Steam Jet Refrigeration Cycle

Chemical Engineering and Processing 41 (2002) 551– 561 www. elsevier. com/locate/cep Evaluation of fume jet ejectors Hisham El-Dessouky *, Hisham Ettouney, Imad Alatiqi, Ghada Al-Nuwaibit Department of Chemical Engineering, College of Engineering and Petroleum, Kuwait Uni6ersity, P. O. Box 5969, Safat 13060, Kuwait Spiritless 4 April 2001; spiritless in revised shape 26 September 2001; certain 27 September 2001 Abstract Fume jet ejectors are an redundant distribute in composure and air circumstancesing, desalination, petroleum re? embryo, petrochemical and chemical industries. The ejectors shape an all distribute of intelligence columns, condensers and other passion veer arrangementes. In this examine, semi-tentative copys are open for intention and rating of fume jet ejectors. The copy confers the entrainment proportion as a character of the dilution proportion and the constrainings of the entrained fume, inducement fume and comforconsideration fume. Also, mutualitys are open for the inducement fume constraining at the nozzle egress as a character of the evaporator and condenser constrainings and the area proportions as a character of the entrainment proportion and the current constrainings. This allows for unmeasured intention of the ejector, wclose de? ing the ejector admonish and the constrainings of the inducement fume, evaporator and condenser confers the entrainment proportion, the inducement fume constraining at the nozzle egress and the morose individuality areas of the diffuser and the nozzle. The open mutualitys are naturalized on great postulatesbase that embraces manufacturer intention postulates and tentative postulates. The copy embraces mutualitys for the choked ? ow delay compression proportions aggravate 1. 8. In attention, a mutuality is supposing for the non-choked ? ow delay compression proportions under 1. 8. The appreciates of the coef? cient of choice (R 2) are 0. 85 and 0. 78 for the choked and non-choked ? w mutualitys, respectively. As for the mutualitys for the inducement fume constraining at the nozzle egress and the area proportions, all enjoy R 2 appreciates aggravate 0. 99. © 2002 Elsevier Science B. V. All hues sly. Keywords: Fume jet ejectors; Choked ? ow; Passion pumps; Animated fume compression 1. Introduction Currently, most of the prevalent subsidence and composure arrangements are naturalized on spontaneous fume compression (MVC). These cycles are powered by a haughty circumstances shape of enthusiasm, electrical enthusiasm. The inef? cient use of the enthusiasm required to is-sue such a arrangement can be generated by the ignition of fossil uels and thus contributes to an extension in greenhouse gases and the race of air pollutants, such as NOx, SOx, distributeiculates and ozone. These pollutants enjoy obstructive proceeds on relevancynal vigor and the environment. In attention, MVC composure and subsidence cycles use unkind chloro-? oro-carbon compounds (CFCs), which, upon quit, contributes to the damnation of the protective ozone flake in the upper sky. * Corresponding originator. Tel. : + 965-4811188x5613; fax: + 9654839498. E -mail address: [email protected] kuniv. edu. kw (H. El-Dessouky). Environmental considerations and the deficiency for ef? cient se of advantageous enthusiasm allure for the bud of arrangementes naturalized on the use of low degree passion. These arrangementes incorporeprimand entrainment and compression of low constraining fume to haughtyer constrainings appropriate for unanalogous arrangements. The compression arrangement takes establish in parching, adsorption, chemical or jet ejector fume compression cycles. Jet ejectors enjoy the isolatedst con? guration incomplete uncertain fume compression cycles. In contrariety to other arrangementes, ejectors are shapeed of a sole individual conjoined to tubing of inducement, entrained and combination currents. Also, ejectors do not embrace valves, rotors or other emotional distributes and are advantageous ommercially in uncertain sizes and for unanalogous applications. Jet ejectors enjoy inferior high and defence absorb than the other con? gurations. On the other laborer, the ocean drawbacks of jet ejectors embrace the succeedingcited: ? Ejectors are intentioned to is-sue at a sole optimum purpose. Deviation from this optimum fruits in ceremonious debasement of the ejector closement. 0255-2701/02/$ - see front stuff © 2002 Elsevier Science B. V. All hues sly. PII: S 0 2 5 5 - 2 7 0 1 ( 0 1 ) 0 0 1 7 6 - 3 552 ? H. El -Dessouky et al. / Chemical Engineering and Processing 41 (2002) 551 – 561 Ejectors enjoy very low animated ef? iency. Applications of jet ejectors embrace composure, air circumstancesing, non-colony of non-condensable gases, bliss of solids and gas vindication. The character of the jet ejector varys considerably in these arrangementes. For pattern, in composure and air conditioembryo cycles, the ejector compresses the entrained fume to haughtyer constraining, which allows for subject-matter at a haughtyer weather. Also, the ejector entrainment arrangement sustains the low constraining on the evaporator face, which allows evaporation at low weather. As a fruit, the unimpassioned evaporator ? uid can be used for composure and subsidence characters. As for the non-colony of non-condensable gases in passion transmit individuals, the ejector entrainment arrangement prevents their fund delayin condensers or evaporators. The closeness of non-condensable gases in passion veer individuals curtails the passion transmit ef? ciency and extensions the subject-matter weather owing of their low animated conductivity. Also, the closeness of these gases enhances dross reactions. However, the ejector cycle for subsidence and composure has inferior ef? ciency than the MVC individuals, but their merits are manifested upon the use of low degree enthusiasm that has spatois conprogression on the environment and inferior ooling and passioning individual absorb. Although the erection and agency principles of jet ejectors are polite-behaved-behaved unconcealed, the succeedingcited individualitys procure a brief resume of the important features of ejectors. This is requisite in manage to supervene the discourse and disminority that supervene. The prevalent fume jet ejector has three ocean distributes: (1) the nozzle; (2) the suction berth; and (3) the diffuser (Fig. 1). The nozzle and the diffuser enjoy the surveying of converging/diverging venturi. The transversions and elongations of uncertain distributes shapeing the nozzle, the diffuser and the suction berth, concomitantly delay the current ? ow reprimand and properties, de? e the ejector compressiveness and closement. The ejector compressiveness is de? ned in stipulations of the ? ow reprimands of the inducement fume and the entrained fume. The sum of the inducement and entrained fume heap ? ow reprimands confers the heap ? ow reprimand of the comforconsideration fume. As for the ejector closement, it is de? ned in stipulations of entrainment, dilution and compression proportions. The entrainment proportion (w ) is the ? ow reprimand of the entrained fume Fig. 1. Variation in current constraining and quickness as a character of colony along the ejector. H. El -Dessouky et al. / Chemical Engineering and Processing 41 (2002) 551 – 561 divided by the tendency reprimand of the inducement fume. As for the dilution proportion (Er), it is de? ned as the proportion of the inducement fume constraining to the entrained fume constraining. The compression proportion (Cr) confers the constraining proportion of the comforconsideration fume to the entrained fume. Variations in the current quickness and constraining as a character of colony inface the ejector, which are shown in Fig. 1, are explained under: ? The inducement fume enters the ejector at purpose (p ) delay a subsonic quickness. ? As the current ? ows in the converging distribute of the ejector, its constraining is poor and its quickness extensions. The current reaches sonic quickness at the nozzle throat, wclose its Mach enumereprimand is resembling to one. The extension in the morose individuality area in the diverging distribute of the nozzle fruits in a inferior of the astound brandish constraining and an extension in its quickness to supersonic provisions. ? At the nozzle egress roll, purpose (2), the inducement fume constraining becomes inferior than the entrained fume constraining and its quickness disposes among 900 and 1200 m/s. ? The entrained fume at purpose (e ) enters the ejector, wclose its quickness extensions and its constraining inferiors to that of purpose (3). ? The inducement fume and entrained fume currents may mix delayin the suction berth and the converging individuality of the diffuser or it may ? ow as two separeprimand treams as it enters the trustworthy morose individuality area of the diffuser, wclose mixing occurs. ? In either circumstance, the combination goes through a astound inface the trustworthy morose individuality area of the diffuser. The astound is associated delay an extension in the combination constraining and contraction of the combination quickness to subsonic provisions, purpose (4). The astound occurs owing of the tail constraining hindrance of the condenser. ? As the subsonic combination emerges from the trustworthy morose individuality area of the diffuser, exalt constraining extension occurs in the diverging individuality of the diffuser, wclose distribute of the kinetic enthusiasm of the combination is converted into constraining. The constraining of the emerging ? uid is subordinately haughtyer than the condenser constraining, purpose (c ). Resume for a enumereprimand of erudition studies on ejector intention and closement evaluation is shown in Consideration 1. The succeedingcited outlines the ocean ? ndings of these studies: ? Optimum ejector agency occurs at the discriminating circumstances. The condenser constraining controls the colony of the astound brandish, wclose an extension in the condenser constraining aggravate the discriminating purpose fruits in a quick discard of the ejector entrainment proportion, past the astound brandish moves towards the nozzle egress. Operating at constrainings under the discriminating purposes has negligible conprogression on the ejector entrainment proportion. 553 ? At the discriminating circumstances, the ejector entrainment proportion extensions at inferior constraining for the boiler and condenser. Also, haughtyer weather for the evaporator extensions the entrainment proportion. ? Use of a fickle situation nozzle can oceantain the optimum provisions for ejector agency. As a fruit, the ejector can be oceantained at discriminating provisions equal if the gratuitous provisions are multiplied. ? Multi-ejector arrangement extensions the gratuitous dispose and improves the aggravateall arrangement ef? ciency. Ejector copying is redundant for emend conception of the compression arrangement, arrangement intention and closement evaluation. Models embrace tentative mutualitys, such as those by Ludwig [1], Power [2] and El-Dessouky and Ettouney [3]. Such copys are spatois to the dispose aggravate which it was open, which limits their use in investigating the closement of new ejector ? uids, intentions or gratuitous provisions. Semi-tentative copys confer past ? exibility in ejector intention and closement evaluation [4,5]. Other ejector copys are naturalized on essential counterpoise equations [6]. This examine is motivated by the deficiency for a isolated mpirical copy that can be used to intention and evaluate the closement of fume jet ejectors. The copy is naturalized on a great postulatesbase extracted from separeprimand ejector manufacturers and a enumereprimand of tentative erudition studies. As get be discussed later, the copy is isolated to use and it eliminates the deficiency for iterative acts. 2. Unrythmical copy The re-examination by Sun and Eames [7] outlined the buds in unrythmical copying and intention of jet ejectors. The re-examination shows that tclose are two basic approaches for ejector dissection. These embrace mixing of the inducement fume and entrained fume, either at trustworthy ressure or at trustworthy area. Intention copys of current mixing at trustworthy constraining are past spiritless in erudition owing the closement of the ejectors intentioned by this manner is past upper to the trustworthy area manner and it compares favorably athwart tentative postulates. The reason for copying the trustworthy constraining intention act was initially open by Keenan [6]. Subsequently, separeprimand investigators enjoy used the copy for intention and closement evaluation of uncertain patterns of jet ejectors. This compromised a enumereprimand of modi? cations in the copy, specially losses delayin the ejector and mixing of the original and subordinate currents. In this individuality, the trustworthy constraining ejector copy is open. The open copy is naturalized on a enumereprimand of erudition studies [8 – 11]. The trustworthy constraining copy is naturalized on the succeedingcited convictions: H. El -Dessouky et al. / Chemical Engineering and Processing 41 (2002) 551 – 561 554 Consideration 1 Resume of erudition studies on ejector intention and closement Reference Fluid Boiler, evaporator and condenser weather (°C) Conclusion [19] R-113 60–100; 5–18; 40–50 Reason for refrigerant election for light arrangement, arrangement closement extensiond delay increasing boiler and evaporator weathers and decreasing condenser weather. 20] R-113; R-114; R-142b; R-718 80–95; 5–13; 25–45 Comparison of ejector and refrigerant closement. Dry, wet and isentropic ?uids. Wet ? uid impairment ejectors due deportment veer during isentropic dilution. R-113 (dry) has the best closement and R142b (wet) has the poorest closement. [21,22] R-114 86; ? 8; 30 Extension in ejector closement using spontaneous compression booster. [8] Insinuate 120–140; 5–10; 30–65 Choking of the entrained ? uid in the mixing berth affects arrangement closement. Maximum COP is succeeded at the discriminating ? ow circumstances. [13] Insinuate 120–140; 5–10; 30–60 Effect of varying the nozzle situation to converge gratuitous circumstances. Extension in COP and subsidence compressiveness by 100%. [23] R-113 70–100; 6–25; 42–50 Entrainment proportion is haughtyly monstrous by the condenser weather specially at low evaporator weather. [24] R-11 82. 2–182. 2; 10; 43. 3 Entrainment proportion is proportional to boiler weather. [25,26] R-114 90; 4; 30 Fully light generator and ejector air circumstanceser. Past ef? cient arrangement requires multi-ejector and unimpassioned enthusiasm storage (unimpassioned storage in either deportment changing representatives, unimpassioned insinuate or ice). [27] R-134A 15; 30 Modeling the conprogression of inducement nozzle on arrangement closement, in which the ejector is used to recaggravate distribute of the is-sue that would be past in the dilution valve using haughty-constraining inducement liquescent. [28] Insinuate 100–165; 10; 30–45 Fully light collector, composure and seainsinuate desalination arrangement. Achievement rests on fume constraining, subsidence insinuate weather and suction constraining. [4] Insinuate [29] Insinuate – Copy of multimark fume ejector composure arrangement using annular ejector in which the original ? uid enters the succor mark at annular nozzle on the facewall. This get extension static constraining for low-constraining current and combination and curtail the quickness of the inducement current and curtail jet mixing losses astound brandish shapeation losses. [24] R11; R113; R114 93. 3; 10; 43. 3 Measure and weigh ejector entrainment proportion as a character of boiler, condenser and evaporator weathers. Entrainment proportion inferiors for off intention agency and extensions for the two mark ejectors. [30] R113; R114; R142b 120–140; 65–80 Conprogression of throat area, colony of ocean nozzle and elongation of the trustworthy area individuality on tailpressure, entrainment proportion and compression proportion. Developed a new ejector plea in which the entrained ? uid is choked, the set lamina fruits assent delay this plea. Fume jet composure should be intentioned for the most manyly most-common provisions rather than the most strict to close important aggravateall ef? ciency. [5] Unrythmical copy use tentative parameters that rest barely on surveying. The parameters are succeeded tentatively for uncertain patterns of ejectors. [31] R134a 5; ? 12, ? 18; 40 Fully ejector and spontaneous compressor for agency of domiciliary refrigerator-freezer extensions entrainment proportion from 7 to 12. 4%. The optimum throat transversion rests on the freezer emperature [9] R11; HR-123 80; 5; 30 Achievement of HR-123 is concordant to R-11 in ejector composure. Optimum closement is closed by the use of fickle surveying ejector when agency provisions veer. H. El -Dessouky et al. / Chemical Engineering and Processing 41 (2002) 551 – 561 1. The inducement fume expands isentropically in the nozzle. Also, the combination of the inducement fume and the entrained fume compresses isentropically in the diffuser. 2. The inducement fume and the entrained fume are saturated and their velocities are negligible. 3. Quickness of the comforconsideration combination leaving the ejector is insigni? patois. 4. Constant isentropic dilution representative and the intellectual gas manner. 5. The mixing of inducement fume and the entrained fume takes establish in the suction berth. 6. The ? ow is adiabatic. 7. Friction losses are de? ned in stipulations of the isentropic ef? ciencies in the nozzle, diffuser and mixing berth. 8. The inducement fume and the entrained fume enjoy the similar molecular ponderosity and speci? c passion proportion. 9. The ejector ? ow is one-dimensional and at firm specify provisions. The copy equations embrace the succeedingcited: ? Overall representative counterpoise (2) Dilution proportion ? ' 2pn k? 1 Pp P2 n (k ? 1/k) ?1 Pe P2 n (k ? 1/k) ?1 (6) M*2 + wM*2 Te/Tp p e ' M 2(k + 1) M 2(k ? 1) + 2 (8) Eq. (8) is used to weigh M*2, M*2, M4 e p Mach enumereprimand of the modified ? ow succeeding the astound brandish 2 M2+ 4 (k ? 1) M5 = (9) 2k 2 M ? 1 (k ? 1) 4 Constraining extension amorose the astound brandish at purpose 4 (10) In Eq. (10) the trustworthy constraining conviction implies that the constraining among purposes 2 and 4 remains trustworthy. Therefore, the succeedingcited ecircumstances absorption applies P2 = P3 = P4. Constraining hoist in the diffuser n Pc p (k ? 1) 2 =d M5+1 P5 2 ? (5) ? (k/k ? 1) (11) wclose pd is the diffuser ef? ciency. The area of the nozzle throat A1 = wclose M is the Mach enumerate, P is the constraining and is the isentropic dilution coef? cient. In the aggravate equation, pn is the nozzle ef? ciency and is de? ned as the proportion among the express enthalpy veer and the enthalpy veer undergone during an isentropic arrangement. Isentropic dilution of the entrained ? uid in the suction berth is open in stipulations of the Mach enumereprimand of the entrained ? uid at the nozzle egress roll P5 1 + kM 2 4 = P4 1 + kM 2 5 (4) Isentropic dilution of the original ? uid in the nozzle is open in stipulations of the Mach enumereprimand of the original ? uid at the nozzle egress roll Mp2 = ? ? (3) Er = Pp/Pe ? ? 2 k? 1 (7) (1 + w )(1 + wTe/Tp) close w is the entrainment proportion and M * is the proportion among the national ? uid quickness to the quickness of probe at discriminating provisions. The alliance among M and M * at any purpose in the ejector is confern by this equation M* = Compression proportion Cr = Pc/Pe ? ? ' The mixing arrangement is copyed by one-dimensional simultaneousness, momentum and enthusiasm equations. These equations are fully to de? ne the discriminating Mach enumereprimand of the combination at purpose 5 in stipulations of the discriminating Mach enumereprimand for the original and entrained ?uids at purpose 2 M* = 4 wclose m is the heap ? ow reprimand and the subscripts c, e and p, de? ne the comforconsideration fume combination, the ntrained fume and the inducement fume or original current. Entrainment proportion w = me/mp ? ? (1) mp + me = mc ? Me2 = 555 mp Pp ' RTp k + 1 kpn 2 (k + 1)/(k ? 1) (12) The area proportion of the nozzle throat and diffuser trustworthy area A1 Pc 1 = A3 Pp (1 + w )(1 + w (Te/Tp)) P2 1/k P (k ? 1)/k 1/2 1? 2 Pc Pc 2 1/(k ? 1) 2 1/2 1? k+1 k+1 1/2 (13) H. El -Dessouky et al. / Chemical Engineering and Processing 41 (2002) 551 – 561 556 ? The area proportion of the nozzle throat and the nozzle egress A2 = A1 ' 1 2 (k ? 1) 2 1+ M p2 2 M p2 (k + 1 2 ? (k + 1)/(k ? 1) (14) ? 3. Redisintegration act ? Two reredisintegration acts for the aggravate copy are shown in Fig. 2. Either act requires iterative calculations. The ? rst act is used for arrangement intention, wclose the arrangement constrainings and the entrainment proportion is de? ned. Iterations are made to projectate the constraining of the inducement fume at the nozzle egress (P2) that confers the similar tail constraining (Pc). The rereharping progression for this act is shown in Fig. 2(a) and it embraces the succeedingcited strides: ? De? ne the intention parameters, which embrace the entrainment proportion (w ), the ? ow reprimand of the comforconsideration ? ? ? ? fume (mc) and the constrainings of the entrained fume, ompressed fume and inducement fume (Pe, Pp, Pc). De? ne the ef? ciencies of the nozzle and diffuser (pn, pd). Weigh the saturation weathers for the comforconsideration fume, entrained fume and inducement fume, which embrace Tc, Tp, Te, using the saturation weather mutuality confern in the postscript. As for the comprehensive gas trustworthy and the speci? c passion proportion for fume, their appreciates are smitten as 0. 462 and 1. 3. The ? ow reprimands of the entrained fume (me) and inducement fume (mp) are weighd from Eqs. (1) and (2). A appreciate for the constraining at purpose 2 (P2) is honord and Eqs. (5) – (11) are unfoldd sequentially to succeed the ressure of the comforconsideration fume (Pc). The weighd constraining of the comforconsideration fume is compared to the intention appreciate. A new appreciate for P2 is honord and the foregoing stride is many until the desired appreciate for the constraining of the comforconsideration fume is reached. Fig. 2. Redisintegration algorithms of the unrythmical copy. (a) Intention act to weigh area proportions. (b) Achievement evaluation to weigh w. H. El -Dessouky et al. / Chemical Engineering and Processing 41 (2002) 551 – 561 ? The ejector morose individuality areas (A1, A2, A3) and the area proportions (A1/A3 and A2/A1) are weighd from Eqs. (12) – (14). The succor reredisintegration act is used for closement evaluation, wclose the morose individuality areas and the entrainment and inducement fume constrainings are de? ned. Iterations are made to projectate the entrainment proportion that de? nes the ejector compressiveness. The rereharping progression for this act is shown in Fig. 2(b) and it embraces the succeedingcited strides: ? De? ne the closement parameters, which embrace the morose individuality areas (A1, A2, A3), the constrainings of the entrained fume (Pe) and the constraining of the original current (Pp). ? De? ne the ef? ciencies of the nozzle and diffuser (pn, pd). ? Weigh the saturation weathers of the original nd entrained currents, Tp and Te, using the saturation weather mutuality confern in the postscript. ? As for the comprehensive gas trustworthy and the speci? c passion proportion for fume, their appreciates are smitten as 0. 462 and 1. 3. ? Weigh the ? ow reprimand of the inducement fume and the properties at the nozzle egress, which embrace mp, P2, Me2, Mp2. These are succeeded by solving Eqs. (5), (6), (12) and (14). ? An honor is made for the entrainment proportion, w. ? This appreciate is used to weigh other arrangement parameters de? ned in Eqs. (7) – (11), which embraces M*2, e M*2, M*, M4, M5, P5, Pc. p 4 ? A new honor for w is succeeded from Eq. 13). ? The deception in w is projectated and a new rereharping is made if requisite. ? The ? ow reprimands of the comforconsideration and entrained fume are weighd from Eqs. (1) and (2). 4. Semi-tentative copy Bud of the semi-tentative copy is cogitation to procure a isolated manner for desigembryo or rating of fume jet ejectors. As shown aggravate, reredisintegration of the unrythmical copy requires an iterative act. Also, it is requisite to de? ne appreciates of pn and pd. The appreciates of these ef? ciencies amplely vary from one examine to another, as shown in Consideration 2. The semi-tentative copy for the fume jet ejector is open aggravate a ample ange of gratuitous provisions. This is closed by using three sets of intention postulates artificial from important ejector manufacturers, which embraces Croll Reynolds, Graham and Schutte – Koerting. Also, separeprimand sets of tentative postulates are extracted from the erudition and are used in the bud of the tentative copy. The semitentative copy embraces a enumereprimand of mutualitys to weigh the entrainment proportion (w ), the constraining at the nozzle egress (P2) and the area proportions in the ejector 557 Consideration 2 Examples of ejector ef? ciencies used in erudition studies Reference [27] [32] [33] [31] [10] [24] [8] [34] pn pd 0. 9 0. 5 0. 7–1 0. 8–1 0. 85–0. 98 0. 85 0. 75 0. 75 0. 8 0. 85 0. 7–1 0. 8–1 0. 65–0. 85 0. 85 0. 9 pm 0. 8 0. 95 (A2/A1) and (A1/A3). The mutuality for the entrainment proportion is open as a character of the dilution proportion and the constrainings of the inducement fume, the entrained fume and the comforconsideration fume. The mutuality for the constraining at the nozzle egress is open as a character of the evaporator and condenser constrainings. The mutualitys for the ejector area proportions are de? ned in stipulations of the arrangement constrainings and the entrainment proportion. Consideration 3 shows a resume of the disposes of the tentative and the intention postulates. The consideration also embraces the disposes for the postulates reputed by Power [12]. A resume of the tentative postulates, which is used to amplify the semi-tentative copy is shown in Consideration 4. The postulates embraces measurements by the succeedingcited investigators: ? Eames et al. [8] succeeded the postulates for a compression proportion of 3 – 6, dilution proportion 160 – 415 and entrainment proportion of 0. 17 – 0. 58. The measurements are succeeded for an area proportion of 90 for the diffuser and the nozzle throat. ? Munday and Bagster [4] succeeded the postulates for a compression proportion of 1. 8 – 2, dilution proportion of 356 – 522 and entrainment proportion of 0. 57 – 0. 905. The measurements are succeeded for an area proportion of 200 for the diffuser and the nozzle throat. ? Aphornratana and Eames [13] succeeded the postulates for a compression proportion of 4. 6 – 5. 3, dilution proportion of 309. 4 and entrainment proportion of 0. 11 – 0. 22. The measurements are succeeded for an area proportion of 81 for the diffuser and the nozzle throat. ? Bagster and Bresnahan [14] succeeded the postulates for a compression proportion of 2. 4 – 3. 4, dilution proportion of 165 – 426 and entrainment proportion of 0. 268 – 0. 42. The measurements are succeeded for an area proportion of 145 for the diffuser and the nozzle throat. ? Sun [15] succeeded the postulates for a compression proportion of . 06 – 3. 86, dilution proportion of 116 – 220 and entrainment proportion of 0. 28 – 0. 59. The measurements are succeeded for an area proportion of 81 for the diffuser and the nozzle throat. ? Chen and Sun [16] succeeded the postulates for a compression proportion of 1. 77 – 2. 76, dilution proportion of 1. 7 – 2. 9 and entrainment proportion of 0. 37 – 0. 62. The measure- H. El -Dessouky et al. / Chemical Engineering and Processing 41 (2002) 551 – 561 558 ments are succeeded for an area proportion of 79. 21 for the diffuser and the nozzle throat. ? Arnold et al. [17] succeeded the postulates for a compression proportion of 2. 47 – 3. 86, dilution proportion of 29. 7 – 46. , and entrainment proportion of 0. 27 – 0. 5. ? Everitt and Riffat [18] succeeded the postulates for a compression proportion of 1. 37 – 2. 3, dilution proportion of 22. 6 – 56. 9 and entrainment proportion of 0. 57. The mutuality for the entrainment proportion of choked ?ow or compression proportions aggravate 1. 8 is confern by W = aErbP cP d ec (e + fP g ) p (h + iP jc) (15) Similarly, the mutuality for the entrainment proportion of un-choked ? ow delay compression proportions under 1. 8 is confern by W = aErbP cP d ec (e + f ln(Pp)) (g + h ln(Pc)) (16) fume compression applications. As shown in Fig. 3, the ? tting fruit is very jocular for entrainment proportions among 0. 2 and 1. This is owing the important distribute of the postulates is ground among entrainment proportions clustered aggravate a dispose of 0. 2 – 0. 8. Examiembryo the tentative postulates ? t shows that the important distribute of the postulates ? t is polite-behaved-behaved delayin the mutuality predictions, bar for a little enumereprimand of purposes, wclose the predictions enjoy great deviations. The mutualitys for the inducement fume constraining at the nozzle egress and the area proportions are succeeded semi-empirically. In this revere, the intention and tentative postulates for the entrainment proportion and arrangement constrainings are used to unfold the unrythmical copy and to weigh the area proportions and inducement fume constraining at the nozzle utlet. The fruits are succeeded for ef? ciencies of 100% for the diffuser, nozzle and mixing and a appreciate of 1. 3 for k. The fruits are then correlated as a character of the arrangement fickles. The succeedingcited kinsfolk confer the mutualitys for the choked ? ow: The trustworthys in Eqs. (15) and (16) are confern as supervenes P2 = 0. 13 P 0. 33P 0. 73 e c (17) A1/A3 = 0. 34 P 1. 09P ? 1. 12w ? 0. 16 c p Entrainment proportion Entrainment proportion mutuality choked mutuality non-choked ?ow (Eq. (15); Fig. 3) ? ow (Eq. (16), Fig. 4) ?1. 89? 10? 5 ?5. 32 5. 04 9. 05? 10? 2 22. 09 ?6. 13 0. 82 ?3. 37? 10? 5 ? ? 0. 79 a 0. 65 b ?1. 54 c 1. 72 d 6. 9v10? 2 e 22. 82 f 4. 21? 10? 4 g 1. 34 h 9. 32 j 1. 28? 10? 1 j 1. 14 R2 0. 85 A2/A1 = 1. 04 P ? 0. 83 c P 0. 86 p w (18) ? 0. 12 (19) The R 2 for each of the aggravate mutualitys is aggravate 0. 99. Similarly, the succeedingcited kinsfolk confer the mutualitys for the un-choked ? ow: P2 = 1. 02 P ? 0. 000762P 0. 99 e c (20) A1/A3 = 0. 32 P 1. 11P ? 1. 13w ? 0. 36 c p (21) A2/A1 = 1. 22 P ? 0. 81P 0. 81w ? 0. 0739 c p (22) 2 Fitting fruits athwart the intention and tentative postulates are shown in Figs. 3 and 4, respectively. The fruits shown in Fig. 3 caggravate the most spiritlessly used dispose for fume jet ejectors, specially in vacuum and The R appreciates for the aggravate three mutualitys are aggravate 0. 99. The semi-tentative ejector intention act involves sequential reredisintegration of Eqs. (1) – (14) concomitantly delay Eq. (17) or Eq. (20) (depending on the ? ow pattern, choked or non-choked). This act is not iterative in contrariety delay the act confern for the unrythmical copy in the foregoing individuality. As for the semi-tentative closement evaluation copy, it involves non-iterative reredisintegration of Eqs. (1) – (14) concomitantly delay Eq. (15) or Eq. (16) for choked or non-choked ? ow, respectively. It should be stressed that twain reredisintegration acts are indepen- Consideration 3 Range of intention and tentative postulates used in copy bud Source Er Cr Pe (kPa) Pc (kPa) Pp (kPa) w Tentative Schutte–Koerting Croll–Rynolds Graham Power 1. 4–6. 19 1. 008–3. 73 1. 25–4. 24 1. 174–4. 04 1. 047–5. 018 1. 6–526. 1 1. 36–32. 45 4. 3–429. 4 4. 644–53. 7 2–1000 0. 872–121. 3 66. 85–2100. 8 3. 447–124. 1 27. 58–170. 27 2. 76–172. 37 2. 3–224. 1 790. 8–2859. 22 446. 06–1480. 27 790. 8–1480. 27 3. 72–510. 2 38. 6–1720 84. 09–2132. 27 6. 2–248. 2 34. 47–301. 27 344. 74–2757. 9 0. 11–1. 132 0. 1–4 0. 1818–2. 5 0. 18–3. 23 0. 2–4 H. El -Dessouky et al. / Chemical Engineering and Processing 41 (2002) 551 – 561 559 Consideration 4 Summary of erudition tentative postulates for fume jet ejectors Ad/At Pp (kPa) Pe (kPa) Pc (kPa) Pp/Pe Pc/Pe w Reference 90 198. 7 232. 3 270. 3 313. 3 361. 6 1. 23 1. 23 1. 23 1. 23 1. 23 3. 8 4. 2 4. 7 5. 3 6 161. 8 189. 1 220. 1 255. 1 294. 4 3. 09 3. 42 3. 83 4. 31 4. 89 0. 59 0. 54 0. 47 0. 39 0. 31 [8] [8] [8] [8] [8] 90 198. 7 232. 3 270. 3 313. 3 361. 6 1. 04 1. 04 1. 04 1. 04 1. 04 3. 6 4. 1 4. 6 5. 1 5. 7 191. 6 223. 9 260. 7 302. 1 348. 7 3. 47 3. 95 4. 44 4. 91 5. 49 0. 5 0. 42 0. 36 0. 29 0. 23 [8] [8] [8] [8] [8] 90 198. 7 232. 3 270. 3 313. 3 361. 6 0. 87 0. 87 0. 87 0. 87 0. 87 3. 4 3. 7 4. 4 5. 1 5. 4 227. 7 266. 2 309. 8 59 414. 4 3. 89 4. 24 5. 04 5. 85 6. 19 0. 4 0. 34 0. 28 0. 25 0. 18 [8] [8] [8] [8] [8] 200 834 400 669 841 690 690 1. 59 1. 59 1. 71 1. 59 1. 94 1. 94 3. 2 3. 07 3. 67 3. 51 3. 38 3. 51 521. 7 250. 2 392. 3 526. 1 356 356 2. 0 1. 92 2. 15 2. 19 1. 74 1. 81 0. 58 1. 13 0. 58 0. 51 0. 86 0. 91 [4] [4] [4] [4] [4] [4] 81 270 270 270 270 270 0. 87 0. 87 0. 87 0. 87 0. 87 4. 1 4. 2 4. 4 4. 5 4. 7 309. 5 309. 5 309. 5 309. 5 309. 5 4. 7 4. 8 5. 04 5. 16 5. 39 0. 22 0. 19 0. 16 0. 14 0. 11 [13] [13] [13] [13] [13] 145 660 578 516 440 381 312 278 1. 55 1. 55 1. 58 1. 57 1. 59 1. 62 1. 68 5. 3 5. 3 5. 3 5. 03 4. 77 4. 23 4. 1 426. 5 373. 5 326. 280. 6 239. 9 192. 6 165. 1 3. 42 3. 42 3. 36 3. 21 3 2. 61 2. 44 0. 27 0. 31 0. 35 0. 38 0. 42 0. 46 0. 42 [14] [14] [14] [14] [14] [14] [14] 143. 4 169. 2 198. 7 232. 3 270. 3 1. 23 1. 23 1. 23 1. 23 1. 23 2. 53 2. 67 3. 15 4 4. 75 116. 8 137. 8 161. 8 189. 1 220. 1 2. 06 2. 17 2. 56 3. 26 3. 87 0. 59 0. 51 0. 43 0. 35 0. 29 [15] [15] [15] [15] [15] 29. 7 33. 5 37. 8 46. 5 2. 47 2. 78 3. 14 3. 86 0. 5 0. 4 0. 3 0. 27 [17] [17] [17] [17] 119. 9 151. 7 224. 1 195. 1 195. 1 186. 2 1. 7 2. 3 3. 9 1. 6 1. 9 2. 9 1. 8 2. 2 3. 3 1. 6 1. 9 2. 8 0. 62 0. 49 0. 34 0. 78 0. 64 0. 37 [16] [16] [16] [16] [16] [16] 2. 3 2. 3 2. 3 56. 9 38. 6 22. 6 . 3 1. 9 1. 4 0. 57 0. 56 0. 57 [18] [18] [18] 81 1720 1720 1720 1720 79. 21 116 153 270 198 198 198 57. 9 47. 4 38. 6 57. 7 51. 4 45. 5 37. 01 67. 6 67. 6 67. 6 121. 3 99. 9 67. 6 1. 02 1. 2 1. 7 143 143 143 143 560 H. El -Dessouky et al. / Chemical Engineering and Processing 41 (2002) 551 – 561 ample dispose of compression, dilution and entrainment proportions, specially those used in industrial applications. The open mutualitys are isolated and very profitable for intention and rating calculations, past it can be used to projectate the entrainment proportion, which, upon speci? cation of the arrangement admonish, can be used to projectate the inducement fume ? w reprimand and the morose individuality areas of the ejector. Acknowledgements Fig. 3. Fitting of the entrainment proportion for compression proportions haughtyer than 1. 8. The originators would affect to claim funding livelihood of the Kuwait University Research Administration, Project No. EC084 entitled ‘Multiple Conprogression Evaporation and Absorption/Adsorption Passion Pumps’. Postscript A. Nomenclature A COP Cr Er m M M* Fig. 4. Fitting of the entrainment proportion for compression proportions inferior than 1. 8. cavity of the nozzle and diffuser ef? ciencies, which varies aggravate a ample dispose, as shown in Consideration 2. 5. Conclusions A semi-tentative copy is open for intention and erformance evaluation of fume jet ejector. The copy embraces mutualitys for the entrainment proportion in choked and non-choked ? ow, the inducement fume constraining at the nozzle egress and the area proportions of the ejector. The mutualitys for the entrainment proportion are succeeded by ? tting athwart a great set of intention postulates and tentative measurements. In attention, the mutualitys for the inducement fume constraining at the nozzle egress and the area proportions are succeeded semi-empirically by solving the unrythmical copy using the intention and tentative postulates for the entrainment proportion and arrangement constrainings. The mutualitys caggravate a P DP R Rs T w morose individuality area (m2) coef? cient of closement, dimensionless compression proportion de? ned as constraining of comforconsideration fume to constraining of entrained fume dilution proportion de? ned as constraining of comforconsideration fume to constraining of entrained fume heap ? ow reprimand (kg/s) Mach enumerate, proportion of ? uid quickness to hurry of probe discriminating Mach enumerate, proportion of ? uid quickness to hurry of probe constraining (kPa) constraining emanate (kPa) comprehensive gas trustworthy (kJ/kg °C) admonish proportion, heap ? ow reprimand of inducement fume to heap ? ow reprimand of entrained fume weather (K) ntrainment proportion, heap ? ow reprimand of entrained fume to heap ? ow reprimand of inducement fume Greek symbols k compressibility proportion p ejector ef? ciency Subscripts 1–7 colonys inface the ejector b boiler c condenser d diffuser e evaporator or entrained fume m mixing n nozzle p original current or inducement fume t throat of the nozzle H. El -Dessouky et al. / Chemical Engineering and Processing 41 (2002) 551 – 561 Postscript B B. 1. Corkinsfolk of saturation constraining and weather The saturation weather mutuality is confern by T = 42. 6776 ? 3892. 7 ? 273. 15 (ln(P /1000) ? 9. 48654) close P is in kPa and T is in °C. The aggravate mutuality is sufficient for the weighd saturation weather aggravate a constraining dispose of 10 – 1750 kPa. The percentage deceptions for the weighd versus the fume consideration appreciates are B 0. 1%. The mutuality for the insinuate fume saturation constraining is confern by ln(P /Pc) = Tc ?1 T + 273. 15 8 ? % fi (0. 01(T + 273. 15 ? 338. 15))(i ? 1) i=1 wclose Tc = 647. 286 K and Pc = 22089 kPa and the appreciates of fi are confern in the succeedingcited consideration f1 f2 f3 f4 ?7. 419242 0. 29721 ?0. 1155286 0. 008685635 f5 f6 f7 f8 0. 001094098 ?0. 00439993 0. 002520658 ?0. 000521868