Reheat Rankine Cycle

10 Key excerpts on "Reheat Rankine Cycle"

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  Waste Heat Recovery in Process Industries

  • Hussam Jouhara(Author)
  • 2021(Publication Date)
  • Wiley-VCH

    (Publisher)

  Figure 1.20 ), and this steam is then reheated and expanded in the second turbine from MP to LP. The main advantage of the reheat is to increase the steam quality to ensure a steadier thermodynamic efficiency.

  Rankine cycles with reheat also ensure a higher overall mechanical efficiency by using two turbines for the cycle compared to only using one. In this configuration, the overall efficiency of the cycle is given by:

  (1.24)

  where, q

  inB

  corresponds to the heat (kJ/kg) provided by the boiler to the fluid and q

  inR

  corresponds to the heat (kJ/kg) provided by the reheater to the fluid (In real-life power plant, the boiler and the superheater use the same heat source.)

  Figure 1.19

  Schematic of the Rankine cycle with reheat.

  Figure 1.20

  T–s diagram of a Rankine cycle with reheat.

  1.2.4.5 Regenerative Rankine Cycles

  To improve energetic and exergetic efficiency of the thermodynamic cycle, the regenerative Rankine cycles extracts a portion of the steam from the turbine to heat the fluid before it is sent to the boiler. This results in a small reduction in the work provided to the turbine but a substantial reduction in the heat input, because the heating phase creates entropy and thus irreversibility if this is all provided by the boiler. The portion of steam used therefore helps the boiler heat the fluid, reducing the fuel required by the boiler and hence both energetic and exergetic efficiencies improve. Furthermore, the average temperature of the heat input by the boiler is increased and this also results in a higher energetic efficiency [8] .

  Regenerative cycles require a new component. A feed water heater (FWH ) also called a regenerator is required, its role being to heat the feed water before it enters the boiler. There are two different kinds of regenerative cycle: the open FWH cycle and the closed FWH cycle.

  Open FWH cycles use an Open FWH. As seen in Figure 1.21 , this component mixes the liquid delivered from pump 1 with the extracted steam arriving from turbine. It corresponds to point 6 on the T–s diagram shown in Figure 1.22

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  Nuclear Reactor Thermal Hydraulics

  An Introduction to Nuclear Heat Transfer and Fluid Flow

  • Robert E. Masterson(Author)
  • 2019(Publication Date)
  • CRC Press

    (Publisher)

  Figure 9.9 . The T–S diagram for the reheat process is shown on the right. The Rankine cycle illustrated here is different than an ideal Rankine cycle because the expansion of the steam takes place in two stages rather than just one. In the first stage (which involves the high-pressure turbine), the hot steam is expanded isentropically to an intermediate pressure, and it is then sent back to the reheaters where it is reheated at constant pressure (usually to the inlet temperature of the high-pressure turbine). It is then expanded isentropically through the low-pressure turbine before being sent on to the condenser. Thus, the total heat input and the total turbine work output when a reheat stage is added to the Rankine cycle are as follows:

  Heat Input Using Reheated Steam

  Q IN

  =

  Q PRIMARY

  +

  Q REHEAT

  =

  (

  h 3

  −

  h 2

  )

  +

  (

  h 5

  −

  h 4

  )

  (9.24)

  and

  Work Output Using Reheated Steam

  W TURBINE

  =

  W TURBINE1

  +

  W TURBINE2

  =

  (

  h 3

  −

  h 4

  )

  +

  (

  h 5

  −

  h 6

  )

  (9.25)

  Obviously, reheating the steam increases the thermal efficiency because more work can be performed by a two-stage turbine for the same energy input (h3 ). Incorporating a single reheating stage between the turbines can increase the overall efficiency by about 2% by increasing the average temperature at which heat is transferred to the steam. The average temperature during the reheating process can be increased even further by increasing the number of expansion and reheating stages and by adding more stages to the turbine drive shaft. However, a point is eventually reached (normally at about three stages) where the resulting gain in thermodynamic efficiency is too small to justify the additional cost and complexity. When this occurs, the expansion and reheating cycle approaches an isothermal process at the maximum temperature shown in Figure 9.10 .

  In most nuclear power plants, this point occurs when more than two reheating stages are used. The theoretical increase in the thermal efficiency from adding a second reheating stage is about half as great as the increase in the thermal efficiency from a single reheating stage alone. For this reason, very few power plants are built with more than two reheating cycles. The thermal efficiency therefore increases as

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  Energy, Entropy and Engines

  An Introduction to Thermodynamics

  • Sanjeev Chandra(Author)
  • 2016(Publication Date)
  • Wiley

    (Publisher)

  Figure 9.4 ) and expands again.

  Figure 9.4

  Rankine power cycle with reheat.

  Reheat does not have much effect on the efficiency of the cycle, because while it increases the work output of the turbine it also requires a greater heat input. However, reheat significantly increases the quality at the exit of the low-pressure turbine. Figure 9.5 shows a Rankine cycle with reheat on a T-s diagram.

  Figure 9.5

  Rankine cycle with reheat.

  The heat added in the boiler per unit mass of fluid is

  (9.11)

  and the total work output from the turbines per unit mass of fluid is

  (9.12)

  Example 9.3

  Problem: Superheated steam at a pressure of 6 MPa and temperature of 400 °C enters the first stage of a turbine in a Rankine cycle where it expands to 0.8 MPa. The steam is then reheated to 300 °C and expanded in the second stage of the turbine which it leaves at a condenser pressure of 30 kPa. Find (a) the work done by the turbine per unit mass of fluid, (b) the heat added per unit mass of fluid and (c) the thermal efficiency of the cycle.

  Find: (a) Work done w per unit mass of fluid, (b) heat added q per unit mass of fluid, (c) thermal efficiency ηth of the cycle.

  Known: Turbine inlet pressure P2 = P3 = 6 MPa, turbine inlet temperature T3 = 400 °C, reheat pressure P4 = P5 = 0.8 MPa, reheat temperature T5 = 300 °C, condenser pressure P1 = P6 = 30 kPa.

  Process Diagram: The Rankine cycle with reheat on a T-s diagram (Figure E9.3 ).

  Figure E9.3

  T-s diagram for a Rankine cycle with reheat.

  Assumptions: Expansion through the turbines is isentropic so ∆S34 = 0 and ∆S56 = 0.

  Governing Equations:

  Work output from turbines

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  Elements of Energy Conversion

  • Charles R. Russell(Author)
  • 2013(Publication Date)
  • Pergamon

    (Publisher)

  This can be avoided and, at the same time, the efficiency of the cycle can be increased by superheating the steam. The amount of superheat is limited by the allowable operating temperatures of the super-heater and turbine. However, these limits have been raised by the development of high-temperature alloys. The Rankine cycle with (pressure volume) (temperature-entropy) FIG. 3-2 Rankine cycle with superheat. superheat (Fig. 3-2) illustrates the expansion extending into the wet steam area until the maximum allowable liquid content of about 10 percent is reached. The efficiency of the cycle can be increased further by reheating the vapor after partial expansion (Fig. 3-3). In addition, the reheat cycle permits a greater pressure ratio between the boiler and the condenser. The condenser temperature and corresponding pressure are established by the cooling water or other heat rejection system. As mentioned previously, the process of mixing cold conden-sate with the high-temperature liquid in the boiler is thermo-dynamically inefficient. Heating of the boiler feed can be made more nearly reversible by the use of regenerative stages-that is, by withdrawing vapor from the turbine at several intermediate temperatures to heat the boiler feed (Figs. 3-4 and 3-5). As many HEAT ENGINES 83 as eight stages of regenerative heating may be justified in a large steam power plant to increase efficiency. As the number of regenerative stages is increased, the efficiency of the cycle ap-proaches that of the Carnot cycle. Λ4 J 4 Φ r ^. * ^. -*_ ♦ FIG. 3-3 Rankine cycle with reheat. FIG. 3-4 Rankine cycle with superheat and regenerative heaters. boiler Regenerative heaters FIG. 3-5 Turbine with feedwater heaters. Nuclear power stations have been built without superheat in order to avoid complexities in the reactor.

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  Analysis of Engineering Cycles

  Thermodynamics and Fluid Mechanics Series

  • R. W. Haywood, W. A. Woods(Authors)
  • 2013(Publication Date)
  • Pergamon

    (Publisher)

  An air preheater is therefore introduced, enabling the flue gases to be further cooled after leaving the économiser by trans-ferring heat to the combustion air fed to the boiler. Advanced Steam-Turbine Plant 149 FIG. 7 .10. The effects of variation in reheat pressure, and of supercritical initial pressure. of the resulting increase in the mean temperature of heat rejection f A more than offset the advantageous effect of the accompanying increase in the mean temperature of heat reception T B . In the case of steam plant, the steam entering the condenser at the design load is always wet, so that the introduction of reheating does not affect the tempera-When discussing the application of reheating to gas-turbine plant, it was seen in §§ 6.8 and 6.9 that the cycle efficiency was not increased unless the plant also incorporated an exhaust-gas heat exchanger. This was because, without such a heat exchanger, the adverse effect 150 Advanced Power and Refrigerating Plants lure of heat rejection, which remains at the saturation temperature corresponding to the condenser vacuum. Hence reheating will increase the ideal cycle efficiency if it results in an increase in T B , and this it does provided that the chosen pressure at which the steam is reheated is not too low. The necessity for this proviso is seen from a study of Fig. 7.10. Cycle 12371 is a simple Rankine cycle. Cycle 1234561 is a rever-sible, single-reheat cycle in which the steam is expanded in the turbine to point 4, and is then reheated in the boiler from 4 to 5 at a fairly high reheat pressure p R before returning to the turbine, in which expansion then continues down to the exhaust pressure. Whether or not, in these circumstances, reheating improves the cycle efficiency can best be decided by noting, as in § 6.8, that the complete reheat cycle may be treated as a compound cycle comprising the non -reheat cycle Ν (12371) of efficiency to which has been added a hypothe-tical cycle R (45674) of efficiency η κ .

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  Introduction to Thermal and Fluid Engineering

  • Allan D. Kraus, James R. Welty, Abdul Aziz(Authors)
  • 2011(Publication Date)
  • CRC Press

    (Publisher)

  8 kJ/kg h 3 = 3654 . 2 kJ/kg h 2 = 180 . 82 kJ/kg h 4 = 2439 . 4 kJ/kg Vapor Power and Refrigeration Cycles 275 The thermal efficency of the cycle is now = 1 − h 4 − h 1 h 3 − h 2 = 1 − 2439 . 4 kJ/kg) − 173 . 8 kJ/kg 3654 . 2 kJ/kg) − 180 . 82 kJ/kg = 1 − 2265 . 6 kJ/kg 3473 . 4 kJ/kg = 1 − 0 . 652 = 0 . 348 ⇐ It is apparent that a lack of attention to the irreversibilities in the pump and turbine (and particularly the turbine) can lead to an enormous disappointment. 9.6 The Rankine Cycle with Superheat and Reheat In the ideal Rankine cycle with both reheat and superheat (Figure 9.10a), the turbine has two stages. After an expansion in stage 1, the high-pressure turbine , the steam is rerouted to the steam generator where it is preheated at constant pressure in a reheater . The steam s T (b) 3 4 2 1 5 6 2 1 (a) 4 5 6 3 Fuel Air Turbine Stage 1 Turbine Stage 2 Pump Pump Cold Water Hot Water Generator Products of Combustion Reheater Condenser FIGURE 9.10 (a) A steam power plant with both superheat and reheat. (b) The T -s diagram for the ideal Rankine cycle. 276 Introduction to Thermal and Fluid Engineering is then led to stage 2, called low-pressure turbine where it is expanded to the condenser pressure. In Figure 9.10b, the T -s diagram for the ideal Rankine cycle with both superheat and reheat, we see that there are six state points. Points 1 through 4 are in their customary location. However, point 5 is the point where the steam is taken from the high-pressure turbine and led back to the reheater inside of the steam generator. Point 6 is located at the end of the constant pressure reheat process and is at the inlet to the low-pressure turbine. At point 4, where the steam is exhausted from the low-pressure turbine, we see that the steam may still be superheated or possess a high quality. This is a significant advantage of the reheat cycle.

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  Marine, Steam Engines, and Turbines

  • S. C. McBirnie(Author)
  • 2013(Publication Date)
  • Butterworth-Heinemann

    (Publisher)

  cylinder will increase, hence the H.P. power will increase and the LP. power diminish. If the reheat pressure is lowered, 1, 2 and 3 will change in the opposite manner. There is therefore no optimum reheat pressure such as there is in the case of a boiler reheater in which the additional cycle heat varies with the reheat pressure. The reheat pressure is chosen to give the best compromise among the three effects stated above. For high cycle efficiency, the reheat pressure should be high, but if it is too high, a prohibitively large reheater is required, and the H.P. power will be relatively low. We may restate these conclusions. The steam reheater degrades the average temperature of the additional cycle heat before the latter is applied to the cycle. The reheat pressure is fixed by considerations other than the conception of an optimum reheat pressure. The improvement in cycle efficiency is relatively small. Although in this chapter, we are supposed to be dealing exclusively with thermodynamical theory, it has, in the present example been necessary to introduce practical features such as the reheater temperature difference. This has been necessary to show that the introduction of the steam reheater —the object of which is practical—does not render the cycle efficiency any worse than that of the comparable cycle with-out the steam reheater. In the case of turbines with a steam reheater, the general principles and the cycle calculations do not differ from those of the foregoing example for which a reheater engine was used. S T E A M -E N G I N E A N D T U R B I N E C Y C L E S A N D E F F I C I E N C I E S 4 0 3 Figure 9.23 Regenerative φ cycle The turbine is supposed to have an infinite number of stages, and from each turbine stage, steam is extracted to heat the feed water in a very small direct-contact feed heater.

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  Sustainable Utility Systems

  Modelling and Optimisation

  • Petar Sabev Varbanov, Jiří Škorpík, Jiří Pospíšil, Jiří Jaromír Klemeš(Authors)
  • 2020(Publication Date)
  • De Gruyter

    (Publisher)

  6.2 Rankine – Clausius cycle (R – C cycle, steam cycle) The steam cycle is the oldest heat cycle which is used in technical practise. For transformation of heat to work through the steam cycle, initially steam piston en-gines were used (Schobert, 2014). The current state of the art in power generation uses steam turbines (US EPA, 2015). The use of a particular mechanism or machine does not change principle of the cycle, even though the steam turbine is a turbo-machine and the piston steam engine is a reciprocating engine. Unlike the internal combustion engine cycle, the steam cycle connects several devices. Figure 6.1 shows the steam cycle for power generation only. The description of each part of the flow chart follows: State 1 – state 2: feed water pressure increase. This is performed by using a boiler feed water pump. The power input to the pump is lower compared with the work of the steam expansion in the steam turbine, because water is almost an incompressible fluid. State 2 – state 3: steam generation . Raising steam (steam generation) in the boiler (Chapter 5) can be divided into three steps. In the first step 2 – 3 ʹ , the water is heated up to the liquid saturation point. This is referred to as boiler feed water pre-heating. The second part of the process is the evaporation of water to the state of steam saturation (3 ʹ – 3 ʹʹ ). The steam is then superheated to state 3 in a super-heater section of the boiler. Obtaining superheated steam is essential for power generation using this cycle, as steam turbines use exactly the superheated part of the steam energy content and steam at the exit of the turbine has to be essentially dry (Varbanov, 2004). Note, states 3 ʹ and 3 ʹʹ are internal to the steam boiler. 3 1 2 4 3'' CT ~ FP SB ST G C Fig. 6.1: Flow chart of Rankine – Clausius cycle.

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  Thermal Design of Nuclear Reactors

  • R. H. S. Winterton(Author)
  • 2014(Publication Date)
  • Pergamon

    (Publisher)

  h cannot be increased because of temperature limitations in the core. Water in particular is not a high-temperature reactor coolant. Since the critical temperature and pressure of water are 374ºC and 221 bar respectively, there is little scope for increasing core outlet temperatures much above the present levels of 310º to 320º (PWR). If the water at the core outlet were brought up to the critical conditions the quite modest improvement in the temperature would be accompanied by one-fifth the density and nearly double the pressure. To achieve the same moderating effect with the reduced density the flow area between the fuel rods would have to be increased by a factor of 5. The increased capital cost of the larger, higher pressure, core would outweigh any improvement in thermal efficiency. In fact, a single pressure vessel to contain the core would be difficult to construct with present techniques.

  The low temperature in the cycle is limited by the availability of cooling water. If cooling water at 15ºC is available from the sea or a river and is allowed to rise in temperature to 25ºC before discharge, and the pinch-point temperature difference in the condenser is 5ºC, then the steam will condense at 30ºC (saturation pressure 0.042 bar). Clearly it will not be possible to do much better than this, so T c is largely fixed by the location of the power station and the time of year.

  FEED WATER HEATING (REGENERATION)

  Heat rejection in the Rankine cycle occurs entirely at the lowest temperature in the cycle, but not all of the heat in the boiler is supplied at the highest temperature; some heat is required to bring the feed water up to the boiling-point.

  If the heat required between points 1 and 2 (Figs. 9.3 and 9.4 ) could be supplied internally within the cycle then all the heat supplied by the reactor would be at the highest temperature, the boiling-point, and for an ideal reversible cycle the efficiency would equal that of the Carnot cycle.

  The way in which this is done is to extract some of the steam at intervals in the turbine, and use this steam to warm the feed water in a number of feed heaters, as shown in Fig. 9.6 . The two feed heaters shown are of the closed type, that is, they are shell and tube heat exchangers with the steam and water flows kept separate. The condensed steam from the higher temperature heater is throttled to the pressure of the steam in the next, lower temperature, feed heater, and mixed with it. The other type of feed heater is the open or direct contact feed heater where the steam bled off from the turbine and the feed water are simply mixed together.

  Fig. 9.6

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  Combined Heating, Cooling & Power Handbook

  Technologies & Applications, Second Edition

  • Neil Petchers(Author)
  • 2020(Publication Date)
  • River Publishers

    (Publisher)

  C ENTRAL U TILITY P LANTS The electric utility industry, which still produces the majority of the nation’s power, has traditionally relied on two basic thermodynamic cycles to generate electric power: the conventional steam turbine Rankine cycle for baseload and intermediate load applications, and the gas turbine Brayton cycle for peaking applications. While these cycles have proven reliable for the utility industry, the use of natural gas or oil fuels and heat recovery technology opens up a number of other cycles that offer significantly better thermodynamic performance for large central power plants, as well as smaller facilities. These newer gas turbine based combined-cycle central power power plants have thermodynamic efficiencies over 50% as compared to the older traditional Rankine cycle based plants with efficien-cies of 30%-to-40%. As is customary in the United States, this chapter presents boiler efficiencies and overall plant efficiencies and heat rates based on Higher Heating Value (HHV), whereas the prime mover heat rates and efficien-cies presented in Chapter 9 and 10 are on a Lower Heating Value (LHV). Refer to Chapter 5 for a discussion of the difference in these ratings. C ONVENTIONAL U TILITY R ANKINE S TEAM C YCLE P LANTS Most large utility plants rely on the conventional Rankine steam cycle, in which high-pressure steam is expanded through a set of turbine wheels to generate mechanical energy, which then drives a generator to make electric power. The high-pressure steam is produced in a steam generator, or boiler, which may be fueled by coal, oil, natural gas, wood, refuse, or nuclear fission. Figure 3-1 is a simplified schematic representation of a large utility supercritical steam power plant, featuring a high-pressure and a low-pressure turbine, with regenera-tion and reheat.

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