Rankine cycle

The Rankine cycle is a mathematical model that is used to predict the performance of steam engines. The Rankine cycle is an idealised thermodynamic cycle of a heat engine that converts heat into mechanical work. The heat is supplied externally to a closed loop, which usually uses water as the working fluid. The Rankine cycle, in the form of steam engines generates about 90% of all electric power used throughout the world,^[1] including virtually all solar thermal, biomass, coal and nuclear power plants. It is named after William John Macquorn Rankine, a Scottishpolymath and Glasgow University professor.

Description

Physical layout of the four main devices used in the Rankine cycle

The Rankine cycle most closely describes the process by which steam-operated heat engines most commonly found in power generation plants generate power. The two most common heating processes used in these power plants are nuclear fission and the combustion of fossil fuels such as coal, natural gas, and oil.

The Rankine cycle is sometimes referred to as a practical Carnot cycle because, when an efficient turbine is used, the TS diagram begins to resemble the Carnot cycle. The main difference is that heat addition (in the boiler) and rejection (in the condenser) are isobaric in the Rankine cycle andisothermal in the theoretical Carnot cycle. A pump is used to pressurize the working fluid received from the condenser as a liquid instead of as a gas. All of the energy in pumping the working fluid through the complete cycle is lost, as is most of the energy of vaporization of the working fluid in the boiler. The vaporization energy is rejected from the cycle through the condenser. But pumping the working fluid through the cycle as a liquid requires a very small fraction of the energy needed to transport it as compared to compressing the working fluid as a gas in a compressor (as in theCarnot cycle).

The efficiency of a Rankine cycle is usually limited by the working fluid. Without the pressure reaching super critical levels for the working fluid, the temperature range the cycle can operate over is quite small: turbine entry temperatures are typically 565°C (the creep limit of stainless steel) and condenser temperatures are around 30°C. This gives a theoretical Carnot efficiency of about 63% compared with an actual efficiency of 42% for a modern coal-fired power station. This low turbine entry temperature (compared with a gas turbine) is why the Rankine cycle is often used as a bottoming cycle in combined-cycle gas turbine power stations.

The working fluid in a Rankine cycle follows a closed loop and is reused constantly. The water vapor with entrained droplets often seen billowing from power stations is generated by the cooling systems (not from the closed-loop Rankine power cycle) and represents the waste heat energy (pumping and condensing) that could not be converted to useful work in the turbine. Note that cooling towers operate using the latent heat of vaporization of the cooling fluid. While many substances could be used in the Rankine cycle, water is usually the fluid of choice due to its favorable properties, such as nontoxic and nonreactive chemistry, abundance, and low cost, as well as its thermodynamic properties.

One of the principal advantages the Rankine cycle holds over others is that during the compression stage relatively little work is required to drive the pump, the working fluid being in its liquid phase at this point. By condensing the fluid, the work required by the pump consumes only 1% to 3% of the turbine power and contributes to a much higher efficiency for a real cycle. The benefit of this is lost somewhat due to the lower heat addition temperature. Gas turbines, for instance, have turbine entry temperatures approaching 1500°C. Nonetheless, the efficiencies of actual large steam cycles and large modern gas turbines are fairly well matched.

[edit]The four processes in the Rankine cycle

Ts diagram of a typical Rankine cycle operating between pressures of 0.06bar and 50bar

There are four processes in the Rankine cycle. These states are identified by numbers (in brown) in the above Ts diagram.

Process 1-2: The working fluid is pumped from low to high pressure. As the fluid is a liquid at this stage the pump requires little input energy.
Process 2-3: The high pressure liquid enters a boiler where it is heated at constant pressure by an external heat source to become a dry saturated vapor. The input energy required can be easily calculated using mollier diagram or h-s chart or enthalpy-entropy chart also known as steam tables.
Process 3-4: The dry saturated vapor expands through a turbine, generating power. This decreases the temperature and pressure of the vapor, and some condensation may occur. The output in this process can be easily calculated using the Enthalpy-entropy chart or the steam tables.
Process 4-1: The wet vapor then enters a condenser where it is condensed at a constant pressure to become a saturated liquid.

In an ideal Rankine cycle the pump and turbine would be isentropic, i.e., the pump and turbine would generate no entropy and hence maximize the net work output. Processes 1-2 and 3-4 would be represented by vertical lines on the T-S diagram and more closely resemble that of the Carnot cycle. The Rankine cycle shown here prevents the vapor ending up in the superheat region after the expansion in the turbine, ^[1] which reduces the energy removed by the condensers.