Screw Compressor Basics

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Outlook to screw compressors today, featuring design basics, thermodynamics and testing evaluation of dry and oil-flooded rotor technology.

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Screw Compressor Modelling, Design and UseScrew Compressor BasicsProfessor N. StosicChair in Positive Displacement Compressor TechnologyCentre forPositive Displacement Compressor Technology City University London, U.K.Screw Compressor TodayHighly competitive market, speciallyin air compression and refrigerationContinuous improvement:more compact, efficient and cost effective compressorsNew rotor generation, rotors optimizedfor certain compressor duty, specializeddesign Scope for innovation, improvement and developmentINTRODUCTIONINTRODUCTIONBasicsView from Front and TopView from Bottom and RearTop and front: AdmissionBottom: Change of volumeBottom and Rear: DischargeINTRODUCTIONBasicsINTRODUCTIONSwedish company SRM, pioneer and leaderScrew compressor profiles, Symmetric, Asymmetric, D and GScrew compressor designScrew compressor technologyLicence system left many screw compressormanufacturers at margins of research anddevelopmentINTRODUCTIONMany companies started their own developmentGardner Denver, Atlas Copco, Compair, Kaeser, GHHTrane, Ingersol-Rand, Hitachi, Fu Sheng, Hanbel, Refcomp HolroydMany more or less successful rotor profilesMany more or less successful screw compressor designsNeed exists to concentrate efforts in R&D Centre for Positive Displacement Compressor TechnologyImproved methods of analysisExperimental validationDesign of critical componentsComplete machine designProduct developmentTraining in machine designINTRODUCTIONMethods AppliedAdvanced Computerized design toolsMachine process modelling 2-D and 3-D Computational Fluid DynamicsModern experimental techniqueComputerized data acquisitionUsersRenown and new companies, large and small manufacturers in the U.K and abroadINTRODUCTIONSCREW COMPRRESSOR GEOMETRYBefore modelling the physical process, the rotor lobe profiles must be defined together with the remaining parameters with which the rotor and housing geometry can be fully specified. Rotor profile: x and y coordinates, pressure angleHelix/lead angle, rotor lengthInterlobe, end and radial clearanceSuction/discharge portsSCREW COMPRESSOR GEOMETRYGeneral case: non-parallel and non-intersecting( ) [ ] [ ]1 1 1 1 1 01 01 01 01 1, , , cos sin , sin cos , t x y z x y x y p + r r1]1

+1]1

0 , cos sin , sin cos 0 , ,01 01 01 01 1 1 1 tytxtytxtytxtr[ ] 0 , , 0 , ,01 011 1 1x yy x 1]1

rGiven profileSCREW COMPRESSOR GEOMETRYMeshing conditionMeshed profileGeneral case: non-parallel and non-intersecting( ) [ ] [ ][ ]2 2 2 2 2 1 1 1 1 102 02 02 02 2, , , , , cos sin , sin coscos sin , sin cos ,t x y z x C y z y zx y x y p + +r r[ ] [ ]( ) ( )22 2 2 02 02 02 02 21 1 2 1 2 1, , sin cos , cos sin ,sin cos , sin cos , cos siny x p x y x y pp y p x C p x C + + 1 ]r1 1 1 1 1 20t t _ _ , ,r r r r r r( ) ( )1 1 1 11 1 2 1 1 1 1 2cot cot 0x y y xC x p p x y p p p Ct t t t _ 1 + + + + 1 ] 1 , ]SCREW COMPRESSOR GEOMETRYGeneral case: non-parallel and non-intersectingcorresponds to the rotor hobbing tool relationSpecial cases:p2=0, rotor - plate milling tool, grinding tool relation=0, screw compressor rotors SCREW COMPRESSOR GEOMETRY0101 0101sin cos 0dy C Cky kxdx i i _ + + ,02 01 0102 01 01cos sin cossin cos sinx x k y k Ciy x k y k Ci + +Meshing conditionRotor profile, =0, i=p2/p1, k=1-1/i Meshed profileRack profile0 01 010 01 01 1cos sinsin cosrrx x yy x y r + Numerical solution of the meshing conditionTask: to find for a zero function Simple iteration method:Fast and reliable, but valid only for certain functionAdditional complicationIn certain areas two or more are the zero functionOnly one is valid, additional values found by half interval method SCREW COMPRESSOR GEOMETRYDemonstrator profileN ROTOR PROFILE- Rack generation procedure - Straight line on the rack - involute rotor contact- Small torque transmitted- Short sealing line- Large displacement- Strong gate rotor, SCREW COMPRESSOR GEOMETRYSCREW COMPRRESSOR THERMODYNAMICSDifferential approach:Set of differential equations solved simultaneouslyEquations of continuity, momentum and energyPreintegrated equations inadequate and inaccurate if high leakage rate and heat transfer is involved in in out outdU dVm h m h Q pd d + ! !in outdmm md ! !2 22 12212lnl l l g gp pm w A Apap _+ ,!Internal EnergyContinuityLeakage Flow, , in in suc suc l g l g oil oilm h m h m h m h + + ! ! ! !, , out out dis dis l l l lm h m h m h +! ! !, in suc l g oilm m m m + +! ! ! !, out dis l lm m m + ! ! ! m wA !SCREW COMPRESSOR THERMODYNAMICSMomentum202ll lgw dp dxw dw fD + + SCREW COMPRESSOR THERMODYNAMICSIdeal Gas( )1 u RTT pR v Real gasp=f1(T,v) u=f2(T,v)Wet vapour( ) ( )1 1f g f gu x u xu v x v xv + +( ), ( ), ( ), ,VU m V vm ( )o o oiloiloil oilh A T TdTd m c ,1oil poilT kTTk+6oil oil S oilo o om c d ckh A h ( ) ( ),oilU mu mu +Oil injectionNumerical solution, Runge-Kutta IV order solver ( )oilU mcTumSCREW COMPRESSOR THERMODYNAMICSCompressor integral parametersin outm m m 1/ 60 m mz n !060 / V m !( )1 2 160n ntF F Lnzm + !vtmm !!indcycleW Vdp 160indindW z nP sindcycleVW dpmt at aind indW WW W ( )21 2 11ln1t apW RT W R T Tp sin dPPV!SCREW COMPRESSOR THERMODYNAMICSCalculation of pressure loads On compressor rotorsRadial forces( )( )Bx B AABy B AAR p dy p y yR p dx p x x Rotor torque( )2 2 2 20.5B BB A B AA AT p xdx p ydy p x x y y + + SCREW COMPRESSOR THERMODYNAMICSBearing reactions androtor deflections22d MEI dzOptimization variables and target functionSingle stage:Rotor variables:r0Female rotor addendumr1Male rotor lobe radiusr2Male rotor tip radiusr3Female rotor tip radiusCompressor variables:Built-in volume ratioOperation variables:Shaft speedOil flowInjection positionOil temperature9 VariablesMultistage:9 Variables x Number of stages+ Interstage pressuresTarget function:Specific power combined with compressor priceF=w1L+w2CSCREW COMPRESSOR OPTIMIZATIONBox constrained simplex method for efficient and reliable multivariable optimization1 2( , ,..., )nf x x x, 1,i i ig x h i n , 1,i i ig y h i n m + yn+1,,ym1 2F w L w C +1 21 2( ) max ( ), ( ),..., ( )( ) min ( ), ( ),..., ( )h kg kf x f x f x f xf x f x f x f x11,1ki i ljix x x xk ( )r lx x x x + ( ) ( )0.5 (1 ) ( )(1 )(2 1)r new r old h hx x cx c x x x c R 1 + + + ]11r rrn knrr rncn k+ _ + ,Dry Oil-Flooded Refrig.r0[mm] 2.62 0.74 0.83r1[mm] 19.9 17.8 19.3r2[mm] 6.9 5.3 4.5r3[mm] 11.2 5.5 5.2Built-in volume ratio 1.83 4.1 3.7Rotor speed [rpm] 7560 3690 3570Oil flow [lit/min] - 12 8Injection position [o] - 65 61Oil temperature [o] - 33 32Oil FreeOil FloodedRefrigerationEXAMPLE OF CALCULATION5-6-128 mm Oil-Flooded Air Compressor7 m3/min, max 10 m3/min at 8 bar (abs)5-14 bar (abs), max 15 bar (max)EXAMPLES OF CALCULATION5/6-128 mm, L/D 1.65Displacement 1.56 l/revInterlobe sealing line 0.13 mBlow-hole area 1.85 mm2Rotors optimized foroil flooded operatedair compressionEXAMPLES OF CALCULATIONCAD Interface: Compressor portsEXAMPLES OF CALCULATIONExperimental verification of the modelEXAMPLES OF CALCULATIONCompressor in the test bedEXAMPLES OF CALCULATIONComparison of thecalculated and test results Flow-PowerEXAMPLES OF CALCULATIONEXAMPLES OF 3-D CFD CALCULATIONMajority of design problems can be solved by the one-dimensional approach, some of them require thetwo dimensional calculation, however, there are situations where 3-D CFD must be applied Such areOil flow distribution,Fluid-Solid Interaction Grid topology- polyhedral- O - grid- H - grid- C - grid Cell shapeGrid generation Grid generation --11Grid generation - 2- Male rotor - Female rotor- Suction port - Discharge port- Suction and discharge receivers- End clearancesRotor connections, clearances, leakage paths Grid topology strongly affects accuracy, efficiency and ease of calculation Full structured block generated hexahedral 3D-O mesh Screw compressor sub-domains:Automatic discretization iscretization process: process:- The rack generating procedure- - Rack Rack - - a rotor with an infinite radius a rotor with an infinite radius- - Divides working domain in two parts Divides working domain in two parts male and female rotor, male and female rotor,Screw Compressor FSI calculations Screw Compressor FSI calculations Comet Comet Mathematical model for screw compressor is based on conservation Mathematical model for screw compressor is based on conservation laws laws of continuity, momentum, energy, concentration and space: of continuity, momentum, energy, concentration and space:s( ) 0V SddV ddt + v v ss( ) bV S S VddV d d dVdt + + v v v v s T s fss( ) +( grad : grad ) phV S ShV V S VdhdV h d ddtds dV p dV d pdVdt + + + + v v s = q sv S v v ss( )o oo o c cV S S Vdc dV c d d S dVdt +