LECTUREFOUR-4Numerical Process Modeling of MarineEnginesLEARNINGOBJECTIVES:To define and calculate sound speed and Mach number.To define nozzles and diffusers and their flowregime:To understand the effect of cross-section variation on Machnumber:To understand the effect of back pressureTo calculatemass flowratefor subsonicand supersonicflowthrough convergingnozzleTo decide turbo speed at a certain operating point·.To decide turbine and compressor isentropic efficiencyTodecide intake (scavenging)pressure and temperature at a·certainoperatingpointTo determine exhaust pressure and temperature at a certainoperating pointTo comply with turbine outlet condition requirements if specifiedor determinethose conditions if not specified21
1 LECTURE FOUR – 4 Numerical Process Modeling of Marine Engines 1 LEARNING OBJECTIVES • To define and calculate sound speed and Mach number • To define nozzles and diffusers and their flow regime • To understand the effect of cross-section variation on Mach number • To understand the effect of back pressure • To calculate mass flow rate for subsonic and supersonic flow through converging nozzle • To decide turbo speed at a certain operating point • To decide turbine and compressor isentropic efficiency • To decide intake (scavenging) pressure and temperature at a certain operating point • To determine exhaust pressure and temperature at a certain operating point • To comply with turbine outlet condition requirements if specified or determine those conditions if not specified 2
FundamentalsofCompressibleIsentropicFlowforengine-turbomatchingNik.XirosSound wavesSound waves areessential inunderstanding compressible flows.-Asoundwaveisa small pressuredisturbancethatpropagates throughagas,liquid,orsolidatavelocitythatdependsonthepropertiesofthemedium.The velocityof sound is an intensivepropertywhosevaluedepends onthestate of the medium through which sound propagates;knowing its value isveryimportantinthestudyofcompressibleflows42
2 Fundamentals of Compressible Isentropic Flow for engine-turbo matching Nik. Xiros 3 Sound waves Sound waves are essential in understanding compressible flows. A sound wave is a small pressure disturbance that propagates through a gas, liquid, or solid at a velocity that depends on the properties of the medium. The velocity of sound is an intensive property whose value depends on the state of the medium through which sound propagates; knowing its value is very important in the study of compressible flows. 4
Sound wavesPROPAGATIONOFSOUNDWAVES-ObserveronwavePistonUndisturbed fluid4Vc-vSp+App+ApV=0p+pp+4pp.T.p2T+A7T+A7p.p.TStationaryControl volune for anobservermovingwithobserverthe wave(b)(a)a)Propagationthroughquiescentfluidas experiencedby stationaryobserverb)PropagationaccordingtoobserveratrestrelativelytothewaveSound wavesThevelocityof sound is an intensivepropertywhosevaluedepends onthestateofthemediumthroughwhichsoundpropagates.Specialcase:anidealgaswithconstantspecificheats.=Vypv=RT:MachnumberM-Lc63
3 Sound waves PROPAGATION OF SOUND WAVES a) Propagation through quiescent fluid as experienced by stationary observer b) Propagation according to observer at rest relatively to the wave 5 Sound waves The velocity of sound is an intensive property whose value depends on the state of the medium through which sound propagates. Special case: an ideal gas with constant specific heats. Mach number 6
Isentropiccompressibleflow.Conservation of energyU=Q-W+m.h.+-m+g+gzmhour +2=W-0+[(-h)++g(2-2)1Stagnation-V-VW=O+mlh.-V22→h,=h+2W-O=0V.-V=0Isentropic compressibleflow equationswc--{-():RatiosTT,P(P2)?Differentialrelationshipsh+- -l- dh--.d=,al--a= --a2cp=pc.=pdp-pp-dp=0=dppYpYRT"CPVr=mRT=p=pRT=E-PRTdr=ct=+=0=dp=cpdl7-1p-ITdp=c,pdT=-pVdvdp=-Vdv"-pmdydp=V2c24
4 Isentropic compressible flow Conservation of energy Stagnation 7 Isentropic compressible flow equations Ratios Differential relationships 8
IsentropiccompressibleflowequationsEffectofcross-sectionvariation-dpdadv=0PAVdAdy=(M°-1)=dp=-pMaVAV9Isentropic compressibleflowThe differential equation derived above shows the variation of velocity with cross-sectional area. Thefollowingfour cases canbeidentifiedCase I: Subsonic (M 1) nozzle, the duct converges in the direction of flow - Velocity increases;enthalpy,pressure and density decrease.Case 2: Supersonic (M > 1) nozzle, the duct diverges in the direction of flow - Velocity inereases;enthalpy,pressure and density decrease.Case 3: Supersonic (M >1) diffuser, the duct converges in the direction of flow -Velocity decreases.enthalpy,pressure and density increase.Case 4: Subsonic (MI) diffuser, the duct diverges in the direction of flow Velocity decreasesenthalpy, pressure and density increase.105
5 Isentropic compressible flow equations Effect of cross-section variation 9 Isentropic compressible flow 10
Isentropiccompressibleflow:backpressureValve to adjustback pressurePo.T.ExhaustregRIsentropic compressibleflow:Subsoniccase.Velocity-/2c,(T-Tr--(e)MassflowratemRTVART.:RT.*4Ep=iVRT12
6 Isentropic compressible flow: back pressure 11 Isentropic compressible flow: Subsonic case Velocity Mass flow rate 12
Isentropiccompressibleflow:Soniccase- Critical pressure and temperature名=h+"#-1+=1+1F==0+2e,T2RT2T--1+号M2Te()产-(*号m学B()e-213Isentropic compressibleflow:Sonic caseCriticalmassflowrate-(p)pNRT-ARm=m=pAc=ART*RT然=m=A62+RT11147
7 Isentropic compressible flow: Sonic case Critical pressure and temperature 13 Isentropic compressible flow: Sonic case Critical mass flow rate 14
CompressibleflowappliedtoturbochargingHowisthetheoryof IsentropicCompressibleFlowrelatedtoanalysisanddesign of turbosupercharging systems for marine engines?ExhaustFuel flowIntercoolerReceiverAirflowExhaustflowEngineScavengingTurbochargerReceiverCyindersTurbineTurbochargerCompressor15Engine-turbochargermatchingNik. Xiros168
8 Compressible flow applied to turbocharging How is the theory of Isentropic Compressible Flow related to analysis and design of turbosupercharging systems for marine engines? 15 Engine-turbocharger matching Nik. Xiros 16
Preparation&prerequisites fromengineanalysisThe following data are neededbefore embarking on turbo matching:(1)Enginegeometryandconfiguration(brakepower,nominalrpm,strokenumber,cylindernumbergeometry,valve/portoverlapetc.)(2) Fuel consumption and required A/F ratio(3)Indicatordiagramorresidual chemical energyoffuel asproportion intheexhaustgas;for 4-strokes,heat transfer fromcylinder walls to aircharge duringintake(4)Engineroomambientatmosphericconditions(airpressure&temperature)(5)Turbineoutletconditionrequirements, ifany17Turbochargergivens(1) Air compressor performance info commonly in formof map(s)(2)Aircompressorgeometrical data(effectiveareaetc.)(3)Gasturbinegeometryandconfigurationdata:flowcorrectionparameternozzleandwheeleffectiveareas,resistancecoefficientetc.189
9 The following data are needed before embarking on turbo matching: (1) Engine geometry and configuration (brake power, nominal rpm, stroke number, cylinder number geometry, valve/port overlap etc.) (2) Fuel consumption and required A/F ratio (3) Indicator diagram or residual chemical energy of fuel as proportion in the exhaust gas; for 4-strokes, heat transfer from cylinder walls to air charge during intake (4) Engine room ambient atmospheric conditions (air pressure & temperature) (5) Turbine outlet condition requirements, if any Preparation & prerequisites from engine analysis 17 (1) Air compressor performance info commonly in form of map(s) (2) Air compressor geometrical data (effective area etc.) (3) Gas turbine geometry and configuration data: flow correction parameter, nozzle and wheel effective areas, resistance coefficient etc. Turbocharger givens 18
StepO:EngineairrequirementsCalculaterflowrequirementsandmasssairsbaseddonbrakepowerefficiency/performancedataaswellasfuel propertiesIf the indicator diagram isprovided instead ofthe directvalueof Ca,calculatetheheatrejectedby the cycle, itwill be neededduring calculation ofexhaustgasspecificenthalpy19Step1:Decideturbo speed and compressorisentropicefficiencyUsing the air mass flow rate calculated in the previous stage use thecompressormapsprovidedto:1)Choose turbocharger shaft speedNrc2)Choosecompressorisentropicefficiency,licGUIDELINESMaximizing efficiency is always good provided the air mass flow raterequirement is met. In general, if higher efficiency is chosen, the speed willneed to be increased to meet the same mass flow rate value. An efficiencyvalue above 0.75 is generally achievable and good, provided that the speed isnot pushed to the machinery's limit aka more than 90-95% of the maximumadmissible.Marine engine turbochargers usually run on a constant efficiency curve (e.g.the 80% line). Then the mass flow rate and compression (pressure) ratio isadjusted to match the engine's operating point by changing the speed of theturbo.2010
10 Calculate mass air flow requirements based on brake power and efficiency/performance data as well as fuel properties If the indicator diagram is provided instead of the direct value of ζa , calculate the heat rejected by the cycle, it will be needed during calculation of exhaust gas specific enthalpy Step 0: Engine air requirements 19 Using the air mass flow rate calculated in the previous stage use the compressor maps provided to: 1) Choose turbocharger shaft speed NTC. 2) Choose compressor isentropic efficiency, ηiC. GUIDELINES: Maximizing efficiency is always good provided the air mass flow rate requirement is met. In general, if higher efficiency is chosen, the speed will need to be increased to meet the same mass flow rate value. An efficiency value above 0.75 is generally achievable and good, provided that the speed is not pushed to the machinery’s limit aka more than 90-95% of the maximum admissible. Marine engine turbochargers usually run on a constant efficiency curve (e.g. the 80% line). Then the mass flow rate and compression (pressure) ratio is adjusted to match the engine’s operating point by changing the speed of the turbo. Step 1: Decide turbo speed and compressor isentropic efficiency 20