At the mean diameter of a gas turbine stage the blade velocity is 350 m/s. The b

Question

At the mean diameter of a gas turbine stage the blade velocity is 350 m/s. The blade angles at inlet and exit are 20 degree and 54 degree respectively and the blades i this section are designed to have a degree of reaction of 50 per cent mean diameter of the blades is 0.432 m and the mean blade height is 0.07 m. Assuming the blades are designed according to vortex theory estimate (a) The flow velocity (b) the angles of blades at the tip and at the root and (c) the degree of reaction at the tip and at the root of the blades.

Explanation / Answer

solution:

1)here blade velocity is given by

Cb=350 m/s

where for 50% reaction turbine is parson reaction turbine for which we get that

alpha=phi=54

theta=beta=20

where flow velocity is given by

Cb=Cf[tan(alpha)-tan(beta)]

Cf=350/[tan54-tan20]=345.70 m/s

2)where blade velocity at tip and root is given by

Cbm=pi*dm*N/60

350=pi*.432*N/60

N=15473.39 rpm

where blade diameter is

rr=rm-(h/2)=.397 m

rt=rm+(h/2)=.467 m

where blade velocity is given by

Cbt=378.35 m/s

Cbm=350 m/s

Cbr=320.89 m/s

where

Cwm=Cf*tan(alpha)=475.81 m/s

Cwt=Cwm(rm/rt)=440.15 m/s

Cwr=Cwm(rm/rr)=517.75 m/s

which gives blade angles as follows

tan(alpha)r=Cwr/Cf=517.75/345.7

(alpha)r=56.26

tan(beta)r=(Cb/Cf)-tan(alpha)r=29.63

tan(alpha)t=Cwt/Cf=440.15/345.7

(alpha)r=51.85

tan(beta)t=(Cb/Cf)-tan(alpha)t=10.13

3)where reaction at tip and rotor is given by

Rx=(tan(beta)2-tan(alpha)1)(Cf/2*Cb)

where mean angle is given by

(alpha )rm=33.6

(beta)rm=28.3

(alpha)tm=40.05

(beta)tm=44.8

Rr=.2563

Rt=.63

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