ACTUAL RANKINE CYCLE VERSUS IDEAL RANKINE CYCLE

We were discussing “Rankine cycle” in our previous post, where we have seen the various components of Rankine cycle and its basic operations also. A steam power plant works on the principle of Rankine cycle and hence we can say that a steam power plant will be designed in such a way that process of each component of power plant will follow the process of Rankine cycle.

Today we will see here the basic concept of actual Rankine cycle process or actual vapour cycle process with the help of this post.

Actual Rankine cycle or actual vapour cycle process

Let us first draw here the theoretical Rankine cycle or ideal Rankine cycle.

Processes of an actual Rankine cycle will be slightly different with the processes of an ideal Rankine cycle, because in practice there will be various irreversibilities in various components of Rankine cycle. Heat losses to surrounding and friction will be the main causes of irreversibilities and we will also discuss here the deviation of actual vapour cycle with the ideal Rankine cycle.

Turbine losses

Let us consider the turbine first. During discussion of the ideal Rankine cycle, we have considered that the process through turbine will be reversible and adiabatic and therefore we have shown the process 1-2 as isentropic process and it is displayed in figure by a vertical line showing that entropy will be constant.

When we consider the actual vapour cycle process, 1-2 process will not be vertical or 1-2 process will not be isentropic. Pressure drop because of friction and loss of heat energy to surrounding are the most important causes of irreversibilities.

We can insulate the turbine in order to reduce the heat loss and hence we can also reduce the irreversibilities due to thermal dissipation. We can insulate the turbine quite enough and we can minimise the loss of heat energy. In some cases we can not say that the loss of heat energy is nill even with proper insulation also or in other way we can say that there will be some loss of heat energy.

We can not avoid the irreversibilities due to friction as we can never say that there will be frictionless flow through the turbine and hence the irreversibilities due to friction must be considered during drawing the actual vapour cycle.

T-S diagram of actual vapour cycle

Now let us consider the process 1-2, process 1-2 line will not be vertical but also it will move towards right side as shown in figure above because according to the principle of increase in entropy there will be increment in entropy during this process.

Actual work done by turbine, W_T = h₁-h¹₂

Ideal work done by turbine, W_{T, Actual} = h₁-h₂

As we know that friction will be present during the process of expansion through the turbine and therefore friction will be converted in terms of intermolecular energy and this intermolecular energy will increase the temperature and hence enthalpy will also be increased.

Therefore h¹₂> h₂

We can also say that actual work done by turbine will be less as compared to the ideal work done by turbine.

Let us see here the turbine efficiency, η_T

η_T = (h₁-h¹₂)/( h₁-h₂)

Pump losses

Similarly, we can see the deviation or changes in process 3-4. Process 3-4 indicates the ideal process for working fluid flowing through feed pump. In practical, process 3-4¹ will be the process for working fluid flowing through feed pump.

Now we will see the ideal work required by the feed pump and also actual work required by the feed pump here.

Actual work required by the feed pump, W_P = h¹₄ – h₃

Ideal work required by the feed pump, W_{P, Actual} = h₄-h₃

As we can easily observe that h¹₄> h₄ and therefore actual work required by the feed pump will be greater as compared to the ideal work required by the feed pump.

Ratio of ideal work required by the feed pump to the actual work required by the feed pump will be termed as efficiency of feed pump.

Let us see here the feed pump efficiency, η_P

η_T = (h₄-h₃)/( h¹₄ – h₃)

So, we have considered here the two important components i.e. turbine and feed pump of rankine cycle and we have also seen here the losses and deviation in curve too.

Boiler

Let us consider the third important component of rankine cycle i.e. Boiler. We have discussed earlier that heat addition will be done at constant pressure in boiler. There will also be loss in pressure in boiler too because of the presence of friction. But we must note it here that pressure drop in boiler will be very less as compared to the boiler pressure. 

We can neglect this pressure drop as it will be very less as compared to the boiler pressure, but we have considered this pressure drop also and it is displayed in PV diagram of actual Rankine cycle.

PV diagram of actual Rankine cycle

If we insulate the boiler in order to avoid the loss of heat energy, then there will be approximate adiabatic process. We can not say that there will be no loss of heat energy, there will be surely some amount of heat energy  which will be lost to the surrounding even with optimum insulation of boiler too.

In simple way we can say that, in practical case or in actual vapour cycle, working fluid at the inlet of turbine will suffer with slightly pressure drop due to friction and also suffer with slightly temperature drop due to heat loss.

Condenser losses

Losses in condenser will be quite less and it will consist loss of pressure and cooling of condensate below the saturation temperature.

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 S. K. Som

Image courtesy: Google

Also read

Difference between Rankine and Carnot cycle

Application of solar energy

Principles of hydraulics

Differential and non-differential hydraulic cylinder

Show that entropy is a property of the system