A Study for Improvement on High Pressure Multistage Reciprocating

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Purdue University

Purdue e-Pubs

International Compressor EngineeringConference

School of Mechanical Engineering

2000

A Study for Improvement on High PressureMultistage Reciprocating Compressor

T. NishikawaSanyo Electric Co.

H. NishikawaSanyo Electric Co.

T. ObokataGunma University

T. IshimaGunma University

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Nishikawa, T.; Nishikawa, H.; Obokata, T.; and Ishima, T., "A Study for Improvement on High Pressure Multistage ReciprocatingCompressor" (2000).International Compressor Engineering Conference. Paper 1373.http://docs.lib.purdue.edu/icec/1373
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A STUDY FOR IMPROVEMENT ON HIGH PRESSUREMULTISTAGE RECIPROCATING COMPRESSOR

Takahiro Nishikawa and Hiroshi NishikawaCompressor Division, Sanyo Electric Co., Ltd.1-1-1, Sakata OizumiMachi, Ora-Gun, Gunma 370-0596, Japan

Tomio Obokata and Tsuneaki IshimaDepartment of Mechanical System Engineering, Gunma University1-5-1, Tenjin, Kiryu-City, Gunma 376-8515, Japan

ABSTRACTCharacteristics for the multistage high pressure reciprocating compressor, whichobtains over 30MPa, have been studied. Th e simulation of flows in th e connectingpipes between cylinder heads an d the inside of them are performed by usingComputational Fluid Dynamics, in which th e compression condition is assumed onedimensional, compressible an d unsteady. Then the performance characteristics are

comprehensively studied by comparing th e numerical results with those of experiments.Consequently, an improvement in thermal efficiency of th e compressor has beenaccomplished.

NOMENCLATUREA Area p Pressurea Sound velocity Q Leakage flow ratec Damping coefficient q Quantity of heatF Fluid force (= APA) r Cylinder radiusH Cylinder height t Timek Spring constant T Gas temperature inside cylinderL Length u Velocitym Valve mass v Cylinder VolumeM Mass of gas in cylinder X Axial coordinate of pipen Polytropic exponent X DisplacementGreek Letters0 Side clearance between Jl Coefficient of frictioncylinder and piston p DensityK Specific heat ratio T Shearing stress (= w(du/dr))Subscr iptscy l Inside of cylinder s Suctiond Discharge top Top dead centerpzpe Inside of pipe 0 Initial valueport Suction and Discharge port valve Minimum sectional area

INTRODUCTIONThe multistage reciprocating compressors have potential in attaining higherpressure with higher thermal efficiency than single stage ones because their cylindersare arranged in series so that they could be applied widely in many industries.However, th e improvement of these kinds of compressors is still demanded to meet thestringent requirements for better performance. For example, in order to increase

Fifteenth International Compressor Engineering Conference atPurdue University, West Lafayette, IN, USA- July 25-28, 2000 105


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the gas flow rate for one compressor, a highervolumetric efficiency is most important. Because thehigher the volumetric efficiency, th e less th e suctionflow losses and the better the utilization of pressurepulsation occurring at th e suction-discharge system.Many research works have been reported on this topicin reciprocating internal combustion engines, whichhave similar induction structure an d working sequencewith reciprocating compressors. However, rarelyliteratures on such topic ar e available for multistagecompressors till now.

Ia ei

In this report, the influence of discharge pressureand the effect of working fluid on the four stagereciprocating compressor are conducted by using th eoriginal numerical simulation program. Thepossibility of applying this simulation program toestimate the compressor performance is also verified.Furthermore, the internal flow of th e connecting pipeand the cylinder head are analyzed, an d th e higherthermal efficiency compressor has been accomplishedusing this program. Figure 1. Solid model ofthe compressorMODEL OF CONSTRUCTION ELEMENTS

To analyze comprehensively, th e simulation model for performance characteristicsof four-stage compressor is divided into three elements: the compression space, th esuction -discharge system and th e connecting pipe. The solid model of th e compressoris shown in Figure i , and the flow diagram of main routine is shown in Figure 2.c START ::::> InnutDataI Select of cvlinder number l Input Parts DimensionCalculation of item Input cyde timeCalculation of various efficiency Prenaration of lnnut files l--- Input Compressor FrequencyCalculation of Bearing Force

Calrulation of Motor torque -----1 Select of Calculation item I Input Pressure ConditionsCalculation of Dvnamic Balance I l Input Properties of FluidInitial kind of conditions etc

r C31culation of Pressure .Temperature -1and Mass of Gas in CvlinderI Calculation of Auid Force I-= ""S.uction valv e open? Divided Time Step lr I SubroutineValveSubroutine Pipe Yesl N J t Calculation of Valve Disnlacement I~ i l i t y of CFL Conditi -= Discharge valve onen?lN G N;;J" Yes I Calndation of Mass Rate on PartsOK

Calculation simultaneous Equations Subroutine Pine(Characteristic Equation) I Calculation of Flow Rate IEquation of Continuity and Leakage* Equation of motion

*Equation of energy I Calculation of Efficiencv IJ.XI.= Outnut Datak: aJculation of Pressure and Velocity_ n Pip;) Continue? -==-l No Flow Rate .Input.CurrentCalrulation of Pressure and VeJocitv on Piue End Outnut of calculated results Pedormance of MotorI Pressure and Velocity at Point< END Gas compressing torquevarious efficiencv

Figure 2. Flow diagram of main routineModel of Compression Space

I

In th e simulation model of th e compression space, a variation of the cylindervolume is calculated from the piston position, then a discharge pressure andtemperature are calculated using given suction pressure and temperature in the each



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process of intake, compression an d discharge respectively, shown as Equations (I) and(2). The compression condition for simulation is treated as the polytropic compression.And it is assumed that the re-expansion of the gas in the clearance volume into thecylinder makes the internal pressurizing of the cylinder pressure during th e intakeprocess. Accordingly, an increase in th e internal pressure JP is given by Equation (3).tl-1

(I ) T.o ( p:ol )--;:1 ~ y l ~ . (2) (3)

Model of Suction-Discharge SystemFigures 3, 4 and 5 show structure of the suction -discharge system, suction valvegeometry and discharge valve geometry respectively. As illustrated in Figures 3 and 4,calculating area is divided into three domains an d four domains respectively. In thecalculation, the pressure and the density are assumed to be constant at each domain.And the position of the valves is calculated by using the New Mark {J method, which isbased on the equation of motion shown as Equation (4), in consideration of a springconstant k and a damping coefficient c.

SuctionValveCylinder

Figure 3. Structure o f suction-discharge system Figure 4. Suction valvegeometry

(4)

Pcyl P..:yl Ucyl

Figure 5. Discharge valvegeometryThe pressure, the flow velocity and the other properties around the periphery of

valves ar e obtained from the calculated results of the gas flow in the cylinder and theyare defined as th e time function. Since the mass flow rate per unit time is constant ateach domain of the suction-discharge system, we can get the equation as following.The equations of continuity dVcytPcytd t = Ps(valv)Us(valve} As(valve) dVcy1P yl -d[" = Pd(port) Ad(port) ud(port)

TheequationsofenergyK Ps(valve) 1 2_____ + -2us (valve)

K - Ps(valve) K Pd(port) 1 2= ----- + - ud(pcrl)

K -1 Pcyt K -1 pd(port) 2The isoentropic equationP s(pcrt) = P s(valve)

KPs(port) Ps(valve)

Pcyt = Pa(port) = Pa(valve)

P ;z p;(pcrt) p;(valve)

Fifteenth International Compressor Engineering Conference atPurdue University, West Lafayette, IN, USA- July 25-28, 2000

K P s(pcrt) 1 2-----+-uK - 1 2 s(port)P s(pcrt)- - - = - : ~ : t . . + ! u 2I 2 d(valve)K - Pd(valve)

(7)(8)

(9)(10)

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Model of Connecting PipeWith the assumption of the compressible unsteady flow in the connecting pipe, thesimulation is performed by using th e method of characteristic. Th e equations ofcontinuity, motion and energy, which are transformed into the characteristicdifferential equations, are expressed as follows.

dP-a 2dp = (K -1)qpdt (11) dP + padu = (K -1)qpdt (12) dP-padu=(K-1)qpdt (13)I

.........71':l t.xXo xH x, x11 x,-12

Figure 6. Meshing example of X-t plane

Co: Equation (11)C+: Equation (12)C_: Equation (13)

Th e values among the mesh points in X-t plane are obtained by proportion, andthe pressure, the flow rate and the density in the pipe are given by using Equations (11),(12) and (13) at every time step. Figure 6 shows th e meshing example of X- t plane.The boundary conditions at the en d of th e connecting pipe ar e adopted by both theisoentropic equation and the conservation equation of energy for the compressiblequasi-steady flow.Case 1 : Outflow from Cylinder to Connecting PipeIn order to consider th e dynamic characteristic of th e valves, the position thathave the minimum sectional area, which is calculated in th e model of thesuction-discharge system, is set as the reference point. Therefore, considering the twoprocesses: from the discharge port to the minimum sectional area and from theminimum sectional area to the end of the connecting pipe, th e equation of continuity,th e conservation equation of energy and the isoentropic equation are expressed as

follows. (14)K Pd(port) = Pd(valve) +_!_U2 = Ppipe _!_ 2 ( 15 )1 1 2 d(valve) 1 + 2 upipeK- Pd(port) K- Pd(valve) K - Ppipe

Pd(por t ) /p;(port) = Pd(valve)l p;(valve) (16)Case 2 : Inflow from Connecting Pipe to CylinderOn the condition for th e inflow from the connecting pipe to th e cylinder, theequation of continuity, th e conservation equation of energy and th e isoentropic equationare expressed as follows.

P pipe u pipe A pipe = P d(valve) ud(valve) Ad(valve)K Ppipe 1 2 K Pd(valve) 1 2 (17)----+-U = +-U_ 1 2 pipe K- 1 2 d(valve) ( 1S)K Ppipe Pd(valve)

P p ip . / P;ipe = P d(valve) p;(valve) (19)where upipe =0, for th e valves ar e closed. And Pd(valveJ is assumed to be equal to Pd(port)in this calculation. An d in th e discrimination for the stability of the solution,Courant-Friedrichs- Lewy (CFL) is adopted, shown as follows.

t:u >


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As a time step Lit is decided in advance, L1X is decided to satisfy this condition. And thecalculations are performed by using th e characteristic differential equations and eachboundary condition.Calculation of Leakage at side clearance between cylinder and piston

In consideration of the balance of pressure that a fluid flow through the minuteclearance between the cylinder and the piston is estimated. The leakage into thecylinder is given by th e following equation.(21)

Thus, the leakage becomes:

Here, u is defined by:6 3Q=fa (uH)dr =Ho )/(6f1L)(Pcy1 -F.) (22)

(23)

CALCULATED RESULTS AND DISCUSSIONThe overall characteristics of the Table 1. Specifications and initial conditionscompressor has been calculated an dstudied to evaluate the performanceusing the simulation models. Thenon -lubrica ted four-stage reciprocatingcompressor is used for verification.Table 1 shows th e specifications of thecompressor and th e initial conditionsfor the characteristic calculation, inwhich five types of working fluids,namely Nitrogen, Carbon Dioxide,

Argon, Helium and Air are applied.Th e characteristics are comparedkeeping th e discharge pressure of thefinal stage between 10 - 30 MPa atvarious compressor rotating speeds.Pressure Traces a t each Stage

Figures 7 through 10 show th ecalculation results of the pressures inth e first through fourth cylinders an dof th e discharge pressures under the

Input DataFirst Sta2eCylinder diameterSuction port diameter X p o r t ~ numberDischarge port diameter Xports numberSecond StageCylinder diameterSuction port diameter X ports numberDischarge port diameterThird StageCylinder diameter Suction port diameter Xports numberDischarge port diameterFourth StageCylinder diameterSuction port diameterDischarge port diameterStrokeFluidRotating speedSuction pressureDischarge pressure

Reference Value0.080m0.008mX60.008mX40.033m0.008mX40.008m

0.022m0.008mX20.008m0.013m0.008m0.008m0.016mNz/C02/Ar/He/Air900-2400min 1O.lSMPal0 .0-30.0MPa

rotating speed of 1800 min 1. Available results of basic experiments performed usingNitrogen as the working fluid are added to these figures. The calculation results aredescribed in the following.

At the second through fourth stage, th e displacement of th e suction valvefluctuates three or four times. And at the first stage, there is hardly fluctuationsat the displacement of th e suction valve. The Discharge pressure fluctuates two or three times with the movement of thedischarge valve at each stage, in which the figures show relatively good conformitybetween the calculation and the experiment results.



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Therefore, th e development of 3-D simulation model that is needed to perform thecalculation in cases where multiple valves are installed will be conducted in the future.However, it can be concluded that th e simulation program enables the calculation of thepressure balance, the evaluation of th e performance characteristics and efficiency of thecompressor.

'Ci., ~ e x p e r i D ; e n t J'1ff ~ l c u l a h o n ~ . . c ' C O - o e.!1>P..o...O OL___________________________________ _JiFI 00JS Q 0 L__ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _DL____ _ _ _ _ __,.K:

0 - - ~ - _ _ j o., 01DC 10 me 1t : 1DCl ! l ~ l0 rn Cr.mk angle phaseFigure 7. Phenomena at first stage

ID K:______

0~ ~ ; HXr-V"---cc:'It:c::,-------------=1DC=---'10:C:\ 1 \ /\!!"~ ' 3 L ~ - 1 ::115 '-------------------------------------'om Cr.mk angle phase

Figure 9. Phenomena at third stage

s . - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - .'0 u --experiment5 - -u l l cu la t i onV I ~ ' C a " O e g >P.. l======='======'o...Q

0 ' - - - - - - - - : : - c ~ ~ _ L _ _ _ _ _ _ _ j ~ ~ I D C ' I t : 1DC 1 0 ~ E ~ E ~ - 2 E]-gt.s0 rn Cr.mk angle phaseFigure 8. Phenomena at second stage

1DC 10 IDC'It:

~ ~ ; I \ f \J\J\J 1~ ' 3 . J: : ~ 1 . 5 L_________________________________ _0 rn Crank angle phaseFigure 10. Phenomena at fourth stage



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The pressure in the connecting pipe isshown in Figure 11, which shows that a phasela g occurs periodically. The cause may dueto th e New Mark {3 method used to solve th eequation of motion. However, th e amplitudeof the pressure is well in agreement with theexperiment results.Effect of Discharge Pressure

The construction element affectedmostly by th e change of th e dischargepressure is the discharge valve section at eachstage. Figure 12 shows the time-series ofdischarge valve lift . There is a tendencythat th e higher the discharge pressure rises,the later th e discharge valve starts to open.This is a phenomenon common to any stage,and the tendency at th e first and secondstages is less than at th e third and fourthstages. The reason is considered that the firstand second stages are affected by th e suctionpressure of th e compressor more easily thanby th e change of the discharge pressure at th eforth stage.Influence of Working Fluids

The calculated results obtained from th esimulation program with Nitrogen, CarbonDioxide, Argon, Helium, and Air as workingfluid is shown in Figure 13. Since i t isassumed that th e compression condition inthis simulation is polytropic compression, th epressure and temperature in each cylinder areaffected by specific heat ratio only.Therefore, th e result show that monoatomicmolecule gas such as Argon an d Helium,which have higher specific heat ratios thanothers, indicates the pressure andtemperature increases 5% an d 6% in eachcylinder respectively. The result ofcalculations show that Helium, having a lowmolecular weight and a high specific heatratio, is th e lowest in flow rate. However, itis only approximately 10% lower thannitrogen, which means sufficient flowcharacteristics. Therefore, it has beenclarified that this compressor has a structurewhich assures sufficient flow rate in caseswhere various types of working fluids areapplied.Improvement in Performance

Based on the calculation results fromFifteenth International Compressor Engineering Conference atPurdue University, West Lafayette, IN, USA- July 25-28, 2000

1-2 Stage Pipe ----experiment--calculation

........., -.2-3 Stage Pipe ................. experiment

--calculation

Crank angle phaseFigure 11. Pressure in connecting pipe

1.2 First Stage"(;""ss0

-----Pressure in Last Stage: lOMPa--Pressure in Last Stage : 20MPa- -P ressu re in Last Stage : 30MPa

-----Pressure in Last Stage: lOMPa- -Pressure i n Last Stage : 20MPa-- Pressure in Last Stage : 30MPa

Crank angle phaseFigure 12. Discharge valve open dynamics5.0.--------------------,

4.5".p:i0

4. 0

- - -+- N2--.-- C02..... A rHeAir

Pressure in Last Stage MPaFigure 13. Gas flow rate o f thevarious workin!! fluids

111


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the simulation model, the improvement of intake efficiency at the suction system isstudied. The calculation is performed by changing the piping length of th e suctionsystem an d suction port diameter focusing on the mass flow rate through each of th emultiple suction ports, which are provided in the suction system. From th e calculatedresult for th e suction system, the specification in which the ratio of th e piping length tothe suction port diameter is kept almost equal has been proposed. The suction systemis illustrated in Figure 14, and the calculated result is shown in Figure 14. Theimproved specification is found to allow the mass flow rate to be almost equal incomparison with the ordinary specification showing uneven mass flow rate in each ofthe suction ports, and the higher thermal efficiency compressor has been developedusing these results.

Suction Port

Figure 14. Suction system

l . O E - 0 3 , - - - ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

. --+-Port3....... Port6- - - -Por t85 . 0 E - 0 4 r - - ~ ~ - - " . . . . - ; - ~ ~ ~ ~ ~ ~ ~ ~ ~ - - - - j \. ...,,' .., ........

,,

Standard Value: 4.7E-04.... ___ .. ___ _ -----------

' '--,--...__________ ..O.OE+OO ~ ~ ~ - - - = - o . - = - o l = - - ~ ~ - 0 ~ . 0 - 2 ~ ~ ~ 0 ~ . - 0 3 ~ _ j Distance( rom Port to Valve) mm

Figure 15. Mass flux of suction port

CONCLUSIONSThe original numerical simulation program proposed here gives th e followingconclusions.

1. This simulation model could conduct the investigation on th e performancecharacteristics of the compressor, and is effective for th e development ofcompressors suitable for wide applications.

2. For Nitrogen, Carbon Dioxide, Argon, Helium, and Air of which properties areemployed in this simulation model, th e sufficient performance characteristics ofthe compressor can be confirmed from the calculated results.3. The high efficiency has been realized by equalizing the ratio of the piping lengthof th e suction system to th e suction port diameter in each of the multiple suctionports.

REFERENCES[1] H.NISHIKAWA,T.NISHIKAWA, "Development of the Non-Lubricated For-Stage

Compressor Compressing up to 24.52MPa", Proceedings of th e internationalCompressor Engineering Conference, Vol.1, pp.183-188(1998)[2] Werner Soedel, "Introduction to Computer Simulation of Positive DisplacementType Compressor" ,Purdue Unv(1972)[3] R.NONAKA,Y.WATABE,A.SUDA, "Performance Simulation for Improvement ofEnergy Efficiency on Rotary Compressor for Room Air Conditioners", JSST,pp.175-180(1994)


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A Study for Improvement on High Pressure Multistage Reciprocating