Subject Code :151906Name Of Subject :Conventional power electronicsName of Unit :Steam Turbine Topic :Parson’s Turbine and condition for maximum efficiency of Parson’s reaction Turbine Name of Faculty : Mr. Mohsin DadiName of Students : (i)Savalia Avani(100870111020) (ii)Patel Jay (100870111021)

Parson’s Turbine

Parson’s turbine is a particular case of reaction turbine in which the degree of reaction is half.

The section of blades of this turbine is the same in both fixed and moving rows of blades.

Sub: CPE Topic: Parson’s Turbine and condition for maximum efficiency of Parson’s Reaction turbine

Parson’s TurbineIn the parson’s turbine, the blade section and the

mean diameter of fixed as well as the moving blades are the same.

The blade height is progresively so increased such that the velocity of steam at exit from each row of blades is uniform throughout the stage.

Sub: CPE Topic: Parson’s Turbine and condition for maximum efficiency of Parson’s Reaction turbine

Thus, the velocity triangle at the inlet and outlet of moving blades will be similar.

The parson’s turbine is designed for 50% reaction,then the equation of degree of reaction can be written as

R=1/2=Vf(cot --cot )/2Vb

therefore,Vb=Vf(cot -- cot )

Also , Vb can be written as

Vb=Vf(cot -cot α)

Vb=Vf(cot α -cot β)

Comparing the equations, α= and = βSub: CPE Topic: Parson’s Turbine and condition for maximum efficiency of Parson’s Reaction turbine

Velocity diagram for Parson’s reaction turbine

Sub: CPE Topic: Parson’s Turbine and condition for maximum efficiency of Parson’s Reaction turbine

Condition for maximum efficiency of parson’s reaction turbineWork done per kg of steam is given by W=Vb(Vw1+Vw2)=Vb[V1cosα+(Vr2cos -Vb)For parson’s turbine , =α and Vr2=V1

Therefore, W=Vb[2V1 cosα- Vb] =V1

2[2VbV1 cosα/v12-Vb

2/V12]

= V12 [2 cosα-2]

Where, =Vb/V1

Sub: CPE Topic: Parson’s Turbine and condition for maximum efficiency of Parson’s Reaction turbine

The kinetic energy supplied to the fixed blade=V12/2g

The kinetic energy supplied to the moving blade= Vr2

2-Vr12/2

Therefore, Total energy supplied to the stage, h=(V1

2/2)+(Vr22-Vr1

2/2)

For symmetrical tri-angels Vr2=V1

h= (V12/2)+(V1

2- Vr12/2 )= V1

2- Vr12/2

Sub: CPE Topic: Parson’s Turbine and condition for maximum efficiency of Parson’s Reaction turbine

Cosidering the ABD from velocity diagram

Vr12= V1

2+ Vb2-2VbV1 cosα

h= V12-(V1

2+ Vb2-2VbV1 cosα)/2

=(V12 +2VbV1 cosα-Vb

2)/2

= V12 /2[1+2Vbcosα/V1-(Vb/V1) 2 ]

h=V12 /2[1+2 cosα- 2 ]

Sub: CPE Topic: Parson’sTurbine and condition for maximum efficiency of Parson’s Reaction turbine

The blade efficiency of the reaction turbine is given by

=Work done(W)/Total energy supplied( h)ƞ =V1

2(2 cosα- 2 )/V12/2(1+2 cosα- 2)

=2(2 cosα- 2)/(1+2 cosα- 2)

=2 (2cosα- )/(1+2 cosα- 2)

=2(1+2 cosα- 2)-2/(1+2 cosα- 2)

=2-2/ 1+2 cosα- 2

Sub: CPE Topic: Parson’sTurbine and condition for maximum efficiency of Parson’s Reaction turbine

The ƞb becomes maximum when factor 1+2 cosα- 2 becomes maximum,

Therefore ,the required condition is

d/d (1+2 cosα- 2 )=0

therefore,2cosα-2 = 0

=cosα

i.e.The conditon for maximum efficiency, =Vb/V1 =cosα

Sub: CPE Topic: Parson’sTurbine and condition for maximum efficiency of Parson’s Reaction turbine

Substituting the value of in the equation,we get

(ƞb)max=2-2/1+2cosαcosα-cos2α

therefore,

Maximum efficiency=

(ƞb)max=2cos2α /1+cos2α

Sub: CPE Topic: Parson’sTurbine and condition for maximum efficiency of Parson’s Reaction turbine