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HOW CAN WE INCREASE THE EFFICIENCY OF THE RANKINE CYCLE

We were discussing “The basic concept of Rankine cycle in a steam power unit ” in our recent post, where we have discussed the various components of steam power cycle and their basic operation too.

As we know that largest source of production of electric power in the world is steam power plants and these steam power plants work on the principle of Rankine cycle or we can say that steam power units are designed to work on Rankine cycle.

If we can try to figure out the methods for increasing the efficiency of Rankine cycle then we will be able to reduce the consumption of fuels or in other words we can say that we will have more work output from the cycle.

Therefore let us see here the various methods by which we can increase the efficiency of the Rankine cycle

Let us first draw here one simple Rankine cycle to refresh the basic concept of heat addition process and heat rejection process in simple Rankine cycle and then we will go ahead to understand the various methods for increasing the efficiency of the Rankine cycle on which steam power units are based.
As we have studied in our previous post that heat energy will be added in simple Rankine cycle during the process of 4-1 and heat energy will be rejected during the process of 2-3. Let us recall the Carnot cycle, we have discussed there that heat energy will be added isothermally and heat energy will be rejected isothermally too. Here in simple Rankine cycle, heat energy will be rejected isothermally but heat energy will not be added to the working fluid isothermally. 

We can see from simple Rankine cycle that heat energy will be added partially at constant temperature and rest of heat energy will be added to the working fluid at varying temperature and this is the main deviation of Rankine cycle with the concept of Carnot cycle. 


Hence we will have lower efficiency for a Rankine cycle as compared with the Carnot cycle efficiency. So we will have one term known as mean temperature of heat addition i.e. Tm1.


Mean temperature of heat addition i.e. Tm1 will be termed as a constant temperature, located between T1 and T4, at which if same quantity of heat energy will be added then we will have same change in entropy as we were having changes in entropy during the process 4-1.



Therefore, Efficiency of a simple rankine cycle will be calculated by following formula.



η= 1-[T2 / Tm1]

Now we will have basic concept behind each modification for enhancing the efficiency of a steam power plant. There will be basically two basic concepts from above formula of efficiency of a steam power cycle. 



First concept, we will have to increase the mean temperature of heat addition i.e. Tm1. Second concept, we will have to decrease the temperature of heat rejection i.e. T2



There is one more way to increase the thermal efficiency of the Rankine cycle by increasing the boiler pressure. 


Now we will discuss these three basic concepts, with the help of this post, for increasing the thermal efficiency of a steam power cycle or Rankine cycle.

Lowering the condenser pressure and temperature of heat rejection

Temperature at which heat energy will be rejected could be lowered by lowering the operating pressure of condenser. Thermal efficiency of the Rankine cycle, as we have discussed earlier, will be increased by reducing the temperature of heat energy rejection.
We can see here, in following TS plane, the effect of lowering the condenser pressure on cycle efficiency. We have maintained temperature of the working fluid constant i.e. T1 at the inlet of the turbine in order to determine the effect of lowering the condenser pressure on cycle efficiency.
We have reduced the condenser pressure from P2 to P2’ and we can easily observe here in TS plane the increase in net work output from the Rankine cycle. We have displayed the increment in net work output of the cycle by the colored area.

Heat energy input will also be increased as a result of lowering the condenser pressure but this increment in heat energy input will be very small and final result will be increase in the efficiency of the cycle as result of lowering the condenser pressure.

We can not reduce the operating pressure of condenser below the saturation pressure corresponding to the temperature of the cooling medium and this pressure will be termed as lower limit on condenser pressure and we will never reduce the condenser pressure below this lower limit.

We have seen the positive point of lowering the condenser pressure i.e. increases in thermal efficiency of the Rankine cycle. Now we must note it here the negative points too from lowering the condenser pressure in Rankine cycle.

As we can see that at the exit of the turbine, working fluid will be at dry saturated vapour state at point 2 at condenser pressure P2. Now let us see, for same inlet temperature of the working fluid i.e. T1 at the inlet of the turbine, the quality of steam at the final stage of the turbine after reducing the condenser pressure to P2’.

We can see that quality of working fluid is reduced after reducing the condenser pressure to P2’. Hence we can say that lowering the condenser pressure will increase the moisture content in steam at the final stage of the turbine. This increased moisture content will surely deteriorate the turbine blade by the process of corrosion and hence efficiency of the turbine will be reduced.

Superheating the steam to high temperature

As we have discussed earlier that we can increase the thermal efficiency of the steam power cycle by increasing the mean temperature of heat energy addition. Mean temperature of heat energy addition could be increased by increasing the temperature of the steam by heating the working fluid to a high degree of superheat. 

We can see the effect of heating the steam to a high degree of superheat over the efficiency of the steam power cycle i.e. Rankine cycle in following figure.
Heat energy input and net work from the cycle will be increased as a result of increasing the temperature of the steam by heating the working fluid to a high degree of superheat. Overall effect will be increase in the thermal efficiency of the Rankine cycle as a result of increasing the temperature of the steam by heating the working fluid to a high degree of superheat.

We will have one more positive result that moisture content in the steam will be reduced at the final stage of the turbine as a result of increasing the temperature of the steam by heating the working fluid to a high degree of superheat.

We must note it here that temperature of heat addition could be increased up to a limit only as it will be restricted by various practical parameters such as material properties of turbine blades. Turbine blade material will not work satisfactory if we increase the maximum temperature of Rankine cycle i.e. T1 above a certain level and that level of temperature will be termed as maximum allowable temperature and we could not increase the temperature T1 of the Rankine cycle beyond this maximum allowable temperature.

Increasing the boiler pressure

We can also increase the boiler pressure in order to increase the efficiency of the Rankine cycle because range of temperature for heat energy addition will be increased.
We can see the effect of increasing the boiler pressure over the efficiency of the steam power cycle i.e. Rankine cycle in following figure.
We have maintained temperature of the working fluid constant i.e. T1 at the inlet of the turbine in order to determine the effect of increasing the boiler pressure over the efficiency of the steam power cycle.

We can see that content of the moisture in the steam will be increased as a result of increasing the boiler pressure and therefore this increased moisture content will surely deteriorate the turbine blade by the process of corrosion and hence efficiency of the turbine will be reduced.

We will see another topic “Difference between Rankine cycle and Carnot Cycle” in our next post.
Do you have any suggestions? Please write in comment box.

References

Thermodynamics an engineering approach by Y. A. Çengel and M. A. Boles
Engineering thermodynamics by P. K. Nag

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