- Email: [email protected]
Performance estimation of an adsorption cooling system for automobile waste heat recovery
Applied Thermal Engineering Vol. 17, No. 12. pp. 1127-l 139. 1997 Q 1997
Published by
PII: s1359-4311(97)00039-2
Elsevier
Science Ltd. All rights reserved Printed in Great Britain 1359-4311/97 $17.00 i 0.00
PERFORMANCE ESTIMATION OF AN ADSORPTION COOLING SYSTEM FOR AUTOMOBILE WASTE HEAT RECOVERY Li Zhi Zhang
and Ling Wang
Research Institute of Internal Combustion Engine, Dalian University of Technology. Dalian 116023, Liaoning Province, China (Received 26 April 1997)
Abstract-This article presents a numerical study of the dynamic performance of an adsorption cooling system for automobile waste heat recovery. A new lumped parameter non-equilibrium model is developed and used to investigate and optimize the waste heat cooling system, which is estimated to be operated in quicker cycles when compared with the time needed to reach equilibrium. The effects of the operating temperatures and the overall heat transfer coefficient on the system performance are extensively investigated. It is found that the SCP is more sensitive to parameter changes than the COP. And improving the UA is the most effective way to obtain an increased SCP, but only in the ranges below the threshold value, which is determined by the overall mass transfer coefficient. 0 1997 Published by Elsevier Science Ltd Keywords-Adsorption
cooling, automobile, waste heat, COP, SCP.
NOMENCLATURE AfZ
cb % COP D, Qo E, hz km L
m n!r P 4 9in 9sr
Ei"
R R, SCP t T UA W WCOE WCOP
heat transfer area between the heating/cooling fluid and zeolite (in zeolite side) (m’) specific heat of the metal adsorber heat exchanger (kJ kg-’ K-‘) specific heat (kJ kg-’ K-‘) coefficient of performance surface diffusivity (m2 s-l) pre-exponent constant (m’s_‘) activation energy of surface diffusion (kJ kg-‘) heat transfer coefficient between the fluids and zeolite (kW m-’ K-‘) overall mass transfer coefficient (s-l) latent heat of evaporization of the refrigerant (kJ kg-‘) mass (kg) mass flow rate of the fluids (kg s-‘) pressure (mbar) heat flow rate (kW) heat flow rate from the heating fluid to the adsorber (kW) isosteric heat (kJ kg-‘) total heat transmitted (kJ) heat transmitted from the heating fluid to the adsorber (kJ) universal gas constant (kJ kg-’ K-‘) average radius of a particle (m) specific cooling power (W kg-’ adsorbent) time (s) temperature (K) overall heat transfer coefficient for unit weight of adsorbent (kW m-3 K-‘) water uptake (kg kg-’ adsorbent) coefficient of waste heat recovery coefficient of waste heat cooling
Greek letters density of dry adsorbent Pa
(kg mm3)
Subscripts
ads av b C
adsorption average adsorber heat exchanger condenser, cooling 1127
1128 CYC des dew
eq f g h 0
v W
wst z
Li Zhi Zhang and Ling Wang cycle
desorption dew point evaporator equilibrium fluid regenerate heating inlet outlet saturation water vapor water liquid waste heat zeolite
INTRODUCTION Adsorption cooling is a promising alternative to traditional vapor compression refrigeration in satisfying the demands of the industry for a diversification of primary energy sources and a reduction in the use of CFCs. The application of adsorption refrigeration to automobiles has other benefits: the cooling system can be powered by engine’s waste heat, which results in gas consumption reduction; and it has no moving parts, which leads to high reliability and silent operation. The basic adsorption cycle [l-3] has a theoretical coefficient of performance of about 0.5. To achieve improved performance, many advanced cycles [4-81, namely, the so called ‘regenerative cycles’ which based on the principle of heat regeneration were proposed. Meunier [9] showed that the performance of an ideal regenerative cycle with an infinite number of cascades can be as high as 1.85, about 68% of the ideal Carnot COP. These researches are very significant in improving the market competitiveness of commercial adsorption cooling/heating machines. However, in the case of automobile waste heat cooling, mechanical simplicity and high reliability will prevail on efficiency. And the waste heat recovery cannot affect the mechanical energy output from the engine. So a two-bed basic zeolite-water adsorption cycle is considered in this study. The feasibility of adsorption cooling for automobile/engine waste heat recovery was studied before, (see [lo, Ill, among others). However, information on its dynamic performance, which is necessary for the design and optimization of the system, is insufficient. Zhu et al. [lo] measured the cooling capacity of a cooling element of a fishing boat diesel engine waste heat chiller and the temperature variation of the adsorbent bed. Their study was purely experimental and no numerical analysis was presented. Suzuki [l l] theoretically studied the effects of UA (overall heat transfer coefficient) on SCP of a passenger car waste heat adsorption air conditioning system, however, no details were outlined with respect to the effects of other parameters which play equal important roles in adsorption refrigeration. Also, in our opinion, the model proposed in his study is not detailed enough for our dynamic analysis of the system performance. Recently, Sami et al. [12] presented an improved dynamic model to study the single adsorber and/or double adsorber systems with heat recovery. The systems they studied employed an air cooled evaporator and an air cooled condenser. Hot oil, superheated steam or exhaust gas could be used as heating fluids for the adsorbers. In these respects, they are similar to the automobile waste heat cooling system we propose. And it gave an insight into the thermodynamics for some of the system components. However, in their analysis, the cycle time was quite long and an equilibrium adsorption state was assumed, while in our case, where the cycle time could be much shorter to obtain an increased SCP, this assumption is invalid and it will jeopardize the accuracy of the analysis. In this study, a detailed non-equilibrium dynamic model is developed to evaluate the influences of various operating parameters upon the performance of an automobile waste heat adsorption cooling system. The dynamic behavior of the various internal and external interactions between the adsorbent and cooling fluids is discussed. In particular, the influences of parameter changes on SCP and the methods to obtain an increased SCP are analyzed. This is
Performance estimation of an adsorption cooling system for automobile waste heat recovery
1129
significant, since the low SCP is the main technological limit associated with the application of adsorption cycles to automobiles waste heat refrigeration.
SYSTEM
DESCRIPTION
The waste heat cooling system analyzed in this article is very simple and can be implemented easily. It comprises four heat exchanges, namely, an air finned forced convection condenser, an air finned forced convection evaporator, and a pair of shell and tube type adsorbers, plus four one-way refrigerant valves, an expansion valve, and an exchange valve, as shown in Fig. 1. The adsorbent is packed in the adsorber heat exchangers, and the heating/cooling fluid flows through the steel tubes of the adsorber heat exchanges. By switching the exchange valve, the two adsorbers can intermittently alternate their functions with each other and a continuous chilled air supply can be obtained. As shown in Fig. 1, when valves 9a, 9d are open and 9b, 9c are closed, adsorber 1 is in heating-desorption process and adsorber 2 is in cooling-adsorption process; when valves 9a, 9d are closed and 9b, 9c are open, adsorber 1 will be in cooling-adsorption process and adsorber 2 will be in heating-desorption process. The heating fluid of the adsorbers is engine’s exhaust gas, and the cooling fluid is ambient air pumped by a blower. The adsorbentadsorbate pair used here is zeolite 13x-water, since the regeneration temperature of zeolite 13xwater is high enough for engine’s exhaust gas heat recovery. The two adsorbers are identical, and they operate the same cycle but out of phase. For simplicity, only one adsorber is considered in the dynamic analysis and performance estimation.
THE
MATHEMATICAL
MODEL
In this model, the temperature and pressure are assumed homogeneous in the components, and a non-equilibrium lumped parameter modeling approach is employed. Other two assumptions are made: (a) the heat capacity of adsorbate in the adsorbed state is equal to that of the liquid phase; (b) the specific heat and the density of dry adsorbent is constant. The governing equations are summarized in the following. Thermodynamic
property
equations
The thermodynamic properties such as the specific heats, the latent heat of evaporization the saturation pressure can be written as the functions of temperature [13].
Fig. 1. Scheme of the adsorption cooling system for automobile waste heat recovery. (1) Adsorber 1. (2) adsorber 2. (3) blower, (4) heat exchange valve, (5) diesel engine, (6) condenser. (7) expansion valve, (8) evaporator, (9a-9d) one-way valves.
and
1130
Li Zhi Zhang and Ling Wang
The specific heats of adsorbate liquid, adsorbate vapor, exhaust gas, and air are expressed in the form; c,=co+ciT+C~P,
(1)
where constants ci (i = 0,1,2) can be derived from least squares curve fit of specific heats values. For instance, the values for water vapor considered as ideal gas are co= 1.68774 kJ kg-’ K-‘; cl = 5.3451 x lo4 kJ kg-’ K-2; c2 = 6.5822 x lo-’ kJ kg-’ K-3. The latent heat of evaporization for pure adsorbate is; L(T) = Lo + ci~T,
(2)
known data for water vapor as adsorbate are Lo = 3171.2 kJ kg-’ and CI~= - 2.4425 kJ kg-’ K-l. The saturation pressure for adsorbate liquid-vapor equilibrium is written in the form; ln(P,) = a, + b,/T,
(3)
where P, is in mbar, known data for water are a, = 20.5896 and b, = - 5098.26. Adsorption equations
Adsorption equilibrium is not assumed. Deviation from equilibrium can be expressed in two different ways. In this study, a linear driving force equation is introduced to account for mass transfer resistance within the pallets, while the resistance in the interparticle voids is neglected, as proposed by some authors [14-171. Then the adsorption rate can be expressed as; g where weq is the equilibrium and it is given by [ 141;
= km&q - w),
uptake at (T,, P,); k,
is the overall mass transfer
km+,
coefficient,
(5) P
and the surface diffusivity D, is given as a function
of temperature
D, = D,oexp(-EJRT,).
Equation
(5) and Eq. (6) can be written together
[14] as; (6)
and simplified as;
k ,,, = klexp(-k,lT,)
(7)
where,
k2 = EJR.
When the T, and P, are kept constant throughout Eq. (4) is written as;
(9)
an adsorption
w = w,,[l - exp(-k,t)],
process, then the solution to (10)
(when T,, P, = constant). Coefficients k, and k2 are obtained from Eq. (7) and Eq. (10) with experimental zeolite 13x-water adsorption curves under constant temperature and pressure. The overall mass transfer coefficient will increase with increasing kl. To an extreme, when kl becomes infinite, then the adsorption state will always maintain equilibrium adsorption state, and the model will become an equilibrium model. To the opposite, when k, equals to zero, the
Performance estimation of an adsorption cooling system for automobile waste heat recovery
mass transfer resistance will become brium equations as following;
infinite.
weq is determined
b(weq)= bo + bl w,q +
1131
by the adsorption-equili-
b2W& + bw&,
(13)
where T, is the adsorbent temperature (IQ P, is the pressure of the adsorber (mbar); numerical values of ai and bi (i = 0, 1, 2, 3) are reported by Cacciola et al. [ 181. The isosteric heat of adsorption is calculated by the equation; qst =
-w&q)>
(14)
where R is the universal gas constant (kJ kg-’ K-l). Conservation
of energy
Isosteric
heating/cooling
adsorbent
processes.
During these two processes, the energy balances for the
and the fluids are;
(15)
hri&(Trav - TJ = c,f6(Tti - Tro)
(16)
where for isosteric heating process, wise is w,,, and the fluid is diesel engine’s exhaust gas; for isosteric cooling process, Wiseis M”,inand the fluid is the ambient air. Tf=, is the calculating average temperature of heating fluid (waste gas) or cooling fluid (ambient air) for the adsorber. For the sake of simplification in normalization, it is defined as;
Tfi - Tfo
Trav= Tz+ q
(17)
$t$)
where Tf, is the outlet temperature of heating/cooling fluids for the adsorber. It varies with changing adsorber temperature during a cycle, and is obtained by iterative techniques in simulations. If we define, UA = h~zA~z/(m,/p,), i.e. overall heat transfer coefficient between the adsorbent bed and the heating/cooling fluid on the basis of the unit weight of adsorbent, then UA is estimated as 1kW mm3K-l for zeolite beds with a heat transfer distance of 5 mm, by assuming the effective thermal conductivity of the packed bed to be around 0.2 W m -r K-’ [l 11. Desorption process. During this process, the energy balance for the adsorbent is; mz(cpz+ cpww+
ctmlm,)~ - mzqst2 =ha&(Tfav
- Tz)
and the heat released at the condenser is; qc = -m, The heat transfered to the adsorber during the isosteric heating and the desorption qin = hr~Ar~(Tr~v- T*)
periods is; (20)
1132
Li Zhi Zhang
and Ling Wang
Table 1. Some parameters used in simulation Symbol or name
Value
Unit
17 0.97 2.74 10.11 70.5 0.023 0.042 0.836 40.04 x 1o-3 905.8 0.47 7.1 1.0 20 2s 5 49
lzf AfZ
hrz he Mu&t &r CP
k,
kz Cb
Tube%gth Fin spacing Tube diameter Number of tubes Number of fins
kW.r?W _)
W.m~i,K-’ W.m-‘.K-’ kg? kg.s-’ kJ.kg-‘.K-’ s-l K kJ.kg-‘.K-’ kg m
and the total heat needed is the integration of qin over these two periods;
Qin = S
qin dt.
(21)
iso+des
Adsorption process. The energy balance for this process is; %(cpz + $Ww +
dw Cbmb/%)
3
-
mzqst
dt
= hfzAfz(Tfav
and the cooling power that can be generated by the evaporator
-
Tz) - m, d”, dt
The total cooling production
?-e)
(22)
during the adsorption phase is;
(2 >
qe= mz
pv (T 2 -
[UTJ - CPW(TC - Tee)].
(23)
is; Qe =
J qedt.
(24)
ad?
System coejkients On the basis of the previous equations, The coefficient of performance;
the system coefficients are defined as the following.
COP =
Qe/Qin
(25)
Table 2. Simulation results for a cycle Symbol TC
TC TZd
=S
TM Ter
Q!” Q. QC
QCWt &yc SCP COP WCOP
Value
Unit
45 10 80 270 450 35 11897.1 4911.7 6023.8 10573.2 107 4s 0.41 0.26
“C “C “C “C “C “C
kJ kJ kJ kJ min Wlkg
1133
Performance estimation of an adsorption cooling system for automobile waste heat recovery
c_._._._._._.--.
0.65 I 0.60 0.55
z
0.50
.........._. c-p
-
-
-
---.
155
-51
scp wcop - WCOE
-47
2
.E 0.45 ”
28 u
2
0.400.35
-43
3
-
0.20’35 0
5
_---
_---
_---
10
20
15
- 39
30
25
35
Fig. 2. Influence of the T, on system performance: T, = 45 “C; T, = 300 “C; T,, = 80 “C; The =450 “C; SCP; - - - WCOP; - - WCOE. Tcfi=35”C. . . . . . . COP:-
-55
0.65 -.-. 0.60
-.-.w._
.. . .. .
0.55
-
-
SCP WCOP - WCOE
--0.50
cop
-.
- 50
2 .g 0.45
3
‘.i!.:
T
-1;:
-_0.25 0.20
Fig.
3.
Influence
---___
I 45
1 40
35
--I 55
I 50 qe cw
/ 60
65
35
of the T, on system performance: T,= 10 “C; Tg= 300 “C; Tad = 80 “Cc ___ sCp; - - - WCOP; -. - WCOE. T,fi=35”C.,.....C0P;
0.70 ,
-.-.-.-.-.-
0.65
-
0.60
- . . . . . . . . . . . . cop
0.65
- ---
0.45
-
0.40
-
0.35
-
0.30
-
o.2 1 50
- 45
SCP WCOP WCOE
-.-
.z 0.50-
8
“C;
50
e 2 %
Thfi=450
-40
2 5
-35
9 m
- 30 _-_-----aI 300
I 350
_ I 400
I 450 Th,j (“c)
Fig. 4. Influence of the The on system performance: Tcfi=35”C. . . . . ..COP. -SCp;---
I 500
I 550
I 600
65i5
T,=45 “C: T,= 10 “C; T,= 250 “C; Tad = 80 “c; wcop;-.-
WCOE.
Li Zhi Zhang and Ling Wang
1134
o.70155
-.-.-.-.-._._
0.65-
5
............
cop
0.60-
-
---
SCP WCOP
0.65-
-.-
WCOE
-50 G 3 3 -45 w
.g 0.50$ s 0.45-
2
u" 0.40-40
0.350.30-
o.251~35 15
20
25
30 35 qfi("C)
40
45
50
55
Fig. 5. Influence of the T,s on system performance: T,=45 “C; T,= 10 “C; T,= 300 “C; Tad= 80 “C; Thfi= 450 “C. COP; scp; - - - WCOP; - - WCOE.
The specific cooling power during a cycle on the basis of the unit weight of adsorbent; SCP = Qel(tcycmz)
(26)
WCOP = Qe/Qw
(27)
The coefficient of waste heat cooling;
The coefficient of waste heat recovery; WCOE = QinlQwst;
(28)
where Qwst is the potential waste heat energy that can be recovered without dew point corrosion, and it can be estimated by;
Qwst =
$&bM(~hfi
(29)
- Tdew),
where mwsr is the total mass of exhaust gas flowed through the adsorber during the isosteric heating and the desorption periods, and Td,, is the dew point temperature of the exhaust gas, which is considered 180°C for diesel engine [19]. Among the coefficients, WCOP determines the cooling capacity an engine can produce with its exhaust gas, while SCP yields the required size of a cooling unit.
1.0
40
..'."."'...'......................,.,,..,,,.,,.., /;
- - - - - _ _ _ _ _ ............
---
cop SCP
WCOP
---WCOE
Fig. 6. Influenceof the T, on system performance:
T,a=35”C.
. . . . . COP;--SCP;---
-5
T,=45 “C; T,= 10 “C; Thfi=450 “C; T,,= 50 “C; WCOp;-.WCOE.
Performance estimation of an adsorption cooling system for automobile waste heat recovery 400, 3753so-
1135
140
.. . ... .
c*p
-
SCP WCOP
---
-30
325y
300-
&Y 275 E g 250._ g 225- 10 200-5
17515
I I 300 350
I I I 400 450 500 Th!i('c)
I I1 7000 I 550 600 650
Fig. 7. The values of the optimum T, with Thfi: T, = 45 “C; T, = 10 “C; Tad= 80 “C; Tcfi=35 “C.
NUMERICAL
RESULTS
AND
DISCUSSION
The previously mentioned set of differential equations developed was first normalized and then solved simultaneously by Runge-Kutta-Fehlberg technique [20]. The time step varied from 1 s to 10 s, based on the length of the cycle time. During each step, iterations were performed to obtain a converged solution. The simulations employed a small test unit which is propotional to a prototype for a standard bus and is being constructed in our laboratory. Some of the parameters considered in the simulations are shown in Table 1. The thermodynamic property values are taken from [13]. The results of the simulation are shown in Table 2. As a result of IQin+ Qe-Qo,t-QJ/(Qin + Qe) < 1.3%, it can be seen that the heat balance for the cycle is satisfied. To further study the cooling system, the influences of the operating conditions and the design parameters on the system performance were estimated. Operating
temperatures
The effects of the evaporating and condensing temperatures on system coefficients are shown in Figs 2 and 3 respectively. The T, and T, have important effects on the SCP, but only have limited effects on the other three coefficients. The COP, SCP, WCOP and WCOE all increase with higher evaporating temperatures or lower condensing temperatures. As the evaporating temperature is increased from 2 to 32 “C, the SCP rises from 40 W kg-’ to 53 W kg-‘, and the COP rises from 0.41 to 0.47. When the condensing temperature is increased from 40 “C to 60 “C, the COP drops from 0.44 to 0.42 and the SCP decreases from 44 to 39 W kg-‘. These -._
<.,
0.7-45
-.-.-.-.-. 0.6-
............ cop SCP --WCOP
0.20.1-
- 30
-.-WCOE O30
, 40
I 50
I / 60 70 T.d('C)
I 80
90
10g5
Fig. 8. Influence of the Tad on system performance: T,=45 "C; T,= 10 ‘C; Ts = 300 “C: Thfi=450 “C; T,fi=35”C.
1136
Li Zhi Zhang and Ling Wang
90 80 u^ 700 2 E g ._ 8
60504030 t
‘1: 0
5
10
15
20
25
30 35 0 Cfi ( C)
40
45
50
55
(
Fig. 9. The values of the optimum Tad with T,,: T, = 45 “C; T, = 10 “C; T,= 300 “C; Tha = 450 “C
- 0.40
- 0.35 “.‘.............
. . . . . . . .._........._,.,...,
- 0.30
. . . . . . . . . . . . cop
-
0
20
40
60 UA
Fig.
10.
- 0.25
SCP
80
120
140
0.2 160
(kW.ti3.K-‘)
Influence of the UA on system performance: ~,,,=0.23;
100
T,=45 “C; T,= 10 “C;
Thfi=450
“C;
T~e=35
“C
W,i,=O.O2.
120looz g
#
SO-
,” 6040 20 -
0I
I
I
\
I
20
40
60
80
I
100
I
I
120
140
UA (kW.ni3.R’)
Fig. 11. Influence of the UA on the cycle time: T,=45 “C; T,= 10 “C; The =450 “C; Tee= 35 “C ~,,,=0.23; W,i,=O.O2.
Performance estimation of an adsorption cooling system for automobile waste heat recovery
1137
tendencies indicate that more energy is supplied to the system and a longer cycle time is resulted when the evaporating temperature decreases or the condensing temperature increases. The WCOEs obtained are above 0.6; and the WCOPs are above 0.25. Figures 4 and 5 show the effects of the temperatures of the heating fluid (waste gas) Thfi and the cooling fluid (ambient air) T,fi on system performance respectively. It can be seen that the variations of the heating and cooling fluids temperatures have strong effects on SCP, but they have small effects on COP, WCOP and WCOE. Increasing the heating fluid temperature or decreasing the cooling fluid temperature can boost SCP. This is because a higher heating fluid temperature or a lower cooling fluid temperature leads to a higher heat transfer rate between the fluid and the adsorbent, which then results in a shorter cycle time and a bigger specific cooling power. However, for heating fluid above 550 “C, the step of the increase for SCP tends to be slower when the heating fluid temperature is further increased. This happens because less refrigerant is desorbed/adsorbed for shorter cycles. It also helps to explain why the COP and the WCOP decrease, though very small, when the heating fluid temperature is increased or the cooling fluid temperature is decreased. It is also noted that the WCOE is nearly constant throughout the variations of The and T,,. The influence of the maximum regenerating temperature Tg on system coefficients are shown in Fig. 6. It is seen that the COP, SCP and the WCOP are increased rapidly, reaches a maximum value and then is decreased gradually with an increase in Tg, while the coefficient of waste heat recovery WCOE drops continuously. Increasing the T, results in more refrigerant desorbed, but it is also leads to more sensible heat losses from the adsorber. And the step of increase becomes smaller when the Tg goes beyond the optimum value, and the sensible heat losses become substantial. In this particular case, the optimum values of Tg for COP, SCP and WCOP are 310, 200 and 180 “C respectively. It is also found that the optimum Tg is The; but it is insensitive to other very sensitive to heating fluid inlet temperature operating temperatures. Figure 7 demonstrates the optimum values of Tg for COP, SCP and WCOP respectively with different Thfi. Figure 8 shows the influence of the minimum adsorption temperature Tad on system performance. The trend of SCP is similar to that in Fig. 6. The SCP is increased rapidly, reaches a maximum value and then is gradually decreased with an increase in Tad. This is because as the Tad increases, the cycle time decreases and the amount of refrigerant adsorbed drops too. The optimum Tad for SCP in this case is 80 “C. The COP, WCOP and WCOE decrease with an increase in Tad, but the tendencies of the decrease are not strong. It is found that the optimum Tad is most sensitive to cooling fluid inlet temperature T,,=,. Figure 9 demonstrates the values of the optimum Tad with various Tee. The values of the optimum Tad for SCP are greater than those for COP and WCOP. The overall heat transfer coefficient
For a standard bus (12.2 m long, 2.6 m wide, 3 m high, 49 seats) with a 207 kW diesel engine, the cooling load is about 17.6 kW, and a conventional air conditioner weights about 300 kg [21]. The waste heat that can be recovered through the exhaust gas from such a bus is at least 70 kW, so a WCOP of 0.25 is required to meet the demand for cooling load and a SCP of the order of 200 W kg-’ is desired to keep the bulk and cost of the equipment within the economic limits demanded by commercial applications. From the previous discussions, it is clear that the demand of WCOP can be easily satisfied. However, the SCPs currently available are very low, no matter how the operating temperatures vary. This is because of the low thermal conductivity of the bed and the low wall heat transfer coefficient between the bed and the exchanger. Fortunately, many efforts [22-241 were made to obtain an improved conductivity: a value of 40W m-l K-i for thermal conductivity was reported by Mauran et al. [22]. And it seems possible that a overall heat transfer coefficient of more than 100 kW mm3K-i can be achieved [25]. If that, the SCP of the system could be increased greatly. By considering future improvement of the heat transfer coefficient for the adsorber (either by heat transfer area intensification or by bed conductivity intensification or by the measures [2224] taken), the effects of the WA on system performance are analyzed and shown in Fig. 10. The resulting cycle time with changing UA is shown in Fig. 11 (with the same operating parameters
1138
Li Zhi Zhang
and Ling Wang
as Fig. 10). In the analysis, we assume the coefficients ki and k2 for overall mass transfer are maintained to their previous values. Then it can be seen that the UA has a tremendous impact on system performance, especially on the SCP. The SCP increases abruptly, and then gradually reaches a stable value with an increase in UA. In this particular case, for UA between 1 and 50 kW me3 K-‘, the SCP rises from 50 to 370 W/kg; for UA beyond 50 kW mV3K-l, the SCP becomes stable, and there would seem to be little merit in achieving a higher SCP by an further increase in UA. We call this turning point the threshold, and the value of UA at this point the threshold value. Increasing the overall heat transfer coefficient is highly effective in the ranges below the threshold value, which in this case is 50 kW mm3K-i. The maximum SCP in this case is about 370 W/kg, which is far below the values estimated by Suzuki [l 11.This difference results from the role played by the overall mass transfer coefficient k,. And opposite to SCP, the COP first decreases, and then gradually goes to a stable value. The decrease of COP reflects an increase in sensible heat losses. For a quickly cycled adsorber, when the amount of cycled refrigerant is given, the cycle time depends not only on the overall heat transfer coefficient, but also on the overall mass transfer coefficient. For the adsorber with a UA higher than the threshold value, the cycle time is determined mainly by the mass diffusion inside the zeolite pallets, which becomes the limiting factor in acquiring a higher SCP. As the threshold value will increase with the overall mass transfer coefficient, this problem can be overcome if the overall mass transfer coefficient is increased with the overall heat transfer coefficient. Since the bed heat transfer intensification usually leads to low permeability for the bed, so how to increase the permeability in intensifying the bed heat transfer becomes very interesting and challenging work.
CONCLUSIONS A non-equilibrium dynamic method of calculating the performances of an adsorption cooling system for automobile waste heat recovery was presented. The influences of operating temperatures, namely, the evaporating temperature, the condensing temperature, the desorption temperature, and the adsorption temperature, on the system coefficients, especially on the specific cooling power of the unit mass of adsorbent, are discussed in detail. It is shown that the SCP is more sensitive to parameter changes than COP, WCOP and WCOE. Improving the overall heat transfer coefficient is the most effective way to increase SCP when the UA is below a threshold value, but not much so when the UA is above the threshold value, which is 50 kW mm3K-’ in this case. The threshold value increases with increasing the mass diffusion rate. Thus, to further increase the SCP, the improvements of both the overall heat transfer coefficient and the overall mass transfer coefficient should be considered. At present, for an automobile waste heat adsorption cooling system, the demand for WCOP can be easily met, but for SCP, further research is needed. Acknowledgements-This Ministry Of Mechanical
research Industry.
project
was
supported
by the Technological
Development
Fund
of the
Chinese
REFERENCES 1. J. J. Guilleminot, F. Meunier and B. Mischler, Etude de cycles intermittents a adsorption solide pour la refrigeration solaire, Revue. Phys. Appl. 15, 441-452 (1980). 2. S. C. Chang and J. A. Roux, Thermodynamic analysis of a solar zeolite refrigeration system, ASME J. Solar Energy Engng 107, 189-195 (1985). 3. R.E. Critoph, Performance limitations of adsorption cycles for solar cooling, Solar Energy 41, 21-31 (1988). 4. S.V. Shelton, W.J. Wepfer and D.J. Miles, Ramp wave analysis of the solid/vapor heat pump, ASME J. Energy Res. Technol. 112, 69-78 (1990). 5. S.V. Shelton, W.J. Wepfer and D.J. Miles, Square wave analysis of the solid-vapor adsorption heat pump, Heat Recovery systems & CHP 9, 233-247 (1989). 6. N. Douss and F. Meunier, Experimental study of cascading adsorption cycles, Chem. Engng. Sci. 44, 225-235 (1989). 7. F. Meunier, Theoretical performances of solid adsorbent cascading cycles using the zeolite-water and active-methanol pairs: four case studies, Heat Recovery Systems & CHP 6, 491-498 (1986). 8. D.I. Tchernev and D.T. Emerson, High eficiency regenerative zeolite heat pump, ASHRAE Trans. 94, 20242032 (1988).
Performance estimation of an adsorption cooling system for automobile waste heat recovery
1139
9. F. Meunier, Second law analysis of a solid adsorption heat pump operating on reversible cascade cycles: application to the seolite-water pair, Heat Recovery Systems & CHP 5, 133-141 (1985). 10. R. Q. Zhu. B. Q. Han. M. Z. Lin and Y. Z. Yu, Experimental investigation on an adsorption system for producing chilled water, Int. J. Refrigeration 15, 31-34 (1992). 11. M. Suzuki, Apphcation of adsorption cooling systems to automobiles. Heat Recovery Systems & CHP 13, 335340 (1993). 12. S.M. Sami and C. Tribes, An improved Thermal Engng 16, 149-161 (1996).
model for predicting
the dynamic
behavior
of adsorption
systems,
Appt.
(in Chinese), Chinese High 13. Ceng danling, Ao Yue, Zhu kexiong and Li Qingrong, Engineering Thermodynamics Education Publishing House. Beijing (1988). 14. A. Sakoda and M. Suzuki. Fundamental study on solar powered adsorption cooiing system, J. Chem. Engng Jpn 17, 52-57 (1984). 15. A. Sakoda and M. Suzuki, Simultaneous transport of heat and adsorbate in closed type adsorption cooling system utiking solar heat, ASME J. Solar Energy Engng 108, 239-245 (1986). 16. E. F. Passos. J. F. Escobedo and F. Meunier, Simulation of an intermittent adsorptive solar cooling system, Solar Energy 42, 103-I 11 (1989). 17. A. Hajji and W.M. Worek. Simulation of a regenerative closed-cycle adsorption cooling/heating system, Energy 16, 643-654 (1991). 18. G. Cacciola and G. Restuccia, Reversible adsorption heat pump: a thermodynamic model, Int. J. Refrigeration 18, loo-106 (1995). 19. Y. Peiyi and Ch. Lin, The studies on automobile waste heat air conditioning, Fluid Engineering (in Chinese) 21(6). 5459 (1993). 20. Cheney. W. and Kincaid, D., Numerical Mathematics and Computing, Brooks/Cole Publishing Company, Monterey,
California, 1985. 21. A.A. Pesaran, Y.O. Parent and D. Bharathan, Non-CFC
air conditioning for transit buses, SAE Trans. 101(2), 750759 (1992). 22. S. Mauran, P. Prades and F. L’haridon, Heat and mass transfer in consolidated reacting beds for thermochemical systems. Heat Recovery Systems & CHP 13, 315-319 (1993). 23. J.J. Guilleminot, A. Choisier, J.B. Chalfen, S. Nicolas and J.L. Reymoney, Heat transfer intensification in fixed bed adsorbers, Heat Recovery Systems & CHP 13, 297-300 (1993). 24. R.E. Critoph and R. Thorpe, Momentum and heat transfer by forced convection infixed beds for granular active carbon, Appl. Thermal Engng 16, 419-427 (1996). 25. F. Meunier, Solid sorption: an alternative to CFCs, Heat Recovery Systems & CHP 13, 289-295 (1993).
Published by
PII: s1359-4311(97)00039-2
Elsevier
Science Ltd. All rights reserved Printed in Great Britain 1359-4311/97 $17.00 i 0.00
PERFORMANCE ESTIMATION OF AN ADSORPTION COOLING SYSTEM FOR AUTOMOBILE WASTE HEAT RECOVERY Li Zhi Zhang
and Ling Wang
Research Institute of Internal Combustion Engine, Dalian University of Technology. Dalian 116023, Liaoning Province, China (Received 26 April 1997)
Abstract-This article presents a numerical study of the dynamic performance of an adsorption cooling system for automobile waste heat recovery. A new lumped parameter non-equilibrium model is developed and used to investigate and optimize the waste heat cooling system, which is estimated to be operated in quicker cycles when compared with the time needed to reach equilibrium. The effects of the operating temperatures and the overall heat transfer coefficient on the system performance are extensively investigated. It is found that the SCP is more sensitive to parameter changes than the COP. And improving the UA is the most effective way to obtain an increased SCP, but only in the ranges below the threshold value, which is determined by the overall mass transfer coefficient. 0 1997 Published by Elsevier Science Ltd Keywords-Adsorption
cooling, automobile, waste heat, COP, SCP.
NOMENCLATURE AfZ
cb % COP D, Qo E, hz km L
m n!r P 4 9in 9sr
Ei"
R R, SCP t T UA W WCOE WCOP
heat transfer area between the heating/cooling fluid and zeolite (in zeolite side) (m’) specific heat of the metal adsorber heat exchanger (kJ kg-’ K-‘) specific heat (kJ kg-’ K-‘) coefficient of performance surface diffusivity (m2 s-l) pre-exponent constant (m’s_‘) activation energy of surface diffusion (kJ kg-‘) heat transfer coefficient between the fluids and zeolite (kW m-’ K-‘) overall mass transfer coefficient (s-l) latent heat of evaporization of the refrigerant (kJ kg-‘) mass (kg) mass flow rate of the fluids (kg s-‘) pressure (mbar) heat flow rate (kW) heat flow rate from the heating fluid to the adsorber (kW) isosteric heat (kJ kg-‘) total heat transmitted (kJ) heat transmitted from the heating fluid to the adsorber (kJ) universal gas constant (kJ kg-’ K-‘) average radius of a particle (m) specific cooling power (W kg-’ adsorbent) time (s) temperature (K) overall heat transfer coefficient for unit weight of adsorbent (kW m-3 K-‘) water uptake (kg kg-’ adsorbent) coefficient of waste heat recovery coefficient of waste heat cooling
Greek letters density of dry adsorbent Pa
(kg mm3)
Subscripts
ads av b C
adsorption average adsorber heat exchanger condenser, cooling 1127
1128 CYC des dew
eq f g h 0
v W
wst z
Li Zhi Zhang and Ling Wang cycle
desorption dew point evaporator equilibrium fluid regenerate heating inlet outlet saturation water vapor water liquid waste heat zeolite
INTRODUCTION Adsorption cooling is a promising alternative to traditional vapor compression refrigeration in satisfying the demands of the industry for a diversification of primary energy sources and a reduction in the use of CFCs. The application of adsorption refrigeration to automobiles has other benefits: the cooling system can be powered by engine’s waste heat, which results in gas consumption reduction; and it has no moving parts, which leads to high reliability and silent operation. The basic adsorption cycle [l-3] has a theoretical coefficient of performance of about 0.5. To achieve improved performance, many advanced cycles [4-81, namely, the so called ‘regenerative cycles’ which based on the principle of heat regeneration were proposed. Meunier [9] showed that the performance of an ideal regenerative cycle with an infinite number of cascades can be as high as 1.85, about 68% of the ideal Carnot COP. These researches are very significant in improving the market competitiveness of commercial adsorption cooling/heating machines. However, in the case of automobile waste heat cooling, mechanical simplicity and high reliability will prevail on efficiency. And the waste heat recovery cannot affect the mechanical energy output from the engine. So a two-bed basic zeolite-water adsorption cycle is considered in this study. The feasibility of adsorption cooling for automobile/engine waste heat recovery was studied before, (see [lo, Ill, among others). However, information on its dynamic performance, which is necessary for the design and optimization of the system, is insufficient. Zhu et al. [lo] measured the cooling capacity of a cooling element of a fishing boat diesel engine waste heat chiller and the temperature variation of the adsorbent bed. Their study was purely experimental and no numerical analysis was presented. Suzuki [l l] theoretically studied the effects of UA (overall heat transfer coefficient) on SCP of a passenger car waste heat adsorption air conditioning system, however, no details were outlined with respect to the effects of other parameters which play equal important roles in adsorption refrigeration. Also, in our opinion, the model proposed in his study is not detailed enough for our dynamic analysis of the system performance. Recently, Sami et al. [12] presented an improved dynamic model to study the single adsorber and/or double adsorber systems with heat recovery. The systems they studied employed an air cooled evaporator and an air cooled condenser. Hot oil, superheated steam or exhaust gas could be used as heating fluids for the adsorbers. In these respects, they are similar to the automobile waste heat cooling system we propose. And it gave an insight into the thermodynamics for some of the system components. However, in their analysis, the cycle time was quite long and an equilibrium adsorption state was assumed, while in our case, where the cycle time could be much shorter to obtain an increased SCP, this assumption is invalid and it will jeopardize the accuracy of the analysis. In this study, a detailed non-equilibrium dynamic model is developed to evaluate the influences of various operating parameters upon the performance of an automobile waste heat adsorption cooling system. The dynamic behavior of the various internal and external interactions between the adsorbent and cooling fluids is discussed. In particular, the influences of parameter changes on SCP and the methods to obtain an increased SCP are analyzed. This is
Performance estimation of an adsorption cooling system for automobile waste heat recovery
1129
significant, since the low SCP is the main technological limit associated with the application of adsorption cycles to automobiles waste heat refrigeration.
SYSTEM
DESCRIPTION
The waste heat cooling system analyzed in this article is very simple and can be implemented easily. It comprises four heat exchanges, namely, an air finned forced convection condenser, an air finned forced convection evaporator, and a pair of shell and tube type adsorbers, plus four one-way refrigerant valves, an expansion valve, and an exchange valve, as shown in Fig. 1. The adsorbent is packed in the adsorber heat exchangers, and the heating/cooling fluid flows through the steel tubes of the adsorber heat exchanges. By switching the exchange valve, the two adsorbers can intermittently alternate their functions with each other and a continuous chilled air supply can be obtained. As shown in Fig. 1, when valves 9a, 9d are open and 9b, 9c are closed, adsorber 1 is in heating-desorption process and adsorber 2 is in cooling-adsorption process; when valves 9a, 9d are closed and 9b, 9c are open, adsorber 1 will be in cooling-adsorption process and adsorber 2 will be in heating-desorption process. The heating fluid of the adsorbers is engine’s exhaust gas, and the cooling fluid is ambient air pumped by a blower. The adsorbentadsorbate pair used here is zeolite 13x-water, since the regeneration temperature of zeolite 13xwater is high enough for engine’s exhaust gas heat recovery. The two adsorbers are identical, and they operate the same cycle but out of phase. For simplicity, only one adsorber is considered in the dynamic analysis and performance estimation.
THE
MATHEMATICAL
MODEL
In this model, the temperature and pressure are assumed homogeneous in the components, and a non-equilibrium lumped parameter modeling approach is employed. Other two assumptions are made: (a) the heat capacity of adsorbate in the adsorbed state is equal to that of the liquid phase; (b) the specific heat and the density of dry adsorbent is constant. The governing equations are summarized in the following. Thermodynamic
property
equations
The thermodynamic properties such as the specific heats, the latent heat of evaporization the saturation pressure can be written as the functions of temperature [13].
Fig. 1. Scheme of the adsorption cooling system for automobile waste heat recovery. (1) Adsorber 1. (2) adsorber 2. (3) blower, (4) heat exchange valve, (5) diesel engine, (6) condenser. (7) expansion valve, (8) evaporator, (9a-9d) one-way valves.
and
1130
Li Zhi Zhang and Ling Wang
The specific heats of adsorbate liquid, adsorbate vapor, exhaust gas, and air are expressed in the form; c,=co+ciT+C~P,
(1)
where constants ci (i = 0,1,2) can be derived from least squares curve fit of specific heats values. For instance, the values for water vapor considered as ideal gas are co= 1.68774 kJ kg-’ K-‘; cl = 5.3451 x lo4 kJ kg-’ K-2; c2 = 6.5822 x lo-’ kJ kg-’ K-3. The latent heat of evaporization for pure adsorbate is; L(T) = Lo + ci~T,
(2)
known data for water vapor as adsorbate are Lo = 3171.2 kJ kg-’ and CI~= - 2.4425 kJ kg-’ K-l. The saturation pressure for adsorbate liquid-vapor equilibrium is written in the form; ln(P,) = a, + b,/T,
(3)
where P, is in mbar, known data for water are a, = 20.5896 and b, = - 5098.26. Adsorption equations
Adsorption equilibrium is not assumed. Deviation from equilibrium can be expressed in two different ways. In this study, a linear driving force equation is introduced to account for mass transfer resistance within the pallets, while the resistance in the interparticle voids is neglected, as proposed by some authors [14-171. Then the adsorption rate can be expressed as; g where weq is the equilibrium and it is given by [ 141;
= km&q - w),
uptake at (T,, P,); k,
is the overall mass transfer
km+,
coefficient,
(5) P
and the surface diffusivity D, is given as a function
of temperature
D, = D,oexp(-EJRT,).
Equation
(5) and Eq. (6) can be written together
[14] as; (6)
and simplified as;
k ,,, = klexp(-k,lT,)
(7)
where,
k2 = EJR.
When the T, and P, are kept constant throughout Eq. (4) is written as;
(9)
an adsorption
w = w,,[l - exp(-k,t)],
process, then the solution to (10)
(when T,, P, = constant). Coefficients k, and k2 are obtained from Eq. (7) and Eq. (10) with experimental zeolite 13x-water adsorption curves under constant temperature and pressure. The overall mass transfer coefficient will increase with increasing kl. To an extreme, when kl becomes infinite, then the adsorption state will always maintain equilibrium adsorption state, and the model will become an equilibrium model. To the opposite, when k, equals to zero, the
Performance estimation of an adsorption cooling system for automobile waste heat recovery
mass transfer resistance will become brium equations as following;
infinite.
weq is determined
b(weq)= bo + bl w,q +
1131
by the adsorption-equili-
b2W& + bw&,
(13)
where T, is the adsorbent temperature (IQ P, is the pressure of the adsorber (mbar); numerical values of ai and bi (i = 0, 1, 2, 3) are reported by Cacciola et al. [ 181. The isosteric heat of adsorption is calculated by the equation; qst =
-w&q)>
(14)
where R is the universal gas constant (kJ kg-’ K-l). Conservation
of energy
Isosteric
heating/cooling
adsorbent
processes.
During these two processes, the energy balances for the
and the fluids are;
(15)
hri&(Trav - TJ = c,f6(Tti - Tro)
(16)
where for isosteric heating process, wise is w,,, and the fluid is diesel engine’s exhaust gas; for isosteric cooling process, Wiseis M”,inand the fluid is the ambient air. Tf=, is the calculating average temperature of heating fluid (waste gas) or cooling fluid (ambient air) for the adsorber. For the sake of simplification in normalization, it is defined as;
Tfi - Tfo
Trav= Tz+ q
(17)
$t$)
where Tf, is the outlet temperature of heating/cooling fluids for the adsorber. It varies with changing adsorber temperature during a cycle, and is obtained by iterative techniques in simulations. If we define, UA = h~zA~z/(m,/p,), i.e. overall heat transfer coefficient between the adsorbent bed and the heating/cooling fluid on the basis of the unit weight of adsorbent, then UA is estimated as 1kW mm3K-l for zeolite beds with a heat transfer distance of 5 mm, by assuming the effective thermal conductivity of the packed bed to be around 0.2 W m -r K-’ [l 11. Desorption process. During this process, the energy balance for the adsorbent is; mz(cpz+ cpww+
ctmlm,)~ - mzqst2 =ha&(Tfav
- Tz)
and the heat released at the condenser is; qc = -m, The heat transfered to the adsorber during the isosteric heating and the desorption qin = hr~Ar~(Tr~v- T*)
periods is; (20)
1132
Li Zhi Zhang
and Ling Wang
Table 1. Some parameters used in simulation Symbol or name
Value
Unit
17 0.97 2.74 10.11 70.5 0.023 0.042 0.836 40.04 x 1o-3 905.8 0.47 7.1 1.0 20 2s 5 49
lzf AfZ
hrz he Mu&t &r CP
k,
kz Cb
Tube%gth Fin spacing Tube diameter Number of tubes Number of fins
kW.r?W _)
W.m~i,K-’ W.m-‘.K-’ kg? kg.s-’ kJ.kg-‘.K-’ s-l K kJ.kg-‘.K-’ kg m
and the total heat needed is the integration of qin over these two periods;
Qin = S
qin dt.
(21)
iso+des
Adsorption process. The energy balance for this process is; %(cpz + $Ww +
dw Cbmb/%)
3
-
mzqst
dt
= hfzAfz(Tfav
and the cooling power that can be generated by the evaporator
-
Tz) - m, d”, dt
The total cooling production
?-e)
(22)
during the adsorption phase is;
(2 >
qe= mz
pv (T 2 -
[UTJ - CPW(TC - Tee)].
(23)
is; Qe =
J qedt.
(24)
ad?
System coejkients On the basis of the previous equations, The coefficient of performance;
the system coefficients are defined as the following.
COP =
Qe/Qin
(25)
Table 2. Simulation results for a cycle Symbol TC
TC TZd
=S
TM Ter
Q!” Q. QC
QCWt &yc SCP COP WCOP
Value
Unit
45 10 80 270 450 35 11897.1 4911.7 6023.8 10573.2 107 4s 0.41 0.26
“C “C “C “C “C “C
kJ kJ kJ kJ min Wlkg
1133
Performance estimation of an adsorption cooling system for automobile waste heat recovery
c_._._._._._.--.
0.65 I 0.60 0.55
z
0.50
.........._. c-p
-
-
-
---.
155
-51
scp wcop - WCOE
-47
2
.E 0.45 ”
28 u
2
0.400.35
-43
3
-
0.20’35 0
5
_---
_---
_---
10
20
15
- 39
30
25
35
Fig. 2. Influence of the T, on system performance: T, = 45 “C; T, = 300 “C; T,, = 80 “C; The =450 “C; SCP; - - - WCOP; - - WCOE. Tcfi=35”C. . . . . . . COP:-
-55
0.65 -.-. 0.60
-.-.w._
.. . .. .
0.55
-
-
SCP WCOP - WCOE
--0.50
cop
-.
- 50
2 .g 0.45
3
‘.i!.:
T
-1;:
-_0.25 0.20
Fig.
3.
Influence
---___
I 45
1 40
35
--I 55
I 50 qe cw
/ 60
65
35
of the T, on system performance: T,= 10 “C; Tg= 300 “C; Tad = 80 “Cc ___ sCp; - - - WCOP; -. - WCOE. T,fi=35”C.,.....C0P;
0.70 ,
-.-.-.-.-.-
0.65
-
0.60
- . . . . . . . . . . . . cop
0.65
- ---
0.45
-
0.40
-
0.35
-
0.30
-
o.2 1 50
- 45
SCP WCOP WCOE
-.-
.z 0.50-
8
“C;
50
e 2 %
Thfi=450
-40
2 5
-35
9 m
- 30 _-_-----aI 300
I 350
_ I 400
I 450 Th,j (“c)
Fig. 4. Influence of the The on system performance: Tcfi=35”C. . . . . ..COP. -SCp;---
I 500
I 550
I 600
65i5
T,=45 “C: T,= 10 “C; T,= 250 “C; Tad = 80 “c; wcop;-.-
WCOE.
Li Zhi Zhang and Ling Wang
1134
o.70155
-.-.-.-.-._._
0.65-
5
............
cop
0.60-
-
---
SCP WCOP
0.65-
-.-
WCOE
-50 G 3 3 -45 w
.g 0.50$ s 0.45-
2
u" 0.40-40
0.350.30-
o.251~35 15
20
25
30 35 qfi("C)
40
45
50
55
Fig. 5. Influence of the T,s on system performance: T,=45 “C; T,= 10 “C; T,= 300 “C; Tad= 80 “C; Thfi= 450 “C. COP; scp; - - - WCOP; - - WCOE.
The specific cooling power during a cycle on the basis of the unit weight of adsorbent; SCP = Qel(tcycmz)
(26)
WCOP = Qe/Qw
(27)
The coefficient of waste heat cooling;
The coefficient of waste heat recovery; WCOE = QinlQwst;
(28)
where Qwst is the potential waste heat energy that can be recovered without dew point corrosion, and it can be estimated by;
Qwst =
$&bM(~hfi
(29)
- Tdew),
where mwsr is the total mass of exhaust gas flowed through the adsorber during the isosteric heating and the desorption periods, and Td,, is the dew point temperature of the exhaust gas, which is considered 180°C for diesel engine [19]. Among the coefficients, WCOP determines the cooling capacity an engine can produce with its exhaust gas, while SCP yields the required size of a cooling unit.
1.0
40
..'."."'...'......................,.,,..,,,.,,.., /;
- - - - - _ _ _ _ _ ............
---
cop SCP
WCOP
---WCOE
Fig. 6. Influenceof the T, on system performance:
T,a=35”C.
. . . . . COP;--SCP;---
-5
T,=45 “C; T,= 10 “C; Thfi=450 “C; T,,= 50 “C; WCOp;-.WCOE.
Performance estimation of an adsorption cooling system for automobile waste heat recovery 400, 3753so-
1135
140
.. . ... .
c*p
-
SCP WCOP
---
-30
325y
300-
&Y 275 E g 250._ g 225- 10 200-5
17515
I I 300 350
I I I 400 450 500 Th!i('c)
I I1 7000 I 550 600 650
Fig. 7. The values of the optimum T, with Thfi: T, = 45 “C; T, = 10 “C; Tad= 80 “C; Tcfi=35 “C.
NUMERICAL
RESULTS
AND
DISCUSSION
The previously mentioned set of differential equations developed was first normalized and then solved simultaneously by Runge-Kutta-Fehlberg technique [20]. The time step varied from 1 s to 10 s, based on the length of the cycle time. During each step, iterations were performed to obtain a converged solution. The simulations employed a small test unit which is propotional to a prototype for a standard bus and is being constructed in our laboratory. Some of the parameters considered in the simulations are shown in Table 1. The thermodynamic property values are taken from [13]. The results of the simulation are shown in Table 2. As a result of IQin+ Qe-Qo,t-QJ/(Qin + Qe) < 1.3%, it can be seen that the heat balance for the cycle is satisfied. To further study the cooling system, the influences of the operating conditions and the design parameters on the system performance were estimated. Operating
temperatures
The effects of the evaporating and condensing temperatures on system coefficients are shown in Figs 2 and 3 respectively. The T, and T, have important effects on the SCP, but only have limited effects on the other three coefficients. The COP, SCP, WCOP and WCOE all increase with higher evaporating temperatures or lower condensing temperatures. As the evaporating temperature is increased from 2 to 32 “C, the SCP rises from 40 W kg-’ to 53 W kg-‘, and the COP rises from 0.41 to 0.47. When the condensing temperature is increased from 40 “C to 60 “C, the COP drops from 0.44 to 0.42 and the SCP decreases from 44 to 39 W kg-‘. These -._
<.,
0.7-45
-.-.-.-.-. 0.6-
............ cop SCP --WCOP
0.20.1-
- 30
-.-WCOE O30
, 40
I 50
I / 60 70 T.d('C)
I 80
90
10g5
Fig. 8. Influence of the Tad on system performance: T,=45 "C; T,= 10 ‘C; Ts = 300 “C: Thfi=450 “C; T,fi=35”C.
1136
Li Zhi Zhang and Ling Wang
90 80 u^ 700 2 E g ._ 8
60504030 t
‘1: 0
5
10
15
20
25
30 35 0 Cfi ( C)
40
45
50
55
(
Fig. 9. The values of the optimum Tad with T,,: T, = 45 “C; T, = 10 “C; T,= 300 “C; Tha = 450 “C
- 0.40
- 0.35 “.‘.............
. . . . . . . .._........._,.,...,
- 0.30
. . . . . . . . . . . . cop
-
0
20
40
60 UA
Fig.
10.
- 0.25
SCP
80
120
140
0.2 160
(kW.ti3.K-‘)
Influence of the UA on system performance: ~,,,=0.23;
100
T,=45 “C; T,= 10 “C;
Thfi=450
“C;
T~e=35
“C
W,i,=O.O2.
120looz g
#
SO-
,” 6040 20 -
0I
I
I
\
I
20
40
60
80
I
100
I
I
120
140
UA (kW.ni3.R’)
Fig. 11. Influence of the UA on the cycle time: T,=45 “C; T,= 10 “C; The =450 “C; Tee= 35 “C ~,,,=0.23; W,i,=O.O2.
Performance estimation of an adsorption cooling system for automobile waste heat recovery
1137
tendencies indicate that more energy is supplied to the system and a longer cycle time is resulted when the evaporating temperature decreases or the condensing temperature increases. The WCOEs obtained are above 0.6; and the WCOPs are above 0.25. Figures 4 and 5 show the effects of the temperatures of the heating fluid (waste gas) Thfi and the cooling fluid (ambient air) T,fi on system performance respectively. It can be seen that the variations of the heating and cooling fluids temperatures have strong effects on SCP, but they have small effects on COP, WCOP and WCOE. Increasing the heating fluid temperature or decreasing the cooling fluid temperature can boost SCP. This is because a higher heating fluid temperature or a lower cooling fluid temperature leads to a higher heat transfer rate between the fluid and the adsorbent, which then results in a shorter cycle time and a bigger specific cooling power. However, for heating fluid above 550 “C, the step of the increase for SCP tends to be slower when the heating fluid temperature is further increased. This happens because less refrigerant is desorbed/adsorbed for shorter cycles. It also helps to explain why the COP and the WCOP decrease, though very small, when the heating fluid temperature is increased or the cooling fluid temperature is decreased. It is also noted that the WCOE is nearly constant throughout the variations of The and T,,. The influence of the maximum regenerating temperature Tg on system coefficients are shown in Fig. 6. It is seen that the COP, SCP and the WCOP are increased rapidly, reaches a maximum value and then is decreased gradually with an increase in Tg, while the coefficient of waste heat recovery WCOE drops continuously. Increasing the T, results in more refrigerant desorbed, but it is also leads to more sensible heat losses from the adsorber. And the step of increase becomes smaller when the Tg goes beyond the optimum value, and the sensible heat losses become substantial. In this particular case, the optimum values of Tg for COP, SCP and WCOP are 310, 200 and 180 “C respectively. It is also found that the optimum Tg is The; but it is insensitive to other very sensitive to heating fluid inlet temperature operating temperatures. Figure 7 demonstrates the optimum values of Tg for COP, SCP and WCOP respectively with different Thfi. Figure 8 shows the influence of the minimum adsorption temperature Tad on system performance. The trend of SCP is similar to that in Fig. 6. The SCP is increased rapidly, reaches a maximum value and then is gradually decreased with an increase in Tad. This is because as the Tad increases, the cycle time decreases and the amount of refrigerant adsorbed drops too. The optimum Tad for SCP in this case is 80 “C. The COP, WCOP and WCOE decrease with an increase in Tad, but the tendencies of the decrease are not strong. It is found that the optimum Tad is most sensitive to cooling fluid inlet temperature T,,=,. Figure 9 demonstrates the values of the optimum Tad with various Tee. The values of the optimum Tad for SCP are greater than those for COP and WCOP. The overall heat transfer coefficient
For a standard bus (12.2 m long, 2.6 m wide, 3 m high, 49 seats) with a 207 kW diesel engine, the cooling load is about 17.6 kW, and a conventional air conditioner weights about 300 kg [21]. The waste heat that can be recovered through the exhaust gas from such a bus is at least 70 kW, so a WCOP of 0.25 is required to meet the demand for cooling load and a SCP of the order of 200 W kg-’ is desired to keep the bulk and cost of the equipment within the economic limits demanded by commercial applications. From the previous discussions, it is clear that the demand of WCOP can be easily satisfied. However, the SCPs currently available are very low, no matter how the operating temperatures vary. This is because of the low thermal conductivity of the bed and the low wall heat transfer coefficient between the bed and the exchanger. Fortunately, many efforts [22-241 were made to obtain an improved conductivity: a value of 40W m-l K-i for thermal conductivity was reported by Mauran et al. [22]. And it seems possible that a overall heat transfer coefficient of more than 100 kW mm3K-i can be achieved [25]. If that, the SCP of the system could be increased greatly. By considering future improvement of the heat transfer coefficient for the adsorber (either by heat transfer area intensification or by bed conductivity intensification or by the measures [2224] taken), the effects of the WA on system performance are analyzed and shown in Fig. 10. The resulting cycle time with changing UA is shown in Fig. 11 (with the same operating parameters
1138
Li Zhi Zhang
and Ling Wang
as Fig. 10). In the analysis, we assume the coefficients ki and k2 for overall mass transfer are maintained to their previous values. Then it can be seen that the UA has a tremendous impact on system performance, especially on the SCP. The SCP increases abruptly, and then gradually reaches a stable value with an increase in UA. In this particular case, for UA between 1 and 50 kW me3 K-‘, the SCP rises from 50 to 370 W/kg; for UA beyond 50 kW mV3K-l, the SCP becomes stable, and there would seem to be little merit in achieving a higher SCP by an further increase in UA. We call this turning point the threshold, and the value of UA at this point the threshold value. Increasing the overall heat transfer coefficient is highly effective in the ranges below the threshold value, which in this case is 50 kW mm3K-i. The maximum SCP in this case is about 370 W/kg, which is far below the values estimated by Suzuki [l 11.This difference results from the role played by the overall mass transfer coefficient k,. And opposite to SCP, the COP first decreases, and then gradually goes to a stable value. The decrease of COP reflects an increase in sensible heat losses. For a quickly cycled adsorber, when the amount of cycled refrigerant is given, the cycle time depends not only on the overall heat transfer coefficient, but also on the overall mass transfer coefficient. For the adsorber with a UA higher than the threshold value, the cycle time is determined mainly by the mass diffusion inside the zeolite pallets, which becomes the limiting factor in acquiring a higher SCP. As the threshold value will increase with the overall mass transfer coefficient, this problem can be overcome if the overall mass transfer coefficient is increased with the overall heat transfer coefficient. Since the bed heat transfer intensification usually leads to low permeability for the bed, so how to increase the permeability in intensifying the bed heat transfer becomes very interesting and challenging work.
CONCLUSIONS A non-equilibrium dynamic method of calculating the performances of an adsorption cooling system for automobile waste heat recovery was presented. The influences of operating temperatures, namely, the evaporating temperature, the condensing temperature, the desorption temperature, and the adsorption temperature, on the system coefficients, especially on the specific cooling power of the unit mass of adsorbent, are discussed in detail. It is shown that the SCP is more sensitive to parameter changes than COP, WCOP and WCOE. Improving the overall heat transfer coefficient is the most effective way to increase SCP when the UA is below a threshold value, but not much so when the UA is above the threshold value, which is 50 kW mm3K-’ in this case. The threshold value increases with increasing the mass diffusion rate. Thus, to further increase the SCP, the improvements of both the overall heat transfer coefficient and the overall mass transfer coefficient should be considered. At present, for an automobile waste heat adsorption cooling system, the demand for WCOP can be easily met, but for SCP, further research is needed. Acknowledgements-This Ministry Of Mechanical
research Industry.
project
was
supported
by the Technological
Development
Fund
of the
Chinese
REFERENCES 1. J. J. Guilleminot, F. Meunier and B. Mischler, Etude de cycles intermittents a adsorption solide pour la refrigeration solaire, Revue. Phys. Appl. 15, 441-452 (1980). 2. S. C. Chang and J. A. Roux, Thermodynamic analysis of a solar zeolite refrigeration system, ASME J. Solar Energy Engng 107, 189-195 (1985). 3. R.E. Critoph, Performance limitations of adsorption cycles for solar cooling, Solar Energy 41, 21-31 (1988). 4. S.V. Shelton, W.J. Wepfer and D.J. Miles, Ramp wave analysis of the solid/vapor heat pump, ASME J. Energy Res. Technol. 112, 69-78 (1990). 5. S.V. Shelton, W.J. Wepfer and D.J. Miles, Square wave analysis of the solid-vapor adsorption heat pump, Heat Recovery systems & CHP 9, 233-247 (1989). 6. N. Douss and F. Meunier, Experimental study of cascading adsorption cycles, Chem. Engng. Sci. 44, 225-235 (1989). 7. F. Meunier, Theoretical performances of solid adsorbent cascading cycles using the zeolite-water and active-methanol pairs: four case studies, Heat Recovery Systems & CHP 6, 491-498 (1986). 8. D.I. Tchernev and D.T. Emerson, High eficiency regenerative zeolite heat pump, ASHRAE Trans. 94, 20242032 (1988).
Performance estimation of an adsorption cooling system for automobile waste heat recovery
1139
9. F. Meunier, Second law analysis of a solid adsorption heat pump operating on reversible cascade cycles: application to the seolite-water pair, Heat Recovery Systems & CHP 5, 133-141 (1985). 10. R. Q. Zhu. B. Q. Han. M. Z. Lin and Y. Z. Yu, Experimental investigation on an adsorption system for producing chilled water, Int. J. Refrigeration 15, 31-34 (1992). 11. M. Suzuki, Apphcation of adsorption cooling systems to automobiles. Heat Recovery Systems & CHP 13, 335340 (1993). 12. S.M. Sami and C. Tribes, An improved Thermal Engng 16, 149-161 (1996).
model for predicting
the dynamic
behavior
of adsorption
systems,
Appt.
(in Chinese), Chinese High 13. Ceng danling, Ao Yue, Zhu kexiong and Li Qingrong, Engineering Thermodynamics Education Publishing House. Beijing (1988). 14. A. Sakoda and M. Suzuki. Fundamental study on solar powered adsorption cooiing system, J. Chem. Engng Jpn 17, 52-57 (1984). 15. A. Sakoda and M. Suzuki, Simultaneous transport of heat and adsorbate in closed type adsorption cooling system utiking solar heat, ASME J. Solar Energy Engng 108, 239-245 (1986). 16. E. F. Passos. J. F. Escobedo and F. Meunier, Simulation of an intermittent adsorptive solar cooling system, Solar Energy 42, 103-I 11 (1989). 17. A. Hajji and W.M. Worek. Simulation of a regenerative closed-cycle adsorption cooling/heating system, Energy 16, 643-654 (1991). 18. G. Cacciola and G. Restuccia, Reversible adsorption heat pump: a thermodynamic model, Int. J. Refrigeration 18, loo-106 (1995). 19. Y. Peiyi and Ch. Lin, The studies on automobile waste heat air conditioning, Fluid Engineering (in Chinese) 21(6). 5459 (1993). 20. Cheney. W. and Kincaid, D., Numerical Mathematics and Computing, Brooks/Cole Publishing Company, Monterey,
California, 1985. 21. A.A. Pesaran, Y.O. Parent and D. Bharathan, Non-CFC
air conditioning for transit buses, SAE Trans. 101(2), 750759 (1992). 22. S. Mauran, P. Prades and F. L’haridon, Heat and mass transfer in consolidated reacting beds for thermochemical systems. Heat Recovery Systems & CHP 13, 315-319 (1993). 23. J.J. Guilleminot, A. Choisier, J.B. Chalfen, S. Nicolas and J.L. Reymoney, Heat transfer intensification in fixed bed adsorbers, Heat Recovery Systems & CHP 13, 297-300 (1993). 24. R.E. Critoph and R. Thorpe, Momentum and heat transfer by forced convection infixed beds for granular active carbon, Appl. Thermal Engng 16, 419-427 (1996). 25. F. Meunier, Solid sorption: an alternative to CFCs, Heat Recovery Systems & CHP 13, 289-295 (1993).