348
`
`AERODYNAMIC DESIGN OF AXIAL-FLOW COMPRESSORS
`
`seriously affect the performance of all stages in
`the compressor. Therefore, the occurrence of
`abrupt stall in the multistage compressor can
`logically be taken as the lower limit of usable
`range at that speed. As pointed out in chapter
`X I , discontinuities in overall performance of
`the compressor may result in compressor surge;
`and, thus, the complete-compressor-stall l i t
`may also be considered to be the surge limit of
`the compressor. As noted in figure 264, this
`limit does not exhibit the customary dip or kink
`at intermediate speeds. If surge were assumed
`to occur at the maximum-pressure-ratio points
`as in reference 248, the general trends would be
`unchanged.
`
`F
`
`.8
`
`c
`C W
`g .6
`+ c
`W 0
`.4
`-
`3
`0
`I
`.2
`
`1.0
`
`Specific weight flow
`33.68/
`
`2 3.4/
`
`Stall
`%’/A Progressive
`\\\Y
`Abrupt
`
`l 0 . d
`
`Flow coefficient
`RQURE 263.-Assumed performance characteristics for
`negative values of pressure coefficient for all stages.
`
`Specific weight flow
`FIGWBE 264.-Computed over-all performance for case 1.
`
`(a) Speed, 100 percent of reference.
`(b) Speed, 80 percent of reference.
`(c) Speed, 50 percent of reference.
`variation of flow coefficient for
`F’IGIJBE 265.-Stagewke
`case I.
`
`UTC-2019.366
`
`

`

`COMPRESSOR OPERATION WITH ONE OR MORE BLADE ROWS STALLED
`
`349
`
`Variation of stage flow coefficients.-In order to
`illustrate the stages that are stalled at various
`inlet flows and speeds, the stage flow coefficient is
`plotted against stage number (fig. 265) for several
`values of inlet flow at speeds of 100, 80, and 50
`percent of
`the reference value. The h e a d y
`shaded area on these plots represents the range of
`progressive stall, and the lightly shaded area
`represents the range of abrupt stall with the
`associated discontinuity of stage pressure coeffi-
`cient (fig. 262).
`At 100 percent of reference speed (fig. 265(a)),
`flow-coefficient variations are shown for the
`reference-point specific flow of 33.5, the approxi-
`mate exit-vane choke flow of 33.68, and the com-
`plete-compressor-stall flow of 33.06. The varia-
`tion of flow coefficient in the front stages is small,
`and thus the specific-weight-flow range at this
`speed is also small. The maximum change in
`flow coefficient occurs in the last stage, and com-
`plete compressor stall results from abrupt stall of
`this stage.
`As the speed is reduced to 80 percent of the
`reference value, the flow coefficients decrease for
`the entrance stage and increase for the exit stage,
`as shown in figure 2651b). At this speed, the
`fist stage operates in the progressive-stall range
`even at the maximum specific weight flow of
`23.40. Complete compressor stall results from
`stall of the ninth stage at a specific weight flow
`of 17.16. It should also be noted that the number
`of stages operating in the progressive-stall range
`increases from one to eight as the flow is decreased
`from the exit-vane choke value of 23.40 to the
`complete-compressor-stall value of 17.16.
`As the speed is further decreased to 50 percent
`the reference value (Sg. 265(c)), the front
`of
`stages move deeper into stall and the rear stages
`closer to choking flow. Complete compressor stall
`results from occurrence of abrupt stall in the fifth
`stage. From five to seven stages operate in the
`progressive-stall range at all flows.
`A comparison of figures 265 (a), (b), and (c)
`shows that at high speeds complete compressor
`stall results from abrupt stall of the rear stages;
`and, as speed is reduced, earlier stages in the
`compressor instigate complete compressor stall.
`As shown by the variation of stage flow co&cient
`and by the assumed abrupt-stall limits (Sg. 265),
`complete compressor stall will only be instigated
`by stages 5,9, m d 12 for this example.
`
`In order to define more clearly the relation of
`stage stall to compressor speed and flow, the
`individual stage stall limits are cross-plotted on the
`in figure 266. This
`computed performance
`figure shows that pro
`e stall exists in from
`one to eight stages €or all speeds below 80 percent
`of the reference value and for the low-flow portion
`of the flow range at speeds of 85 and 90 percent.
`It should be noted that, near the complete-
`compressor-stall point at 90-percent speed (fig.
`266), nearly all the stages stall at approximately
`In fact,
`the same value of specific weight flow.
`stages 2 to 5 stall at a slightly higher value of
`inlet flow than stage 1. As pointed out in chapter
`XI, rotating stall is a prevalent source of com-
`pressor blade vibration. Therefore, this range of
`operation where progressive stall exists is ex-
`tremely important with respect to engine re-
`liability.
`In general, the computed progressive-stall limits
`this hypothetical compressor (fig. 266) are
`of
`verified by experimental studies of rotating stall
`in multistage compressors. The speeds at which
`this type stall are encountered are somewhat
`
`Specific weight flow
`FIGURE 266.-Relation of stage stall and over-all
`compressor performance for case I.
`
`UTC-2019.367
`
`

`

`350
`AERODYNAMIC DESIGN OF AXIAL-FLOW COMPRESSORS
`higher than discussed in chapter XI. The speed
`at which inlet-stage s t d l first occurs, however,
`would be a function of stage characteristics as well
`as design-point matching. For this example,
`all stages were assumed to have identical
`teristics up to the stall point and were matched at
`a constant value of flow coefEcient of 0.69. Mach
`number effects, which were ignored in this analysis,
`may also vary the speed at whieh inlet-stage stall
`is first encountered. A.s can be seen from the
`stage curves of *e
`261, a reduction in rotational
`speed, which corresponds to a reduction in stage-
`inlet Mach number, results in an increase in the
`maximum obtainable flow coefficient of
`the exit
`stage of a multistage compressor. Correspond-
`ingly, a decrease in inlet Mach number of the
`first stage would tend to decrease the flow co-
`efficient at which stall of this stage is encountered.
`Both of these effects would tend to decrease the
`speed at which first-stage stall is encountered in
`the multistage compressor but would not alter
`the trends indicated by the computed compressor
`performance.
`The lines of abrupt stall (Sg. 266) show that,
`for speeds up to 70 percent of the reference value,
`complete compressor stall results from abrupt
`stall of the fifth stage; for speeds of 75 to 90
`percent, from abrupt stall of the ninth stage;
`and for speeds of 95 percent and higher, from
`abrupt stall of the twelfth stage. The resulting
`complete-compressor-stall limit, however, is free
`the normal dip or kink that is frequently
`of
`encountered in high-pressure-ratio multistage com-
`pressors.
`
`The stage characteristics used for stages 1 to 4
`of case I1 are given in figure 267. These stage
`performance characteristics were obtained by
`arbitrarily modifying the pressure-coefficient char-
`acteristics used in case I and computing the modi-
`fied efficiency curves assuming no change in the
`actual work input from that of case I. A small
`discontinuity in the performance of stage 1 was
`assumed as shown in figure 267(a). The un-
`stalling hysteresis effect is also indicated in this
`figure. Stall recovery was assumed to occur
`at a flow coefficient of 0.60, whereas stall origi-
`nally occurred at a flow coefficient of 0.565. To
`evaluate interaction effects, stages 1 to 4 were
`assumed to operate on the lower or stalled por-
`tions of
`their performance curves (fig. 267)
`whenever any of these stages encountered stall.
`The stage performance characteristics for stages
`5 to 12 were identical to those of case I (figs.
`262 (b) and (c)).
`Performance with front stages unstalled.-The
`calculated performance map for case I1 for the
`condition of no stall in the front stages is presented
`in figure 268(a). This performance map is identi-
`cal to the high-speed part of the map for case
`I (figs. 264 and 266) except for the complete-
`compressor-stall limit at speeds below 95 percent
`of the reference value. In case I1 the stall of
`one of the front stages leads to a discontinuity
`of over-all performance because of the assumed
`interaction effects. Thus, an envelope of
`the
`progressive-stall limits for case I (fig. 266) repre-
`sents the complete-compressor-stall limit for case
`I1 for speeds from 80 to approximately 95 percent
`of reference speed. No operation with the front
`stage unstalled is obtainable below 80-percent
`speed.
`Performance with first stage stalled.-The
`computed performance for case I1 for the condition
`of stall in the first stage and interactions in
`stages 2 to 4 is shown in figure 268(b) for speeds
`of 50 to 95 percent of the reference speed. The
`upper limit of flow for speeds of 85, 90, and 95
`percent of the reference value was determined
`by the u n s t a l l i flow coefficient for the first
`stage. At 95-percent speed, the front-stage un-
`stalling limit intersects the ninth-stage stall-
`limit line (fig. 26803)). Therefore, this was the
`maximum speed for which calculations of per-
`formance with the front stage stalled were made.
`Complete compressor stall at speeds of 50 to 70
`
`CASE II
`Case I1 was computed to evaluate the effects
`of small discontinuities resulting from interaction
`effects in the first few stages of a multistage
`compressor, and also to evaluate the effects of
`unstailing hysteresis of the inlet stage. Inter-
`action effects were aasumed to exist in the first
`four stages. The detailed flow studies of the 10-
`stage research compressor discussed in chapter
`XI reveal that flow fluctuations of
`rotating
`stall increased through the first four stages and
`then decreased through the remaining stages.
`Therefore, the assumption of interaction effects
`in four stages appeared reasonable. The magni-
`tude of the decrease in performance was arbi-
`trarily chosen.
`
`UTC-2019.368
`
`

`

`COMPRESSOR OPERATION WITH ONE OR MORE BLADE ROWS STALLED
`
`351
`
`percent results from discontinuities due to the
`occurrence of abrupt stall of
`the fifth stage;
`and at speeds of 75 to 95 percent, from abrupt
`stall of the ninth stage.
`The efficiencies for case I1 at intermediate
`speeds are somewhat lower than for case I.
`This decrease in efficiency is a direct result of the
`decrease in pressure coefficient assumed for stages
`1 to 4 for the condition of progressive stall and
`stage interaction effects in these stages.
`complete
`Complete performance map.-The
`performance map for case I1 is obtained by super-
`imposing the performance maps for operation
`with the inlet stage unstalled and the pedormance
`
`map for operation with the inlet stage stalled
`and interactions in stages 2 to 4 (figs. 268 (a) and
`(b)). The resulting performance in terms of
`pressure ratio against specific weight flow is given
`in figure 268(c) for a range of speeds from 50
`the reference value. For a
`to 110 percent of
`range of speeds from 80 to 95 percent of the refer-
`ence value, operation with both the inlet stage
`stalled and the inlet stage unstalled is possible.
`Thus, in this intermediate-speed range, the ex-
`istence of double performance curves and two
`complete-compressor-stall or surge points at a
`given speed is indicated. The double curves
`of this analysis were obtained as a result of a
`
`UTC-2019.369
`
`

`

`352
`352
`
`AERODYNAMIC DESIGN OF AXW-FLOW COMPRESSORS
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`(a) Front stage unstalled.
`(c) Composite performance (superimposition of
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`figs. 268(a) and (_b)).
`stage on exit-vane choke line.
`
`FIGURE 268.--Computed over-all performance for case II.
`
`UTC-2019.370
`
`UTC-2019.370
`
`

`

`COMPRESSOR OPERATION ’WITH ONE OR MORE BLADE ROWS STALLED
`
`353
`
`small discontinuity in the performance char-
`acteristics of the first stage and interactions in
`stages 2 to 4. These results are verified by the
`multiple performance curves obtained in the
`experimental investigations reported in refer-
`ences 292 and 293.
`It should be noted that, for the computations of
`case 11, a small discontinuity in the pressure-
`coefficient curve of stage 1 was assumed. Similar
`results would be obtained, however, if the per-
`formance of stage 1 were assumed to be continuous,
`provided discontinuities of stage performance as
`a result of interaction were assumed for any of
`the following stages.
`Transition from stalled to unstalled operation of
`inlet stage.-Reference
`293 indicates multiple
`values of surge-point performance for inter-
`mediate-speed operation. In these tests,
`the
`particular surge point obtained depended upon
`the schedule of speed and flow that preceded the
`occurrence of surge. The double-valued curves
`of figure 268(c) and the dependence of com-
`pressor performance on the manner in which a
`particular operating point is approached indicate
`the necessity of studying the transition from
`compressor operation with the inlet stage stalled
`to operation with the inlet stage unstalled.
`The usual operating schedule in compressor-
`component testing is to start at maximum or
`choke flow for a given speed and increase the
`throttling
`in successive steps until surge is
`obtained. Since cornpressor operation at maxi-
`mum flow at low and intermediate speeds is
`normally set by the choke of
`the exit vanes,
`transition from stalled to unstalled operation of
`the inlet stage can be considered to occur along
`the exit-vane choke limit of figure 268 (c). Thus,
`as the compressor speed is increased, the choking
`limit of the exit vanes will prevent unstalling of
`the inlet stages for this case until a speed of 85
`percent of the reference value is attained. Un-
`stalling of the inlet stage and alleviation of the
`resulting interaction effects will result in a
`transient change of operation from the exit-vane
`choke point on the dashed speed curve to the
`exit-vane choke point on the solid speed curve.
`For this example, the specific weight flow in-
`creases from 26 to 26.3 and the pressure ratio
`from 4.23 to 4.30. The efficiency is not changed
`appreciably. For the purposes of this chapter,
`the transient conditions following unsta,lling of
`
`691-564 0-65-24
`
`ered, and the com-
`to change discon-
`
`the inlet stage are
`pressor operation
`tinuously from th
`for inlet stage
`The type of over-all p
`from the normal
`techniques described is given in figure 268 (d).
`For speeds up to 85 percent of the reference value,
`the compressor would operate with the front
`stage stalled; and for speeds above 85 percent,
`with the front stage unstalled. Therefore, both
`branches of the performance curve are given at this
`crossover speed of 85 percent of the reference value.
`Complete-compressor-stall
`limit.-The
`com-
`plete-compressor-stall limit will follow the dis-
`continuity points of the dashed speed curves up
`to the crossover speed and the discontinuity point
`on the solid curves above this speed. Thus,
`a stall-limit line faired through these points
`exhibits the dip common to most high-pressure-
`ratio axial-flow compressors. As indicated by
`this analysis of m e 11, however, two discrete
`stall-limit lines exist, the low-speed stall limit
`representing the mode of operation with the front
`stages stalled and the high-speed stall limit
`representing the mode of operation with no stages
`stalled. Since these two stall-limit lines may
`overlap in the intermediate-speed range where
`multiple performance characteristics may exist,
`a continuous stall-limit line should not be faired
`through the stall points for the complete range of
`speeds. In presentation of experimental data,
`however, the compressor stall or surge line is
`faired through a finite number of points and is
`generally considered a continuous function of
`flow, pressure ratio, and speed.
`The analysis of case I1 shows that the dip in
`the compressor stall or surge limit that is experi-
`mentally found to exist for intermediate-speed
`operation of high-pressure-ratio multistage com-
`pressors can be simulated by assuming a small
`discontinuity in the performance characteristics
`of the inlet stage and interaction effects in stages
`2 to 4. Similar results would be obtained from
`any combination of discontinuous performance
`characteristics of the inlet stages. For example,
`the performance characteristics of the first stage
`of the 16-stage compressor reported in reference
`253 were continuous, but discontinuities did exist
`in the characteristics of a few stages after the first.
`It should al&o be noted that relatively continuous
`
`*
`
`UTC-2019.371
`
`

`

`354
`
`AERODYNAMIC DESIGN OF Axw;-FLOW COMPRESSORS
`
`stage characteristics will result in a fairly smooth
`surge or stall-limit line, as indicated in reference
`257.
`The transition from the complete-compressor-
`stall limit for operation with the inlet stage stalled
`to that for operation with the inlet unstalled de-
`pends on the manner in which this limit is ap-
`proached. If the compressor-discharge throttling
`is sufficient to cause the compressor to operate
`appreciably above the exit-vane choke limit as
`speed is increased, unstalling of the front stage
`may not be achieved until a speed appreciably
`greater than 85 percent of the reference value is
`attained. In the range of speeds from 85 to 95
`percent of
`the reference value, the complete-
`compressor-stall limit may follow that of figure
`268(b). But, if the speed is first increased above
`the value for unstalling of the inlet stage and then
`reduced, complete compressor stall may occur on
`the limit of Sgure 268(a) for speeds of 80 to some
`what over 90 percent of
`the reference value.
`Thus, for case 11, double-valued compressor stall
`points at a given speed may be obtained for the
`range of speeds from 80 to 95 percent of reference
`speed, as indicated in figure 268(c). As previously
`discussed, this phenomenon has been observed in
`experimental studies of multistage axial-flow-
`compressor performance. For cases where un-
`stalling of groups of stages or alleviation of inter-
`action effects occurs stepwise, even more than
`two compressor performance characteristic curves
`may be obtained at a given value of speed.
`For maximum engine acceleration, the compres-
`sor operating line in an engine will be very close
`to the surge or stall limit at low and intermediate
`speeds. Thus, the intermediate-speed complete-
`compressor-stall limit obtained by normal com-
`pressor rating techniques may not be representa-
`the complete-compressor-stall or surge
`tive of
`limit obtained during engine acceleration. There-
`fore, when multiple operating curves exist at any
`compressor speed, performance evaluations must
`include all possible operating conditions. This
`may be done by approaching a given operating
`point by varying compressor speed at each of
`several fixed system throttle settings, as well as
`by variation of throttle settings at a fixed speed.
`Speed changes must include both increases and
`decreases in rotational speed. An operating tech-
`nique such as this will give performance maps of
`the type shown in @e
`268(c) for those cases
`
`where multiple performance curves exist for a
`given compressor rotational speed. The data of
`reference 293 indicate six separate performance
`curves at approximately 75 percent of design
`speed. For this compressor, the performance
`characteristic that exhibited no stall in the inlet
`stages was easily duplicated. Points on the
`performance characteristics for the condition of
`stall in the inlet stages were in general duplicable,
`but minor variations in the method of approach
`to this particular speed would result in operation
`on difFerent curves of the separate performance
`characteristics for the condition of stall in the inlet
`stages. Thus, estimation of the cornpressor per-
`formance in the actual engine based on compressor-
`component tests may be difficult for this inter-
`mediate-speed range. During component testing
`of compressors, however, it is desirable to evaluate
`all possible performance characteristics in this
`intermediate-speed range where multiple charac-
`teristics may exist.
`Effect of unstalling hysteresis.-For case I1 a
`hysteresis effect was assumed in the unstalling
`characteristic of the inlet stage. This had no
`effect on the general trend of complete-compressor-
`stall characteristics, except with respect to the
`speed at which transition from stalled to unstalled
`operation of the inlet stage was achieved. For no
`hysteresis effect, unstalling of the inlet stage along
`the exit-vane choke line (fig. 208(b)) would be
`achieved at 81.5 percent of reference speed rather
`than at 85 percent as for the case with hysteresis.
`Possible discontinuities in the complete-compres-
`sor-stall limit and the potential of double-valued
`points between speeds of 80 to 93 percent can be
`seen from figure 268(c).
`Part-speed efficiency.-At 85-percent speed,
`the transition speed, the maximum computed
`efsciency for operation with no stage stalled was
`0.86; whereas the maximum efsciency was 0.84
`at this speed for the condition of inlet stage stalled
`and interactions in &ages 2 to 4. This small
`difference in computed efEciency simply reflects
`the small changes in stage performance that were
`assumed to result from inletstage stall and the
`attendant interactions (fig. 267). Thus, no con-
`clusive results can be obtained from these com-
`Interaction effects or sharp
`puted efsciencies.
`decreases in stage efficiency as a result of stage
`stall will, however, afFect compressor efficiency
`adversely.
`
`UTC-2019.372
`
`

`

`COMPRESSOR OPERATION 'WITH ONE OR MORE B U b E ROWS BTAIILED
`
`355
`The performance of this case for the condition
`of unstalled operation of
`
`CASE III
`In order to evaluate more serious in
`effects, calculations were made for case
`assumed the same conditions in st
`as for case I1 and, in addition, ass
`action effects in stages 5 to 8.
`performance curves for these mid
`given in figure 269. As
`pressure-coefficient curve
`arbitrarily modified and the efficiency curve was
`computed from the pressure coefficient by assum-
`ing no change in total work input for the stage.
`The magnitude of discontinuity of pressure co-
`efficient is representative of that for an abrupt
`type of stage stall. When progressive stall
`existed in stage 1, stages 5 to 8 were assumed to
`operate on the dashed curves of figure 269. The
`performance of stagm 9 to 12 was identical to
`that for case I.
`
`-
`.- .-
`
`c
`C
`al
`V
`.I-
`al
`0 V
`?!
`3
`u) u) h"
`
`Flow coefficient
`FIGURE 269.-humed
`performance characteristics for
`stages 5 to 8 for case 111.
`
`percent of the reference value indicate the necm-
`sity of varying the mode of testing in component
`rating so that all possible
`ressor operating
`conditions can be evaluated.
`Transition from stalled to unstalled operation of
`inlet stage.-For case 111, if compressor speed is
`increased along the exit-vane choke limit, inlet-
`stage unstalling will be effected at 94 percent of
`the reference speed. At this speed the transient
`change in computed pressure ratio would be from
`4.85 to 5.2, the change in specific weight flow
`would be from 28.3 to 30.9, and the change in
`efficiency from 0.71 to 0.81. Thus, for large inter-
`action effects, unstalling of the inlet stage is oc-
`companied by relatively large increases in weight
`flow, pressure ratio, and efficiency. The transi-
`tion speed of 94 percent is shown in figure 270(b)
`for both the condition of stall in the inlet stage
`and interactions in stages 2 to 8 and the condition
`of no stall in the inlet stage and no interactions.
`If interaction effects of the magnitude assumed for
`this case do exist and the compressor operating
`characteristic follows a throttling line Close to the
`complete-compressor-stall limit, unstalling of the
`inlet stage may not be achieved even at design
`speed. By increasing the speed to a value above
`that for unstalliag of the inlet stage and then
`decreasing the speed, stall-free operation might be
`obtained down to 80 paroent of the
`at low values of pressure ratio.
`. Complete-compressor-stall limit.-For
`the high-
`speed portion of the compressor map where no
`stages are stalled (fig. 268(a)), at speeds above 95
`percent of the reference value, complete compres-
`sor stall results from abrupt stall of the twelfth
`80 to approximat
`stage; and at'speeds
`e s l t o 4 a n d t h e
`s. For the operating condi-
`tions where stall in the inlet stage and interactions
`in stages 2 to 8 exist (&. 270(a)), complete com-
`pressor stall for s p e e d s p to 95 per&&
`of the
`
`UTC-2019.373
`
`

`

`AERODYNAMIC DESIGN OF AXIAL-FLOW COMPRESSORS
`
`356
`reference value results from abrupt stall of the
`ninth stage, and for higher speeds, from abrupt
`stall of the twelfth stage.
`The complete-compressor-stall-limit line indica-
`Ced for case I11 for the norm,al component rating
`technique can be obtained from figure 270(b).
`This stall-limit line would follow the complete-
`compressor-stall-limit points for the dashed
`curves (fig. 270(a)) up to 94 percent of reference
`speed. In this speed range the compressor would
`operate with the first stage stalled and interactions
`in stages 2 to 8. For speeds above 94 percent,
`the stall-limit line .Will follow the complete-com-
`pressor-stall-limit points for the solid speed curves,
`which represent a condition of stall-free operation
`for all stages.
`Effect of unstalling hysteresis.-If
`the hysteresis
`effect on unstalling of the inlet stage were ne-
`glected, the first stage in this case would become
`unstalled at 91.5 percent of reference speed for
`operation along the exit-vane choke limit. The
`general trend of performance and complete-
`compressor-stall limit would, however, be un-
`changed. The effect of
`inlet-stage unstalling
`hysteresis is to increase the speed at which the
`It
`
`stall in the inlet
`indicate a reductio
`percent compared w1
`
`some multistage axial-flow compressors may
`result from severe interaction effects.
`Multiple-valued performance characteristics.-
`Both cases I1 and I11 indicate the potential of two
`separate curves in this general speed range.
`If at any given value of speed the potential of
`different degrees of deterioration of stage per-
`formance due to interactions is considered, then
`more than two performance curves may be
`obtained. For example, if the characteristics for
`85-percent speed are considered for cases I to 111,
`the performance characteristics shown in figure 271
`are obtained. Curve I represents a condition of
`unstalled operation for all stages; curve IT, a
`condition of stall in the inlet stages and inter-
`
`stall limit
`Exit-vane choke limit
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`Specific weight flow
`(a) Front stage stalled and interactions in
`(b) Composite performance (superimposition of
`stages 2 to 8.
`figs. 268(a) and 270(a)).
`FIQWBE 270.-Computed over-all performance for caSe 111.
`
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`

`COMPRESSOR OPERATION WIT€€ ONE OR MORE BLADE ROWS STALLED
`
`357
`
`the compressor stages for some speed lower than
`the design value, as suggested in reference 248.
`In addition to 'improving part-speed performance,
`such compromises in
`matching may reduce
`the speed at which
`ive stall is encountered
`and thus decrease t
`tial of blade vibrations
`stall. To evaluate these
`excited by rot
`potentials, case
`as computed. In this case,
`the reference-point flow coefficients of the stages
`were varied as shown in table VIII (b) from a value
`of 0.760 in the inlet stage to a value of 0.630 in
`the twelfth stage. The principal purpose of this
`study was to investigate variations of stage
`operation with speed. Therefore, no interactions
`were considered. The stage characteristics used
`for the individual stages were identical to those
`for case I (fig. 262).
`com-
`Computed over-all performance.-The
`puted over-all performance map for case IV is
`given in figure 272(a) as a plot of over-all total-
`pressure ratio against specific weight flow. For
`this case as for case I, complete compressor stall
`was assumed to occur when abrupt stage stall was
`encountered in any stage. Complete compressor
`stall for case IV results from abrupt stall of the
`fifth stage for speeds of 50, 60, and 70 percent of
`the reference value, from abrupt stall of the ninth
`stage for speeds of 80 and 90 percent, and from
`abrupt stall of the twelfth stage for 100 and 110
`percent. These results are similar to those for
`case I.
`The peak efficiencies calculated for case IV
`varied from approximately 0.74 at 50 percent of
`reference speed to a maximum of 0.87 at 90-percent
`speed, and decreased to 0.85 at the reference speed.
`Stage progressive-stall limits.--In order
`to
`determine the speed at which various stages
`reach the flow coefficient for progressive stall
`(0.565), the progressive-stall limits for stages 1 to 8
`are cross-plotted on the computed performance
`map in figure 272(b). This figure shows that the
`first stage is stalled over almost the entire flow
`range at 70 percent of reference speed, and over
`only the low-flow portion of the compressor flow
`range at 80-percent speed. The first-stage stall
`limit intersects the complete-compressor-stall limit
`at approximately 85 percent of reference speed.
`Consideration of the stall limits of stages 2 to 7
`indicates that at 90-percent speed stage 7 is the
`first stage to encounter progressive stall.
`In the
`Fange of approximately 70- to 85-percent speed,
`
`Specific weight flow
`FIGURE 27l.-Comparison
`of computed performance at
`85-percent speed for cases I to 111.
`actions in stages 2 to 4 as obtained for case 11;
`and curve 111, a condition of stall in the inlet
`stages and interactions in stages 2 to 8 as obtained
`for case 111. Such variations in performance
`may be a result of changes in the number of stages
`that exhibit this deterioration of performance or
`changes in the magnitude of
`the performance
`deterioration of each stage that is affected.
`Variations of stall interaction effects, therefore,
`will result in a multiplicity of over-all performance
`characteristics at a given speed; and the com-
`pressor flow, pressure ratio, and efficiency will
`increase with decreasing severity of stall and
`interaction effects. The particular performance
`obtained will depend on the previous history of
`speed and flow as well as the hysteresis effect
`accompanying changes of stall pattern in any
`given compressor. Needless to say, flow dis-
`tortions at the compressor inlet can aggravate
`these adverse effects.
`
`CASE IV
`Since part-speed performance problems of high-
`pressure-ratio axial-flow compressors can be attrib-
`uted to stalling of the inlet stages as a result of
`flow limitations of the rear stages, some improve-
`ment in part-speed performance may be expected
`by matching the front stages near their choking
`value of flow coefficient and the rear stages near
`their stalling value of flow coefficient. This stage-
`matching compromise is equivalent to matching
`
`UTC-2019.375
`
`

`

`358
`358
`
`AERODYNAMIC DESIGN OF AXIAL-FLOW COMPRESSORS
`AERODYNAMIC DESIGN OF AXIAL-FLOW COMPRESSORS
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`UTC-2019.376
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`UTC-2019.376
`
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`

`

`COMPRESSOR OPERATION WITH ONE OR MORE BLADE ROWS STALLED
`
`359
`
`several of the front stages approac