Superheated steam at 18 MPa, 560^∘ C, enters the turbine of a vapor power plant. The pressure at

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Superheated steam at 18 MPa, 560^∘ C, enters the turbine of...

Superheated steam at $18 \mathrm{MPa}, 560^{\circ} \mathrm{C}$, enters the turbine of a vapor power plant. The pressure at the exit of the turbine is $0.06$ bar, and liquid leaves the condenser at $0.045$ bar, $26^{\circ} \mathrm{C}$. The pressure is increased to $18.2 \mathrm{MPa}$ across the pump. The turbine and pump have isentropic efficiencies of 82 and $77 \%$, respectively. For the cycle, determine (a) the net work per unit mass of steam flow, in $\mathrm{kJ} / \mathrm{kg}$. (b) the heat transfer to steam passing through the boiler, in kJ per $\mathrm{kg}$ of steam flowing. (c) the thermal efficiency. (d) the heat transfer to cooling water passing through the condenser, in $\mathrm{kJ}$ per $\mathrm{kg}$ of steam condensed.

Superheated steam at $18 \mathrm{MPa}, 560^{\circ} \mathrm{C}$, enters the turbine of a vapor power plant. The pressure at the exit of the turbine is $0.06$ bar, and liquid leaves the condenser at $0.045$ bar, $26^{\circ} \mathrm{C}$. The pressure is increased to $18.2 \mathrm{MPa}$ across the pump. The turbine and pump have isentropic efficiencies of 82 and $77 \%$, respectively. For the cycle, determine
(a) the net work per unit mass of steam flow, in $\mathrm{kJ} / \mathrm{kg}$.
(b) the heat transfer to steam passing through the boiler, in kJ per $\mathrm{kg}$ of steam flowing.
(c) the thermal efficiency.
(d) the heat transfer to cooling water passing through the condenser, in $\mathrm{kJ}$ per $\mathrm{kg}$ of steam condensed.

Key Concepts

Rankine Cycle

The Rankine cycle is a thermodynamic cycle used to model steam power plants. It encompasses the processes of heat addition in a boiler, expansion in a turbine to produce work, condensation of the steam, and pumping of the liquid back to the boiler pressure. This cycle forms the basis for analyzing the performance and efficiency of vapor power plants.

Superheated Steam

Superheated steam refers to steam that has been heated beyond its saturation temperature at a given pressure, ensuring that it is entirely in the vapor phase. Its use in turbine inlets increases the thermal efficiency and work output of the cycle by reducing condensation within the turbine and providing a higher quality vapor for expansion.

Isentropic Efficiency

Isentropic efficiency is a measure of the performance of real devices like turbines and pumps compared to their ideal, reversible (isentropic) counterparts. It quantifies the loss of work or the extra work required in non-ideal processes by comparing the actual process with the ideal one, enabling more realistic performance evaluations of the cycle components.

Turbine Work Calculations

Turbine work calculations involve determining the amount of energy extracted from the high-pressure, high-temperature vapor as it expands to a lower pressure. The actual work output is adjusted by the turbine’s isentropic efficiency, showing the impact of irreversibilities on the conversion of thermal energy to mechanical work.

Pump Work Calculations

Pump work calculations focus on the energy required to increase the pressure of the liquid in the cycle. Since pumps also operate with inefficiencies (described by their isentropic efficiency), the actual work input typically exceeds the ideal value, and this must be taken into account when determining the net work produced by the cycle.

Thermal Efficiency

Thermal efficiency is the ratio of net work output from the cycle to the heat input in the boiler. It quantifies the overall performance of the cycle in converting thermal energy into useful mechanical work, and is influenced by component efficiencies and the temperature and pressure levels at which the cycle operates.

Heat Transfer Calculations

Heat transfer calculations in the context of power cycles involve determining the energy added to the working fluid in the boiler and the energy rejected in the condenser. These calculations are crucial for performing energy balances, evaluating system performance, and understanding the relationship between heat input, work output, and efficiency.

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