analysis of screw compressor performance based on indicator diagr

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Purdue University

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International Compressor Engineering Conference School of Mechanical Engineering

1992

Analysis of Screw Compressor Performance Basedon Indicator Diagrams

K . MiyoshiKobe Steel Ltd.; Japan

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Miyoshi, K., "Analysis of Screw Compressor Performance Based on Indicator Diagrams" (1992). International Compressor EngineeringConference. Paper 815.hp://docs.lib.purdue.edu/icec/815
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A ~ A L Y S J S Of SCREW COUPRESSOR P E R P O R ~ A \ C E BASED ON I ~ D l C A T O R D I A G R A ~ S Kirotada MiroshiSenior Researcher. Del'elopmenl Center,Kobe Steel Ltd.Kobe, Japan

-\BSTH\CTBr means of a small pressure seusor built Into the tooth root on !hedisch.nge side of the female rotor. the pressure change in the groove can bemeasured from the midpoint of the suetion slrohe to the complc t ion of thedischarge. Indicator diagrams 11crc cotlccted fo r a single stage c \C IC and theind1cated horsepoiiCr 11as calculated. In this manner.11e could dete rmine the gascompression conditions inside the and thus the data could be analqed forfurthering the studies on high-efficienc' profiles.I. In troduct ion.

Scre11 compressor performance has in the past been e\perimentalII sough t fromoperating data by rar1ing the rotation specn and pressure ratio to m atch eachrotor outer diameter and built-in ratio. l iu lle \c r . il> it 11as tmpo>s1ble to grasp the pressure rise phenomenon inside the rotor groorc. lh1s method 11as notuseful in stud1ing looth Profile or imprurements in the discharge and suctionport's. . \s fur changing th e rotor tooth Profile . the high PriCe of the cutterblade for processing the rotor profile and the neccssar1 jigs has to date been anImPediment to rea liz ing t r ia l product ion and te s t runs in order to makeperfo rmance compar isons .The author has been successful in grasping the lo ss of gas due lo leakagebet11een rotor groo1es and the e\cessilc compression phenomenon at the dischargePort b1 computing pressure changes inside the rotor groore during compressoropera! ion. The following is a report 011 the resulls of m1 >tud1.\omenclature( \ :D:k:L:

L th:LPI :I : ll:I I i:

\lo :mh:mac:P:ps:

Pd:R:T:t : I :

I o:I i :

l) ad : Tl I:1r i:() :

Constant 1o!ume specific heat. J (kg K)Rotor diameter . mmSpecific hea t ratioCompression 11orh. IITheoret leal adiabatic compression power. WIndicated po1er. "Rotor length. mmGas weight. kgGroo1e gas leak-in weight. hgGroo\"c gas lenkout 11eight. kgTheoretical suction gas we igh t flow rate. hg 1 s- \c tua l suction gas 11eighl f!o11 rate. kg /s\tale rotor rotation. rpmGas pressure. PaSuet ion gas pressure. l'a Discharge gas pressure. PaGas constant. J, Ikg KlGas temperature. KTime. sec.Gas ,-aJume. m'Theoretical strohe 10lume. m'Built-in 1o!ume ratioAdiabalic cfficiencrlulumctric e f f i c i e n ~ 'Built-in pressure ratio."\":Male rotor rotation angle. dcg.

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2. Theoretical Calculation of Performanc.eIn order to analyze screw compressor performance, changes in the seal area

and o lum c o f the rotor groove space were com puted for eer1 rotation angle ofthe male rotor. based on uhich increases in gas pressure and temperaturefol\ouing the rotor rotation are ~ i m u l a t c d in order to c o n ~ l r u c t un indicatordiagram '' ' - 121 Fig. I shows rotor groa1e conditions during compression.

Groove IT ,P

l"ig. 1 Cross-sect ion of sere" com pressor

Ps

ror the com pulat. ion. the fo \lo11illg suppositions were used.( 1 I Changes in gas condition o r 1olume in the groo1e arc stable:121 Gas pas;ing through the sea l area and discharge port is considered adiabaticchange;(3) Gas cooling effect b1 rotor or casing is not consider ed:( . j) Gas relocitl due to rotor rot at ion is not cons idered. The change in gas 11eight

in G roare l can be e\presed b!:cl \1, = ~ \ 1 , d :--1, -d \I d--dl___ = dT-

The cnerg)d 1. = d ~ ci( ' d t

- ~ \1,d \1 n- d-T ..

eq u a lian is:h C I T , - cl_}!_,_ li C1 T ,d t

'1 C d T - C1 T dM+:> I ef t - d - t -The com pression 11ork is:

From the equation of status:__c_!_p_p dV -y-

I ll

12!

131

111

151

Br com puti ng equati ons I l l to (5), changes in pressure and temperature insidethe groove can be simulated.

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3. \le t hod of col Iee l ing indicator diagrams\s lhc screw compressor is so slTuclurcd that the groo1e volume is reduced aslhe male and female rotors are engaged . gas is compressed to"ards lhe dischargeside. Therefore if a small piezoelectric pressure sensor is built into the bott om of lhe discharge side female root. changes in pressure Inside th e gruo1e from themidpoint of suet ion stroke to the cumplct ion of suetion. and from the start ofcompress ion to the complcl ion of discharge. can be measured.Table I the main rotor specifications and Fig . 2 is a oflhc measurement of Indicator Pressure.,\s can be seen in the figure . lhc cord of the compact pressure sensor passesth rough !he throuRh hole al the center of the rotor and is connected to the slipring b ra Te[lon coupling. Signals sent to the signal analyzer. mounted outside. l ia rhc ; l ip ring. The rolar1side flange of the slip ring has a notch1n "hich a displacement gauge is e\lernalI) mounted in order to determine theroror suction angle/position.

Table I \la in specificatrons of rotorCombination o f lobes number

Rotor diameterHoto r lengthlrap !male rotor)Burtt-in 1o lume ratio

FFT

IIa1cfemale mmmmdeg

Computer

16Ioo. 0Iu. 0300. 0? "- J

Fig . 2 Pressure sensor mountin g diagram The signal anal1zer Picks up lhe displacement gauge rotation signal and thePressure sensor signal al the same time: the sampling speed and the pressurerange are changed orer to match changes in the pressure ratio and rotation speed during the lest so that highlr precise data can be obtained.For this test. measurements "ere made at the conditions of: rotor outerdiamercr'IOO. built-in volume ralioo\'12.5, gas=R-22.Fig. 3 s h o ~ s the data so gathered correlated with the male rotor rotationangle f) on lhc abscissa and the change in pressure ratio P/P s on the ordinate.In this figure, lhe peak l'a lue appearing al the pitch of j.fQ' is the signalper rotation of the female rotor. The 0 rotation angle is the poin t at "hichcompression s ta r ts , and a sudden pressure drop is seen at the point at ~ h i c h discharge ends in lhe vicinity of 390 , .

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Pd 1.19MPo Ps O.SOMPo Ts 3C6

N 2700rpm

"'........ 4 PIPsa..

Suction End Discharge End0 o ~ ~ ~ l 8 ~ 0 ~ - 3 ~ 6 0 ~ . _ - 0 ~ ~ ~ 1 ~ 8 0 ~ ~ 3 6 ~ 0 ~ ~ 5 4 ' 0 e deg

P1g. 3 Pressure change and rotor rotation angle

Indicator d iag ram and compressor efficicncThe sere\\ compressor's built-in 1o!umc ratio Vi is qcsigned to be 2.5 . flenceit is so structured that the discharge port is opened hen the stroke volume d ropsto about "0'.. ilie a reciprocal compressor. the screw compressor has nod1scharge 1al1e o r suction ralre. and so the suct1on port can be made larger tomatch suction stroke, and the pressure of the suction port can be used assuetIon pressure.The pressure inside the rotor groo1e continues rising; but. at the start o f discharge. the f low area o f gas at the tim e o f port opening becomes extremely sma II.fig. l is a comparison of the actual and simulated indicator d i a ~ r a m s at

male rotor rotation speeds of 3550 rpm and 2100 rpm. In Fig .J, line a brepresents suction stroke, line b-e is compressi-on stroke. line c-d is dischargestroke. and line bc' -d' represents result o f computation. In that figure. thearea within the line a bc da is the actual indicated horsepower Lpv; if thetheoretical adiabatic compression po11er at theoretical suction gas weight flow rate mth is Lth , th e I 'O lum e tric efficienc1 T/ 1 can be e'presscd bl' :161

The adiabatic cfficicncr nad is:I) ad= l,_!__h_ / n1-L PI 171

Br comparing the results of equation IGI and (7) 11 ith bcd and b-c'-d ' in the P-V cune. thai part 11hcre h o r s e p o ~ e r loss is generated can be round, mak ingit possible to determine which points to im prorc in rotor profile and port shapein rei ation to perfo rm ance .Br comparing the theoretleal indicator d iagram 11i th th e m e a ~ u r e d diagram in Fig . -1, i t can be seen that the gas pressure is high shortly aft

er compress io .n starts . but it drops short!\ befo re discharge. This is thought to be due to thefact that the seal betw een lh e rotors at the suction side suffers less gas leakage due to the presence of the o i 1 film. but on the discharge side the oi I film isbroken by \he high differential pressure, resulting in greater gas leakage.

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4

"'2a..

'.eii0"'.. 4'..

2

00

1.94MPa Ps QSOMPa Ts 4CN 3550rpm

Calculated ,- ~ M e a s u r e d N 2700rpm

_E_PsDischarge

20 40 60 80V/Vo% fig. Indicator100

fig. 5 and Fig. oarc indicator diagrams ~ h e n the pressure ratio is 1ar cdh ile suetion pressure Is kept constant. These figures sho" the result o f mak ngthe pressure ratio greater than the design value of 3.11. In addition. suet onpressure Ps 0. 33 \ll'a data ha1c also been gathered in order to studr the effect ata high pressure ratio . From these figures. it can be seen that the pressureduring the compression stage is affected great!) bv the discharge pressure evenif the built-in pressure ratio is kept constant.Therefore. it mar be assumed that the leakage of gas Is great frum the rotorend seal and the t lp seal at the discharge side. On the other hand. as thedischarge port area is proportional to the rotat ion angle at the s ta r t ofdischarge, the pressure inside the gruure dues not chan l!e !1 shortI\ afterthe port is opened cren at a pressure rut io other th an th e design ratio. Thus thepressure ratio can be within a broad range.

"'..'..6

Ps Q50MPaPd/Ps:2.40Ts 4C2.7 3.0X 0

V/Vo %

N 3550rpm3.5 3.9+

Fig . 5 Indicator diag ram s "h en pressure ratio is raried (J)

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I l l a.......a..

Ps Q35MPo Pd/ Ps:3.4[J

Ts. -6C3.8 4.4)( 0

V/Vo %

N 3550rpm5.0 5.4+ 0

Fig . G Indicator diagram s when p ressure ralto is 1uricd (21

5. Indicator diagram during changes in rotation speedFig. 7 shows 1olumctric efficienc) 111 and adiabatic efficicncv 17 ad ~ h e n r o tor r o t at ion speed i s ,. ar i ed 11 hi Ie s uc t i on pressure i s ke p t co ns tan t. The r at i o s

sho11n are based on volumetric cfficienc1 n \ 'O and adiabatic efficienc) TJ ado at arotation speed of 3500 rpm and discharge pressure of l.53 \ll'a.Ps Q50MPa Ts 4CPd 1.19MPa Pd 1.53MPo Pd l94MPa

~ v / ~ v o c::. o o

0"C0t:::""......

~ v o , I]Odo : Pd 1.53MPa AT3550rpm

1.0r-

0 .8

-g 0.6


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In !he figure. the volumetric cffic iencr increases due to the increase of ale rolor ro tarian speed. a l tr ibu tab le to !he fact !hal the increase in olalion speed resulls in the shortening o f gas tim e per groove.Regarding changes in ralio. the greater !he pressure differencee tween the and the sue! io n port. !he greater the 11cig ht of leak gas.he rcf o r e. 1he hi g he r I h c di scharge p r c s su r c, Ihc I ow_e r t he vuIume t r i cfficicnc).Hcgarding adiabalic efficiency, al Pd 1.53 Ml'a. "hich is close to !h e designressure rJlio of 3.0. the difference be111een rolumctric dficiencv and adiabaticfficiency is smaller than for olher discharge pressures. This is due Ia th e facthat under operaling conditions 11hich del iatc from the design pressure ratio, the oss due to c\ccssi1e compression increases inside !he rotor groo1e. which islear from !he indicator diagrams obtained. fig. 8 and Pig. nare indicatoriagrams 11hen rotalion speed is \ 'a ricd 11hile pressure ratio is kepi conslanl.ookin g at these figures. it can be seen thai !he gas pressure from the end ofuction to the s tart of discharge is higher at lo"er rolalion s p e e d ~ and !halhere is much gas leakage from the upstream groo1e.

pi g. 8

"'_......a_

Pd 1.53MPa Ps 0.50MPa Ts 4CN rpm 1800 3550 5400G r - - - ~ - - ~ - - ~ - - - r o - - ~ - - ~ x ~ - - - r ~ o ~ - - ~ - - ~

0 o ~ ~ ~ 2 ~ 0 - - ~ ~ 4 ~ 0 - - ~ ~ 6 ~ 0 ~ ~ ~ 8 0 ~ ~ ~ 1 0 0 . VIVo %

Indicator d iag ram s when rotation speed is 1aricd I JJ

Pd 1.94MPo Ps 0.50MPo Ts 4"CN R .P .M 1800 3550 5400G r - - - T - - - ~ - - - r - - - r - - ~ o - - ~ ~ - x ~ - - ~ - 0 ~ ~ - - ~

0 o ~ ~ ~ 2 0 ~ ~ ~ 4 ~ 0 - - ~ - 6 ~ 0 - - ~ - 8 ~ 0 - - ~ ~ I O O V/Vo %

F i ~ 9 Indicator d iagram s when rotation speed is varied 121

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Once the discharge port is opened. as the discharge port area rem ains stablein rclation to the change in rot ation speed. and as the change of g roo l 'c volumeper time is large, gas inside the groore does no t completely [l011 out. causingexcessire compression. leading to po11er loss. For this reason. it is necessary todesign the port for the high rota! ion speed range by taking into account therange of pressure increase during discharge.Fig . 10 sho"s the pressure difference OP bctaeen the peak pressure raluc andthe discharge port pressure 11lue. This figure sho11s that the greater the rotationspeed and the greater the dcliation of pressure ratio from the built-in pressureratio. the greater becomes the or l l lue during discharge, locring adiabatic cfficienC\.

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Ps 0.50MPo Ts 4CPd 1.19MPa Pd 1.53MPo Pd 1.94MPa) ( c 08070603::

""' 50~ 40....J3020100 1800 3600 5400

N rpmF1g. ll Indicated h o r s ~ p o w e r when rotation sp eed is 1aried

Ps 0.50MPa Ts 4CPd 1.19MPo Pd 1.53MPo Pd 1.94MPa

X CJ 02 . 0 ~ - - - - - - - - - - - ,

1.5 I,......:2 ~ 0E 1.0 ~

0.5)0

1:0 ~ 1 7 8 0 ~ 0 ~ - 3 ~ 6 0 ~ 0 ~ ~ 5 ~ 4 ~ 0 0 ~

N rpmFig. 12 Suction gas weight flow rate when rotation speed is varied

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7. Cone Ius ionsUr plotting the indicator diagrams of a screw c o m p r c ~ s n r . it as possible tograsp gas leakage condi lions between groores and changes in prnsure on both sidesof the port uhen rota! ion speed and pressure ratio ~ e r e raricd. 81 comparing theindicator d i a g r a m ~ thus collectert. it 11as found that discharge pressure greatlraffects the pressure in the rotor groote short before discharge.llegarding opera I ing conditions 11here both rot at ion speed and pressure ratio

are abore their respectire design liriiits. for a high rotation speed i t isncceisar to design the port br taking into account the range of pressureincrease at the time of discharge. but for a high pressure ratio. as there is nosudden pressure rise eten shortt) after the discharge port is opened. pressureratio can be set in a 11ioer range.In the future. the author hopes to appl1 these measurement data to analqcseal gap flow conditions and pulsation phenomenon in the gruoiC during discharge.from the standpoint of mixed p h a s ~ toi I and gas) flo" compression. aim1ng toimproe simulation reliabilit1.This work i& one of the & D programs of Technology Research lssociat ion o[Super Ileal Pump Energ1 \ccumulat ion ~ ) s t e m . entrusted by ~ e \ 1 Encrg) and IndustrialTcchuo I og) De\ e Iopmen t Organ i Zd t ion I \EDO J.flcfcrence:I I J Stngh, Pa11an: J. Purdue Compressor r.nginecring Conf.121 Sangfors, H . Purdue Compressor Engineering Conf. 11ge41. 519IIU84l. :J28

analysis of screw compressor performance based on indicator diagr

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