1. Performance Analysis of Steam Turbines
P M V Subbarao
Professor
Mechanical Engineering Department
I I T Delhi
Selection of Best Design and Operating Variables…….

2. Selection of The Velocity TrianglesUb
Vr1
Va1 b1 a1 a2 b2
Va2
Vr2 U
Vr1
Va1
Vr2
Va2 b1 a1 a2 b2 U
Vr1
Va1
Vr2
Va2 b1 a1 a2 b2
Va1: Inlet Absolute Velocity
Vr1: Inlet Relative Velocity
Vr2: Exit Relative Velocity
Va2:Exit Absolute Velocity U
Vr1
Va1
Vr2
Va2 b1 a1 a2 b2
a1: Inlet flow Angle.
b1: Inlet Blade Angle.
b2: Exit Blade Angle.
a2: Exit flow Angle.

3. Blade Shape

4. The kinematics of Flowing Fluid Work TransactionsUb
Vr1
Va1
Vr2
Va2 b1 a1 a2 b2 U
Vr1
Va1
Vr2
Va2 b1 a1 a2 b2
The steam is delivered to the wheel at an angle a1 and velocity Va1.
The selection of angle a1 is a compromise.
An increase in 1, reduces the value of useful component (Absolute circumferential Component).
This is also called Inlet Whirl Velocity, Vw1 = Va1 cos(1).
An increase in 1, increases the value of axial component, also called as flow component.
This is responsible for definite mass flow rate between to successive blade.
Flow component Vf1 = Va1sin(1) = Vr1 sin(1).
The absolute inlet velocity can be considered as a resultant of blade velocity and inlet relative velocity.
The two points of interest are those at the inlet and exit of the blade.

5. Identification of The Action by A Blade on Flowing Fluid
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 ideal blade, Vr2 = Vr1
This blade is known as an ideal impulse Blade
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.

6. Newton’s Second Law for an Impulse Blade:
Vr1
Va1
Vr2
Va2 b1 a1 a2 b2
The tangential force acting of the jet is:
F = mass flow rate X Change of velocity in the tangential direction
Tangential relative velocity at blade Inlet : Vr1 cos(b1).
Tangential relative velocity at blade exit : -Vr2 cos(b2).
Change in velocity in tangential direction: -Vr2 cos(b2) – Vr1 cos(b1).
-(Vr2 cos(b2) + Vr1 cos(b1)).
Tangential Force,

7. The Driving Force on Rotor Wheel
The reaction to this force provides the driving thrust on the wheel.
Power Output of the turbine :
Diagram Efficiency or Blade efficiency:

8. Turbine : A SSSF Isentropic Device
out T
No heat transfer. Change in potential energy is negligible
There is a single fluid entering and leaving…

9. Stagnation or Total Enthalpy of Steam
Define Stagnation enthalpy or total enthalpy as

10. SSSF ANALYSIS of Nozzles (Fixed Blade Row)
First Laws for CV in SSSF Mode:
No heat transfer : Adiabatic devices and No work transfer : fixed blades. Single inlet and outlet.

11. SSSF ANALYSIS of Rotor (Moving Blade Row)
There is a single fluid entering and leaving…

12. Performance Measure for A Turbine
Diagram Efficiency or Blade efficiency:

13. Some Trigonometry ??? U
Vr1
Va1
Vr2
Va2 b1 a1 a2 b2

14. Clues to Find Optimal Shape of An Ideal Impulse Blade
Vr1
Va1
Vr2
Va2 b1 a1 a2 b2
Define blade speed ratio, 

15. Maximum Efficiency of an Ideal Impulse Blade
Vr1
Va1
Vr2
Va2 b1 a1 a2 b2
Consider kinematic variable as optimization variable, for a symmetric blade.

16. Optimal Kinematic Conditions
If symmetric blade is not possible?????

17. Possibility of A Turbine with Single Nozzle & Rotor
Mean Peripheral Speed of the Blade = 825 m/s

18. An Invention that Made Electricity Very Cheap
The modern steam turbine was invented in 1884 by the Englishman Sir Charles Parsons.
The first model was connected to a dynamo that generated 7.5 kW (10 hp) of electricity.
The invention of Parson's steam turbine made cheap and plentiful electricity possible and revolutionized marine transport and naval warfare.
His patent was licensed and the turbine scaled-up shortly after by an American, George Westinghouse.
The Parson's turbine also turned out to be easy to scale up.

19. A Device Easy to Scale up
Parsons had the satisfaction of seeing his invention adopted for all major world power stations, and the size of generators had increased from his first 7.5 kW set up to units of 50,000 kW capacity.
Within Parson's lifetime the generating capacity of a unit was scaled up by about 10,000 times.
The total output from turbo-generators constructed by his firm C. A. Parsons and Company and by their licensees, for land purposes alone, had exceeded thirty million horse-power.

20. 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.

21. Worlds Largest turbine