Investigation of an experimental ejector refrigeration machine operating with refrigerant R245fa at design and off-design working conditions. Part 1. Theoretical analysis

Investigation of an experimental ejector

refrigeration machine operating with refrigerant

R245fa at design and off-design working

conditions. Part 1. Theoretical analysis

K.O. Shestopalov

, B.J. Huang

, V.O. Petrenko

, O.S. Volovyk

Odessa, Ukraine

a r t i c l e i n f o

Article history: Received 18 July 2014 Received in revised form 29 December 2014 Accepted 27 January 2015 Available online 5 March 2015 Keywords:

Ejector

Ejector refrigeration machine R245fa

Performance characteristics 1-D analysis

a b s t r a c t

The ejector refrigeration machine (ERM) offers several advantages over other heat-driven refrigeration machine, including simplicity in design and operation, high reliability and low installation cost, which enable its wide application in the production of cooling. In this paper the theoretical analysis of ejector design and ejector refrigeration cycle performance is presented. It is shown that ERM performance characteristics depend strongly on the operating conditions, the efficiency of the ejector used, and the thermodynamic properties of the refrigerant used. A 1-D model for the prediction of the entrainment ratiou, and an optimal design for ejectors with cylindrical and conical-cylindrical mixing chambers are presented in this paper. In order to increase ERM performance values, it is necessary first of all to improve the performance of the ejector.

© 2015 Elsevier Ltd and IIR. All rights reserved.

Une

etude du fonctionnement d

'un systeme frigorifique

exp

erimental 

a

ejecteur avec le frigorig

ene R245fa aux

conditions de travail de conception et hors-conception.

1

ere

partie- Analyse th

eorique

Mots-cl
es : Ejecteur ; Machine frigorifique a
ejecteur ; R245fa ; Caract
eristiques de performance ; Analyse unidimensionnelle

* Corresponding author. New Energy Center, Department of Mechanical Engineering, National Taiwan University, Taipei 106, Taiwan. Tel.:þ886 2 23634790.

E-mail address:[email protected](K.O. Shestopalov).

w w w . i i fi i r . o r g

Available online at

www.sciencedirect.com

ScienceDirect

journal homepage: w ww.elsevier.com/locate /ijrefrig

http://dx.doi.org/10.1016/j.ijrefrig.2015.01.016

1.

Introduction

The widespread use of cooling and air-conditioning systems in summer causes a serious electrical peak load problem, and

electrical power generation has an environmental impact as well. There are many thermal energy types in the world, including solar thermal, waste and exhaust heat, and geothermal and biomass energy. For several decades, scientists have been looking for a suitable cooling technology that can be powered directly by thermal energy. A heat-driven ejector cooling cycle looks very promising for this need and offers interesting alternatives for air conditioning and space cooling. The New Energy Center at National Taiwan University has long been devoted to the development of solar ejector cooling technology, particularly with ejector refrigeration machines (ERMs) operating with low-boiling point working fluids (Huang et al., 1985, 1999, 2010a, 2010b). These machines have several advantages over other heat-driven refrigeration cycles, including low temperature heat supply, simplicity in design and operation, the possibility of freezing-temperature opera-tion, high reliability, and low installation cost. These make ERMs more attractive than other heat-driven refrigeration cycles and represent a real opportunity for the further devel-opment and wide application of these cooling machines. At present, the relatively low coefficients of performance (COPs) of ERMs are the main reason that they are rarely used. This low efficiency is caused mainly by irreversibilities in the ejector. In order to increase the COP values, it is necessary first of all to improve the performance of the ejector.

Many researchers have recently studied, both theoretically and experimentally, low-boiling refrigerants in ERMs (Sun, 1999; Cizungu et al., 2001; Selvaraju and Mani, 2004, 2006). A comparison of system performance was carried out for the same ejector geometry using the environmentally friendly working fluids R123, R134a, R152a, and R717. The results suggested that, for different boiler temperatures, the entrainment ratio and the system efficiency depend mainly on the ejector geometry and the compression ratio.

The basic ejector theory was developed by Munday and Bagster in 1977. Many other research studies have been car-ried out to investigate the performance of the ejector refrig-eration cycle with different refrigerants. The structure of the ejector has a great influence on the performance of the ejector. Recently, computational fluid dynamics (CFD) anal-ysis has provided a powerful tool for the study of supersonic ejectors (Sriveerakul et al., 2007a, 2007b; Scott et al., 2008; Varga et al., 2009).

An improved 1-D model for the prediction of the entrain-ment ratiou, and an optimal design for ejectors with cylin-drical and conical-cylincylin-drical mixing chambers are presented in this paper. The governing equations were derived on the basis of one dimensional model ofSokolov and Zinger (1989).

2.

Theoretical analysis of ejector design and

ejector refrigeration cycle performance

The main components of an ERM include an ejector, a generator, an evaporator, a condenser, an expansion valve, and a feed pump. Fig. 1 shows the arrangement of these components. The process of a continuously operating ERM is characterized by points 1e9 inFig. 2, which is a thermody-namic ejector refrigeration cycle in the pressure-enthalpy di-agram. A low-boiling refrigerant is heated and vaporized in Nomenclature

A area, mm2

a sonic velocity, m s1

C ejector compression ratio

cp constant pressure specific heat, kJ kg1K1

COP coefficient of performance

CCMC conical-cylindrical mixing chamber CMC cylindrical mixing chamber

E ejector expansion ratio

ERM ejector refrigeration machine h specific enthalpy, kJ kg1 M molecular weight, kg kmol1

_

m mass flow rate, kg s1

P pressure, bar

Q heat flow, kW

q specific heat, kJ kg1

R universal gas constant, J K1mol1 r latent heat, kJ kg1; s specific entropy, kJ kg1K1 T temperature, C or K V gas velocity, m s1 v specific volume, m3_kg1 _ W power, W Greek letters

a, b, s, f ejector area ratios g ratio of specific heats ε, l, П gas-dynamic functions h coefficient of efficiency

Q dimensionless temperature

r density, kg m3

4 velocity coefficient

j converging angle at mixing chamber entrance

u entrainment ratio Subscripts c condenser x critical e evaporator fp feed pump g generator m mixture max maximum mech mechanical opt optimum p primary s secondary suc suction t nozzle throat therm thermal

y ejector choking section

1, 2, 3, f cross-sections of the ejector (Fig. 3,Eqs. (2)e(4)) 1, 2, 3…9 cycle states in theFigs. 1e2, Eq.(6)

the generator using thermal energy Qg at relatively high

pressure Pg. This primary vapor, with a mass flow rate of _mp, passes through the supersonic nozzle, drawing secondary vapor with a mass flow rate of _ms into the ejector from the evaporator. The two streams mix in the ejector and leave it after the recovery of pressure in the ejector's diffuser. The combined stream flows to the condenser, where it is condensed to liquid at intermediate pressure Pc. The heat of

condensation Qcis released into the environment.

From the condenser, a portion of the liquid is returned to the generator via an electrically driven feed pump, consuming mechanical work _Wmech, while the remainder is expanded through an expansion valve. Thereafter, the vaporeliquid flow of the refrigerant enters the evaporator, where the liquid is evaporated at low temperature Teand pressure Peto produce

the necessary cooling effect Qe. The vapor from the evaporator

is finally entrained by the ejector, thus completing the cycle. From the aforesaid, it follows that the supersonic ejector is the key component in the ejector cooling cycle, and supplies suction, compression, and discharge of the secondary vapor by using the primary vapor. Two choking phenomena exist in ejector performance: one in the primary flow through the supersonic nozzle and the other in the suction flow in the mixing chamber (Huang et al., 1985).

Fig. 3illustrates the structure of supersonic ejectors with (a) cylindrical and (b) conical-cylindrical mixing chambers.

The geometry of the ejector is characterized by the configuration of the nozzle (At e the primary nozzle throat

area; A1e the primary nozzle exit area) and the cross-section

areas of the other parts of the ejector (A2e the entrance area

of the mixing chamber; A3e the area of the cylindrical section

of the mixing chamber).

The operating conditions of an ejector are specified by operating pressures Pe, Pc, and Pg, the expansion pressure

ratio, E¼ Pg/Pe, and the compression pressure ratio, C¼ Pc/Pe.

The performance of an ejector is measured by its entrain-ment ratiou, which is defined as:

u ¼m_s

_ mp

(1) The design of an ejector flow profile with a CMC is defined by the area ratio a, which can be found from the relation: a¼A3

At

(2) The primary nozzle design is determined by the area ratio:

f¼A1 At

(3) The most important geometrical parameters of the ejector are the area ratios A3/Atand A1/At. When the value of A3/Atis

low, the jet devices have a high compression pressure ratio C, but the entrainment ratiou is low. When the value of A3/At

increases, the compression pressure ratio C decreases, but the entrainment ratio u increases. The second geometrical parameter A1/Atdetermines the pressure of the working vapor

at the exit of the nozzle. Insufficient or excessive expansion of the working fluid in the nozzle results in an increase in energy loss during the outflow and in a decrease in ejector efficiency. The design of a CCMC is specified by the area ratio a, the converging angle j at the mixing chamber entrance, and the area ratio b, which is given as:

b¼A2 A3

(4) Construction, geometry, and the surface condition of the supersonic ejector flow profile must provide the most effective utilization of primary flow energy for suction, compression,

Fig. 1e Diagram of an ejector refrigeration machine.

Fig. 2e Diagram of the ejector refrigeration cycle.

Fig. 3e Structure of ejectors with (a) cylindrical and (b) conical-cylindrical mixing chambers.

and discharge of the secondary vapor (Petrenko, 1978; Huang et al., 1999; Petrenko et al., 2005a, 2005b; Eames et al., 2007).

To maintain optimum performance, the geometry of the ejector flow profile must be varied. This variation in geometry should first take place in the primary nozzle throat area Atand

in mixing chamber area A3.

On the basis on the improved 1-D theory of ejector design, the area ratio a and the optimum value of b can be found by making use of variational calculation. The value of bopt

cor-responds to the maximum entrainment ratiou. Supplemen-tary data for the determination of the a, bopt, and the optimal

converging angle j are given inPetrenko (1978)andPetrenko et al. (2005a).

Two kinds of energies are required to drive the ejector cooling cycle: thermal energy Qginput to the generator, and

mechanical (electrical) energy _Wmechto power the feed pump. Since these energies are obtained from two dissimilar sources, with entirely different specific energy values and prices, the performance of the ERM can be correctly specified by equal use of two COPs, namely COPtherm and COPmech (Petrenko, 2001, 2009). The value of COPthermis defined as Qedivided by

Qg, and the value of COPmechis the ratio between Qeand the

mechanical power _W_mechused by the mechanical feed pump. They can be expressed asEqs. (5) and (6):

COPtherm¼ Qe Qg¼ _ msqe _ mpqg¼ u qe qg; (5) COPmech¼ Qe _ Wmech ¼ hfpm_sqe _ mpv5
Pg Pc ¼ hfpuqe v5
Pg Pc ; (6) where v5and hfpare the specific volume of refrigerant intake

and the feed pump coefficient of efficiency, respectively; (Pge

Pc) is the generating and condensing pressure difference, in kPa.

According to Eq. (5), in order to increase COPtherm, it is

necessary to raise the entrainment ratio u and the specific cooling capacity qe, as well as decrease the specific generating

heat qg. At the specified evaporating temperature Tethis

re-quires the generating temperature Tgto be increased and the

condensing temperature Tcto be decreased. From Eq.(6), it

follows that in order to increase COPmech, it is necessary to

raise the entrainment ratiou, the specific cooling capacity qe

and the feed pump coefficient of efficiency hfp, and to decrease

the pump pressure difference (Pge Pc). Thus, analysis ofEqs. (5) and (6) shows that the characteristics of COPtherm and

COPmech depend strongly on the operating conditions, the

efficiency of the ejector used, and the thermodynamic prop-erties of the refrigerant used. Maximum efficiency can only be obtained if the cycle of the ERM is completely reversible.

Obviously, reliable performance of ERMs greatly depends on the reliability of feed pump operation, which is the critical component in the ejector cycle. This electrically actuated pump is the only element in the heat-driven ERM that has moving parts, and it therefore determines the operational safety, leak resistance, and lifetime of the whole system.

The safe performance and coefficient of efficiency of the feed pump are largely dependent on the pressure difference (Pg e Pc). To decrease this pressure difference, and thus to

increase the dependability and effectiveness of the system as a whole, the use of low-pressure refrigerants in the ejector cycle is preferable.

3.

Ejector analysis and performance

The design equations for the 1-D mathematical model for the prediction of the entrainment ratiou, and the optimal design for ejectors with a CMC and conical-cylindrical mixing cham-bers (CCMC) presented in this paper were derived on the basis of the one-dimensional model ofSokolov and Zinger (1989).

A schematic view of an ejector with cylindrical and conical-cylindrical mixing chambers is shown inFig. 3.

The following assumptions were made for the analysis: 1. primary and secondary flows have identical adiabatic

in-dexes g and the universal gas constant R;

2. before entering the mixing chamber in the section between the output cross-section of the nozzle (exit of the nozzle) 1e1 and the inlet cross-section of the mixing chamber 2e2, the primary flow does not expand and does not mix with the entrained flow;

3. the thickness of the output cross-section of the nozzle edge is negligible;

4. in cross-section yey both flows have static pressure that is equal to the critical pressure of the entrained flow, i.e., Pрy¼ Psy¼ Ps,Пsх;

5. initial velocities of the primary and secondary flows are negligible because they are much lower compared to the velocities of these flows in the mixing chamber.

Three laws define the processes that refer to all jet devices:  the mass-conservation law:

_

mm¼ _mрþ _ms¼ _mрð1 þ uÞ; (7)

 the energy-conservation law:

hp$ _mpþ hs$ _ms¼ hm$ _mm (8)

 the momentum-conservation law: 42$
_ mp$Vp2þ _ms$Vs2  
m_pþ _ms  $V3 ¼ P3$A3þ ZA3 A2 P dA Pp2$Ap2 Ps2$As2: (9) The value of Z A3 A2

P dA represents the momentum caused by the reaction of the wall of the conical entrance region under the constant-pressure condition; this value can be calculated from Eq.(10):

ZA3 A2 Р dA ¼ 0:5$A3$ðb  1Þ$
Ps2þ P3$П3f  ; (10)

whereП3fis a pressure ratio at the entrance and exit of the

cylindrical part of the mixing chamber, it can be found from: П3f¼ Pf P3¼  P2 P3 d ¼  Ps Pm d $ _П s2 Пm3 d ; d¼ lgP3 Pf lgP3 P2 ¼lg P3 lg Pf lg P3 lg P2:

3.1. Gas dynamic functions

Gas dynamic functions are used for the prediction of the entrainment ratiou in methodology ofSokolov and Zinger (1989), which make calculation of ejector entrainment ratio easier.

- The reduced isentropic velocity l is defined as a ratio of flow velocity Vaduring its isentropic (adiabatic) flow and

critical velocity Vx:

l¼Va Vx;

(11) where Vxcan be calculated as:

Vx¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2$g gþ 1$ P0 r0 s ; (12)

P0andr0are the pressure and the specific density

respec-tively at stagnation condition.

The reduced pressureП is defined as a ratio of the pressure Р of the isentropic moving gas in a given cross-section and a stagnation pressureР0: П ¼  1g_g 1_{þ 1}$l2 g g1 (13) The reduced mass velocityε is defined as a ratio of the area of flow critical cross-section Axand the area of flow

cross-sectionА (Sokolov and Zinger (1989): ε ¼Ax A ¼ lmax$  П Пx 1 g $ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 Пg1 g q ¼  gþ 1 g g g1 $l$  1g_g 1_{þ 1}$l2 1 g1 ; (14) where lmax¼ ffiffiffiffiffiffiffiffiffiffiffiffi gþ 1 g 1 s ; (15) Пx¼  2 gþ 1 g g1 : (16) 3.2. Governing equations

The velocities of primary, secondary, and mixed flows Vр2, Vs2,

and V3in typical cross-sections of the mixing chamber can be

expressed as follows: Vp2¼ 41$apx$lp2; apx¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2$g gþ 1$ Pp rp s ; (17) Vs2¼ 44$asx$ls2; asx¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2$g gþ 1$ Ps rs s ; (18) V3¼ amx 43 $lm3; amx¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2$g gþ 1$ Pm rm s : (19)

The areas of primary, secondary and mixed flows can be determined fromEqs. (20)e(22):

Ap2¼ _ mp$apx gp$Пpx$Pp$εp2; (20) As2¼ _ ms$asx gs$Пsx$Ps$εs2; (21) A3¼
_ mpþ _ms  $amx gm$Пmx$Pm$εm3: (22) The velocities of flows in typical cross-sections are expressed through critical velocities of working flow (арх),

entrained flow (аsx), and mixed flow (amx), as follows fromEqs. (17)e(19). If the critical velocities if the flows are known, the critical cross-sections of the working, entrained, and mixed flows can be determined from Eqs. (20)e(22). From these equations the ejector flow profile can be built. These equa-tions result from the mass conservation law (Eq.(7)).

After substitution of expressions (17e19) for velocities Vр2,

Vs2, and V3, expressions (20e22) for cross-sections of flows

Ap2, As2, and A3, the values of static pressures Ps2¼ Пs2,Psand

P3¼ Pm,Пm3, and the value of momentum from the reaction of

the entry converge for the cone wall, that is Eq.(10)into Eq.(9)

according to the mass-conservation law (7), we get Eq.(23)for the calculation of the entrainment ratio of the ejector working with the substances with the same physical properties (Sokolov and Zinger (1989):

u ¼K1$lp2 lm3 K3 lm3þ K4 K2$ls2$p ;1ffiffiffiffiQ (23) Here, K1¼ 41$42$43; (24) K2¼ 42$43$44; (25) K3¼4 εp2$ Pm Pp$ ( Пm3 Ps Pm$ b 0:5$ðb  1Þ$Пs2  " 1þ  Pm Ps 1d $ _П m3 Пs2 1d#!) ; (26) K4¼4 εs2$ Pm Ps$ ( Пm3 Пm2$ b 0:5$ðb  1Þ  " 1þ  Pm Ps 1d $  Пm3 Пs2 1d#!) ; (27) 4 ¼ 43 g$Пx$b; (28) Q ¼Ts Tp¼ a2 sx a2 px (29) 41,42,43and44are the experimental velocity coefficients

of the nozzle, mixing chamber, diffuser, and entrance part of the mixing chamber, respectively (those allow for accounting the irreversibility of the flow through ejector);

dis the coefficient characterizing the increment of pressure at the conical part of the mixing chamber;

Q is the dimensionless temperature.

It can be seen from these equations that it is necessary for the determination ofu to have gas-dynamic functions of the primary and secondary flows in the inlet cross-section of

mixing chamber (lр2,Пр2,εр2and ls2,Пs2,εs2) and of the mixed

flow at the exit from the mixing chamber (lm3,Пm3,εm3).

Gas-dynamic functions of the primary flow are determined from Eq.(30): lp2¼ lmax$ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1  Ps Pp g1 g v u u t _{; ε} p2¼ lp2$  Ps Pp$ 1 Пx 1 g : (30)

The properties of the entrained flow in the cross-section

2e2, and of the mixed flow in cross-section 3e3cannot be selected optionally, since they are related through the geom-etry of the mixing chamber.

Reciprocally, they are connected by Eq.(31)(Sokolov and Zinger (1989): εs2¼ u$ ffiffiffiffi Q p b$
1þ u$p ffiffiffiffiQ$Ps Pm$ 1 εm3 Ps Pp$ 1 εр2 : (31)

The goal of the calculation consists in determining the optimum gas-dynamic functions ls2 and lm3of these flows,

namely, the value at which the entrainment ratiou peaks. To properly solve this problem, it is necessary to impose certain limitations on the ejector operating at choking condition.

3.3. Limitations on the ejector operating at choking condition

The basis of the one-dimensional model of Sokolov and Zinger is the theory of the limiting regimes occurring at choking condition (Sokolov and Zinger, 1989).

In one-dimensional analysis, there are three possible lo-cations where limiting regime can occur: (I) at the inlet cross-section2e2of the mixing chamber; (II) somewhere along the entrance section yey of the mixing chamber; and (III) at the exit cross-section3e3of the mixing chamber before the inlet to the diffuser (Sokolov and Zinger, 1989; Guangming et al., 2010).

Considering the above, limiting regime I occurs when the secondary flow reaches sonic velocity at cross section2e2, and therefore, the value ls2must not exceed 1.

When the ejector operates at limiting regime III, the ve-locity of the mixed flow at the exit section of the mixing chamber 3e3 cannot be higher than the critical velocity, and the value of lm3must not exceed 1.

When the ejector operates at limiting regime II, the velocity of the secondary flow at cross-section yey cannot be higher than the critical value; therefore, the value of lsymust not

exceed 1.

By analogy with Eq.(31), the reduced mass velocity of the secondary flowεsyat the section yey is determined from:

εsy¼ u s$ð1 þ uÞ$amx asx$ Ps Pm$ 1 εm3 amx asx$ Ps Pp$ 1 εр2 ; (32)

where s¼ Ay/A3, s¼ 1 for an ejector with a cylindrical mixing

chamber, and 1< s < b for an ejector with a conical-cylindrical mixing chamber.

Since the velocity of the secondary flow Vsyat cross-section

yey equals the critical velocity Vsxat limiting regime II, the

valueεsy¼ εsx¼ 1.

On the basis of Eq.(32), the value ofu, which corresponds to limiting regime II, can be calculated by:

u ¼s$ Ps Pm$ 1 εm3 Ps Pm$ 1 εpy 1 s$Ps Pm$ 1 εm3 $ 1ffiffiffiffi Q p : (33)

3.4. Optimization of gas-dynamic functions determination

According to the methodology ofSokolov and Zinger (1989), the optimum gas-dynamic functions ls2and lm3determining

by the linear method of successive approximation, which is laborious and has low calculation accuracy.

As an alternative to the Sokolov and Zinger method, the authors offer a new approach for the determination of the maximum entrainment ratio. This method consists in solving of a nonlinear programming problem for objective function, which has the form:

u ¼ uðx1; x2; z1; z2…ziÞ0MAX; (34)

under the following constraints:

ceqiðx1; x2; z1; z2…zkÞ ¼ 0; i ¼ 1; 2 (35)

0< xn 1; n ¼ 1; 2; 3; (36)

whereх1,х2 are the independent variables; and z1, z2,…, zk

denote the parameters of the objective function.

For specific physical quantities, problem (34e36) is repre-sented by the following. The objective function is prerepre-sented by the expression:

u ¼K1$lp2 lm3 K3

lm3þ K4 K2$ls2$p1ffiffiffiffiQ

(37) for determination of the entrainment ratio (23), where ls2¼ x1

and lm3 ¼ х2 are independent variables; х1 is the reduced

isentropic velocity of the secondary flow at the entrance sec-tion of the mixing chamber ls2;х2is the reduced isentropic

velocity of the mixed flow at the exit section of the mixing chamber lm3.

Nonlinear restrictions ceqi(x1, x2, z1, z2…zk) ¼ 0 can be

written as the following equations: ceq1¼  s Pm Pp$ εm3 εpy  $ðlm3þ K4 K2$ls2Þ   s Pm Ps$ε m3  $
lm3þ K3 K1$lp2¼ 0; (38) ceq2¼  s Pm Pp$ εm3 εpy  $  bPm Ps$ εm3 εs2    s Pm Ps$εm3  $  bPm Pp$ εm3 εp2  ¼ 0: (39)

Linear restrictions on the nonlinear programming prob-lem, in the form of 0< xn 1, can be written as the following

equations:

0< lm3 1; 0 < ls2 1; 0 < lsy 1; (40)

It is worth noting that the linear restriction 0< lsy 1 for

the objective function (38) is implicit, and it reveals a nonlinear restriction (39).

The problem of nonlinear programming (37e39) is solved by gradient methods in the environment of the computer mathematics package MatLab by means of the add-on module Optimization Toolbox. The advantages of the sug-gested method with the use of modern computer technolo-gies are in totally automating the determination of the entrainment ratio maximum for different refrigerants in a wide range of operating conditions, as well as in its high accuracy and calculating speed. The values of the gas-dynamic functions, lm3 and ls2, obtained from solving the

problems (37e39), were substituted into Eqs. (23), (26) and (27), from which the maximum of entrainment ratiou was determined.

Automating the calculation of the entrainment ratio maximum makes it possible to determine the optimal value of bfor an ejector with a CCMC. The simulation flowchart for the optimal value of b determination when the maximum of the entrainment ratio for the given design conditions is reached, is shown inFig. 4.

Analysis ofEqs. (26e27),(32e33), and(38e39)shows that to determine the entrainment ratio of an ejector with a CCMC, in addition we must have the values of41,42,43,44, b, s, and d.

Hereinafter the following experimental constants were used: 41¼ 0.95, 42¼ 0.975, 43¼ 0.9, 44¼ 0.925, d ¼ 0.5, and s ¼ b

(Sokolov and Zinger, 1989; Guangming et al., 2010).

4.

Determination of the ejector geometry

The operating conditions for which the ejector and ERM were developed for the selected refrigerants were characterized by the design parameters of the ejector cooling cycle Te, Pe, Tc,

Pc, Tg, and Pg, and by the cooling capacity of Qe. The values of

Te and Qe were assigned in accordance with the

re-quirements of refrigeration users. The temperature Tcwas

selected on the basis of the design parameters of the ambient environment and the mode of rejection of condensation heat. The value of Tgwas determined by taking into account

the temperature and the kind of heating medium, the mode of generation of the heat supply, and the properties of the refrigerant used.

To determine the geometry of the ejector and the design values of ERM, it is necessary to build its cycle and to deter-mine the specific heat load qe. On the basis of the methodology

developed in Section3of this paper, the design value of the entrainment ratio maximumumaxwas calculated. Mass flow

rate of entrained flow m_s was determined from the given cooling capacity: _ ms¼ Qe qe¼ Qe h8 h7; (41) Mass flow rate of primary flow _mpwas determined from Eq. (1): _ mp¼ _ ms umax: (42) The computed values of _ms and _mp were then used to

design the ejector and to determine the calculated geometries, which were intended to provide maximum efficiency of operation at the rated conditions.

For the determination of cross-section areas At, A1, and A2

of the ejector flow profile (Fig. 3), the following equations were used (Sokolov and Zinger (1989):

At¼ _ mp$apx g$Пx$Pp; (43) A1¼ At εp2; (44) A2¼ A1þ As2; (45) where As2¼ _ ms$asx$εs2 g$Пx$Ps : (46) For the ejector with a CMC, the area of the exit cross-section was AI

3¼ A2, while the value of AII3 for the ejector

with a CCMC was determined from the following equation: AII

3¼

A2

bopt

(47) The main geometric parameter of the ejector A3/At, which

provides the design valueu, was calculated from Eq.(48): A3 At¼ Pp
1þ up ffiffiffiq Pmεm3 : (48) The area ratio of the nozzle A1/Atwas found from:

A1

At¼

1 εP1:

(49)

5.

Refrigerant selection for the experimental

ERM

The analysis and comparison of performance characteristics for various refrigerants showed that, from thermodynamic

Fig. 4e Simulation flowchart for the determination of the optimal value ofb and the maximum value of u.

and operating viewpoints, the most suitable refrigerants for ERMs were low-pressure types with a high critical tempera-ture Tcr, a large specific latent heat of vaporization at

tem-peratures Teand Tg, a low specific heat of the liquid refrigerant

in the range of operating temperatures (TgeTe), and a normal

boiling point temperature Tb about Te (Petrenko, 2001; Petrenko et al., 2005a; Mazur, 2003).

Fig. 5 shows saturation curves of eight low-pressure

working fluids, including two hydrocarbons, in a T-s dia-gram, andTable 1presents several parameters of these re-frigerants for comparison, in order to allow selection of the most appropriate one.

Hydrocarbons are well-known gases and can be found in a number of general applications. Their use in systems for commercial refrigeration, chillers, and heat pumps is well established (Granryd, 2001). Results of investigations of ERMs operating with various hydrocarbon refrigerants have also been reported in recent years (Selvaraju and Mani, 2004;

Pridasawas and Lundqvist, 2007; Nehdi et al., 2008; Boumaraf and Lallemand, 2009; Roman and Hernandez, 2009, 2011). Several hydrocarbons have favorable character-istics as refrigerants from a thermodynamic as well as a heat transfer point of view. They have excellent environmental characteristics: no ozone depleting potential and negligible global warming potential. Hydrocarbons have been used as refrigerants for many years in the petrochemical industry. Experience gained in recent years indicates that hydrocarbons can be implemented in an economical way for a number of other applications. However, safety precautions due to their flammability must be seriously taken into account (Granryd, 2001).

FromFig. 5andTable 1it follows that all the low-pressure refrigerants presented have not only relatively high critical temperatures and rather low critical and operating pressures, but also positive-slope saturated-vapor lines, except refrig-erant R142b, which has an almost vertical saturated-vapor line. Fig. 5e Saturation curves of different low-pressure refrigerants in a T-s diagram.

Table 1e Characteristics of different low-pressure refrigerants.

Property Refrigerant

R123 R141b R142b R236fa R245ca R245fa R600 R600a

Chemical Formula C2F3HCl2 C2FH3Cl2 C2H3F2Cl C3H2F6 C3H3F5 CHF2CH2CF3 C4H10 C4H10

Molecular Weight M, kg kmol1 152.93 116.9 100.5 152.04 134.05 134.05 58.13 58.13 Normal Boiling Temperature Tb_,_{C 27.87 32.20 9.80 1.44 25.13 14.90 0.50 11.61}

Critical Temperature Tcr_,_{C 183.8 208.0 137.4 124.92 174.4 154.05 152.0 134.7}

Critical Pressure Pcr_{, bar 36.7 43.4 42.0 32.0 39.3 36.4 37.9 36.4}

Specific Heat Capacity of Liquidср

at T¼ 30_{C, kJ kg}1_K1

1.025 1.15 1.19 1.28 1.34 1.37 2.47 2.49 Latent Heat r at T¼ 8_{C, kJ kg}1 _{178.3 234.0 209.4 155.4 210.0 200.6 377.9 347.8}

Ozone Depletion Potential 0.02 0.11 0.06 0.00 0.00 0.00 0.00 0.00 Global Warming Potential 76 630 2270 6300 950 950 <10 <10

Therefore, the actual near-isentropic expansion of the saturated vapor of all these working fluids in the nozzle of the ejector is realized in the dry-vapor regions with beneficial ef-fects on the reliability of the flow-through parts of the ejector, as well as on the performance of the ejector.

The analysis and comparison of performance characteris-ticsu, COPtherm, and COPmechof these refrigerants for design

conditions of Tg¼ 95С, Tс¼ 32С, and Te¼ 12C and of hfp¼ 0.5

for ejectors with a CMC or a CCMC are shown inFig. 6. FromFig. 6a, we observe that, for different refrigerants, the values ofu vary across a range of 0.52e0.58 for the CMC and from 0.56 to 0.65 for the CCMC.Fig. 6b shows the variation in COPthermwhose small range of change is similar to the

vari-ation of the entrainment ratiou. The range of COPthermis from

0.38 to 0.45 for the CMC and from 0.41 to 0.51 for the CCMC. This proves the importance of improving ejector design in order to obtain the maximum entrainment ratio, which in turn will maximize cycle performance.

Fig. 6c indicates clearly, in contrast toFig. 6a and b, that the discrepancy of COPmechis much bigger thanu and COPtherm:

from 33.36 to 138.56 kW kW1for the CMC and from 33.93 to 164.18 kW kW1for the CCMC. This contrast is caused by the contribution of the pressure difference (Pge Pc) and the

spe-cific cooling capacity qeof various refrigerants. It follows from

this that refrigerants with a smaller pressure difference (Pge

Pc) and a larger latent heat can make full use of the COPmech.

On the other hand, the refrigerants with a higher u and COPtherm and a lower pressure difference (Pge Pc), such as

R141b, R123, and R245ca, have a normal boiling point tem-perature Tbthat is much higher than the ERM working

evap-orating temperature Te, and consequently have a vacuum in

evaporator. As a result of this, it is necessary to have an additional device to evacuate air from the ejector system.

Comparative analysis shows that refrigerant R141b, which has the highest critical temperature, has the highest efficiency for a CCMC. The lowest efficiency occurs with refrigerant R236fa which has the lowest critical temperature. Other re-frigerants have similar COPthermvalues. Note that refrigerant

R141b is toxic, and refrigerants R142b and R123 do not meet modern environmental requirements. Refrigerant R245ca also can be considered as a prospective working fluid for ERMs, but only for higher evaporating temperatures in the evaporator, for instance, in cascade refrigeration machines, where the ERM acts as the topping cycle.

The obtained results (Fig. 6a) also demonstrate convinc-ingly that the application of a CCMC under the same operating conditions causes performance improvement up to 23.6% in comparison to ejectors with a CMC. The lowest improvement was observed for refrigerants R142b and R600a. The en-hancements for refrigerant R142b were only 0.7% and 1.5% in u and COPtherm, respectively; and for refrigerant R600a, it is a

little higher: 0.8% and 1.7% inu and COPtherm, respectively.

The maximum growth of the same performance characteris-tics reached 22.7% and 23.6% for R245ca. Further to this, the improvement in COPmechfor each refrigerant was the same as

improvement inu.

Comparative analysis confirmed that the environmentally friendly natural low-pressure hydrocarbons butane (R600) and isobutane (R600a) and working fluid R245fa offer the best performance combination. Refrigerant R245fa also has good thermodynamic properties, reasonable working pressures, and a high critical temperature, which makes it a useful candidate for an ejector cooling cycle. In addition, it is non-corrosive, non-toxic, and non-flammable, which makes its application nonhazardous without additional safety mea-sures. For these reasons, we have selected refrigerant R245fa as the most suitable working fluid for general purpose appli-cations in the present study.

6.

Conclusions

Theoretical analysis of ejector design and ejector refrigeration cycle performance was carried out. Analysis showed that the performance characteristics of ejectors and the ejector refrigeration cycle depend strongly on the operating condi-tions, the efficiency of the ejector used, and the thermody-namic properties of the refrigerant used.

Reliable performance of the ejector system substantially depends on the reliability of feed pump operation, which is the critical component in the ejector cycle. This electrically actuated pump is the only element in the heat-driven ERM that has moving parts, and it therefore determines the oper-ational safety, leak resistance and lifetime of the whole system.

We propose an improved 1-D model for the prediction of the entrainment ratiou, and an optimal design for ejectors with a CMC and a CCMC.

Comparative analysis of the performance characteristics of eight low-pressure refrigerants confirms that the environ-mentally friendly hydrocarbons butane (R600) and isobutane (R600a) and working fluid R245fa offer the best performance combinations. Refrigerant R245fa was selected as the most suitable working fluid for general purpose applications in the present study.

Acknowledgments

This publication is based on the work supported by Award No.KUK-C1-014-12, made by King Abdullah University of Sci-ence and Technology (KAUST), Saudi Arabia.

r e f e r e n c e s

Boumaraf, L., Lallemand, A., 2009. Modeling of an ejector refrigerating system operating in dimensioning and off-dimensioning conditions with the working fluids R142b and R600a. Appl. Therm. Eng. 29, 265e274.

Cizungu, K., Mani, A., Groll, M., 2001. Performance comparison of vapour jet refrigeration system with environment friendly working fluids. Appl. Therm. Eng. 21, 585e598.

Eames, I.W., Ablwaifa, A.E., Petrenko, V.O., 2007. Results of an experimental study of an advanced jet-pump refrigerator operating with R245fa. Appl. Therm. Eng. 27, 2833e2840.

Granryd, E., 2001. Hydrocarbons as refrigerantse an overview. Int. J. Refrigeration 24, 15e24.

Guangming, C., Xiaoxiao, X., Shuang, L., Lixia, L., Liming, T., 2010. An experimental and theoretical study of a CO2ejector. Int. J.

Refrigeration 33, 915e921.

Huang, B.J., Chang, J.M., Wang, C.P., Petrenko, V.O., 1999. A 1-D analysis of ejector performance. Int. J. Refrigeration 22 (5), 354e364.

Huang, B.J., Jiang, C.B., Hu, F.L., 1985. Ejector performance characteristics and design analysis of jet refrigeration system. J. Eng. Gas Turb. Power 107, 792e802.

Huang, B.J., Liu, R.H., Wu, J.H., Yen, J.W., Hsu, H.Y., Chang, J.M., 2010a. Field test of solar-assisted cooling system. In: Proc. EuroSun 2010 (Graz, Austria).

Huang, B.J., Yen, C.W., Wu, J.H., Liu, J.H., Hsu, H.Y., Petrenko, V.O., Chang, J.M., Lu, C.W., 2010b. Optimal control and performance test of solar-assisted cooling system. Appl. Therm. Eng. 30, 2243e2252.

Mazur, V., 2003. Optimum refrigerant selection for low-temperature engineering. Low Temp. Cryog. Refrig. 101e118.

Munday, J.T., Bagster, D.F., 1977. A new ejector theory applied to steam jet refrigeration. Ind. Eng. Chem. Process Des. Dev. 16, 442e449.

Nehdi, E., Kairouani, L., Elakhdar, M., 2008. A solar ejector air conditioning system using environment-friendly working fluids. Int. J. Energ. Res. 32, 1194e1201.

Petrenko, V.O., 1978. Investigation of Ejector Cooling Machine Operating with Refrigerant R142b. Odessa Technological Institute of Refrigeration Industry, Ukraine. Ph.D. thesis.

Petrenko, V.O., 2001. Principle of working fluid selection for ejector refrigerating systems. Refrig. Eng. Technol. 1 (70), 16e21.

Petrenko, V.O., 2009. Application of innovative ejector chillers and air conditioners operating with low-boiling refrigerants in trigeneration systems. In: Proc. Eurotherm Seminar No.85 September 7e9. Louvain-la-Neuve, Belgium.

Petrenko, V.O., Chumak, I.G., Volovyk, O.S., 2005a. Comparative analysis of the performance characteristics of an ejector refrigerating machine utilizing various low-boiling working fluids. Refrig. Eng. Technol. 5 (97), 25e35.

Petrenko, V.O., Volovyk, O.S., Ierin, V.O., 2005b. Areas of effective application of ejector refrigeration machines using low-boiling refrigerants. Refrig. Eng. Technol. 1 (93), 17e30.

Pridasawas, W., Lundqvist, P., 2007. A year-round dynamic simulation of solar-driven ejector refrigeration system with iso-butane as a refrigerant. Int. J. Refrigeration 30, 840e850.

Roman, R., Hernandez, J.I., 2009. Performance of ejector cooling systems using hydrocarbon refrigerants. In: Proc. Eurotherm Seminar No.85 September 7e9, Louvain-la-Neuve, Belgium.

Roman, R., Hernandez, J.I., 2011. Performance of ejector cooling systems using low ecological impact refrigerants. Int. J. Refrigeration 34, 1707e1716.

Selvaraju, A., Mani, A., 2004. Analysis of an ejector with environment friendly refrigerants. Appl. Therm. Eng. 24, 827e838.

Selvaraju, A., Mani, A., 2006. Experimental investigation on R134a vapour ejector refrigeration system. Int. J. Refrigeration 29, 1160e1166.

Scott, D., Aidoun, Z., Bellache, O., Ouzzane, M., 2008. CFD simulations of a supersonic ejector for use in refrigeration applications. In: International Refrigeration and Air Conditioning Conference at Purdue.

Sokolov, E.Y., Zinger, N.M., 1989. Jet Devices. Energoatomizdat, Moscow, p. 352.

Sriveerakul, T., Aphornratana, S., Chunnanond, K., 2007a. Performance prediction of steam ejector using computational fluid dynamics: part 1. Validation of the CFD results. Int. J. Therm. Sci. 46, 812e822.

Sriveerakul, T., Aphornratana, S., Chunnanond, K., 2007b. Performance prediction of steam ejector using computational fluid dynamics: part 2. Flow structure of a steam ejector influenced by operating pressures and geometries. Int. J. Therm. Sci. 46, 823e833.

Sun, D.W., 1999. Comparative study of the performance of an ejector refrigeration cycle operating with various refrigerants. Energ. Convers. Manage. 40, 873e884.

Varga, S., Oliveira, A.C., Diaconu, B., 2009. Numerical assessment of steam ejector efficiencies using CFD. Int. J. Refrigeration 32, 1203e1211.