# RANKINE CYCLE

### Basic Cycle

The Rankine cycle is the fundamental operating cycle of all power plants where an operating fluid is continuously evaporated and condensed. The selection of operating fluid depends mainly on the available temperature range. Figure 1 shows the idealized Rankine cycle.

The pressure-enthalpy (p-h) and temperature-entropy (T-s) diagrams of this cycle are given in Figure 2. The Rankine cycle operates in the following steps:

• 1-2-3 Isobaric Heat Transfer. High pressure liquid enters the boiler from the feed pump (1) and is heated to the saturation temperature (2). Further addition of energy causes evaporation of the liquid until it is fully converted to saturated steam (3).

• 3-4 Isentropic Expansion. The vapor is expanded in the turbine, thus producing work which may be converted to electricity. In practice, the expansion is limited by the temperature of the cooling medium and by the erosion of the turbine blades by liquid entrainment in the vapor stream as the process moves further into the two-phase region. Exit vapor qualities should be greater than 90%.

• 4-5 Isobaric Heat Rejection. The vapor-liquid mixture leaving the turbine (4) is condensed at low pressure, usually in a surface condenser using cooling water. In well designed and maintained condensers, the pressure of the vapor is well below atmospheric pressure, approaching the saturation pressure of the operating fluid at the cooling water temperature.

• 5-1 Isentropic Compression. The pressure of the condensate is raised in the feed pump. Because of the low specific volume of liquids, the pump work is relatively small and often neglected in thermodynamic calculations.

The efficiency of power cycles is defined as

(1)

Values of heat and work can be determined by applying the First Law of Thermodynamics to each step. The steam quality x at the turbine outlet is determined from the assumption of isentropic expansion, i.e.,

(2)

where is the entropy of vapor and Si* the entropy of liquid.

### Inefficiencies of Real Rankine Cycles

The efficiency of the ideal Rankine cycle as described in the previous section is close to the Carnot efficiency (see Carnot Cycle). In real plants, each stage of the Rankine cycle is associated with irreversible processes, reducing the overall efficiency. Turbine and pump irreversibilities can be included in the calculation of the overall cycle efficiency by defining a turbine efficiency according to Figure 3

(3)

where subscript act indicates actual values and subscript is indicates isentropic values and a pump efficiency

(4)

If ηt and ηp are known, the actual enthalpy after the compression and expansion steps can be determined from the values for the isentropic processes. The turbine efficiency directly reduces the work produced in the turbine and, therefore the overall efficiency. The inefficiency of the pump increases the enthalpy of the liquid leaving the pump and, therefore, reduces the amount of energy required to evaporate the liquid. However, the energy to drive the pump is usually more expensive than the energy to feed the boiler.

Even the most sophisticated boilers transform only 40% of the fuel energy into useable steam energy. There are two main reasons for this wastage:

• The combustion gas temperatures are between 1000°C and 2000°C, which is considerably higher than the highest vapor temperatures. The transfer of heat across a large temperature difference increases the entropy.

• Combustion (oxidation) at technically feasible temperatures is highly irreversible.

Since the heat transfer surface in the condenser has a finite value, the condensation will occur at a temperature higher than the temperature of the cooling medium. Again, heat transfer occurs across a temperature difference, causing the generation of entropy. The deposition of dirt in condensers during operation with cooling water reduces the efficiency.

### Increasing the Efficiency of Rankine Cycles

#### Pressure difference

The net work produced in the Rankine cycle is represented by the area of the cycle process in Figure 2. Obviously, this area can be increased by increasing the pressure in the boiler and reducing the pressure in the condenser.

#### Superheating and reheating

The irreversibility of any process is reduced if it is performed as close as possible to the temperatures of the high temperature and low temperature reservoirs. This is achieved by operating the condenser at subatmospheric pressure. The temperature in the boiler is limited by the saturation pressure. Further increase in temperature is possible by superheating the saturated vapor, see Figure 4.

This has the additional advantage that the vapor quality after the turbine is increased and, therefore the erosion of the turbine blades is reduced. It is quite common to reheat the vapor after expansion in the high pressure turbine and expand the reheated vapor in a second, low pressure turbine.

#### Feed water preheating

The cold liquid leaving the feed pump is mixed with the saturated liquid in the boiler and/or re-heated to the boiling temperature. The resulting irreversibility reduces the efficiency of the boiler. According to the Carnot process, the highest efficiency is reached if heat transfer occurs isothermally. To preheat the feed liquid to its saturation temperature, bleed vapor from various positions of the turbine is passed through external heat exchangers (regenerators), as shown in Figure 5.

Ideally, the temperature of the bleed steam should be as close as possible to the temperature of the feed liquid.

#### Combined cycles

The high combustion temperature of the fuel is better utilized if a gas turbine or Brayton engine is used as "topping cycle" in conjunction with a Rankine cycle. In this case, the hot gas leaving the turbine is used to provide the energy input to the boiler. In co-generation systems, the energy rejected by the Rankine cycle is used for space heating, process steam or other low temperature applications.