Taking up a characteristic of a centrifugal compressor with an adjustable inlet guide grid University Duisburg-Essen Faculty for engineering sciences Department of mechanical engineering Turbomachinery Prof. Dr.-Ing. F.-K. Benra Table of contents 1 Introduction2 2 Theoretical bases3 2.1 Velocity-triangle of the compressor stage..................................................................... 3 2.2 Compressionwork, internal efficiency .......................................................................... 3 3 Characteristic curves und controlling of compressors4 3.1 Theoretical and measured characteristic curves............................................................ 43.2 Regulation ..................................................................................................................... 5 3.2.1 Regulation by changing the rpm ....................................................................... 6 3.2.2 Suction throttle regulation................................................................................. 6 3.2.3 Regulation by blowing off or Umblasen?? ....................................................... 7 3.2.4 Regulation by adjustable installations within the compressor .......................... 7 4 Description of the plant9 4.1 General operational data................................................................................................ 9 4.2 Components of the plant ............................................................................................... 9 5 Measuring instruments11 5.1 Measuring point plan................................................................................................... 11 5.2 Measuring methods and instruments......................................................................... 12 5.2.1 Temperature measurement .............................................................................. 12 5.2.2 Volume flow rate measurement ...................................................................... 12 5.2.3 Pressure measurement ..................................................................................... 12 5.2.4 Speed measurement......................................................................................... 13 6 Investigational procedures 7 Interpretation of test results 15 7.1 Evaluation of the measured values under test conditions ........................................... 15 7.2 Conversion on reference conditions............................................................................ 16 1 List of used symbols SymbolMeaningUnit AdCross section of the orifice openingm2 ADTubing cross sectionm2 A*Closest flow passage aream2 cAbsolute speedm/s cpSpecific heat capacitykJ/Kg K gGravitationm/s2 hEnthalpykJ/kg lHeight of the liquid columnm mAperture ratio - MMach number - nNumber of revolutionsmin-1 nPolytropic exponent- pPressurebar PDrive powerkW RGas constantkJ/kg K TTemperatureK uCircumferential speedm/s V&Volume flow ratem3/s & Relative speedm/s ySpecific flow workJ/kg zgeodetic heightm Flow coefficient- Expansion number- Isentropic exponent- Efficiency- Densitykg/m3 Pressure ratio- Vapor% Indices dynDynamic portion mMeridional component, mechanical MotDrive refReference condition redReduced tTotal size uCircumferential component 2 1 Introduction InTurbomachineriesthecontinuouscurrentofthefluidgetsenergyextractedwhichis suppliedtotheshaftasmechanicalenergy(Turbopowermachine).Otherwisemechanical energy is supplied by the shaft to the rotor which submits it to the fluid as pressure- or kinetic energy (Turboworkmachine). Thecentrifugal-compressorisaTurboworkmachineinwhichthepressure-heighteningis achievedbyconvertingofkineticenergy.Theprocessofcompressionhappensinradial streamed rotors and stators. Fig. 1.1 shows the areas in which several compressor-types are used. You can see that radial-compressors are used for volume flow rates from 1500 to 400000 m3/h and for pressures till 500bars.Independenceofflowrateandpressure-ratiotheyarecarriedoutinseveral arrangements, e.g. singlestaged - multistaged, singleflow - multiflow. The purpose of centrifugal-compressors in modern techniques is varied. They are used for Compressed-air plant Charging ofinternal combustion engineAs compressors in gasturbineplants As an so called process-compressor for unit-operations As cooling fan Fig. 1.1: Operative ranges of several compressor-types Theyareusedforoperativeranges,whichmeansforseveralcombinationsofratingslike pressure-ratio,massflow,efficiencyetcetera. The relation between these parameters canbe displayedinacharacteristicdiagram.Inthisexperimentitisyourtasktodeterminea characteristicofacentrifugal-compressorandcompareitwiththeonegivenbythe manufacturer. 3 2 Theoretical bases 2.1 Velocity-triangle of the compressor stage The task of a compressor stage exists in the continuous compression of the incoming fluid.. Fig. 2.1: Velocity-triangle at the rotor Thestreamingfluidreachestheentryofthebladedwheelwithanabsolutespeedc1.The currentcanbewithorwithoutaspin.Youcanadjustthisbythediffuserplate(stator).The currentisinfluencedowingtotherotationofthebladedwheel.Thefluidstreamsintothe channel with a relative speed which depends on the vectors of the velocity-triangle. (Pic. 2.1) The energy conversion in a rotary grid of turbo machinery is described with the help of the kinematic main equation. 1.Shape2 2 1 t uMh a u c u cm1 u = = = &2.Shape2 2 2 2 22 1 2 1 2 12 2 2tc c u uh a2 = + + = 2.2 Compressionwork, internal efficiency

The work which is converted in turbo machinery corresponds to within the condition of an adiabatic change of state the complete enthalpy difference between the plane in front of the firstbladedwheelandbehindthelastone.(Thisderivesfromthe1.Axiomforstationary flow-processes) By setting ahead an isentropic change of state and looking upon the fluid as an ideal gas, the following term derives: 1211( ) 11tt s ttph RTp | | = | \ . (How to derive this should be known by every student!) At a change of state, the change of the total enthalpy is given by: ( )1,2 2 1 t p th c T T = t 4 The ratio between isentropic and real difference of the total enthalpy is equal to the definition of the total isentropic efficiency: ( )( ) ( )( )1,2 2 1t ts stVst p th hh c T T = = t or ( )( )12112 11ttttVst tpTpT T | | | \ . = Finally we get the term for the necessary output to run the machine: 1,2 1,2 t tm mm h V hP = =&& 3 Characteristic curves und controlling of compressors 3.1 Theoretical and measured characteristic curves The theoretical curve of a compressor can be derived from the velocity triangles. A spin-free inflowistobepresent.Furthermorewetaketheassumptionofequalcm (whichis characterizing for the flow rate) at entry and exit. Fig. 3.1 shows the dependence of the volume flow to the velocity triangles directly. The angle of flow 2 is decisive. Fig. 3.1: Velocity triangle at exit of the rotor The straight line yth (Pic. 3.2), which is derived by this, is only correct for an infinite number of blades, which means it is a theoretical straight line. If you look upon a limited number of blades the lift of delivery is reduced about yz. The friction losses yr cause a further sinking of the characteristic curve, which becomes the larger,thehighertheflowrateis.Thecollisionlosses,whichresultfromanunfavourable incidentflowoftheprofilenose,areconsideredbyyst.Thecollisionlossesbecomethe largerthefurtherawaybythedesignpointthemachineisoperated.Finallytheclearance losses cause a further shift of the characteristic around V, which causes an additional waste oftheefficiency.Theexecutionofthisviewfordifferentnumbersofrevolutionsmakes predicting the characteristic diagram for a machine possible. In a characteristic diagram pressure ratio, efficiency or enthalpy characteristics are laid above massflow,volumefloworflowratecharacteristics.Forthis,theentrancesizesmustbekept constant.Acharacteristicshowsthedependenceforconstantnumberofrevolutions, mentioned above. 5 Fig. 3.2: Theoretical compressor characteristic The operating point of a machine is given by the consumer. As you can see in Fig 3.2, its the intersection between the compressor and plant characteristic. For practice, a stable instrument range of a compressor is from great importance. Fig. 3.3: Compressor- and Plant-characteristics Thestableworkareaismarkedatsmallervolumeflowratesbythepumpingborderandat larger volume flow rates by the sip border. 3.2 Regulation The regulation of turbo machinery divides itself into two main areas: I.The static controller action: Here the possible regulatory interventions and their economy are examined to connection with the machine. II.The dynamic controller action: Thisfieldcoversthetemporalsequenceofthecontrolprocedure.Ofspecialmeaningare layout and reaction as well as the stability of the controlling system. The dynamic behaviour 6 ofthecompressorplantanditscomponents(Pipings,radiator,valves,etc...)atfastload changes has to be known. These changes result in the case of driving on and off as well as in the case of incidents (Breakdown of the electricity mains). If a fast switch-off takes place, the drain valve must open, in order to prevent the pumping of the compressor. Inthefollowingexample(Fig.3.4)thechangeoftheoperatingpointsispresentedasa function of the opening-time t of the valve. Fig. 3.4: Dynamic properties of a compressor at a fast switch off As you can see, the operating points for the times t=2s and t=1,6s for smaller volume flow rates - are beyond the stability range. To avoid a pumping of the compressor, a valve floating time t