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Organic Rankine Cycle Efficiency

Organic Rankine Cycle –
 
The thermodynamic cycle for steam power plant is Rankine cycle. Many limitations of Carnot cycle are eliminated in Rankine cycle by superheating the steam in a turbine and condensing it completely in the condenser. Each of the four processes constituting the cycle is a theoretical process that may be nearly achieved in an actual power cycle.
 
 
 
 
 
In an ideal Rankine cycle, there is no pressure drop during the evaporation and condensation. Also, in the absence of irreversibility and heat interaction with the surroundings, the expansion and the compression in the turbine would be isentropic.
 

H – S Diagram

 

T – S Diagram

P – V Diagram

 
 
The flow is a Rankine cycle is as follows –
1   
     1.   Turbine
2   2.     Condenser
3   3.     Cooling Water
4   4.     Pump
5   5.     Boiler
 
The four processes involved in the complete cycle are different from each other and each process requires a separate component. Further it may be noted that the working fluid is water which exists in liquid phase during the part of the cycle and vapor phase in the remaining part of the cycle.

Process  1 – 2 :

Reversible adiabatic expansion in the turbine from pressure p1 to p2 to produce the work output.

Process  2 – 3 :

Heat transfer from the steam in the condenser. Steam is condensed to saturated water at 3.

Process  3 – 4 :

Reversible adiabatic compression of water in the pump takes place. This is isentropic compression. The pressure of water increases from p2 to p1. P2 is the condenser pressure and p1 is the boiler pressure.
The temperature of the water at 4 is less than the saturation temperature corresponding to the boiler pressure.

Process  4 – 1 :

Heat transfer to water at constant pressure in the boiler to produce the steam. Initially, the temperature increases to 4’. This is the saturation temperature. It remains constant during the evaporation which is from 4 to 1. Thus the working fluid returns to state point to complete the cycle.
Efficiency of the Rankine cycle is the ratio of work done to heat absorbed.
Work done = h1 – h2
Heat absorbed = h1 – hf3
 

Derivation

NRankine = Rankine cycle efficiency
             = work done / Heat absorbed
 
Work done = Heat absorbed – Heat rejected
 
Heat absorbed during the process 3-4-4’-1,
                = (Heat absorbed during  process 4’-1) +
                    (Heat absorbed during process 3-4-4’)
              = h fg1  + ( h f1 – h f2 )
              = ( h fg1 + h ‘fg1  ) – ( hf2 )
           = h1 – hf2
 
Heat rejected
    
          = h2  – hf3
             = hf2   + x2.hfg2  – hf3
            =x2.hfg2
 
Work Done = Heat absorbed – Heat Rejected
= ( h1 – hf2 ) – x2hfg2.
= h1 – ( hf2 + x2hfg2 )
= h1 – h2.
Rankine Cycle Efficiency = Work Done / Heat Absorbed
= h1 – h2 / h1 – hf3.

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