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# Parson’s Turbine and condition for maximum efficiency of Parson’s reaction Turbine

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### Parson’s Turbine and condition for maximum efficiency of Parson’s reaction Turbine

1. 1. Subject Code :151906Name Of Subject :Conventional power electronicsName of Unit :Steam TurbineTopic :Parson’s Turbine and condition for maximum efficiency of Parson’s reaction TurbineName of Faculty : Mr. Mohsin DadiName of Students : (i)Savalia Avani(100870111020) (ii)Patel Jay (100870111021)
2. 2. 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
3. 3. Parson’s Turbine In 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
4. 4. 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, condition for maximum efficiencySub: CPE Topic: Parson’s Turbine and α= and = β of Parson’s Reaction turbine
5. 5. Velocity diagram for Parson’s reaction turbine Sub: CPE Topic: Parson’s Turbine and condition for maximumefficiency of Parson’s Reaction turbine
6. 6. Condition for maximum efficiency of parson’s reaction turbine Work 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] =V12[2VbV1 cosα/v12-Vb2/V12] = V12 [2 cosα-2] Where, =Vb/V1Sub: CPE Topic: Parson’s Turbine and condition for maximum efficiency of Parson’s Reaction turbine
7. 7. The kinetic energy supplied to the fixed blade=V12/2g The kinetic energy supplied to the moving blade= Vr22-Vr12/2 Therefore, Total energy supplied to the stage, h=(V12/2)+(Vr22-Vr12/2) For symmetrical tri-angels Vr2=V1 h= (V12/2)+(V12- Vr12/2 )= V12- Vr12/2Sub: CPE Topic: Parson’s Turbine and condition for maximum efficiency of Parson’s Reaction turbine
8. 8. Cosidering the ABD from velocity diagram Vr12= V12+ Vb2-2VbV1 cosα h= V12-(V12+ Vb2-2VbV1 cosα)/2 =(V12 +2VbV1 cosα-Vb2)/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
9. 9. The blade efficiency of the reaction turbine is given by ƞ=Work done(W)/Total energy supplied( h) =V12(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- 2Sub: CPE Topic: Parson’sTurbine and condition for maximumefficiency of Parson’s Reaction turbine
10. 10. 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 Topic: Parson’sTurbine and condition for maximum efficiencySub: CPE of Parson’s Reaction turbine
11. 11. Substituting the value of in the equation,we get (ƞb)max=2-2/1+2cosαcosα-cos2α therefore, Maximum efficiency= (ƞb)max=2cos2α /1+cos2αSub: CPE Topic: Parson’sTurbine and condition for maximum efficiency of Parson’s Reaction turbine