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Centrifugal Compressors

Design of Centrifugal Compressor elements – Impellers, Vanes etc.

Other Design Possibilities: a) Double-sided impeller : b) Multi-staged compressor

Other important issues to be designed

Slip factor

In a real compressor relative velocity vector V 2 is at angle β 2 because of non-radial exit from the impeller tip as the real viscous flow detaches near the tip from the impeller vane (trailing) surface

s φ 2 2 *

0.63.π / N σ = 1 - 1 -. tanβ

s

0.63.π σ = 1- N

Stanitz formula ,

which, for a radial vane,

φ 2 r^2 2

**_C

U_**

2

r2 2 σ 1 ( / )cosβ

1 (V /U )

σ 1 ( / )

N

N

π

π

= −

−

= − 2

2 tanβ

cosβ

Wisner’s definition

Stodola Definition

Where & N= no. of blades

No dependence on backsweep

β 2 <-45^0 ; N>

β 2 >-45^0 ; N>

00 < β 2 <-60^0

Forward Curved Vanes

Small Volume

High Pressure ratio

High speed High noise , Low Efficiency

Backward curved Vanes

Large Volume and size

Low to High Pr Ratio

High Efficiency, Low Noise

Radial Vanes Medium Volume and Size

Medium to High Pr ratio

Good Efficiency

Radial Vaned CCs have been used in A/C engines for 50

years. Now, well designed backward curved vaned CCs are increasingly being used for higher efficiency.

At the compr. entry face

a 1 1

C tanβ = U

U 1 = ω.reye where r (^) eye varies from the root to the tip of the eye

Thus for a high speed compressor (or large sized) β 1 shall vary hugely from root to tip of the eye.

Under off-design operations,

at any radius, incidence, ir^ (^ )

---

i =r β - β** (^1 1) r

High positive incidence i (≥ +5^0 ) may precipitate early flow separation inside the impeller vane passage, even near the eye, specially if high diffusion ( i.e. high adverse pressure gradient ) is being attempted inside the impeller vanes.

To be decided by designer

At the exit plane of the impeller, the exiting flow deviates from the trailing edge and lag behind in rotational mode. This is often referred to as the lag or deviation angle.

av 2 2

δ = β - β

which is an average at the passage exit, and β 2 * is the impeller vane exit angle set by design

Diffusion Limit :

An upper limit of realistic diffusion limit V 2 /V 1 ≈ 0. In rotating diffuser V 2 /V 1 < 0. In Impeller design, ρ 1 A 1 / ρ 2 A 2 > 2.

Backward curved vanes + splitter

Reduction in deviation angle at the impeller exit under off-design operating conditions is to be designed in to the impeller and the vane designs.

Vaneless diffuser

.( - 1). ) 0C = 1 +^ 0c

γ η γ γ - π

  = (^)    

2 03 s 2 1 w 2 01 01

pΨ. (σ. U - U .C p a

The general relationship for Compressor Pressure ratio is given by

• Theoretical energy density (Hth ) transfer is highest with forward curved vanes, in which most of the energy would be available in kinetic form, Hdyn at the impeller exit.
• While a radial impeller gives almost 50-50 split of static (H (^) static ) and dynamic heads (H (^) dyn) at the impeller exit, the backward curved vanes give high static pressure development in the impeller.
• Pre-swirl ( α 1 > 0 ) reduces the work done by compressor

With Speed Control and Flow Control

• In aircraft engines, rotating speed is variable during actual running.
• Thus the zone of operation is bounded between the points a,b,c and d.
• The ηmin lines and the speed lines, nmax and nmin , define the boundaries (shaded area) of operation.

• If more control variables are available it may be possible to extend the zone of operation of the compressor. All possible means of extending these boundaries further are being explored.
• Variable geometry (stagger) Inlet and exit (diffuser) guide vanes to be explored

Stall and Surge control

• Surging tends to originate in diffuser passages where frictional effects of the vane retard the flow.
• Flow reversal may vary from one blade passage to the next.
• The surging is reduced by making the number of diffuser vanes an odd number mis-match of the impeller vanes. In this way pressure fluctuations are more likely to be evened out over the annular vaneless circumference.

Losses : Ideal and Real Characteristics

• Most of the losses are still found by rigorous rig test.
• CFD gives good 1 st cut estimation of loss analysis