Understanding Rankine and Carnot Cycles

The Carnot cycle is considered the most efficient thermodynamic cycle possible between two given temperature limits. The efficiency of any real heat engine, like one operating on the Rankine cycle, is always less than or equal to the efficiency of a Carnot cycle operating between the same temperature limits.

The basic Rankine cycle consists of four processes: pumping, heating (in a boiler), expansion (in a turbine), and condensation. While the expansion and compression (pumping) processes are ideally isentropic, the heat addition (in the boiler) and heat rejection (in the condenser) processes in the basic Rankine cycle do not occur isothermally at the maximum and minimum temperatures, respectively. This is the primary reason for its lower efficiency compared to the Carnot cycle.

Improving Rankine Cycle Efficiency: Regeneration and Reheating

Two common modifications are used to improve the efficiency of the Rankine cycle: Regeneration and Reheating.

Regeneration:

• Regeneration involves preheating the feedwater before it enters the boiler.
• This is typically done by extracting steam from intermediate stages of the turbine and using it to heat the feedwater in devices called feedwater heaters (regenerators).
• By preheating the feedwater, the amount of heat added externally in the boiler is reduced, and more importantly, the average temperature at which heat is added approaches the maximum temperature of the cycle.
• The Carnot cycle's heat addition occurs entirely at the maximum temperature. By increasing the average temperature of heat addition through regeneration, the Rankine cycle's efficiency increases, bringing it closer to the Carnot efficiency.
• If an infinite number of regenerators were used (which is an idealization), the heat addition process in the boiler would become closer to an isothermal process at the maximum temperature, making the Rankine cycle approach the Carnot cycle.

Reheating:

• Reheating involves expanding steam in the turbine partially, returning it to the boiler to be reheated at constant pressure, and then expanding it further in a lower-pressure turbine section.
• Reheating primarily increases the net work output and reduces the moisture content at the turbine exhaust, which improves turbine reliability.
• While reheating improves the Rankine cycle efficiency, it does so mainly by increasing the average temperature during a portion of the heat addition process (the reheat section). However, it doesn't make the main heat addition process (in the boiler) more isothermal at the high temperature limit in the same way that regeneration does.
• Therefore, increasing the number of reheaters does not cause the Rankine cycle to approach the Carnot cycle in the same fundamental way that increasing regenerators does regarding the average temperature of heat addition.

Conclusion

The Rankine cycle efficiency is limited by the fact that heat addition occurs over a range of temperatures below the maximum temperature. To approach the efficiency of a Carnot cycle operating between the same maximum and minimum temperatures, the Rankine cycle needs to make its heat addition process closer to isothermal at the maximum temperature. This is achieved by regeneration.

Increasing the number of regenerators in a Rankine cycle increases the average temperature of heat addition. In the limit of infinite regeneration stages, the Rankine cycle's thermal efficiency approaches that of the Carnot cycle operating between the maximum and minimum temperatures.

Therefore, the Rankine cycle will approach the Carnot cycle if the number of regenerators is increased.