# ⌛ The Rankine Cycle

In ideal case no friction, reversible processes, perfect design **The Rankine Cycle,** Why Should Parents Get Children Vaccinated? heat engine The Rankine Cycle have a Carnot **The Rankine Cycle** of. Addison-Wesley **The Rankine Cycle.** Ott, W. History General Entropy Gas laws. The Rankine Cycle Posts. Blog Archive.

Thermodynamics : Ideal and non-ideal Rankine cycle, Rankine cycle with reheating (34 of 51)

In almost all thermal power stations coal, gas, nuclear , water is used as the working fluid used in a closed loop between boiler, steam turbine and condenser , and the coolant used to exchange the waste heat to a water body or carry it away by evaporation in a cooling tower. Water and steam are a common medium because their properties are very well known. In these tables the basic and key properties, such as pressure, temperature, enthalpy, density and specific heat, are tabulated along the vapor-liquid saturation curve as a function of both temperature and pressure.

Further comprehensive authoritative data can be found at the NIST Webbook page on thermophysical properties of fluids. See also: Steam Tables. When the vapor quality is equal to 0, it is referred to as the saturated liquid state single-phase. On the other hand, when the vapor quality is equal to 1, it is referred to as the saturated vapor state or dry steam single-phase. Between these two states, we talk about vapor-liquid mixture or wet steam two-phase mixture.

At constant pressure, an addition of energy does not changes the temperature of the mixture, but the vapor quality and specific volume changes. In general, when a material changes phase from solid to liquid, or from liquid to gas a certain amount of energy is involved in this change of phase. Latent heat is the amount of heat added to or removed from a substance to produce a change in phase. When latent heat is added, no temperature change occurs. The enthalpy of vaporization is a function of the pressure at which that transformation takes place. Latent heat of vaporization — water at 16 MPa pressure inside a pressurizer. The heat of vaporization diminishes with increasing pressure, while the boiling point increases. It vanishes completely at a certain point called the critical point.

Above the critical point, the liquid and vapor phases are indistinguishable, and the substance is called a supercritical fluid. In an ideal Rankine cycle, the system executing the cycle undergoes a series of four processes: two isentropic reversible adiabatic processes alternated with two isobaric processes:. Isentropic compression compression in centrifugal pumps — The liquid condensate is compressed adiabatically from state 1 to state 2 by centrifugal pumps usually by condensate pumps and then by feedwater pumps.

The liquid condensatei s pumped from the condenser into the higher pressure boiler. On the other hand the entropy remains unchanged. During a Rankine cycle, work is done on the fluid by the pumps between states 1 and 2 i sentropic compression. Work is done by the fluid in the turbine between stages 3 and 4 i sentropic expansion. The difference between the work done by the fluid and the work done on the fluid is the net work produced by the cycle and it corresponds to the area enclosed by the cycle curve in pV diagram. The working fluid in a Rankine cycle follows a closed loop and is reused constantly.

As can be seen, it is convenient to use enthalpy and the first law in terms of enthalpy in analysis of this thermodynamic cycle. This form of the law simplifies the description of energy transfer. At constant pressure , the enthalpy change equals the energy transferred from the environment through heating:. At constant entropy , i. See also: Why power engineers use enthalpy? An isentropic process is a thermodynamic process , in which the entropy of the fluid or gas remains constant. It means the isentropic process is a special case of an adiabatic process in which there is no transfer of heat or matter.

It is a reversible adiabatic process. The assumption of no heat transfer is very important, since we can use the adiabatic approximation only in very rapid processes. For a closed system, we can write the first law of thermodynamics in terms of enthalpy :. The heat transfer into or out of the system does work, but also changes the internal energy of the system. The classical form of the first law of thermodynamics is the following equation:.

In an isobaric process and the ideal gas, part of heat added to the system will be used to do work and part of heat added will increase the internal energy increase the temperature. Therefore it is convenient to use the enthalpy instead of the internal energy. The Rankine cycle is often plotted on a pressure volume diagram pV diagram and on a temperature-entropy diagram Ts diagram. When plotted on a pressure volume diagram , the isobaric processes follow the isobaric lines for the gas the horizontal lines , adiabatic processes move between these horizontal lines and the area bounded by the complete cycle path represents the total work that can be done during one cycle.

The temperature-entropy diagram Ts diagram in which the thermodynamic state is specified by a point on a graph with specific entropy s as the horizontal axis and absolute temperature T as the vertical axis. Ts diagrams are a useful and common tool, particularly because it helps to visualize the heat transfer during a process. For reversible ideal processes, the area under the T-s curve of a process is the heat transferred to the system during that process. Since energy is conserved according to the first law of thermodynamics and energy cannot be be converted to work completely, the heat input, Q H , must equal the work done, W, plus the heat that must be dissipated as waste heat Q C into the environment. Therefore we can rewrite the formula for thermal efficiency as:.

This is very useful formula, but here we express the thermal efficiency using the first law in terms of enthalpy. Typically most of nuclear power plants operates multi-stage condensing steam turbines. The steam must be reheated in order to avoid damages that could be caused to blades of steam turbine by low quality steam. The reheater heats the steam point D and then the steam is directed to the low-pressure stage of steam turbine, where expands point E to F. The exhausted steam then condenses in the condenser and it is at a pressure well below atmospheric absolute pressure of 0. In this case, steam generators, steam turbine, condensers and feedwater pumps constitute a heat engine, that is subject to the efficiency limitations imposed by the second law of thermodynamics.

In ideal case no friction, reversible processes, perfect design , this heat engine would have a Carnot efficiency of. But the nuclear power plant is the real heat engine , in which thermodynamic processes are somehow irreversible. They are not done infinitely slowly. In real devices such as turbines, pumps, and compressors a mechanical friction and heat losses cause further efficiency losses. To calculate the thermal efficiency of the simplest Rankine cycle without reheating engineers use the first law of thermodynamics in terms of enthalpy rather than in terms of internal energy. In this equation the term Vdp is a flow process work.

There are no changes in control volume. As can be seen, this form of the law simplifies the description of energy transfer. It is obvious, it will be very useful in analysis of both thermodynamic cycles used in power engineering, i. The enthalpy can be made into an intensive , or specific , variable by dividing by the mass. Engineers use the specific enthalpy in thermodynamic analysis more than the enthalpy itself. It is tabulated in the steam tables along with specific volume and specific internal energy. The thermal efficiency of such simple Rankine cycle and in terms of specific enthalpies would be:.

It is very simple equation and for determination of the thermal efficiency you can use data from steam tables. The reason lies in relatively low steam temperature 6 MPa ; Sub-critical fossil fuel power plants, that are operated under critical pressure i. As was discussed, an efficiency can range between 0 and 1. Each heat engine is somehow inefficient. This inefficiency can be attributed to three causes. There are several methods, how can be the thermal efficiency of the Rankine cycle improved. Assuming that the maximum temperature is limited by the pressure inside the reactor pressure vessel, these methods are:. The case of the decrease in the average temperature at which energy is rejected, requires a decrease in the pressure inside condenser i.

The lowest feasible condenser pressure is the saturation pressure corresponding to the ambient temperature i. The goal of maintaining the lowest practical turbine exhaust pressure is a primary reason for including the condenser in a thermal power plant. Power From the Sun. PV Magazine. Renewable Energy. Thermodynamic cycles. Without phase change hot air engines. Categories : Thermodynamic cycles. Namespaces Article Talk. Views Read Edit View history. Help Learn to edit Community portal Recent changes Upload file. Download as PDF Printable version. Laws Zeroth First Second Third. Heat engines Heat pumps Thermal efficiency.

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Topics by country Marketing and policy trends. Software Details. Software details. Easy to use software for steady-state simulation and optimization of processes that includes a complete thermodynamic package. Popular equation-based solver that includes a database of fluid thermodynamic and transport properties. High-level language and interactive environment for numerical computation, visualization, and programming. Graphical development environment and validated, packaged physical libraries for system simulation.

Simple ORC model. Tool for the thermodynamic analysis and optimization of systems for the production of electricity, heat and refrigeration. Dynamic model of a waste heat recovery system. Object-oriented, declarative, multi-domain modeling language for component-oriented modeling of complex systems. Download the CyclePad design of the fixed Rankine cycle from here. Whalley, P. Basic Engineering Thermodynamics. Oxford University Press. ISBN: Go to or. Contributed by: M.

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