Gnutek, Z.

Kalinowski, E.

English

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Purdue UniversityPurdue e-PubsInternational Compressor Engineering Conference School of Mechanical Engineering1992Analysis of Operation of Muldsliding-VaneVacuum PumpsZ. GnutekTechnical University of WroclawE. KalinowskiTechnical University of WroclawFollow this and additional works at: https://docs.lib.purdue.edu/icecThis document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact epubs@purdue.edu foradditional information.Complete proceedings may be acquired in print and on CD-ROM directly from the Ray W. Herrick Laboratories at https://engineering.purdue.edu/Herrick/Events/orderlit.htmlGnutek, Z. and Kalinowski, E., "Analysis of Operation of Muldsliding-Vane Vacuum Pumps" (1992). International CompressorEngineering Conference. Paper 792.https://docs.lib.purdue.edu/icec/792ANALYSIS OF OPERATION OF "ULTISLIDING-VANE V~CUU" PU"PS Zbignie• Gnutek, Eugeniusz K•lino•ski Institute of Heat Enginee~ing and Fluid "•~hani~s, Techni~•l Unive~sity of ~~oel••• ~~o~l••• Poland llbctr•ct The paper presents thereodynaei~ analysis of p~o~ess~s th•t occur in eultisliding-vane vacuue pueps, operating in the tank-eeptying layout. For a puep •ith a clearance sp•c:e, lieit value of v•cuue obtainable has been detereined, as Nell •s t•nk eeptying rate •nd po•er required to drive the puep. A foreul• for egzergetic efficiency of pueping process hac been derived. An experi .. ntal eethod of indicator dia9rae deterein•tion has been discussed for • eultisliding-vane vacuue puep •ithout a clearance space. Noeeno::lature: b - vane thickness l! - egzergy e - eccentricity L - length of •orking chaeber • - ... ss n0b - rot•tional speed N - poNer p - pressure r - rotor radius R - cylinder radius R1 - individual gas const•nt T - teeperature v - voluee y - radial clearance Zk(~) - rel•tive cross-sectional area of vane eachine a 1 - a 4 - angles describing positions of control edges A - angle bet•een successive vanes coepression ratio < - tiee ~ - angular coordinate L.. In traduction "ultisliding-vane rotational vacuue pueps are usu•lly regarded [1,Z0 6J as a special case of eultisliding-vane rotational coepressors. This is justified by the fact, that processes Nithin a vacuue puep are sieilar, or soeetiees identical, to those •ithin coepressors. Ha.ever, •hen taking the function of • puep •ithin a B T v z z tied) ~ • t pp T v p p ---·~---pt' T;. __.... Fig. 1. Outline of a systee0 fro. whi~h g•s is being reeoved 47 technic&l syste• into eonsider&tion, on• e&n point out & nu•ber of the l&tter·s functional goals, •hich justify the need for sep&r&te tre&t•ent &s f&r •s thtr•odyn&•ic &nalysia of •ultialiding-vane rotational v&cuu• pu•ps is concerned. One of the• is the process of t&nk .. ptying. It is present in a&ny br&nches of technology •nd in labor•tories. Fig. 1 outlin•s & syste•, fro• •hieh gas is being re•oved. lts initi•l theraodyn••ic p&ra .. ters are Pzo T7 •nd V2" P&ra•eters of an &ret, into •hich QIS is being trtnsferred, tre p0, T0 tnd V = ~- The design ide& of the puap is presented in Fig. ·2. NDt specified. in the picture is the design ptra•eter L, i.e. length of the •orking ch••ber. Pu•p ti•ing control (Fig. &chieved by •eans of proper localization of the control edges <K 1 to K4>. 3) is Their type. Therefore, for •ultisliding-v&ne constant value char&cteristic of thea, v&cuu• pu•ps one can reason&bly spetk of •hich is internal co•pression ratio [6]. • It is deter•ined by for•ul&e: - for adi&batic co•pression - for isotheraal co•pression pu•ps: (1) o = l:~= Zk("'4) (2) •T P• vk Zk<al-X.l •here: p•' V• - g&s pressure &nd •orking ch••ber volu.. at the beginning of cc•pr•5sian !I pk' Vk - 91s pressure &nd eorking ch&aber volu•e 1t the end of co•pression, Zk( ) - relttive eross-section&l area of the •orking ch••ber IS a funetion of angular position specified in the parentheses [4]. depends on des.ign consequently "'• is dependent on the p&r&•eters &nd the type of co•pression process. 48 In a tank/vacuu• pu•pl~•bient syste•, introduction of the extern~! co•pres5ion r~tio [6J is ~lso jult1f1~ble ~~~ording to for•ul&: Pt a,.-- C:S> z Ps Nhere: Pt - gag pressure in the discharge pipe, Ps - g~s pressure in the su~tion pipe. "ultisliding-v~ne v~cuu• pu•ps, Nhich re•ove 9~5 fro• ~ closed t~nk, oper~te at variable extern~! co•pression ratio (p5 = pp ~ ide•l· This results in pr~ctic~l inequality of extern~! and intern~! co•pres5ion ratios, otherNise being the •ost f~vour~ble case. __ Multisliding-v~ne Vacuum Pump Nith ~Clearance Space Depending on radi~l cle~rance •~gnitude y, various physic~! •odels of •ultisliding-v~ne v~cuu• pu•p operation are relevant. If y ~ 0, no •ediu• flux flo•s back fro• the delivery ~rea to the suction ~rea. If y > 0 ~nd ~3 - a 2 > A (see Fig. 2), there exists~ clearance sp~ce •ithin the •ultisliding-v~ne pu•p, due to Nhich so•e part of the ••diu• exhibiting para•eters like in the delivery area (or si•ilar) returns to the suction area. Presence of the return g~5 flu• i•plies, that pressure in the 5yste• (tank) lo•ers until the •~ss •ss o~ the •Orking •ediu• •ithin the •orking cha•ber being just closed during filling period equ~ls the reverse flu• •a5s •r· In the ~bsence of other type5 of return flux, the •r •~ss ••aunts to: p v Fig. 3. p V di~gra• of a •ulti-sliding-v~ne vacuu• pu•p •ith clearance «pace (4) • = R2 · L · Z (01 ) · ss . k 4 (5) Allo•ing for (4) &nd (5) and equ&tion ess ~ •r• tr&nsfore&tionsz obt.ined after T p ~ 0 (6) In the &bove for•ul~e, pp and TP are g&s pressure and te•perature in the tank &t &ny eo•ent, rel~tively. Rel~tionship bet•een the li•it pressure obt&inable pp and nu•ber of vanes, ensuing fro• equ&tion (6), is sho•n in Fi9. 4. The foreul~ c&n ~lso be 49 40tJOO ·~ Pa.l . . y/R "'0,001 i b/R = 0 i 5000 PD = 0, t H Pa · To = TP ~1931<. . 1000 . 1000 . IJ/R-005 . . . 5/JO . _L . . gjf<.{)~ v . . . ~ 1.00 . 2 6 8 10 IZ 14 (6 fB ~ 22 Siail•r di•or•• c•n bv ••de, Mhvn •11 return fluras •ri •r~ known. If ,. '----f.--f.--. z 4 .B6 •zr= f J •ri · d< (7) ,. D then the equ•tion •§s = eZr should bv used. Dyn•aics of puaping process depends both on propvrtie§ of • aulti§liding-v•n• v•cuua pu•P• •nd volu•• of •n •re• being ev•cu•ted. Assu•ing T0 = T2 •nd isoth•r••l coaprassion/erp•nsion, g•s prassurv within the t•nk •t •ny •oaent < c•n be detarained fro• the foraul• [4]: { Zk(et4)-Zk(otz) [ 1- Zk(ot4) ]z·nob·<+ Zk(e<z)} pp( <) "' PD. Z ( ) Z ( ) k ""4 li k 00 4 (8) ii v t -"here: = -2~ - rel•Uvv volu•• of thv •nk bl!1ng ev•cu;oted. R L The ti•e el•psed until pressure v•lue p is obt•ined ••ounts to: [ Po zkc"'">-Zk<"'z> ] ln p Zk(a4)-Zk(ot2) ,. = [ zk (a") ] (9) l n · ln 1----Db ii "o•ent•ry delivery of • aultisliding-v;one v;ocuua puap is •v•lu•ted froa the equ;otiona (10) (11) so "o•ent•~r d~iving po.,r of the pu•p is •s follows; N ( <) = R2 · L · n b · p (<) · IN (<) I + Nf p 0 p p (12) { [ Zk<"'4) - l . Zk(Oil-;>.,.) . ""z(<) - Zk("'t-"-l ] } (13) •h•re Nf - wa~k dissipAted due to friction of v•nes [2, 4]. "o•entAry, ti•e-vArying e~te~n•l co•pres5ian rAtio is equAl to; Po O"l(T) = m (14) p Fig. 5 shows relAtionships esisting between pp(rJ, ;p(.,.) And INP(.,.) I for A selected set of design v•~iAbles • . (lj, iiip(lj. ~~~ Pp 10 (k 90 0 2.0 20 R. 18 1B 8 0 1,6 16 7i 0 1.~ 14 0 1.2 1Z 50 1.0 10 0,8 B 30 0,6 6 M £j D,Z !l 0 0 0 1\ Z<& -1 j S/R .. 0,15 ji:(R•ti / h----_ Y/R = 0,001;" Pu • !J,f11fb, -/ \ ~ f<., 1.4 i fl,,.~.!5t; V•;7JOD. 7 \ ~ L \ ' I'/· \ .~v"" m.(t') 1\ pp('t)/ ~ / "~ "" / \ INp(t)l ~ / ~ ------...... 0 100 200 3IJO 400 Fig. 5. RelAtion betw.en p (·!") 0 ; (T) •nd llil (T) I p p p fa~ A ~ltisliding-vAne vAcuu• pu.p with cl•Ar•nce sp•ce n In o~der to •sses the~•odyn••ic effectiveness of the puwp, the •••e vAlues c•n be us•d •s those for co•p~essors [1, 2, 6]. The effectiveness of gAs r••ov•l f~o• 51 •ith the use of egzergetic effic;i.ncy [5]: .O.IIzb "J')bp = L (15) n01p •here: .o.Jzb - egzergy incre01se •ithin • c;losed syste• li•ited by t•nk ••lls, LnilP - •ork of the pu•p-drive engine. Egzergy incre01se •ithin • c;losed .o.llzb =II- V (pp- p 0 J = R2 - L V . syste• li•ited by t•nk ••lls ••ounts to [5): { R.PPT [cp-1 p T (T - T - T - ln Tpl + p 0 0 0 + T 0 · Ri ·. ln :: ] - ( p p- p 0 l _} ( 16) •herel B - the su• of potent1•1, kinetic; and ther•ic; egzergy for o•s cont•ined in the t•nk. 3. Multislidinq-vane ~Pump ~ithout Clearance Space As •lre•dy ••ntioned, • v•cuu• pu•p •ith y ~ 0 is conspicuous by the fac;t, thilt (•leost) no ••diu• flu• flo•s b•c:k through the rildi•l cle•r•nc;e. This •akes nec;eSsilry to introduce • correction into the p = p(V) rel•tion representation for 01ny •orking ch••ber. In • v•cuu• pu•p •ith non-zero cle•r•nce sp01c;e, volu•e of· the •orking ch••ber never re•ches null. In • v•cuu• pu•p •ith no c:le•r•nce sp•ce, volu•e of the Marking cha•ber changes fro• v = 0 to V = v•a• •nd then •o•in to V ~ 0 (see Fig. 6). Fig. 6. For•atton 01nd disappe•r•nce of the •orking c:h••ber for • pu•p •ithout cle•r•nce space A ne• •orking c;h••ber st•rts for•ing, •hen the preceding v•ne of this eorking ch••ber, which position corresponds to the •ngle of ~ s n - ~. p01sses cylinder/rotor contact point. It is fully for .. d, Mhen the closing v01ne co••s to p ~ n position. The cha•ber starts to vanish, •hen the closing v•ne h•• turned by the OlftQle of ~ 3n - ~. and .nds when ~ s 3n. The rotor turns by an angle of & during the period bet•e•n for••tion beginning •nd co•plete disappear•nce of the cha•ber, & being equal to: & = 3 · n - ( n - A ) = 2 · n + A = 2 (17) Thit ••ant, thilt the full •orkin9 c;y,le duration of a •ultisliding-v•ne vacuu• pu•p •ith y ~ 0 dependc on nu•ber of v•n•~ 01nd corr•sponds to the rotor rotation by- an anQle of e. This rtlitionship holds also for one- and t•o-vine pu•ps. The nec;essity above •entioned of introdu~ing • correction into the P .p(V) rel•tion repretentation for the y ~ o case •rose fro• interpreting e•pert•ental d•t• 52 obt~ined fro• •ultisliding-v~n• v•~uu~ pu•p tests [3]. Fig. 7 pres•nts ~ plot of ••peri•enhlly derived relAtionship of prenure versus ~h••b•r position fo·r ;a sele~ted type of ;a foursliding-v.ane v•~uu• pu•p •ithout cle.ar;ance •P•~•· The plot 150 p [ k Pa.J ~ 100 J 50 f-'""' 1 . fdlina d.i~ - com;{es SIOn Cf 0 h;as b•en obt•in•d by p.astinQ togeth•r a nueber of pressure vs. ti•e fro• .an oscilloscope screen ;and produced by •e.asuring points arr~nged the pu•p body. curves t.aken radidly in The rel;ation thus derived h•s been next tr.ansfor•ed to the p = f(~) rel~tion. Nu•ber .and .arr•nge•ent of the ••asurinq points h.ave been so s•l•cted, ;as to obt.ain the pressure sensing of •orking ch;a•b•r pressure during the •hole •orkino cycle. Fig. 8 sho•s p - V di•gr.a• derived by .an;alyzing the plot of Fig. 7. 150 p[kPa.) - rl\ 50 ~ V[ The di.agr••s indic.ate th•t the process running in the •orking ch••ber c.an be divided into three st~ges, th•t of filling, co•pressing .and disch;arging. Absence of elp•nsion st•ge provides justific.ation for regarding ;a v.acuu• pu•p •ith y ~ 0 .as .an ide.al co•pressor. "ultisliding-v;ane v.acuu• pu•ps, ;ap.art fro• dr••b•cks (friction), displ•r .a nu•ber of ;adv.ant.ages, o•ing to •hich th•y are re•dily used .as initi.al or lo• v.acuu• pu•ps. Their ther•odyn••ic description ho•ever is . not co•pletely consistent •i th th•t of •ultisliding-v;ane co•pressors, especi.ally if they ~re used in the t;ank-e•ptying l.ayout. "ultisliding-v;ane pu•ps •ith (y ~ Ol ;and •ithout (y ~ 0) cle;ar.ance sp;ace should be distinguished bet•een .and differently described. The 53 ~uthors propose ~lso the e•ploy••nt of e91ergetic t~nk-.. ptying effectiv•ness. efficiency [1], Chlu•skij M. "Rot~cjonnyje koepressory v~kuu•-n~sosy". "asinostrojenije, "oskv~, 1971 r. [2]. Golovincov A.G. "Rotacjonnyje ko•pressory•. "•sinostrojenije, "oskv~, 1964 r. [3], Gnutek z. "Opr~co•~nie •yni~ b~d•ri po•p praznio•ych ••• •, R~port P.Wr. I - 20 SPR 30/90. Wrocr•• 1990 r. [4]. Gnutek z. "Analiza proces~ ter•odyn~•icJnych • rop~tko•ych ·~szyn~ch rotacyjnych", cJ. 1, cz. 11, cJ. Ill, Raporty P.Wr. I - 20 SPR 24/91; 29191; 31191. Wrocl•• 1991 r, [5]. Sz•rgut J. "Ter•odyna•i~·. PWN, Warsza•• 1995 r. [6]. W•rczak W. "Spr~rki ziebnicze•, WNT, Warsz••~ 1987 r. 54 

Analysis of Operation of Muldsliding-Vane Vacuum Pumps

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Analysis of Operation of Muldsliding-Vane Vacuum Pumps

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