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Ideal Verses Actual Rankine Cycle

Rankine Cycle is a known mechanical cycle which is being commonly used in the power plants for converting the pressure energy of steam into mechanical energy using steam turbines. Major components of it are rotating steam turbine and boiler pump and stationary condenser and boiler. Boiler is used for heating the water for generation of steam at required pressure and temperature as per the requirement of the turbine for power generation. Turbine exhaust is directed to the radial or axial flow condenser for condensing the steam to condensate and recycled back to the boiler through boiler pumps for heating again.
The efficiency of the ideal Rankine cycle as described in the earlier section is close to the efficiency of Carnot Cycle. But in real plants, each stage of the Rankine cycle is associated with some irreversible processes and thus the efficiency of the actual Rankine cycle is far lower than the ideal Rankine cycle efficiency.

Given below Fig. 1-a and Fig 1-b represents the Rankine cycle on P-v and T-s diagram ideal verses actual in rankine cycle v vs p and s vs t

Rankine Cycle Representation are as follows on P-v and T-s diagrams:
Ideal Rankine Cycle1-2'-b-3'-4'-1
Actual Rankine Cycle1-2-b-3-4-1
Critical Point (CP) is in centre of the curve as shown in Fig 1-a and 1-b above. The curved lines on the left side of the CP are saturated- liquid lines and the region/area to the left of these lines are called as sub-cooled liquid regions.
Similarly curved lines on the right side of the CP are saturated- vapour lines and the region/area to the right of these lines are called as super-heat vapour regions.

Energy Analysis of Ideal Rankine Cycle

All components of Rankine cycle (Boiler, turbine, condenser and pump) are examples of steady flow process and to be analysed accordingly. Energy balance for the Ideal cycle is as follows:
Ideal Rankine Cycle Components Heat Work
Boiler feed Pump Wpump-in
Boiler
Turbine
Condenser
Thermal efficiency of Ideal Rankine cycle

Energy Analysis of Actual Rankine Cycle

The actual vapour cycle differs from the ideal Rankine Cycle, as a result of irreversibility in various components. Two major factors of irreversibility are Fluid friction and the heat loss.

Fluid Friction

It causes major pressure drop in the boiler circuitry and also in the condenser and the piping circuit of the low pressure piping. Because of the fluid friction pressure drop in the boiler circuitry, the pressure of the steam leaving the boiler will be at somewhat lower pressure. Also the steam has to be conveyed to steam turbine via steam piping which also accounts for further pressure drop. So the steam which reaches the turbine stop valve will be at lower pressure than that of the boiler discharge pressure and the same is represented by 3’ ( Fig-1a) in the actual Rankine Cycle instead of 3 in the Iideal Rankine Cycle.
If we don’t want to compromise on the turbine output, then we must compensate for the pressure drop/loss and restore the turbine inlet pressure to point 3 in Fig 1-a, by increasing the boiler pump pressure sufficiently higher to compensate the losses/drop and in the process increasing the size of the pump and the requirement of input power. The other reason of irreversibility is the loss of heat in steam in its transportation and malfunctioning of the steam traps etc.

Thus in order to compensate for these losses we need to generate more steam and that too at higher pressure for the desired rated power generation from the turbine, as a result lowering the cycle efficiency.
Energy balance for the actual Rankine Cycle is as follows:

Actual Rankine Cycle ComponentsHeatWork
Boiler feed Pump Wpump-in
Boiler
Turbine
Condenser
Thermal efficiency of Ideal Rankine cycle

While calculating the over all cycle efficiency Turbine and pump irreversibilities needs to be given due importance. For small units usually pump work are negligible and can be neglected but in larger units pump work is appreciable and can’t be neglected like that.
Actual/Practical Rankine cycle is based on the deviation of flow in turbine and pressure requirement in pump from the isentropic one and is defined as follows:  Where,
h2a Actual enthalpy at the pump exit
h4a Actual enthalpy at the turbine exit
h2s Ideal isentropic enthalpy at the pump exit
h4s Ideal isentropic enthalpy at the turbine exit

Other factors Irreversibility are:

Other factors responsible for irreversibility of actual vapour power cycle are:
  • Sub-cooling of condensate in condenser
  • Losses associated with bearings
  • Steam leakages
  • Condenser air-leaks



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