Design and parametric investigation of an ejector in an air-conditioning system

Applied Thermal Engineering 20 (2000) 213±226

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Design and parametric investigation of an ejector in an air-conditioning system E.D. Rogdakis*, G.K. Alexis National Technical University of Athens, Mechanical Engineering Department, Thermal Section, 42 Patission Street, 10682, Athens, Greece Received 27 October 1998; accepted 24 January 1999

Abstract This paper discusses the behavior of ammonia (R-717) through an ejector, operating in an airconditioning system with a low temperature thermal source. For the detailed calculation of the proposed system a method has been developed, which employs analytical functions describing the thermodynamic properties of the ammonia. The proposed cycle has been compared with the Carnot cycle working at the same temperature levels. The in¯uence of three major parameters: generator, condenser and evaporator temperature, on ejector eciency and coecient of performance is discussed. Also the maximum value of COP was estimated by correlation of the three temperatures for constant superheated temperature (1008C). The design conditions were generator temperature (76.11±79.578C), condenser temperature (34± 428C) and evaporator temperature (4±128C). # 1999 Elsevier Science Ltd. All rights reserved. Keywords: Ammonia; Ejector; COP; Refrigeration cycle; Shocking phenomena

1. Introduction Ejectors are used in several di€erent engineering applications, and have several advantages over conventional compression systems. These include no moving parts in the compressor (except the pump) and hence no requirement for lubrication. The relatively low capital cost, simplicity of operation, reliability and very low maintenance cost are other advantages. An improved ejector theory was developed by Munday and Bagster [1]. This theory depends

* Corresponding author. Tel.: +301-772-3966; fax: +301-772-3670. 1359-4311/00/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 9 - 4 3 1 1 ( 9 9 ) 0 0 0 1 3 - 7

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Nomenclature A Bi COP P Pcr Px Py Q T V W h m n s w x

area of cross section of constant area duct [m2] constants in Eq. (31) coecient of performance pressure [bar] pressure at sonic ¯ow of secondary vapors [bar] pressure before the shock [bar] pressure after the shock [bar] heat rate [kW] temperature [8C] velocity [m/s] work rate [kW] enthalpy [kJ/kg] mass ¯ow [kg/s] isentropic eciency entropy [kJ/kg K] ¯ow entrainment ratio quality

Greek symbols constants in Eqs. (36) and (37) aij, bij Z ejector eciency n speci®c volume [m3/kg] Subscripts 1, 2, . . . cycle locations a, b, . . . ejector locations c condenser e evaporator f saturated liquid g generator, saturated vapor p pump

on the assumption of two discrete streams, the motive stream and the secondary stream. The two streams maintain their identity down the converging duct of the di€user. At some section the secondary ¯ow reaches sonic velocity. A thermodynamic shock and mixing occur at the very end of the converging cone resulting in a transient supersonic mixed stream. There is no supersonic deceleration and a shock takes place immediately on mixing. The mixed stream will shock to the subsonic velocity, found by the intersection of the Fanno and Rayleigh lines. After that the stream is brought to near-zero velocity in the subsonic di€user.

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In the present work this theory is used to develop a computer model of an ejector with particular reference to air-conditioning applications, using ammonia at various operating conditions as the working refrigerant. The performance of the ejector depends on both the operating conditions and ejector geometry. The ejector geometry is not related in the present study. Fig. 1(a) illustrates the operation of the ejector system. High pressure superheated vapor is raised in the generator (1). This vapor passes through a (converging/diverging) nozzle, drawing ammonia vapor into the ejector from the evaporator (2) where ammonia remaining there is cooled by evaporation. The two streams mix in the ejector and leave it after a recovery of pressure in the di€user part of the ejector (3). Then, heat is rejected from the ¯uid to the surroundings, resulting in condensate at the exit of the condenser (4). This is divided into two streams. One enters the evaporator after a pressure reduction in the expansion valve (5) and the other enters the generator after a pressure rise in the pump (6). A computer program, based on Munday and Bagster's theory, was written in order to calculate the behavior of the ejector and the performance of ejector system for a range of parameters. For thermodynamic properties of ammonia, the equations proposed by Ziegler and Trepp [2] have been used. 2. Ejector analysis and performance An ejector is a device in which a high pressure jet of ¯uid (motive stream) is used to entrain low pressure ¯uid (secondary stream). The resulting mixture is discharged at a pressure that lies between the driving pressure and the suction pressure. Rao and Singh [3] and Kouremenos et al. [4] showed that the model based on the conservation of ¯uid momentum in the mixing process gives results in close agreement with

Fig. 1. Schematic view of ejectorÐair conditioning system and ejector.

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those obtained from available design charts. To better understand how a typical ejector functions, a description of its operation is given on a Mollier chart in Fig. 2. A schematic view of ejector is shown in Fig. 1(b). Superheated motive ammonia enters the ejector at a high pressure Pg, temperature T1 and zero velocity (i.e. stagnation condition) corresponding to state (1) and expands to a pressure at state (a1), with eciency n1a1=0.8. The motive stream emerges from the nozzle and remains as an identi®able stream for some distance downstream. The saturated secondary vapor enters the ejector at pressure Pe and zero velocity (i.e. stagnation condition) corresponding to state (2) and expand adiabatically to a pressure at state (a2). The pressures at states (a1) and (a2) corresponding to pressure at sonic ¯ow of secondary vapor Pcr. The speci®c heat ratio for ammonia can be 1.40 to 1.50. According to Harris and Fischer [5] and Stoecker [6] mixing is assumed to occur approximately at constant pressure Pcr. In general the mixing zone may be expected to take place in some region (a±b) of the converging cone. Munday and Bagster [1] estimated that the resulting velocity of the mixture is always supersonic. Since the supersonic mixed stream is decelerated in a converging section with corresponding rise in pressure Px , region (b±c) and an assumed eciency of nbc=0.8. If the stream is still supersonic at the end of the cone (c), a shock will occur in the duct of constant cross-section, resulting in a subsonic stream (d). The intersection of the Fanno and Rayleigh lines determines the pressure Py and temperature Td after shock e€ect. The stream is then brought to near-zero velocity (i.e. stagnation condition) corresponding to state (3) in the di€user, with an assumed eciency of nd3=0.8. In the present work this theory is used with the assumption that the ¯uid momentum is conserved in the mixing section, i.e.

Fig. 2. Mollier chart of an ammonia ejector.

E.D. Rogdakis, G.K. Alexis / Applied Thermal Engineering 20 (2000) 213±226

Va1 ‡ wVa2 ˆ …1 ‡ w†Vb

217

…1†

It is obvious that the velocity Va2 is directly proportional to the quantity (h2ÿha2). If this quantity is signi®cantly less than the quantity (h1ÿha1), the velocity Va2 will be signi®cantly less than the velocity Va1 too. Thus, the contribution of velocity Va2 in the momentum equation will be negligible. Kouremenos et al. [4] assumed that the velocity Va2 is a negligible quantity, but in the present work this velocity takes signi®cant values. Also the overall energy balance equation can be written as: h1 ‡ wh2 ˆ …1 ‡ w†h3

…2†

h1 ˆ h…T1 ,P1 †

…3†

h2 ˆ h…T2 ,P2 †

…4†

where w=me/mg is the ¯ow entrainment ratio (kg of secondary stream per kg of motive stream). The governing equations for each section in the ejector are: NozzleÐthe energy balance equation between points (1) and (a1) is: V 2a1 =2 ˆ h1 ÿ ha1

…5†

The enthalpy ha1 is calculated from the system of equations: s1 ˆ s…T1 ,P1 † ˆ sas ˆ x as sgas ‡ …1-x as †sfas

…6†

has ˆ x as hgas ‡ …1 ÿ x as †hfas

…7†

n1a1 ˆ …h1 ÿ ha1 †=…h1 ÿ has †

…8†

Intake pipeÐthe energy balance equation between points (2) and (a2) is: V 2a2 =2 ˆ h2 ÿ ha2

…9†

The enthalpy ha2 is calculated from the system of equations: s2 ˆ s…T2 ,P2 † ˆ sa2 ˆ x a2 sga2 ‡ …1 ÿ x a2 †sfa2

…10†

ha2 ˆ x a2 hga2 ‡ …1 ÿ x a2 †hfa2

…11†

Converging coneÐassuming a value for w…0
…12†

The enthalpy hb is calculated from Eqs. (1) and (12). Assuming a value for the pressure Px …Pb
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nc are calculated from the system of equations: hb ˆ x b hgb ‡ …1 ÿ x b †hfb

…13†

sb ˆ x b sgb ‡ …1 ÿ x b †sfb

…14†

scs ˆ sb ˆ x cs sgcs ‡ …1 ÿ x cs †sfcs

…15†

hcs ˆ x cs hgcs ‡ …1 ÿ x cs †hfcs

…16†

nbc ˆ …hb ÿ hcs †=…hb ÿ hc †

…17†

hc ˆ x c hgc ‡ …1 ÿ x c †hfc

…18†

nc ˆ x c ngc ‡ …1 ÿ x c †nfc

…19†

Constant cross-sectionÐassuming a constant value for the ratio m/A = 2500, the pressure Pd ˆ Py and the temperature Td are calculated from the intersection of Fanno and Rayleigh lines: hd ‡ n2d …m=A†2 =2 ˆ c1

…20†

Pd ‡ nd …m=A†2 ˆ c2

…21†

hd ˆ h…Td ,Pd †

…22†

nd ˆ n…Td ,Pd †

…23†

The constants c1, c2 are calculated from the same equations at state (c). Di€userÐthe temperature T3 is calculated from the system of equations: sd ˆ s…Td , Pd †

…24†

s3s ˆ sd ˆ s…T3s ,Pd †

…25†

h3s ˆ h…T3s ,Pd †

…26†

nd3 ˆ …hd ÿ h3s †=…hd ÿ h3 †

…27†

h3 ˆ h…T3 ,P3 †

…28†

Given the pressures for the states (1)±(3) and using iterative calculations, the maximum value of the ratio w can be found. The superheated temperature T1=1008C is constant. The performance of an ejector can be represented by the ¯ow entrainment ratio in terms of

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219

the pressures of primary and secondary vapors (generator and evaporator pressure, respectively), and the back pressure (condenser pressure). By ®xing the actuating pressure Pg and the secondary pressure Pe (or the evaporator temperature Te), or the back pressure (or the condenser temperature Te), we calculated the ¯ow entrainment ratio at various condenser temperatures or at various evaporator temperatures, respectively. Fig. 3 shows the e€ect of pressure Px on ¯ow entrainment ratio w, under di€erent evaporator temperature Te, when the generator pressure is Pg=40 bar and condenser temperature is Tc=408C. Also Fig. 4 shows the e€ect of the pressure Px on ¯ow entrainment ratio w, under di€erent condenser temperatures Tc, when the Pg=40 bar and evaporator temperature is Te=108C. From Figs. 3 and 4 it can be seen that at any evaporator temperature and at any condenser temperature there is a maximum ¯ow entrainment ratio. Fig. 5 shows some calculated results for Pg=38, 39, 40, 41 bar and Te=108C. It can be seen that maximum ¯ow entrainment ratio increases with increasing generator pressure Pg and decreases with rising condenser temperature Tc, when the evaporator temperature is constant. A measure of ejector eciency of compression is proposed by ASHRAE [7]: Z ˆ …mg ‡ me †…h3 ÿ h2 †=mg …h1 ÿ has ˆ …1 ‡ w†…h3 ÿ h2 †=…h1 ÿ has †

…29†

The numerator of this ratio is the actual compression energy recovered and the denominator is the theoretical energy available in the motive stream. In Fig. 6, it can be seen that this ratio increases with increasing evaporator temperature Te and decreasing generator pressure Pg. It is noticed that the ejector eciency Z is independent of pressure Px and condenser pressure Pc. In Fig. 7, by ®xing the generator pressure Pg and evaporator temperature Te, the Mach number before the shock e€ect is shown to increase with increasing condenser temperature Te and decreasing pressure Px . In addition the Mach number after the shock e€ect increases with increasing condenser temperature Te and decreases with decreasing pressure Px .

Fig. 3. The e€ect of pressure Px under di€erent evaporator temperatures Te on ¯ow entrainment ratio w for generator pressure Pg=40 bar and condenser temperature Tc=408C.

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Fig. 4. The e€ect of pressure Px under di€erent condenser temperatures Tc on ¯ow entrainment ratio w for generator pressure Pg=40 bar and evaporator temperature Te=108C.

3. Performance of the proposed air-conditioning system In the present air-conditioning system was studied the in¯uence of the parameters on the behavior of ejector and system performance. The following assumptions were made in order to estimate the coecient of performance: 1. The exit of condenser is at saturated liquid state. 2. The ¯uid at the exit of evaporator is at saturated vapor state.

Fig. 5. The e€ect of condenser temperature Tc under di€erent generator pressures Pg on maximum ¯ow entrainment ratio wmax for evaporator temperature Te=108C.

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Fig. 6. The e€ect of evaporator temperature Te under di€erent generator pressures Pg on ejector eciency Z.

Fig. 7. The e€ect of pressure Px under di€erent condenser temperatures Tc on Mach number for generator pressure Pg=40 bar and evaporator temperature Te=108C.

3. The ¯uid at the exit of generator is at superheated vapor state. 4. The expansion through the expansion valve is a throttling process. The basic equations obtained from the conservation law for energy are: Evaporator Qe ˆ me …h2 ÿ h5 †

…30†

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Generator Qg ˆ mg …h1 ÿ h6 †

…31†

Pump Wp ˆ mg …h6 ÿ h4 †

…32†

Thus the COP of the system is determined by its operating conditions and may be calculated from equation: COP ˆ Qe =…Qg ‡ Wp † ˆ w…h2 ÿ h5 †=…h1 ÿ h4 †

…33†

The equivalent coecient of performance for Carnot cycle is calculated from the equation: COPc ˆ …Tg ÿ Tc †Te =Tg …Tc ÿ Te †

…34†

The in¯uence of evaporator temperature Te under di€erent condenser temperatures Tc on maximum coecient of performance is shown in Fig. 8, for a constant generator pressure Pg. It can be seen that the maximum coecient of performance increases with increasing evaporator temperature and decreasing condenser temperature. The equivalent chart for the Carnot cycle is shown in Fig. 9. The maximum coecient of performance COPmax depends proportionally on generator pressure Pg (see Fig. 10). Thus, the COPmax increases with increasing generator pressure Pg and increasing evaporator temperature, when the condenser temperature Tc is constant. The maximum value of COPmax can be estimated by correlation of generator temperature at

Fig. 8. The e€ect of evaporator temperature Te under di€erent condenser temperatures Tc on maximum coecient of performance COPmax for generator pressure Pg=40 bar.

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223

Fig. 9. The e€ect of evaporator temperature Te under di€erent condenser temperatures Tc on coecient of performance COPc (Carnot) for generator pressure Pg=40 bar.

saturated vapor state Tg (76.11±79.578C), condenser and evaporator temperature Tc (34±428C) and Te (4±128C), respectively, and constant superheated temperature (1008C). COP max ˆ

1 X Bi
T ig

…35†

iˆ0

Fig. 10. The e€ect of generator pressure Pg under di€erent evaporator temperatures Te on maximum coecient of performance COPmax for condenser temperature Tc=408C.

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Table 1 Values of constants aij j i

0

1

2

3

0 1 2

ÿ0.36200814 2.0276094  10ÿ2 ÿ4.9802132  10ÿ4

0.6154286 ÿ3.2918457  10ÿ2 4.3401073  10ÿ4

ÿ7.0376334  10ÿ2 3.8395295  10ÿ3 ÿ5.179187  10ÿ5

3.0223042  10ÿ3 ÿ1.6396927  10ÿ4 2.1992149  10ÿ6

B0 ˆ

2 X iˆ0

B1 ˆ

2 X iˆ0

T ic




T ic


3 X jˆ0 3 X jˆ0

aij
T je

…36†

bij
T je

…37†

Values of the constants aij and bij are given in Tables 1 and 2. The maximum error is less 21%. The in¯uence of pressure ratio Pe/Pc under di€erent condenser temperatures Tc on maximum ¯ow entrainment ratio wmax is shown in Fig. 11, for constant generator pressure Pg=40 bar. It can be seen that the maximum ¯ow entrainment ratio increases with increasing pressure ratio and decreasing condenser temperature. The performance of the system can be estimated as the evaporation per unit of motive stream as a function of evaporator temperature. Fig. 12 shows the performance as a function of evaporator temperature Te under di€erent condenser temperature Tc for constant generator pressure Pg. 4. Conclusions Studies on the performance characteristics of an ejector were carried out. For the detailed calculation of the proposed cycle, a method and a corresponding computer mode have been Table 2 Values of constants bij j i

0

1

2

3

0 1 2

2.0996843  10ÿ2 ÿ8.4952586  10ÿ4 1.1338905  10ÿ5

ÿ5.4333481  10ÿ3 3.188928  10ÿ4 ÿ4.4693205  10ÿ6

7.4325452  10ÿ4 ÿ4.1646156  10ÿ5 5.7854213  10ÿ7

ÿ2.6151059  10ÿ5 1.5297906  10ÿ6 ÿ2.1793358  10ÿ8

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Fig. 11. The e€ect of pressure ratio Pe/Pc under di€erent condenser temperatures Tc on maximum ¯ow entrainment ratio wmax for generator pressure Pg=40 bar.

developed, which employ analytical functions describing the thermodynamic properties of the ammonia. The shock phenomena on the entrained vapor play important role in ejector performance and the COP of the system. The pressure before the shock in the ejector, which is calculated from the assumed model, was shown not to be a constant but to vary with operation conditions and entrainment ratio. The region of Mach number and vapor velocity, before

Fig. 12. The e€ect of evaporator temperature Te under di€erent condenser temperatures Tc on performance of the system for generator pressure Pg=40 bar.

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shock e€ect, for Pg=40 bar, Tc=408C and Te=108C was 1.122±1.497 and 501±652 m/s, respectively. Also the region of ejector eciency Z for the present work was 0.291±0.345. It was found that there are three independent system design variables for the ejector system, namely, the pressure (or temperature) of the generator, condenser and evaporator. It was found that at ®xed evaporator temperature, the COPmax, as well as the cooling capacity, increases with increasing generator pressure, but the condenser temperature decreases. In other words, this work yielded the fact that the highest operating eciency can be achieved if the generator pressure increases with decreasing condenser temperature when the evaporator temperature is ®xed. The region of COPmax and COPc for this study area was 0.042±0.446 and 0.712±1.675, respectively. Also this study showed that the maximum coecient of performance is a linear function of generator temperature, a quadratic function of condenser temperature and a cubic function of evaporator temperature. References [1] J.T. Munday, D.F. Bagster, A new ejector theory applied to steam jet refrigeration, Ind. Engng. Chem., Proc. Des. Dev. 16 (4) (1977) 442±449. [2] B. Ziegler, Ch Trepp, Equation of state for ammonia water mixture, Rev. Int. Froid 7 (2) (1984) 101±106. [3] S.P.R. Rao, R.P. Singh, Performance characteristics of single-stage jet ejectors using two simple models, Chem. Engng. Commun. 66 (1988) 207±219. [4] D.A. Kouremenos, E.D. Rogdakis, G.K. Alexis, Optimization of enhance steam-ejector applied to steam jet refrigeration, Proc. ASME, Anaheim, CA, 38 (1998) 19±26. [5] L.S. Harris, A.S. Fischer, Characteristics of the steam-jet vacuum pump, J. Engng. Ind. 86 (1954) 358±364. [6] W.F. Stoecker, Refrigeration and air-conditioning, McGraw-Hill, New York, 1958. [7] ASHRAE, Steam-jet refrigeration equipment, equipment handbook, Chap. 13, 13.1±13.6, 1979.