Thermodynamics II

🧊Thermodynamics II Unit 5 – Rankine & Combined Vapor Power Cycles

Rankine and combined vapor power cycles are essential in modern power generation. These systems convert thermal energy into mechanical work using water as the working fluid, with the Rankine cycle forming the basis for steam power plants worldwide. Efficiency improvements in Rankine cycles include increasing boiler pressure, superheating steam, and using regeneration. Combined cycles integrate gas and steam turbines for higher overall efficiency, making them popular for power generation due to their flexibility and quick start-up times.

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 (ηth\eta_{th}) measures the effectiveness of converting heat input into net work output
  • Isentropic efficiency (ηs\eta_{s}) quantifies the deviation of real processes from the ideal isentropic process
  • Carnot efficiency (ηCarnot\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
    • Q˙W˙=ΔH˙\dot{Q} - \dot{W} = \Delta \dot{H}, where Q˙\dot{Q} is heat transfer rate, W˙\dot{W} is work rate, and ΔH˙\Delta \dot{H} is the change in enthalpy rate
  • Second Law of Thermodynamics (entropy generation and irreversibility) is considered for real processes
    • Isentropic efficiency (ηs\eta_{s}) accounts for irreversibilities in turbines and pumps
  • Thermal efficiency (ηth\eta_{th}) is calculated as the ratio of net work output to heat input
    • ηth=W˙netQ˙in\eta_{th} = \frac{\dot{W}_{net}}{\dot{Q}_{in}}, where W˙net\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


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© 2024 Fiveable Inc. All rights reserved.
AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.