Example – Adiabatic Expansion in Gas Turbine

Example of Adiabatic Expansion

P-V diagram - adiabatic process
Assume an adiabatic expansion of helium (3 → 4) in a gas turbine (Brayton cycle).

Assume an adiabatic expansion of helium (3 → 4) in a gas turbine. Since helium behaves almost as an ideal gas, use the ideal gas law to calculate outlet temperature of the gas (T4,real). In this turbines the high-pressure stage receives gas (point 3 at the figure; p3 = 6.7 MPa; T3 = 1190 K (917°C)) from a heat exchanger and exhaust it to another heat exchanger, where the outlet pressure is p4 = 2.78 MPa (point 4).

Solution:

The outlet temperature of the gas, T4,real, can be calculated using p, V, T Relation for adiabatic process. Note that, it is the same relation as for the isentropic process, therefore results must be identical. It this case, we calculate the expansion for different gas turbine (less efficient) as in case of Isentropic Expansion in Gas Turbine.

p,V,T relation - isentropic process

In this equation the factor for helium is equal to κ=cp/cv=1.66. From the previous equation follows that the outlet temperature of the gas, T4,real, is:

adiabatic process - example

See also: Mayer’s relation

Main characteristics of adiabatic process
Main characteristics of adiabatic process

See also: First Law of Thermodynamics

See also: Ideal Gas Law

See also: What is Enthalpy

Adiabatic Process in Gas Turbine

first law - example - brayton cycle
Ideal Brayton cycle consist of four thermodynamic processes. Two isentropic processes and two isobaric processes.

Let assume the Brayton cycle that describes the workings of a constant pressure heat engineModern gas turbine engines and airbreathing jet engines also follow the Brayton cycle.

The Brayton cycle consist of four thermodynamic processes. Two adiabatic processes and two isobaric processes.

  1. adiabatic compression – ambient air is drawn into the compressor, where it is pressurized (1 → 2). The work required for the compressor is given by WC = H2 – H1.
  2. isobaric heat addition – the compressed air then runs through a combustion chamber, where fuel is burned and air or another medium is heated (2 → 3). It is a constant-pressure process, since the chamber is open to flow in and out. The net heat added is given by Qadd = H– H2
  3. adiabatic expansion – the heated, pressurized air then expands on turbine, gives up its energy. The work done by turbine is given by WT = H4 – H3
  4. isobaric heat rejection – the residual heat must be rejected in order to close the cycle. The net heat rejected is given by Qre = H– H1

As can be seen, we can describe and calculate (e.g. thermal efficiency) such cycles (similarly for Rankine cycle) using enthalpies.

See also: Thermal Efficiency of Brayton Cycle

 
References:
Nuclear and Reactor Physics:
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  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
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  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.

See above:

Adiabatic Process