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658 CHAPTER 39 ' 1965 Guide And: Data Book place'at or beyond the exit plane of the cone than when the expansion process is completed within the con6 itself, giving rise to a normal shock at this point Such a condition* would arise at higher than design evaporator temperature and at start-up if no shortening of the cone took place. Incidentally, complete elimination of the divergent cone so .that only a convergent nozzle remains will only.reduce ejector perform ance by about 5 percent' It is imperative that the nozzle axis coincide with the main ejector axis and'it is usual for the nozzle to be so mounted that its axial position relative to the inlet of the mixing,sec tion at Station X of Fig. 3 can be varied to achieve optimum performance. It can be shown theoretically (and this has heen supported by test data) that the use of superheated' motive steam causes a slight decrease in ejector efficiency. While saturated steam is the most efficient motive steam condition for ejector operation, such a steam condition .is difficult,to control due to heat losses. Since drops of wet steam can cause serious erosion of both noszle and main ejector parts due to the very High velocities encountered, a few.degrees.6f superheat is often used to effectively eliminate the erosion hazard from ejectors. In actual installations, erosion is virtu ally nonexistant. Good thermal insulation on the steam lines and good steam trapping practices also contribute'to this situation. '*' Ejector Suction Opening and Suction Chamber - ' The ejector suction opening is generally sized to give anaverage vapor velocity.of about,250 fps. .The suction chamber is a volume in which.the entering water vapor is turned 90 deg and accelerated to some optimum .velocity at Station X (Tig. 3). It can be shown both theoretically* and experimentally that there is an optimum velocity at Station X of the vapor, entering the mixing section for every ejector design condition. Typically, the vapor velocity increases as the design pressure ratio of the ejector (condenser to evaporator, pressure) ^de creases. For steam-jet refrigeration units employed on com-, fort air conditioning applications the vapor velocity may.ty' typically 400 to 600 fps at Station X (based on evaporator, state conditions). Mixing Section The mixing section is conical in shape. Most ejector mami-r facturers use a single cone angle between Station X and T/ while a few employ a double cone in series arrangement'with: the larger included angle cone starting at Station X and the smaller cone ending at Station 1. The length of the miying section is often expressed in terms of throat diameters' at' Station 1 to 2. For steam-jet refrigeration work, the "dring section will be 6 to 8 throat diameters long, with an average value of 7. It can be shown theoretically* and by test that the* optimum-mixing section cone angle will decrease with de^ creasing ejector design pressure ratio. For a design pressure- ratio of 'one, the cone angle becomes -zero and a cylindrical constant area mixing section results. For the typical steam- jet ejector on refrigeration service, the mixing section included' cone angle is about 6 deg.4 A larger angle will result in a loss- of ejector efficiency and a smaller angle will result in the ejector being unable to compress design vapor flow to the design condensing pressure..... -- . Constant Area Section ; The constant area section is the supersonic shock diffuser' section (Stations 1-2). In an ideal ohe^iimensional analysis, the pressure rise in this section might be expected to' take place across a normal shock of essentially zero axial length'. This is not the real situation.1'Because:of a thick boundary layer and a very peaked velocity profile' (as opposed .to tile ideal case of no boundary layer and a uniform velocity profile) the shock'is not'fully normal but includes complex oblique shock patterns* as well, and in'practice several throat'diame* tors of axial length are required .to complete'this pressure recovery process.* During load variation, this complex and lengthy shock pattern shifts axially. For a broad and efficient ejector operating characteristic this constant area"throat sec tion istypically 3 to 5 throat diameters long (with`5 diameters a- preferred-'length)' to' accommodate the shock pattern and its axial movement under load. The constant'area-section diameter'is; critical'for a :specific design and although the literature gives several methods for computing this dimension; none are precisely-accurate.'^'* Only ejector manufacturers pbssess' data with which-.to accurately =predict 'the .thirst diameterjfor ejectors of all rises and operating requirements. Subsonic Diffuser /' ' 1 The subsonic diffuser is always conicaFin riiape with'an included anglc range of 5 to 12'deg; although 8 to 10 deg is most pommon. An axial. length of 4 to i2 throat diameter?'is found in practice with a_5 diameter length most common'; A small included angle of-5 to 7 deg would5be more'efficient if sufficient'axial length were' available to decelerate the flow to the typical-average leaving velocity of .250 fps at' Station 3 (Fig! 3). Hpwever, ejector manufacturers have atterapted'to standardize, ejector rizes and'usually employ cone angles greater than 7 deg in order to keep within length limitations (which'are often quite arbitrary). Typical Ejector=Function, i "To better understand'how a typical ejector functions,7a brief description of its. operation trill be'given on a. Mollier Diagram (see fig.' 4). The saturated motive steam enters*the ejector'at a total pressure (165'psia) corresponding to state t and expands to a static pressure (0.10 psia)'at state A. The steam yetocity will be about'4400 fps and contain 24.5 percent moisture: Saturated vapor (ait 45'F evaporator temperature) enters* the'ejector at a total pressure (0.147 psia)'correspond ing to state 0 and expands to tire static pressure P, at.state B. The vapor velocity will be about'. 1000 fps here. 'The two streams start to mix at Station Jf.in the ejector.*. .Mixing is assumed to be completed at Station 1, and this corresponds to state l where the mixture velocity is about 3400 fps. Mixing Steam-Jet Refrigeration Equipment 659 is to toke place at constant static pressure. An ejector djgr-huTge pressure of 5.15 psia would be theoretically possible fin this example) if the available kinetic energy at state 1 could be transformed into potential energy at state 4. Due to loses, a pressure rise to only 1.10 psia (the condenser pressure corresponding to 105 F condensing temperature) is actually realized. In theory and in practice this diffusion process can be to take place in two parts. The first is supersonic shock d;ff,,gtnn from state 1 to state 2 (between Stations I and 2) and the second is subsonic diffusion from state 2 to state 3 (between Stations 2 and 3).. Since the ejector exit velocity at Station 3 is finrteand not .zero, a small loss in available energy from ideal must occur. This loss is too small to show on the.diagram, however. Static pressure P corre sponds to conditions at Station 3 and is fixed by- toe con densing temperature (105 F). Note that virtually the entire ejector process occurs within. the wet region of the Mollier'Diagram below the saturation line.'Both mbtive steam and vapor enter the ejector at essen tially saturated conditions. The motive steam often expands ihto a region of 20 percent moisture (24.5 percent moisture in the previous example). Because of this,'the'specific heat ratio'for'steam will be found to be 1.10 to 1.15,-and not.l'.3 as On the saturation line. The difference in enthalpy between state l and state A is the miring loss. A measure of the effi ciency of compression'of an ejector is : *............... - {K-h<)(G, + 'G,) -A.) tcAere. ... A = enthalpy, Btu per pound. . ' . G, mass'now rate of steam, pounds per hoar. * : Gi fibw rate of vapor, pounds per hour. The numerator,of this ratio is the actual compression-energy recovered, ' and the denominator is the theoretical energy' available in toe motive steam. This ratio is about 0;27,forthe example given. The steam rate in the example would be 27.5 lb per (hr) (ton of refrigeration).v~ ; TWO-FLUID SYSTEMS - One possible method to theoretically improve ejector- per formance is'the use of a two-fluid system. By utilizing one fluid (of higher molecular weight) as the motive fluid and the other (of lower.molecular .weight) for a refrigerant, an.im provement in ejector performance is possible. During .the 1930's-a mercury-water system,* was marketed in limited quantities for cooling household.refrigerators. However;'the problems and potential hazards outweighed the small. im provement realized. Some more recent efforts in developing a two-fluid system can be noted occasionally-in the literature11 and in patents11 granted. However, all of these'systems, while having superior ejector efficiency require higher compression ratios. This increased..work of compression is necessary -to separate the constituents of the mixture in the condenser. Therefore, two-fluid systems seldom offer 'a . performance advantage over a conventional single-fluid.system. - FJg.,5 .... Steam Demand for Typical Steam Jet "*.Refrigeration Systems the-system design conditions were identical in making this comparison.- -.7 f The steam rate required to produce a ton of refrigeration varies-widely fordifferent steam-jet.systems. If-the com ponents have been properly designed, the steam rate is a func tion.of-steam pressure, condenser temperature, and evapora tor temperature. Fig. 5 shows the effect of both condenser, temperature and evaporator temperature at a constant steam pressure of-100 psig. In industrial practice, actual steam consumption will vary within about 5 percent of the curves shown.- For example, with 100 F condensing temperature and 45 F chilled water temperature, a steam consumption of. 25.5 lb per ton-hour is.typica! of comfort cooling applications when using 100 psig saturated motive steam. The amount of steam required to produce one ton of cooling effect decreases with decreasing condenser-temperature, and with, increasing chilled water temperature. The steam rate is low,- therefore, when the ejector pressure ratio or temperature lift is low. - f '.Figs. 6,-7, and s show the effect of steam pressure on the steam -requirements at 90, 100,. and 110-F-. condenser, tem peratures respectively. These-curves show that it is more economical to operate at the highest steam pressure available, although prepares above 100 prig have a diminishing effect on the steam requirements. The influence of steam pressure is significantly more pronounced with chilled water tempera tures below 45 F than at higher chilled water .temperature. Pressures below; 30 psig increase steam requirements so. rapidly, that even when the low-pressure steam is cheaply, available it is not always economical to use ,this.steam for jet refrigeration cooling. ^-Steam-jet units have a high overload capacity without much increase, in condenser water temperaturebecauae as the load: increases the chilled water temperature increases, and for the same motive steam flow the pounds of. vapor (hence refrigerr. PERFORMANCE The efforts that have been made in recent years to improve the performance of steam-jet refrigeration have often gone unpublicized. In this field, lack of literature on this subject is oot necessarily a measure of the development work being conducted by ejector manufacturers. However, the actual performance of steam-jet refrigeration units over the past thirty years has improved about 10 percent. This assumes that Fig. 6 .... Effect of Steam Pressure on Steam Demand at 90 F Condenser Temperature