Rankine Cycle

The Rankine cycle is the ideal thermodynamic cycle for vapor power plants, particularly steam power plants. It models the conversion of heat into work using a working fluid (typically water/steam) that undergoes phase change. The ideal cycle consists of four internally reversible processes: (1) Isentropic compression in a pump (saturated liquid at state 1 to compressed liquid at state 2). (2) Constant-pressure heat addition in a boiler (compressed liquid to superheated vapor at state 3). (3) Isentropic expansion in a turbine (superheated vapor to wet vapor at state 4). (4) Constant-pressure heat rejection in a condenser (wet vapor to saturated liquid at state 1). On a T-s diagram, the Rankine cycle appears as a rectangle-like shape crossing the vapor dome. The area under the heat-addition curve represents q_in, and the area under the heat-rejection curve represents q_out. Net work output equals the difference: w_net = q_in − q_out. Energy analysis uses steam tables or property software to find enthalpy (h) and entropy (s) at each state. For the ideal cycle: pump work w_p = h₂ − h₁ ≈ v₁(P₂ − P₁) for incompressible liquid; turbine work w_t = h₃ − h₄; heat added q_in = h₃ − h₂; heat rejected q_out = h₄ − h₁. Thermal efficiency is η_th = w_net / q_in = (w_t − w_p) / q_in = 1 − q_out / q_in. Real Rankine cycles have irreversibilities: pump and turbine isentropic efficiencies (η_p < 100%, η_t < 100%) reduce net work. Common modifications improve efficiency: (1) Increasing boiler pressure raises average heat-addition temperature but increases moisture at turbine exit. (2) Superheating steam to higher temperatures increases efficiency and reduces turbine-exit moisture (moisture should stay below ~10% to prevent blade erosion). (3) Reheat (expanding in stages with reheating between) increases efficiency and reduces moisture. (4) Regeneration (feedwater heating using extracted steam) increases efficiency by raising average heat-addition temperature. The condenser pressure is limited by the cooling medium temperature (typically 30–40°C for river/ocean cooling), setting a lower bound on T_L. Lower condenser pressure increases efficiency but requires larger condensers and increases moisture content.