🧊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.
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) measures the effectiveness of converting heat input into net work output
Isentropic efficiency (ηs) quantifies the deviation of real processes from the ideal isentropic process
Carnot efficiency (ηCarnot) 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˙, where Q˙ is heat transfer rate, W˙ is work rate, and ΔH˙ is the change in enthalpy rate
Second Law of Thermodynamics (entropy generation and irreversibility) is considered for real processes
Isentropic efficiency (ηs) accounts for irreversibilities in turbines and pumps
Thermal efficiency (ηth) is calculated as the ratio of net work output to heat input
ηth=Q˙inW˙net, where 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