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EFFICIENCIES CALCULATED IN STEAM PLANT

 For the steady flow operation of a turbine, neglecting changes in K.E. and P.E. 

 Maximum or Ideal Work output per unit mass of steam. 

 (Wt)max = (Wt)ideal = h1 - h2s

                =  Reversible and adiabatic enthalpy drop in turbine.




 This work is , however, not obtainable, since no real process is reversible. The expansion process is accompanied by irreversiblities. The actual final state 2 can be defined, since the temperature, pressure, and quality can be found by actual measurement. The actual path 1-2 is not known and its nature is immaterial, since the work output is here being expressed in terms of  the change of a property, a enthalpy. Accordingly, the work done by the turbine in irreversible adiabatic expansion from 1 to 2 is, 

(Wt)actual = h1-h2 

This work is known as internal work, since only the irreversibility within the flow passages of the turbine are  affecting the state of the steam at the turbine exhaust.

Internal Output = Ideal output - Friction and other losses within the turbine casing 

If  Wx is the steam flow rate in kg/h 

Internal output = Ws(h1-h2) kJ/h 

Ideal Output = Ws (h1-h2s) kJ/h

The internal efficiency of the turbine is defined as 

N internal = Internal output / Ideal output = (h1 - h2) / (h1 - h2s)

Work output available at the shaft is less than the internal output because of the external losses in the bearings , etc.

ie, brake output or shaft output = Internal output - External Losses

                                                  = Ideal Output - Internal and External Losses 

                                                  = (KW * 3600 kJ / h)

The brake efficiency of the turbine is defined as ,

N brake = Brake output / Ideal output 

              =  KW * 3600 / Ws(h1-h2)  

The Mechanical efficiency of the turbine is defined as,

 N mech = Brake output / Internal output 

               = KW * 3600 /  Ws (h1-h2) 

ie, N brake = N internal * N mech 

While the internal efficiency takes into consideration the internal losses, and the mechanical efficiency considers only the external losses, the brake efficiency takes into account both the internal and external losses ( with respect to turbine casing). 

The generator ( or alternator) efficiency is defined as 

N generator = Output at generator terminals / Brake output of turbine. 

The efficiency of the boiler is defined as 

N boiler  = Energy Utilized / Energy supplied = (Ws(h1-h4)) / (Wf  * C.V)

where Wf is the fuel burning rate in the boiler (kg / h) and C.V is the calorific value of  the fuel (kJ /kg), i.e., the heat energy released by the complete combustion of unit mass of fuel. 

The power plant is an energy converter from fuel to electricity and the overall efficiency of the plant is defined as 


      (Wf *C.V) kJ /h                                                                           (KW * 3600) kJ /h 

------------------>----Fuel --------------------POWER PLANT----------->--Electricity------------------

                              Powerplant - An energy converter from fuel to electricity 


N overall = N plant = ( kW * 3600) /  (Wf *C.V )

This may be expressed as follows :

N overall = (kW * 3600) / (Wf * C.V) 

                = (Ws(h1-h4) / Wf (C*V)) * (Ws(h1-h2) / Ws(h1-h4)) * (Brake Output / Ws(h1-h2)) * (kW *3600 / Brake output)

   N overall = N boiler * N cycle * N turbine(mech) * N generator 

where pump work has been neglected in the expression for cycle efficiency.  


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