Simple Vapour Power Cycles: Carnot & Rankine Steam Plant Cycles | Thermodynamics

In this article we will discuss about simple vapour power cycles. Learn about:- 1. Carnot Cycle and Steam Plant 2. Rankine Cycle.

The heat energy released due to the combustion of fuel will be utilised in the boilers for converting water into steam (i.e., vapour) and this steam is then expanded into the steam engine/steam turbines to obtain useful work. The steam after producing work output is generally condensed in the condensers. If the condensate is pure, then it is pumped as feed water to the boiler by means of a feed pump.

1. Carnot Cycle and Steam Plant:

As we know, the Carnot cycle has the greatest possible efficiency between any two given temperature limits T₁ and T₂ and is given by η_th = (T₁ – T₂)/T₁. It is important therefore to see whether Carnot cycle can be successfully applied to the steam plant.

Process 1-2:

This is an isothermal heat addition process and during this, water in the boiler gets converted into steam at constant temperature and pressure.

At point 2, steam is dry saturated.

Process 2-3:

The steam is expanded adiabatically isentropically in the steam turbine or steam engine from pressure P₁ to P_b.

Process 3-4:

The steam after producing work output in the turbine enters the condenser. During this process isothermal heat rejection q_r takes place and results into condensation of steam.

Process 4-1:

Partially condensed steam at 4 is fed into the feed pump, which pumps/compresses the mixture of wet steam and condensate isentropically to boiler pressure.

Even though, the Carnot efficiency is maximum for a given value T₁ and T₂. But because of some inherent practical difficulties, Carnot cycle cannot be applied for the steam plant.

Carnot cycle when applied to S.P.P. is practical upto a point that. Isothermal heat addition and the adiabatic expansion of steam in the turbine, which is quite reasonable.

The impractical part is in handling of steam in the condenser and pump. In the condenser, the steam is only partially condensed and the condensation must be stopped at 4. Also the feed pump must be capable of handling both wet steam and condensate.

A slight modification is made to this Carnot cycle which however produces a more practical cycle, called Rankine cycle. This cycle is accepted as, the practical but ideal cycle for the steam plant even though it has reduced thermal efficiency.

2. Rankine Cycle:

To obtain Rankine cycle, modification made to Carnot cycle, is that, instead of stopping the condensation at some intermediate condition, the condensation is completed.

On T-S diagram Carnot cycle, would be 1′-2-3-4′. For Rankine cycle, however, condensation is continued until it is complete at 4. At this point there is all water. This can be successfully dealt with by the feed pump.

Process 4-1:

Pumping process, where water of condenser pressure P_b is raised to boiler pressure P₁. The pumping compression process is isentropic. At point (1) temperature is lower than T_sat. Subcooled state.

Process 1-2: (1 – 1′ and 1′ – 2)

During 1-1′ feed water is heated to T_sat (may occur in economiser/boiler itself.) During 1′ – 2 heat added q_t at constant temperature and pressure P₁ convert water into steam in the boiler.

Process 2-3:

Isentropic expansion of steam in the turbine from boiler pressure P₁ to back pressure P_b, which results into turbine work W_T.

Process 3-4:

The steam is condensed at constant pressure P_b in the condenser. The steam rejects heat q_r to the cooling water.

It should be noted that the steam generated in the boiler or steam entering the turbine may be wet, dry-saturated and superheated. Correspondingly the expansion process in the turbine will be 2′-3′, 2-3, 2″-3″ respectively.

Analysis of Rankine Cycle (Assuming 1 kg of Steam):

From Eq. (5) we get q – w = Δ h

Process 1-2:

In the boiler heat q_i converts water into steam

q_i = h₂– h₁ (since q = 0)

Process 2-3:

In the turbine, when the steam expands, work will be produced.

W_T = h₂ – h₃ kJ/kg (since q = 0)

Process 3-4:

In the condenser condensation will be completed and an amount of heat q_r is rejected to the cooling water.

q_r = h₄-h₃

i.e., q_r = – [h₃ – h₄] Negative sign implies heat rejection.

Process 4—1:

Note:

For solving the problems we can read the value of h₄ = h_f from steam tables at back pressure P_b, h₂ and h₃ can be determined with the help of Mollier diagram or by calculations from steam tables. Since W_p = h₁-h₄ the volume of h₁ can be determined by using Eq. (8) i.e., by finding W_p.

It should be noted that η_R < η_carnot because the mean temperature of heat addition process in Rankine cycle is lower than the mean temperature of heat addition process in Carnot cycle. Whereas the mean temperature of heat rejection process in both the cycles is same.

In order to improve the efficiency of Rankine cycle, superheated steam has to be used, as represented by the process 2-2″. It improves the cycle efficiency, as it increases the mean temperature of heat addition process in the boiler. Also when the superheated steam is used, it reduces the corrosion of turbines.

The Rankine efficiency has the same form as before, from Fig. 14.3 on similar lines-

Effect of Inlet Pressure (Boiler Pressure) and Back Pressure (Exhaust Pressure) and Superheat on Rankine Efficiency:

The effect of inlet pressure, back pressure and the superheat on the performance of Rankine cycle can be studied with the help of T-S diagram as shown in fig. 14.4.

Boiler or Inlet Pressure:

If the boiler pressure is raised, the evaporation line is raised as the saturation temperature is increased from 4-1 to em. The maximum temperature t₁ is kept constant i.e., t_m, = t₁. 1-2-3-4-1 is the basic cycle taken for comparison.

With increased boiler pressure, keeping the condenser pressure and temperature constant, the new cycle will be m 03 qem. The amount of heat rejected is decreased given by C20 pc and difference in the heat added –b341cb and bqempb is small and the thermal efficiency increases. It is experimentally found that at p₁ = 170 bar and p₂ = 0.14 bar, the efficiency is maximum and decrease with increase in p₁.

Condenser Pressure and Temperature is Lowered:

The new cycle will be 1 dk 41. Work done is increased and heat rejected will be less so that the efficiency will be increased. Nature, however, precisely defines the limit of improvement that may be obtained by this means. Atmo­spheric temperature and therefore temperature of the cooling water puts the limits of the steam temperature and pressure.

Superheat:

If the steam is dry and saturated at the inlet of turbine, and if the steam is superheated then the work is increased and the proportional rise of work is more than the heat supplied so that the efficiency of the Rankine cycle increases.

It is interesting to note that condensing plants commonly operate more efficiently in the winter than in summer because of the lower cooling water temperature in the winter.