Thermodynamics II Unit 5 Review: Rankine & Combined Vapor Power Cycles

Key Concepts and Definitions

• Rankine cycle converts heat into work using water as the working fluid in a closed loop
• Vapor power cycle operates by vaporizing and condensing a working fluid (water) to produce mechanical work
• Thermal efficiency ($\eta_{th}$) measures the effectiveness of converting heat input into net work output
• Isentropic efficiency ($\eta_{s}$) quantifies the deviation of real processes from the ideal isentropic process
• Carnot efficiency ($\eta_{Carnot}$) represents the maximum theoretical efficiency achievable by a heat engine operating between two thermal reservoirs
• Reheat process involves partially expanding the steam, reheating it, and then completing the expansion to improve efficiency
• Regeneration process preheats the feedwater using steam extracted from the turbine to increase cycle efficiency

Rankine Cycle Basics

• Rankine cycle consists of four main processes: compression, heat addition, expansion, and heat rejection
• Working fluid (water) undergoes phase changes during the cycle (liquid to vapor and back to liquid)
• Heat is added to the working fluid in a boiler or steam generator to produce high-pressure steam
• Steam expands in a turbine, generating mechanical work and reducing pressure and temperature
• Expanded steam is condensed back into liquid form in a condenser, rejecting heat to a cooling medium (cooling water or air)
• Condensed liquid is pumped back to the boiler, completing the cycle
• Pressure-volume (P-v) and temperature-entropy (T-s) diagrams are used to visualize and analyze the Rankine cycle

Components of a Rankine Cycle

• Boiler or steam generator heats the working fluid to produce high-pressure steam
  • Heat source can be fossil fuels (coal, oil, natural gas), nuclear energy, or renewable sources (solar, geothermal)
• Turbine expands the high-pressure steam, converting thermal energy into mechanical work
  • Steam turbines are typically multi-stage, with high-pressure and low-pressure sections
• Condenser condenses the low-pressure steam back into liquid form
  • Cooling is achieved using cooling water from a nearby source (river, lake, or cooling tower) or air-cooled condensers
• Feedwater pump increases the pressure of the condensed liquid and pumps it back to the boiler
  • Pumping requires a small fraction of the turbine's work output
• Feedwater heaters preheat the feedwater using extracted steam from the turbine (in regenerative Rankine cycles)
• Deaerator removes dissolved gases (air and carbon dioxide) from the feedwater to prevent corrosion in the boiler

Thermodynamic Analysis of Rankine Cycles

• First Law of Thermodynamics (energy conservation) is applied to each component of the cycle
  • $\dot{Q} - \dot{W} = \Delta \dot{H}$, where $\dot{Q}$ is heat transfer rate, $\dot{W}$ is work rate, and $\Delta \dot{H}$ is the change in enthalpy rate
• Second Law of Thermodynamics (entropy generation and irreversibility) is considered for real processes
  • Isentropic efficiency ($\eta_{s}$) accounts for irreversibilities in turbines and pumps
• Thermal efficiency ($\eta_{th}$) is calculated as the ratio of net work output to heat input
  • $\eta_{th} = \frac{\dot{W}_{net}}{\dot{Q}_{in}}$, where $\dot{W}_{net}$ is the difference between turbine work and pump work
• Specific enthalpy (h) and specific entropy (s) are used to analyze the thermodynamic states of the working fluid
• Steam tables and Mollier diagrams (h-s diagrams) are used to determine the properties of the working fluid at each state in the cycle

Efficiency Improvements in Rankine Cycles

• Increasing the boiler pressure increases the average temperature at which heat is added, improving cycle efficiency
  • Supercritical Rankine cycles operate above the critical point of water (220.6 bar and 374°C) for higher efficiency
• Increasing the turbine inlet temperature (superheating) raises the average temperature of heat addition, enhancing efficiency
  • Materials limitations and steam quality considerations limit the extent of superheating
• Lowering the condenser pressure reduces the average temperature at which heat is rejected, increasing efficiency
  • Condenser pressure is limited by the temperature of the available cooling medium and the size of the condenser
• Regenerative heating using feedwater heaters extracts steam from the turbine to preheat the feedwater, improving efficiency
  • Closed feedwater heaters mix the extracted steam with the feedwater, while open feedwater heaters (deaerators) directly contact the steam and feedwater
• Reheating the steam after partial expansion in the turbine increases the average temperature of heat addition and reduces moisture content in the turbine
  • Single or double reheat stages are commonly used in modern power plants

Combined Vapor Power Cycles

• Combined cycles integrate gas turbine (Brayton) and steam turbine (Rankine) cycles for higher overall efficiency
  • Exhaust heat from the gas turbine serves as the heat source for the steam turbine cycle
• Topping cycle (gas turbine) operates at a higher average temperature than the bottoming cycle (steam turbine)
• Heat recovery steam generator (HRSG) uses the hot exhaust gases from the gas turbine to generate steam for the Rankine cycle
  • HRSG can be single-pressure, dual-pressure, or triple-pressure, depending on the steam requirements and optimization
• Combined cycles offer higher efficiency than individual gas turbine or steam turbine cycles
  • Efficiencies over 60% are achievable with state-of-the-art combined cycle power plants
• Flexibility in fuel use (natural gas, syngas, or distillate oil) and quick start-up times make combined cycles attractive for power generation

Real-World Applications

• Coal-fired steam power plants use the Rankine cycle with steam temperatures around 600°C and pressures up to 300 bar
  • Efficiency improvements through advanced ultra-supercritical (A-USC) technologies aim to achieve temperatures up to 700°C and pressures up to 350 bar
• Nuclear power plants employ the Rankine cycle with lower steam temperatures (around 300°C) due to reactor limitations
  • Pressurized water reactors (PWRs) and boiling water reactors (BWRs) are the most common types of nuclear power plants
• Concentrated solar power (CSP) plants use solar energy to generate steam for the Rankine cycle
  • Parabolic trough, linear Fresnel, and solar tower systems concentrate sunlight to heat a working fluid (oil, molten salt, or water) for steam generation
• Geothermal power plants utilize the Rankine cycle with lower temperature heat sources (150-300°C)
  • Binary cycle plants use a secondary working fluid (e.g., pentane or butane) to generate power from lower temperature geothermal resources
• Organic Rankine Cycle (ORC) systems use organic fluids (hydrocarbons or refrigerants) instead of water for low-temperature heat recovery applications
  • Waste heat recovery, biomass power generation, and low-temperature geothermal are common applications of ORC systems

Problem-Solving Strategies

• Identify the type of Rankine cycle (simple, reheat, regenerative, or combined) and the given parameters
• Sketch the cycle on P-v and T-s diagrams, labeling each state point and process
• Determine the thermodynamic properties (pressure, temperature, specific enthalpy, and specific entropy) at each state using steam tables or Mollier diagrams
  • Use interpolation or approximation when necessary
• Apply the First Law of Thermodynamics to each component (boiler, turbine, condenser, and pump) to calculate heat transfer and work
  • Consider isentropic efficiencies for turbines and pumps in real cycles
• Calculate the thermal efficiency of the cycle using the net work output and heat input
• Analyze the effects of changing operating parameters (boiler pressure, turbine inlet temperature, condenser pressure) on cycle efficiency
• Consider the trade-offs between efficiency, cost, and practical limitations when optimizing the cycle
• Validate the results using the Second Law of Thermodynamics and check for consistency with the given data and assumptions