# Indian Institute of Technology Delhi by mikesanye

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```									  Theory of Steam/gas Turbines

P M V Subbarao
Professor
Mechanical Engineering Department
I I T Delhi

Modeling of Flow in Turbomachines….
Steam Turbine Stage Grouping
• In view of the specifics of the steam path design, all stages of a
condensing steam turbine are divided into four groups
• Governing stages
• Stages with high pressure and low volume discharge of steam
• Intermediate stages with relatively low pressure and high
volume discharge of steam
• Last stages in the lowest-pressure range,
• Characterized by a very high volume discharge.
• The design of turbine stages and the dimensions of turbine
elements in the steam path depend substantially on the volume
discharge.
• The specific volume of steam increases in a turbine
substantially from first to last stages.
Options for Power Generation Split among the Modules
of a Steam Turbine
Power Split between the modules

50.0
45.0
Percent of generated power

40.0

35.0
30.0
HP
25.0
IP
20.0
LP
15.0
10.0

5.0
0.0
A   B    C    D   E
OEM
Multi-Staging of Large Steam Turbine
• Consider a case of isentropic expansion from 30MPa, 6500C to
3500C.
• Isentropic Drop in enthalpy available for conversion: 540kJ/kg.
Pure Impulse Option:
• Velocity of jet: 1039 m/s
• Velocity of blade : 519.5 m/s.
• A blade tip speed of 519.5m/s is not possible, which is pretty
high for practical uses.
• Compounding is achieved by using more than one set of nozzles
& blades in a series, keyed to a common shaft.
• 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,
• b) velocity compounded and
• c) pressure and velocity compounded impulse turbines.

• The number of modules & number of stages in a module are
important elements affecting the overall cost of the power
plant.
• Each module contains number of stages.
• The capacity of a stage depends on the type of aerofoil shape
• It is a blade & Stage syndrome.

• The blades of an ST are the components that receive the most
attention.
• Basic analysis generates a design parameter called degree of
reaction.
• An efficient HP/IP blading is the use of variable reaction for
each stage in the blade path length instead of the constant 50
percent reaction.
• Improvements of 1 percent and higher in module efficiency
have been reported by using VR.

• A typical optimization process for the HP or IP turbine could
contain more than 40 variables, such as:
• pressure drop between the stationary and rotating blades,
• enthalpy drop across the stages,
• Subject to more than 100 design constraints

and square of mean rotor speed.

h0,stage        h0,stage
                  
U   2
rm  2

Flow Coefficient: Ratio of the axial velocity entering to the
mean rotor speed.

V f ,stage exit       V f ,stage exit
                       
U                    rm
Regions of Design




Design Variables of a Stage
• The following are stage data:
• Steam flow rate, (kg/sec) obtained from heat cycle
calculation of turbine plant.
• Average diameter, d(m) for a stage obtained from a
special diagram.
• Rotational frequency, n (rps) ,given/obtained from grid
frequency
• Tangential velocity at average diameter u (m/s)
• Isentropic enthalpy drop, (kJ/kg) obtained from h-s
diagram.
• Flow velocity, (m/s).
• Velocity ratio
•   Degree of reaction, assumed.
•   Isentropic enthalpy drop in nozzle cascade, kJ/kg
•   Specific volume before the nozzle cascade (theoretical),
(m3/kg.
(theoretical), (m3/kg).
•   Theoretical steam velocity at nozzle exit, m/s.
•   Discharge coefficient of nozzle cascade,
•   Angle of velocity vector .
•   Exit area of nozzle cascade
Euler Axial Turbine Equation

Vtangential, out
Vtangential, in

Applying conservation of angular momentum,
the torque, T, must be equal to the time rate of change of angular
momentum in a stream tube that flows through the device

T  mVw,in rin  Vw,out rout 

This is true whether the blade row is rotating or not.
Axial Flow Fluid Machines

The power, P of a fluid Machine

P  T  mU Vw,in  Vw,out   mh0,in  h0,out 
                      
Two Dimensional Theory of Turbines
a0         Station : 0

Va0

Station : 1
b1                     Va1
a1
Vr1
Ub
Ub

a2      S2ation : 3
Vr2              b2
Va2
Ub
Axial Turbine Stator Exit/Rotor Inlet Velocity Triangle

Va1
Va1    Vw1

Vr1
Vw1
Vf1               b1    Vf1

Va0

Vf0
U
a2         a1       b2         b1
Va2                        Va1        Vr1
Vr2

Va1: Inlet Absolute Velocity
Vr1: Inlet Relative Velocity
Vr2: Exit Relative Velocity
Va2:Exit Absolute Velocity

a1: Inlet Nozzle Angle.
a2: inlet Nozzle Angle (next stage).
Impulse-Reaction Axial Flow Turbine

Vw2                             Vw1
U
a2         a1       b2             b1
Va2                        Va1            Vr1
Vr2

P  T  mU Vw,in  Vw,out   mh0,in  h0,out 
                      

                       
P  T  mU Vw,in  Vw,out  mh0,in  h0,out 
                   
Impulse-Reaction turbine : Group Behaviour of
Aerofoils
• This utilizes the principle of impulse and reaction.
• There are a number of rows of moving blades attached to
the rotor and 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
are also of nozzle shape.
• The relative velocity increases in the moving blades.
P  T  mU Vw1  Vw 2   mh00  h02 
                  

h00  h01
P  T  mU Vw1  Vw 2   mh01  h02 
                  

      Va2        Va22  
P  T  mU Vw1  Vw 2   m h1   1   h2  
                  
      2          2  
                      
U
a2         a1       b2         b1
Va1        Vr1
Va2        Vr2
      Vw21 V f21          Vw21 V f21  
P  T  mU Vw1  Vw 2   m h1  
                                       h2             
      2     2             2     2 
                                     
       Vw21 V f21          Vw21 V f21  
U Vw1  Vw 2    h1               h2             
       2     2             2     2 
                                      

       Vw21 V f21          Vw21 V f21  
U Vw1  Vw 2    h1               h2             
       2     2             2     2 
                                      

Conservation of mass :
1 A1V f 1  2 A2V f 2

Simplification of design: constant flow velocity

V f 1  V f 2  1 A1   2 A2
Simplification of design: constant flow area

A1  A2  1V f 1   2V f 2

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