Rankine Power Cycles

Rankine Power Cycles

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Figure 8.11: Rankine power cycle with two-phase working fluid [Moran and Shapiro, Fundamentals of Engineering Thermodynamics]

A schematic of the components of a Rankine cycle is shown in Figure 8.11. The cycle is shown on clip_image002clip_image003 , clip_image004clip_image005 , and clip_image006clip_image005[1] coordinates in Figure 8.12. The processes in the Rankine cycle are as follows:

  1. clip_image007: Cold liquid at initial temperature clip_image008is pressurized reversibly to a high pressure by a pump. In this process, the volume changes slightly.
  2. clip_image009: Reversible constant pressure heating in a boiler to temperature clip_image010.
  3. clip_image011: Heat added at constant temperature clip_image010[1](constant pressure), with transition of liquid to vapor.
  4. clip_image012: Isentropic expansion through a turbine. The quality decreases from unity at point clip_image013to clip_image014.
  5. clip_image015: Liquid-vapor mixture condensed at temperature clip_image008[1]by extracting heat.

[clip_image002[1]clip_image003[1] coordinates] clip_image016[clip_image004[1]clip_image005[2] coordinates] clip_image017[clip_image006[1]clip_image005[3] coordinates] clip_image018

Figure 8.12: Rankine cycle diagram. Stations correspond to those in Figure 8.11

In the Rankine cycle, the mean temperature at which heat is supplied is less than the maximum temperature, clip_image010[2], so that the efficiency is less than that of a Carnot cycle working between the same maximum and minimum temperatures. The heat absorption takes place at constant pressure over clip_image019, but only the part clip_image020is isothermal. The heat rejected occurs over clip_image021; this is at both constant temperature and pressure.

To examine the efficiency of the Rankine cycle, we define a mean effective temperature, clip_image022, in terms of the heat exchanged and the entropy differences:

clip_image023

clip_image024

 

clip_image025

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The thermal efficiency of the cycle is

clip_image027

The compression and expansion processes are isentropic, so the entropy differences are related by

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The thermal efficiency can be written in terms of the mean effective temperatures as

clip_image029

For the Rankine cycle, clip_image030, clip_image031. From this equation we see not only the reason that the cycle efficiency is less than that of a Carnot cycle, but the direction to move in terms of cycle design (increased clip_image032) if we wish to increase the efficiency.

There are several features that should be noted about Figure 8.12 and the Rankine cycle in general:

  1. The clip_image004[2]clip_image005[4] and the clip_image006[2]clip_image005[5] diagrams are not similar in shape, as they were with the perfect gas with constant specific heats. The slope of a constant pressure reversible heat addition line is, as derived in Chapter 6,

clip_image033

In the two-phase region, constant pressure means also constant temperature, so the slope of the constant pressure heat addition line is constant and the line is straight.

  1. The effect of irreversibilities is represented by the dashed line from clip_image013[1]to clip_image035. Irreversible behavior during the expansion results in a value of entropy clip_image036at the end state of the clip_image035[1]expansion that is higher than clip_image037. The enthalpy at the end of the expansion (the turbine exit) is thus higher for the irreversible process than for the reversible process, and, as seen for the Brayton cycle, the turbine work is thus lower in the irreversible case.
  2. The Rankine cycle is less efficient than the Carnot cycle for given maximum and minimum temperatures, but, as said earlier, it is more effective as a practical power production device.

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