File Name: rankine cycle pv and ts diagram .zip
The Rankine cycle is a model used to predict the performance of steam turbine systems. It was also used to study the performance of reciprocating steam engines.
rankine cycle diagram
These shortcomings inherent in a steam power plant realizing the Carnot cycle with wet steam can be partly remedied if heat is rejected from the wet steam in the condenser before the entire steam condenses.
Its compressibility is also negligible compared with that of wet steam. Water is displaced from the condenser into the boiler and its pressure is simultaneously increased not with the aid of compressors but pumps of compact design, simple arrangement and actuated by a rather low-power drive.
Such a cycle was suggested in the 's almost simultaneously by the Scottish engineer and physicist W. Rankine and by R. Clausius, and the cycle is usually called the Rankine cycle.
The schematic layout of a steam power plant operating on a Rankine cycle is similar to the schematic layout depicted in Fig. Figure Water is then compressed in the pump from the pressure p 2 to the pressure p 1 ; this adiabatic process is represented on the T-s diagram by the vertical line The length of line is small; as was already mentioned in Chapter 6, in the liquid region the isobars are plotted on the T-s diagram very close to one another.
Therefore, in plotting the Rankine cycle on a T-s diagram, in the water region the isobars are shown as merging with the left boundary curve. The small length of adiabat is evidence of the small amount of work expended by the pump to compress the water. It will be recalled that, as was shown in Sec. It will also be recalled that for adiabatic compression, in accordance with Eq.
Equations 7. As to the mechanical work done by a pump, taking in Eq. The mechanical work done by a pump to compress water is also small. The same result can be obtained, using equation 8. For this purpose, with the aid of an i-s diagram or Steam Tables, we find the difference between the enthalpies of water on a given isentrop at pressures p 1 and p 2.
The dry saturated vapour, generated in the boiler, passes into the turbine; the process of steam expansion in the turbine is represented by the adiabat The waste wet steam is exhausted into the condenser and the vapour cycle closes. From the viewpoint of thermal efficiency the Rankine cycle seems to be less expedient than the reversible Carnot cycle depicted in Fig. However, allowing for the practical conditions under which the cycle is to be realized and also for the considerably smaller effect of the irreversibility of the process of water compression, compared with the compression of wet vapour, on the overall efficiency of a cycle, the Rankine cycle is more economical than the corresponding Carnot cycle for wet steam.
At the same time the replacement of the cumbersome compressor, ensuring compression of the wet steam with a compact feed water pump permits a substantial reduction in the costs involved in building a steam power plant, and a simplification of its maintenance. The thermal efficiency of the Rankine cycle is increased by superheating the steam in a special element of the steam boiler, the steam superheater denoted SH in Fig. The T-s diagram of the Rankine cycle with superheated steam is shown in Fig.
With superheating the mean temperature of heat addition increases compared with the temperature at which heat is added in a cycle without superheat. Consequently the thermal efficiency of the cycle increases too. It can be seen from Fig. The Rankine cycle with superheat is the basic cycle for thermopower plants with application in up-to-date heat and power engineering.
The heat rejected in the cycle, q 2 , is equivalent to area ab-a, and the work output of the cycle, to area Since in the Rankine cycle the processes of heat addition and rejection are isobaric, and in an isobaric process the quantity of heat added rejected is equal to the difference between the enthalpies of the working medium at the beginning and end of the cycle, as applied to the Rankine cycle, we can then write.
Taking the above relationship into account, from the general expression for thermal efficiency of a cycle,. This equation can be presented in the following form:. If we introduce the following notations:. In accordance with Eq. Equation 7. Taking into account Eq.
Equations The entropy of water in this state is equal to 0. Substituting these values into Eq. It is clear, in accordance with Eq. If the work done by the pump, , is negligible compared with the drop in enthalpy in the turbine, , i. This relationship is quite suitable for estimating calculations of low-pressure steam power cycles. When dealing with high-pressure steam power plants the work of the pump cannot be ignored. Let us find the dependence of the thermal efficiency of the Rankine cycle on the initial conditions of the steam.
Thus, the temperature interval of the cycle widens and the thermal efficiency rises. A further reduction of condenser pressure is inexpedient. First, a greater rarefaction vacuum causes the specific volume of the exhaust steam flowing into the condenser from the turbine to increase, requiring a larger condenser and much longer blades in the last turbine stages. To illustrate, Fig. If T 1 is constant, an increase in the pressure p 1 also leads to a rise of the thermal efficiency of the cycle; the higher the p 1 the greater the cycle areas ratio and the higher the mean temperature of heat addition Fig.
However, with rising p 1 at the same superheat temperature, the wetness of exhaust steam at the turbine exit increases involving a drop in turbine relative internal efficiency.
In Fig. It is clear that the higher the steam pressure p 1 and temperature T 1 , the higher the thermal efficiency of the Rankine cycle.
Thus, to raise the thermal efficiency of a Rankine cycle, in principle an attempt should be made to raise the initial steam conditions. A further increase in the initial steam conditions is restricted by the properties of the construction materials presently available: at high pressures and temperatures the strength of pearlitic grades of steel deteriorates, and they must be replaced with considerably more expensive austenitic steels.
Although such a change permits operation at higher p 1 and T 1 , resulting in a somewhat higher thermal efficiency of the cycle, investments increase. In other words, although fuel is saved, more expensive metals are consumed. Considering the problem from this viewpoint, a further increase in initial steam conditions is inexpedient, especially where cheap grades of fuel are available. This problem is solved on the basis of a comprehensive technical and economic analysis. Actually, due to the resistance to steam flow offered by the steam pipeline and the inevitable heat losses, the pressure and temperature of steam drop somewhat.
This also pertains to the example considered in Sec.
This improves the efficiency of the cycle, as more of the heat flow into the cycle occurs at higher temperature. Save my name, email, and website in this browser for the next time I comment. Its pressure also rises from P4 to P1. By superheating, state 3 will move to the right and up in the diagram and hence produce a drier steam after expansion. The problems with the Carnot Cycle are as follows.
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. Rankine Cycle.
Application of the First law of thermodynamics to the control volume pump, steam generator, turbine and condenser , gives. The thermal efficiency of the Rankine cycle is given by,. Energy absorbed. Pump and Turbine do not operate isentropically in practice. In the actual turbine, the work delivered is less than the isentropic turbine.
Rankine Cycle – pV, Ts diagram
The questions posted on the site are solely user generated, Doubtnut has no ownership or control over the nature and content of those questions. Doubtnut is not responsible for any discrepancies concerning the duplicity of content over those questions. Study Materials. Crash Course.
These shortcomings inherent in a steam power plant realizing the Carnot cycle with wet steam can be partly remedied if heat is rejected from the wet steam in the condenser before the entire steam condenses. Its compressibility is also negligible compared with that of wet steam. Water is displaced from the condenser into the boiler and its pressure is simultaneously increased not with the aid of compressors but pumps of compact design, simple arrangement and actuated by a rather low-power drive.
Thermodynamic cycles can be divided into two general categories: power cycles, which produce a net power output, and refrigeration and heat pump cycles, which consume a net power input. The thermodynamic power cycles can be categorized as gas cycles and vapor cycles. In gas cycles, the working fluid remains in the gas phase throughout the entire cycle. In vapor cycles, the working fluid exits as vapor phase during one part of the cycle and as liquid phase during another part of the cycle. Steam power plants run vapor power cycles with water as the working fluid.
The Rankine cycle is the fundamental operating cycle of all power plants where an operating fluid is continuously evaporated and condensed.
Но… Послышался щелчок положенной на рычаг трубки. Беккер беззвучно выругался и повесил трубку. Третья попытка провалилась. Он помнил, что сказал Клушар: немец нанял девушку на весь уик-энд.
Коммандер, вы ни в чем не виноваты! - воскликнула. - Если бы Танкадо был жив, мы могли бы заключить с ним сделку, и у нас был бы выбор. Но Стратмор ее не слышал.
Черный лед. В центре помещения из пола торчала, подобно носу исполинской торпеды, верхняя часть машины, ради которой было возведено все здание. Ее черный лоснящийся верх поднимался на двадцать три фута, а сама она уходила далеко вниз, под пол.