Heat engine efficiency can be found by using either:
Carnot Cycle efficiency: Ratio of temperature difference between inlet and outlet to inlet temperature.
Rankine cycle efficiency: Ratio of heat energy at the turbine inlet and outlet to the total heat energy taken from the steam. 2. Example of calculating the Carnot Cycle and Rankine Cycle Efficiency.
Explained by Example:
A turbine is supplied with superheated steam at 96 bar at 490oC. The exhaust is at 0.09 bar and at 12 % wetness.
Temperature of saturated steam is : 43.7oC
Determine and Compare the Carnot Cycle and Rankine cycle.
Procedure to determine the Carnot cycle efficiency :
Procedure to determine the Rankine cycle efficiency :
Sensible heat in condensate corresponding to exhaust pressure of 0.09 bar in KJ/Kg = 183.3 3. Steam-Phase diagram is a graphical representation of data provided in the steam table. Steam-Phase diagram provides the relationship between enthalpy, temperature corresponding to various pressures. Liquid Enthalpy hf. This is represented by line A-B on the phase-diagram. When the water starts receiving heat from 0o C, then it receives all its liquid entahlpy along the saturated water line A-B on the phase diagram
Enthalpy of Saturated Steam (hfg): Any further heat addition results in change in phase to saturated steam and is represented by (hfg) on phase diagram i.e B-C.
Dryness Fraction (x): When heat is applied then the liquid start changing its phase from liquid to vapour and then the dryness fraction of the mixture starts increasing i.e moving towards unity. In the phase diagram dryness fraction of the mixture is 0.5 at exactly mid of the line BC. Similarly at point c on the phase diagram dryness fraction value is 1.
Line C-D Point c is in the saturated vapour line, any further heat addition results in increasing the steam temperature i.e beginning of steam superheating represented by line C-D.
Liquid Zone → Region towards left side of the saturated liquid line
Super heat zone → Region towards right side of the saturated vapour line
Two phase Zone → Area between the saturated liquid and saturated vapour line is mixture liquid and vapour. Mixture with varied dryness fractions.
Critical Point → It is the Apex point where saturated liquid and saturated vapour lines meet. Enthalpy of evaporation diminishes to zero at critical point, it means that water changes directly to steam at critical point and thereafter.
Maximum temperature which liquid can attain or exist is equivalent to critical point.
Critical point Parameters → Temperature 374.15oC
Pressure → 221.2 bar
Values above this are super-critical values and are useful in increasing the efficiency of the rankine cycle.