Rankine Cycle

The Rankine cycle is the basic thermodynamic cycle for steam power plants. It consists of four idealized processes: isentropic compression of liquid water in the pump, isobaric heat addition in the boiler to produce superheated steam, isentropic expansion of steam in the turbine to produce work, and isobaric heat rejection in the condenser to condense steam back to saturated liquid. Practical cycles include irreversibilities (pump and turbine efficiencies), feedwater heaters (regeneration), reheaters, and multiple pressure levels to increase efficiency and control steam quality at turbine exhaust. Efficiency improvements focus on increasing the average temperature of heat addition and reducing irreversibilities and turbine-exit moisture.

Governing FormulaKey relations (per unit mass, SI units): - Pump work (ideal, liquid approximation): wp ≈ v (P2 - P1) (J/kg) - Turbine work (per unit mass): wt = h1 - h2 (kJ/kg) - Pump work (enthalpy): wp = h4 - h3 (kJ/kg) - Heat added in boiler: qin = h1 - h4 (kJ/kg) - Heat rejected in condenser: qout = h2 - h3 (kJ/kg) - Net work: wnet = wt - wp = (h1 - h2) - (h4 - h3) (kJ/kg) - Thermal efficiency: ηth = wnet / qin = [(h1 - h2) - (h4 - h3)] / (h1 - h4) - Turbine isentropic efficiency: ηt = (h1 - h2_actual) / (h1 - h2s) - Steam dryness (quality) at turbine exit: x = (h_exit - hf) / (hg - hf) Assumptions typically used: steady flow, one-dimensional, negligible kinetic and potential energy changes, enthalpies in kJ/kg, pressures in Pa, specific volumes in m^3/kg.

Knowledge Check

10 Questions

1.In the ideal Rankine cycle which two components operate approximately at constant pressure (isobaric)? State assumptions: ideal Rankine, steady flow.

2.For a Rankine cycle with state enthalpies h1 (turbine inlet), h2 (turbine exit), h3 (condenser exit, saturated liquid), and h4 (pump outlet), which expression correctly gives the thermal efficiency ηth? Use enthalpy units kJ/kg.

3.A simple Rankine cycle has state enthalpies h1 = 2800 kJ/kg (turbine inlet), h2 = 2000 kJ/kg (turbine exit), h3 = 200 kJ/kg (saturated liquid at condenser exit), and h4 = 210 kJ/kg (pump outlet). Calculate the cycle thermal efficiency (in percent). Assumptions: steady flow, enthalpies given are correct.

4.A steam turbine inlet has h1 = 3200 kJ/kg. The isentropic expansion would give h2s = 2200 kJ/kg, but the actual turbine outlet enthalpy is h2 = 2400 kJ/kg. What is the turbine isentropic efficiency (in percent)?

5.Estimate the ideal pump work (in kJ/kg) for pumping saturated liquid from condenser pressure 10 kPa to boiler pressure 8 MPa. Use v = 1.00×10^-3 m^3/kg for the liquid (assume incompressible) and state pressures in Pa.

6.If the condenser pressure is increased (i.e., condensing temperature rises) while all other cycle parameters remain the same, how does the ideal Rankine cycle thermal efficiency change (qualitatively)?

7.Which statement correctly describes the primary benefit of adding a reheat stage between high-pressure and low-pressure turbine stages (reheating steam once in the boiler between expansions)?

8.What is the principal thermodynamic effect of using feedwater heaters (regeneration) in a Rankine cycle with open feedwater heaters? Choose the best answer.

9.If the turbine inlet temperature is increased while the boiler pressure is held constant (all else equal), what is the expected effect on the ideal Rankine cycle thermal efficiency?

10.Steam leaves a turbine at enthalpy h2 = 2100 kJ/kg. At the condenser pressure the saturated liquid enthalpy is hf = 200 kJ/kg and the saturated vapor enthalpy is hg = 2700 kJ/kg. What is the dryness fraction (quality) x at the turbine exit (expressed as a percentage)?