ME 400 Thermodynamics of Propulsion and Power Systems Department of Mechanical and Nuclear Engineering Pennsylvania State University Lecture 14 Rankine Cycle I Reading Assignment Chap 10 1 3 Questions Can you draw a T s diagram of the Rankin cycle and conduct the cycle Can you consider the pump and turbine isentropic efficiencies in the Rankine analysis cycle analysis 1 Vapor power cycle The majority of power plants over 80 of power generation are variations of vapor power plants The working fluid of vapor power plants is water alternately vaporized and condensed The basic components of a simplified fossil fuel vapor power plant are illustrated in the figure below The overall plant can be broken into the four major subsystems A to D on the diagram 1 Subsystem A the focus of our considerations is subsystem A where energy conversion from heat to work occurs Subsystem B the function of subsystem B is to supply heat to vaporize the water passing through the boiler There are a variety of heat sources to vaporize the water to steam including combustion of fossil fuel nuclear reaction nuclear power plants solar energy solar power plants and waste heat from internal combustion engines combined power plants Subsystem C subsystem C is the cooling water circuit to condense the vapor leaving the turbine For general power plants the cooling water is sent to a cooling tower where energy taken from the vapor is rejected to the atmosphere The cooling water is recirculated through the condenser Subsystem D the vapor produced in the boiler passes through a turbine where it expands to a lower pressure and produces a work The shaft of the turbine is connected to an electric generator Review of Thermodynamics I Property diagrams for vaporization boiling Condensation Chap 3 4 a P v diagram b T s diagram 2 3 The Carnot vapor cycle We can theoretically make a Carnot cycle under the saturation dome or over the saturation dome as shown below However the Carnot cycle is not a realistic practical model for vapor power cycles due to reasons in the textbook Chap 10 1 for more details 4 Rankine cycle The ideal cycle for vapor power cycles The Rankine cycle is the ideal practical in terms of operating regions cycle for vapor power plants consisting of the following four reversible processes Isentropic reversible adiabatic compression process 1 2 in a pump Constant pressure heat addition process 2 3 in a boiler steam generator Constant pressure heat rejection process 4 1 in a condenser Isentropic reversible adiabatic expansion process 3 4 in a turbine 3 5 Rankine Cycle Analysis Review The first law of thermodynamics for a steady state open system KE PE ignored single inlet outlet Q W mh mh e i 0 or q w h i h e 0 Pump q 0 Pw Pw s 1 s 2 h 1 h 2 v P P 1 1 where where 1 1 2 Review of Thermodynamics I Reversible steady flow work Chap 7 10 1st law for a reversible steady state flow q rev w rev dh 0 q rev dh vdP Tds Tds q rev dh vdP 2 1 vdP KE PE 2nd law By combining the two equations revw If KE and PE are ignored 0w Boiler Turbine Condenser q 0 0w vdP revw 2 1 inq h 3 h 2 Tw s 3 h h 3 4 s 4 outq h 4 h 1 4 Thermal efficiency 6 Deviation of actual vapor power cycles from idealized ones 1 Common sources of irreversibilities in the actual vapor power cycle Pressure drops in the boiler condenser piping due to fluid friction Heat loss from the steam to the surroundings Irreversibilities occurring within the pump and the turbine Other losses such as subcooling in the condenser leaks of steam and air and mechanical frictions in moving parts 2 Isentropic efficiencies Pump efficiency P w s w a h 2 h 2 s a h 1 h 1 Turbine efficiency T w a w s h 3 h 3 h 4 h 4 a s 5 Example 13 1 Rankin cycle analysis Consider a steam power plant operating on the simple ideal Rankine cycle Steam enters the turbine at 10 MPa and 500 C and is condensed in the condenser at a pressure of 50 kPa a Determine the thermal efficiency of this cycle Now let s consider the losses in the Rankine cycle The pump outlet pressure is 10 MPa and the turbine outlet pressure is 50 KPa However due to heat and pressure losses in the boiler steam pressure and temperature at the inlet of the turbine are 9 MPa and 450 C In addition the inlet pressure of the saturated water is 40 kPa due to pressure drop in the condenser When the isentropic efficiency of the turbine is 90 and the isentropic efficiency of the pump is 85 Determine b the thermal efficiency of the cycle Answers Pw kJ kg Tw kJ kg 1082 0 904 3 netw kJ kg 1071 8 904 3 inq kJ kg 3024 3 2928 4 35 4 30 5 Ideal Actual 10 2 12 0 6 7 8