Rankine Cycle – Thermodynamics as Energy Conversion Science<\/figcaption><\/figure>\nTypically most nuclear power plants<\/strong> operate multi-stage condensing steam turbines<\/strong>. In these turbines, the high-pressure stage receives steam (this steam is nearly saturated steam – x = 0.995 – point C at the figure) from a steam generator and exhausts it to a moisture separator-reheater (point D). The steam must be reheated to avoid damages caused to the steam turbine blades by low-quality steam. The reheater heats the steam (point D), and then the steam is directed to the low-pressure stage of the steam turbine, where it expands (point E to F). The exhausted steam is well below atmospheric pressure and is in a partially condensed state (point F), typically of a quality near 90%.<\/p>\nSpecific Enthalpy of Wet Steam<\/strong><\/h2>\nThe specific enthalpy of saturated liquid water<\/strong> (x=0) and dry steam<\/strong> (x=1) can be picked from steam tables. In the case of wet steam<\/strong>, the actual enthalpy can be calculated with the vapor quality, x,<\/em> and the specific enthalpies of saturated liquid water and dry steam:<\/p>\nh<\/em>wet<\/sub><\/em> = h<\/em>s<\/sub><\/em> x + (1 – x ) h<\/em>l<\/sub><\/em> \u00a0\u00a0\u00a0\u00a0<\/em>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/em><\/p>\nwhere<\/em><\/p>\nh<\/em>wet<\/sub><\/em> = enthalpy of wet steam (J\/kg)<\/em><\/p>\nh<\/em>s<\/sub><\/em> = enthalpy of “dry” steam (J\/kg)<\/em><\/p>\nh<\/em>l<\/sub><\/em> = enthalpy of saturated liquid water (J\/kg)<\/em><\/p>\nAs can be seen, wet steam will always have lower enthalpy than dry steam.<\/p>\n
Specific Entropy of Wet Steam<\/h2>\n
Similarly, the specific entropy of saturated liquid water (x=0) and dry steam (x=1) can be picked from steam tables. In the case of wet steam, the actual entropy can be calculated with the vapor quality, x,<\/em> and the specific entropies of saturated liquid water and dry steam:<\/p>\ns<\/em>wet<\/sub><\/em> = s<\/em>s<\/sub><\/em> x + (1 – x ) s<\/em>l<\/sub><\/em> \u00a0\u00a0\u00a0\u00a0<\/em>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/em><\/p>\nwhere<\/em><\/p>\ns<\/em>wet<\/sub><\/em> = entropy of wet steam (J\/kg K)<\/em><\/p>\ns<\/em>s<\/sub><\/em> = entropy of “dry” steam (J\/kg K)<\/em><\/p>\ns<\/em>l<\/sub><\/em> = entropy of saturated liquid water (J\/kg K)<\/em><\/p>\nSpecific Volume of Wet Steam<\/h2>\n
Similarly, the specific volume of saturated liquid water (x=0) and dry steam (x=1) can be picked from steam tables. In the case of wet steam, the actual specific volume can be calculated with the vapor quality, x,<\/em> and the specific volumes of saturated liquid water and dry steam:<\/p>\nv<\/em>wet<\/sub><\/em> = v<\/em>s<\/sub><\/em> x + (1 – x ) v<\/em>l<\/sub><\/em> \u00a0\u00a0\u00a0\u00a0<\/em>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/em><\/p>\nwhere<\/em><\/p>\nv<\/em>wet<\/sub><\/em> = specific volume of wet steam (m<\/em>3<\/sup><\/em>\/kg)<\/em><\/p>\nv<\/em>s<\/sub><\/em> = specific volume of “dry” steam (m<\/em>3<\/sup><\/em>\/kg)<\/em><\/p>\nv<\/em>l<\/sub><\/em> = specific volume of saturated liquid water (m<\/em>3<\/sup><\/em>\/kg)<\/em><\/p>\nExample:<\/strong><\/p>\nA high-pressure steam turbine stage operates at a steady state with inlet conditions of \u00a06 MPa, t = 275.6\u00b0C, x = 1 (point C). Steam leaves this turbine stage at a pressure of 1.15 MPa, 186\u00b0C, and x = 0.87 (point D). Calculate the enthalpy difference between these two states.<\/p>\n
The enthalpy for the state C can be picked directly from steam tables, whereas the enthalpy for the state D must be calculated using vapor quality:<\/p>\n
h<\/em><\/strong>