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T-S Diagram For Heat Engines

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In 1872, an American engineer, George Bailey Brayton, advanced heat engines study by patenting a constant pressure internal combustion engine, initially using vaporized gas but later using liquid fuels such as kerosene. This heat engine is known as "Brayton's  Ready Motor". The original Brayton engine used a piston compressor and piston expander instead of a gas turbine and gas compressor.

Today, modern gas turbine engines and airbreathing jet engines are also constant-pressure heat engines. Therefore we describe their thermodynamics by the Brayton cycle. In general, the Brayton cycle describes the workings of a constant-pressure heat engine.

It is one of the most common thermodynamic cycles found in gas turbine power plants or airplanes. In contrast to the Carnot cycle, the Brayton cycle does not execute isothermal processes because these must be performed very slowly. In an ideal Brayton cycle, the system executing the cycle undergoes a series of four processes: two isentropic (reversible adiabatic) processes alternated with two isobaric processes.

Since Carnot's principle states that no engine can be more efficient than a reversible engine (a Carnot heat engine) operating between the same high temperature and low-temperature reservoirs, a gas turbine based on the Brayton cycle must have lower efficiency than the Carnot efficiency.

A large single-cycle gas turbine typically produces for example 300 megawatts of electric power and has 35–40% thermal efficiency. Modern Combined Cycle Gas Turbine (CCGT) plants, in which the thermodynamic cycle of consists of two power plant cycles (e.g., the Brayton cycle and the Rankine cycle), can achieve a thermal efficiency of around 55%.

open Brayton cycle - Gas Turbine

Brayton Cycle – pV, Ts diagram

The Brayton cycle is often plotted on a pressure-volume diagram (pV diagram) and a temperature-entropy diagram (Ts diagram).

Brayton Cycle - Ts diagram
Brayton Cycle – Ts diagram

When plotted on a pressure-volume diagram, the isobaric processes follow the isobaric lines for the gas (the horizontal lines), adiabatic processes move between these horizontal lines, and the area bounded by the complete cycle path represents the total work that can be done during one cycle.

The temperature-entropy diagram (Ts diagram) in which a point specifies the thermodynamic state on a graph with specific entropy (s) as the horizontal axis and absolute temperature (T) as the vertical axis. Ts diagrams are a useful and common tool, particularly because it helps to visualize the heat transfer during a process. For reversible (ideal) processes, the area under the T-s curve of a process is the heat transferred to the system during that process.

Ts diagram of the Brayton cycle with reheat and regeneration
Ts diagram of the Brayton cycle with reheat and regeneration
Brayton cycle - reheat - intercooling - regeneration
Ts diagram of Brayton cycle with reheat, intercooling and heat regeneration

References:

Nuclear and Reactor Physics:

  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467
  6. Kenneth S. Krane. Introductory Nuclear Physics, 3rd Edition, Wiley, 1987, ISBN: 978-0471805533
  7. G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965
  8. Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.
  9. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.

Advanced Reactor Physics:

  1. K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2.
  2. K. O. Ott, R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, 1985, ISBN: 0-894-48029-4.
  3. D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2.
  4. E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.

Other References:

Diesel Engine – Car Recycling

Source: https://www.nuclear-power.com/nuclear-engineering/thermodynamics/thermodynamic-cycles/brayton-cycle-gas-turbine-engine/brayton-cycle-pv-ts-diagram/

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