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.

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 Rankine cycle, if we can figure out the methods for increasing the efficiency of the Rankine cycle and therefore we have already discussed the various methods for increasing the efficiency of the rankine cycle in our recent post.

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 basic concept of regenerative Rankine cycle with feedwater heater.

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. we have already discussed the concept of mean temperature of heat addition in our post "Concept of regeneration in Rankine cycle".

Therefore, Efficiency of a simple rankine cycle will be calculated by following formula.
Î·= 1-[T2Â / Tm1]
In order to increase the efficiency of the Rankine cycle we will have to increase the mean temperature of heat addition i.e. Tm1. 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 have seen the basic concept of regeneration in Rankine cycle in our previous post for increasing the mean temperature of heat addition and hence efficiency of the Rankine cycle.

We must note it here that the 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.

### So let us see the regenerative Rankine cycle with feedwater heater with the help of this post

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. A feedwater heater is basically defined as one type of heat exchanger where heat will be transferred from the steam to the feedwater by the process of mixing the two fluid streams i.e. open feedwater heaters or without mixing them i.e. closed feedwater heaters.

### Let us see the block diagram of regenerative Rankine cycle with feedwater heater

Let us see the following block diagram, high temperature and high pressure steam will be entered in to the turbine at state 1 and will be expanded through the turbine up to condenser pressure at state 2 but we must note it here that 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 at state 2 as shown in following figure.
In this case we have used single feedwater heater as shown in figure and state of the extracted steam displayed here by the state 5. Let if 1 Kg of steam is entering to the turbine from boiler and as we have discussed that certain quantity of the steam will be extracted hence let Y kg of steam is extracted from the turbine at state 5 as shown in figure and therefore (1-Y) kg of steam will be expanded through the turbine up to the condenser pressure.

Expanded steam will process through condenser as usual and will reach to state 3. At state 3, working fluid will be in liquid state and here working fluid will enter to the feed pump where feed pump will pressurize it and will deliver at state 4.

Working fluid, at state 4, will enter to the feedwater heater also termed as heat exchanger where working fluid (condensate from condenser) will be mixed with extracted steam from the turbine. Process will be controlled in such a fashion that discharge of feedwater heater or heat exchanger will be in the state of saturated liquid state and it will be displayed here by the state 6 as shown in figure.

Working fluid at the state 6 will enter in to the feed pump and feed pump will pressurize the working fluid up to the boiler pressure at state 7 and working fluid will enter in to the boiler at state 7 as shown in figure.

Heat energy addition to the working fluid will be carried out in the boiler during the process 7 to 1. Working fluid will enter in to the boiler at state 7 and will be heated to state 1 as displayed in block diagram and TS diagram too.

### Let us see the process briefly here as displayed in TS diagram

Process 1-2: Expansion of steam through the turbine with constant entropy

Process 2-3: Condensation process through the condenser at constant pressure

Process 3-4: Pressurization of the working fluid by the feed pump I up to the pressure at which working fluid will enter in to the feedwater heater for mixing with the extracted steam

Process 4-6: Working fluid at state 4 and extracted steam at state 5 will be entered in to the feedwater heater and hence process 4-6 will be termed as heat energy addition to the working fluid internally in the heat exchanger or feedwater heater.

Process 6-7: Pressurization of the working fluid by the feed pump II up to the boiler pressure at which working fluid will enter in to the boiler for heat energy addition

Process 7-1: Heat energy addition to the working fluid at constant pressure during the process 7-1

Work done by the turbine
WT = (h1-h5) + (1-Y) (h5-h2)

Net work from the cycle
W Net = WT â€“ (WP1 + WP2)
Let us ignore the pump works as it will be quite small as compared to the work done by the turbine and therefore we can say that net work from the cycle will be equivalent to the work from the turbine.
W Net = (h1-h5) + (1-Y) (h5-h2)
Net input heat energy
Q =h1-h7
We can also see that during the process 4-6, heat energy will be added but we must note it here that this heat energy addition will be done by the extracted steam in the heat exchanger or feedwater heater and hence this is an internal heat addition and hence we do not have to write this addition of energy as input energy.

Efficiency of the cycle with regeneration with single feedwater heater will be calculated as mentioned here
Î·= [(h1-h5) + (1-Y) (h5-h2)]/ (h1-h7)

Do you have any suggestions? Please write in comment box.
We will see another topic in our next post in the category of thermal engineering.

### Reference:

Engineering thermodynamics by P. K. Nag
Engineering thermodynamics by Prof P. K. Das