleÂs : SysteÁme frigori®que ; SysteÁme aÁ adsorption ; Ammoniac ; Charbon actif ; Prototype ; Performance
* Tel.: +44-24-76-523523; fax: +44-24-76-418922. E-mail address: [email protected] 0140-7007/01/$20.00 # 2001 Elsevier Science Ltd and IIR. All rights reserved. PII: S0140-7007(00)00026-8
R.E. Critoph / International Journal of Refrigeration 24 (2001) 428±437
Nomenclature
Tads out
COP Cpa Cpc hgenerator
Tcon mean
K L n q SCP T
Coecient of performance Adsorbate speci®c heat (J kg 1 K 1) Carbon speci®c heat (J kg 1 K 1) Heat transfer coecient of generator tube/®n (W m 2 K 1) Constant characterising sorption pair in Eq. (1) Latent heat of adsorbate at the system pressure (kJ kg 1) Constant characterising sorption pair in Eq. (1) Heat input per unit mass of carbon (J kg 1) Speci®c cooling power (W kg 1 adsorbent) Temperature (K)
1. Introduction It is well known that the major challenges for adsorption cycles are: . To improve heat transfer in adsorbate beds, thereby reducing size and cost. . To improve regenerative heat transfer between beds, thereby increasing COP.
Current progress is reviewed by Meunier [1]. Bed conductivities have been improved from 0.1 W m 1 K 1 [2,3] to 0.4 W m 1 K 1 for monolithic carbons [4] and 5 W m 1 K 1 for graphite composites [5]. Cooling and heating COP and the SCP of a range of sorption machines are given in [6]. It is not possible to generalise about them, since many dierent applications were studied, but it is probably true to say that in air conditioning applications adsorption machines need to be improved if they are to compete with multiple-eect lithium bromide absorption systems. The ideas presented below aim at both improving the eciency and reducing the cost of adsorption refrigeration and heat pumping. They are the subjects of a patent [7]. 2. Concept In order to achieve good regeneration between adsorption and desorption it is necessary to either employ some form of thermal wave [8,9] or many beds [10]. This study examines the possibility of using many simple modular beds in an arrangement that allows eective heat transfer between them. A single module is
Tcon out Tdes out Tev mean Tev Tsat x x0
out
429
Mean temperature of air leaving adsorption section over complete cycle ( C) Mean condensing temperature over complete cycle ( C) Mean temperature of air leaving condensing section over complete cycle ( C) Mean temperature of air leaving desorption section over complete cycle ( C) Mean evaporating temperature over complete cycle ( C) Mean temperature of air leaving evaporating section over complete cycle ( C) Saturation temperature (K) mass concentration (kg adsorbate/kg adsorbent) limiting mass concentration (kg adsorbate/kg adsorbent)
shown schematically in Fig. 1. It is a tube having a sorption generator at one end and a combined evaporator and condenser at the other. The ®rst such module that we have made has a stainless steel tube 12.7 mm in diameter and 500 mm long containing the generator. It is lined with a 3 mm layer of monolithic carbon provided by Sutclie Carbons Ltd. The carbon shape is formed within the tube and so the heat transfer between steel and carbon is very high. The other end of the module is a receiver for the liquid adsorbate; ammonia in our work. The optional wire gauze acts as a wick to keep the liquid in contact with the wall. The adiabatic section separates the generator and receiver, reducing longitudinal conduction between them. Heat may be transferred to or from the generator and receiver by passing air or any other ¯uid across them. Fins can enhance this if necessary. In desorption, the generator is heated and desorbed refrigerant condenses in the receiver, which is cooled. In adsorption the generator is cooled and heat is provided to boil the refrigerant in the receiver. The whole module is the very simplest type of adsorption refrigerator or heat pump. It is possible to combine many such modules in an assembly that allows regenerative heating between them. Figs. 2 and 3 show one possible way of doing this in schematic form. In this example the machine is an airto-air heat pump or air conditioner. Sixteen modules are
Fig. 1. Section through a sorption module. Fig. 1. ScheÂma : coupe d'un module aÁ sorption.
430
R.E. Critoph / International Journal of Refrigeration 24 (2001) 428±437
Fig. 2. Schematic view of a complete system. Fig. 2. ScheÂma d'un systeÁme inteÂgral.
shown, arranged in a cylindrical shell. All rotate about the central axis (X in Fig. 2) typically completing one revolution in ten minutes. Air is blown over the tubes, counter¯ow to their direction of motion and exchanging heat with them. Seals prevent the air from travelling directly between the adsorbing and desorbing zones but allow the tubes to pass through when necessary. Consider the path of a single tube beginning at position 1 in Fig. 3. The carbon is at its coldest, perhaps 50 C and has maximum concentration. As it moves clockwise through the annular duct it is heated by air ¯owing in the opposite direction. If the `thermal mass ¯ow rate' of the generator is approximately the same as that of the air, then the desorption section acts like a counter¯ow heat exchanger with capacity ratio close to unity. In reality, the eective speci®c heat of the carbon varies during a cycle but it is still possible to balance the ¯ow rates quite well. The result is that by the time the module reaches the end of the desorption section it is perhaps at 200 C. Whilst the carbon is heated it desorbs ammonia which condenses in the receiver section of the module. In an air conditioning application, a stream of ambient temperature air cools the receiver section. A similar process occurs in the adsorbing section, but with evaporation occurring in the receiver, which cools the airstream passing over it. In the course of cooling down, the generator tubes heat the stream of ambient air
induced at position 2. This pre-heated air is removed from the annular duct at position 3 and heated by an external high grade heat source before being re-introduced to the duct at position 4. The greater the number of modules, the better the approximation to a continuous process with counter¯ow regeneration of heat.
Fig. 3. Section through the generators. Fig. 3. ScheÂma : coupe des geÂneÂrateurs.
R.E. Critoph / International Journal of Refrigeration 24 (2001) 428±437
The advantages of the system are the absence of refrigerant valves and complex or expensive heat exchangers. Potential problems might include the sealing mechanism to direct the air ¯ows and possible degradation of the carbon due to thermal shock.
431
includes as many `real' eects as possible and will be used to design a complete system. The governing equations are as follows: . Carbon properties: The mass concentration of the carbon is described by:
3. Initial experimentation Previous experience with monolithic carbon [11] suggested that monolithic carbon should be proof against the thermal cycling and could be made to adhere strongly to the tube wall. A manufacturing technique was devised and a 500 mm length of 12.7 mm outside diameter 0.9 mm wall thickness stainless steel tube was lined with 3 mm of active carbon, as shown in Fig. 4. A simple test rig (Fig. 5) was built which subjected the generator to alternating ¯ows of hot (150 C) and ambient air whist the receiver was kept in a ¯ow of ambient air. An optional glass receiver allowed observation of the quantity of liquid ammonia building up or boiling. Repeated heating and cooling for tens of cycles showed no tendency for the carbon to break up and drop into the receiver. This was encouraging, but obviously in a real system there will be many thousands of cycles and further testing is necessary. 4. Simulation model In order to assess the system as a potential air conditioner, heat pump or refrigerator a simulation programme was written in MatlabTM. The programme
Fig. 4. End view of an experimental module.
Fig. 5. Test rig to heat and cool a single module.
Fig. 4. Vue en bout d'un module expeÂrimental.
Fig. 5. Banc d'essai utilise pour chauer et refroidir un module.
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R.E. Critoph / International Journal of Refrigeration 24 (2001) 428±437
x x0
T K Tsat
n 1
1
A Cpc xCpa
The equation is a modi®ed Dubinin Astakhov form, ®tted to measured data as described in [4]. For the carbon used in the initial tests, x0 , K and n were 0.3629, 3.6571 and 0.94, respectively. The conductivity is 0.44 Wm 1 K 1 and the speci®c heat is 1125 J kg 1 K 1. One dimensional radial conduction within the tube and carbon is assumed and satisfactory accuracy is obtained when modelling the 3 mm layer as six isothermal sub-layers of equal thickness. The thermal resistance between the carbon and steel is neglected since the manufacturing method ensures intimate contact. The surrounding stainless steel tube is modelled as a single isothermal layer. It is possible to include the eects of external ®ns on the tube by lumping their thermal mass and area in with that of the tube. Heat transfer to or from the tube/ ®n assembly is calculated using an assumed heat transfer coecient and area. The eectiveness from air to tube/ ®n is calculated based on the coecient, the mass ¯ow of air and the assumption that the tube/®n is isothermal. The ®n eciency expected in practice is very close to unity. The pressure is assumed uniform throughout each module. The radial mass permeability of the monolithic carbon and means of calculating the pressure drop are given in [12] for a larger diameter case. Application of the same method implies maximum pressure drops of the order of 10±100 Pa, with a negligible eect on performance. The model also assumes zero heat conduction axially along the adiabatic zone (but does include the sensible heat of the gas ¯owing through it). The greatest temperature dierences are in desorption, with a mean value of 100 C. Using a modelled wall thickness of 0.9 mm the mean conduction heat ¯ux would be 0.7 Watts per module in desorption for an adiabatic zone that is 40 mm long. This could be signi®cant, but the most recent designs use tubing of 0.25 mm thickness which reduce the heat leakage to manageable levels. A simple explicit scheme is used to solve the heat transfer equations. The only diculty is that the eective speci®c heat of the carbon is a function of both the concentration and the relative rates of change of pressure and temperature. Given Eq. (1), it can be shown by considering both sensible heat and heat of desorption that: dq @x 2 A H dT @T p HL
T Tsat
3
and after substituting (1) and dierentiating dq AB dT
B
where
dTsat T dT Tsat
4
BL
T T Knx Tsat T2sat
5 n 1
1
6
If the rise in pressure during a small time step is known the expression for eective speci®c heat can be put into the heat transfer energy balance equations to solve for the temperature rise. The assumption is made that the pressure is uniform throughout the module and so the same pressure rise must apply to all elemental layers. The overriding boundary condition that allows solution of all the elemental energy balances is that the total mass of ammonia in the module is constant with time. The ammonia can exist in three forms: adsorbate within the carbon, liquid in the receiver and gas in the remaining free volume. The solution of the equations is done in the following order: 1. Calculate the heat transfer in or out of the receiver based on external heat transfer area and coecient, air mass ¯ow rate and log mean temperature dierence. The receiver is assumed to be at Tsat . 2. Guess dTsat . 3. Calculate the mass of ammonia that is condensed or evaporated in this time step. The calculation includes the eect of the sensible heat of the gas that must be de-superheated before condensation at Tsat and the thermal mass of the receiver and liquid ammonia that must increase in temperature by dTsat . In evaporation only the latter eect operates. 4. Calculate the new carbon and steel temperatures based on the assumed pressure rise. 5. Calculate the new concentrations using the new pressure and temperatures in (1). 6. In evaporation take the sensible cooling eect of gas from the evaporator into account by reducing the temperature of the inner carbon layer based on the current eective speci®c heat. Since the gas must pass through the inner layer to be adsorbed by the outer layers, this is a reasonable assumption. Recalculate the concentration of the inner layer. 7. Calculate the mass of gas in the void space (the gas constant for ammonia is calculated from a polynomial based on data in [13]). Calculate the total mass of ammonia in the system (given the assumed Tsat ) and the dierence between it and the initial ammonia charge. 8. Use Newton±Raphson iteration of steps 2±7 for Tsat until the ammonia mass error is one part in 104. 9. Calculate the temperature of the air leaving the tube/®ns and passing on to the next module.
R.E. Critoph / International Journal of Refrigeration 24 (2001) 428±437
This process is repeated in turn for all the modules in the direction of the moving air so that the air temperature at any module is continuously updated. After a predetermined simulation time each tube is indexed by one positional step. The inlet temperature of ambient air (position 2) and of externally heated air (position 4) is held constant. The programme is terminated after a set number of complete revolutions (i.e. cycles). Normally four revolutions is sucient to damp out starting transients and ensure that the processes in each module approximate to a true thermodynamic cycle each revolution. The simulation also allows receivers leaving the evaporating or condensing airstreams to be kept adiabatic for some time rather than immediately entering the other (condensing or evaporating) airstream. If this is not done the ®rst few tubes may condense when they should switch to evaporating or vice-versa. 5. Results of a base case simulation The example presented is one that gives reasonable performance but is not optimised in many respects. There are many design parameters and many dierent functions (COP, SCP, economics, etc.) that may be optimised and so the concept of a single optimum design is not necessarily useful. The key design parameters and operating conditions chosen are in Table 1. After four revolutions the COP in cooling is 0.60 and the COP in heating is 1.53 rather than 1+cooling COP. The disparity is due to the fact that conditions at the start of the ®nal revolution are not precisely those at the Table 1 Design and operating parameters of base case example Tableau 1 ParameÁtres de fonctionnement et de conception pour le cas de base Parameter
Value
Number of modules in desorption zone Number of modules in adsorption zone Number of receivers adiabatic during desorption Number of receivers adiabatic during adsorption Generator length Generator diameter Generator ®nning
16 16 3
Generator duct air velocity Air heater outlet temperature Generator air inlet temperature Condenser air inlet temperature Evaporator air inlet temperature Time for one complete revolution or cycle
3 1m 12.7 mm Aluminium, 3 mm pitch, 25.4 mm square. 1.0 m s 1 200 C 30 C 30 C 15 C 864 s
433
end. The major performance indicators are given in Table 2. The behaviour of the system is shown in Fig. 6 (a±j). Figs. 6 (a)±(c) show the mean carbon temperature, the pressure and the mass of liquid ammonia in the receiver respectively of all 32 modules with time. They show how the starting transients develop and then damp towards regular cyclic behaviour. The transient form is a result of the constant heater outlet temperature Ð a constant power heater would produce a dierent transient. It can be seen in Fig. 6 (c) that in the regular cyclic state there is never less than about 6 g of liquid in the receiver. It represents a loss, since its mass is needlessly heated and cooled in each cycle. For these particular conditions the charge of ammonia in each module could be reduced. Fig. 6 (d) shows the temperatures of the 32 module generator sections and of the air passing over them at the end of the fourth revolution. The instant in time taken is at the end of the 27 s time period after which the modules would be indexed to their next position. Intermediate temperatures at non-integer values of module number are not actual temperatures (they are straight lines joining the values at integer module numbers), but give a good indication of the way the carbon temperatures vary with time over a complete cycle. There are seven module temperatures: those of the tube/®n and of the six sub-layers of carbon. The ®gure shows a good match between the thermal capacity of the air ¯ow and `module ¯ow'. The desorption air cools nearly linearly with position as the generator temperatures increase. Fig. 6 (e) shows how the concentrations of the sublayers vary with position in the cycle. The concentration swing is from 20 to 5%. It is noticeable that the variation between layers is much greater when cold. The temperature variation between sub-layers is not larger at the cold end of the cycle, but the eect on mass concentration is exaggerated because of the form of the characteristic equation. The evaporating or condensing temperature of each module is unsteady, as is illustrated by Fig. 6 (f) of Tsat Table 2 Base case performance indicators Tableau 2 Indicateurs de performance pour le cas de base Performance indicator
Value
COP cooling 0.60 COP heating 1.52 Cooling power 291 W SCP 142 W kg Mean temperature of air entering heater 170 C Mean temperature of air leaving desorption zone 51 C Mean condensing temperature 38 C Mean evaporating temperature 8.9 C
1
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R.E. Critoph / International Journal of Refrigeration 24 (2001) 428±437
Fig. 6. (a) Carbon temperature vs time for one in four of the modules; (b) pressure vs time for one in four of the modules; (c) mass of liquid vs time for one in four of the modules; (d) temperatures of all module sub-layers and air at the end of simulation; (e) concentration of all module sub-layers at the end of simulation; (f) Saturation temperature of all modules at the end of simulation; (g) power input per unit carbon mass of a single module during one cycle; (h) mean carbon temperature of a single module during one cycle; (i) mean carbon concentration of a single module during one cycle; (j) mean eective speci®c heat of carbon vs. mean temperature during one cycle. Fig. 6. (a) TempeÂrature du carbone actif en fonction du temps pour un module sur quatre ; (b) pression en fonction du temps pour un module sur quatre ; (c) masse du liquide en fonction du temps pour un module sur quatre ; (d) tempeÂratures de toutes les sous-couches et de l'air aÁ la ®n de la simulation ; (e) concentrations de toutes les sous-couches aÁ la ®n de la simulation ; (f) tempeÂrature de saturation de tous les modules aÁ la ®n de la simulation ; (g) eÂnergie par unite de masse de carbone pour un seul module pendant un cycle ; (h) tempeÂrature moyenne du carbone d'un seul module pendant un cycle ; (i) concentration moyenne du carbone d'un seul module pendant un cycle ; (j) chaleur massique moyenne du carbone en fonction de le tempeÂrature moyenne pendant un cycle.
R.E. Critoph / International Journal of Refrigeration 24 (2001) 428±437
435
Fig. 6. (continued) Fig. 6. xxx.
of the modules at the end of four revolutions. Receivers 1±3 and 17±19 are adiabatic, 4±16 are condensing in air at 30 C and 20±32 are evaporating in air at 15 . Figs. 6 (g)±(j) show the behaviour of an individual module during the ®nal revolution of 864 s. The rate of heat input or output per mass of carbon is shown in Fig. 6 (g). It is close to 1000 W kg 1 for most of the cycle. Figs. 6 (h) and (i) show the carbon mean temperature and concentration respectively. Both show fairly linear behaviour. Fig. 6 (j) shows the variation of the `mean eective speci®c heat' of the carbon with its mean temperature. This is the heat addition per unit temperature rise, including the eect of enthalpy of desorption as given by Eq. (4) and it is path dependent. The crosses show where, every 27 s, the module moved from one location to the next. The total heat load between two temperatures is the area under the curve. With perfect regeneration the high grade heat input would be the area of the right hand loop, 80 kJ kg 1. The simulation, with realistic heat transfer, heat load of tube/®ns and imperfect regeneration has a heat input of 204 kJ kg 1.
6. Key parameters and their eect on performance There are more than one hundred parameters that are inputs to the simulation but the eect of ®ve major ones are illustrated here: Thermal capacity ratio, number of modules, temperature of air leaving the heater, generator heat transfer coecient and the evaporator air inlet temperature. The results are shown in Table 3 and Figs. 7±9. The capacity ratio eect is illustrated by varying the generator air duct velocity. In the base case it is 1.0 m s 1 and alternative cases at 1.1 and 0.9 m s 1 have been simulated. The reduced COP of both cases is shown in Table 3. The reasons are revealed in Fig. 7, which is as Fig. 6 (d) for the base case but with both high and low ¯ow cases superimposed. The de®cit or surplus thermal capacity of the air results in the air temperature deviating widely from the generator temperature at either the hot or cold end. The eectiveness and degree of regeneration are thereby reduced. Similar eects are observed if the rotational speed of the modules is varied.
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R.E. Critoph / International Journal of Refrigeration 24 (2001) 428±437
Table 3 Parametric study results Tableau 3 ReÂsultats de l'eÂtude sur les parameÁtres Parameter
Base case value
Air speed (m s 1)
1.0
New value 1.1 0.9
COP (cooling)
SCP (W kg 1)
Tads out ( C)
Tdes out ( C)
Tev out ( C)
Tcon ( C)
0.56 0.57
176 110
164 173
59 48
9.7 10.8
36.4 36.1
8.0 9.2
38.5 38.1
out
Tev mean ( C)
Tcon mean ( C)
Heater temperature ( C)
200
250 225 175 150
0.54 0.58 0.61 0.60
175 160 121 101
209 190 150 129
60 55 48 45
9.8 9.8 10.7 11.5
37.3 36.6 35.8 34.7
8.0 8.1 9.3 10.2
39.4 38.3 37.6 36.2
hgenerator
120
60 180
0.54 0.61
139 142
167 171
55 50
10.5 10.4
36.0 36.3
9.0 8.8
37.8 38.1
Evaporator air ( C)
15
20 10
0.69 0.52
159 127
171 169
50 52
15.2 5.6
36.9 35.7
13.7 4.1
38.8 37.3
Number of modules
32
24 40 50 64
0.44 0.71 0.82 0.91
158 125 107 89
166 173 174 176
56 48 45 43
9.5 11.1 11.8 12.3
36.9 35.7 35.0 34.1
7.4 9.9 10.8 12.3
39.0 37.2 36.4 34.2
0.60
142
170
51
10.4
36.2
8.9
38.1
Base case
The variation in COP and SCP with the heater exit temperature is shown in Fig. 8. It is noticeable that the COP is comparatively insensitive to heater temperature in the range chosen, although it does have a peak at around 175 C. At higher temperatures, although a little more ammonia can be desorbed, not all of the sensible heat load can be regenerated and COP drops. However, the cooling power rises with increasing heater temperature in a linear fashion. The minimum mean concentration for
a heater temperature of 250 C is 3% whereas for 150 C it is 10%. The variation of performance with heat transfer coecient over the generator ®ns is evident from Table 3. At high values of hgenerator the eectiveness of a single tube ®n is so close to unity that further gains are minor. In reality hgenerator is a function of the air speed but is treated as an independent variable here in order to separate the eects on heat transfer and thermal capacity. The evaporating and condensing temperatures are determined by the air inlet temperatures to the separate evaporators and condensers. The variation is illustrated
Fig. 7. Temperatures of all module sub-layers for air velocities of 0.9 and 1.1 m s 1.
Fig. 8. COP and SCP vs heater exit temperature.
Fig. 7. TempeÂratures de toutes les sous-couches de modules pour les vitesse d'air de 0,9 et 1,1 m.s 1.
Fig. 8. Le COP et le SCP en fonction de la tempeÂrature aÁ la sortie du bouilleur.
R.E. Critoph / International Journal of Refrigeration 24 (2001) 428±437
437
Acknowledgements The authors thank Waterlink Sutclie Carbons for their support and supply of materials and The Engineering and Physical Sciences Research Council for funding this project under grant GR/M65403.
References
Fig. 9. COP and SCP vs number of modules. Fig. 9. Figure 9. Le COP et le SCP en fonction du nombre de modules.
in Table 3; COP varies linearly from 0.52 to 0.69 as the inlet temperature to the evaporator increases from 10 to 20 C. The variation in COP and SCP with the number of tube modules is non-linear over the range chosen. In the limit of one tube there is no regeneration and for an in®nite number of tubes there will be maximum regeneration. Assuming the `mass ¯ow rate' of modules to be constant the SCP will decrease with an increasing number of tubes. Fig. 9 shows the variation for 24 to 64 tubes. The improvement in COP at high module numbers is due mainly to the improved regeneration, but also to the reduced temperature lift resulting from the reduced evaporator and condenser load. 7. Conclusions and future work A new continuous adsorption refrigeration system has been described which uses a number of simple tubular modules. A single module has been made and tested and a programme written to simulate many modules in a real system. The design has not yet been optimised but a parametric study has revealed the way in which key parameters aect COP and SCP. It is hoped to build a small prototype system within a year. Future work will also attempt a Second Law analysis of the system in order to discover the ideal limitations of the concept.
[1] Meunier F. Adsorption heat pump technology: possibilities and limits. In: Proceedings of the Int. Sorption Heat Pump Conf., Munich, March 1999. p. 25±35. [2] Douss N, Meunier F, Sun LM. Predictive model and experimental results for a two adsorber solid adsorption heat pump. I & EC Research XXXX;27:310±6. [3] Critoph RE, Turner L. Heat transfer in granular activated carbon beds in the presence of adsorbable gases. Int J Heat and Mass Transfer 1995;38(9):1577±85. [4] Critoph RE, Tamainot-Telto Z. Thermophysical properties of monolithic carbon. Int J Heat and Mass Transfer, in press. [5] Guilleminot JJ. From pellet to consolidated adsorbent bed. In: Meunier F, editor. Proceedings of Fundamentals of Adsorption, vol. 6. Elsevier, 1998. [6] Pons M, et al. Thermodynamic based comparison of sorption systems for cooling and heat pumping. Int J Refrigeration 1999;22(1):5±17. [7] Critoph RE. Thermal regenerative compressive device, UK patent application 9922339.8, ®led 21 September 1999. [8] Critoph RE. Forced convection adsorption cycles. Applied Thermal Engineering 1998;18:799±807. [9] Miles DJ, et al. Gas ®red sorption heat pump development. In: Proceedings of Solid Sorption Refrigeration, Paris. LIMSI, 1992. [10] Meunier F. Second law analysis of a solid adsorption heat pump operating on reversible cascaded cycles: application to the zeolite water pair. Heat Recovery Systems and CHP 1985;5:133±41. [11] Critoph RE, Tamainot-Telto Z, Davies GNL. Adsorption refrigerator using a monolithic carbon-aluminium laminate adsorbent and ammonia refrigerant. In: Proceedings of the Int. Sorption Heat Pump Conf., Munich, March 1999, p. 349±353. [12] Critoph RE, Tamainot-Telto Z. Monolithic carbon for sorption refrigeration and heat pump applications. Applied Thermal Engineering, in press. [13] Anon. Thermodynamic and physical properties of ammonia. International Institute of Refrigeration, 1981.
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Simulation of a continuous multiple-bed regenerative adsorption cycle R.E. Critoph * School of Engineering, University of Warwick, Coventry CV4 7AL, UK Received 22 November 1999; received in revised form 15 March 2000; accepted 16 March 2000
Abstract A refrigeration/heat-pump system based on a number of simple tubular adsorption modules is described. A single module is comprised of a generator and a receiver/condenser/evaporator. A single generator consisting of a 12.7 mm stainless steel tube lined with 3 mm of monolithic active carbon has been manufactured. A complete module has been tested in a simple rig, which subjects it to alternating hot and cold airstreams, desorbing and adsorbing ammonia. A complete system, consisting of 32 modules has been modelled in detail and its predicted performance is presented. Key parameters have been varied and their eect on the performance discussed. # 2001 Elsevier Science Ltd and IIR. All rights reserved. Keywords: Refrigerating system; Adsorption system; Ammonia; Activated charcoal; Prototype; Performance
Simulation d'un cycle aÁ adsorption continu et reÂgeÂneÂrateur aÁ plusieurs lits ReÂsume Un systeÁme frigori®que/pompe aÁ chaleur, base sur des modules tubulaires aÁ absorption, est deÂcrit. Un simple module comprend essentiellement un geÂneÂrateur et un eÂvaporateur-condenseur. Le geÂneÂrateur consiste en un tube en acier (de 0,5 m de long et de 12,7 mm de diameÁtre exteÂrieur) contenant du carbone actif monolithique concentrique au tube et d'une eÂpaisseur de 3 mm. Ledit simple module a eÂte fabrique et teste sur un banc d'essais permettant de soumettre le geÂneÂrateur aÁ des ¯ux d'air alternativement chaud et froid engendrant ainsi la deÂsorption du frigorigeÁne (ammoniac). Un systeÁme complet comprenant 32 modules est modeÂlise et ses performances preÂvues sont preÂsenteÂes. La variation des parameÁtres cleÂs dudit modeÁle a permis d'analyser leurs eets sur les performances du systeÁme # 2001 Elsevier Science Ltd and IIR. All rights reserved. Mots cleÂs : SysteÁme frigori®que ; SysteÁme aÁ adsorption ; Ammoniac ; Charbon actif ; Prototype ; Performance
* Tel.: +44-24-76-523523; fax: +44-24-76-418922. E-mail address: [email protected] 0140-7007/01/$20.00 # 2001 Elsevier Science Ltd and IIR. All rights reserved. PII: S0140-7007(00)00026-8
R.E. Critoph / International Journal of Refrigeration 24 (2001) 428±437
Nomenclature
Tads out
COP Cpa Cpc hgenerator
Tcon mean
K L n q SCP T
Coecient of performance Adsorbate speci®c heat (J kg 1 K 1) Carbon speci®c heat (J kg 1 K 1) Heat transfer coecient of generator tube/®n (W m 2 K 1) Constant characterising sorption pair in Eq. (1) Latent heat of adsorbate at the system pressure (kJ kg 1) Constant characterising sorption pair in Eq. (1) Heat input per unit mass of carbon (J kg 1) Speci®c cooling power (W kg 1 adsorbent) Temperature (K)
1. Introduction It is well known that the major challenges for adsorption cycles are: . To improve heat transfer in adsorbate beds, thereby reducing size and cost. . To improve regenerative heat transfer between beds, thereby increasing COP.
Current progress is reviewed by Meunier [1]. Bed conductivities have been improved from 0.1 W m 1 K 1 [2,3] to 0.4 W m 1 K 1 for monolithic carbons [4] and 5 W m 1 K 1 for graphite composites [5]. Cooling and heating COP and the SCP of a range of sorption machines are given in [6]. It is not possible to generalise about them, since many dierent applications were studied, but it is probably true to say that in air conditioning applications adsorption machines need to be improved if they are to compete with multiple-eect lithium bromide absorption systems. The ideas presented below aim at both improving the eciency and reducing the cost of adsorption refrigeration and heat pumping. They are the subjects of a patent [7]. 2. Concept In order to achieve good regeneration between adsorption and desorption it is necessary to either employ some form of thermal wave [8,9] or many beds [10]. This study examines the possibility of using many simple modular beds in an arrangement that allows eective heat transfer between them. A single module is
Tcon out Tdes out Tev mean Tev Tsat x x0
out
429
Mean temperature of air leaving adsorption section over complete cycle ( C) Mean condensing temperature over complete cycle ( C) Mean temperature of air leaving condensing section over complete cycle ( C) Mean temperature of air leaving desorption section over complete cycle ( C) Mean evaporating temperature over complete cycle ( C) Mean temperature of air leaving evaporating section over complete cycle ( C) Saturation temperature (K) mass concentration (kg adsorbate/kg adsorbent) limiting mass concentration (kg adsorbate/kg adsorbent)
shown schematically in Fig. 1. It is a tube having a sorption generator at one end and a combined evaporator and condenser at the other. The ®rst such module that we have made has a stainless steel tube 12.7 mm in diameter and 500 mm long containing the generator. It is lined with a 3 mm layer of monolithic carbon provided by Sutclie Carbons Ltd. The carbon shape is formed within the tube and so the heat transfer between steel and carbon is very high. The other end of the module is a receiver for the liquid adsorbate; ammonia in our work. The optional wire gauze acts as a wick to keep the liquid in contact with the wall. The adiabatic section separates the generator and receiver, reducing longitudinal conduction between them. Heat may be transferred to or from the generator and receiver by passing air or any other ¯uid across them. Fins can enhance this if necessary. In desorption, the generator is heated and desorbed refrigerant condenses in the receiver, which is cooled. In adsorption the generator is cooled and heat is provided to boil the refrigerant in the receiver. The whole module is the very simplest type of adsorption refrigerator or heat pump. It is possible to combine many such modules in an assembly that allows regenerative heating between them. Figs. 2 and 3 show one possible way of doing this in schematic form. In this example the machine is an airto-air heat pump or air conditioner. Sixteen modules are
Fig. 1. Section through a sorption module. Fig. 1. ScheÂma : coupe d'un module aÁ sorption.
430
R.E. Critoph / International Journal of Refrigeration 24 (2001) 428±437
Fig. 2. Schematic view of a complete system. Fig. 2. ScheÂma d'un systeÁme inteÂgral.
shown, arranged in a cylindrical shell. All rotate about the central axis (X in Fig. 2) typically completing one revolution in ten minutes. Air is blown over the tubes, counter¯ow to their direction of motion and exchanging heat with them. Seals prevent the air from travelling directly between the adsorbing and desorbing zones but allow the tubes to pass through when necessary. Consider the path of a single tube beginning at position 1 in Fig. 3. The carbon is at its coldest, perhaps 50 C and has maximum concentration. As it moves clockwise through the annular duct it is heated by air ¯owing in the opposite direction. If the `thermal mass ¯ow rate' of the generator is approximately the same as that of the air, then the desorption section acts like a counter¯ow heat exchanger with capacity ratio close to unity. In reality, the eective speci®c heat of the carbon varies during a cycle but it is still possible to balance the ¯ow rates quite well. The result is that by the time the module reaches the end of the desorption section it is perhaps at 200 C. Whilst the carbon is heated it desorbs ammonia which condenses in the receiver section of the module. In an air conditioning application, a stream of ambient temperature air cools the receiver section. A similar process occurs in the adsorbing section, but with evaporation occurring in the receiver, which cools the airstream passing over it. In the course of cooling down, the generator tubes heat the stream of ambient air
induced at position 2. This pre-heated air is removed from the annular duct at position 3 and heated by an external high grade heat source before being re-introduced to the duct at position 4. The greater the number of modules, the better the approximation to a continuous process with counter¯ow regeneration of heat.
Fig. 3. Section through the generators. Fig. 3. ScheÂma : coupe des geÂneÂrateurs.
R.E. Critoph / International Journal of Refrigeration 24 (2001) 428±437
The advantages of the system are the absence of refrigerant valves and complex or expensive heat exchangers. Potential problems might include the sealing mechanism to direct the air ¯ows and possible degradation of the carbon due to thermal shock.
431
includes as many `real' eects as possible and will be used to design a complete system. The governing equations are as follows: . Carbon properties: The mass concentration of the carbon is described by:
3. Initial experimentation Previous experience with monolithic carbon [11] suggested that monolithic carbon should be proof against the thermal cycling and could be made to adhere strongly to the tube wall. A manufacturing technique was devised and a 500 mm length of 12.7 mm outside diameter 0.9 mm wall thickness stainless steel tube was lined with 3 mm of active carbon, as shown in Fig. 4. A simple test rig (Fig. 5) was built which subjected the generator to alternating ¯ows of hot (150 C) and ambient air whist the receiver was kept in a ¯ow of ambient air. An optional glass receiver allowed observation of the quantity of liquid ammonia building up or boiling. Repeated heating and cooling for tens of cycles showed no tendency for the carbon to break up and drop into the receiver. This was encouraging, but obviously in a real system there will be many thousands of cycles and further testing is necessary. 4. Simulation model In order to assess the system as a potential air conditioner, heat pump or refrigerator a simulation programme was written in MatlabTM. The programme
Fig. 4. End view of an experimental module.
Fig. 5. Test rig to heat and cool a single module.
Fig. 4. Vue en bout d'un module expeÂrimental.
Fig. 5. Banc d'essai utilise pour chauer et refroidir un module.
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R.E. Critoph / International Journal of Refrigeration 24 (2001) 428±437
x x0
T K Tsat
n 1
1
A Cpc xCpa
The equation is a modi®ed Dubinin Astakhov form, ®tted to measured data as described in [4]. For the carbon used in the initial tests, x0 , K and n were 0.3629, 3.6571 and 0.94, respectively. The conductivity is 0.44 Wm 1 K 1 and the speci®c heat is 1125 J kg 1 K 1. One dimensional radial conduction within the tube and carbon is assumed and satisfactory accuracy is obtained when modelling the 3 mm layer as six isothermal sub-layers of equal thickness. The thermal resistance between the carbon and steel is neglected since the manufacturing method ensures intimate contact. The surrounding stainless steel tube is modelled as a single isothermal layer. It is possible to include the eects of external ®ns on the tube by lumping their thermal mass and area in with that of the tube. Heat transfer to or from the tube/ ®n assembly is calculated using an assumed heat transfer coecient and area. The eectiveness from air to tube/ ®n is calculated based on the coecient, the mass ¯ow of air and the assumption that the tube/®n is isothermal. The ®n eciency expected in practice is very close to unity. The pressure is assumed uniform throughout each module. The radial mass permeability of the monolithic carbon and means of calculating the pressure drop are given in [12] for a larger diameter case. Application of the same method implies maximum pressure drops of the order of 10±100 Pa, with a negligible eect on performance. The model also assumes zero heat conduction axially along the adiabatic zone (but does include the sensible heat of the gas ¯owing through it). The greatest temperature dierences are in desorption, with a mean value of 100 C. Using a modelled wall thickness of 0.9 mm the mean conduction heat ¯ux would be 0.7 Watts per module in desorption for an adiabatic zone that is 40 mm long. This could be signi®cant, but the most recent designs use tubing of 0.25 mm thickness which reduce the heat leakage to manageable levels. A simple explicit scheme is used to solve the heat transfer equations. The only diculty is that the eective speci®c heat of the carbon is a function of both the concentration and the relative rates of change of pressure and temperature. Given Eq. (1), it can be shown by considering both sensible heat and heat of desorption that: dq @x 2 A H dT @T p HL
T Tsat
3
and after substituting (1) and dierentiating dq AB dT
B
where
dTsat T dT Tsat
4
BL
T T Knx Tsat T2sat
5 n 1
1
6
If the rise in pressure during a small time step is known the expression for eective speci®c heat can be put into the heat transfer energy balance equations to solve for the temperature rise. The assumption is made that the pressure is uniform throughout the module and so the same pressure rise must apply to all elemental layers. The overriding boundary condition that allows solution of all the elemental energy balances is that the total mass of ammonia in the module is constant with time. The ammonia can exist in three forms: adsorbate within the carbon, liquid in the receiver and gas in the remaining free volume. The solution of the equations is done in the following order: 1. Calculate the heat transfer in or out of the receiver based on external heat transfer area and coecient, air mass ¯ow rate and log mean temperature dierence. The receiver is assumed to be at Tsat . 2. Guess dTsat . 3. Calculate the mass of ammonia that is condensed or evaporated in this time step. The calculation includes the eect of the sensible heat of the gas that must be de-superheated before condensation at Tsat and the thermal mass of the receiver and liquid ammonia that must increase in temperature by dTsat . In evaporation only the latter eect operates. 4. Calculate the new carbon and steel temperatures based on the assumed pressure rise. 5. Calculate the new concentrations using the new pressure and temperatures in (1). 6. In evaporation take the sensible cooling eect of gas from the evaporator into account by reducing the temperature of the inner carbon layer based on the current eective speci®c heat. Since the gas must pass through the inner layer to be adsorbed by the outer layers, this is a reasonable assumption. Recalculate the concentration of the inner layer. 7. Calculate the mass of gas in the void space (the gas constant for ammonia is calculated from a polynomial based on data in [13]). Calculate the total mass of ammonia in the system (given the assumed Tsat ) and the dierence between it and the initial ammonia charge. 8. Use Newton±Raphson iteration of steps 2±7 for Tsat until the ammonia mass error is one part in 104. 9. Calculate the temperature of the air leaving the tube/®ns and passing on to the next module.
R.E. Critoph / International Journal of Refrigeration 24 (2001) 428±437
This process is repeated in turn for all the modules in the direction of the moving air so that the air temperature at any module is continuously updated. After a predetermined simulation time each tube is indexed by one positional step. The inlet temperature of ambient air (position 2) and of externally heated air (position 4) is held constant. The programme is terminated after a set number of complete revolutions (i.e. cycles). Normally four revolutions is sucient to damp out starting transients and ensure that the processes in each module approximate to a true thermodynamic cycle each revolution. The simulation also allows receivers leaving the evaporating or condensing airstreams to be kept adiabatic for some time rather than immediately entering the other (condensing or evaporating) airstream. If this is not done the ®rst few tubes may condense when they should switch to evaporating or vice-versa. 5. Results of a base case simulation The example presented is one that gives reasonable performance but is not optimised in many respects. There are many design parameters and many dierent functions (COP, SCP, economics, etc.) that may be optimised and so the concept of a single optimum design is not necessarily useful. The key design parameters and operating conditions chosen are in Table 1. After four revolutions the COP in cooling is 0.60 and the COP in heating is 1.53 rather than 1+cooling COP. The disparity is due to the fact that conditions at the start of the ®nal revolution are not precisely those at the Table 1 Design and operating parameters of base case example Tableau 1 ParameÁtres de fonctionnement et de conception pour le cas de base Parameter
Value
Number of modules in desorption zone Number of modules in adsorption zone Number of receivers adiabatic during desorption Number of receivers adiabatic during adsorption Generator length Generator diameter Generator ®nning
16 16 3
Generator duct air velocity Air heater outlet temperature Generator air inlet temperature Condenser air inlet temperature Evaporator air inlet temperature Time for one complete revolution or cycle
3 1m 12.7 mm Aluminium, 3 mm pitch, 25.4 mm square. 1.0 m s 1 200 C 30 C 30 C 15 C 864 s
433
end. The major performance indicators are given in Table 2. The behaviour of the system is shown in Fig. 6 (a±j). Figs. 6 (a)±(c) show the mean carbon temperature, the pressure and the mass of liquid ammonia in the receiver respectively of all 32 modules with time. They show how the starting transients develop and then damp towards regular cyclic behaviour. The transient form is a result of the constant heater outlet temperature Ð a constant power heater would produce a dierent transient. It can be seen in Fig. 6 (c) that in the regular cyclic state there is never less than about 6 g of liquid in the receiver. It represents a loss, since its mass is needlessly heated and cooled in each cycle. For these particular conditions the charge of ammonia in each module could be reduced. Fig. 6 (d) shows the temperatures of the 32 module generator sections and of the air passing over them at the end of the fourth revolution. The instant in time taken is at the end of the 27 s time period after which the modules would be indexed to their next position. Intermediate temperatures at non-integer values of module number are not actual temperatures (they are straight lines joining the values at integer module numbers), but give a good indication of the way the carbon temperatures vary with time over a complete cycle. There are seven module temperatures: those of the tube/®n and of the six sub-layers of carbon. The ®gure shows a good match between the thermal capacity of the air ¯ow and `module ¯ow'. The desorption air cools nearly linearly with position as the generator temperatures increase. Fig. 6 (e) shows how the concentrations of the sublayers vary with position in the cycle. The concentration swing is from 20 to 5%. It is noticeable that the variation between layers is much greater when cold. The temperature variation between sub-layers is not larger at the cold end of the cycle, but the eect on mass concentration is exaggerated because of the form of the characteristic equation. The evaporating or condensing temperature of each module is unsteady, as is illustrated by Fig. 6 (f) of Tsat Table 2 Base case performance indicators Tableau 2 Indicateurs de performance pour le cas de base Performance indicator
Value
COP cooling 0.60 COP heating 1.52 Cooling power 291 W SCP 142 W kg Mean temperature of air entering heater 170 C Mean temperature of air leaving desorption zone 51 C Mean condensing temperature 38 C Mean evaporating temperature 8.9 C
1
434
R.E. Critoph / International Journal of Refrigeration 24 (2001) 428±437
Fig. 6. (a) Carbon temperature vs time for one in four of the modules; (b) pressure vs time for one in four of the modules; (c) mass of liquid vs time for one in four of the modules; (d) temperatures of all module sub-layers and air at the end of simulation; (e) concentration of all module sub-layers at the end of simulation; (f) Saturation temperature of all modules at the end of simulation; (g) power input per unit carbon mass of a single module during one cycle; (h) mean carbon temperature of a single module during one cycle; (i) mean carbon concentration of a single module during one cycle; (j) mean eective speci®c heat of carbon vs. mean temperature during one cycle. Fig. 6. (a) TempeÂrature du carbone actif en fonction du temps pour un module sur quatre ; (b) pression en fonction du temps pour un module sur quatre ; (c) masse du liquide en fonction du temps pour un module sur quatre ; (d) tempeÂratures de toutes les sous-couches et de l'air aÁ la ®n de la simulation ; (e) concentrations de toutes les sous-couches aÁ la ®n de la simulation ; (f) tempeÂrature de saturation de tous les modules aÁ la ®n de la simulation ; (g) eÂnergie par unite de masse de carbone pour un seul module pendant un cycle ; (h) tempeÂrature moyenne du carbone d'un seul module pendant un cycle ; (i) concentration moyenne du carbone d'un seul module pendant un cycle ; (j) chaleur massique moyenne du carbone en fonction de le tempeÂrature moyenne pendant un cycle.
R.E. Critoph / International Journal of Refrigeration 24 (2001) 428±437
435
Fig. 6. (continued) Fig. 6. xxx.
of the modules at the end of four revolutions. Receivers 1±3 and 17±19 are adiabatic, 4±16 are condensing in air at 30 C and 20±32 are evaporating in air at 15 . Figs. 6 (g)±(j) show the behaviour of an individual module during the ®nal revolution of 864 s. The rate of heat input or output per mass of carbon is shown in Fig. 6 (g). It is close to 1000 W kg 1 for most of the cycle. Figs. 6 (h) and (i) show the carbon mean temperature and concentration respectively. Both show fairly linear behaviour. Fig. 6 (j) shows the variation of the `mean eective speci®c heat' of the carbon with its mean temperature. This is the heat addition per unit temperature rise, including the eect of enthalpy of desorption as given by Eq. (4) and it is path dependent. The crosses show where, every 27 s, the module moved from one location to the next. The total heat load between two temperatures is the area under the curve. With perfect regeneration the high grade heat input would be the area of the right hand loop, 80 kJ kg 1. The simulation, with realistic heat transfer, heat load of tube/®ns and imperfect regeneration has a heat input of 204 kJ kg 1.
6. Key parameters and their eect on performance There are more than one hundred parameters that are inputs to the simulation but the eect of ®ve major ones are illustrated here: Thermal capacity ratio, number of modules, temperature of air leaving the heater, generator heat transfer coecient and the evaporator air inlet temperature. The results are shown in Table 3 and Figs. 7±9. The capacity ratio eect is illustrated by varying the generator air duct velocity. In the base case it is 1.0 m s 1 and alternative cases at 1.1 and 0.9 m s 1 have been simulated. The reduced COP of both cases is shown in Table 3. The reasons are revealed in Fig. 7, which is as Fig. 6 (d) for the base case but with both high and low ¯ow cases superimposed. The de®cit or surplus thermal capacity of the air results in the air temperature deviating widely from the generator temperature at either the hot or cold end. The eectiveness and degree of regeneration are thereby reduced. Similar eects are observed if the rotational speed of the modules is varied.
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R.E. Critoph / International Journal of Refrigeration 24 (2001) 428±437
Table 3 Parametric study results Tableau 3 ReÂsultats de l'eÂtude sur les parameÁtres Parameter
Base case value
Air speed (m s 1)
1.0
New value 1.1 0.9
COP (cooling)
SCP (W kg 1)
Tads out ( C)
Tdes out ( C)
Tev out ( C)
Tcon ( C)
0.56 0.57
176 110
164 173
59 48
9.7 10.8
36.4 36.1
8.0 9.2
38.5 38.1
out
Tev mean ( C)
Tcon mean ( C)
Heater temperature ( C)
200
250 225 175 150
0.54 0.58 0.61 0.60
175 160 121 101
209 190 150 129
60 55 48 45
9.8 9.8 10.7 11.5
37.3 36.6 35.8 34.7
8.0 8.1 9.3 10.2
39.4 38.3 37.6 36.2
hgenerator
120
60 180
0.54 0.61
139 142
167 171
55 50
10.5 10.4
36.0 36.3
9.0 8.8
37.8 38.1
Evaporator air ( C)
15
20 10
0.69 0.52
159 127
171 169
50 52
15.2 5.6
36.9 35.7
13.7 4.1
38.8 37.3
Number of modules
32
24 40 50 64
0.44 0.71 0.82 0.91
158 125 107 89
166 173 174 176
56 48 45 43
9.5 11.1 11.8 12.3
36.9 35.7 35.0 34.1
7.4 9.9 10.8 12.3
39.0 37.2 36.4 34.2
0.60
142
170
51
10.4
36.2
8.9
38.1
Base case
The variation in COP and SCP with the heater exit temperature is shown in Fig. 8. It is noticeable that the COP is comparatively insensitive to heater temperature in the range chosen, although it does have a peak at around 175 C. At higher temperatures, although a little more ammonia can be desorbed, not all of the sensible heat load can be regenerated and COP drops. However, the cooling power rises with increasing heater temperature in a linear fashion. The minimum mean concentration for
a heater temperature of 250 C is 3% whereas for 150 C it is 10%. The variation of performance with heat transfer coecient over the generator ®ns is evident from Table 3. At high values of hgenerator the eectiveness of a single tube ®n is so close to unity that further gains are minor. In reality hgenerator is a function of the air speed but is treated as an independent variable here in order to separate the eects on heat transfer and thermal capacity. The evaporating and condensing temperatures are determined by the air inlet temperatures to the separate evaporators and condensers. The variation is illustrated
Fig. 7. Temperatures of all module sub-layers for air velocities of 0.9 and 1.1 m s 1.
Fig. 8. COP and SCP vs heater exit temperature.
Fig. 7. TempeÂratures de toutes les sous-couches de modules pour les vitesse d'air de 0,9 et 1,1 m.s 1.
Fig. 8. Le COP et le SCP en fonction de la tempeÂrature aÁ la sortie du bouilleur.
R.E. Critoph / International Journal of Refrigeration 24 (2001) 428±437
437
Acknowledgements The authors thank Waterlink Sutclie Carbons for their support and supply of materials and The Engineering and Physical Sciences Research Council for funding this project under grant GR/M65403.
References
Fig. 9. COP and SCP vs number of modules. Fig. 9. Figure 9. Le COP et le SCP en fonction du nombre de modules.
in Table 3; COP varies linearly from 0.52 to 0.69 as the inlet temperature to the evaporator increases from 10 to 20 C. The variation in COP and SCP with the number of tube modules is non-linear over the range chosen. In the limit of one tube there is no regeneration and for an in®nite number of tubes there will be maximum regeneration. Assuming the `mass ¯ow rate' of modules to be constant the SCP will decrease with an increasing number of tubes. Fig. 9 shows the variation for 24 to 64 tubes. The improvement in COP at high module numbers is due mainly to the improved regeneration, but also to the reduced temperature lift resulting from the reduced evaporator and condenser load. 7. Conclusions and future work A new continuous adsorption refrigeration system has been described which uses a number of simple tubular modules. A single module has been made and tested and a programme written to simulate many modules in a real system. The design has not yet been optimised but a parametric study has revealed the way in which key parameters aect COP and SCP. It is hoped to build a small prototype system within a year. Future work will also attempt a Second Law analysis of the system in order to discover the ideal limitations of the concept.
[1] Meunier F. Adsorption heat pump technology: possibilities and limits. In: Proceedings of the Int. Sorption Heat Pump Conf., Munich, March 1999. p. 25±35. [2] Douss N, Meunier F, Sun LM. Predictive model and experimental results for a two adsorber solid adsorption heat pump. I & EC Research XXXX;27:310±6. [3] Critoph RE, Turner L. Heat transfer in granular activated carbon beds in the presence of adsorbable gases. Int J Heat and Mass Transfer 1995;38(9):1577±85. [4] Critoph RE, Tamainot-Telto Z. Thermophysical properties of monolithic carbon. Int J Heat and Mass Transfer, in press. [5] Guilleminot JJ. From pellet to consolidated adsorbent bed. In: Meunier F, editor. Proceedings of Fundamentals of Adsorption, vol. 6. Elsevier, 1998. [6] Pons M, et al. Thermodynamic based comparison of sorption systems for cooling and heat pumping. Int J Refrigeration 1999;22(1):5±17. [7] Critoph RE. Thermal regenerative compressive device, UK patent application 9922339.8, ®led 21 September 1999. [8] Critoph RE. Forced convection adsorption cycles. Applied Thermal Engineering 1998;18:799±807. [9] Miles DJ, et al. Gas ®red sorption heat pump development. In: Proceedings of Solid Sorption Refrigeration, Paris. LIMSI, 1992. [10] Meunier F. Second law analysis of a solid adsorption heat pump operating on reversible cascaded cycles: application to the zeolite water pair. Heat Recovery Systems and CHP 1985;5:133±41. [11] Critoph RE, Tamainot-Telto Z, Davies GNL. Adsorption refrigerator using a monolithic carbon-aluminium laminate adsorbent and ammonia refrigerant. In: Proceedings of the Int. Sorption Heat Pump Conf., Munich, March 1999, p. 349±353. [12] Critoph RE, Tamainot-Telto Z. Monolithic carbon for sorption refrigeration and heat pump applications. Applied Thermal Engineering, in press. [13] Anon. Thermodynamic and physical properties of ammonia. International Institute of Refrigeration, 1981.