BASIC CONCEPT OF AN IDEAL REGENERATIVE RANKINE CYCLE

We were discussing “Concept of regeneration in Rankine cycle” in our recent post, where we have discussed the basic concept of regeneration. We have also drawn there a simple Rankine cycle and we have also studied there the concept to increase the efficiency of the Rankine cycle.

So, today we will apply that concept of regeneration here with Rankine cycle and we will see that how we can increase the efficiency of the Rankine cycle. When we will apply the concept of regeneration with simple Rankine cycle then we will have one modified Rankine cycle which will be termed as Ideal regenerative cycle.

So let us see the Ideal regenerative cycle with the help of this post

Let us first draw here one simple Rankine cycle to refresh the basic concept of heat addition and heat rejection in simple Rankine cycle and then we will go ahead to understand the concept of ideal regenerative cycle by drawing the block diagram for ideal regenerative cycle.

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.

For steam power cycle such as Rankine cycle, we have studied earlier the concept of mean temperature of heat addition in our recent post and we have concluded there that we will have to increase the mean temperature of heat addition in order to improve the efficiency of the Rankine cycle.

Mean temperature of heat addition in Rankine cycle could be increased by increasing the amount of heat energy supplied at high temperature by the process of increasing superheat, by using reheat or by using higher temperature and higher pressure of steam.

In simple, if we can increase the mean temperature of heat addition in Rankine cycle by increasing the maximum temperature of the Rankine cycle i.e. T1.

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.

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.

As we can see the above Rankine cycle, considerable quantity of heat energy will be added to the working fluid during its liquid phase or during sensible heating or during subcooled region. Only less part of heat energy addition will be added at maximum temperature i.e. at T₁.

If we want to increase the efficiency of the cycle, we must be aware that all heat energy must be supplied at maximum temperature of the cycle i.e. at temperature T₁ in this cycle and hence we will have to think the method by which we can permit the feed water to enter in to the boiler at state 5 so that all heat energy supplied by boiler to the working fluid will be carried out at maximum temperature of the Rankine cycle i.e. T₁ in this case.

Let us see the block diagram of ideal regenerative cycle

If we can use the heat energy of the high temperature steam, which is flowing through the turbine during the expansion process 1-2, to heat the feed water from 4 to 5 then all heat energy supplied by the boiler will be done at maximum temperature of the cycle.

Hence mean temperature of heat addition will be T₁ itself because all heat energy supplied by the boiler to the working fluid will be completed at maximum temperature T₁ during process 5 to 1.

Therefore, feed water leaving the feed pump will be circulated around the casing of the turbine in opposite direction of the direction of steam flow during expansion process 1-2 in the turbine.

The basic concept of regenration in rankine cycle is that we will have to make an arrangement to heat the feed water leaving the feed pump by the high temperature steam flowing through the turbine during the process 1-2.

Let us see the arrangement of an ideal regenerative cycle with the help of following block diagram

So if feed water will reach to dry saturated liquid state, by receiving heat energy from the hot steam flowing through turbine, before entering to the boiler then all heat energy supplied by the boiler to the working fluid will be done at maximum temperature of the cycle and hence mean temperature of heat addition will be T₁ and therefore in that situation we will have higher efficiency of the Rankine cycle.

We must note it here that the above solution of increasing the efficiency of the Rankine cycle by the concept of regeneration is practically not suitable because it will be quite difficult to design the heat exchanger suitable for above solution and also at the final stage of the turbine there will be increment in the content of moisture in the steam.

If we consider the case of practical regeneration process for a Rankine cycle, high temperature and high pressure steam will enter in to the turbine at state 1. Entire steam will not be expanded up to the condenser pressure through the turbine but also certain quantity of the steam will be extracted through various points from turbine and will be used for heating the feedwater and rest quantity of steam will be expanded up to the condenser pressure.

Device where feedwater will be heated by the concept of regeneration will be termed as feedwater heater.

We will discuss the “Regenerative cycle with feedwater heater” in our next post.

Do you have any suggestions? Please write in comment box.

Reference:

Engineering thermodynamics by P. K. Nag

Engineering thermodynamics by Prof S. K. Som

Image courtesy: Google

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