THE RANKINE CYCLE BASIC DEFINITION AND TUTORIALS


The Rankine cycle is the most widely used cycle for electric power generation. Figure 2.1 illustrates a simplified flow diagram of a Rankine cycle. Figure 2.2(a, b) shows the ideal Rankine cycle on P-v and T-s diagrams.

FIGURE 2.1 Schematic flow diagram of a Rankine cycle.

Cycle 1-2-3-4-B-1 is a saturated Rankine cycle (saturated vapor enters the turbine). Cycle 1′-2′-3-4-B-1′ is a superheated Rankine cycle.

The cycles shown are internally reversible. The processes through the turbine and pump are adiabatic reversible. Hence, vertical on the T-s diagram. There are no pressure losses in the piping. Line 4-B-1-1′ is a constant-pressure line.

The reversible Rankine cycle has the following processes:
Line 1-2 or 1′-2′. Adiabatic reversible expansion through the turbine. The exhaust vapor at point 2 or point 2′ is usually in the two-phase region.

Line 2-3 or 2′-3. Constant-temperature and, being a two-phase mixture process, constant- pressure heat rejection in the condenser.

Line 3-4. Adiabatic reversible compression by the pump of saturated liquid at the condenser pressure, point 3, to subcooled liquid at the steam generator pressure, point 4.

Line 3-4 is vertical on both the P-v and T-s diagrams because the liquid is essentially incompressible and the pump is adiabatic reversible.

Line 4-1 or 4-1′. Constant-pressure heat addition in the steam generator. Line 4-B-1-1′ is a constant-pressure line on both diagrams. Portion 4-B represents bringing the subcooled liquid, point 4, to saturated liquid at point B. Section 4-B in the steam generator is called an economizer.

Portion B-1 represents heating the saturated liquid to saturated vapor at constant pressure and temperature (being a two-phase mixture), and section B-1 in the steam generator is called the boiler or evaporator. Portion 1-1′, in the superheat cycle, represents heating the saturated vapor at point 1 to point 1′. Section 1 1′ in the steam generator is called a superheater.


FIGURE 2.2 Ideal Rankine cycles of the (a) P-V and (b) T-s diagrams. Line 1-2-3-4-B-1 saturated cycle. Line 1′-2′-3-4-B-1′ superheated cycle. CP critical point.


Following is the thermodynamic analysis based on a unit mass of vapor in the cycle: Heat added
qA = h1- h4 Btu/lbm (or J/kg) (2.1)
Turbine work
wT = h1 - h2 Btu/lbm (or J/kg) (2.2)
Heat rejected
|qR| = h2 - h3 Btu/lbm (or J/kg) (2.3)
Pump work
|wp| = h4 - h3 (2.4)

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