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Vapour power cycle Rankine cycle Comparision rankine cycle with carnot cycle

● Rankine cycle Defination:- → professor rankine, who made significant contributions to the engineering and scientific development, modified the carnot cycle and presented a technically feasible cycle, called the rankine cycle.

→ it is also a reversible cycle but it differs from the Carnot cycle in the following respects. the condensation process is allowed to proceed to completion; the exhaust steam from the engine/turbine is completely condensed. at the end of condensation process the working fluid is only liquid and not a mixture of liquid and vapour. The pressure of liquid water can be easily raised to the boiler pressure by employing a small sized pump.

Stem power plant operating on simple rankine cycle

→A boiler which generates steam at constant pressure →A boiler which generates steam at constant pressure. →An engine or turbine in which steam expands isentropically and work is done. →a condenser in which heat is removed from the exhaust steam and it is completely converted into water at constant pressure. →a hot well in which the condensate is collected. →a pump which raises the pressure of liquid water to the boiler pressure and pumps it into the boiler for conversion into steam.

Process 1-2 : isentropic expansion turbine work, wt=h1-h3 Process 2-3 : constant pressure process heat rejected, ,Q2=h2 -h3 Process 3-3’ : Reversible adiabatic Pump Work, WP = H3' - H3 = ∫vdp = vf3 (p1 -p2) Process 3’-1 : Constant Pressure Process Heat Supplied, Q1 = h1 - h3‘ Net work of the cycle, Wn = Wt - Wp = (H1 - H2) - (H3' - H3)

= (h1 - h2) - (h3' - h3) / (h1 - h3) - (h3' - h3) Thermal Efficiency of the Rankine Cycle, η Rankine = Net Work / Heat Input = (h1 - h2) - (h3' - h3) / h1 - h3' = (h1 - h2) - (h3' - h3) / (h1 - h3) - (h3' - h3) The compression process in the pump is being carried out with liquid only for which the specific volume is small. Consequently the pump work (h3' - h3) is quite small compared to the turbine work and can be neglected. The Rankine cycle efficiency then approximately becomes η Rankine = h1 - h2 / h1 - h3

Comparision of Rankine Cycle with Carnot Cycle: →consider the Carnot Cycle and Rankine cycle operating between the same boiling and condensation temperature. →1-2-3-4 represent the Carnot cycle, and 1-2-3’-4 represent the Rankine cycle in which the pump work has been neglected. →It may be recalled that on T-s diagram, the area en-closed by cyclic processes represents the work done and area under the line representing heat addition gives the heat input to the cycle.

Comparison between Carnot and rankine cycle

Thus for the Carnot cycle, Work Done = area 1-2-3-4 = area c Heat Input = area under the line 4-1 = area c + area d ηc = work done / heat input = c / c + d Let 1-2-3’-5 be another reversible Carnot cycle, which will have thermal efficiency given by = (a+b+c)/(a+b+c+d+e) From Carnot’s theorem, two reversible cycles operating within the same temperature limits have the same thermal efficiency. Accordingly efficiency of the given Carnot cycle 1-2-3-4 can be put as

ηc = (a+b+c)/(a+b+c+d+e) or 1 - ηc = (d+e)/( a+b+c+d+e) ηc = (a+b+c)/(a+b+c+d+e) or 1 - ηc = (d+e)/( a+b+c+d+e) ... (i) The Rankine cycle 1-2-3'-4 has thermal efficiency given by ηR = Work done / Heat input = (b+c)/(b+c+d+e) 1 - ηR = (d+e)/(b+c+d+e) ...(ii) From identities (i) and (ii) it is obvious that 1 - ηc < 1 – ηR or ηc > ηR That is the Carnot cycle is more efficient than a Rankine cycle when both are operating within the same temperature limits.

→The above aspect also stems from the fact that for the Carnot cycle the entire heat input is during the process 4-1 which takes place at the maximum cycle temperature. →For the Rankine cycle, the heat addition does not take place at the maximum cycle temperature. → The temperature during sensible heating 3’-4 is much lower and is continuously changing, and that lowers the average temperature at which heat is supplied and accordingly the efficiency of Rankine cycle goes down.

Reference book :- Thermal science and engineering Dr.D.S.kumar