The Brayton cycle is a key gas power cycle used in gas turbines for power generation and propulsion. It consists of compression, combustion, expansion, and exhaust processes, utilizing air as the working fluid. Understanding its principles is crucial for analyzing gas turbine performance.

Variations of the Brayton cycle, such as regeneration, intercooling, and combined cycles, aim to improve efficiency and power output. These modifications address limitations of the basic cycle and find applications in diverse industries, from power plants to aircraft engines.

Brayton cycle principles

Basic components and operation

• The Brayton cycle is a thermodynamic cycle that describes the operation of a gas turbine engine
• It is an open system that uses atmospheric air as the working fluid
• The basic components of a Brayton cycle include:
  • Compressor: Draws in atmospheric air and increases its pressure, while simultaneously raising its temperature due to the compression process
  • Combustion chamber (or heat exchanger): Heat is added to the compressed air through the burning of fuel, further increasing the temperature and enthalpy of the working fluid at constant pressure
  • Turbine: The high-temperature, high-pressure gas expands through the turbine, converting the thermal and kinetic energy into mechanical work, which drives the compressor and any additional load (electric generator)
  • Exhaust nozzle: The exhaust gases are released to the atmosphere, which may also contribute to the overall thrust in the case of jet engines

Advantages and applications

• Brayton cycle gas turbines offer several advantages:
  • High power-to-weight ratio: Compact and lightweight design compared to other power generation systems (reciprocating engines, steam turbines)
  • Fuel flexibility: Can operate on various fuels (natural gas, diesel, kerosene, biogas)
  • Low emissions: Produce lower emissions of nitrogen oxides (NOx) and carbon monoxide (CO) compared to reciprocating engines
  • Quick startup and load response: Can reach full power output rapidly and respond quickly to changes in load demand
• Brayton cycle gas turbines find applications in various sectors:
  • Power generation: Used in simple cycle and combined cycle power plants for electricity production
  • Aviation: Jet engines for aircraft propulsion (turbojets, turbofans, turboprops)
  • Industrial: Mechanical drive applications (pumps, compressors) and combined heat and power (CHP) systems
  • Marine: Propulsion and power generation for ships and offshore platforms

Thermodynamic processes in the Brayton cycle

Isentropic compression and expansion

• The Brayton cycle consists of four primary thermodynamic processes, with isentropic compression and expansion being two of them
• Isentropic compression (1-2): The compressor ideally performs an isentropic (constant entropy) compression of the working fluid, increasing its pressure and temperature
  • In reality, the compression process is not truly isentropic due to irreversibilities (friction, turbulence), resulting in a higher temperature rise and entropy generation
• Isentropic expansion (3-4): The high-temperature, high-pressure gas expands through the turbine, ideally in an isentropic process, converting thermal and kinetic energy into mechanical work
  • Similar to the compression process, the actual expansion process is not truly isentropic due to irreversibilities, resulting in a lower temperature drop and work output compared to the ideal case

Isobaric heat addition and rejection

• The other two thermodynamic processes in the Brayton cycle are isobaric heat addition and rejection
• Isobaric heat addition (2-3): Heat is added to the working fluid at constant pressure in the combustion chamber or heat exchanger, increasing its temperature and enthalpy
  • The heat addition process is typically achieved through the combustion of fuel (natural gas, kerosene) in the combustion chamber
  • In some applications, a heat exchanger may be used to add heat from an external source (exhaust gases, solar energy) without direct combustion
• Isobaric heat rejection (4-1): The exhaust gases are released to the atmosphere at constant pressure, rejecting heat and returning the working fluid to its initial state
  • The heat rejection process occurs as the exhaust gases exit the turbine and are discharged through the exhaust nozzle
  • In open cycle gas turbines, the exhaust gases are released directly to the atmosphere, while in closed cycle systems, a heat exchanger may be used to reject heat to a cooling medium (water, air)

Factors affecting Brayton cycle performance

Pressure ratio and turbine inlet temperature

• Compressor pressure ratio: A higher pressure ratio generally improves the thermal efficiency of the cycle but also increases the compressor work input and may lead to higher thermal stresses on the components
  • Optimal pressure ratio depends on factors such as the turbine inlet temperature, component efficiencies, and the specific application
  • Typical pressure ratios in modern gas turbines range from 10:1 to 40:1
• Turbine inlet temperature (TIT): Increasing the TIT enhances the thermal efficiency and work output of the cycle
  • Higher TITs allow for more energy to be extracted by the turbine, improving the overall cycle performance
  • The maximum achievable TIT is limited by the material properties of the turbine blades and the effectiveness of the cooling systems
  • Advanced materials (single crystal superalloys, ceramic matrix composites) and cooling techniques (film cooling, internal blade cooling) enable higher TITs while maintaining acceptable blade life

Component efficiencies and losses

• Component efficiencies: The isentropic efficiencies of the compressor and turbine, as well as the combustion efficiency, directly impact the overall performance of the Brayton cycle
  • Higher component efficiencies result in improved cycle efficiency and work output
  • Advancements in aerodynamic design, materials, and manufacturing techniques contribute to increasing component efficiencies
• Pressure losses: Pressure losses in the combustion chamber, heat exchangers, and ducts reduce the overall efficiency of the cycle
  • Pressure losses increase the required compressor work and decrease the available turbine work, negatively impacting cycle performance
  • Minimizing pressure losses through optimized design and layout of the flow path is crucial for improving cycle efficiency
• Ambient conditions: The temperature and pressure of the ambient air affect the cycle performance
  • Lower ambient temperatures and higher pressures generally improve the efficiency and work output of the gas turbine
  • Gas turbine performance is often rated at ISO conditions (15°C, 1 atm) for standardized comparison, but actual performance varies with ambient conditions

Modifications to the Brayton cycle

Regeneration and intercooling

• Regeneration: A regenerative Brayton cycle incorporates a heat exchanger (regenerator) that transfers heat from the hot turbine exhaust to the compressed air before it enters the combustion chamber
  • Preheating the compressed air reduces the fuel consumption and improves thermal efficiency
  • Regeneration is particularly effective when the turbine exhaust temperature is significantly higher than the compressor discharge temperature
• Intercooling: In a multi-stage compression process, intercooling involves cooling the working fluid between compression stages
  • Reduces the compressor work input and improves the overall cycle efficiency
  • Particularly beneficial for cycles with high pressure ratios, as it helps to reduce the compressor discharge temperature and improves the isentropic efficiency of the compression process
  • Intercooling can be achieved using air-to-air or air-to-water heat exchangers between the compression stages

Reheating and combined cycle

• Reheating: In a multi-stage expansion process, reheating involves heating the working fluid between the turbine stages
  • Increases the work output of the turbine and improves the overall cycle efficiency
  • Helps to maintain a higher average temperature during the expansion process, increasing the available energy for work extraction
  • Reheating can be accomplished by routing the working fluid back to the combustion chamber or using a separate reheating combustor
• Combined cycle: A combined cycle power plant integrates a Brayton cycle gas turbine with a Rankine cycle steam turbine
  • The hot exhaust gases from the gas turbine serve as the heat source for the steam generator in the Rankine cycle
  • Combining the two cycles improves the overall plant efficiency, as the waste heat from the gas turbine is utilized for steam generation
  • Combined cycle power plants can achieve thermal efficiencies up to 60%, significantly higher than either cycle alone

Cogeneration and advanced cycles

• Cogeneration (Combined Heat and Power): In a cogeneration system, the waste heat from the Brayton cycle gas turbine is used for process heating, district heating, or other thermal applications
  • Increases the overall energy utilization efficiency of the system, as both electricity and useful heat are generated from the same fuel input
  • Cogeneration systems are commonly used in industries with high heat demands (paper, chemical, food processing) and for district heating in urban areas
• Advanced cycles: Researchers and engineers continue to develop advanced Brayton cycle configurations to improve efficiency and performance
  • Supercritical CO2 (sCO2) cycles: Use supercritical carbon dioxide as the working fluid, offering the potential for higher efficiencies and more compact turbomachinery compared to conventional gas turbines
  • Closed cycle gas turbines: Operate with a closed loop working fluid (helium, nitrogen), allowing for higher temperatures and pressures, and enabling nuclear or solar heat sources to be used instead of combustion
  • Humid air turbines (HAT): Introduce water or steam into the compressed air to increase the mass flow rate and reduce the compressor work, leading to improved cycle efficiency

Brayton cycle efficiency and work output

Thermal efficiency calculation

• The thermal efficiency of a Brayton cycle is defined as the ratio of the net work output to the heat input
  • Thermal efficiency = (Net work output) / (Heat input)
  • Net work output = (Turbine work output) - (Compressor work input)
• For an ideal Brayton cycle with perfect gas behavior and constant specific heats, the thermal efficiency can be expressed as a function of the pressure ratio (rp) and the specific heat ratio (k):
  • Thermal efficiency = 1 - (1 / rp^((k-1)/k))
  • This equation shows that increasing the pressure ratio improves the ideal thermal efficiency, subject to practical limitations
• Actual thermal efficiency is lower than the ideal efficiency due to irreversibilities and losses in the cycle components
  • Isentropic efficiencies of the compressor and turbine, pressure losses, and heat transfer losses contribute to the deviation from the ideal cycle
  • The actual thermal efficiency can be determined by considering these factors and using the real state properties of the working fluid at each point in the cycle

Work output determination

• The work output of the turbine and the work input of the compressor can be calculated using the enthalpies of the working fluid at each state point
  • Turbine work output = (Mass flow rate) × (Enthalpy at turbine inlet - Enthalpy at turbine outlet)
  • Compressor work input = (Mass flow rate) × (Enthalpy at compressor outlet - Enthalpy at compressor inlet)
  • The enthalpy values can be determined using thermodynamic tables or equations of state for the working fluid
• To account for irreversibilities in real Brayton cycles, isentropic efficiencies are introduced for the compressor and turbine:
  • Isentropic efficiency of compressor = (Ideal compressor work input) / (Actual compressor work input)
  • Isentropic efficiency of turbine = (Actual turbine work output) / (Ideal turbine work output)
  • These efficiencies relate the actual work input or output to the ideal (isentropic) values, providing a measure of the component's performance
• The actual work output of the Brayton cycle is the difference between the actual turbine work output and the actual compressor work input
  • Actual net work output = (Actual turbine work output) - (Actual compressor work input)
  • This value represents the useful mechanical power available for driving a load or generating electricity
• Maximizing the work output requires optimizing various cycle parameters, such as the pressure ratio, turbine inlet temperature, and component efficiencies, while considering the practical limitations and trade-offs involved in the design and operation of the gas turbine system