Koai, K.

Soedel, W.

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Purdue UniversityPurdue e-PubsInternational Compressor Engineering Conference School of Mechanical Engineering1990Contributions to the Understanding of FlowPulsation Levels and Performance of a Twin ScrewCompressor Equipped With a Slide Valve and aStopper for Capacity ControlK. KoaiPurdue UniversityW. SoedelPurdue UniversityFollow 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.htmlKoai, K. and Soedel, W., "Contributions to the Understanding of Flow Pulsation Levels and Performance of a Twin Screw CompressorEquipped With a Slide Valve and a Stopper for Capacity Control" (1990). International Compressor Engineering Conference. Paper 728.https://docs.lib.purdue.edu/icec/728CONTRIBUTIONS TO THE UNDERSTANDING OF FLOW PULSATION LEVELS AND PERFORMANCE OF A TWIN SCREW COMPRESSOR EQUIPPED WITH A SLIDE VALVE AND A STOPPER FOR CAPACITY CONTROL by Kwang-lu Koai and Werner Soedel Ray W. Herrick Laboratories Mecbanic:al Engineering School Purdue University West Lafayette, Indiana 47907 U.S.A. Abstract This paper discusses from a theoretical viewpoint the flow pulsation of a twin screw compressor and how it is related to performance. The compressor is equipped with a stopper in addition to a slide valve for controlling its capacity and the compression ratio. The volume ratio(V;), the flow capacity, the power consumption rate and the flow pulsation level are detennined based on a geomelrical characterization in terms of volume versus shaft angle as input and a thermodynamic analysis of a screw compressor for no leakage. Typical results are sbown in a plot form for various operating conditions defined by the stopper stroke, the bypass port opening area, the driving rotor speed and the compressor discharge pressure. Introduction Traditionally the capacity of a twin screw compressor is controlled by a slide valve, which is a wedge shaped solid block constituting a pan of the rotor housing. Activated by a control mechanism, the slide valve can move in the direction parallel to the axes of the rotors. Figure (1) shows the shapes of a typical slide valve and a rotor housing. At full load, the front end of the slide valve is in contact with its facing plane on the stationary pan of the rotor housing and the medium in the compression chamber is totally enclosed after the suction port closes. The shape of the rear end of the slide valve is designed to allow the discharge of the compressed gas in the radial direction at a certain Vi ratio at full load. At partial loads, the slide valve is pulled a distance toward the exhaust end of the compressor and a bypass pon is created in front of the valve, which leads the medium in the compression chamber to flow back to the suction side of the compressor. Also the radial discharge pon on the slide valve moves by the same distance as the stroke of the slide valve. Both the flow capacity and the compression ratio change following the slide valve movement. Figure 2 shows the slide valve, the bypass pon and the radial discharge port viewed from the compressor top. A recent development in the compressor industry is to introduce a second slide valve or stopper in front of the original slide valve for better control of the screw compressor( reference 1 ). With the combined action of two valves, the control of the compressor is diversified. There is some interest in how screw compressors of this type perform at various operating conditions. This paper attempts to conaibme to the understanding by way of a theoretical simulation and to extend the discussion by including flow pulsation level predictions. Geometric Characterization and Thermodynamic Analysis The volume curve and seal line curves of a screw compressor can be generated based on its screw profile and fundamental geomeaic data. If the dimensions and the strokes of the slide valve and the stopper are known, the pon area curve can be determined too. The thermodynamic analysis of a screw compressor is conducted following stepwise the evolution of the compression chamber. By solving the simultaneous equations based on ideal gas and isentropic flow assumptions, the conservation laws and assuming no leakage, the gas conditions and the port flows can be calculated for each step. Figures 6, 7 and 8 and show the pon area curves, the volume curves, the internal pressures, the port flows and the masses of the medium in the compression chamber of a typical 60 hp screw compressor at various valve positions as designated in Figures 3(b ), 4(b) and 5(b ). Other operating conditions are: R22 refrigerant as the medium, driving rotor speed 59. 2 cycle per second, and compressor inlet/outlet conditions of 83.2psia/55°F and 24lpsia/180°F. Figure 9, 10 and 11 show the corresponding pressure-volume diagrams. These diagrams and the calculated flow conditions determine the compressor performances. i.e. the effective volume ratio, the flow capacity, the power consumption rate and the flow pulsation level can be evaluated. For an ideal single stage refrigeration cycle, these performances represent: the chamber pressure when the discharge pon opens, or equivalently the "overpressure" or "underpressure" level, the heat capacity, the inverse of the coefficient of performance( COP), and the pressure pulsations respectively under the operating conditions specified. Figure 12 shows such performances of the example compressor at different combinations of the stopper location and the spacing between the slide valve and the stopper. Other operating conditions are the same as before. Figures 13 and 14 arc the same as ~igucc 12, except that the performances at different rotating speeds or compressor outlet pressures are exammed. 388 Flow Pulsation and Performance ( 1) With the inll"oduction of a stopper in addition to the conventional slide val.ve, the control of a twin SCl'ew compressor can be achieved with more flexibility. The flow pulsanon and the perf~ance of the twin screw compressor vary as functions of the stopper stroke and the bypass pon openmg. (2) The effective volume ratio(V;0 ), which is the volume ratio with_!! density correction for the chamber volume at the closing of the suction port, is subject to the geomeaic lirnitattons of the screw compressor design. As can be seen from Figures 12(a), 13(a) and 14(a): . A. The Vie value can not exceed the limit set by the locations of the ending line of the suction port and the starting line of the axial discharge port on the rotor housing. This limit can occur only wi~ the bypass port fully closed. Point A's in the figures correspond to the situation that the :radi~ discharge pon on the slide valve coincides with the axial discharge pon. The radial discharge port disappears as the slide valve is pushed further toww:d the discharge side of the compressor. If the stopper and the slide valve together are pulled beyond point A away from the discharge side, the Vie value drops gradually. . . . . B. If the bypass pon opens, the highest Vie pomt occurs when the radial discharge pon on the slide valve coincides with the axial discharge port too(points B,C&D). The Vi• value drops gradually when the slide valve is pulled or pushed away from this highest point. Maltimum Vie values at all panialloads are approximately the same because they are mainl_y_ controlled by the length of ?te slide valve. They are lower than the maximum Vie for full load condition because the bypass pon IS usually designed to close at a cenain time lag after the suction port closes. (3) The flow rare of the medium is detennined by the density of the inlet gas and the timing for the compre-ssion process to start. At full load and assuming no leakage, the flow rate is constant because the compression process starts when the suction port closes( no bypass pon). For panialloads, the flow rate decreases as the slide valve is pulled toward the compressor discharge end and the chamber is not closed to the suction gas until the bypass port closes. At the same stopper location, the larger the bypass port opening is, the less the flow rate will be. ( 4) The power consumption rate, defined as the power required for transponing a unit mass flow through the compressor, is detetmined by dividing the work obtained from the P-V diagram by the mass flow per chamber. As can be seen from Figures (9),(10) and (11), the higher the over/under pressure level (the chamber pressure at the start of discharging relalive to the compressor outlet pressure) is or the earlier the compression process statts, the more work will be required for each chamber. If the compression process starts at approximately the same time, the power consumption rate will be roughly proponional to the ratio of the over/under pressure level to the mass flow rate. (5) The gas pulsation level is roughly proponional to the over/under pressure level and inversely proportional to the increasing rate of the discharge port area at the start of the discharge process. (6) By comparing Figures 12,13 and 14, we see that: A. The Vie ClllVCS are almost the same because they Mpresent the geometric properties of the screw compressor that do not change. The density conection factors are approximately the same for different stroke amngements with bypass port opening. B. The flow rate plots are the same if the compressor geometry, the suction gas density and the rotation speed are kept the same. Its value changes proportionally with the rotation speed. C. The over/under pressure behavior depends on the compressor inlet and outlet conditions. The averaged gas pulsation level changes consistently with the over/under pressure leveL (7)1n response to a load demand change of the refrigeration system, there are in general two ways for the compressor to catch up: by changing the mass flow rate or by changing the compression ratio, or both. The control system of the screw compressor may be designed by following the above general trends to properly move the stopper and the slide valve or change the rotation speed of the driving rotor to cope with the system load call, such that the optimal values of the equivalent volume ratio, the power consumption rate( or equivalently COP) and the gas pulsation can be obtained Refercnres (l)David N. Shaw, "SCREW COMPRESSORS, CONTROL OF V; AND CAPACITY --THE CONFUIT' Proceedings of the 1988 International Compressor Engineering Conference at Purdue pp236-243. (2)Lar.; Sjoholm, "VARIABLE VOLUME-RATIO AND CAPACITY CONTROL IN 1WIN SCREW COMPRESSORS" Proceedings of the 1986 International Compressor Engineering Conference at Purdue pp494-508. (3)Kwang-lu Koai and Werner Soedel, "GAS PULSATION IN1WIN SCREW COMPRESSORS-PART I: DETERMINATION OF PORT FLOW AND INTERPRETATION OF PERIODIC VOLUME SOURCE "Proceedings of the 1990 International Compressor Engineering Conference at Purdue( to appear). As;kngwlcd gemcpt The support of this work by United Technologies Carrier is gratefully acknowledged. 389 SLIDE ~ MALE FEMALE ~OTO~ ~TOR Exhaust End MALE AcTOR Suction EM RADIAL DISCHARGE PORT Figure I: Cross seetlonal View oC a Slide Valve and a Rotor Housin1 Figure 2: Top View oC the Interior of a Sc:rew Com pressor (a) (a) Exnaust Cnd MALE ROTOR (b) BYPASS PORT Exhaust End U•O.!Icm Suction EM Pi1ure 3: Stopper Loc:ated at the ReCereoee Position (a) No Bypass OpeoiDI (b) 0.:5 c:m. Bypat~ Port Opeoin1 (b) SYPASS PORT FEI1ALE ROTOR •u-o --IU•O.Scm Suction End (a) (xMust End MALE ROTOR Suction End Suction End Pushed 2 em with respect to th:etre~:e~ Position toward the l!%haust End (a) No Bypass Openin1 (b) 0.5 em Bypass Port Opening V•O V•2cm Figure :;: Stopper Pulled 2 em vith respect to the Reterenee Position away from. the Exhaust End (a) No Bypass Opeoinl (b) 0.5 em Bypass Port Openina 390 (a) (b) (c;) (d) (e) e u <J' .: .. " < t: 0 Cl. B u " ~" B " 0 > .. " ... B .. .Q <.J .. " .... e .. ..:1 <.J .. ..... :::!! " ~"' 0 ..: .... t; Cl. .. ... .. ... e .. .., <.J .9 : .. :::!! bypass port c:losed bypass port opened by 0 . .5 em 100.00 80.00 80.00 ~ . . - - ' . . . ; . . . ~0.00 20.00 0.00 ·200.00 o.oo 200.00 400.00 600.00 800.00 Male Rotor Rotation Anale (degree) 250.00~------~----------~~---------------, 200.00 150.00 100.00 50.00 0 .oo +.,.....,,....,.. ........ .foo!::...,....,....l"""""T"""T""..,....r-r"+T"""1 ....... ..,.u.T"""T..,...,.,.....-j ·200.00 0.00 200.00 600.00 800.00 Male Rotor Rotation Anale (dearee) 700.00~-------r------~------------~------~ 600.00 500.00 ~00.00 300.00 200.00 100.001l~~~:t~~~~:;~~~~~~~~~~~ 0.00.: -200.00 o.oo 200.00 800.00 aoo.oo Male Rotor Rotation Anale (dearee) o.o8 0.06 o.o~ 0.02 0.00 -0.02 -200.00 0.00 200.00 ~oo.oo 600.00 800.00 Male Rotor Rotation Anale (dearee) 6.00 5.00 4.00 3.00 2.00 1.00 0.00 ·200.00 o.oo 200.00 ~00.00 600.00 80o.oo Male Rotor Rotation Anale (derrree) Piaure 6: Chamber Conditions vith Stopper Located at the Reference Position (a) Port Area (sq em) (b) Chamber Volume (cu em) (cl Chamber Pressure (psial (dl Port Ptov (c:u M/s) (e) Mus in Chamber <al 391 a " ~ .. .. (a) .. < .. .. 8. a u ~ ~ .. a (b) ~ 0 > .. .. "' a .. "' u .. .. ~ .. .. ;: (c) .. .. .. llo .. .. "' a .. ,<:1 u .. ..... ::s ~ (d) ~ ~ "" -.: 0 llo 3 .. .. "' a(e) .. ,<:1 u .!! = .. ::s bypass port closed bypass port opened by 0.:5 em 100.00 ao.oo 60.00 40.00 20.00 0.00 -200.00 0.00 200.00 400.00 600.00 aoo.oo Mate Rotor Rotation Angle (degree) 250.00 ..,...---..,.-------:::=::c--------. 200.00 150.00 100.00 so.oo o.oo 4-'T'""lr-T'"'T"~:....,....,-,..;."T".,....,r-T'+T"'T---r'....-,.......;o-......,r-1 -200.00 o.oo 200.00 400.00 soo.oo Mate Rotor Rotation Ansle (degree) aoo.oo 700.00 -a-----,,---~------,--------, 600.00 500.00 400.00 300.00 200.00 100.00 ---......... - ........ '"-. . . . . . . . . . - - - - :· . . . . . . . .~ . - - -o.oo +-r-T""'T--r--hr-T'-r-T"'i--r...,.-T""'T"T""T""r-T"T"T-1...,......,..-...-l -200.00 o.oa 0.06..; 0.00 200.00 400.00 600.00 Male Rotor Rotation Ansle (clesree) • •' • • • • '•' •' '•' '• •'·----.- • 'I' 800.00 0.04..; . 0.02 0.00 . ..: ............ ~·f'\···-:-" .. .. -0.02 -200.00 0.00 200.00 400.00 600.00 800.00 Male Rotor Rotation Ansle (dearee) 6.00 s.oo 4.00 3.00 2.00 1.00-. o.oo ·200.00 o.oo 200.00 400.00 600.00 800.00 Male Rotor Rotation Angle (degree) Fisure 7: Chamber Conclitiona vlth Stopper Pushed Z em tovard the Ethaust End (a) Port Area (sq em) (b) Chamber Volume (c:u em) (c) Chamber Pressure (psial (d) Port Flow (cu M/sl (e l Mass in Chamber (g) 392 Ei u ~ .. .. (a) .. < ... .. 0 llo Ei u " ~.. El " (b) 0 > .. .. .CI B .. .<:1 v -~ ... :! (e) = .. ~ .. .. .... B .. .... v .. ..... :2 " ~(d) .. 0 ;;:: i llo 3 .. .. .... El .. (e) .<:1 v ..!! .. .. .. :2 100.00 80.00 ~· . .. .... .. .... :-... ... . .. 60.00 ........ :· ...... . 40.00 ·'· ................ . . . 20.00 0.00 -200.00 0.00 200.00 400.00 600.00 800.00 Mate Rotor Rotation Angle (deareel ::::::1.. ·1·~ ...... : . .. . ·>· I 150.00 . --- ...  -- --- .. - .. - ·  ... -100.00 ..... ---····· ·----···. ··- -~······ 5::::-~ . -2oo.oo o.oo 2oo.oo 40o.oo soo.oo eoo.oo Male Rotor Rot.ac.ion An&le (degree) 700.00;r-------r------~------~----~~-----. 600.00-soo.oo -j 400.00 300.00 200.00 100.00 -· ...... ·- ·- .. -· : ........ -- -· -· .. ·: .... ·- -· -· .... ··~- ---- .. ···-· .. ·:·- ..... ··:- ..... - _-, ... - .... .. " .... - ..... -· ·:· .. ·- ... ·;··- ..... ;. " ...... ' ........... - ... -_- ...... - ·-··· .. -. -:· .. -- .... ·-· .... ·:· .. ---o.oo~,-~~~~~-r+1·-r~~-~1 -r,-~~-r~r4 ·200.00 0.00 200.00 400.00 600.00 Male Rotor Rot.aLion Antle (deane) 800.00 i~I··••·····E•• :. • ·. • .~·····ITD•····I ·0.06- I I I .....---r----r I I ' ' I I -200.00 0.00 200.00 400.00 600.00 800.00 Male Rotor Rotation Ansie (dqree) 6.00 ..,.-----'"T"------------------, 5.00 4.00 3.00 2.00 1.00 0.00 +'"T"",....,--r-t-'~--r-.-.;-,r-r-r,.....,r-r-r~ri-r..,..1"'"""T-I ·200.00 0.00 200.00 •oo.oo 600.00 800.00 Male Rotor Rotation Angle (degree) Figure S: Chamber Conditions vit.b. Stopper Pulled 2 em away from tbe E:zbaust End (a) Port Area (sq em) (b) Chamber Volume (cu em) (c) Cha111ber Pressure (psia) (d) Port Flov (cu M/s) (e) Ma:Js in Cba111ber (g) 393 .; ~ ~ : .. ~ .. .. -" El • .... .... -~ .. ~ .. .. " : .. .. l>o .. .. J:> El .. .... .... bypass port c:tosed 700.00 bypass port opened by 0.3 c:m 600.00 500.00 400.00 300.00 200.00 100.00 0.00 0.00 50.00 100.00 150.00 200.00 250.00 Chamber Volume (cu em) Fi1ure (9) Preuure Volume D1anam viUl Stopper Located at the Reference Position 600.00 500.00 •oo.oo 300.00 200.00 100.00 0.00 n no 50.00 100.00 150.00 200.00 250.00 Chamber Volume (eu em) Figure (10) Pressure Volume Diasram vith Stopper Pushed 2 em loward the ~haun End 700.00-r--------------~------~------------~ 600.00- ..... . 500.00 •oo.oo- · · · · · - - - ·: · · · · · · · ·: · · · - - - - ·.· · - · · - · · ·- · · · · -300.00-o.oo-~,-~-T~~~~,-~1-r,-~ro-r,-~-~1 -r-r~ 0.00 50.00 1 oo.oo 150-~n 200.00 250.00 Chamber Volume (1:u em I Figure ( 11 l Pressure Volume Diagram vith Stopper Pulled 2 c:m avay from the ~haust End 394 <; 5 > ~ 4 .. .. Bypan Port o...,ain•: a -o.o ... ,. 0 3 o., ... > 2., ... ;;. 6.o ... ~ 2 > ·; ... "ul14cll'f'CQu'*" .. 1 ·8 ·6 -~ ·2 0 2 ~ 6 Stopper Stroke (cllll 1600 1400 .. .... !!! 1200 Bypaos Port Op.,a.!ftl: ! -o.o ... .. .. 1000 o., •• ~ 2., ... iL BOO 6.o • ., 600 400 ·8 ·6 ·4 ·2 0 2 ~ 6 Stopper Stroke (em) .. 55 a !. 50 v Dypau Port Opea.ia1: " -O.Ocm .." 45 O.Scm .g 2., ... "' 6.0cm II •o : " 8 35 .. ~ ~ 30 ·8 -6 -4 -2 0 2 4 6 Stopper Stroke (em) 0.02 .... .. .. BYI>IU Port o .... aine: ~ -o.Ocm ... O.Q1 ~0-~CID ! _2.5cm _6.0cm -; a. ~ ... 0.00 -8 -6 -~ ·2 0 2 4 6 Stopper Stroke (em) Fiaure 12: Performances of 1 Typical 60 HP Screw Compressor at 2·U Ptia Co~aprc .. or OuUcl Pretoure oatS 5':1.2 CPS Sp.,ed 395 5 . > ! 4 "' Bypau Port Openiaa: 0 -- O.Ocm 8 3 -o.s .... " 0 ---z.s .... > -6.0cm ~ 2 > ·a ... 1 "' -8 -6 -4 -2 0 2 4 6 Stopper Stroke (era) 1600 1400 ..... 1200 llyp.,o Pon Opealna: .. ! ---o.o .... .. 1000 D.Scm "' Z.Scm ! 800 6.Dera "" 600 . 400 -8 -6 -4 -2 0 2 4 6 Stopper Stroke (era) ;:; ..... eo a !: ! 70 . "' llyp~ Opelli111: a .5! o.oc• i. GO -o.s .... a -2.Sc• " -6.0e• ~ 50 ... . .. 40 0 "' -8 -6 -4 -2 0 2 4 6 Stopper Stroke (em) 0.03 -.. ... u -; 0.02 Bypaos Port Opelliaa: ,. " -o.o ... ,_, -o.scm c ·E z.se., 0.01 -6.0CIIl :; a. ll Q <;: 0.00 -8 -6 -4 -2 0 2 4 6 Stopper Stroke (em l Flaure 13: Perrormaaeeo ot a Typical 60 HP Screw Co111pre11or at 3SO Psi& Co~aprenor Outlet Pressure a114 59.2 CPS Spoed 396 5 .. e 4 ·~ 8ypau Port o,_aln&: "' -o.oca s 3 -o.sc .. .. 0 --- 2.5cm _6.oc .. ;:. ! 2 ;; > "llndetpn,u.~· -; "' 1 "' ·8 ·6 ·4 ·2 0 2 4 6 Stopper Stroke (em) 1600 1400 .... .. 1200 Bypaoo Port OpeoiDI: -O.Ocm ~ ---o.sc .. .. 1000 ---2.5ca £ 6.oc .. 800 600 400 ·8 ·6 ·4 ·2 0 2 4 6 .. Stopper Stroke (em) .... B so ~ ~ 45 llyp .. s Port o,_oioa: .. ~ - O.Ocm o.sc .. a. 40 -2.5cm B 6.oc .. ~ a -0 35 u .. . ;o 0 30 "" ·8 ·6 ·4 ·2 0 2 4 6 Stopper Stroke (em) .... 0.02 u . Bypau Port Opeoloa: > . -o.oc .. .... ---0.5em d .g 0.01 -Z.5cm = --6.0cm -; ... ;o 0 ;;: 0.00 ·8 ·6 ·4 ·2 0 2 4 6 Stdpper Strdke (em) Fi&ure 1 ~: Performance• of a Typical 60 HP Screw Compressor u H 1 Psla Compressor Outlet Preuure an4 65.0 CPS Spee4 397 

Contributions to the Understanding of Flow Pulsation Levels and Performance of a Twin Screw Compressor Equipped With a Slide Valve and a Stopper for Capacity Control

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Contributions to the Understanding of Flow Pulsation Levels and Performance of a Twin Screw Compressor Equipped With a Slide Valve and a Stopper for Capacity Control

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