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Boiler and Condenser Pressures – Rankine Cycle

As in the Carnot, Otto, and Brayton cycle, the thermal efficiency tends to increase as the average temperature at which energy is added by heat transfer increases and/or the average temperature at which energy is rejected decreases. This is the common feature of all thermodynamic cycles.

Condenser Pressure

Rankine Cycle - condenser pressure
Decreasing the turbine exhaust pressure increases the network per cycle and decreases the vapor quality of outlet steam.

The case of the decrease in the average temperature at which energy is rejected requires a decrease in the pressure inside the condenser (i.e., the decrease in the saturation temperature). The lowest feasible condenser pressure is the saturation pressure corresponding to the ambient temperature (i.e., the absolute pressure of 0.008 MPa, which corresponds to 41.5°C). The goal of maintaining the lowest practical turbine exhaust pressure is a primary reason for including the condenser in a thermal power plant. The condenser provides a vacuum that maximizes the energy extracted from the steam, resulting in a significant increase in network and thermal efficiency. But also this parameter (condenser pressure) has its engineering limits:

  • Decreasing the turbine exhaust pressure decreases the vapor quality (or dryness fraction). At some point, the expansion must be ended to avoid damages caused to steam turbine blades by low-quality steam.
  • Decreasing the turbine exhaust pressure significantly increases the specific volume of exhausted steam, which requires huge blades in the last rows of the low-pressure stage of the steam turbine.

In typical wet steam turbines, the exhausted steam condenses in the condenser, and it is at a pressure well below atmospheric (absolute pressure of 0.008 MPa, which corresponds to 41.5°C). This steam is in a partially condensed state (point F), typically of a quality near 90%. Note that there is always a temperature difference between (around ΔT = 14°C) the condenser temperature and the ambient temperature, which originates from condensers’ finite size and efficiency.

Typical parameters in a condenser of condensing turbines
Typical parameters in a condenser of condensing turbines

Boiler Pressure

Rankine Cycle - boiler pressure
An increase in the boiler pressure is the result, limited by the material of the reactor pressure vessel.

The increase in the average temperature at which energy is added by heat transfer requires either superheating of steam produced or an increase in the pressure in the boiler (steam generator). Superheating is not typical for nuclear power plants.

Typically most nuclear power plants operate multi-stage condensing steam turbines. The high-pressure stage receives steam (this steam is nearly saturated steam – x = 0.995 – point C at the figure; 6 MPa; 275.6°C). Since neither the steam generator is 100% efficient, there is always a temperature difference between the saturation temperature (secondary side) and the temperature of the primary coolant.

Steam generator - counterflow heat exchanger
Temperature gradients in a typical PWR steam generator.

The hot primary coolant (330°C; 626°F) is pumped into the steam generator through the primary inlet in a typical pressurized water reactor. This requires maintaining very high pressures to keep the water in a liquid state. To prevent boiling of the primary coolant and provide a subcooling margin (the difference between the pressurizer temperature and the highest temperature in the reactor core), pressures around 16 MPa are typical for PWRs. The reactor pressure vessel is the key component, which limits the thermal efficiency of each nuclear power plant since the reactor vessel must withstand high pressures.

Typical parameters at the inlet of condensing turbines of PWRs.
Typical parameters at the inlet of condensing turbines of PWRs.
 
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

See above:

Rankine Cycle