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Turbomachinery Centrifugal Compressors Class 13
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Centrifugal Compressor Design
Geometry Rothalpy Impeller Design Considerations Eye – Inducer Slip Diffuser Design Considerations Volute Design Considerations
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Centrifugal Compressor Components
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Centrifugal Compressor Components
Collector scroll and vanes may be replaced with vaneless diffuser
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Centrifugal Compressor Components
Centrifugal compressor= impeller+diffuser Geometrical Definitions Eye: L.E. of impeller Impeller: raises energy level of fluid by increasing radius Inducer: portion of impeller from eye to region where flow turns radial Diffuser: converts K.E. from impeller into P.E.. Adding vanes reduces size of diffuser Scroll or volute: collects flow from diffuser and delivers to outlet
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Centrifugal Compressor Design
Compressor’s role is to produce high pressure flow High 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 ½ pressure rise in impeller passage ½ pressure rise in diffuser passage Diffuser may have vanes, but stator passages must have increasing area Volute cross-section area increases gradually to exit
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Centrifugal Compressor Design
In 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 compressors If no prewhirl Cu1=0 See result shown later is Example 1
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Centrifugal Compressor Design: T.E.
Blade TE shape for opt. performance Forward: against rotation Radial Backward: with rotation
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Straight Back Forward
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Centrifugal Compressor Design: T.E.
Radial T.E. Ideal no-slip view Increased Cr/Wr for same U does not change Cu or work T02/T01 unchanged with increased Cr
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Centrifugal Compressor Design: T.E.
Backward T.E. Increased Cr/Wr for same U decreases Cu or work T02/T01 decreases with increased Cr Stable side of compressor map
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Centrifugal Compressor Design: T.E.
Forward T.E. Increased Cr/Wr for same U increases Cu or work T02/T01 increases with increased Cr Unstable side of compressor map
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Centrifugal Compressor Design: T.E.
Radial T.E.
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Centrifugal Compressor Design: T.E.
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] Backswept Impellor
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Centrifugal Compressor Design: T.E.
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Centrifugal Compressor Design: L.E.
Prewhirl [in the direction of rotation] added from added upstream guide vanes In high PR compressors, may be necessary to provide prerotation to reduce high relative inlet velocity. Also reduces incidence / reduces twist lower bending stresses Vane radial design impact on inducer Free vortex Cu 1/r: high incidence at low rh/rt designs Forced vortex Cu rn Wo Wn - IGV will allow untwisted impellor inlet - Untwist will reduce rotor root bending stresses
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Centrifugal Compressor Design: Tip
Tip Leakage Issues Flow from pressure [+] to suction [-] side over tip Flow from downstream [+] to upstream [-]
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Review: Axial Compressor Slip
Slip: 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
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Centrifugal Compressor Slip
Slip: 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 eddy Relative eddy with throughflow
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Centrifugal Compressor Slip
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Axial Compressor Slip
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Axial Compressor Slip
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Centrifugal Compressor Slip
"Slip" (Deviation) Reduces Swirl & Work Slip Factor Vs
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Centrifugal Compressor Slip
Several Correlations for Centrifugal Impeller Slip Factor Weisner Stodola Stanitz
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Centrifugal Compressor Design
In general, with possible prewhirl Cu10 Introduce work done-input factor In turbines [work done] < 1, due to boundary layer effects In compressors [work input] > 1, need more power to account for boundary layer effects
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Centrifugal Compressor Design
Impeller Performance Effects:
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Centrifugal Compressor Design
Backward sweep Splitter impeller vane Reduce effect of slip by using splitter vane to reduce diffusion
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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
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Centrifugal Compressor Design
Assume no more iteration is needed
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Centrifugal Compressor Design
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Centrifugal Compressor Design
Example #2: Dixon 7.1 A 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 correlation Assume R=287 J/(kg-C), p01=101.3 bar, T01=288K Assume
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Centrifugal Compressor Design
1- Determine the impeller vane exit speed 2- Determine the volumetric flow rate Stannitz 21.98
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Centrifugal Compressor Design
2- Determine the volumetric flow rate cont’d 3- Power required if mechanical efficiency is 0.95 4- Determine specific speed No swirl
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Axial vs. Radial Machines
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Diffuser Design: Sta. 23 Rotation 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
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Centrifugal Compressor Design
Example #3: Will work through design of each component separately Know U2, slip, not p02, T02,
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Centrifugal Compressor Design: Sta. 1
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Centrifugal Compressor Design: Sta. 2
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Centrifugal Compressor Design: Sta. 2
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Centrifugal Compressor Design
Impeller Performance: Efficiency up to 90 to 95% Polytropic Small size reduces efficiency Thickness, finish affect performance Clearance Multi-stage usually shrouded because axial location (and therefore, ) difficult to control
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Diffuser Design: Sta. 23 Basic Parameters h = height of 2D diffuser
Y = entrance width L = Length B = entrance boundary layer blockage W = inlet velocity Rotation Number h
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Diffuser Design: Sta. 23
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Radial Diffuser Performance: Sta. 23
Pressure coefficient [compressor-type definition] Effectiveness, Diffuser Efficiency
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Diffuser Issues Jet Flow Appreciable Stall No Stall
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Radial Diffuser Design: Sta. 23
Diffusers for Centrifugal Impellers: Rotor Exit Flow Often Contains: High Swirl up to 80 High Velocity M>1 often Distortion Impeller Separation Unsteady Flow Rotating Distortion
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Radial Diffuser Design: Sta. 23
Diffuser reduces velocity & swirl Diffuser Configurations: Vaneless inexpensive, limited effectiveness, work over wide range of operation, large, ok for industrial use Vaned more expensive, better performance, smaller, sensitive to incidence effects Pipe most expensive, best performance, compact, complete angle control
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Vaneless Diffuser Performance: Sta. 23
Vaneless Diffuser: removes swirl of fluid by increasing radius Continuity: Inviscid Tangential Momentum, (Friction Important for quantitative calculations!). For constant angular momentum:
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Vaneless Diffuser Performance: Sta. 23
Swirl angle Increases - compressible flow Constant - incompressible flow Reduced by friction
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Vaneless Diffuser Performance: Sta. 23
Flow trace for vaneless, incompressible diffuser Ex: Radius ratio=2, =77.6: =180 ! In other words, radius will grow by factor of 2.26 as flow revolves 1800 around the diffuser Lot's of friction in Vaneless Diffusers Flow path in vaneless, incompressible diffuser is log spiral outward radially and circumferentially
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Vaneless Diffuser Performance: Sta. 23
Diffuser Flow not Simple 1D Inviscid Analysis with Momentum and Continuity Gives Incorrect Pressure Rise in Diffuser (Too High) Need More Physics for Valid Solution – Friction !
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Centrifugal Compressor Design: Sta. 23
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Vaned Diffuser Design: Sta. 23
Vaned Diffusers Vanes added to remove swirl of fluid at a higher rate than done by increasing radius Better Performance BUT matching is critical Steifel 1972 34% increase in throat area, same vane shape 15% greater rotor flow
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Vaned Diffuser Design: Sta. 23
Diffuser Performance Rundstadler & Deane 2D & Conical diffusers Large Range of: Area Ratio Length/Height Aspect Ratio Mach No. Reynolds No. Blockage Effect of increasing diffuser angle: range of steady and transient flows Blockage drives effectiveness!
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Vaned Diffuser Design: Sta. 23
Diffuser Geometry Throat area is critical Pipe Diffuser better with M>1
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Vaned Diffuser Design: Sta. 23
Throat Blockage Drives Effectiveness
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Vaned Diffuser Design: Sta. 23
Throat Blockage Driven by diffusion between blade exit and throat
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Volute and Vaneless Diffuser: Sta. 34
Impeller, Vaneless Diffuser, and Volute
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Volute: Sta. 34 Radius characteristic of volute is Rv
Rv is function of angular position, usually linear from entrance to exit
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Volute Design Volute Design Considerations
Effects overall performance Tongue aligned at only one Cx/U Pressure Loss Space requirements Flow Uniformity
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Volute Design Volute designed for uniform flow around circumference at diffuser exit Angular momentum sets swirl velocity Volute area set to match uniform flow from diffuser by angular momentum and continuity
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Volute Design Common design practice is to maintain simple conservation of angular momentum along mean streamline in volute [r=rV]
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Volute Design The Best Volute Design is Not Perfect
Stagnation point on tongue creates local high pressure Curvature stops at end of volute changing radial pressure gradient Tongue incidence at off-design 3 creates general distortion Vanes or dual volutes used to reduce distortion
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Volute Design .
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Volute Design Volute exit radial velocity is arbitrary and can be changed to optimize diffusion.
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Volute Design
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Volute Design
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Volute Design
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Volute Design
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