top of page
Power Station

Basic Thermodynamic Analysis of Power Cycles

Gas Turbine Cycle

Schematic of of a Recuperated Gas Turbine Cycle

A regenerative Brayton cycle is schematically shown. Air at state 1 enters the compressor at 300 K and 1 bar. The pressure ratio is 8, and the compressor and the turbine operate with isentropic efficiencies of 80% and 89%, respectively. The effectiveness of the regenerative heat exchanger is 82%. Hot air at state 4 leaves the combustor at 1200 K. The exhaust of the cycle (state 6) is discharged to the environment. Neglect any pressure drop in the flow path of the air. Per unit mass flow rate of the air, determine (a) the work requirement of the compressor; (b) the work production of the turbine; (c) the heat added to the air in the combustor; (d) the net work production of the cycle; (e) the thermal efficiency of the cycle; (f) the mass flow rate of the air if the net power production of the cycle is 80 kW. Use k = 1.4 in your calculations.

Schematic of a Steam Power Cycle

Steam Power Cycle

A Rankine cycle with one closed heater and one open heater is schematically shown. Steam leaving the boiler at 500 °C and 10 MPa (state 8) is expanded in the turbine to 7 kPa (state 11). At the location of 500 kPa (state 9) and 250 kPa (state 10), steam is extracted from the turbine to preheat the water in the open and the closed heaters, respectively. The temperature of the water at state 5 is the condensation temperature of the extracted steam at state 10, all of which condenses within the closed heater. The condensate is then throttled (state 4) through a valve to the condenser pressure. The exit flow of the open heat is saturated liquid. The isentropic efficiencies of the turbine and pumps are 92% and 72% respectively. The rate of heat transfer in the boiler is 5 MW. Determine (a) the steam mass flow rate at state 8; (b) the steam mass flow rate at the extraction points; (c) the power production of the turbine; (d) the thermal efficiency of the cycle.

Combined Cycle Power Plant

Schematic of a Combined Cycle Power Plant

A simple Brayton cycle with a net power output of 1 MW is combined with a regenerative Rankine cycle operating with steam as the working fluid. Air at 20 °C and 100 kPa enters the compressor where it is pressurized to 1.2 MPa. The isentropic efficiency of the compressor is 80%. The gas turbine operating with an isentropic efficiency of 90% receives hot air at 1000 °C. The exhaust stream of the gas turbine at 110 kPa is sent to a heat exchanger to produce 0.546 kg/s steam at 485 °C and 4.5 MPa. The exhaust gas at 100 kPa is finally discharged to the atmosphere. Steam is extracted from the turbine at 550 kPa. The preheated water leaving the open heater is saturated liquid. The water leaving the condenser is at 36 °C and 9.5 kPa. The isentropic efficiency of the steam turbine is 89%. Both pumps operate with an identical isentropic efficiency of 75%. Determine (a) the mass flow rate of the air; (b) the mass flow rate of the extracted steam; (c) the temperature at state 5; (d) the quality at the exhaust of the steam turbine; (e) the power output of the Rankine cycle; (f) the thermal efficiency of the combined cycle.

Integrated gas turbine and solid oxide fuel cell cycle

Gas Turbine SOFC Cycle

A combined gas turbine and solid oxide fuel cell (SOFC) cycle is schematically shown. The fuel is hydrogen, and air is used as an oxidizer. Both the air and hydrogen are supplied to the system at 298 K and 1 bar and compressed through individual compressors up to 6 bar. In practice, only a fraction of the fuel is consumed within the fuel cell, so the fuel utilization factor is Uf = 0.8. The unused portion of the fuel is burned in a downstream combustor. The SOFC stack consists of 100 cells each with a surface area of 840 cm^2. The operating voltage, current density, and temperature of the SOFC are 0.68 V, 300m A/cm^2, and 1023 K, respectively. The DC-AC inverter efficiency is 0.96. The isentropic efficiencies of the gas turbine and compressors are 0.90 and 0.83, respectively. The AC generator efficiency is 0.98. All components operate adiabatically. Neglect any pressure or temperature drop between the adjacent components. Determine the net power production and the thermal efficiency of the cycle.

Integrated Gasification Combined Cycle

Integrated gasification combined cycle

An integrated gasification combined cycle is schematically shown in the figure. Solid fuel with a lower heating value of 18080 kJ/lg is converted to syngas in the gasifier. The syngas composition is H2 (15.8%), CO (22.4%), CO2 (11%), CH4 (1%), H2O (9.3%), N2 (40.5%). The syngas exiting the gasifier at 973 K is cooled and desulphurized. The cleaned gas at 573 K is fed to the water gas shift (WGS) reactor where the carbon monoxide reacts with water supplied separately to yield additional hydrogen and carbon dioxide. Air at 298 K and 1 bar is pressurized to 15 bar within the compressor. It is then split between the gasifier and the combustor. The gaseous fuel leaving the WGS reactor is combusted in the air which yields combustion products comprising CO2/H2O/O2/N2 at 1623 K. The combustion products are expanded within the turbine down to the atmospheric pressure. The rate at which the solid fuel is supplied to the gasifier is 0.5 kg/s. The air flowrate required for the gasification process is 0.8 Nm^3/s. The isentropic efficiencies of the compressor and turbine are 0.85 and 0.9, respectively. Determine the thermal efficiency of the cycle.

Inregrated gasification combined cycle with oxycombustion CO2 capture

IGCC with Oxy-Combustion CO2 Capture

An integrated gasification combined cycle employs oxy-combustion technology. The gasification agent and the oxidizer for burning the fuel gas is oxygen which is produced by an air separation unit (ASU). Solid fuel with a lower heating value of 18080 kJ/lg is converted to syngas in the gasifier. The syngas composition is H2 (27%), CO (38%), CO2 (19%), H2O (16%). The syngas exiting the gasifier at 1073 K is cooled and desulphurized. The cleaned gas at 573 K is fed to the water gas shift (WGS) reactor where the carbon monoxide reacts with water supplied separately to yield additional hydrogen and carbon dioxide. The ASU consumes 200 kWh/ton to split air into oxygen and nitrogen at 298 K and 1 bar. The oxygen is then compressed to 15 bar within the oxygen compressor. It is then split between the gasifier and the combustor. The gaseous fuel leaving the WGS reactor is burned in the combustor yielding combustion products comprising CO2/H2O at 1323 K. The combustion products are expanded within the turbine down to 1 bar. The hot gases are then cooled in a heat exchanger to condense and separate the steam content of the turbine exhaust. The cool carbon dioxide leaving the heat exchanger (state 9) is pressurized using the CO2 compressor to the combustion pressure. A portion of the compressed CO2 flow is sent to storage and the rest is recycled and heated within the heat exchanger before it is fed to the combustor. The rate at which the solid fuel is supplied to the gasifier is 0.5 kg/s. The oxygen flowrate required for the gasification process is 0.3 Nm^3/s. The isentropic efficiencies of the compressors and turbine are 0.85 and 0.9, respectively. The temperature difference at the hot side of the heat exchanger is 30K. Determine the thermal efficiency of the cycle.

bottom of page