Theory of turbo machinery / Turbomaskinernas teori. Dixon, chapter 7. Centrifugal Pumps, Fans and Compressors

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1 Theory of turbo machinery / Turbomaskinernas teori Dixon, chapter 7 Centrifugal Pumps, Fans and Compressors

2 And to thy speed add wings. (MILTON, Paradise Lost.)

3 What do radial machines look like? Swept wings or not? Slip (deviation). Example. Material adopted from: Alvarez, Energiteknik KSB: Selecting centrifugal pumps

4 Specific speed: Dimensionless flow to head ratio so that D is eliminated. Values of flow and head at max efficiency 1/ 1 3/ 4 1 φ N s = = ψ NQ 1/ ( gh ) 3/ 4

5 Three examples of characteristic curves for pumps of differing specific speeds. a: radial impeller, n q 0; b: mixed flow impeller, n q 80; c: axial flow impeller, n q 00.

6 Pump characteristics H/Q characteristics normally stable (the developed head falls as the flow rate Q in-creases) For low specific speeds, the head H may in the low flow range drop as the flow rate decreases(shown by the dash line) Steep, flat or unstable characteristic curve This may cause problems in some applications

7 Specific speed (from Japixe-Baines)

8 Types: Axial, mixed and radial flow direction Shrouded or unshrouded Shrouded impellers

9 Main components Impeller: D, 3D, Backsweep? Axial inlet, radial inlet Diffuser: Vaneless, Vaned (Vane type)? Diffuser ratio Pipe diffuser Volute Airfoil diffuser Vaneless diffuser Impeller axial inlet

10 FIG. 7.. Radial-flow pump and velocity triangles.

11 FIG Centrifugal compressor stage and velocity diagrams at impeller entry and exit. 3 1

12 x [ ] W = gh = U c U c c = U c θ 1 θ1 = θ1 = 0 θ

13 FIG Mollier diagram for the complete centrifugal compressor stage.

14 c = c c θ r ( ) c = w U c θ r Right triangle Left triangle Setting them equal: ( ) c c = w U U c + c θ θ θ Solving for Uc θ c + U w Uc θ c θ = the same way Uc θ 1 1

15 1 Wx = gh = U c U c = c c + U U w w ( ) ( ) ( ) θ 1 θ Change in dynamic pressure Change in static pressure Reaction: R change in static pressure = = total pressure change ( ) ( U ) U1 w w1 ( ) ( ) ( c ) c1 + U U1 w w1

16 Example Compare pumps at 1. Same inlet velocity, radially directed: cθ 1 = 0, cr1 = c1. Constant radial velocity: cr1 = cr 3. Same speed of rotation and same inner and outer diameter Consequences [ c 0] U 1. Work: gh = U c U c = = = c. Change in dynamic pressure: θ 1 θ1 θ1 θ ρ ( ) ρ ρc ( ) θ Δ Pd = c c1 = cr + cθ c1 =

17 Example The total pressure rise Δ = = Pt ρgh ρ U c θ The ratio of the dynamic and total pressure drop becomes: Δ Pd ρc c = = ΔP ρu c U t θ θ θ At a fixed rc : large β will decrease the dynamic part of the pressure rise c θ

18 Example = c w w c r β c r c U = c θ c θ = U β = 0 Backward swept

19 Slip c θ reduced gh decreases

20 FIG Actual and hypothetical velocity diagrams at exit from an impeller with back swept vanes.

21 Stodola: A relative eddy with angular velocity Ω = U r FIG (a) Relative eddy without any throughflow. (b) Relative flow at impeller exit (throughflow added to relative eddy).

22 Slip velocity is the product of the relative eddy and the radius of a circle which can be inscribed within the channel ' cθs = cθ cθ =Ωd FIG Flow model for Stodola slip factor. With Z being the number of vanes: ' ( π ) cos d r Z β

23 Example (same assumptions as before) Head- Volume characteristics Q= A c r where A is the exit area of the impeller gh = U c θ cθ = U c tan β = U Qtan β A r Combining these equations: ( tan β ) gh U U Q A U gh β > 0 c θ β = 0 = Q

24 Example Losses: a-b: Slip (finite number of vanes) b-c: Friction Q c-d: Other losses from 3d flows d Instable region Q

25 Operating point

26 Pipe flow friction factor

27 Pipe flow friction factor

In this lecture... Centrifugal compressors Thermodynamics of centrifugal compressors Components of a centrifugal compressor

Lect- 3 In this lecture... Centrifugal compressors Thermodynamics of centrifugal compressors Components of a centrifugal compressor Centrifugal compressors Centrifugal compressors were used in the first