1 Turbomachinery Centrifugal Compressors Class 13.

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Transcript of 1 Turbomachinery Centrifugal Compressors Class 13.

  • *TurbomachineryCentrifugal Compressors

    Class 13

  • *Centrifugal Compressor Design Geometry Rothalpy Impeller Design Considerations Eye Inducer Slip Diffuser Design Considerations Volute Design Considerations

  • *Centrifugal Compressor Components

  • *Centrifugal Compressor ComponentsCollector scroll and vanes may be replaced with vaneless diffuser

  • *Centrifugal Compressor ComponentsCentrifugal compressor= impeller+diffuser Geometrical Definitions

    Eye: L.E. of impellerImpeller: raises energy level of fluid by increasing radiusInducer: portion of impeller from eye to region where flow turns radialDiffuser: converts K.E. from impeller into P.E.. Adding vanes reduces size of diffuserScroll or volute: collects flow from diffuser and delivers to outlet

  • *Centrifugal Compressor DesignCompressors role is to produce high pressure flowHigh pressure is achieved by imparting kinetic energy to flow by impeller / rotor.Kinetic energy is converted to high pressure in diffuser / stator.As radius increases, pressure increases pressure rise in impeller passage pressure rise in diffuser passageDiffuser may have vanes, but stator passages must have increasing areaVolute cross-section area increases gradually to exit

  • *Centrifugal Compressor DesignIn class we defined "Rothalpy" for rotors:

    Since across the impeller I1=I2 then the change in swirl velocity U

    explains why static enthalpy rise is so large for centrifugal compared to single-stage axial compressorsIf no prewhirl Cu1=0

    See result shown later is Example 1

  • *

  • *Centrifugal Compressor Design: T.E.Blade TE shape for opt. performance Forward: against rotation Radial Backward: with rotation

  • *BackForwardStraight

  • Centrifugal Compressor Design: T.E.Radial T.E.Ideal no-slip viewIncreased Cr/Wr for same U does not change Cu or workT02/T01 unchanged with increased Cr*

  • Centrifugal Compressor Design: T.E.Backward T.E.Increased Cr/Wr for same U decreases Cu or workT02/T01 decreases with increased CrStable side of compressor map*

  • Centrifugal Compressor Design: T.E.Forward T.E.Increased Cr/Wr for same U increases Cu or workT02/T01 increases with increased CrUnstable side of compressor map*

  • *Centrifugal Compressor Design: T.E.Radial T.E.

  • *Centrifugal Compressor Design: T.E.Backswept Impellor Radial: dotted triangle Backswept: solid

    Same radial component, same mass flow

    Relative velocity increased, absolute decreased

    Increases efficiency, but reduces work absorbing capacity [Cw2 lower]

  • Centrifugal Compressor Design: T.E.

  • *Prewhirl [in the direction of rotation] added from added upstream guide vanesIn high PR compressors, may be necessary to provide prerotation to reduce high relative inlet velocity. Also reduces incidence / reduces twist lower bending stressesVane radial design impact on inducerFree vortex Cu 1/r: high incidence at low rh/rt designsForced vortex Cu rnCentrifugal Compressor Design: L.E.- IGV will allow untwisted impellor inlet- Untwist will reduce rotor root bending stresses

  • Centrifugal Compressor Design: TipTip Leakage IssuesFlow from pressure [+] to suction [-] side over tipFlow from downstream [+] to upstream [-]*

  • *Review: Axial Compressor SlipSlip: flow does not leave impeller at metal angle

    Carter's Rule:

    Blade turning & solidity are important

    Viscosity plays small role within low loss incidence range

    T.E. thickness & shape significant

  • *Centrifugal Compressor SlipSlip: flow does not leave impeller at metal angle [even for inviscid flow] due to less than perfect guidance from blade.If absolute flow enters impeller with no swirl, =0.If impeller has swirl (wheel speed) , relative to the impeller the flow has an angular velocity - called the relative eddy [from Helmholtz theorem].Effect of superimposing relative eddy and through flow at exit is one basis for concept of slip.Relative eddyRelative eddy with throughflow

  • Centrifugal Compressor Slip

  • *Axial Compressor Slip

  • *Axial Compressor Slip

  • *Centrifugal Compressor Slip"Slip" (Deviation) Reduces Swirl & Work

    Slip Factor

    Vs

  • *Centrifugal Compressor SlipSeveral Correlations for Centrifugal Impeller Slip Factor

    Weisner

    Stodola

    Stanitz

  • *Centrifugal Compressor DesignIn general, with possible prewhirl Cu10

    Introduce work done-input factor In turbines [work done] < 1, due to boundary layer effectsIn compressors [work input] > 1, need more power to account for boundary layer effects

  • *Centrifugal Compressor DesignImpeller Performance Effects:

  • *Centrifugal Compressor DesignSplitter impeller vaneReduce effect of slip by using splitter vane to reduce diffusionBackward sweep

  • *Centrifugal Compressor Design Calculate inlet blade angle at root and tip Calculate Mach number at eye tip Assume no whirl at inlet

    Axial velocity can be determined from continuity but density needs trail and error iteration

  • *Centrifugal Compressor DesignAssume no more iteration is needed

  • *Centrifugal Compressor Design

  • *Centrifugal Compressor DesignExample #2: Dixon 7.1A radial vaned centrifugal impeller is required to provide a supply of pressurized air to a furnace. The specification requires that the fan produce a p0 rise equal to 7.5 cm of water at a volumetric flow rate (Q) of 0.2 m3/s. The fan impeller is made from [Z=30] thin sheet metal vanes, the ratio of the passage width to exit height=2 and r=0.1.Assume ad=0.75, m=0.95, slip can be estimated from Stanitz correlationAssume R=287 J/(kg-C), p01=101.3 bar, T01=288KAssume

  • *Centrifugal Compressor Design1- Determine the impeller vane exit speed

    2- Determine the volumetric flow rateStannitz21.98

  • *Centrifugal Compressor Design2- Determine the volumetric flow rate contd

    3- Power required if mechanical efficiency is 0.95

    4- Determine specific speedNo swirl

  • *Axial vs. Radial Machines

  • *Diffuser Design: Sta. 23Rotation Effect on Diffuser Pressure Rise

    Rotation reduces boundary layer thickness and limits pressure rise in radial portion of impeller

    Johnston & Rothe varied area ratio & rotational speed in 2D diffuser test

    Rotated Diffuser with flow axis radial

  • *Centrifugal Compressor Design Example #3: Will work through design of each component separatelyKnow U2, slip, not p02, T02,

    VelDiag

    2982980000

    298298298298298298

    0

    298

    0

    298

    0

    298

    0

    298

    Cu2

    Vs

    U2

    W2

    C2

    b2*

    Wu2i

    Cr2

    Impeller Exit Velocity Diagram

    Homewrk12

    Centrifugal Compressor & Diffuser

    Given

    D1 hub3.00inR53.349ft.lbf/lbm/R

    D1 shroud6.00inCp0.24BTU/lbm/R

    D212.00inalpha 10.00degrees

    D3 diffuser20.52inback sweep30.00degrees

    N27,500RPMNo. blades32.00

    Flow3.50lbm/secb20.350in.

    Pt114.70psiaSlip FactorWeisner

    Tt1519.00Imp Eff90.00%Poly, T-T

    gamma1.40Diff Cp0.40

    Find

    a)Velocity diagram & flow properties at impeller inlet

    b)Velocity diagram & flow properties at impeller exit

    c)Velocity diagram & flow properties at diffuser exit

    d)Adiabatic total to static efficiency at rotor & diffuser

    e)Adiabatic total to total efficiency at rotor & diffuser

    Station 1Station 2 (Cont'd)

    A1 sq in21.2058Pr t-t3.8224

    Dm1 in4.5000Tr1.5306

    U1 ft/sec539.9612Eta - ad87.98%

    FPt0.2784

    guess M0.2929Pr t-s2.1851

    Calc M0.2930Eta - ad47.16%

    error-0.0000

    Tt/T1.0172Alpha275.4492

    Pt/P1.0614a21275.5646

    T510.2420M20.9308

    P13.8500

    C1 = Cx1324.3767Diffuser

    U1 = Wu1539.9612

    W1629.9035P341.7482

    Beta 159.0050Cu3672.0671

    Station 2

    Guess Al377.4467

    U21439.8966Cr3149.6501

    Slip Factor0.9177C3688.5269

    Vs118.4382T3754.9461

    A213.1947rho30.1493

    Poly Exp't0.3175Area 322.5629

    Guess Pt256.1893Flow3.5000

    Tt2794.3942Error-0.0000

    delta ho66.0946

    Cu21149.2347Po349.8952

    Wu2-290.6620Pr t-t3.3942

    Wu2i-172.2238Eta ad t-t0.7875

    Cr298.3004

    C1187.3177Pr t-s2.8400

    T677.0886Eta ad t-s0.6548

    P232.1208

    rho0.1280

    flow3.5000

    error-0.0000

    Rotor Discharge Velocity Daigram

    XY

    0298

    1440298

    2900

    0298

    2900

    118298

    2900

    290298

    2900

    1440298

    Homewrk12

    &R&DBAR

    Circumference - Degrees

    Density - lbm/ft^3

    Density vs CircumferenceVolute Mean Flow

    1

    &R&DBAR

    Ptv

    Psv

    Circumference - Degrees

    Pressure - psia

    Pressure vs CircumferenceVolute Mean Flow

  • *Centrifugal Compressor Design: Sta. 1

    VelDiag

    2982980000

    298298298298298298

    0

    298

    0

    298

    0

    298

    0

    298

    Cu2

    Vs

    U2

    W2

    C2

    b2*

    Wu2i

    Cr2

    Impeller Exit Velocity Diagram

    Homewrk12

    Centrifugal Compressor & Diffuser

    Given

    D1 hub3.00inR53.349ft.lbf/lbm/R

    D1 shroud6.00inCp0.24BTU/lbm/R

    D212.00inalpha 10.00degrees

    D3 diffuser20.52inback sweep30.00degrees

    N27,500RPMNo. blades32.00

    Flow3.50lb/secb20.350in.

    Pt114.70psiaSlip FactorWeisner

    Tt1519.00Imp Eff90.00%Poly, T-T

    gamma1.4