The Rankine Cycle

Say we wish to convert a fossil-fuel, nuclear, or solar energy source into net electrical power. To accompftsh this task, we can use a Rankine cycle. The Rankine cycle is an idealized vapor power system that contains the major components foimd in more detailed, practical steam power plants. While hydroelectric and wind are possible alternative sources, the steam power plant is presently the dominant producer of electrical power. 

Since the process is reversible with negligible heat transfer, the entropy remains constant, as depicted by the vertical line in the Ts diagram  

The steam enters as a superheated vapor, and does not condense signiflcantly in the turbine. If the steam were saturated when it entered the turbine, a significant fraction of hquid would be formed when the temperature dropped isentropicaUy. The dashed fine on the Ts diagram illustrates this case. This option is impractical, since too much hquid causes erosion and wear of the turbine blades. 

The steam next enters a condenser it exits in state 3 as saturated liquid water. The change of phase occurs at constant pressure and requires that energy be removed from the flowing stream via heat. Thus, a low-temperature reservoir is needed. A first-law balance arormd the condenser gives  

Next it is desired to raise the pressure of the liquid, which is accomplished using a compressor. High-pressure water exits the compressor in state 4. The work required to compress the liquid is given by  

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The efficiency of the Rankine cycle itself can be increased by higher motive steam pressures and superheat temperatures, and lower surface condenser pressures in addition to rotating equipment selection. These parameters are generally optimized on the basis of materials of constmction as well as equipment sizes. Typical high pressure steam system conditions are in excess of 10,350 kPa (1500 psi) and 510 °C. 

Because of the simplicity and reUabiUty of the Rankine cycle, faciUties employing this method have dominated the power industry in the twentieth century and typically play an important role in most modem combined-cycle faciUties. Water is the working fluid of choice in nearly all Rankine cycle power plants because water is nontoxic, abundant, and low cost. 

Fossil Fuel-Fired Plants. In modem, fossil fuel-fired power plants, the Rankine cycle typically operates as a closed loop. In describing the steam—water cycle of a modem Rankine cycle plant, it is easiest to start with the condensate system (see Fig. 1). Condensate is the water that remains after the steam employed by the plant s steam turbines exhausts into the plant s condenser, where it is collected for reuse in the cycle. Many modem power plants employ a series of heat exchangers to boost efficiency. As a first step, the condensate is heated in a series of heat exchangers, usually sheU-and-tube heat exchangers, by steam extracted from strategic locations on the plant s steam turbines (see HeaT-EXCHANGETECHNOLOGy). 

An external combustion engine that has been widely supported as a low-emission power source is the Rankine cycle steam engine. Many different types of expanders can be used to convert the energy in the working fluid... 

For the Rankine cycle, the area enclosed by the line segments connecting points 1, 2, 3, 4, 1 on Figure 2-36 represents the net heat transferred into the system per unit mass, because... 

The efficiency of power cycles such as the Rankine cycle is given by the ratio of the net work out to the heat added. Thus from Figure 2-36 the efficiency is... 

A concept of the cycle of thermodynamic processes, introduced later than the Carnot cycle. Modifications of the Rankine cycle are of practical importance in boiler design, in relating the successive thermodynamic changes as water is converted to steam, expands and converted to mechanical energy in a turbine, then condenses and returns to the boiler. 

The Rankine cycle diagram placed adjacent the Brayton cycle in Figure 9-15 is indicated as a simple steam cycle with superheat, but no reheat and no multi-pressure steam generation. The thermodynamic advantage of the Rankine bottoming cycle is the lowered temperature of heat rejection, in the steam condenser, from the overall combined cycles. 

Another advantage is that the IGCC system generates electricity by both combustion (Brayton cycle) and steam (Rankine cycle) turbines. The inclusion of the Brayton topping cycle improves efficiency compared to a conventional power plant s Rankine cycle-only generating wstem. Typically about two-thirds of the power generated comes from the Brayton cycle and one-third from the Rankine cycle. 

The Rankine cycle is a modified Carnot cycle for overcoming the difficulties with the latter cycle when the working fluid is a vapor. In the Rankine cycle, the heating and cooling processes occur at constant pressure. Figure 2.4 shows the devices used in a basic Rankine cycle, and Fig. 2.5 is the T-s diagram of the basic Rankine cycle. 

Applying the first and second laws of thermodynamics of the open system to each of the four processes of the Rankine cycle yields ... 

A steam power plant operates on the Rankine cycle. The steam enters the turbine at 7 MPa and 550°C. It discharges to the condenser at 20 kPa. Determine the quality of the steam at the exit of the turbine, pump work, turbine work, heat added to the boiler, and thermal cycle efficiency. 

The power output of the Rankine cycle can be controlled by a throttling valve. The inlet steam pressure and temperature may be throttled down to a lower pressure and temperature if desired. Adding a throttling valve to the Rankine cycle decreases the cycle efficiency. The throttling Rankine cycle is shown in Fig. 2.10. An example illustrating the throttling Rankine cycle is given in Example 2.6. 

The thermal efficiency of the Rankine cycle can be significantly increased by using higher boiler pressure, but this requires ever-increasing superheats. Since the maximum temperature in the superheater is limited by the temperature the boiler tubes can stand, superheater temperatures are usually restricted. Since the major fraction of the heat supplied to the Rankine cycle is supplied in the boiler, the boiler temperatures (and hence pressures) must be increased if cycle efficiency improvements are to be obtained. 

The thermal efficiency of the Rankine cycle can be increased by the use of regenerative heat exchange as shown in Fig. 2.15. In the regenerative cycle, a portion of the partially expanded steam is drawn off between the high-and low-pressure turbines. The steam is used to preheat the condensed... 

COMMENTS (1) From the example, it is seen that the efficiency of the regenerative Rankine cycle is better than that of the Rankine cycle without regenerator. 

Much of this chapter has been concerned with various modifications to the simple Rankine cycle at high temperature. In the following five sections, the Rankine cycle that makes possible use of energy sources at low temperature, such as solar, geothermal, ocean thermal, solar pond, and waste heat, will be discussed. Because of the small temperature range available, only a simple Rankine cycle can be used and the cycle efficiency will be low. This is not critical economically, because the fuel is free. 

The answers are rate of heat added in the low-temperature heat exchanger = 125.6 kW, rate of heat added in the high-temperature heat exchanger = 2501 kW, net power produced by the Rankine cycle = 357 kW, and efficiency of the solar heat engine = 357/(125.6-I-2501)= 13.59%. 

However, the temperature range of the Rankine cycle is severely limited by the nature of the working fluid— water. Adding superheat in an attempt to circumvent this will remove the cycle from isothermal heat addition. Increasing the temperature range without superheating leads to excessive moisture content in the vapor turbines, resulting in blade erosion. 

The Carnot cycle is not a practical model for vapor power cycles because of cavitation and corrosion problems. The modified Carnot model for vapor power cycles is the basic Rankine cycle, which consists of two isobaric and two isentropic processes. The basic elements of the basic Rankine cycle are pump, boiler, turbine, and condenser. The Rankine cycle is the most popular heat engine to produce commercial power. The thermal cycle efficiency of the basic Rankine cycle can be improved by adding a superheater, regenerating, and reheater, among other means. 

A Brayton/Rankine cycle (Fig. 5.12) uses water as the working fluid with 1 kg/sec mass flow rate through the Rankine cycle, and air as the working... 

What is the heat source for the Rankine cycle in the combined Brayton/Rankine cycle ... 

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