Lecture PPTs (28) - Lect 32 1 Lect-32 In this lecture...

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1 Lect- 32
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 2 Lect-32 In this lecture... Centrifugal compressors Coriolis acceleration Slip factor Performance characteristics Stall and surge
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 3 Lect-32 Coriolis acceleration We have discussed earlier that pressure change due to the centrifugal force field is not a cause of boundary layer separation. This can also be explained by the Coriolis forces that are present in centrifugal compressor rotors. Let us consider a fluid element travelling radially outward in the passage of a rotor. We shall examine the velocity triangles of this fluid during a time period dt.
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 4 Lect-32 Ω r V Ω Ω dr Vd θ dC w dC V d θ C C’ Ω r Ω (r+dr) Coriolis acceleration
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 5 Lect-32 Coriolis acceleration The magnitude of the relative velocity is unchanged, but the particle has suffered an absolute change of velocity. V P r magnitude, of direction tangential the in gradient pressure a requires it and V a , on accelerati Coriolis the Thus, , dt V Vdt dC , or Vd dr dC w w Ω ρ θ Ω Ω Ω θ Ω θ 2 1 2 = = + = + =
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 6 Lect-32 Coriolis acceleration The existence of the tangential pressure gradient means that there will be a positive gradient of V in the tangential direction. This means that there will be a tangential variation in relative velocity. ( ) Ω θ θ θ θ ρ 2 1 2 1 2 = = = d dV r , Therefore d dV r V rd / V d rd dP
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 7 Lect-32 Coriolis acceleration V C w2 C 2 V 2 U 2 Straight radial blades
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