Influence of valve dynamics on compressor performance A.M. Bredesen

L'influence de la dynamique d#terminerlesfacteursquiinfluentsurrimportance des pertes.

des soupapes sur le I l a ~t~ r#alis# une s~rie de simulations sur rendement des ordinateur sous diverses conditions de fonctionne-

ment. Les r#sultats montrent que la force du gazA . compresse urs piston (#quation (1)) et le chiffre Mach M a , (#quation (5))

d#terminent le niveau des pertes pour une d#viation de force donn#e. La Fig. 4 montre ~ quelles pertes

Les soupapes des compresseurs ~ piston peuvent volum#triques on peut s'attendre. Les conditions les engendrer des pertes volum#triques Iorsqu'elles ne plus critiques ont lieu avec une valeur de A . basse et fonctionnent pas correctement. Les pertes ont leur un chiffre Mach #lev#. et i l faut ici #tre tr#s attentif origine dans le cas o£1 la force des ressorts de au dimensionnement dynamique.

soupape s'#loigne de la force optimale qui se calcule L'#tude montre que les pertes inutiles peuvent #tre selon les #quations (1). (2) et (3). #vit#es si la force des ressorts se maintient aux C'est avec les soupapes d'aspiration que le probl#me alentours de 50 & 150% de la force optimale des est le plus important et le but de ce rapport est de ressorts.

The valves of piston compressors can cause conditions. The results show that the gas forceA, volumetric losses if they do not function properly and (equation (1)) and the Mach number M a , (equation these losses originate from the condition where the (5)) determine the level of losses for a given force force of valve springs differs from the optimal force difference. Fig. 4 shows the kind of volumetric losses which can be calculated from equations (1), (2) and that can be expected. The most critical conditions (3). occurred with a IowA, value and high Mach This problem is particularly critical with suction number, hence careful attention should be given to valves and the purpose of this report is to determine dynamic design for such conditions. the factors which influence these losses. This study has revealed that unnecessary losses can These determinations were realised via a series of be avoided if spring forces are maintained at about

50 to 150% of the optimal force of springs. computer simulations giving various operating

The development of computer models has opened simulations and measurements alike have new possibil it ies in valve design. The capability of indicated that irregular operation - especially in a proposed prototype may be evaluated by suction valves - may considerably reduce capacity simulation, and many t ime-consuming practical and also energy efficiency 3. These losses can experiments can be eliminated. The simulation frequently be eliminated or reduced by adjusting model also allows a closer study of the losses the springs. Simple design equations have been associated with valve behaviour, developed for this purpose.

One major problem is the calculation of energy The losses produced by unsuitable valve consumption in the valve, another its dynamic behaviour will vary, and the aim of this report is design. This involves selection of appropriate to discuss the factors control l ing them and the springs to control its behaviour in such a way circumstances in which they may become critical. that heavy oscil lations or delayed closing are The discussion will be limited to the volumetric avoided. An important aspect is that the extra losses caused by suction valve behaviour only. mechanical strain caused by irregular operation, The relevance to power saving is evident which might limit the life of the valve, can be however, since unnecessary energy losses could reduced, be avoided by optimizing the valve dynamically.

Yet another aspect of the dynamic problem is the influence on compressor performance. Computer

The author is atthe Institutt for kj¢leteknikk, Norges tekniske Problems of valve dynamics h~gskole, Universitetet i Trondheim, Norway. Paper presented at meeting of IIR Commission B2, Delft, The The fundamentals of valve dynamics have been Netherlands treated previously5, 6, but some main points will be

0 1 4 0 - 7 0 0 7 / 7 9 / 0 1 0 0 1 7 - O 5 $02.00 Volume 2 Number 1 January 1979 © 1979 IPC Business Press Ltd. and IIR. 17

" cases heseoscato s a asoeadtofati+ue ~ , ~ failure.

'~ The losses mentioned are produced solely by t ~ " - - - - - " ~ I ° unsuitable valve dynamics caused by a poorly

<+ <" b i adjusted spring force. Computer simulation a ~ programs and auxiliary design equations have eo ,e~e, eo eo e,

LDC LDC been developed at our Institute in Trondheim t o l t &o , ~ / P+° ~.~',/ deal with such problems4, 5. The computer

I ~ , - - ~ , ~ - ' ' ~ simulates the valve behaviour and cylinder , , ' - process and calculates the amount of gas

t ransported through the valve as well as the I f ~4'~ l energy losses. In this way the influence on

<" C ~ d compressor performance may be evaluated. The eo~e, eo 'co: e, model has been calibrated against practical

LBC LDC experiments including measurements of valve Fig. 1 Suction valve behaviour and cylinder pressure variation displacement 4. with different spring forces, a- optimum Spring force, b-spr ings too strong, c -springs too weak, d -springs much too strong The most important design equations - (1), (2) and

(3) - make it possible to calculate directly the F/~?. 1 Compor tementdesc lape ts d'aspiration etvariation de la optimum spring force F~o of a compressor at the pression du cyl indre en fonct /on de diff6rentes forces de ressort, intended working conditions. a - force de ressort opt/male, b - ressorts trop fa/bles, c - /essorts t ropfor ts , d - r e s s o r t s b e a u c o u p t r o p f o r t s A . = ( 1 / 2 Acy, r ~ 2 C~A~ Pc (1)

\ " rnv ho

briefly recapitulated to provide a background for the new results to be presented. B+-- 3.22 A.O.S3-discharge valve, B .= 2.16 A, °.sl -

suction valve (2) The behaviour of automatic valves depends mainly upon the balance between the process F~o = m~ ~2 ho B, (3) forces produced by the gas f lowing through the valve and the directing forces usually provided by The+important factor is the maximum spring force mechanical springs. For given compressor and F+~o for the fully opened valve, since this will operating condit ions the process forces are:fixed, dec ide the critical starting point 80 of the closing. and the problem facing the designer is to When this has been calculated, the initial spring prescribe suitable springs so that near optimum force F~o and spring stiffness C~ may be adapted

rather freely. performance is obtained, as demonstrated for a suction valve in Fig. la. The valve should open promptly, stay fully open during the greater part These tools have proved their usefulness in of the intake period, and close wi thout practical.valv,'~ design 3, In the present oscil lations at pressure equalization between investigation they have been applied to study the cylinder and suction chamber ( ~c -- ~e). factors influencing the dynamic losses and to decide

the critical condit ions when excessive losses may Normally the pressure equalization occurs near Idc, but it could be delayed, occur.

The starting point of the closing motion 80 is the critical factor. Fig. lb demonstrates what happens when the springs are too weak. The Analys is p r o c e d u r e valve will start to close too late, and some gas returns to the suction chamber before the valve Numerous computer simulations have been made finally closes ( ~?~> ~). to investigate howthe losses vary. A medium-sized

piston compressor was chosen as a model, and the If the springs are too strong, as in Fig. lc, the suction valve geometry, compressor speed and valve will start to close early, so that the gas evaporating temperature were varied systemati- f low is choked. Thef low area is reduced, and the cally. The working condit ions given in Table 1 were pressure drop across the valve must increase to assumed. let through the gas required by the piston

displacement..The valve could also close Table 1 W o r k i n g c o n d i t i o n s used in c o m p u t e r altogether before Idc. Both of these effects wil reduce the pressure and mass content in the s i m u l a t i o n

cylinder at Idc, and the start of the actual Tab leau 1. Cond i t i ons de f o n c t i o n n e m e n t compression 8+ will be delayed. The delayA8 rs a direct measure of the volumetric losses, ut i l i s#es dans la s i m u l a t i o n p a r o r d i n a t e u r

If the springs are much too strong, the gas force cannot hold the valve against the stop at all, and Refrigerant R22

Evaporating temperature to = O, -20,-40, -60°C the valve will oscillate - Fig. 1 d. It is totally out of Compressor speed n = 16.7, 25.0, 27.2Hz control from a dy[lamic point of view, and both (1 000, 1 500, 1 750rpm) volumetric and energy efficiency suffer. In critical

18 International Journal of Refrigeration

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r 1r Tr (opt.) ' - (opt.)

a 80o ? b 80o 0 c 80o d 180o ? LDC LDC LDC LDC

Fig. 2 Simulated suction valvebehavi•urdemonstratingthemf•uenceofthedimensionlessgasforceA•.Thebehavi•urissimulateda•t differentspring force ratios Rsand four differentA.values. Constant Mach numberMa.= 0,21, corresponding ton = 16.7 Hz(1 000 rpm). a- to =60°C,A.= 11.6,Fsmo = 6.2 N, b- to= -40°C,A*= 34.6, Fsmo= 10.9 N, c-to= -20°C,A.= 83.1,Fsmo = 17.0 N, d - to= 0°C. A,= 176.6, Fsmo= 25 N

f~/g. 2 Comportement sJmul6 des clapets d'a'spiration montrant /'influence de 7a force du gaz sans dimensions A ., Le comportement est s/m u /e b diff#rentes forces du ressort Rs eta quatre va/eurs diff#rent es de A .. Nombre (Je Mach constant Ma ~ = O, 21, correspondant a n = 16. 7 Hz ( l O00t m / n 1). a - t o = 60 ° C,A.---- I 1,6, Fsmo=6,2N, b - t o = - 4 0 ° C , A , = 3 4 , 6 , Fsmo = 10,9N, c - t o = - 2 0 ° C , A , = 8 3 , l,Fsmo= 17,0N, d - t o=O ° C , A , = 176,6, Fsmo--- 25 N

The dynamic losses occur when the maximum more stable, so that greater imbalance is needed to spring force Fsm differs from the optimum Fsmo produce oscillations andsimilar reductions in f low calculated in (1), (2) and (3). The imbalance is area.

defined by the spring force ratio All this applies to springs that are too strong. When Rs =Fsm/Fsmo (4) the springs are too weak, the same tendency

prevails. The closing delay and losses are greatest For each valve geometry and operating condition at IowA.values. This is because the energy the optimum spring force was calculated. Then availableto close the valve under back-flow simulations were carried out with different springs, condit ions depends upon the dimensionless gas selected to vary the force ratio Rs systematically in force: the range 0.0 to 6.0.

I n f / u e n c e o f M a c h n u m b e r M a . T h e Mach number is F a c t o r s d e c i d i n g v a l v e l o s s e s defined in the ordinary way Once a dynamic imbalance exists, the losses

M a , = w ~ m / a o (5) produced appear to depend mainly upon two factors: the dimensionless gas fo rceA. ; and, the w~m = Wpm(AcyJozAo) (6) Mach number Ma. of the gas flow.

Lorentzen 2, Frenkel 1 and others have demonstrated The size of the initial spring force F~o may have that in suction valves Mach numbers above about some influence under certain conditions. 0.4 give volumetric losses, even with optimum valve

/ n f / u e n c e o f d / m e n s / o n / e s s g a s f o r c e A . The behaviour. This is caused by an excessive pressure drop that produces delayed pressure equalization. dimensionless gas force is defined by (1).It is Such condit ions should therefore be avoided. " needed to calculate the optir~um spring force, but

its importance goes still further. The simulations In the present investigation the simulations were have revealed that it may also be used toclassify carried out at three different Mach numbers the valve behaviour and its susceptibil i ty tO between 0.21 and 0.38. The effect is demonstrated imbalance. This is demonstrated in Fig. 2, showing in Fig. 3, presenting the simulated suction valve the simulated suction valve behaviour at different behaviour for different force ratios and Mach force ratios Rsand four differentA., values, numbers with a constant dimensionless gas force. corresponding tO evaporating temperatures The moment of pressure equalization Be is indicated between-60°C and 0°C with R22. The compressor by arrows to allow an evaluation of the volumetric speed is maintained at a constant value, losses produced.

The valve is obviously more vulnerable to dynamic It can be seen that the Mach number has little effect imbalance at IowA, values. The closing period at on the valve behaviour as such. It will however opt imum behaviour is long, so thatvery little affect the pressure losses and thus the disturbance is needed to make the valve oscillate susceptibil i ty to f low area reductions caused by too throughout the tr:ar)sport per.led, thereby reducing stror/g springs. The losses produced by unsuitable the mean ftow area considerably. For high valve behaviour therefore grow with increasing dimensionless gas forces the valve beh~aviour is Mach number. If the springs are too weak, the

Volume 2 Number 1 January 1979 19

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,.:,.oLr<oo,> _ / ' , r R , = , o = = (opt.)

I H- t t a i8o%-0 b 180"0," C 180"0. O

LDC LDC LDC

Fig. 3 Simulated suction valvebehavi•urdemonstratingtheinfluenceoftheMachnumberMa••Thebehavi•uriss•mu•atedfordifferent spring force ratiosRs and three different Mach numbers with constant dimensionless gas force .4.= 83.1 .The arrows indicate the time of pressure equalization ~)e, a -Ma. = 0,21. b-Ma. = 0,32, c-Ma. = 0.38

Fig. 3 Compor tement simule des clapets d'aspiration montrant / ' influence du nombre de Mach Ma. . Le comportemenz est simu/6 D dlff6rentes forces du ressort Rs eta trois nombres de Mach differents avec une force de gaz sans dimensions constante de A . = 83, 1. Les f /eches/ndiquent le temps d~gal isat ion de/a pression Oe, a Ma , = 0,21, b - Ma . = 0,32, c - Ma *= O, 38

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Fig. 4 Simulated volumetr ic IossesA~kat di f ferent spring force ratios Rs and operat ing condit ions. The operat ing condi t ions are defined by the dimensionless gas fo rceA , and the Mach number M a . . Fso/Fsm = 0.5, a - Ma. = 0 . 3 8 , b - M a . = 0 32, c - Ma. = 0 . 2 1 , - o - A , = l 1 6 , - - A . - A . = 3 4 . 6 , - . - ~ - . - A =83 .1 , - . . -m- . . -A .=176 .6

Fig. 4 Pertes vo lum6t r /ques s imul#esA~, b d i f f#rentes forces de ressor t Rs et d l f f6rentes cond i t i ons de f onc t i onnemen t . Les cond i t i ons de f o n c u o n n e m e n t son t def in ies p a r / a fo rce du gaz sans d imens ions A * et /e h o m b r e de M a c h M a . . / : so /Fsm = O, 5, a - M a . = O, 38, b - M a . = 0,32, c - M a . = 0 ,21, - o - A * = I 1,6, - - A - - A . = 34 ,6 , . - V - . - A , = 83, 1, -..- [3-..- A , = 176, 6

Mach number has less inf luence because the loss possib le to calculate the d imens ion less gas force mechan isms are di f ferent. A,, the Mach number M a . and the op t imum spring

force Fsmo. The d iagrams are restr icted to a l imi ted V o / u m e t r / c / o s s e s a t d i f f e r e n t o p e r a t i n g c o n d i t i o n s set of operat ing condi t ions, but may be used to In Fig. 4 the s imulated vo lumet r ic losses are evaluate what losses a certain imbalance is l ikely to presented as funct ions of the force ratio Rs, wi th the cause or the to lerances which must be appl ied in d imens ion less gas forceA. , as the index and wi th the design. one d iagram for each Mach number M a . . The d iagrams refer to an ini t ial spr ing force ratio Fso/Fsm The addi t ional losses produced at force ratios = 0.5. around 2.0 are due to extra valve opening. This

ef fect wi l l vary, but the main factor is natura l ly the Given a compressor and operat ing condi t ions it is overal l var iat ion.

2 0 I n t # r n ~ t i n n ~ l Inl i r n ~ l n { l:7,-~#r; . . . . + ;^~

The diagrams in Fig. 4 reflect clearly the The overall results show that s l i gh t l yweakspr ings conc lus ions reached in the previous sections, wi l l be less crit ical than stronger springs, with When the spr ings are too weak, the losses increase regard to vo lumetr ic losses. To avoid unnecessary wi th decreasing gas forceA., but they are capacity reduct ion the designer is well advised to s igni f icant only at values of Rs below about 0.5. In keep wi th in force ratios from 0.5 to 1.5. This should this region the Mach number has little effect, be a suff ic ient ra[~ge in most cases.

When the spr ings are too powerful, the losses vary both ,with, the dimensionless ,gas force A. and the C o n c l u s i o n s Mach numbecMa ' .Zhe i'nitial spring force could also :have an effect i , :but oniy at force ratios above Computer s imulat ion analysis has shown that 3:0,:and ih i s inf luence has !been :omitted here. The vo lumetr ic losses produced by irregular suct ion Ios:se:s:arb clohsiderable for:ai high Mach number valve behaviour depend upon the dimensionless

, ~:, , , I ' 1 ' and :lowld,~menslonl~ss gas:force. Great care must gas fo rceA .and the Mach number M a . of the gas th"erefo, r~:ibe exerci;sed in dynamic design for such f lowing through the valve. Proper dynamic design is condit ionS, crucial at IowA~ values and high Mach numbers.

The ; l~sses:at:the:lowMach n u m b e r M a , = 0.21 are In designing a specifc valve the equat ions and insig~:ifib:;aht.;irregular valve behaviour could available computer model can be used to in~ro~sd6'severe ossels even here but th s w advantage. Crit ical losses may be avoided and o¢cur,:only::at'=hlgher force r:atlos. Then the valve energy saved if the force ratio R~ is kept between w0,ul;d~,c,,ose a,nd terminate ~he gas f low before Idc. 0.5 and 1.5. The volumetr ic losses at other force T , , , : , , . , . , : Rebegin'n n"g Of th~s effeC~ can be detected n the ratios can be evaluated from Fig. 4. There is little d:ila!~i:i~~i i:h:i,Fig~ 4. doubt that more care n valve design wil l pay off.

References has worked since then at the Diwsion of Refrigeration

1 , Fre~kel;,Mi!l. Kolbenverdichter (Piston compressors)VEB Engineering in Trondheim, V ' ~ ' ierl~g:;~rechnik, Bertin(1969 pp. 747 where he isnowanlnstitute

2 I'o'rent~'en, G. Leveri:ngsgrad og virkningsgrad for kj~le- Engineer. In 1974 he kornp!re'ssore:r(Volumetric and energy efficiency of obtained the degree of Dr refrlig~ikatin9 compressors) Fiskeridirektoratet, Bergen Ing. in refrigeration

9 9;i;:pp. i 164 engineering, 3 Vili~d,.~n;: ~',i BredeSen, A.M. Optimering av kompressor- He is working on problems

Vdnilil~ilki" R~u'ltater fra et dansk:norsk samarbeidsprosjekt relating to valve dynamics on (:Opli!.ilm'i~ati~n bficompressor.val~/es -Results from a Danish- piston compressors and has

:N;0r;~e~iam!;o0peration p-oject) 10th Nordiska Kylkon- i produced several publica- g r e ~ ; i Fl~!lsi:nki (1977) tions on this topic. Since s l i ~ i , 4 ~ re'~'~s~hi~,~JVI.Cor~putefsimulationofvalvedynamiesasan 1973 he has also worked in ~]id i~!'~eSig~i~i Proc. of the 1974 Purdue Compressor a group administered bythe

'h!~~llO'gf:Confere!hce (1:974) 171-177 5 Bl~b~!,=~n Ai?lVI. Dynamic ;modelling of compressor valves, Dr Ing. Arne M. Bredesen NorwegianFisheries andUniversitYhas been°f

~t~'r,n'a't:lbn'al Congress of Refrigeration, Moscow(1975) was born in 1944 in Larvik, involved in projects on PaPule;B! !2-q'3 ' Norway. He graduated in industrial fish processing.

6 '~{:a~$~:::A::"M. iVal~e dynamics of piston compressors 1968 from the Dr Technical Bredesen has been a W;~i~'klr~;:!a'}:~i~at pump conditibn:s liB Commission 82, University of Norway as a member of Commission 82 861g'~8~:e,(1!i977) mechanical engineer and of the IIR since 1975.

N omenc ' l a tu re : Suct ion pressure pso, 105Nm -2

Max mu m va ye f, owarea Ao, m 2 Spring force ratio Rs " Vatve plat~Ifr0nt area Av, m 2 Crank radius r, m

Cy iindeir cross section Acy~, m 2 Evaporating temperature to, °C DirnerliSion'lesis gas force A . Mean gas veloci ty in valve wgm, m s -~ ACdusti'~ ~lobi{y, ao, m s -1 Mean piston veloci ty (= 4nr ) wpm, m s -1 D:imers::ioh[esisl i gas force B , Flow coeff ic ient SP[!r!d~i: Stfff:]e~s, Cs, N m -1 Volumetr ic eff ic iency X D, rag:c!deff:ibient : Cd Crank angle t~, degree M~i~i:~ ~'l;!ium'i ~pr:ingfforce! Fs~, N Starting point of c losing 19o, degree O;ptt m ~ mi:~!pri:nig force F~ .... N Crank angle at valve closure ~o, degree Initi!a:l ~p,rilhg fb'rce F~o, N Crank angle at pressure ~ degree ' , I : i e ,

mi~ va lye lift m va' !i

M'axi~miu : ho, equal izat ion S~c[tiio;h!, re!l ift hs, m Dens i t yo fgas f l ow ing th rough pc, kg m -3 ~;~:~ i~b~!ber M a . the valve v~i~e! ~liate;ilmass mv, kg Compressor angular veloci ty o~, rad s -1 C0;~:lilgi~ss;i(::):r sipeed n, Hz ( : 2n ~ ) C;~ii:bl d ,: ,i, ,:: , let ,p:Ir~essure pc, 10 s Nm -2 Lower dead centre Idc

Volume 2 Number 1 January 1979 21