5.1 Rankine Cycle Analysis and Efficiency

The Rankine cycle is the backbone of vapor power systems, turning heat into electricity in power plants worldwide. It uses water's phase changes to efficiently convert thermal energy to mechanical work, with key components like boilers, turbines, and condensers working together.

Analyzing the Rankine cycle's efficiency is crucial for optimizing power plant performance. Factors like operating pressures, temperatures, and component efficiencies all impact overall system effectiveness. Understanding these relationships helps engineers design more efficient and sustainable power generation systems.

Rankine Cycle Components and Processes

Basic Rankine Cycle Components

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• The basic Rankine cycle consists of four main components a pump, a boiler, a turbine, and a condenser
• The pump increases the pressure of the working fluid, moving it from the condenser to the boiler
  • Pumps in Rankine cycles are typically centrifugal pumps driven by electric motors
• The boiler adds heat to the working fluid at constant pressure, converting it from a liquid to a superheated vapor
  • Boilers can be fired by various fuels such as coal, natural gas, or nuclear energy
• The turbine expands the high-pressure, high-temperature vapor, generating mechanical work and reducing pressure and temperature
  • Steam turbines in Rankine cycles are usually multi-stage turbines with multiple sets of blades
• The condenser cools the turbine exhaust vapor at constant pressure, converting it back to a liquid state
  • Condensers typically use cooling water from a nearby source (rivers, lakes, or cooling towers) to remove heat from the working fluid

Working Fluid Phase Changes and Circulation

• The working fluid in a Rankine cycle, typically water, undergoes phase changes as it circulates through the system
  • Water is chosen as the working fluid due to its favorable properties, such as high enthalpy of vaporization and thermal stability
• The condensed liquid from the condenser is pumped back to the boiler, completing the cycle
  • The working fluid continuously circulates through the closed-loop Rankine cycle, repeating the processes of compression, heat addition, expansion, and heat rejection
• The phase changes of the working fluid enable efficient heat transfer and work extraction in the Rankine cycle
  • Latent heat of vaporization allows a large amount of heat to be added in the boiler without a significant temperature increase
  • Latent heat of condensation enables efficient heat rejection in the condenser while maintaining a constant temperature

Rankine Cycle Efficiency and Power Output

Thermal Efficiency Calculation

• Thermal efficiency is the ratio of the net work output to the heat input in a Rankine cycle
  • Thermal efficiency measures how effectively the Rankine cycle converts heat input into useful work output
• Net work output is the difference between the work produced by the turbine and the work consumed by the pump
  • The pump work is usually much smaller than the turbine work, resulting in a positive net work output
• Heat input is the amount of heat added to the working fluid in the boiler
  • Heat input is determined by the enthalpy difference between the boiler inlet and outlet states
• The thermal efficiency equation for a Rankine cycle is ηth = (wt - wp) / qin, where wt is the turbine work, wp is the pump work, and qin is the heat input
  • Example A Rankine cycle produces 100 MW of turbine work, consumes 5 MW of pump work, and has a heat input of 200 MW. The thermal efficiency is (100 MW - 5 MW) / 200 MW = 0.475 or 47.5%

Power Output Calculation

• Power output is the rate at which the Rankine cycle produces work, typically measured in watts or horsepower
  • Power output determines the generating capacity of a Rankine cycle power plant
• The first law of thermodynamics is applied to each component of the Rankine cycle to determine the energy balance and calculate the heat and work interactions
  • The steady-flow energy equation is used for the pump, boiler, turbine, and condenser to analyze the energy transfers
• The enthalpies of the working fluid at each state point in the cycle are used to calculate the heat input, heat rejection, and work output
  • Enthalpy values are obtained from thermodynamic property tables or equations of state based on the pressure and temperature or quality of the working fluid at each state point

Factors Affecting Rankine Cycle Efficiency

Operating Pressures and Temperatures

• The thermal efficiency of a Rankine cycle is influenced by several factors, including the operating pressures and temperatures of the boiler and condenser
• Increasing the boiler pressure and temperature raises the average temperature at which heat is added, improving thermal efficiency
  • Higher boiler temperatures result in a higher quality of the working fluid at the turbine inlet, increasing the available energy for work extraction
• Lowering the condenser pressure reduces the temperature at which heat is rejected, enhancing thermal efficiency
  • Lower condenser pressures lead to a lower turbine outlet temperature, reducing the amount of heat rejected to the environment

Component Efficiencies and Irreversibilities

• The isentropic efficiencies of the turbine and pump affect the overall efficiency of the Rankine cycle
  • Isentropic efficiency measures the deviation of the actual component performance from the ideal isentropic process
  • Higher isentropic efficiencies of the turbine and pump result in improved cycle efficiency
• The presence of irreversibilities, such as friction and heat loss, reduces the actual thermal efficiency compared to the ideal Rankine cycle
  • Irreversibilities cause entropy generation and decrease the available work output
• Minimizing irreversibilities through proper design, insulation, and maintenance can help improve the overall efficiency of the Rankine cycle
  • Example Using high-quality steam turbine blades with smooth surfaces and optimized geometries can reduce frictional losses and improve turbine efficiency

Cycle Modifications for Efficiency Improvement

• Superheat and reheat stages can be added to the basic Rankine cycle to increase the average temperature of heat addition and improve efficiency
  • Superheating involves heating the vapor above its saturation temperature, increasing the available energy for work extraction in the turbine
  • Reheating involves expanding the steam in stages, with additional heat input between stages, to raise the average temperature of heat addition
• The working fluid properties, such as the specific heat capacity and latent heat of vaporization, influence the Rankine cycle efficiency
  • Working fluids with higher specific heat capacities and latent heat of vaporization can absorb and release more heat, leading to improved cycle efficiency
  • Organic Rankine Cycles (ORCs) use organic fluids (hydrocarbons or refrigerants) instead of water to better match the heat source characteristics and improve efficiency in low-temperature applications

Rankine Cycle Performance Analysis T-s vs P-h Diagrams

Temperature-Entropy (T-s) Diagrams

• Temperature-entropy (T-s) diagrams are graphical representations of the thermodynamic states and processes in a Rankine cycle
• On a T-s diagram, the Rankine cycle appears as a closed loop, with the area enclosed by the loop representing the net work output
  • The larger the area enclosed by the cycle on the T-s diagram, the greater the net work output
• The heat input and heat rejection processes are represented by the area under the curves on the T-s diagram
  • The area under the boiler curve represents the heat input, while the area under the condenser curve represents the heat rejection
• The thermodynamic properties of the working fluid at each state point can be determined using the T-s diagram
  • The temperature, entropy, and quality (for two-phase states) can be read directly from the T-s diagram or interpolated between constant pressure lines and saturated liquid/vapor curves

Pressure-Enthalpy (P-h) Diagrams

• Pressure-enthalpy (P-h) diagrams are another graphical representation of the thermodynamic states and processes in a Rankine cycle
• On a P-h diagram, the Rankine cycle also appears as a closed loop, with the area enclosed by the loop representing the net work output
  • The larger the area enclosed by the cycle on the P-h diagram, the greater the net work output
• The constant pressure processes (boiler and condenser) appear as horizontal lines on the P-h diagram
  • The boiler process follows a horizontal line at the boiler pressure, while the condenser process follows a horizontal line at the condenser pressure
• The quality of the working fluid at various points in the cycle can be determined using the P-h diagram
  • The quality can be determined by the position of the state point relative to the saturated liquid and saturated vapor lines on the P-h diagram
• The effect of changing operating conditions, such as boiler and condenser pressures, on the Rankine cycle performance can be visualized using P-h diagrams
  • Changing the boiler or condenser pressure shifts the corresponding horizontal lines on the P-h diagram, altering the cycle shape and performance