LESSON - 32 RANKINE CYCLE WITH INCOMPLETE EVAPORATION, RANKINE CYCLE WITH SUPER HEAT, MODIFIED RANKINE CYCLE, PERFORMANCE CRITERIA FOR VAPOUR CYCLES, DESIRABLE PROPERTIES OF WORKING FLUID USED FOR POWER PLANTS

32.1. RANKINE CYCLE WITH INCOMPLETE EVAPORATION

If the steam produced in the boiler is not dry (i.e. During Process 5-1: Water at saturated condition 5 is heated up at constant pressure and constant saturation temperature to wet steam at state 1'.

The Rankine cycle with incomplete evaporation is shown in Fig.  32.1. The Rankin cycle with incomplete evaporation is represented on p-v and T-s diagrams as shown in Figure 32.2.

 

 Fig. 32.1. Rankine cycle with incomplete evaporation steam turbine power plant

 

 

 

 

 

 

 

 

Fig. 32.2. Rankine cycle with incomplete evaporationon p-v and T-s diagrams

1'-2'-3-4-5-1': Rankine cycle with incomplete evaporation

1-2-3-4-5-1   : Rankine cycle with complete evaporation for comparison purpose. 

Total heat addition in boiler, (Process 4-5-1': Heat addition in boiler)

        qA= 4q1 = h1' – hsub,4                       (since   4w1' = 0)                  (from 1st law of thermodynamics for flow process)

                 where  h1'  = (hf,1' + x1' hfg,1')

The remaining energy transaction in different components are to be calculated exactly the same way as in the Rankine cycle

Turbine work, (Process 1'-2')

          wt = h1' – h2'

Heat rejected in the condenser, (Process 2'-3)

  qR = h2' – hf,3

Net work done during cycle, wnet = Heat added (qA) – heat rejected (qR)

    = (h1' –hsub,4) – (h2' – hf,3)  

Thermal efficiency,  

    

Rankine Cycle with Incomplete Evaporation Neglecting Pump Work

In a Rankine cycle with incomplete evaporation, the pump work may be neglected as it is very small compared with other energy transfers. Hence we have

wp= 0    

Rankine cycle with incomplete evaporation on p-v and T-s diagrams (neglecting pump work) is shown in Figure 32.3.

 

Fig.: 32.3.  Rankine cycle with incomplete evaporation on p-v and T-s diagrams (neglecting pump work)

 Total heat addition in boiler in process 3-1 is given by,  

qA= 3q1  = h1' –hf,3                   since 3w1'  = 0           (from 1st law of thermodynamics for flow process)

 Total heat rejected in condenser,  

qR = 2q3 =  h2' – hf,3                 since  2'w3 = 0            (from 1st law of thermodynamics for flow process)

Net work done during cycle, wnet = Heat added (qA) – heat rejected (qR)

    = (h1' –hf,3) -(h2' – hf,3) 

                                                         =  (h1' –h2')

Therefore, Thermal efficiency   

32.2  RANKINE CYCLE WITH SUPERHEATED STEAM

The Rankine cycle with superheating is shown in Fig.  32.4. The Rankine cycle with superheating is represented on p-v and T-s diagrams as shown in Figure 32.5.  The steam is superheated to temperature T1'' before it enters the turbine.

 

Fig. 32.4. Rankine cycle with Superheated Steam of steam turbine power plant

Fig. 32.5. Rankine cycle with superheated steam on p-v and T-s diagrams

1''-2''-3-4-5-1'': Rankine cycle with superheated steam

1-2-3-4-1: Rankine cycle with complete evaporation for comparison purpose

Total heat addition in boiler,  (Process 4-5-1'': Heat addition in boiler)

qA= 4q1 = hsup,1'' – hsub,4                   (since   4w1'' = 0)                  (from 1st law of thermodynamics for flow process)

The remaining energy transaction in different components are to be calculated exactly the same way as in the Rankine cycle

Turbine work, (Process 1''-2")

wt = hsup,1''  – h2''

Heat rejected in the condenser,  (Process 2"-3)

qR = h2'' – hf,3

Net work done during cycle, wnet = Heat added (qA) – heat rejected (qR)

= (hsup,1'' – hsub,4) – (h2'' – hf,3)  

Thermal efficiency, 

                                                                                                                    

   

Advantages:   1. The work output/cycle increases proportional to area 1-1''-2''-2

                       2. Dryness fraction of steam at outlet of turbine increases

                       3. Specific steam consumption decreases

                       4. Thermal efficiency increases

Rankine Cycle with Superheated Steam Neglecting Pump Work

In a Rankine cycle with superheated Steam,the pump work may be neglected as it is very small compared with other energy transfers. Hence we have

wp= 0    

Rankine cycle with superheated Steam on p-v and T-s diagrams (neglecting pump work) is shown in Figure 32.6.

 

Fig. 32.6. Rankine cycle with Superheated Steam on p-v and T-s diagrams (neglecting pump work)

Total heat addition in boiler in process 3-1 is given by,  

qA= 3q1  = hsup,1'' – hf,3                      since 3w1''  = 0         (from 1st law of thermodynamics for flow process)

Total heat rejected in condenser,  

qR = 2q3 =  h2'' – hf,3                           since  2''w3 = 0         (from 1st law of thermodynamics for flow process)

Net work done during cycle, wnet = Heat added (qA) – heat rejected (qR)

    = (hsup,1'' –hf,3) -(h2'' – hf,3) 

    =   (hsup,1'' –h2'')                               

Therefore, Thermal efficiency  

32.3. MODIFIED RANKINE CYCLE (INCOMPLETE EXPANSION CYCLE)

If in Rankine cycle the adiabatic expansion of steam is not completed, it is called the incomplete expansion cycle or modified Rankine cycle. This cycle is mainly employed in steam engine power plants. In this cycle the expansion is terminated at a release pressure ‘PR’ which is above the condenser pressure ‘PL’ and then steam is released at constant volume to the condenser pressure. 

The Modified Rankine cycle is shown in Fig.  32.7. The Modified Rankine cycle is represented on p-v and T-s diagrams as shown in Figure 32.8. 

 

Fig. 32.7. Modified Rankine cycle of steam engine power plant

Fig. 32.8. Modified Rankine cycle on p-v and T-s diagrams

Advantage of expansion of steam up to release pressure P2':

It can be seen that work output represented by hatched area (called toe) is very small. However, it increases the size of engine cylinder. Some times it even does not equal the work being lost through friction etc. Therefore, the expansion is terminated at point 2' itself. Such a cycle is called Modified Rankine Cycle. So cycle 1-2'-3'-3-4-5-1 is Modified Rankine Cycle.   

Total heat addition in boiler, (Process 4-5-1: Heat addition in boiler)

qA= 4q1 =  hg,1 – hsub,4                            (since   4w1 = 0)              (from 1st law of thermodynamics for flow process)

Net work done during cycle, wnet = 1w2' + 2'w3' − 3w4

 = (hg,1 – h2')  +   -  (hsub,4 – hf,3) 

= (hg,1 – h2')  + v2' (p2' – p3) -  (hsub,4 – hf,3)                                                

Where  3w4 = (hsub,4 – hf,3)   is  pump work , wp

Thermal efficiency, 

     

Modified Rankine Cycle Neglecting Pump Work

In a Modified Rankine cycle, the pump work may be neglected as it is very small compared with other energy transfers. Hence we have

wp= 0    

Modified Rankine cycle on p-v and T-s diagrams (neglecting pump work) is shown in Figure 32.9.

 

 

 

 

 

 

Fig. 32.9. Modified Rankine cycle on p-v and T-s diagrams (neglecting pump work)

Total heat addition in boiler in process 3-1 is given by,  

qA = 3q1  = (hg,1 - hf,3)                    since 3w1  = 0                      (from 1st law of thermodynamics for flow process)

Net work done during cycle, wnet = 1w2' + 2'w3'

    = (hg,1– h2′)  + v2' (p2' – p3)

Therefore, Thermal efficiency, 

32.4. PERFORMANCE CRITERIA FOR VAPOUR CYCLES

The following terms, in addition to thermal efficiency, are used for the comparision of performance of vapour cycles

 (i) Thermal Efficiency Ratio or relative efficiency =

(ii) Work ratio =

(iii) Specific fuel consumption/steam rate/ specific rate of steam flow =

=

 ......… (because 1 kWh =3600 kJ)

 (iv) Metallurgical limit           

It is maximum possible temperature of the working fluid which can be achieved during the cycle keeping in view the life (function of material it is made of) span of highly stressed parts of the steam engine/turbine power plant

Highly stressed parts:  boiler tubes (in boilers), turbine blades (in Turbine),   piston & cylinder (in steam engine)

32.5. DESIRABLE PROPERTIES OF WORKING FLUID USED FOR POWER PLANTS 

There are several vapors which have physical properties suitable for working fluid. They are steam, mercury vapor, sulphur dioxide, diphenyl oxide and certain hydro-carbons. The following are the requirements of an ideal working fluid for steam turbine power plant

  1. Ample amount should be available at low cost.

  2. Critical temperature should be higher than metallurgical limits.

  3. Reasonable saturation pressure at maximum temperature of the cycle from metallurgical point of view of boiler.

  4. Steep saturated vapor line to minimum moisture problem in expansion of steam in the turbine.

  5. It should wet the boiler surface enveloping it and should be chemically stable at the maximum temperature of the boiler.

  6. Saturation pressure at minimum temperature of the cycle should be higher than atmospheric, otherwise the maintenance of the condenser will be costly.

  7. Low liquid specific heat so that most of the heat is added at the maximum temperature.

  8. Considerable decrease of volume upon condensation.

  9. Non-toxic and non-corrosive

  10. Freezing point should be much below the normal atmospheric pressure.

Among all types of working fluids, water satisfies the maximum requirements. Its general, abundance at low cost is of prime importance due to which it is selected as the working fluid in steam turbine power plant.

Last modified: Wednesday, 11 September 2013, 5:11 AM