2. Fig. 2 Thermodynamic cycle of a booster assisted ejector
refrigeration system
resulting in a superheated vapor at state 3. This vapor goes into
the condenser and by means of the thermal power extraction QCO ,˙
a phase change at isobar p3 occurs and results in a saturated liquid
at state 4. Later, this saturated liquid is divided, part goes to the
pump and the remainder to the expansion valve. The pump re-
ceives this liquid and compresses it until it reaches the subcooled
˙
state 5 with the addition of the mechanical power Wp. With the
˙
supply of the thermal power QGE , the generator at isobar p1 heats,
evaporates and superheats the incoming subcooled liquid up to
Fig. 1 „a… Main components of a booster assisted ejector re- state 1. The other part of the saturated liquid coming from the
frigeration system. „b… Schematic diagram of an ejector condenser, flows adiabatically through the expansion valve and
results in a saturated liquid-vapor mixture in state 6. This satu-
rated mixture goes into the evaporator, where the liquid becomes
change from the subsonic to the sonic condition of low-pressure saturated vapor in state 7 at isobar p6 by the addition of the ther-
vapor at the mixing chamber inlet, after it has just entered the ˙
mal power QEV . Then, the booster receives this vapor and com-
ejector. ˙
presses it up to pressure pDIS by the mechanical power Wb trans-
Therefore, for the understanding of a booster assisted ejector ferred, so the superheated state 2 is reached and thereby the cycle
refrigeration system, the knowledge of its operation conditions is is completed.
necessary. A parametric study with Lu’s ejector model in transi- According to its thermodynamic cycle, the booster assisted
tion regime, gives system operating conditions and ejector’s op- ejector refrigeration system is a four-temperature system, 4T, that
erational and geometrical features. Also, the thermodynamic results from a series coupling between an ejector refrigeration
analysis of this information yields the best system operation con- system and a mechanical compression system, whose interface is
ditions. The study considers generator and condenser temperatures a heat exchanger. So, the first system is represented by the states
for a solar powered system. 1, 3, 4, 5 and 2, 3, 4, 4 and the mechanical by the states 2, 4 , 6,
7. A hypothetical constant pressure thermal energy exchange is
Booster Assisted Ejector Refrigeration System carried out at the heat exchanger between two refrigerant mass
The ejector is a device without moving parts and comprised of flows of the same magnitude, one that is heated from states 4 to
a primary fluid’s convergent-divergent nozzle, a mixing chamber 2, expanded previously from state 4 to 4 , and another that is
and a diffuser, as Fig. 1 b shows. Two fluids with different pres- cooled from states 2 to 4 , expanded later from state 4 to 6. The
sures interact through an adiabatic thermo-compression process representation of this 4T system with its corresponding reversible
and the resulting mixture undergoes a recompression process that cycle in a T-s diagram is shown in Fig. 3.
finishes at an intermediate mixing pressure. In the first process, The ideal supplied mechanical and thermal energy together
the primary fluid, at high pressure, is expanded adiabatically with the cooling capacity, from the T-s diagram, are
through the convergent divergent nozzle. At nozzle exit the low- QEV TEV SREF (1)
pressure secondary fluid is entrained, and as a consequence of the
momentum exchange, the mixing process starts and continues Wbr SREF TDIS TEV (2)
along the chamber. The secondary fluid pressure is increasing un-
til both fluids reach uniform properties and a complete mixing is QGE TGE STM (3)
achieved. Later, a recompression process is carried out at the dif- Wr STM TGE TCO (4)
fuser in order to increase its exit pressure.
System composition and corresponding cycle thermodynamic Wr SREF TCO TDIS (5)
states are shown in Figs. 1 and 2. The generator, condenser,
evaporator, ejector, pump and expansion valve constitute the ejec- The 4T system efficiency is defined as
tor system. The booster, coupled between the evaporator and ejec- QEV
tor, is the added element. The system fluid flow is as follows: s (6)
QGE Wbr
Superheated vapor coming from the generator, at state 1, and the
superheated vapor leaving the booster, in state 2, enter the ejector Substitution of Eqs. 1 to 3 into 6 , results in
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3. ˙
in which P is the ejector entropy production rate. The ejector
efficiency is also obtained from a control volume in which there is
no entropy production, in a similar way to the combined isentro-
pic expansion and compression processes of the primary and sec-
ondary fluids 5 , resulting in
m2 h3r h2
˙
EJ (14)
m1 h1 h3r
˙
where subscript r refers to the reversible thermo-compression and
recompression processes. For this case, the mass and energy con-
servation equations give the following reversible entrainment ratio
h1 h3r
Ur (15)
h3r h2
Finally, combining Eqs. 10 , 15 and 14 the ejector efficiency
is found as
U
EJ (14 )
Ur
Fig. 3 „a… The 4T ejector and compression refrigeration sys-
tem and „b… its ideal thermodynamic cycle which compares a real parameter with its ideal value.
The area ratio is another important ejector parameter that is
related with its geometry and is defined as
TEV SREF Amc
(7) (16)
s
TGE STM SREF TDIS TEV A*
Factorizing TGE in the above relation’s denominator and incorpo- where A* is the main nozzle throat area and Amc is the mixing
rating SREF after equalizing Eqs. 4 and 5 , gives chamber area whose diameters are indicated in Fig. 1 b . The
parameter is obtained with Lu’s model 3 .
TGE TCO
TEV TCO TDIS Pump. Applying the conservation equations to the pump’s re-
s (8) versible adiabatic compression process results in
TGE TDIS TEV TGE TCO
1 ˙
TGE TCO TDIS Wpr m1 h5r h4
˙ (17)
Factorizing and regrouping terms in Eq. 8 results in ˙
where Wpr is the mechanical power transferred and h5r is the final
TEV TGE TCO state’s enthalpy. In practice, this mechanical power is equal to the
s (9) required in the isentropic compression of an incompressible fluid,
TGE TCO TTEV TCO TDIS TEV giving
This equation allows the evaluation of the ideal system efficiency,
that groups the ejector and mechanical compression subsystems, h5r v4 p5 p4 h4 (18)
showing its four temperature dependence. The highest values for with specific volume v4 .
this ideal system efficiency are obtained for highest TGE , TDIS and
TEV and lowest TCO . Booster. Repeating the above procedure for the booster, re-
sults in
Element and System Thermodynamic Relations ˙
Wbr m2 h2r h7
˙ (19)
The steady state conservation equations for mass and energy
without losses are considered for all system elements, except for ˙
where Wbr is the mechanical power transferred and h2r is the final
the ejector in which a real model is used and its entropy produc- state’s enthalpy of the isentropic process.
tion rate could be evaluated. Refrigeration System. The efficiency for a booster assisted
ejector refrigeration system is determined by its coefficient of per-
System Elements formance, COPs , defined as
Ejector. Applying the conservation and entropy production
rate equation on the ejector control volume and employing the ˙
QEV
entrainment ratio U, defined as COPs (20)
˙ ˙ ˙
QGE Wpr Wbr
m2
˙
U (10) that is the refrigeration power produced per each unit of power
m1
˙ supplied to the system and differs from Eq. 6 by considering
the following relations are found ˙
Wpr . Substitution of each one of aforementioned power amounts
gives
m3 m1 1 U
˙ ˙ (11)
U h7 h6
h1 Uh2 COPs (20 )
h3 (12) h1 h4 U h2r h7
1 U
Similarly, the exergy efficiency, s , is defined as the ratio of the
s1 Us2 P˙
s3 (13) evaporator exergy change to the generator, pump and booster ex-
1 U m1 1 U
˙ ergy changes, resulting in
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4. ˙ and booster discharge temperatures and the lowest condenser tem-
EEV perature. TDIS corresponds to pDIS’s saturation temperature.
s (21)
˙ ˙ ˙
EGE Eb Ec In regard to the ejector, its behavior is given by the tendencies
of the ejector’s efficiency, EJ , entrainment ratio, U, area ratio, ,
which takes final form as and main nozzle throat area, A* . Typical plots of EJ and U
U e6 e7 versus TGE and pDIS are shown in the double plot of Fig. 5. In the
s (21 ) first, the considered pDIS corresponds to the lowest booster dis-
e1 e4 U e2r e7
charge pressure because the ejector is demanded to work at its
A similar relation to Eqs. 20 and 21 is the supplied energy maximum capacity. So, when TCO is kept constant and TGE in-
ratio, Er, defined as creases, EJ behavior describes an ascending-convex curve. The
EJ values decrease and their respective slopes increase as TCO
˙ ˙
Wp Wb grows. Therefore, the highest ejector efficiency is achieved at the
Er (22) highest generator and the lowest condenser temperatures for a
˙
QGE certain booster discharge pressure. Any separation from this con-
giving the final expression dition, a generation temperature decrease or a condenser tempera-
ture increase, will result in a lower ejector efficiency. U behavior
h5r h4 U h2r h7 also describes an ascending-convex curve with an almost constant
Er (22 )
h1 h5r slope. U values and their slopes are higher at lower TCO . Conse-
quently, the highest EJ and U are reached at the highest TGE and
Parametric Study of a Solar Booster Assisted Ejector lowest TCO . So, for a TGE of 90°C and a TCO of 20°C the highest
Refrigeration System EJ and U are about 0.26 and 0.6, respectively. In the second plot
a highest common TGE of 85°C is considered. When TCO is kept
Refrigerant R134a was selected as the system working fluid constant and pDIS increases, EJ shows an ascending-convex ten-
after considering its thermodynamic and ecological characteris- dency with a maximum. U tendency is also ascending and convex
tics, as well, as its commercial availability. Thermodynamically, with an almost constant slope. At the highest TGE , EJ and U are
R134a isentropic lines have a lower slope than the saturated vapor higher again at lower TCO and only EJ reaches a maximum at an
curve. Therefore, to avoid any condensation along the ejector’s intermediate pDIS . Consequently, for a TGE of 85°C and a TCO of
main nozzle expansion, a generator vapor superheating of 5°C is 20°C, the highest EJ and the corresponding U are about 0.26 and
fixed. The evaporator temperature and its cooling capacity are 0.75, respectively.
maintained at constant values of 10°C and 1 kW, respectively. Figure 6 shows the behavior of ejector geometrical parameters
Considering that the refrigeration system is located in a tropical A* and . In the first plot, when TCO is kept constant and TGE
zone and will consequently be solar powered, the independent increases, the A* behavior describes a descending-concave curve.
variable ranges were fixed as follows
The lowest A* value with respective lowest slope are reached at
20°C TCO 40°C with TCO 10°C the highest TGE and lowest TCO . The behavior traces an
ascending-concave curve with its highest value and slope at the
TCO 10°C TGE 90°C with TGE 5°C highest TGE and the lowest TCO . If the behaviors of A* and are
in which the generator saturation temperature defines its working compared, their inverse relationship is revealed. According to
pressure pGE . Also, TCO and TEV define the condenser and evapo- Eq. 16 , the lowest A* and highest result in the smallest mix-
rator working pressures. ing chamber area, Amc, that belongs to the smallest ejector. Be-
sides, when comparing first plots of Figs. 5 and 6, the highest U
n pCO pEV corresponds to this smallest ejector. On the other hand, and for the
pDIS pEV with n 6 to 18
24 second plot in Fig. 6, when TCO is kept constant and pDIS in-
where pDIS is the booster discharge pressure. It takes values above creases, the A* behavior also describes a descending-concave
pEV from 0.25 to 0.75 of (pCO pEV), with a rate of change of curve. The lowest A* and respective lowest slope are reached at
1/24 of this pressure difference. As a result of having a constant the lowest TCO and highest pDIS and TGE . The behavior traces
TEV , this booster discharge pressure only changes with n and an ascending-convex curve with pDIS . Its rate of increase becomes
pCO . The corresponding value for pEV is 0.2 MPa while pCO takes slower and almost stops at a high TCO . The highest values are
respectively the values of 0.572, 0.770 and 1.017 MPa for con- reached again at the lowest TCO with highest TGE and correspond-
denser temperatures of 20, 30 and 40°C. ing highest pDIS . Therefore, the same inverse relation between A*
and holds. In this case, the lowest A* and highest , of about
9.3, correspond to the lowest TCO of 20°C, highest TGE of 85°C
Results and Discussion and respective highest pDIS of 0.39 MPa. This value agrees with
The results were plotted in a three-dimensional space with TCO , typical experimental values that lie between 4 and 10 6 .
TGE and pDIS as independent variables. The surfaces obtained were The system behavior is characterized by the tendency of its
bounded and evolved with respect to pDIS and TGE , according to coefficient of performance, COPs , exergy efficiency, s , and sup-
the 3D space considered. The surface intersection with different plied energy ratio, Er, which are shown in Figs. 7 and 8. In the
planes, defined by constant values of independent variables TGE first plot of Fig. 7, when TCO is kept constant and TGE increases,
and pDIS, was analyzed for condenser temperatures of 20, 30 and the COPs behavior describes ascending-convex curves with high-
40°C at lowest pDIS with n 6 and high TGE of 85°C. Table 1 est values and slopes at lowest TCO . As s behavior is similar to
presents the results for the ejector and refrigeration system for COPs , its values decrease as TCO increases. For the second plot of
three booster discharge pressures given by n 6, 8 and 12. Fig. 7, when TCO is constant and pDIS is increased, the COPs also
The ideal system efficiency, s , and the system’s coefficient of describes an ascending-convex curve. So, the highest COPs are
performance, COPs , against the booster discharge temperature, reached at the lowest TCO and the corresponding highest pDIS.
TDIS , are shown in Fig. 4, for a common high TGE of 85°C and Again, the s COPs behaviors are similar.
three different values of TCO . In this plot, for a constant TCO , the Figure 8 shows the Er behavior. In the first plot, when TGE
ideal efficiency s grows as TDIS increases. A maximum value is grows, Er describes an ascending-convex curve with an almost
reached at the highest TDIS and lowest TCO . The COPs has a constant slope. Er values decrease and their respective slopes in-
similar trend as s with values lower by about one fifth. There- crease at higher condenser temperatures. In regard to the second
fore, the maxima s and COPs are reached at the highest generator plot, Er describes an ascending-concave curve whose values and
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6. Fig. 6 Plots of A* and against TGE and pDIS for different TCO
when pDIS„nÄ6… and TGEÄ85°C Fig. 8 Plots of Er against TGE and pDIS for different TCO when
pDIS„nÄ6… and TGEÄ85°C
slope decrease as TCO increases. Since Er represents the ratio
between the mechanical and thermal power supplied to the sys- ˙
tem, it is important to point out that any increase in TCO implies a highest ejector efficiency the QCO values are 2.9, 3.1 and 4.4 times
higher system power supply, even if Er is fixed. higher than the refrigeration capacity of 1 kW, for the condenser
Again, the highest COPs , s and Er are reached at the highest temperatures of 20, 30 and 40°C, respectively.
TGE , lowest TCO and the respective highest pDIS . Therefore, The most important ejector and system results, for a unitary
above values result in the most efficient system in which the ejec- cooling capacity, are presented in Table 1. For an extrapolation of
˙
the refrigeration capacity QEV and according to the conservation
tor has the smallest size and lowest compression ratio. Also, these
generator and condenser temperatures with respective saturation equations, the system power amounts and the ejector geometrical
temperature for pDIS , correspond to the highest ideal efficiency. ˙
parameter A* grow linearly with QEV . Dimensionless system and
Nevertheless, this condition only makes full use of the mechanical ejector parameters keep constant. Also, from an engineering point
compression. of view, the reversible mechanical and thermal power can be
On the other hand, at constant TCO , the rate of increase of s transformed into real values, when appropriate mechanical effi-
with respect to pDIS decreases at highest booster discharge pres- ciencies and thermal effectivenesses are considered. Therefore,
sures. Thus, at intermediate pDIS values a moderate change in pDIS the values presented in Table 1 are very useful as reference, in the
causes a quite larger change in s . At this condition, the ejector case of designing a system powered with thermal solar energy, or
has its highest efficiency and works at a higher compression ratio. another low temperature thermal source, in conjunction with elec-
Therefore, the system takes a full advantage on thermocompres- trical energy of the grid.
˙ ˙
sion and as a consequence, QGE grows and Wbr decreases, giving According to the second plot of Fig. 7 and the data presented in
a balanced supply of thermal and mechanical energy to the system Table 1, a booster assisted ejector refrigeration system for ice
˙
that derives in an efficient use of energy. This change in QGE and making, that provides a cooling capacity of 1 kW with a TEV of
˙ br cause a decrease in COPs and Er values with a slight increase 10°C and a TGE of 85°C, has: 1 a highest COPs of 0.7 with a
W ˙ ˙ ˙
˙ Wbr of 0.08 kW, a QGE of 1.4 kW and a QCO of 2.5 kW for a TCO
in QCO . So, as shown in Table 1, for a high TGE pf 85°C and
of 20°C and a pDIS of 0.39 MPa. 2 a highest COPs of 0.47 with a
˙ ˙ ˙
Wbr of 0.12 kW, a QGE of 2 kW and a QCO of 3.2 kW for a TCO of
30°C and a pDIS of 0.49 MPa. 3 a highest COPs of 0.3 with a Wbr ˙
˙ ˙
of 0.17 kW, a QGE of 3.2 kW and a QCO of 4.4 kW for a TCO of
40°C and a pDIS of 0.6 MPa. At this relatively low TGE of 85°C,
excellent for solar powered refrigeration systems, the aforemen-
tioned values for ice making become attractive and their COPs
values were found to be competitive with those of solar absorption
systems.
Conclusions
Three-dimensional surfaces of dependent variables were ob-
tained with TCO , TGE and pDIS as independent variables. Depen-
dent variables were grouped in ejector behavior and system be-
havior, whose surfaces were bounded and evolved with respect to
TCO , when it is considered as a parameter.
In regard to the ejector behavior, it is observed that a maximum
EJ value is reached for the highest generator temperature and the
lowest condenser temperature for an intermediate booster dis-
charge pressure. If condenser temperature is increased, the corre-
Fig. 7 Plots of COPs and s against TGE and pDIS for different sponding maximum EJ value is reached at a higher booster dis-
TCO when pDIS„nÄ6… and TGEÄ85°C charge pressure.
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7. For an ice making temperature TEV of 10°C, the maximum r compression ratio dimensionless
ideal system efficiency s is reached at the highest TGE and TDIS s specific entropy kJ/kgK
for lowest TCO . Also, the extreme values of lowest A* and high- S entropy kJ/K
est , U, COPs , s and Er correspond to these TGE , TCO and T temperature (°C)
respective highest pDIS . Just mentioned A* and parameters cor- U entrainment ratio dimensionless
respond to the smallest ejector with lowest compression ratio. W ejector mechanical energy, mechanical energy kJ
However, according to the rate of increase of exergy efficiency, ˙
Wb booster mechanical power kW
the selection of a system with the highest ejector efficiency results ˙
Wp pump mechanical power kW
in a system with a balanced mechanical and thermal energy sup- increment
ply whose ejector achieves a higher compression ratio. exergy efficiency dimensionless
In practice, the condenser temperature is fixed by the environ- efficiency dimensionless
mental conditions and a variety of generator temperature and ejector area ratio dimensionless
booster discharge pressure could be chosen, according to the ther- Subscripts and superscripts
mal and mechanical energy available and economically allowed.
For a moderate generator temperature of 85°C, easily achieved by * main nozzle throat
flat plate collectors of good quality, the following average values CO condenser
˙
were obtained: COPs of 0.58, 0.36 and 0.21; QGE of 1.8, 3, and 6 DIS booster discharge
˙ ˙
kW; QCO of 2.9, 4.12 and 7.16 kW; Wbr of 0.065, 0.095 and 0.14 EJ ejector
kW with average pDIS of 0.34, 0.41 and 0.5 MPa for respective EV evaporator
TCO of 20, 30 and 40°C. For the highest ejector efficiency and a GE generator
condenser temperature of 20°C, the main energy parameter values mc mixing chamber
˙ ˙ ˙ r reversible; ratio
are: COPs of 0.531, QGE of 1.806 kW, QCO of 2.882 kW and Wbr
REF refrigerator
of 0.059 kW for a pDIS of 0.324 MPa. Therefore, the results indi-
s booster assisted ejector refrigeration system
cate that these systems could be a solution for solar refrigeration
TM thermal machine
using off-the-shelf components. As a thermodynamic or designing
1, . . . ,7 cycle thermodynamic states
guide, Table 1 summarizes the most important ejector and system
parameters.
Nomenclature References
2 1 Sokolov, M., and Hershgal, D., 1990, ‘‘Enhanced Ejector Refrigeration Cycles
A area (m ) Powered by Low Grade Heat-Part 1: System characterization,’’ Int. J. Refrig.,
COP coefficient of performance dimensionless 13 November , pp. 351–356.
d diameter m 2 Dorantes, R., Estrada, C. A., and Pilatowsky, I., 1996, ‘‘Mathematical Simu-
e specific exergy kJ/kg lation of a Solar Ejector-compression Refrigeration System,’’ Appl. Therm.
Eng., 16 8/9 , pp. 669– 675.
Er supplied energy ratio dimensionless ´ ´
3 Lu, L.-T., 1984, ‘‘Etudes Theorique et Experimtale de la Production de Froid
˙
E exergy flow rate change kW `
Par Machine Tritherme a Ejecteur de Fluide Frigorigene,’’ Ph.D. thesis, Lab-
h specific enthalpy kJ/kg ´
oratoire d’Energetique et d’Automatique, de I’INSA de Lyon, France.
4 Sokolov, M., and Hershgal, D., 1990, ‘‘Enhanced Ejector Refrigeration Cycles
m
˙ mass flow rate kg/s Powered by Low Grade Heat-Part 2: Design Procedures,’’ Int. J. Refrig., 13
n coefficient that defines pDIS November , pp. 357–363.
p pressure MPa 5 Mooney, D. A., 1955, Introduction to Thermodynamics and Heat Transfer,
˙
P rate of entropy production kW/K Prentice Hall, Englewood Cliffs, USA, pp. 279 and 302.
´
6 Nahdi, E., Champoussin, J. C., Hostache, G. y., and Cheron, J., 1993, ‘‘Les
Q heat kJ ` ´ ´ ´
Parametres Geometriques Optima d’un Ejecto-compresseur Frigorifique,’’ Int.
˙
Q heat flow kW J. Refrig., 16 1 , pp. 67–72.
Journal of Solar Energy Engineering FEBRUARY 2005, Vol. 127 Õ 59
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