Rankine Cycle In Thermodynamics And Its Process

 For each process  in the vapor power cycle, it is possible to assume a hypothetical or ideal process which   represents the basic intended operation and involves no extraneous effects. For the steam boiler, this   would be a reversible constant pressure heating process of water to form steam, for the turbine the ideal   process would be a reversible adiabatic expansion of steam, for the condenser it would be a reversible   constant pressure heat rejection as the steam condenses till it becomes saturated liquid , and for the pump, the ideal process would be the reversible adiabatic compression of this liquid ending at the initial pressure. when all these four processes are ideal, the cycle is an ideal cycle, called a Rankine cycle. This is a reversible cycle. The cycle has been plotted on p-v, T-s, and h-s planes. For any given pressure, the steam approaching the turbine may be dry saturated (state 1) wet (state 1'), or super heated (state 1''), but the fluid approaching the pump is , in each case, saturated liquid ( State 3). Steam expands reversibly and adiabatically in the turbine from state 1 to state 2 (or 1' to 2', or 1" to 2 "), the steam leaving the turbine condenses to water in the condenser reversibly at constant pressure from state 2 (or 2' , or 2 ") to state 3, the water at state 3 is then pumped to the boiler at state 4 reversibly and adiabatically , and water is heated in the boiler to form steam reversibly at constant pressure from state 4 to state 1 or (1' or 1 "). 

For a simple nuclear power plant, the boiler is replaced by a nuclear reactor where heat released by nuclear fission is utilised in generation of steam. Other features of the plant are similar to conventional steam plant. 

For purposes of analysis the Rankine cycle is assumed to be carried out in a steady flow operation. Applying the steady flow energy equation to each of the processes on the basis of unit mass of fluid, and neglecting changes in the kinetic and potential energy, the work and heat quantities can be evaluated in terms of  the properties of the fluid. 

For 1 kg fluid ,

The SFEE for the boiler (control volume) gives 

h4 + Q1 = h1 

Q1 = h1 - h4 

the SFEE For the turbine as the control volume gives 

h1 = Wt + h2 

Wt  = h1 - h2 

Similarly , the SFEE for the condenser is, 

h2 = Q2 + h3 

Q2 = h2 - h3 

and the SFEE for the pump gives

h3 + Wp = h4 

Wp = h4 - h3 

 The efficiency of  the Rankine cycle is then given by , 

n = Wnet / Q1  = (Wt - Wp) / Q1 = ((h1- h2) - (h4 - h3 )) /  ( h1 - h4 ) 

The pump handles liquid water which is incompressible, i.e, its density or specific volume undergoes little change with an increase in pressure. For reversible adiabatic compression, by the use of  the general property relation, 

Tds = dh -vdp; ds=0

dh = vdp 

Since change in specific volume is negligible 

delta h = v delta p

 

or

h4 - h3 = v3 (p1-p2)

If v is in m3 / kg and p is the bar , 

h4-h3 = v3(p1-p2) * 10^5 J/kg 

Usually, the pump work is quite small compared to the turbine work and is sometimes neglected. then h4 = h3, and the cycle efficiency approximately becomes 

n = ( h1-h2) / ( h1 - h4 )

The capacity of steam plant is often expressed in terms of steam rate, which is defined as the rate of steam flow (kg/h) required to produce unit shaft output (1 kW). therfore, 

Steam rate = 1 / (Wt -Wp)  ((kg/kj). ((kj/s)/ kW) 

                  =  3600 / (Wt -Wp )  kJ  / kWh 

The cycle efficiency is sometimes expressed alternatively as heat rate which is the rate of  heat input Q1 required to produce unit work output (1KW) 

Heat rate = 3600 /Ncycle  kJ / kWh .

In steam or gas power plants , the pressure rise in the pump or compressor is equal to the pressure drop in the turbine if we neglect the pressure losses in various other components. In steam plants,  the pump handles liquid, which has very small specific volume, and the turbine handles vapour, whose specific volume many times larger. Therefore, the work output of the turbine is much larger than the work input to the pump. This is one of the reasons for the overwhelming popularity of steam power plants in steam generation.

If we were to compress the steam exiting the turbine back to the turbine inlet pressure before cooling it first in the condenser in order to save the heat rejected , we would have to supply all the work produced by the turbine back to the compressor. In reality, the required work input would be still greater than the work output of the turbine because of the irreversiblities or energy present in both processes.