Parson’s Turbine and condition for maximum efficiency of Parson’s reaction Turbine
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The document discusses Parson's turbine and the condition for maximum efficiency of a Parson's reaction turbine. It explains that in a Parson's turbine, the blade section and mean diameter are the same for fixed and moving blades. It also derives equations showing that for maximum efficiency, the ratio of absolute velocity of steam at the moving blade outlet to inlet (β) must be equal to the blade angle (α). This results in symmetrical velocity triangles and maximum work output from the turbine.
![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/V1
Sub: CPE Topic: Parson’s Turbine and condition for maximum efficiency
of Parson’s Reaction turbine](https://image.slidesharecdn.com/ec5cpe1920-130405073245-phpapp01/85/Parson-s-Turbine-and-condition-for-maximum-efficiency-of-Parson-s-reaction-Turbine-6-320.jpg)
![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](https://image.slidesharecdn.com/ec5cpe1920-130405073245-phpapp01/85/Parson-s-Turbine-and-condition-for-maximum-efficiency-of-Parson-s-reaction-Turbine-8-320.jpg)
Parson’s Turbine and condition for maximum efficiency of Parson’s reaction Turbine
- 1. Subject Code :151906 Name Of Subject :Conventional power electronics Name of Unit :Steam Turbine Topic :Parson’s Turbine and condition for maximum efficiency of Parson’s reaction Turbine Name of Faculty : Mr. Mohsin Dadi Name of Students : (i)Savalia Avani(100870111020) (ii)Patel Jay (100870111021)
- 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. 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. 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 efficiency Sub: CPE Topic: Parson’s Turbine and α= and = β of Parson’s Reaction turbine
- 5. Velocity diagram for Parson’s reaction turbine Sub: CPE Topic: Parson’s Turbine and condition for maximum efficiency of Parson’s Reaction turbine
- 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/V1 Sub: CPE Topic: Parson’s Turbine and condition for maximum efficiency of Parson’s Reaction turbine
- 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- Vr12/2 Sub: CPE Topic: Parson’s Turbine and condition for maximum efficiency of Parson’s Reaction turbine
- 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. 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- 2 Sub: CPE Topic: Parson’sTurbine and condition for maximum efficiency of Parson’s Reaction turbine
- 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 efficiency Sub: CPE of Parson’s Reaction turbine
- 11. 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