🔥Thermodynamics I Unit 10 – Vapor and Combined Power Cycles

Key Concepts and Definitions

• Vapor power cycles convert heat into work through the use of a working fluid that undergoes phase changes (typically water/steam)
• Rankine cycle is the most common vapor power cycle consists of four main processes: compression, heat addition, expansion, and heat rejection
• Thermal efficiency ($\eta_{th}$) measures the effectiveness of a heat engine in converting heat input to useful work output calculated as $\eta_{th} = \frac{W_{net}}{Q_{in}}$
• Isentropic efficiency ($\eta_{s}$) compares the actual performance of a turbine or pump to the ideal isentropic process
  • For a turbine: $\eta_{s,t} = \frac{h_{1} - h_{2}}{h_{1} - h_{2s}}$
  • For a pump: $\eta_{s,p} = \frac{h_{2s} - h_{1}}{h_{2} - h_{1}}$
• Carnot efficiency ($\eta_{Carnot}$) represents the maximum theoretical efficiency achievable by a heat engine operating between a hot reservoir at temperature $T_{H}$ and a cold reservoir at temperature $T_{C}$: $\eta_{Carnot} = 1 - \frac{T_{C}}{T_{H}}$
• Reheat involves partially expanding the steam in a high-pressure turbine, reheating it, and then further expanding it in a low-pressure turbine
• Regeneration preheats the feedwater entering the boiler using steam extracted from the turbine at an intermediate stage

Vapor Power Cycle Basics

• Vapor power cycles harness the phase change of a working fluid (usually water) to convert heat into mechanical work
• The working fluid undergoes a series of thermodynamic processes in a closed loop, including compression, heat addition, expansion, and heat rejection
• In the compression stage, the liquid working fluid is pressurized by a pump, increasing its pressure and temperature
• During heat addition, the high-pressure liquid is heated in a boiler, converting it into high-pressure, high-temperature vapor (steam)
• The high-pressure steam expands through a turbine, generating mechanical work and reducing its pressure and temperature
• In the heat rejection stage, the low-pressure steam is condensed back into a liquid in a condenser, completing the cycle
• The net work output of the cycle is the difference between the work generated by the turbine and the work consumed by the pump
• The heat input is provided by an external source (combustion of fuel, nuclear reaction, solar energy, etc.)
• The efficiency of the cycle depends on factors such as the working fluid properties, operating temperatures and pressures, and component efficiencies

Rankine Cycle Analysis

• The Rankine cycle is the most widely used vapor power cycle consists of four main processes: compression in a pump, heat addition in a boiler, expansion in a turbine, and heat rejection in a condenser
• Process 1-2: Isentropic compression in the pump raises the pressure of the liquid working fluid from the condenser pressure to the boiler pressure
• Process 2-3: Constant-pressure heat addition in the boiler converts the high-pressure liquid into high-pressure, high-temperature steam
• Process 3-4: Isentropic expansion in the turbine generates mechanical work and reduces the steam pressure and temperature
• Process 4-1: Constant-pressure heat rejection in the condenser converts the low-pressure steam back into a saturated liquid
• The thermal efficiency of the Rankine cycle can be calculated as: $\eta_{th} = \frac{w_{turbine} - w_{pump}}{q_{in}}$
  • $w_{turbine}$ is the specific work output of the turbine (kJ/kg)
  • $w_{pump}$ is the specific work input to the pump (kJ/kg)
  • $q_{in}$ is the specific heat input to the boiler (kJ/kg)
• Increasing the boiler pressure and temperature or decreasing the condenser pressure can improve the cycle efficiency

Improving Cycle Efficiency

• Several modifications can be made to the basic Rankine cycle to enhance its efficiency and performance
• Superheating the steam to a higher temperature before it enters the turbine increases the average temperature at which heat is added, improving cycle efficiency
• Reheating the steam after partial expansion in the turbine and then further expanding it in a second stage increases the average temperature of heat addition and reduces moisture content in the turbine
• Regenerative heating uses steam extracted from the turbine at intermediate stages to preheat the feedwater entering the boiler, reducing the heat input required and improving efficiency
• Increasing the boiler pressure raises the average temperature of heat addition and improves efficiency, but it also increases the moisture content in the turbine exhaust
• Lowering the condenser pressure reduces the temperature of heat rejection and improves efficiency, but it may lead to air leakage and increased turbine exhaust moisture
• Using multiple pressure levels in the boiler and turbine allows for better matching of the working fluid temperature profile with the heat source and sink, enhancing overall efficiency
• Selecting an appropriate working fluid with favorable thermodynamic properties (high critical temperature, low specific volume, etc.) can optimize cycle performance for specific operating conditions

Combined Power Cycles

• Combined power cycles integrate multiple thermodynamic cycles to achieve higher overall efficiencies by utilizing waste heat from one cycle as the input for another
• Gas-steam combined cycles (GSCC) combine a gas turbine (Brayton) cycle with a steam turbine (Rankine) cycle
  • The high-temperature exhaust gases from the gas turbine serve as the heat source for the steam cycle
  • This arrangement allows for efficient utilization of the gas turbine's waste heat, resulting in overall efficiencies up to 60%
• Combined heat and power (CHP) systems, also known as cogeneration, produce both electricity and useful heat from a single fuel source
  • The waste heat from the power generation process is used for space heating, industrial processes, or district heating
  • CHP systems can achieve overall efficiencies of 80% or higher by effectively utilizing the waste heat
• Organic Rankine cycles (ORC) use organic fluids with lower boiling points as the working fluid, allowing for power generation from low-temperature heat sources (geothermal, solar, industrial waste heat)
• Kalina cycles employ a mixture of ammonia and water as the working fluid, which has a variable boiling point that allows for better matching with the heat source temperature profile
• Supercritical CO2 cycles operate with carbon dioxide above its critical point, offering high efficiency and compact turbomachinery due to the fluid's high density and low compressibility

Real-World Applications

• Vapor power cycles are widely used in various industries for electricity generation and mechanical power production
• Coal-fired power plants use the Rankine cycle with steam as the working fluid, generating a significant portion of the world's electricity
• Nuclear power plants also employ the Rankine cycle, with the nuclear reactor serving as the heat source for the steam generation
• Natural gas-fired combined cycle power plants (NGCC) integrate a gas turbine cycle with a steam turbine cycle, achieving high efficiencies and reduced emissions compared to coal-fired plants
• Concentrated solar power (CSP) plants use solar energy to generate steam for a Rankine cycle, providing a renewable source of electricity
• Geothermal power plants harness the heat from the Earth's interior to produce steam for a Rankine cycle or use an organic Rankine cycle for lower-temperature resources
• Industrial facilities, such as chemical plants, refineries, and paper mills, often employ combined heat and power (CHP) systems to meet their electricity and process heat demands efficiently
• Waste heat recovery systems in various industries use organic Rankine cycles (ORC) to generate electricity from low-temperature waste heat, improving overall energy efficiency

Problem-Solving Techniques

• When analyzing vapor power cycles, it is essential to follow a systematic approach to problem-solving
• Start by identifying the given information, such as the working fluid, operating temperatures and pressures, and component efficiencies
• Determine the thermodynamic state of the working fluid at each point in the cycle using property tables, charts, or equations of state
• Apply the appropriate energy balance equations for each component (boiler, turbine, condenser, pump) to calculate heat transfer and work interactions
• Use the isentropic efficiency equations to account for irreversibilities in the turbine and pump, relating the actual process to the ideal isentropic process
• Calculate the net work output of the cycle by subtracting the pump work from the turbine work
• Determine the heat input to the cycle, typically by applying an energy balance to the boiler
• Evaluate the thermal efficiency of the cycle using the net work output and heat input values
• If required, analyze the effects of modifications such as superheating, reheating, or regeneration on the cycle performance
• Compare the calculated performance metrics (efficiency, work output, heat input) to the Carnot efficiency or other relevant benchmarks to assess the cycle's effectiveness
• Consider the limitations and assumptions made in the analysis, such as neglecting pressure drops, heat losses, or component inefficiencies, and discuss their potential impact on the results

Key Takeaways and Review

• Vapor power cycles, particularly the Rankine cycle, are widely used for electricity generation and mechanical power production
• The Rankine cycle consists of four main processes: compression in a pump, heat addition in a boiler, expansion in a turbine, and heat rejection in a condenser
• The thermal efficiency of a vapor power cycle depends on factors such as the working fluid properties, operating temperatures and pressures, and component efficiencies
• Modifications such as superheating, reheating, and regeneration can improve the efficiency of the Rankine cycle by increasing the average temperature of heat addition or reducing the heat input required
• Combined power cycles, such as gas-steam combined cycles (GSCC) and combined heat and power (CHP) systems, integrate multiple thermodynamic cycles to achieve higher overall efficiencies
• Organic Rankine cycles (ORC) and Kalina cycles are used for power generation from low-temperature heat sources or for better matching with the heat source temperature profile
• Real-world applications of vapor power cycles include coal-fired and nuclear power plants, natural gas-fired combined cycle plants, concentrated solar power plants, geothermal power plants, and industrial CHP systems
• When solving problems related to vapor power cycles, it is important to follow a systematic approach, applying energy balance equations, isentropic efficiency relations, and thermodynamic property data to analyze cycle performance