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