Glossary

13.1 Rankine and Brayton cycles

2 min read•july 23, 2024

Power plants use two main thermodynamic cycles: Rankine and Brayton. The , used in steam power plants, involves water changing phases. The , used in , keeps air in gas form throughout.

Both cycles have similar processes but differ in working fluids and heat rejection. Rankine cycles are generally more efficient due to lower heat rejection temperatures. Understanding these cycles is key to analyzing systems.

Rankine Cycle

Components of Rankine cycle

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  • heats working fluid (water) to produce high-pressure steam
  • expands steam converting thermal energy to mechanical work (electricity generation)
  • condenses low-pressure steam back into liquid form (heat rejection to environment)
  • pressurizes liquid working fluid and returns it to boiler completing the cycle

Processes in Rankine cycle

  1. Isentropic compression in pump pressurizes working fluid
  2. Isobaric heat addition in boiler heats working fluid at constant pressure producing steam
  3. Isentropic expansion in turbine expands steam generating mechanical work
  4. Isobaric heat rejection in condenser condenses steam back into liquid at constant pressure
  • Applications in power generation include steam power plants (coal, nuclear) using Rankine cycle as fundamental thermodynamic cycle

Brayton Cycle

Components of Brayton cycle

  • compresses working fluid (air) to high pressure
  • heats compressed air by burning fuel (natural gas, kerosene)
  • Turbine expands hot, high-pressure gases converting thermal energy to mechanical work
  • (optional) cools exhaust gases and preheats compressed air improving efficiency

Processes in Brayton cycle

  1. Isentropic compression in compressor compresses working fluid
  2. Isobaric heat addition in combustion chamber heats working fluid at constant pressure
  3. Isentropic expansion in turbine expands hot gases generating mechanical work
  4. Isobaric heat rejection to atmosphere or via heat exchanger at constant pressure
  • Applications in gas turbines include jet engines for aircraft propulsion and gas turbine power plants for electricity generation

Rankine vs Brayton cycle efficiency

  • Rankine cycle uses water undergoing phase changes, Brayton cycle uses gas (air) remaining gaseous
  • Both have isobaric heat addition, but Rankine has isobaric heat rejection while Brayton has isobaric or heat exchanger rejection
  • Both involve isentropic compression and expansion processes
  • Rankine efficiency depends on max/min fluid temperatures, Brayton on compressor pressure ratio and max/min temperatures
  • Brayton cycles generally have lower efficiencies than Rankine due to higher heat rejection temperature

Calculations for thermodynamic cycles

  • Rankine cycle
    • Net work output Wnet=Wt−WpW_{net} = W_t - W_p (turbine work minus pump work)
    • Heat input QbQ_b added in boiler
    • ηth=WnetQb=Wt−WpQb\eta_{th} = \frac{W_{net}}{Q_b} = \frac{W_t - W_p}{Q_b}
  • Brayton cycle
    • Net work output Wnet=Wt−WcW_{net} = W_t - W_c (turbine work minus compressor work)
    • Heat input QinQ_{in} added in combustion chamber
    • Thermal efficiency ηth=WnetQin=Wt−WcQin\eta_{th} = \frac{W_{net}}{Q_{in}} = \frac{W_t - W_c}{Q_{in}}
    • Pressure ratio rpr_p (compressor outlet to inlet pressures) affects efficiency
      • ηth=1−1rp(γ−1)/γ\eta_{th} = 1 - \frac{1}{r_p^{(\gamma-1)/\gamma}} where γ\gamma is specific heat ratio

Key Terms to Review (21)

Boiler: A boiler is a closed vessel used to heat water or other fluids, transforming them into steam or hot water for various applications such as power generation, heating systems, and industrial processes. In the context of thermodynamic cycles, particularly the Rankine cycle, the boiler plays a critical role in converting water into steam, which is then used to drive turbines and generate electricity.
Brayton Cycle: The Brayton Cycle is a thermodynamic cycle that describes the operation of a gas turbine engine, where air is compressed, heated, and then expanded to produce work. It consists of two main processes: isentropic compression and isentropic expansion, with a constant pressure heat addition phase. This cycle is fundamental to understanding the efficiency and performance of jet engines and power plants that utilize gas turbines.
Brayton Efficiency: Brayton efficiency refers to the measure of how effectively a Brayton cycle converts thermal energy into mechanical work. It is a crucial aspect of gas turbine engines, where the cycle operates between two temperature limits to produce power. Understanding Brayton efficiency helps in optimizing engine performance and fuel consumption, making it an important factor in thermal systems.
Combustion chamber: A combustion chamber is a space within an engine where fuel and air mix and ignite, producing hot gases that drive the engine's power generation process. This area is critical for the efficiency of thermodynamic cycles, as it directly impacts the conversion of fuel energy into mechanical work through controlled combustion. The design and operation of the combustion chamber influence performance characteristics such as pressure, temperature, and emissions.
Compressor: A compressor is a mechanical device that increases the pressure of a gas by reducing its volume. In thermodynamic systems, compressors are crucial for enhancing the efficiency of processes such as refrigeration and heat pumps, as well as in power cycles like the Rankine and Brayton cycles. By compressing refrigerants or working fluids, they facilitate the transfer of heat energy and enable the transformation of low-energy states into high-energy states, which is essential for achieving the desired thermal performance in these systems.
Condenser: A condenser is a heat exchanger that transforms vapor into liquid by removing heat from the vapor through cooling. This process is essential for cycles that involve phase changes, as it facilitates the effective transfer of heat and enhances the efficiency of refrigeration, heat pumps, and power generation systems. In various thermodynamic cycles, condensers play a critical role in ensuring that the working fluid can continuously circulate and maintain optimal operation.
First Law of Thermodynamics: The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another. This principle emphasizes the conservation of energy within a closed system, illustrating how energy transfers and transformations impact thermodynamic processes and systems.
Gas turbines: Gas turbines are a type of internal combustion engine that convert natural gas or other fuels into mechanical energy through the process of combustion. They work by drawing in air, compressing it, mixing it with fuel, igniting the mixture, and then expelling the high-speed exhaust gases to produce thrust or drive a generator. This technology is key in power generation and propulsion systems, often associated with efficiency and high power-to-weight ratios.
Heat exchanger: A heat exchanger is a device designed to transfer heat between two or more fluids without mixing them. It plays a crucial role in many thermal systems, allowing for efficient energy transfer and temperature control in processes such as power generation and refrigeration.
Heat rate: Heat rate is a measure of the efficiency of a power plant or energy conversion system, expressed as the amount of energy input required to produce a unit of electricity, typically measured in BTUs per kilowatt-hour (BTU/kWh). It indicates how well a system converts fuel into electrical energy and is crucial for evaluating the performance of both Rankine and Brayton cycles as well as combined cycles and cogeneration systems. A lower heat rate signifies higher efficiency, meaning less fuel consumption is needed to generate power.
Isentropic process: An isentropic process is a thermodynamic process that occurs at constant entropy, implying that it is both adiabatic (no heat transfer) and reversible. In this context, it is essential for analyzing idealized cycles, as it helps simplify calculations and understand the efficiency of energy conversion in systems such as heat engines and refrigerators. Recognizing isentropic processes aids in understanding the performance limits of various cycles and the conditions under which they operate efficiently.
Isobaric Process: An isobaric process is a thermodynamic process that occurs at constant pressure. In such a process, any heat transfer into or out of the system results in a change in volume, while the pressure remains unchanged. This constancy of pressure plays a significant role in various energy exchanges and mechanical work done by or on the system.
P-v diagram: A p-v diagram, or pressure-volume diagram, is a graphical representation that illustrates the relationship between the pressure and volume of a thermodynamic system during various processes. This diagram is crucial for visualizing work done by or on the system, as well as understanding different thermodynamic cycles, including how heat engines operate and the efficiency of these processes. The area under the curve in a p-v diagram corresponds to the work performed during the process, making it an essential tool for analyzing both practical applications and theoretical concepts in thermodynamics.
Power generation: Power generation is the process of converting various forms of energy into electrical energy for use in homes, industries, and businesses. This conversion can take place through different methods and cycles, which are crucial for efficient energy production and utilization. Understanding how different systems function, like those involving heat engines and thermodynamic cycles, is vital to optimizing energy use and reducing environmental impacts.
Pump: A pump is a mechanical device used to move fluids (liquids or gases) from one place to another by creating pressure differentials. In thermodynamic cycles, such as those involving heat engines, pumps play a crucial role in circulating working fluids, allowing the system to maintain its operation efficiently and effectively.
Rankine Cycle: The Rankine Cycle is a thermodynamic cycle that converts heat into work, typically used in steam power plants. It involves the processes of heating, phase change, and cooling of a working fluid, usually water, to generate mechanical energy that can be converted into electricity. This cycle is vital in understanding how energy is transformed and utilized in various applications, linking thermal efficiency and energy conversion principles.
Second law of thermodynamics: The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time, and it dictates the direction of thermodynamic processes. This principle establishes that energy transformations are not 100% efficient, highlighting the inherent tendency for systems to move towards a state of greater disorder or randomness, affecting heat transfer, the performance of engines, and various processes in nature.
Specific Work: Specific work refers to the amount of work done per unit mass of a substance during a thermodynamic process. This concept is essential in analyzing various energy cycles, as it helps quantify the energy output or input relative to the mass of the working fluid, providing insight into the efficiency and performance of these cycles.
T-s diagram: A t-s diagram, or temperature-entropy diagram, is a graphical representation used in thermodynamics to illustrate the relationship between temperature and entropy for a substance during various thermodynamic processes. It helps visualize the changes in state of working fluids in cycles, particularly in power generation and refrigeration systems, allowing for easier analysis of efficiency and performance.
Thermal Efficiency: Thermal efficiency is a measure of how well a system converts heat energy into useful work. It's expressed as a ratio of the work output of the system to the heat input, highlighting how effectively a thermal system operates. Understanding thermal efficiency is crucial for evaluating energy performance in various thermodynamic applications, including engines and power cycles.
Turbine: A turbine is a mechanical device that converts the energy of a fluid into mechanical work, typically in the form of rotational motion. It plays a critical role in power generation systems, utilizing steam, gas, or water to drive the turbine blades and produce energy. In thermodynamic cycles, turbines are essential for converting thermal energy into useful work, thus facilitating efficient energy production.
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