1. Analysis of Multi Stage Steam Turbines
P M V Subbarao
Professor
Mechanical Engineering Department
I I T Delhi
Moderate speed of turbine suffices for the highest economy …….

2. From Books of Sir Charles Parson
In 1884 or four years previously, I dealt with the turbine problem in a different way.
It seemed to me that moderate surface velocities and speeds of rotation were essential if the turbine motor was to receive general acceptance as a prime mover.
I therefore decided to split up the fall in pressure of the steam into small fractional expansions over a large number of turbines in series, so that the velocity of the steam nowhere should be great.
A moderate speed of turbine suffices for the highest economy.
Speed of Power Plant Steam Turbines in India = 3000rpm.

3. Worlds Largest Steam turbine:1770 MW

4. Strategy for Multi Staging

5. Stage Loading and Flow CoefficientUb
Vr1
Va1
Vr2
Va2 b1 a1 a2 b2
Vf2
Vf1
Stage Loading Coefficient: Ratio of specific enthalpy drop in a stage and square of mean rotor speed.
Flow Coefficient: Ratio of the axial velocity entering to the mean rotor speed.

6. Impulse-Reaction Stage of A Turbine
This utilizes the principle of impulse and reaction.
There are a number of rows of moving blades attached to the rotor and equal number of fixed blades attached to the casing.
The fixed blades are set in a reversed manner compared to the moving blades, and act as nozzles.
The fixed blade channels are of nozzle shape and there is a some drop in pressure accompanied by an increase in velocity.
The fluid then passes over the moving blades and, as in the pure impulse turbine, a force is exerted on the blades by the fluid.
There is further drop in pressure as the fluid passes through the moving blades, since moving blade channels are also of nozzle shape.
The relative velocity increases in the moving blades.

7. Basics of A Reaction StageU
Vr1
Va1
Vr2
Va2 b1 a1 a2 b2
The reaction effect is an addition to impulse effect.
The degree of reaction p Vr Va

8. First Law Analysis of Reaction Stage
First law for fixed blades:
First law for moving blades: 2 1
Gross enthalpy drop available to the stage:

9. Velocity Triangles for A Reaction StageUb
Vr1
Va1
Vr2
Va2 b1 a1 a2 b2
If the steam is to enter and leave the blades without shock or much losses, then relative velocity should be tangential to the blade inlet tip.
Vr1 should enter at an angle 1, the inlet blade angle.
Similarly, Vr2 should leave at 2, the exit blade angle.
In an impulse reaction blade, Vr2 > Vr1
The flow velocities between two successive blade at inlet and exit are Vf1 & Vf2.
The axial (basic useful) components or whirl velocities at inlet and exit are Vw1 & Vw2.

10. The Action in An Impulse-Reaction Stage
Vrw2
Vrw1 Ub
Vr1
Va1
Vr2
Va2 b1 a1 a2 b2
Newton’s Second Law for an Impulse-reaction Blade:
The tangential force acting of the jet is:
F = mass flow rate X Change of velocity in the tangential direction
Tangential relative (Whirl) velocity at blade Inlet : Vr1 cos(b1).
Tangential relative (Whirl) velocity at blade exit : -Vr2 cos(b2).
Change in velocity in tangential direction: -Vr2 cos(b2) – Vr1 cos(b1).
Tangential Force on steam jet,

11. The Reaction in A Reaction Turbine
The reaction to this force provides the driving thrust on the wheel.
The driving force on wheel
Power Output of the blade :
Diagram Efficiency of a Reaction Blade efficiency:

12. Parson (50% Reaction) TurbineUb
Vr1
Va1 b1 a1
For a multi-stage Parson turbine

13. Parson (50% Reaction) TurbineUb
Vr1
Va1 b1 a1
In a 50% reaction stage, the moving blades are a mirror image of the fixed blades, so Va1 = Vr2
α1 = β2
Power Output of the blade :

14. Some Trigonometry ??? Ub
Vr1
Va1 b1 a1

15. Efficiency of Parson Stage
Define blade speed ratio, 

16. Maximum Efficiency of an Ideal Parson BladeUb
Vr1
Va1 b1 a1
Consider kinematic variable as optimization variable, for a symmetric blade.

17. Optimal Kinematic Conditions for Parson Blade
If =50% is not feasible?????
Develop a generalized expression for optimal blade speed ratio for a
Reaction turbine with DOR, .
Date of Submission: 2 April 2018

18. Diagram of Large Power Plant Turbine : 500 MW

19. Block Diagram of A Large Steam Turbine
Main Steam
Reheat Steam HP IP LP
Steam for
Reheating
OFWH 4
CFWH 3
CFWH 2
CFWH 6
CFWH 5
CFWH 1
Condenser

20. Pressure Variation along The Stages : 500 MW

21. Temperature Variation Along The Stages : 500 MW

22. HP Turbine per stage Enthalpy drop

23. IP Turbine per stage Enthalpy drop

24. LP Turbine per stage Enthalpy drop

25. Compounding (Multi Staging) of an Impulse turbine
Compounding is done to reduce the rotational speed of the impulse turbine to practical limits.
Compounding is achieved by using more than one set of nozzles, blades, rotors, in a series, keyed to a common shaft; so that either the steam pressure or the jet velocity is absorbed by the turbine in stages.
Three main types of compounded impulse turbines are:
a) Pressure compounded Steam Turbine : The Rateau Design
b) velocity compounded Steam Turbine : The Curtis Design
c) pressure and velocity compounded Impulse turbines : The Rateau-curtis Design.

26. Impulse Turbines with pressure stages
Multistage turbines with pressure stages have found a wide field of usage in industry as prime movers (~ 10 MW).
The number pressure stages vary from 4 to 5.
The distribution of enthalpy drop in a large number of pressure stages enables the attainment of lower velocities for the steam flowing through the system of moving blades.
As a result more advantageous values of blade speed ratio and blade friction factor are obtained .

27. The Rateau Turbine

28. The Curtis Design

29. A System of Velocity Triangles for Curtis Turbine
Vr1,1
Va1,1
Vr2,1
Va2,1
b1,1
a1,1
1a2
b2,1 U
Vr1,2
Va1,2
Vr2,2
Va2,2
B1,2
a1,2
a2,2
b2,2 U
Vr1,3
Va1,3
Vr2,3
Va2,3
b1,3
a1,3
a2,3
b2,3

30. Multistage Impulse Turbine : GE Product

31. Current Practice
Purely multistage impulse turbines are mainly preferred in medium capacities of power generations.(30 – 60 MW units).
The main advantages are simplicity of construction, low costs, reliability and convenience of operation.
The height of blades in last stages of multistage turbine rapidly increase.
It is difficult to obtain tall, smooth and streamlined shape for the turbine.
Turbines of compound impulse stages are considered obsolete at present.
It is current practice for multistage turbines to allow for some amount enthalpy drop to take place in the moving blades as well.