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- 1. centritugal compressor: : Introduction Centrífuga¡ compressors are second only to reciprocating compressors in numbers of Inachines in service. ln the process plant arena, the leader in numbers is too close to call with any degree of certainty. Where capac- ity or horsepower rather than numbers is considered as a measure. the centrifugal. without a doubt, heads the compressor ñcld. During the past 30 years, the centrífuga] compressor, because of its simglicity and larger capacity/ size ratio. compared to the reciprocating machine. became much more popular for use in process plants that were growing in size. The ce ompressor does not exhibit the inertially induced shaking forces of the reciprocator and, therefore, does not need the sente massive foundation. Initiully. the efficiency of the centrífuga¡ was not as high as that of a well-maintained reciprocating compressor. However, the cen- trífuga¡ established its hold on lhe market in an era of cheap energy. when power cost was rarvely, if ever, evaluated. IQ
- 2. Frnlnfugal ("nmprrnnn ? IU The centrífuga! compressor has been around for quite a long time. Originally. ° . = . ' I um. " r' : m . ' . - ~ ' u e. :. l' high-volume service. ln the early l930s. the main application was in the steel industry, where it was used chiefry as ari oxídation air compressor for blast furnaces. 'I'lic centrífuga] displaced the reciprocating blowing engines that were being used at the time. The centrífuga¡ was employed in the coal-to-eolte conversion process, where it was used to draw ol! ” the gas from the coke ovens. ln the late 19305, the beginning of air conditioning for movie theaters. deportment stores. and later office buildings, gave birth to a generation of small centrifugals. which gained the advantage because of smaller size and absence of shlking forces. These forces were difficult to cmitain when a compatible capacity reciprocating compressor was used in a populated environment. lt was the smaller compressor design that was able to penetram the general process plant market, which had historically belonged to the reciprocating compressor. As stated previ- ously. the growth of plant size and low-cost energy helped bring the cen- trifugal compressor into prominence in the 19505. As the compressor grew in popularíty. developrnerits were begun to improve reliabilíty, per- fomiance. and efficiency. “With the increase in energy cost in the mid 19705. efficiency improvements moved from Inst to first priority in the ullocation of development funds. Prior to this tum of evems. most devel- opment had concentrated on making the machine reliable. a goal which was reasonably well achieved Run time between overhauls currently is three years or more with six-year run times not unusual. As plant size increased. the pressure to moiritain or improve reliability was very high because of the large economic impact of a nonscheduled shutdown. This being the case, even with an increase in the etficiency emphasis. there is no sympathy for an energy versus reliability trade-oii'. The operating groups tend to evaluate reliability tirsl. with the energy cost as secondary. 'nie centrífuga¡ compressor has been aged in an agximate range of l.0D0 cfm to 150.000 cfm. Plant air package centrifugals are available ' more efficient compressors that are available in the lower ranges. Pressure because of the wide range of applications. Pressure ratio is my the best para meter for ' the centrifugg commr to other QE of corrigem Polytropic head, as defined in Chapter 2, is much more definitiva tu the dynamic machine but does not mean much numerically to a @eng-- sure ratios of up to 3 and mg are available for single-stage commssors. operating ori air or nitrogen. Multistage machines. of the process type. gen- erally operate at a pressure ratio o esst per impe er'. i Ii" r' "Ut
- 3. l34 t'«, -,›r›prc›snrr. ' Srlrcrinv¡ um! Sin/ ig classification A better definition of a eo ressor st* e can be made here to rcvcnl confusion later on. Up to this point. in the positive displacement com- pressors. a compressing entity and a stage were one and the same; lor example. a cylinder is a stage in the reciprocating compressor. The ccn trifugzil and the other dynamic compressors to be discussed have the problem ol" a dual vemacular, one used by thc machine design enginccr and the one used by the process engineer. To the machine builder, a stage is an impeller-dimuzer pair, whereas the process designer tends to think of a stage as a process block that equates to an uncoolcd section of one or morc impeller and diffuser sets. There is no problem with the single impeller machine as the two are synonymous. The confusion comes with the usc ol' the multiple impeller machine. To make everyone equally happy or unhappy. as the case may be. hereinafter. a process compression stage will be referred to as an uncooled section. whenever the term . viage- must be used in the process connotation, it will be called a process stage. The multiwhcclcd machine will retain the name of multistagc. and thc individual impeller and diffuser pairs will be called a stage. With the foregoing discussion as an entreé to thc types of centrífuga] comprcssors. it seems redundant to classify them as single and multi? stage. A cross classilication can bc established by the manner in which the machine casing is constructed, whether it has an axial or radial joint. More eommonly. this type of constmciion is referred to as horizontal and ircrticul split. For simplicity. the second terminology will be used. The overhung style of single stage is an example of the vertical split type ol compressor (see Figure S-l). An example of the horizontally split corn- pressor i». the common multistzige. Maintenance of the horizontallv s lit compressor is very simple and straightfnrward. as the rotor may he removed without disttirbing the impcllcrs, Whcn the pressure is too high to maintain a proper joint se or or low molecular weight service another style commonly used is referred to as a harrel compressor (ser: Figure 5-2). The banal uses a vertical split consuuction. ln the multistage it is constructed with : i rcmovablc. horizontally split. inncr harrel that permits thc removal of the rotor without removing thc impellcrs. Many overhung compressors do not pennit the removal ol' the rotor without first removing the impeller. Another common type of compressor is manufactured in an integrally gcared configuration. lt is basically an overhung style machine mounted on a gear box and uses the gear pinion shall extension to mount ill":
- 4. Cenrrilúgal Compre mm 135 ) Figura 5-1. Single-stage, vertscaily split. overhung style centrífuga! compressor. (Comesy of Elliot! mimar! ” . ... . -~. .._; s . à '/ 4 5 7m¡ Í _ A' r ' É_ l a " ' M Í ' ; l ¡ L! .. .r Í( ' t' TF¡ “ÍX/ ' A, n; _ _ à , vg f. x- v * Ç ta. ¡ , ¡ ' ' t a › Ji' " 1 1 N 7.¡ *í T _ ¡'N r. . _ . ' ' - . f | 1 a A u 4_ à) _ a n”, _l ¡f! mr . .À ; ' . qr - A I, r . .a _I ' v ¡ -, ¡ . r _ n . A 1 E, x x' 1x1; ' _-' x M 1 . _. l Figure 5-2. Multlstage Barrel type compressor. (counesy o! Nuovo Pignons)
- 5. Í38 t 'nutpressorss Selection and String impeller (see Figure 5-3). The casing is also attached to the gear box, This style is built in both the single and multistage configuration. The most common form of multistage is the plant air compressor, which also has intercoolers included as pan of the machine package. Flqure 5-3. Ovemung. geamox mounted centrífuga¡ compressor. (Caurtasy ofAUas copw camptec me) Arrangement The single stage can be arranged, as has been discussed in the previous paragraphs. in the overhung style. Figure 5-4 shows a schematic of the compressor. Note that the flow enters axially and exits in a tangential direction. For a comprehensive discussion, it should be mentioned that the overhung style is, on very rare occasions, constructed in the multi- stage form, usually overhanging no more than two impellers. The over- hung compressor is generally more competitively priced than the between-hearing design. Cateful application must be made because the overhung impeller configuration is more sensitive to unbalance than the between-hearing design. If impeller fouling is anticipated. this design may not be acceptable.
- 6. (ü-nntfrcigul (iimprtartttri Í37 à IN OUT Figure 5-4. Dlagrarn ot a single-stage ovamung type centrífuga¡ compressor. A less common form of the single stage is shown in Figure 5-5. In this form. the impeller is located between two bcarings. as is thc multistagc. This type of compressor is sometimes referred to as a bean¡ type single stage. The flow cntcrs and leaves in a tangcntial direction with the noz- zles located in the horizontal plane. The between-hearing single stage is found most commonly in pipe line booster service where the inherent rigidity of' the two outboard bearings is desirable. Figure S-ó is a How diagram and schcmatic layout of thc intcgrzilly gcarcd compressor, :ind Figure 5-7 shows explodcd view. It consists of three impellers, thc first located on one pinion. which would have ; i lower speed than the other pinion that him mounted the remaining two impcllers. This amingement is common to thc plant air compressor. Con- figurations such as this are used in process air and gas services, with the number of stages set to match the application. Figure 5-8 shows the multistage zirrangement. The now path is straight through thc compressor. moving through each impeller 'in tum. This typc of centrífuga¡ compressor is probably the most common of any found in process service. with applications ranging from air to gas. The liittcr includes various process gases and basic refrigeration service.
- 7. Í38 r 'umprvrrnrr SEÍeTHUH and . String OUT m Figure 6-5. olagram ol a beam type single-stage compressor. Figure 5-6. Flow oiaoram and sdiematlc ot an integralty geared compressor.
- 8. ( 'rnlriru eu¡ ('nni(ire. i.iairi l39 Figure 5-1. An explodiu! view ot an ¡nttagriitly geared compressor. (cowtesy of anger Turbooompresson Figure 5-8. Diagram of a multlstage centritugal compressor with a straight-through now path. Figures 5~9 and S-IO depict the two most common forms of in-oul arrangements. 'This urrangement is also referred to as : i compound com- pressor. ln these applications. thc flow out of the compressor is taken through an intcrcoolcr and back to the compressor. The arrangement is not limited to cooling because some services use this iirrangement to remove and scnib the gas stream at a particular pressure level. Provision for liquid removal must be made if one of the gas components rcachcs its saturation
- 9. '40 Cuntputsttrs. Selection and String OU? Figure 5-10. Diagram of a double-cooled centrífuga¡ mmpressor. temperature in the process of cooling. Figure 5-!0 shows a double-cooled or double compound compressor. This arrangcment is used mostly when the gas being compressed has a temperature limit. The limit may bc imposed by the materials of construction or where the gas becomes more reactiva with an increase in temperature and thus sets the limit in a given application. Polymer fonnation is generally related to temperature and may form the basis for an upper temperature limit. However. with the extemal cooling, the amount ol' compression needed can be accomplishetll in a single case. The physical space needed to locate the multiple nozzlcs nonnally limits the number ol' ín-out points to the two shown. The amingement shown in Figure S-ll is referred to as tt double-flow compressor (see also l-'Igure S-l2). As indicated in the figure, the flow enters the case at two points, is compressed by one or more stages at each end. and then enters the double-flow impeller. The flow passes through each individual section ol' the double-flow impeller and joins ; tt
- 10. (Írnrrifiqeul Cnmprexxurs 1M Figura 5-12. A double-flow compressor with inlels on each end and a common center discharge. (courtesy of Emo! ! Bauman» the díffuser. 'There are various physical arrangcments to accomplish the double-flow compression. One variation is Io use two back-to-back stages for the Fmnl compression and join the flow either imemally. prior to leaving the case. or join two separate outlet nozzles outside the case.
- 11. 142 f rlmprntart' Stlcrlion mid Sizuig From ll process point of view, thc flow should hejoined prior to cxitmg the dischargc nozzle. Another trariation of this arrangement is to use it in the single-stage configuration. where only a single inlet and outlet nozzle is used. The llow entcrs the case and is divided to each side of the doublcdlmt' impeller . md then joins at the impeller exit prior to entering the dilluscr. Figure 5- i 3 shows a schcmatic diagram of the flow in this machine. The advantage of thc double-flow arrangcntent is. of course, that in the same Casing «i/ .e, it doubles the flow. HOWCVCI', the reulization ol' the advan- tage is morte complex. The losscs in the flow paths through the double- flow impeller must. in theory, be identical. ln practice, of course, this is not possible. 'lhe sensitivity is a function of the total head level. The lower the levels. the more nearly' thc paths must be thc same. The single-stage configuration. the lower head compressor, will exhibit the highest degree of sensitivity to the flow imbalance and have its perfor~ mance most adversely affected. The multistagc configuration. while not as sensitive to the flow anomalies because of the higher head generated_ will benefit from careful flow path design to keep the flow balanced to each section of the double flow inlets. lf a number of options are open for ; i given application, the double-flow option should not be the ñrst choice; although, it should be evaluated because successful applications in SCFVICC indicate that with careful design the compressor will perform satisfactorily. The arrangement in Figure 5-14, generally called “back to back. " IN nonnally considered useful in solving difficult thmst balance pmhlems where the conventional thmst hearing and balance drum size are made Figure 5-13. Diagram of a double-flow compressor with flow split intemally.
- 12. (Ímlntupgul Cumpmurnrx 143 Figure H4. Diagram of an arrangemem med to overcome a thmst balanca problem. quate or become excessively large. The balance dmm will be described in detail in u following section. The flow is removed pan way through the compressor and reintroduced at the opposite end. then allowed to exit at the center. Because centrifugal impellers inhcrenrly exhibit a unidirec- rional thnist. this arrangement can be used to reduce the net rotor thrust. The obvious use is for applications generating high thrusts. higher than can be readily controlled by a nonnal size thrust hearing and balance drum. An evaluation of the cross leakage between the two discharge noz- zles must be made and compared to the balance drum leakagc to deter- mine the desirability of the "back to back. " lt can be combined with the sidestream modas. discussed in the next paragraph, to possihly help sway a close evaluation. ln some rare cases, this design has been used for two different services. Unfortunately. it is difficult to totally isolate the two streams because of the potential cross lcakage. ln cases where the two services may have a common source. or the mixing of the streams does not cause a problem. it is possible ro generate savings by using only one compressor case. A very common compressor design used in thc chemical industry. par- ticularly in large refrigeration systems. is the . ridesrream compressor (see Figure 5-IS). Gas enters the first impeller and passes through two impcllers. As the main stream approaches the third impeller. it is joined by a second stream of gas. mixed. and then sent through the third impeller. The properties of the gas stream are modified at the mixing point. as the sidestrcam is rarely at the same temperature as the sueam from the second impeller. ln refrigeration service, this stream is taken from an exchanger where it is flashed to a vapor, resulting in a stream temperature near saturation. As such. the sidestream would act to cool
- 13. 144 4 'v-mprvsiurs* Srlruiur: um] . Many Figure 5-15. Diagram of flow path through a sldastraam compressor. the total stream. The weight flow to the third impeller is thc combined weight How ol' the two streams. The second sidestream follows the same logic. To show the llexibility' of the arrangement, the last sídestream is indicated as an extraction. This stream could be used where hcatcd gas at less than dischargc pressure is required. Using the extraction saves the energy needed to comprcss this quantity of ga»- to the full discharge pressure and then thmttling for the heating service. One potential application of nn extraction stream is for use in a reboilcr. The airangcmcnt shown was arbitrarily chosen to illus- trate the available options. The total number of sidestream nozzles is lim- ited only hy the physical space required to locate them on the case. Three nozzles are not uncommon. When applications are more complex than can be aocommodatcd by a single-case compressor. multiple cases. can be used. The most frequently used is the tzindem-driven series flow amingcmcnt using a common driver (see Figure 5-16). A gear unit may be included in the compressor train. either between cases or between the driver and the compressas. The indi- vidual compressor cases may take the fonn of any of the types described before. The maximum number of compressors is generally limited to three Longer, tandem-driven series-connected compressor trains tend to encounter specific speed problems. ln the longer traitis, the double-flow arrangement can be useful in permitting more compressors to run at the same speed. At the inlet. where flow is the highest. the gas stream is divid- ed into parallel streams and the volume is reduced by compression to a value within the specific speed capability of a single-flow compressor. The
- 14. Centrífuga¡ Campreavsurx 145 , í *Wu . ' o i _¡' ¡ l, h _ l ' 4 v _ n , W . .'. _,.4r. ,A_. -x . ,~'~"›V . ~ . r M' 4]¡ t. › 7 z t Í' ~ - . u " 7 ' › I 'ih y Lv v . l l A 'K', 5' ' ' ' Via' ”_-T “ÚrT-i . ut _. _ j» u, .-. _ ¡IÍ V» ' ' ' ¡gÃW ' ¡ __ ' , w_ 'i A P! › , kgfm . - . " . ' - . '_ "H '_ _E A t Wu' . [xl _. . Í L '*" ~ -, , ~ 4 . IX”, _x I v j' x Í v i 1 r' 'ía j( . N H. V* | f' ' ' _ ll" 't' k ' I u¡ t1¡ q t »o 1;; » ^ na' o t S' 7 “t l. I ' »i ' IV¡ l Figure 5-16. A tandem driven multi-body centrífuga! compressor train with a steam turbina driver. (Caurtesy of Demag Delaval Turbomachinery com. )
- 15. F56 I'Ír›rn¡›re. r.tur. r. Sffttllün and . Éizinx alternative to the double-flow amangement is the use of a speed increasing gear between compressor bodies to pcmiit the flow matching of down- stream stages. This is one case where the double-flow compressor should be comidcrcd first. When longer ! mins are needed, the cases are grouped with several individual drivers. maintaining the series flow concept. One installation that can be recalled used nine individual cases. scparatcly dn- ven and series connected, for a very high pressure air application. Drive Methods Historically, the most popular driver for the centrífuga] compressor has been the steam turbine. Steam turbines can readily be speed matched to the compressor. Prior to the upsurge in energy costs. reliability, simplici- ty. and operational Convenience were the primary factors in driver selec- tion. The steam turbine, with its ability to operate over a relatively wide speed range, was ideal for the centrifugal compressor, which could bc matched to the process load by speed modulation. Vith the advent of energy as a more significant consideration in driver selection. the electric motor received a higher degree of attention. While motors were probably . second to the steam turbine in general industry usage. the limitations imposed by a constant speed driver tended to dis- ooumge their use in process plants. But because fossil fuel can be mori: etficiently convened to electricity in large central generating statiom, the cost of electrical energy for motors became such that they began to dis- place the more convenient steam turbinas. Local steam generation cannot he accomplished at a competitive energy cost in many instnnces. While large electric drivers using variable frequency conversion to provide for variable speed are relatively new. they provide an altemative to the steam turbine. 'No primary factors that have prevented universal acceptance of thc variable frequency system are cost and experience. As more units are fumished. and with the passing of time. the negative factors will undoubtedly begin to diniinish. Electric motors. whether speed controlled or not. are either inducnnn or xynchmnous in design. Size and plant electric system requirements . set the parameters for motor selection. Synchronous motors normally receive consideration only for the larger drives. with the individual plant setting the minimum size at which the synchronous machine is used. Regardless of which motor type is selected. a speed increasing gear vxill be needed. because motor speed is rarely high enough to match the nec- essary centrífuga] compressor speed.
- 16. Cenrrifii qu! C : iniprirsrorr 147' As an alternate to the drivers mentioned. a s turbine ma be selected au the dnver. If exhztust heat recovg or regeneration is used, the efficiency ol' the gas turbine is guite attractive. Unfortunatcl . the as turbine is ex nsive and in some cases has demonstrated high maintenance cost. lt should be understood that gas turbines are relatively stzndardized even though they cover : a wide range of power and speed. They are not custom engineered to thc spaiiic application for a power and speed as is cnxromary' with steam turbinas. ln many applications. a speed matching gear must be included. Vhldl odds the complication of another piece of equipment, subsequently higher capital cost_ and potentially decneased reliability. This gear : ilso inhcrcntly has a high pitch-line velocity making for one of the mote dillicult ZIPPÍÍÇYBUOKIS. Despite some of the hurdles just mentioned. the gas turbine is w' - used in offshore installations because of its superior powcr-to-weight ratio over other drivers. lt is quite popular for use in remote locutions w cre. the package concept minimizes the need for support equipment. As ¡ul example. thc north slope of Alaska is estimated to have in excess of 1.5 mil- lion horsepovirer in gas turbine powered compressors. The remaining driver is the gas um", which can only be consid- ered it' the process stream has the potential for energy recovery. The expandcr can be either cryogcnic or hot gas in design depcnding on the application. Normnlly the cryogenic expandcrs are relatively small in size and may be integral with the compressor. ThCSC are rclatively special purpose and do not have a wide range of application. The hot~gas expandcr tends to be a larger machine and makes an excellent driver iii that it can he speed matched to the compressor and may have variable . speed czipability. The expandcr must operate at high tem ratures to hzivc sufñcient energy foi' a reasonable output @wet level. 'The high tempera- ture does make the supply piping design somewhat complex and also makes the cost of thc expandcr higher than a comparably sized steam tur- bine. Alignment maintenance is more ditTicult than with other drivers. lt would seem íiurly obvious that the economic retum of this driver would have to be quite favorable to entice someone to consider at. Thcr- are numerous successful installations using the expander. so it is : l viabl: ;ilremative to consider under proper circumstnnces. Perionnance comprassicn cycle Figure 5-I7 is a section of a typical multistage compressor. which should aid the reader in following the flow path through the machine
- 17. 148 z' Will/ ÍÍ¡ uma, .Yrlrt ! Inu mu! Stunt / Y/ ¡Vl/ /7 Figura 5-11. How path through typical stages on a muttlstage unit. (Counesy of Elliott company) Gas enters the impeller from one of several sources. ln the Case of the first impeller of a multistage. thc now has moved through an inlet nozzle and is collected in a plenum fmm which it is then directed into thc ñrst impeller. Another possible path occurs when the flow has passed through one or more stages and approaches the impeller through a channel referred to as a return passagc. ln thc return passage. thc flow stream passes through a set of vanes. 'lhe vanes are called straightener vanes, il' the flow is directed axially at the impeller entrance (eye). or guide vanes. if the flow IS modified by the addition of prerotation. The final possible path occurs when the flow comes into the compressor from a sidestream nozzle. This stream is directed into thc flow stream to mix and be direct- ed into the impeller eye using one of two alternative methods as shovm on Figure S-lfl. One method is by way ol' a blank section between thc stages where the stream mixing point is immediately ahead ol' the impeller inlet. This method is used if the sidestrcam flow is large in com- parison to the through flow. The altemativc is used when the flow is small compared to the through How. and consists ol' injecting the llou intu the retum passagc from the previous stage. The latter has better mix- ing. and takes less axial space, but has a higher pressure drop. For the former. the oppositc is true. lt has a lower pressure drop. but exhibiis somcwhat poorer mixing and uses more axial space, normally at least a
- 18. Cenmñcgal Conweunn 149 x . I 'n . ' n . n' l , . O 'l . _ : Àxxr › ›F Y Y Flyns-tttmmttmsotüaethulilastunlowsimhbrmbu (mnuyolflüattwntprm full-stage pitch in length A stage pitch is defined as the axial distance measured from the entrance of one im_p_eller to the same location on the Stnge pitch may be a constant, as on low-volume ratio staging, or variable, as may be found in higherwolume ratio stages The variable stage pitch is commonly used on higher flow coefficient s. The importance of physical length will become apparent as the entire compressor is explored. but at this point, it will suffoe to say that there never seems to be enough. Generally. there are no vanes in the inlet of an axial entry compressor (see Figure 5-19). Norrnally there is no more than the plenum divider vane in the inlet section of the typical multistage compressor. although there are designs that me vanes in this area. These are extemally mov- ahle and are used to provide flow control for constant speed machines. The use of these vanes will be explored further in the section on capaci- ty control. After the flow has been introduced into the compressor and has been acted on by one or more stages. it must be extracted. Because there is a relatively large amount of velocity head available in the stream. care must he used when designing the discharge section to keep the head loss low and maintain overall efficiency. The flow from the last stage is goth-
- 19. l50 (Ínrnpressors: Selection and Sizmg Figure 6-19. The impeller bracos can be seen ln thts vlew through the inlet of a single-stage compressor. (comasy otimas como compras. Inc. ) ered in some fonn of Collector. nomially a scroll, in an effort to convert as much of the remaining velocity head as possible into pressure. With intermediate extraction, or for some of the in-out designs. a compromise must be made. reducing large passages to preserve axial length. Having gotten the flow in and out of the machine, a closer examina- tion of just how the compression takes place is needed. An important concept to ntnintain throughout the following discussion is that all work done to the gas must be done by the active element, the impeller. The sta- tionary element is passive, that is. it cannot contribute any additional energy to the stage. lt can only convert the energy and unfortunately con- tribute to the losses. Figure S-20 is a schematic diagram of an impeller and the basic inlet and outlet flow vector triangles. The impeller will be covered in detail in the following sections; there- fore. a brief review of the various impeller components is in order. The
- 20. Centrífuga! C nmrlnsmrc 151 IÍ ¡MPELLIR HIGH CROSS SECYION IMPILL! ll ÀIIÀL CROSS SIC? |00| Figure 5-20. Impeller inlet and outlet ttow vector trtangles. impeller consists of a set ot' vanes radially oriented on a hub. The vanes are enclosed either by a rotating or stationary front and rear shroud. I_f both front and rear shroud are station . the im ller is referred to as an o n t' ller. lf the rear shroud 's t ' part of the impeller assembl . it is referred to as semi-o en. If th nt s rou is also attached to the vanes and rotates with the assembly. it is referred to as a closed impeller. The vanes may be forw curv . ta . or ac w curve as s own diagramatically in Figure 5-21. Forward curved vanes are normally only used in fans or blowers. and rnrely, if ever. used in centrifugnl compressors. Figure S-2l includes an outlet velocity vector triangle for thc various vane Shapes. Figure S-20 shows a backward curved impeller that includes the inlet and outlet velocity vector triangle. Because most of the compressors used in process applications are either baclrwanl curved or radial. only these two types will be covered in detail.
- 21. Íü fbmprrr mn” . Ya-Irrnmt : md . SL-tn g' uu¡ buena¡ Viva num-m¡ V¡ m¡ W n. v 1 / _ f' / '¡ 2 a Figure 5-21. Diagrarn deplcting backwards, radial and forward curved blades. Vector 'lrlanglas Cras cntcrs the impeller vanes at the diameter d¡. The absolute _uns velocity npproaching the vunes is V¡. As shown in Figure 5-20. the gas a roachcs the vane in a radial direction after entering the impeller in nn Luger. The vane leading edge velocity is represented by the velocity vector u. . The net velocity is thc relative velocity V, ¡. lt should bc noted for this basic example that the relative velocity vector aligns itself with the vane single Bh resulting in zero incidence. ln this idealizcd case. the meridional flow vector VM¡ is aligned with and equal to the absolute velocity. After passing between the vanes. the gas exits thc impeller at the diameter dz. 'lhe velocity of thc gas just prior to leaving the impeller is the relative velocity Vá and leaves at thc vane angle B¡ in the idealized example. By the addition of the impeller tip velocity vector u¡. the absolute leaving velocity V¡ is generated. The angle of the absolute llow vector is a2. This is the velocity and direction which thc gas assumes as
- 22. Ccurtnmgul Cnmprrrsu n 153 it leaves the impeller and enters the diffuser. The meridional velocity Vm¡ is shown by the radial vector passing through the aipex of the outlet velocity triangle. lf the vane was radial, rather than backward leaning. B¡ v 90°. the relative velocity and the meridional velocity would hc- equal and ; ilignetl Slip ln real world application. the gas leaving the impeller will not follow the vane exit angle. The deviation from the geometric angle is referred to as . vlip. The leaving angle will be referred to as the gas angle B', Figure 5-22 shows the discharge velocity vector triangle. including the effect of slip. The terms on the ideal triangle are the same as those used in Figure 5-20. Superimposed over the ideal triangle is the velocity triangle. including the effect of slip. Note that the terms are indicated with thc prime (') symbol. While there are numcrous papers written on the subject of slip. none seem to present a complete answer. One of the better papers. which summarizes the field and brings the subject into focus. is the onc by Wicsncr [7]. ln this book. for the purpose of understanding the work- ingx of the centrífuga¡ compressor. the Stodola slip equution will be used. lt is probably one of the oldest and has been used in practical design prior to the advent of some of the more sophisticated methods available now. Rctuming to the triangle under discussion, the gas angle, B', às always less than the gcometric angle. B2. ln Figure 5-22. projectrons ; irc Flguna 5-22. Dlscharge velocity vector trlangle showing me silent ot stlp.
- 23. ÍH C impressor: : Selection and String made onto the tip velocity vector from the absolute gas vectors. V¡ and V3. These are labeled as Vu¡ and V5. respccrively. and have the designa- tion of tangentinl component of the absolute velocity. From these vxtors. some simple relationships can be presented that will give a reasonable explanation of how the centrifugnl compressor goornetry relntes to its ability to compress gas. The ideal work input ooefñcient. Ç. . is given by the following expression: f Via3_ "m" - 15.1) u. where Vu¡ = tangential component of the absolute velocity u¡ = impeller tip velocity The ideal head input to the stage is given by um. .., = (ug); u: <s.2› The Stodola slip factor is defined as E sinB¡ nv Slipzu¡ ts 3) where B¡ = geometric vane exit angle n, = number of vanes in the impeller The slip factor SF follovvs. SF = E (5.4: V112 Reference is made to Figure 5-22. where ç¡ = ta. , - slip (5.5) Substituting into Equation 5.4 yield: the following slip factor equnion:
- 24. Cffllflfilfü' Cntmprrxtnn Í5I5 spa_ "T [““"521 iv. n, ,Í u! .. The actual work input coeíñcient. Ç. is written by taking the ideal work input cocñicient. Equation 5.1. and modifying by the addition nf the slip factor. SF. The geometric re| ationship of the Stodola slip function is shown in Figure 5-23. r Vu* L_ = --' (SF) (5.7' “1 By replacing the ideal work input coefñcient with actual work input cocfficient. the actual head input can be written as H_ cit/ ¡nçuâ ¡5.8› If the head ooefñcient is written as u = n: t* *h 'IC' 9~ "P": Úgvíb: “('. ' "t4 Ê- . QI' - 1 f l__r , É. ? . __. ___. _ , __ ? a : a9 JE 35 4D ac : a 5;. 55 a¡ Nutzer c' V-! Wli N, Figure 5-23. Geomatríc relationship of stodola slip function
- 25. ÍSÕ ( 'unrprecr. iur. i. . Selenium and . Smur- VilCfU n stage efficiency. then HW, = l l/ gniuã (5.10) For adiabatic head, the head coefficient is defined as ti, and Equation 2.70 is rccalled. The geometric and the themiodynamic head relation- ships for a stage may be equated. _rpa _ k EZ¡ l Has Jg _ZSWRTyÉUFl _ll líill N N Similarly. for polytropic head. the head eoefficient is defined as p, and Equation 2.73 is recalled. the geornetric and thcrrnodynamic head rcla~ tionshíps. nn a per-stage basis. may be cquated as above. s - ~l gnu: u _y n _, , H = g : law RT¡: T(TP n 'D (Sds. ) P ln the previous paragmplm. the term axei/ ic speed has been used 'This is a generalized turbornachinery term used quite successfully with pumps and to some extent with turbines. lt can be used with turbocompressors tc help delimit the various kinds of machines. lt is also used as a general term to describe the need for a correction on multistage machines when the wheel geomeiry at the current speed will no longer support a reason- ahle efficiency. For compiessors. specific speed is paired with specific diameter to include the geometric factors. ln centrífuga] compressors. attempts have been made to correlate efficiency directly to these parame- ters. Most designers feel the relationships. while satisfactory to sc¡ bounds. are not adequate for describing impeller efñciency with good re»- olution. Definitions for specific speed. N, and specific diameter. D. . are _ Nei” i5 IJ D _' -âfà- (5.l4f
- 26. t' 'y-nrnrugul (irmprprmv Reaction The outlet vane nngle for the normal centrífuga! compressor varia-s from radial to a backward leaning ungle. An ideal vector tip triangle. with no . slip. is shown in Figure 5-24. Three angles : tre illustrated to show thc effect ul' varying the vane outlet angle. Rvavriun is defined as the ratio of the static head converte-d in the impeller to the total head produced by the stage. Resutting in a more philosophical sense. the object ot' thc compressor stage ix tn increase the pressure of the gas stream. and reaction gives the relationship of the div¡ sion of effort between the impeller and the diffuser. Ideal reaction. R. . is defined as R_ --ípzmpl (5.l5' (mc of the practical aspects of reaction is that for tl well-proponioned stage, the higher the reaction. the higher the efficiency. Again. using u philosophical approach to explain, for a given stage the impeller IS more efficient than the diffuscr. This is particularly true for the typical process compressor that uses a simple vaneless diffuser. [Í thc radial vane impeller is used for thc reference, it will have nn ideal reaction of 504'. as ealculated using Equation 5.15. Because the static head conversion ts evcnly divided between the impeller and the diffuser. the net stage en¡ 990W 544- VWUF UD lfíãngle Without slip. showing the efloct ol different exit vane anglas.
- 27. 158 (Wma-nunca: Selection and String ciency ts the numeric average of the impeller efficiency and the ditTuser efficiency. Figure 5-25 shows that as the vane angle decteases, the reac- tion increases. If the efficiency is evaluated for the lower angle. the net stage efficiency is now the weighted average of the two component indi-- vidual efñciencies. with the higher impeller efficiency contributing a greater influence. A numeric example may help to illustrate the idea. Exlnllloâd Assunte impeller efficiency = .90 Ditfuser eñicicrtcy = .60 Calculate an idea! stage efficiency for a radial and a 45° backward lcaning impeller. For the radial impeller. using Equation 5.15. R. = .50 50x .9o= .45 50x m: .30 .45 + .30 = .75 net stage efficiency aura* e, I í a _ ___p__. _ Ar 4 i RÊLí'ICH . . A¡ 3D ED 30 mate. a¡ üliñ-üflhmotlcllllldbnvdlfnndb.
- 28. Crumfugul Ctmrpretvnn 159 For a 45° backward leaning impeller, R. = .75 The diffuser then converts l - R, or .25 .75 x .90 = .68 .25 x .60 = .i5 n68 4- , lS = .83 net stage efficiency The example indicate: that an improvement of seven percentage points was achieved by bncltward leading the vanes 45°. 'lhe obvious question arises. Why not malte all impellers high reaction? Maybe this can be put into a good/ bad analogy. The good is better efficiency. The bad is a lower head produced by the stage. To see why the head is less. review Figure 5-24. lt can be seen that as the outlet angle. B2. is decreased. the tangential component of the absolute velocity. V”, is decreased. li' Equatíon 5.1 is recallcrl, it should be noted that a decrease in V. ; will decrease the value ot' the head input coeliicient. Ç. . By carrying a lower value of Ç¡ into Equa- tion 5.9. the head ooefficiertt, tt. is decreased. ln Equation 5.10. it is obvi- ous that for a lower p. the output head is decreased. There is some relief in that in Equation 5.9. the stage efficiency n inerentes to offset the lowered Ç. However, in real life. this is not enough to malte up the difference and the output head of a higher reaction stage is indeed lower. There are sever- al effects that influence a commercial design and. again, the designer is faced with tradeoffs. Bquation 5.10 indicatcs that increase in the tip velocity u¡ would olfset the loss in u. impeller stresses and rotor dynam- ics must also be considered and may act to limit the amount of eorrection that can be made. Another possibility is using additional stages. A well- proportioned stage is assumed. which brings to light the fact that the high reaction stage leads to use more axial length. This tends to counter the addition of extra stages. especially where the length of the rotor is begin- ning to cause critical speed problems. Despite the conflicts. changing reaction can sometimes aid the designer in achieving a higher efficiency. Another benefit is a steeper lead-capacity curve. Also in smne cases. the higher reaction stage seems to perform better where fouling is evident. 351W Many of the steps used in sizing estimates are also useful for checking bitls or cvaluating existing equipment. ln the latter two endeavors. there
- 29. ÍW t 'vmprerrurr' Selection and Shure rs une advantage: someone else has established the initial evaluation cri- teriar When working from a material balance flow sheet as . i starting point, rt is sometimes difficult to envision what the compressor should look like, Except for the addition of u few rules ol' thumb, ,post of thc tools needed have already been established. The method outlincd is bau-d on the more conventional multistage compressor-s used in pftlccsx Cl vice. Earlier, integrally geared. as well as direct expander driven cum- prcssors. were bricfly described. These compressors may also be sizcd h) the method outlined. but because they ane tailoned for higher head . ser- vice. modifications to the method regarding the head per . stage and thc head coefticient ane necessary. To start, convert the flow to values estimated to be the compressor inlet ' ' . itiall' e l tro ic head nation( uation 2.73) will be used with n as the polytropic compression exponcnt. ll' prior knowledge of the gas indicates a substantial nonlinear tendency. the real gas compres- wion exponent (Equation 2.76) should be substituted. As discussed in Chapter 2. an appmximation may bc made by using the linear average of the inlet and outlet lí v¡ lues as ¡Ee exmnent or for the detennination of the polytropic exmnent. ll' only the inlet value of lt is known, don't be too concemcd. The calculations will be repeated several times as knowledge of the process for the oompression cycle is developed. After selecting the k value. use Bquution 2.7l and an cstimatg stage efñcicncy of 759v' to develop thc polytropic COMESSÍOII exponent n. The molecular weight. inlct tempgature, and inlet pressure are cont- bined with the compressibility and discha c ressure in uatio 2. 'i to tro l . The average of inlet and outlet COITIPÍCM» ibiltty' should be u* using the Elytropic disch_arge temgmture calou- ! aged bv the following gguation to evaluate the discharge oompnessibilitv. ll' T1 ›T› lp u l5 i0) where T¡ . - absolute discharge temperature of the uncooled section 'l', x absolute inlet temperature of the uncooled section To detennine the number of stages. using the impeller and diffuser defined as the stag, assume l0,000 lt-lb/ lb of head gr stage. This value can be used if the molecular weight i2¡ in the range of 28 to 30. For other
- 30. Cenlnlttuul ("ntnprriuu v. TÕÍ molecular weights. this initial value mLlSl be modified. As a rule of thumb. lower the head E stage by l00 ft-lbllb for each unit increase in molectt lar weight. Conversei . mise the allowable head per stage 200 ft lb/ lb for ; t m unit decrease in molecular weight. The mle of thumb gives the st resu ts for a molecular weight range of 2 through 70. Because this sizing prou- dure is being used only to establish the rough size of the compressor. lhc upper range may be extended with some loss in accuracy. Once the head per stage has been established, the number ol' st es can be estimar la ing e total head. as calculated by the head guation. and dividin b the head r stage value. A fraction is usually munded to the next whole number. However. if thc fraction is less than .2. it may bc droppcd. E: stage. This method assumes an uncooled or no sidestream compras sor. If either ot' the two are involved. the uneooled sections can be est¡ mated, taken one al a time. Assumptions for between-section pressure drop or sidcstream mixing can be added to the calculation as appropriate to account tor all fztcets of the process. When all calculations are cum- pletcd. lhe compressor sections can be arranged to fonn a complete untl Before proceeding. a few limits need to be considered. 'lhe tempera- ture, it' not limited by any other consideralion. should not exoecd 475%'. This limitation is arbitmry. as centrifuguls may be built to higher limits. hut the estimator is cautioned not to venture too far into this region with- out additional considerations. The number of stages per casing should not exceed 8 for rotor dynamics considerations. Also. knowledge of auxiliary uate exactly how far to ven ture in this direction. Vendor literature advertises the availability of as many as ten stages; however, an estimate should never go to the edge without a background of considerable experience. These limits can also be used to evaluate pmposals and help to determine tt series of questions for the Vendor skining the upper limits. e ins assuntin a head coelTicient ual to .48. Equa- tion 5.12 can be used to calculate the tip speed, uz. Figure 5-26 can be used to volume calculaled earlier. The diagonal line on the diagram marks the right extremity ol' each impcllefs flow range to guide the user in making the first selection. ThLtip speed and diameter cam be used to cnlculatc an approximate speed. N. by N' 5"- til¡ ! Til 1
- 31. 162 t 3 rvnprexlrtn. Selection and Sum¡- o w b lMPElLEñ ¡AIHETEH ¡INCNI S) 3 . z l _ › _v3_ / I , .E__í_. _______. . b r I u M 'i0 ? l voww: tem - IV) Figure 5-28. Estímation ot impeller diameter using Inlat volume. where d¡ = impeller outside diameter To summurize the sizing to this mim: the inlet volume. an overall head. number of sta s head sta e, im ller ti . speed, and impeller diante- ter have been established. The one pammeter of interest still tnissing is the efficiency. To obtain an estimate of efficiency without empírica¡ data. a generalizar! form may be used. As in the previous Chapters. where esti~ mates were involved, the data presented is just one way to approach the problem, and any other reasonable source such as specific vendor data may be used. To use the generalized curve, Figure 5-26, the volume for the first and last stage must be developed. The volume for the ñrst stage is the inlet volume. The volume for the last stage, Õ"" can be estimated by QR * L¡ (SÁB)
- 32. ("t-ntnfuxnl Crmpnvmri 153 where 0," = inlet volume ru -= pressure ratio for an unoooled section I = number of stages in the uncooled section Use the inlet and the last «ag volume for the uncooled section and use the following equation to calculate the inlet flow coelñcient ô. Õ=7ÍX)NQd'¡ i5.l9“ › 2 where Q_ = volumetric flow. (tl/ min N = mtational speed, rpm d: = impeller diameter, ill. Note: This equation is not in the primitive fonn. While õ is basically dimensionless, the constant 700 is not easily derived; therefore. units were assigned. The value for the ñrst-stage flow coeñicient should not exceed . l for a 2D type imEller and for a 3D design, the uEEr value can be as high as . l5. The value for the last stage should be no less than . OI. lt' the flow coeflicients should fall outside these limits. another impeller diameter should be selected. lt may be necessary to ¡ntgmlalc to obtain n reason- able diameter from Figure 5-26. This can be done because this is an esti- trary line of compressor frames. The dia- gram was set up to give the user an idea of how a compressor line might be organized. A vendor may quote values outside the guidelines due to the constraints of his available frame sizes. For estimatcs. values as close as possible to the given guidelines are recommended. At the time of a proposal. the benefit of stages beyond either extreme value of flow coef- ñcient can be evaluated. It should be noted at this point that not all ven- dors report their ! low coeñicients on the same basis. If necessary. the parameters for flow coeñicient should be obtained to permit evaluation with Equation 5.19. An average of efficiency can be calculated from two efñciencies selected from Figure 5-27. The figure includes efficiency values for 2D and 3D impeller designs. While it would appear obvious that only 3D impeller: : should be used. there is a caveat. Generally. 3D impeller: require more space. that is. the axial stage spacing (stage pitch)
- 33. ÍM t 'v -ttrprr. ttor. t' Sela-non amd Sum): g0? [ ' C-: PNL ! I ñoel-v -1]›~ ; iir-zz-l-cxkí_ "'T**~~it _ _ 5 1 | gun? -› ~ - ~ - p-v _4% a se e ele . ç o f l r i r J 'Êoi oo: aos oo7 ooo o n o : :i 015 Flow Cotilltdont Figure 5-27. centrífuga¡ stage efficiency vs. now eoeftlclenct tor 20 and 30 blading. is longer. This will result in a longer compressor. which makes for possí- ble rotor dynamic problems and docs also increase cosL Also. it should be pointed out that the increase in efficiency begins above flow coeff- cients of .04. 'lhe increase in stage pitch can vgy from approximately l. l to 1.3 times a 2D stage pitch with the values increasing with increased flow coeflicient. For the 2D imEller. it should be noted that the peak efficiency occurs at a flow coefficient of approximately .07. The 3D imp_eller p_eak efficiency value curve is hmader and QCCUIS in the range of from .07 to values as high as L3. At this point. after a first pass through the calculation. a new polytropic CXEECM should be calculatod. All values calculated to this ppint should be rechecked to see il' original estimates were reasonable. lf the deviation appears significant. a second pass should be made to improve the accura- cy. Equation 2.78 can be used to calculate the power for the uncooled soc~ tion. For an estimate. use a value of 1% for the mechanical losses. lf time pcmtits and a more accurate estimate is desired, panicularly if the compressor is inter-cooled or has sidestreams, the velocity head losses through the nozzlcs can be estimated using the values from Table 2-2. This is possible where the nozzle sizes are available or can reaudily be estimated. When coolers are involved. the drop through the cooler should (of lhc stage following the element) and recalculate a modified res ' ' r the section. The cooler pressure drop can be approximated by using 2%
- 34. ("eum/ rural (Ílmiprrtvnri 155 of the absolute pressure at the entranoe to the cooler. Because thc per centage gives unrealistic values at the lower pressures. a lower limit ot' 3 psi should be used. Compressor: : with in-out nozzles used to take gm fmm the compressor for external cooling and retum to the compressor can experience some temperature crossover in the internal sections of lht' machine. Unless the design has speciñcally provided for a heat barricr. healing of the return gas can be expected. For a first estimate, a l0°F riw should be used. Balance pistons will be described in the mechanical wc tion of this chaptcr. Briefly. thc balance piston contributes a parasitic lim to the compressor not accounted for in the stage efficiency. The weight flow passing from the balance piston area. normally thc dischargc. and entering the suction must be added to the flow catering the first stage u; the . stage receiving the balance piston flow. Unfonunately. the flow is nut the only problem. as the retum flow also acts to heat the inlet gas. Fui discharge pressures ol' 150 psia or less. a value of 1% can be used. Fur pressures ia ut un er . sia, a value o . ..é is . i rcuxoiiahle starting poinL An equation for the healing is -_"Í. .t_'i. _B_lÍ ijzn¡ '~+BP u where t, = impeller inlet temperature t¡ z» nozzle inlet temperature t. , = temperature at the balance piston BP = balance piston Ieakage fraction The relationships are given to help the user size a compressor from scratch. The same relationships can be used in the bid evaluation process. The vendonprovided geometry and perfomance values can be compared to the original sizing. which should have been performed prior to going out for the bid. The veridoris results can be evaluated using some of the titles of thumb or guidelines provided. Any deviations can be used as a focus for additional discussions. Also. some insigbt can be gained into the vcndor's sizing techniques, particularly the way the vendor trinis out a selection. incremental wheel sizing is fairly universal. Some vcndors also offer fixed guide vane sections as pan of a stage to aid in the achievement of a particular performance speciñcation.
- 35. tee z 'umprnmrxr Srlnctiim and Swing Example 5-2 Lking the results ol' Example 2-2. size a centrifugal air compressor using the sízirig procedure. A summary of the results is: Ql = 6.l7l cfm inlet volume tg_ r 437.5 lbslmín mw ~ 28.46 molecular weight P¡ = 14.7 psia inlet pressure t, r 90.0°F inlet temperature T. = 550°R absolute inlet temperature Rm ~ 54.29 specific gas constant Add the following conditions to complete the application: ' z 1.395 isentropic exponent for air P-__ «r 40 pain discharge pressure Assumed polytropic efficiency np = .75 Step l. Calculate the polytropic exponent using Equaiion 2.7l. n~l l.395-l l -Aíx 1.395 É ›" 72.378 ll " -=2.646 n~| .n= l.608 From Equation 2.64.
- 36. Cenmiupul C nnrpranrnrs l67 r , 40/ l 4.7 r_. r 2 ? ll pressure ratio Step 2. Calculate the total required polytropic head using Eqllílllüll 2.73. assurriing a value for Zn¡ = l: Hp: | ›< 54.29›<S50›<2.646 (2.721 37"- l) H, = 36338.4 ft-lb/ lb overall polytropic head Step 3. Detennine the number of stages, z. required using the recom- rriendcd 10.000 ft-lhflb head per stage. 1 36338.4/ 10.000 z. - 3.63 stages. round off to 4 Culculutc : i new head per stage using four stages: H, : 36.338.414 H, = 9.085 ft-lb/ lb Step 4. Use the geometria form ot' Equation 5.12 to calculate a tip speed to produce the head per stage just caleulated Also, use the recom- mended head coefficient tt : .48 in the equation. u¡ 2 (9.085 x 32.2/.48)'5 u¡ : 780.7 fps impeller tip speed Fmm Figure 5-26 and the inlet volume. select an initial impeller diameter. 3 = 17.3 inchcs impeller diameter Use Equation 5.l7 to calculate the initial speed. N. and use the conver Sion factors of 12 tri/ ft and 60 secs/ min.
- 37. 168 4 mwrexsum. Sefvvnun and Smnx s s «›<›, s12.›g_822 t i n x 17.3 - 10. 342 rpm shañ speed Step 5. The volume into lhe last impeller. in this example stagc 4 inlcl. is calculalcd using lhe Fquation 5.18. 6,171 Qt z ¡l-¡ni-IM “uma Q. , = 3.869 cfm volume at last stage To obxain an cfñcicncy for lhe gcomcuy selected. thc value of thc now cocñicicnt must bc calculalcd using Equation 5.19 for the first inlct : md the last stage tlow. õ :1700 x 6,l7l)/ (10,342 x 17.33) õ - 08| fim stage flow cocfñcicnl 5 . -. (700 x 3,so9)/ (10.342 x 17.3% ô r . O51 last stage flow cocfñcicnt Using the flow coefñcienls just calculated and Figure S-26, uu: com: - sponding efñciencies may bc looked up: a: _osl. n,, = .79 õ: .OSI. np: .79 11m avcmge is rather easy lo calculate. p¡ 1_ . -. ,70 the average eñiciency Step 6. Rocalculatc the polytropic cxponem using Equation 2.7l and the new efficiency.
- 38. tíizrvmfugar' Comprei-rar: 169 n-l l.39S-ix l n 1.395 ? i5 n-l -› = 359 n l'. -2.7s7 n *l n ¡559 Using the new polylropic exponent, calculate the discharge temperature : Losing Equation 5.l6. T¡ t S50 x 2.7215” T3 ~_- 7R7.8°R t¡ = 787.8 ~460 u: r 127.8°F discharge temperature Calculale the power required using Equation 2.78 and the recommended l W for mechanical losses. _ 337.5 x 36. 333.4 w › , " 33.000›<.79 + . Olw, w. . z 609.8 + 6.¡ W'¡__ : 615.9 hp total for the compressor Note. the polytmpíc head was no( recalculated as the change in elTciency only made an approximate 1% difference in original value and is well within the accuracy of an estimate.
- 39. Í70 ( 'nmpressnrs' Selrrrion and . Sizing Example 5-3 For a sample problem that will include some of the additional losses that are norrmlly encountered in an actual situation. size a compressor m the following given conditions for a hydrocarbon gas: mw 2 53.0 k, r 1.23 Z¡ : (197 l¡ r R5°F P, 240 psia P¡ = l20 psia w -: 2.050 lh/ rnin Step I. Use Equation 2.5 to calculate the specific gas constant. R = l.545l53 R _' 29 IS Step 2. Conven the inlet temperature to absolute. T. ~. x5 + 460 T, = 545°R Step 3. Calculate the polytropic exponent using Equation 2.7l_ Assume an efficiency of n, e .75. Use as kn¡ = lc¡ : 1.23. n-l l.23-l l _à_ X n 1.23 11-' = .249 ll ll =4.0ll n-I n= 1.332
- 40. Ctntrífltgal Compressor. : 171 Step 4. From Equation 2.64. r, , = l20/40 r_ = 3.0 pressure ratio Step 5. Calculate the estimated discharge temperature using Equation 5.14. T, = 545 x 3 34° T; = 7l6.7°R absolute discharge temperature estimate Convento °F: t; = 716.7 - 460 t3 2Sh.7°F Correct for the balance piston lealtage using l% for pnessunes of l50 psiu and under. 111o weight flow into the impeller must be increased to account for the leakage. w z 1.01 x 2.050 w = 2.0705 lbfrnin net flow to the impeller. 'lhe temperature at the entrance to the impeller- 'us increased because of the hot leakage. Calculate the corrected impeller inlet temperature using Equation 5.20. t z gts + 256.7(.0|) “ 1.0¡ 1,, = 86.7°F corrected impeller inlet temperature Convert to absolute: T_ s 86.7 + 460 TW = 546.7°R Step 6. Substituir: into Equation 2. IO and using l44 in¡lft7. _ ¡A9_7_ x 29.15 x 546.7 , 7. 4Ox|44 X2005 Q¡ O, = 5. S57 cfm inlet flow to the impeller
- 41. 171 r nmpreuorx. Selection and Sizmg Step 7. Calculate the total required polylropic head using Equution 2.73. mxuming the average value of Zn. , = .97. Hp - n97 x 29.l5 x 546.7 x4.0ll(33” - l) HE, ~* 19.508 ft-lb/ lb total polytropic head required Step 8. Detcnninc the number of stages required using the modified rulu nt' thumb on head per stage. HM. iu. . - 10.000 › ((53 - 29H00) u_ = 7.600. tt-lb/ lb z _ 2.57 stages. round off to 3 Calculate a new head per stage using three stages. Hp = 1950813 Hp : r 6,5027 (t-lb/ lh head per stage Step 9. Use the geometric portion of Equation 5. l 2 to calculate u required tip speed. which will produce the head per stage. Use the recom- mended head coeñicient p = .48 for the calculation. u; = (6.502.7 x 32.2l.48)"2 u¡ 2 660.5 fps impeller tip speed Step 10. From Figure 5-26 and the inlet volume, select an initial impeller diameter. d; 2 l7 3 in. initial impeller diameter Use Equation 5.17 to calculzite the initial speed. N. N: @›<l2x660.5 rtxl7.3 N = 8.750 rpm compressor shaft speed Sup ll. The volume into the last impeller is culculated with the use m? Equution 5.18.
- 42. CrmI/ /ugul ("l int/ un m¡ t Í73 5.557 Un _q QM Í 1.206 cfm volume into last stage With the volumes just calculated, calculate the inlet flow coefftcient foi each of the two stages using Equation 5. l9. ô r l 700 x 5.557)/ (8.750 x 173)* õ = .O86 Íiist stage flow cocfiicicnt a (mn x 3.206)I(8.750 x i7.3›°' õ = .O50 last stage flow coefficiertt Look up the efiiciencies for the two flow coefficients on Figure 5-27. nr - .79 tirst stage efficiency ii', r .79 last stage efliciency n¡ .70 average of the two cmCÍCDCÍcs Step 12. Recalculate the polytropic exponent using Equation 2.7 l und the new average eflieiency'. n~l I.23v-l I X ti | .23 ,793 ' ,336 n l +424 tt »i With the new polytmpic exponent. calculate the discharge temperature by substituting into Equation 5.16. T, .- 546.7 x 3.236 l; = 7085°R absolute discharge temperature i, = 703.5 - 460 t, - 248.5"F discharge temperature
- 43. 174 F4 »ot-impurm. Selection and String Sup 13. Calculate the power required using Equation 2.78. allotving 1°? for thc mechanical losses, Use the conversion 33.000 ft-lb/ min/ hp. w_ z +.0,“› 't 33.000›< .793 ” wp = 1.543.¡ + 15.4 WP = l.5S8.5 hp shaft horscpowcr There i5 no need to recalmilate the polytropic head for the changed efñ- ciency because the head difference from the original value is negligible. Another item to note is that the horscpowcr is 15% higher than if thc balance piston had been neglected. The interesting part is not the value itself. but the fact that the slight temperature addition at the impeller inlet is responsible for 5% of the increase and the remainder is the 1% weight How increase through the compressor. As the small. but significant “real life" items are included. the actual efficiency is being eroded. If the cal- culation had been made with only the original weight flow. the equiva- lent efficiency would prorate to .781. Example 5-4 This example presents a gas with a temperature limit and is typiczilly found in a halogen mixture. A multi-section compressor is required to accommodate the limit. 'This example illustrates one approach for th: : division of work between the sections to achieve il discharge temperature within the specified bound. mw = N) k. : H5 x3.; I . t3 Zi = .98 Z; = .96 t. = 80°F N_ = 24 psia 5 = IOS psia w -= 3.200 lbs/ min
- 44. Fmrnybgcil Cwnprrsiurt 175 The temperature. t1. is limited to a value of 265°F Step l. Use Equation 2.5 to ealculate the specific gas constant. R r 1.545/69 R=22J9 Step 2. Convert the inlet temperature to absolute. '. = 80 + 460 T¡ = 540°R Substitute into Equation 2.10 and using the conversion constant of I44 inÊ/ ftz. calculate the inlet volume. ; as x 22.39 ›< su) x 0'; 24›<l44 um Q, = l0.971 cfm inlet now Step 3. Calculate the overall poltropie exponent using Equation 2.7l and an assumed polytropic efficiency ot' t1, = .75. = (1.35 + l.33)/2 km¡ : l The average was used in evaluating k because the values were not all that different. u_l.34--lx I n l.34 75 "i-dans Il 1 -2955 n- l n= l.5ll
- 45. Í75 t 7 'ntpmrsonx Selection and Sizmg Step 4. Fmm Equation 2.64, rÍ_ z HIS/ Zn¡ r, _ 4.175 overall pressure ratio Step 5. Calculate the díscharge temperature for the total pressure ratio to check against the started temperature limit. using the assumed efficien- cy. np = .75 and the polytropic exponent Apply Equation 5.14. T; 54o ›< 4.375 W* r, _- XSOJPR l_- s 889.3 - 460 l; _- 420.3°F discharge temperature Since the limit is 265°F and the overall temperature is obviously m excess of this limit. intercooling is required. lntercooler outlet temperature must be determined. lf cooling water ut 90°F and an approach temperature of l5°F ane assumod. the gas outlet from the cooler returning to the compressor will be IOS°F. ll' Equution 3.l2 is borrowed from the reciprocating compressor chap- ter and used for an uncooled section. the pressure ratio per section may be calculated assumíng an approximate equal-work division. For the ñrst trial. assume the limit of temperature may he achieved in two SOCÚDns, rp 2 4 175” pressure ratio per section x r 2.092 il* z 2.092 x 24 P¡ : Sl) 2 psia ñrst section discharge pressure From thc mle of thumb given for estimating intercooler pressure drop. a value of 2 psi is used because it is larger than 2% of the absolute pressure ut thc cooler. The pressure drop must be made up by the compressor by additional head. and can be added to the ñrst or second section pressure ratio. By applying a little experience, the guessing can be improved. The front section has a lower inlet temperature and is generally more efli~ cient. so the best location for additional pressure would be in the first
- 46. (Ímlnfumtl Cumprnum 177 section. The first section discharge pressure is 50.2 + 2 = 52.2 psia. A new pressure ratio for the ñrst section must be evaluated r. _. = 52.2124 r, .=3.l75 Step 6. Evaluate the discharge temperature, oontinuing the use of the previously calculated polytropic exponent, T3 = s4m2.175)~“' _. = 702.2°R x, = 702.2 ~ 460 t¡ = 242.2°F ñrst section discharge temperature This temperature is within the limit. intercooler outlet pressure is 50.2 psia. Calculate the second section pressure ratio. rp = IOS/50.2 l'¡. = 2.092 Evaluate the Section 2 discharge temperature. 1'¡ = 565(2.o92)-1“ 'l', = 725°R t _. = 725 - 460 l_› = 265°F discharge temperature Because the temperature just ealculated is right on the temperature limit and there is margin in the Section l temperature. the pressure may be arbitrarily adjusted to the first section to better balance the temperatura. A Section l disclulrgc pressure of 54.5 psia is selected. which results in a new pressure ratio. rp = 54.5124 - 7 3 r, - -. ..71
- 47. ÍTB ("umprersnrri Selection um¡ Sir/ ni' Now calculate a new Section l discharge temperature for the pressure just assurned. 'r' 540(2.27r›3-'“ °R - 460 .5 °F 7l ll fu) ía . rj Il u¡ u b¡ ll~l r IJ tu r - 5 The temperature is still within the required limit. Correct the cooler outlet pressure and evaluate a new ratio for Section 2. The corrected cooler out- let pressure is 52.5 psia. n, = 105/525 rr, = 2.0 Recalculate the discharge temperature for Section 2. using the previous cooler outlet temperature. _. . = sbsaoym T; r mma l: - 714.2 -460 l; - 254.2°F The temperature is now below the 26S°F limit and consistem with the Section l temperature. At this point, the initial assumplion for 2 sections can be considered a firm value. Step 7. Calculate the polytmpic head for each section. using the overall average compressibility of 24m = .97. Section l Hp = .97 x 22.39 ›< 540 x2.956(2.27l)"”“ Hp = ll.074 ft-lb/ lb Section 2 H, = .97 x 22.39 x 565 >< 2.956( 2.0)** H1, = 9.576 ft-lb/ lb
- 48. Centrrftrgul Cumpre uurr 179 Step 8. Develop the allowable head per stage by the use of one of thc mles of thumb. na v 10.000 - ((69 ~ 29›u0o» rrpp = 5.000 ñ-lb/ lb Divide the total head per section by the allowable head per stage to develop the number of stages required in each section. Section l 7. = 11.074/6000 . r. = l.84 stages. round offto 2 Section 2 z = 9.576/6000 1 = L6 stages. round offto 2 Step 9. Calcular: a head per stage for each section based on two stages each, Section l Hp = r 1.0740 Hp = 5.537 ft-lb/ lb head per stage, Section l Section 2 llp = 9.57612 Hp = 4.788 h-lb/ lb head per stage. Section 2 Use the geometric portion of Bquation 5.12 to calculate the tip speed. Assume u, = .48 for the pressure coefñcient. Section I u, = 45.537 x :52.2/ASP u¡ = 6119.5 fps tip speed first two stages Section 2 u¡ = (4.788 x 32.2/.48)-5
- 49. ÍÚ Cnmprenorr' Selection and Sizing u¡ = 566.7 fps tip speed last two stages Sup 10. From Figure 5-26 and the inlet volume to the ñrst section. select an initial impeller diameter. d: z in. Because the second section shares a common shnft with the first section, it is not necessary to look up a new impeller sim. Apply the Section l impeller diameter. Equation 5.15. and the conversion constants of t2 in. /ft and 60 sec/ min. to calculate a shañ speed. N _ |2x60x566.7 nx5.588 N = 5.588 rpm With the sltaft speed and the tip speed calculnted in Step 9 for thc Section 2 stages. calculate nn impeller diameter using Equation S. l5. d : t2_›<60›<$66.7 ' nx25 d¡ = 23.24 in. Section 2 impeller diameter Sup II. Calcular: the inlet volume into Section 2. Use 2m = 97. P¡ = 52.5 psia, and t, = l05°F. Substimte into Equntion 2.10 as was done in Step 2. _ .97 x 22.39 x sos x Q' 52.5 x ¡44 3. 200 Q, = S. 194 cfm inlet volume into Section 2 Calarlate the last impeller volume for each section using Equation 5,18. Section l : n97: 0'” = Í2.27¡'”›"¡3" 0,, = 8. 363.4 cfm last stage volume. Section l
- 50. C enmfugnl C nmprcsmn 181 Section 2 Q __ 5.193_ | ~ (lot/ Swim O. , = 4,1294 cfm last stage volume. Section 2 Use Equation 5.19 to evaluate the flow coeñicient for the First and last impeller of each section. Section l õ = (700 x 10.970/6588 x 25') õ = .O88 flow cocfficient. first stage ô = (700 x 8.364.4)l(5.588 x 25') õ 'r . O67 flow coeñicient. last stage Section 2 5 r (700 x 5.l94)/ ($.588 x 23.243) õ = .O52 flow coefñcicnt. first stage õ r' (700 x 4,l29.4)I(5,588 x 23.243) ô r . (141 flow coefticient. last stage Step 12. Use Figure 5-27 and the flow coeflicients to determine the etTiciencies for the stages. Section l õ : .O88. 1], r .79 õ : = . O67. 11,. = .80 Tha: average is nr _ 795 Section 2 õ 052. np = .793 õ v: 04141,, = .78
- 51. 182 Fumprctrsorx: Selection and String The average is q, .- .787 Sup IJ. Recalculate the polytropic exponem. Section l Use km¡ = 1.345 _n_-_ = 1.345 -l x _i_ n l.34S .795 71 = .323 II . JL : 3_| n - l Section 2 Use tem: : mas n-l l.335-l l x: : T 1.335 ,737 33-5310 n ›-n-= 'ã. l36 n-l Step N. Use the polytropic exponenis calculated in the previous step and iecalctilate the discharge temperature of each section to correct for the average stage efficiency. Section l T¡ = 540(2.27l P” ' _ = 703.8°R l¡ = 703.8 - 460 l; = 243.8“F final Section l dischaige temperature. Section 2 T, = 56$(2.0)3"' T. : = 704.8°R
- 52. Cenrnruivu! Fwnprex inn 133 t; - "O48 ~ 460 t7 = 244.14%? final Section 2 discharge temperature. 'lhe temperature is approximately 20°F below the 26S°F temperature limit, The sections differ by less than PF. This is probably just luck because that good a balance is not really necessary. Also. it should he noted that to maintain simplicity the additional factors were ignored. such as thc l0°F temperature pickup in thc retum stream due to intemal wall heat transfer. Also. nozzle pressure drops for the exit and return were not used. Balance piston leakage »vas not used as it was in Example 5-3 When all the factors ane used. the pressures for each section would undoubtedly need additional adjustmcnt as would the efficiency. Howev- er. tor the actual compression process. the values are quite realistic. and for doing an estimate, this simpler approach may be quite adequate. Step l5. To complete the estimate. calculate the shaft power. using the conversion of 33.000 ft-lb/ min/ hp. Section l w L1.200xll.074 '“ " miooxrws WF ~ 1350.8 hp gas horscpowcr. Section l Section 2 w _ 3.200 x 9.575 V ' 13.000 x .737 WF - l. |79.9 hp gas horscpower. Section 2 C ombinc the two gas horsepower values and add 1% for the mechanh Cal losses. wr 1.350,3 + 1.1799 + 25.3 “g, 1556.0 hp compressor shaft power Fan Laws These relationships were actually developed for pumps instead of co yarcvcr yuscumratin gcom prcssorsthanwre being considered for rcapplication. The equations used to this point are adequate to perform any rerate calculation; however. looking at the fan
- 53. 184 r mnprcWsu/ i . SielrrrtunundSictng' laws may help establish another perspective. The following rclallonshipx are ; t statement of the fan laws'. Q, u.' . sm HpotNz t5 33a VPuNJ (SAM ___, The equations have been expressed as proportionals; however. they can be used by simply "ratioing" an old to a new value. T0 add credibili- ty to fan law adaptation. recall the flow cocfñcient. Equation 5.19. The term Q/ N is used which shows a direct promrtion between volume , and speed N. Equation S. l 2 indicates the head. Hp. to be a function of the tip speed. u¡ squared. The tip speed is. in tum. a direct function of speed making head proportional to speed. Finally. the power, W is a function of head multiplied by flow, from which the dcd mwer. propor- tiunul to the speed cuhed. may be made. curve shape Figure 1-3 presented a general form perfomance curve for each ol' the compressors. The centrífuga! compressor exhibited a relatively flat curve compared to the other machines. Flat is defined as a relativcl low head rise for a volume change. Translat - tively low pressure change for a given volume change. lt is important to understand some of the basics that contribute to the curve shape. Figure 5-24 shows that if the flow is reduced for the radial wheel. a reduction occurs in the vector. Va, but there is no influence on the tangen- rial component of the absolute velocity. Vu¡ ln fact. the ratio of Vdg/ u¡ = l. ln this case, the ideal curve would be llat, something that really does not curve. the Vu vector will increase with a decrease in tlow. This is shown as decrease in the length of the Va vector. raising the work input eoefii- cient and putting a slope into the curve. 'Diem if the 45° vector triangle is examined. thc same thing will happen: Vu; will increase for a decrease in the flow Because the angle B¡ is less, the V_, ¡ faster for 45“ than for 60”. making for a steeper curve. This is consistem with the earlier statement about the higher reaction wheel having a steeper curve. Flow passing through an ímEIIer is constant! ! changing in volume because of the compressible nature of the gas. If an im ller is o mted
- 54. ( 'rntnfugal CFNVVWEXAYIFK Í85 first with a light molecular w-eigvht gas and then a heav! gas. the curve will be si. r with th li h as because e volume mtio is hi her foi' the heavy gas. An examination of Equation 5.12 shows that head for ; i given gcomctry is fixed. within reasonablc limits. Therefore. substituting different molecular weights in the head equation will indicate a higher c w directly proportional to the molecular weight. Since the geometry vai». not modified to match the different volume mtio, the vectors. Vhs. ;irc shorter for the lower outlet volume. As such, the change to the vector "_. ; is not : Ls great and the curve is not as steep. The compressibility of the gas going through the impeller causes some problems. The assumption in the use of the fan law. when speeding up an impeller. is that the inlet volume follows the speed in a propoitional mari- ner. At the same time. the head is increased as a function of the speed squared. Just as the head increases with a given gas. so does the pressure ratio and therefore thc volume ratio. lt wasn't pointed out. but the alert reader may have rioticed that the outlet uiangle, not the inlet triangle. Vias used to discuss the curve shape. The problem is that thc outlet vol- umc is not exactly proportional to the inlet volume. For a l0'-. Y~'c- speed change. the compressor docs not truly respond with a 21% head change. For small speed changes the problem is not serious; however. the biisiu should be remembered if a compressor is being rcratcd. Onc last item should be noted regarding the shape of the curve. As stages are put together. the overall flow range of the combined stages is never larger and. in most cases. is less than the smallest flow range of the individual stages. Because of the compounding effect, as the volume h changed. the combined curve is always steeper. Surge '~ a lef nd a ccntrifu al com rcssor ressure volume curve does not reach zero flow. The minimum flow int is labcled as the surge imu : in is t e owest flow at which stable operation can bc achieved. Attempted operation to the left of that point moves the compres- sor into surge. ln full surge the compressor exhibits an extreme instability: it backflows to a point and then temporarily exhibits forward flow. 'This oscillating flow is accompanied by a large variety of noises. depending on the geometry and nature of the installation. Sometimes it is a deep low frequency booming sound and for other machines it is a squeal. 'lhe pitts-

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