10.2 Reheat and regenerative vapor power cycles

Vapor power cycles are the backbone of electricity generation. Reheat and regenerative cycles take the basic Rankine cycle up a notch, boosting efficiency by clever steam manipulation. These upgrades squeeze more power from the same fuel, making our power plants greener and more cost-effective.

Understanding these cycles is crucial for grasping modern power generation. We'll explore how reheating steam and preheating feedwater can significantly improve cycle performance. These concepts are key to designing and optimizing real-world power plants, where every percentage point of efficiency matters.

Reheat and Regenerative Cycles

Reheat Cycles

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• Reheat cycles expand steam in stages, with reheating between stages to increase the average temperature at which heat is added
• In a reheat cycle, steam is only partially expanded in the turbine before being sent back to the boiler for reheating, then returned to the turbine for further expansion
  • Example: In a single-stage reheat cycle, steam is expanded in the high-pressure turbine, reheated in the boiler, and then expanded in the low-pressure turbine
  • The reheating process allows the steam to enter the low-pressure turbine at a higher temperature, increasing the overall efficiency of the cycle
• The number of reheat stages depends on factors such as the size of the power plant and the desired efficiency improvement
  • Multiple reheat stages can be used in large power plants to further increase the efficiency (e.g., double reheat or triple reheat cycles)

Regenerative Cycles

• Regenerative cycles extract steam at various points in the turbine and use it to preheat the feedwater before it enters the boiler
• Open feedwater heaters mix the extracted steam directly with the feedwater, while closed feedwater heaters transfer heat from the extracted steam to the feedwater through a heat exchanger
  • Open feedwater heaters are simpler in design but may result in a slight loss of steam quality due to direct mixing
  • Closed feedwater heaters maintain the separation between the extracted steam and the feedwater, allowing for better control of the feedwater conditions
• The number of feedwater heaters used in a regenerative cycle depends on factors such as the size of the power plant and the desired efficiency improvement
  • Modern power plants may employ multiple feedwater heaters (e.g., low-pressure heaters, high-pressure heaters, and a deaerator) to maximize the efficiency gains from regenerative heating

Cycle Performance Comparisons

Basic Rankine Cycle

• The basic Rankine cycle consists of four processes: isentropic compression in the pump, constant-pressure heat addition in the boiler, isentropic expansion in the turbine, and constant-pressure heat rejection in the condenser
• The thermal efficiency of the basic Rankine cycle is limited by the average temperature at which heat is added and the temperature at which heat is rejected

Reheat Cycle Comparison

• Reheat cycles improve upon the basic Rankine cycle by increasing the average temperature at which heat is added, resulting in a higher thermal efficiency
• The efficiency improvement achieved by a reheat cycle depends on factors such as the number of reheat stages and the pressure ratios across each stage
  • Example: A single-stage reheat cycle with an optimal reheat pressure can achieve an efficiency improvement of 4-5% compared to the basic Rankine cycle

Regenerative Cycle Comparison

• Regenerative cycles improve the efficiency of the basic Rankine cycle by preheating the feedwater using extracted steam, reducing the amount of heat input required in the boiler
• The efficiency improvement achieved by a regenerative cycle depends on the number of feedwater heaters used and the extraction pressures at each stage
  • Example: A regenerative cycle with multiple feedwater heaters can achieve an efficiency improvement of 10-12% compared to the basic Rankine cycle

Combined Reheat and Regenerative Cycle Comparison

• The combined use of reheat and regenerative processes can result in significant efficiency improvements compared to the basic Rankine cycle
• Modern power plants employing both reheat and regenerative cycles can achieve thermal efficiencies of over 40%
  • Example: A supercritical power plant with double reheat and multiple feedwater heaters can achieve a thermal efficiency of around 45-48%

Efficiency Improvements

Reheat Cycle Efficiency

• Reheat cycles increase the thermal efficiency by raising the average temperature at which heat is added, which increases the net work output for a given heat input
• The efficiency improvement achieved by a reheat cycle depends on factors such as the number of reheat stages and the pressure ratios across each stage
  • Increasing the number of reheat stages generally leads to higher efficiency improvements but also increases the complexity and cost of the power plant
  • The optimal reheat pressure is typically determined based on a trade-off between efficiency gains and practical considerations (e.g., materials, equipment limitations)

Regenerative Cycle Efficiency

• Regenerative cycles improve the thermal efficiency by reducing the amount of heat input required in the boiler, as the feedwater is preheated using extracted steam
• The efficiency improvement achieved by a regenerative cycle depends on the number of feedwater heaters used and the extraction pressures at each stage
  • Increasing the number of feedwater heaters generally leads to higher efficiency improvements but also increases the complexity and cost of the power plant
  • The extraction pressures are typically optimized to maximize the overall efficiency of the regenerative cycle while considering practical limitations (e.g., turbine design, available space)

Combined Reheat and Regenerative Cycle Efficiency

• The combined use of reheat and regenerative processes can result in significant efficiency improvements compared to the basic Rankine cycle
• Modern power plants employing both reheat and regenerative cycles can achieve thermal efficiencies of over 40%
  • The efficiency gains from reheat and regenerative processes are not simply additive; the overall improvement depends on the specific design and operating parameters of the power plant
  • Advanced technologies such as supercritical steam conditions, ultra-supercritical materials, and advanced turbine designs can further enhance the efficiency of combined reheat and regenerative cycles

Thermodynamic Analysis of Cycles

Thermodynamic Properties

• Analyzing reheat and regenerative cycles requires the use of thermodynamic properties such as enthalpy, entropy, and specific volume, which can be obtained from steam tables or property charts
• The thermodynamic states at each point in the cycle (e.g., turbine inlet, extraction points, condenser inlet) must be determined to calculate the performance parameters
  • Example: In a regenerative cycle, the enthalpy and entropy values at the extraction points are needed to determine the mass flow rates of the extracted steam and the feedwater

Performance Parameter Calculations

• The performance of a reheat cycle can be evaluated by calculating the turbine work output, pump work input, heat input in the boiler and reheater, and the thermal efficiency
• In a regenerative cycle, the mass flow rates of the extracted steam and the feedwater at each heater must be determined to calculate the thermodynamic states and performance parameters
  • The efficiency of a regenerative cycle can be evaluated by calculating the turbine work output, pump work input, heat input in the boiler, and the heat recovered by the feedwater heaters
  • The mass and energy balance equations for each feedwater heater must be solved simultaneously to determine the state points and mass flow rates

Visualization and Optimization Tools

• The use of a temperature-entropy (T-s) diagram can aid in visualizing the processes and state points in reheat and regenerative cycles, and in calculating the performance parameters
  • Example: On a T-s diagram, the area under the curve represents the heat input, while the area enclosed by the cycle represents the net work output
• Computer software and simulation tools can be used to model and optimize the design of reheat and regenerative cycles for specific power plant applications
  • These tools can perform complex thermodynamic calculations, evaluate the impact of design changes on cycle performance, and help identify the optimal operating parameters for a given set of constraints (e.g., fuel cost, environmental regulations)