But it must be noted that nuclear power plants are much more complex than fossil fuel power plants and it is much easier to burn fossil fuel ,than to generate energy from nuclear fuel. They are not done infinitely slowly. In general, the Rankine cycle is an idealized thermodynamic cycle of a constant pressure heat engine that converts part of heat into mechanical work. January 1993. This parameter reduces the overall efficiency and work output. Steam leaves this stage of turbine at a pressure of 0.008 MPa, 41.5°C and x = ??? Physics of Nuclear Kinetics. Copyright 2020 Nuclear Power for Everybody | All Rights Reserved | Powered by, Thermal Efficiency Improvement – Rankine Cycle. 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. Note that, there is always a temperature difference between (around ΔT = 14°C) the condenser temperature and the ambient temperature, which originates from finite size and efficiency of condensers. Construction, operation of a gas turbine are entirely different to steam turbine. Unlike with reciprocating engines, for instance, compression, heating and expansion are continuous and they occur simultaneously. The work required for the compressor is given by WPumps = H2 – H1. The liquid condensatei s pumped from the condenser into the higher pressure boiler. While many substances could be used as the working fluid in the Rankine cycle (inorganic or even organic), water is usually the fluid of choice due to its favorable properties, such as its non-toxic and unreactive chemistry, abundance, and low cost, as well as its thermodynamic properties. Typically most of nuclear power plants operates multi-stage condensing wet steam turbines (the high pressure stage runs on saturated steam). The exhausted steam then condenses in the condenser and it is at a pressure well below atmospheric (absolute pressure of 0.008 MPa), and is in a partially condensed state (point F), typically of a quality near 90%. A disadvantage is that water moderated reactors have to use high pressure primary circuit in order to keep water in liquid state and in order to achieve sufficient thermodynamic efficiency. 174 = 1787 + 53.2 = 1840 kJ/kg. Above the critical point, the liquid and vapor phases are indistinguishable, and the substance is called a supercritical fluid. As can be seen in the article “Steam Generator”, the feedwater (secondary circuit) at the inlet of the steam generator may have about ~230°C (446°F) and then is heated to the boiling point of that fluid (280°C; 536°F; 6,5MPa) and evaporated. Heat regeneration causes a decrease in the mass flow rate through low-pressure stage of the steam turbine, thus increases LP Isentropic Turbine Efficiency. At constant pressure, an addition of energy does not changes the temperature of the mixture, but the vapor quality and specific volume changes. 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). A disadvantage is that water moderated reactors have to use high pressure primary circuit in order to keep water in liquid state and in order to achieve sufficient thermodynamic efficiency. Since the temperature of the primary coolant is limited by the pressure inside the reactor, superheaters (except a moisture separator reheater) are not used in nuclear power plants and they operate usually a single wet steam turbine. This ratio is known as the Isentropic Turbine/Pump/Nozzle Efficiency. Since this feature allows to increase the peak temperature, the supercritical water reactors are considered a promising advancement for nuclear power plants because of its high thermal efficiency (~45 % vs. ~33 % for current LWRs). Heat regeneration increases the thermal efficiency, since more of the heat flow into the cycle occurs at higher temperature. The basic operation of the steam turbine is similar to the gas turbine except that the working fluid is water and steam (with a phase change) instead of air or gas. This requires maintaining of very high pressures to keep the water in the liquid state. In this equation the term Vdp is a flow process work. The process for creating steam to produce work using a steam turbine is based on the Rankine cycle. The heat transfer into or out of the system does work, but also changes the internal energy of the system. In this process, the surroundings do work on the fluid, increasing its enthalpy (h = u+pv) and compressing it (increasing its pressure). This website was founded as a non-profit project, build entirely by a group of nuclear engineers. If you want to get in touch with us, please do not hesitate to contact us via e-mail: The Rankine cycle describes the performance of steam turbine systems. In contrast to Carnot cycle, the Rankine cycle does not execute isothermal processes, because these must be performed very slowly. In contrast to Carnot cycle, the Rankine cycle does not execute isothermal processes, because these must be performed very slowly. As can be seen, it is convenient to use enthalpy and the first law in terms of enthalpy in analysis of this thermodynamic cycle. It was observed that more than two stages of reheating are unnecessary, since the next stage increases the cycle efficiency only half as much as the preceding stage. change in pressure. (point 4). This steam is in a partially condensed state (point F), typically of a quality near 90%. the enthalpy difference between these two states (3 → 4), which corresponds to the work done by the steam, W, the enthalpy difference between these two states (1 → 2), which corresponds to the work done by pumps, W, the enthalpy difference between these two states (2 → 3), which corresponds to the net heat added in the steam generator, the thermodynamic efficiency of this cycle and compare this value with the Carnot’s efficiency. Introductory Nuclear Physics, 3rd Edition, Wiley, 1987, ISBN: 978-0471805533, G.R.Keepin. the enthalpy difference between these two states (3 → 4), which corresponds to the work done by the steam, W, the enthalpy difference between these two states (1 → 2), which corresponds to the work done by pumps, W, the enthalpy difference between these two states (2 → 3), which corresponds to the net heat added in the steam generator, the thermodynamic efficiency of this cycle and compare this value with the Carnot’s efficiency. Higher efficiencies can be attained by increasing the temperature of the steam. 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. They are not done infinitely slowly. As that steam flows past a turbine’s spinning blades, the steam expands and cools. lower than 22.1 MPa), can achieve 36–40% efficiency. 0.694 + (1 – 0.694) . In this cycle the heat is supplied externally to a closed loop, which usually uses water (in a liquid and vapor phase) as the working fluid. For an ideal cycle, compute Higher efficiencies can be attained by increasing the temperature of the steam. At constant pressure, the enthalpy change equals the energy transferred from the environment through heating: It is obvious, it will be very useful in analysis of both thermodynamic cycles used in power engineering, i.e. When the vapor quality is equal to 0, it is referred to as the saturated liquid state (single-phase). In general the thermal efficiency, ηth, of any heat engine is defined as the ratio of the work it does, W, to the heat input at the high temperature, QH. As is shown in Fig. with steam pressures exceeding the critical pressure of water 22.1 MPa, and turbine inlet temperatures exceeding 600 °C). Essentially, the deaerator is a mixing vessel obeying the first law of thermodynamics. The exhausted steam is at a pressure well below atmospheric, and, as can be seen from the picture, the steam is in a partially condensed state (point F), typically of a quality near 90%, but it is much higher vapor quality, than that it would be without reheat. This form of the law simplifies the description of energy transfer. We define parameters ηT,  ηP, ηN, as a ratio of real work done by device to work by device when operated under isentropic conditions (in case of turbine). Typically most of nuclear power plants operates multi-stage condensing steam turbines. Such as a steam turbine used to drive a power generator in the power plant. There are several methods, how can be the thermal efficiency of the Rankine cycle improved. As the turbine produce rotatory motion, it is most appropriate for the operation of electrical generators. As the generators must rotate at synchronous speeds with respect to the frequency of the electrical system, the most common rotation speeds are 3,0… Latent heat of vaporization – water at 0.1 MPa (atmospheric pressure), Latent heat of vaporization – water at 3 MPa (pressure inside a steam generator), Latent heat of vaporization – water at 16 MPa (pressure inside a pressurizer). Main purpose of this project is to help the public learn some interesting and important information about the peaceful uses of nuclear energy. Rankine developed a complete theory of the steam engine and indeed of all heat engines. around 30 MPa) and use multiple stage reheat reach about 48% efficiency. This example models a steam turbine system based on the Rankine Cycle. In case of the Rankine cycle, the Ideal Gas Law almost cannot be used (steam do not follow pV=nRT), therefore all important parameters of water and steam are tabulated in so called “Steam Tables“. The specific entropy of saturated liquid water (x=0) and dry steam (x=1) can be picked from steam tables. The cycle includes superheating and reheating to prevent condensation at the high-pressure turbine and the low-pressure turbine, respectively. where the temperature of the hot reservoir is 275.6°C (548.7K), the temperature of the cold reservoir is 41.5°C (314.7K). As can be seen, there are many SCWR designs, but all SCWRs have a key feature, that is the use of water beyond the thermodynamic critical point as primary coolant. Further comprehensive authoritative data can be found at the NIST Webbook page on thermophysical properties of fluids. But it must be noted that nuclear power plants are much more complex than fossil fuel power plants and it is much easier to burn fossil fuel ,than to generate energy from nuclear fuel. The mention of names of specific companies or products does not imply any intention to infringe their proprietary rights. With a reheater, the flow is extracted after a partial expansion (point D), run back through the heat exchanger to heat it back up to the peak temperature (point E), and then passed to the low-pressure turbine. These parameters describe how efficiently a turbine, compressor or nozzle approximates a corresponding isentropic device. As steam is expanded through the turbine it starts to condense in the wet region along the 'Wilson line' which corresponds to a wetness factor of 3-4% (see Fig 1.50). This website does not use any proprietary data. Introductory Nuclear Physics, 3rd Edition, Wiley, 1987, ISBN: 978-0471805533, G.R.Keepin. This valve often does not control the steam flow other than to completely stop it. In these turbines the high-pressure stage receives steam (this steam is nearly saturated steam – x = 0.995 – point C at the figure; 6 MPa; 275.6°C). Note that, there is no heat regeneration in this cycle. Steam is first heated in a steam generation system (for example, in boilers or waste heat recovery systems), where it reaches a high temperature, around 400°C to 600°C. But the nuclear power plant is the real heat engine, in which thermodynamic processes are somehow irreversible. 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. But the condensate at the condenser outlet may have about 40°C, so the heat regeneration in typical PWR is significant and very important: In general, the heat exchangers used in regeneration may be classified as either regenerators or recuperators. It then expands to the condenser pressure of 35 kPa. Since we do not know the exact vapor quality of the outlet steam, we have to determine this parameter. Engineers use the specific enthalpy in thermodynamic analysis more than the enthalpy itself. High pressure and low pressure stages of the turbine are usually on the same shaft to drive a common generator, but they have separate cases. Reheat allows to deliver more of the heat at a temperature close to the peak of the cycle. Typically most of nuclear power plants operates multi-stage condensing steam turbines. 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. Work is done by the fluid in the turbine between stages 3 and 4 (isentropic expansion). At constant pressure, the enthalpy change equals the energy transferred from the environment through heating: It is obvious, it will be very useful in analysis of both thermodynamic cycles used in power engineering, i.e. ηth = (945 – 5.7) / 2605.3 = 0.361 = 36.1%. But currently, improved materials and methods of fabrication have permitted significant increases in the maximum pressures, with corresponding increases in thermal efficiency. But this requires an increase in pressures inside boilers or steam generators. On the other hand the entropy remains unchanged. Sub-critical fossil fuel power plants, that are operated under critical pressure (i.e. This requires the addition of another type of heat exchanger called a superheater, which produces the superheated steam. The Rankine cycle is an idealized thermodynamic cycle of a heat engine that converts heat into mechanical work while undergoing phase change. Most efficient and also very complex coal-fired power plants that are operated at “ultra critical” pressures (i.e. This energy breaks down the intermolecular attractive forces, and also must provide the energy necessary to expand the gas (the pΔV work). High pressure and low pressure stages of the turbine are usually on the same shaft to drive a common generator, but they have separate cases. The term supercritical in this context refers to the thermodynamic critical point of water (TCR = 374 °C;  pCR = 22.1 MPa), and must not be confused with the criticality of the reactor core, that describes changes in the neutron population in the reactor core. 174 = 1787 + 53.2 = 1840 kJ/kg. greater than 22.1 MPa). Please support us at Patreon.com so that we can add one more member to the team and will be able to release 2 educational videos/month. The Rankine cycle was named after him and describes the performance of steam turbine systems, though the theoretical principle also applies to reciprocating engines such as steam locomotives. Since energy is conserved according to the first law of thermodynamics and energy cannot be be converted to work completely, the heat input, QH, must equal the work done, W, plus the heat that must be dissipated as waste heat QC into the environment. Answer: dH = dQ + Vdp, first law of thermodynamics in terms of enthalpy, What is Supercritical Rankine Cycle - Definition, What is Reheat Steam Turbine - Definition, What is Condensing Steam Turbine - Definition, What is Four Stroke Diesel Engine – Definition, What is Boiler and Condenser Pressure – Rankine Cycle – Definition, Sub-critical fossil fuel power plants, that are operated under, Supercritical fossil fuel power plants, that are operated at, Decreasing the turbine exhaust pressure decreases the vapor quality (or dryness fraction). The turbine is a mechanical device or mechanical mechanism that converts thermal energy to mechanical/kinetic energy. Since the temperature of the primary coolant is limited by the pressure inside the reactor, superheaters (except a moisture separator reheater) are not used in nuclear power plants and they operate usually a single wet steam turbine. in isentropic process, the enthalpy change equals the flow process work done on or by the system. around 30 MPa) and use multiple stage reheat reach about 48% efficiency. Between these two states, we talk about vapor-liquid mixture or wet steam (two-phase mixture). the decrease in the saturation temperature). The heat of vaporization diminishes with increasing pressure, while the boiling point increases. use of a multistage turbine with a reheater. In previous chapters we assumed that the steam expansion is isentropic and therefore we used T4,is  as the outlet temperature of the gas. Work is done by the fluid in the turbine between stages 3 and 4 (isentropic expansion). In a typical pressurized water reactor, the hot primary coolant (water 330°C; 626°F) is pumped into the steam generator through primary inlet. Our Website follows all legal requirements to protect your privacy. use steam turbines connected to electric generators to produce about 80% of the electricityof the planet. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983). Our steam turbines equip 41% of the world’s combined-cycle plants, 30% of fossil power plants, and 50% of the world’s nuclear power plants. Their properties are tabulated in so called “Steam Tables”. Rankine developed a complete theory of the steam engine and indeed of all heat engines. This work,  Vdp, is used for open flow systems like a turbine or a pump in which there is a “dp”, i.e. 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. with steam pressures exceeding the critical pressure of water 22.1 MPa, and turbine inlet temperatures exceeding 600 °C). In this case assume a simple cycle without reheat  and without with condensing steam turbine running on saturated steam (dry steam). Addison-Wesley Pub. This requires maintaining of very high pressures to keep the water in the liquid state. It is similar as in boiling water reactors, steam will be supplied directly to the steam turbine and the feed water from the steam cycle will be supplied back to the core. Steam turbines are also often applied in the renewable energy sector. The strength of this impulsive force depends on the mass and speed change of the moving object. K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2. Note that at the last stage of expansion the steam has very high specific volume. The heat transfer into or out of the system does work, but also changes the internal energy of the system. In these turbines the high-pressure stage receives steam (this steam is nearly saturated steam – x = 0.995 – point C at the figure) from a steam generator and exhaust it to moisture separator-reheater (point D). The enthalpy of vaporization is a function of the pressure at which that transformation takes place. 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. As can be seen also wet steam turbines (e.g. 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. These assumptions are only applicable with ideal cycles. The use of the reheater involves splitting the turbine, i.e. Therefore it is convenient to use the enthalpy instead of the internal energy. In modern nuclear power plants the overall thermal efficiency is about one-third (33%), so 3000 MWth of thermal power from the fission reaction is needed to generate 1000 MWe of electrical power. used in nuclear power plants) use superheated steam especially at the inlet of low-pressure stages. It means the isentropic process is a special case of an adiabatic process in which there is no transfer of heat or matter. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467, Kenneth S. Krane. Both processes are very similar in its manner: The process of superheating is the only way to increase the peak temperature of the Rankine cycle (and to increase efficiency) without increasing the boiler pressure. For example, water has the highest specific heat of any common substance –  4.19 kJ/kg K. Moreover it has very high heat of vaporization, which makes it an effective coolant and medium in thermal power plants and other energy industry. As was discussed, an efficiency can range between 0 and 1. The exhausted steam is at a pressure well below atmospheric, and, as can be seen from the picture, the steam is in a partially condensed state (point F), typically of a quality near 90%, but it is much higher vapor quality, than that it would be without reheat. Williams. Superheating is not typical for nuclear power plants. The reactor pressure vessel is the key component, which limits the thermal efficiency of each nuclear power plant, since the reactor vessel must withstand high pressures. in isentropic process, the enthalpy change equals the flow process work done on or by the system: See also: Why power engineers use enthalpy? A steam plant works on the Rankine cycle with reheat. The Rankine cycle was named after him and describes the performance of steam turbine systems, though the theoretical principle also applies to reciprocating engines such as steam locomotives. This work,  Vdp, is used for open flow systems like a turbine or a pump in which there is a “dp”, i.e. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983). An isentropic process is a thermodynamic process, in which the entropy of the fluid or gas remains constant. 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). At constant pressure, an addition of energy does not changes the temperature of the mixture, but the vapor quality and specific volume changes. Decreasing the turbine exhaust pressure significantly increases the specific volume of exhausted steam, which requires huge blades in last rows of low-pressure stage of the steam turbine. However, metallurgical considerations place an upper limits on such pressures. Water and steam also reacts with metals commonly found in industries such as steel and copper that are oxidized faster by untreated water and steam. This requires the addition of another type of heat exchanger called a reheater. During a Rankine cycle, work is done on the fluid by the pumps between states 1 and 2 (isentropic compression). 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.e. The combination of these two turbines together help in efficiently producing power in these plants. 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. Physics of Nuclear Kinetics. In general the thermal efficiency, ηth, of any heat engine is defined as the ratio of the work it does, W, to the heat input at the high temperature, QH. Latent heat is the amount of heat added to or removed from a substance to produce a change in phase. Superheated vapor or superheated steam is a vapor at a temperature higher than its boiling point at the absolute pressure where the temperature is measured. This example models a steam turbine system based on the Rankine Cycle. 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). Engineers use the specific enthalpy in thermodynamic analysis more than the enthalpy itself. E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.
2020 steam turbine works on which cycle