Rankine Cycle of Steam Power Plant

Steam turbine power plant follows the Rankine cycle during one complete cycle of steam though different component of power plant for electricity production. Steam turbine power plant consists of five main components boiler, turbine, recuperator, condenser and pump (Yamamoto, 2001). Work starts from the boiler which heats the water to make steam at required temperature and pressure. Steam is then used by the steam turbine to rotate generator attached to it. Steam then passes though condenser which convert steam into water again. Some of steam is directed into condenser through recuperator to heat up the water coming from condenser. This increases the efficiency of the system. Pump is placed between condenser and recuperator to provide the require flow rate to the water (Yamamoto, 2001). 

Ranking Cycle Working

Pump

Pump of power plant has only one function and that is to provide the fluid with the required pressure and low rate so that the fluid can circulate the entire power plant without any issue. The work input of the pump is very small as compared to the all other components work input or work output. 

Boiler

Boiler of the power plant is the main work input component of the power plant which makes use of the heat provided by the burning of the fossil fuel to heat the fluid present inside the boiler. Heating the fluid converts the liquid into high temperature and high pressure vapor. This high temperature and high pressure fluid will do work in turbine stage.

Turbine

Turbine of the power plant perform two task, one is the absorbing the energy of the high temperature and high pressure fluid to rotate itself and second the use its rotation to generate electricity through generator. In this stage work in done by the fluid onto the turbine blades so the this stage is considered as the work output stage of the power plant

Condenser

Condenser of the power plant is heat rejection unit of the power plant which removes the unnecessary heat from the fluid. Condenser is cooling tower or a heat exchanger which absorbs heat from fluid and converts the vapor into liquid state. Liquid coming out of the condenser enters the pump to complete the circuit of the power plant. 

Thermodynamic Working of Rankine Cycle

Isobaric Heat Transfer 

As the Rankine cycle starts from the pump of power plant the heat or energy input by the pump is considered as the isobaric heat transfer in to the fluid and it is presented as point 1 to 2 in T-S graph and P-H graph of Rankine cycle (Yamamoto, 2001). Similarly in boiler of the power plant the heat in provided to the fluid until it converted into the high temperature high pressure steam and this process of heat transfer is also isobaric heat transfer. Boiler of power plant is present as the point 2 to 3 in T-S graph and P-H graph of the Rankine cycle. 

Isentropic Expansion

The next stage of the Rankine cycle is the turbine stage which receives high temperature high pressure fluid in vapor state. Vapor enters the turbine where they expand in turbine by rotating the blades of the turbine. This process reduces both temperature and pressure of the vapors thus making the process of expansion as isentropic expansion. This process of isentropic expansion is presented as 3 to 4 in T-S graph and P-H graph of Rankine cycle. At the end of the turbine stage the fluid exit in two states that is in liquid and vapor state, this is due to the reason that the reduction in temperature and pressure convert some of vapor into liquid while other remain in the state of vapor (Yamamoto, 2001).

Isobaric Heat Rejection 

Vapor and liquid coming out of turbine has still very high enthalpy and entropy due to which is needed to be condensed into liquid state by lowering the enthalpy and entropy of the fluid. The process of removing the heat without lowering the temperature and pressure of the vapor is called the isobaric heat rejection. This process of isobaric heat rejection is presented as 4 to 5 in T-S graph and P-H graph. The fluid should be in liquid state before it enters the pump and boiler of the power plant and due to which the condenser should remove enough heat from fluid to convert vapor into liquid.

Isentropic Compression

As vapor is converted into the liquid state by the condenser the flow rate of the fluid decrease and pressure required at the boiler feed is also higher as compared to the pressure of the fluid after condenser. The role of the pump is to provide fluid the required flow rate and pressure and the process of increase in pressure and flow rate is the isentropic compression process where temperature and pressure of the fluid increase a little but enthalpy and entropy remain constant. 

Rankine Cycle Calculation

The major calculations involve in the power plant controlling Rankine Cycle are about the work and heat added by the pump and boiler of the power plant respectively, work done by the turbine of power plant and heat rejected by the condenser of the power plant. 

Heat Addition in Rankine Cycle

Work and heat added in fluid of the power plant controlled by the Rankine cycle is done by the pump and boiler of the power plant respectively. Work added by the pump is very small as compared to the boiler of power plant but still the heat added by the pump of a large power plant is considerably high. 

Heat added by pump

Work added by pump in fluid of Rankine cycle is the calculated by the change in enthalpy of the fluid coming into the pump and going out of the pump. It can be calculated as follow

                                        W pump=Hout-Hin

As enthalpy before the pump stage is presented as H5 in the P-h graph and enthalpy out of the pump is presented as the H1 in the P-h graph so

                                         W pump=H1-H5

Heat Added by Boiler

Heat added by boiler in fluid of Rankine cycle is the calculated by the change in enthalpy of the fluid coming into the boiler and going out of the boiler. It can be calculated as follow

                                        Q boiler=m(Hout-Hin)

As enthalpy before the boiler stage is presented as H1 in the P-h graph and enthalpy out of the pump is presented as the H3 in the P-h graph so

                                        Q boiler=m(H3-H1)

Work Done in Rankine Cycle

Work done by fluid and heat rejected by the fluid of the power plant controlled by the Rankine cycle is done by the turbine and condenser of the power plant. Work done by the fluid on the turbine is much more as compared heat rejected by the condenser of the power plant.

Work done on Turbine

Work done by fluid on turbine of Rankine cycle is the calculated by the change in enthalpy of the fluid coming into the turbine and going out of the turbine. It can be calculated as follow

                                    W turbine=m(Hout-Hin)

As enthalpy before the turbine stage is presented as H3 in the P-h graph and enthalpy out of the turbine is presented as the H4 in the P-h graph so

                                    W turbine=m(H3-H4)

Heat Rejected by Condenser

Heat rejected by condenser in fluid of Rankine cycle is the calculated by the change in enthalpy of the fluid coming into the condenser and going out of the condenser. It can be calculated as follow

                                    Q condenser=m(Hout-Hin)

As enthalpy before the condenser stage is presented as H4 in the P-h graph and enthalpy out of the condenser is presented as the H5 in the P-h graph so

                                    Q condenser=m(H4-H5)

Energy Balance of Rankine Cycle

For an ideal case the heat and work provided to the fluid by the boiler and pump of the Rankine cycle is utilized fully in the turbine and condenser of the Rankine cycle in the form of work and heat respectively. Due to the complete consumption of heat and work done onto the system the equation of energy balance of an Ideal Rankine Cycle can be written as follow

                           (Q boiler-Q condenser)-(W turbine-W pump)=0

Thermal Efficiency of Rankine Cycle

Ability of the turbine of the Rankine Cycle to convert the heat provided to the fluid by the boiler into useful work is called the efficiency of the Rankine Cycle. It can be calculated as follow

                        efficiency=1-(q condenser)/(q boiler)

In the above formula the heat removed or the heat involve in the condenser is used. The heat present in fluid before it enters the condenser stage is the heat left after the turbine stage. Heat consumed by the turbine is considered in this manner.

Thermal Efficiency of Steam Turbine

Thermal efficiency of the steam turbine can be calculated as the work done by the turbine divided by the input provided by the boiler. The turbine work can be calculated as the heat removed or the decrease in enthalpy of the steam after the turbine stage and boiler input can be calculated as the increase in enthalpy after the boiler stage.

                            Turbine efficiency=(W turbine)/(Q boiler)

                            Turbine efficiency=(H3-H4)/(H3-H1)

Carnot Efficiency

Carnot efficiency is the maximum theoretical efficiency which a heat engine can have while converting high temperature into work. If a heat engine work between a high temperature source and low temperature reservoir then the efficiency of the Carnot engine can be written as  

                            Carnot efficiency=Work/( Input)*100

                            Carnot efficiency=(Thot-Tcold)/Thot*100

                            Carnot efficiency=1-Tcold/Thot*100

Pump Efficiency

The efficiency of the pump is predefined by the manufacturer in most of and it depends on the density of the fluid to move, flow rate at which fluid will move, heat which pump can attain and the power input given to the pump.

                    pump efficiency=(ρ*g*Q*H)/(Power or Work input)