Properties of Liquid Metals

Properties of Liquid Metals

Properties of Liquid Metals

In physics, liquid metal consists of alloy with very low melting points which form a eutectic that is liquid at room temperature. In reactor engineering, liquid metals are alloys with low melting point allowing for reactor coolant to be liquid in operating range of temperatures (usually above the room temperature).

thermal vs. fast reactor neutron spectrum
The spectrum of neutron energies produced by fission vary significantly with certain reactor design. thermal vs. fast reactor neutron spectrum

Liquid metals can be used as a reactor coolant because they have excellent heat transfer properties and can be employed in low-pressure systems as is the case of sodium-cooled fast reactors (SFRs). The unique feature of metals as far as their structure is concerned is the presence of charge carriers, specifically free electrons, giving them high electrical conductivity, high thermal conductivity. The use of liquid metal coolants made it possible to provide high rate of heat transfer in power plants as well as the temperatures of working surfaces of their constructions close to coolant temperature.

Moreover, liquid metals used in reactor engineering are very weak absorbers of neutrons allowing for liquid metal reactors to operate with fast neutron spectrum. A liquid metal fast reactor is a high power density reactor, which does not need neutron moderator.

The main differences between thermal and fast reactors are, of course, in neutron cross-sections, that exhibit significant energy dependency. It can be characterized by capture-to-fission ratio, which is lower in fast reactors. There is also a difference in the number of neutrons produced per one fission, which is higher in fast reactors than in thermal reactors. These very important differences are caused primarily by differences in neutron fluxes. Therefore it is very important to know detailed neutron energy distribution in a reactor core.

The disadvantage of many liquid metals is also their high chemical activity at interaction with oxygen, water and structural materials, which may cause heat transfer deterioration in the plant under certain conditions.

Conversion Factor for Fast Reactors
As was written, the conversion factor in a light water reactor is about 0.5, i.e. the production of new nuclear fuel is much less than its consumption. This is caused, among other things, by the relatively low value of the neutron yield factor. For a fast neutron spectrum, there are differences in both the number of neutrons produced per one fission and, of course, in the capture-to-fission ratio, which is lower for fast reactors. The number of neutrons produced per one fission is also higher in fast reactors than in thermal reactors. These two features are of importance in the neutron economy and contributes to the fact the fast reactors have a large excess of neutrons in the core. The breeding ratio in these reactors can vary over a rather wide range, depending on the neutron energy spectrum. A large breeding ratio favors a hard neutron spectrum. The superior neutron economy of a fast neutron reactor makes it possible to build a reactor that, after its initial fuel charge of plutonium, requires only natural (or even depleted) uranium feedstock as input to its fuel cycle. Russian BN-350 liquid-metal-cooled reactor was operated with a breeding ratio of over 1.2.

Sodium and NaK – Reactor Coolant

Sodium-cooled fast reactors (SFRs) are the most common fast reactor design. They use molten sodium or a eutectic sodium-potassium alloy (NaK) as the reactor coolant. Melting and boiling points of sodium and NaK are:

  • sodium-potassium alloy- eutectic
    Source: License: Public domain


    • melting point – 97.72°C
    • boiling point – 883°C
  • NaK – eutectic mixture
    • melting point – (-12°C)
    • boiling point – 785°C
Sodium-cooled Fast Reactor (SFR).
Sodium-cooled Fast Reactor (SFR).

NaK containing 40% to 90% potassium by weight is liquid at room temperature. The eutectic mixture consists of 77% potassium and 23% sodium. Sodium and NaK do not corrode steel to any significant degree and are compatible with many nuclear fuels, allowing for a wide choice of structural materials. Because sodium reacts violently with water, however, SFRs require the placement of an intermediate heat exchanger between the reactor core and the steam generator. This hi-tech technology requires a lot of experience, therefore only few countries have developed their own fast reactor design.

Lead and Lead-bismuth Eutectic – Reactor Coolant

Lead, lead-bismuth eutectic, and other metals have also been proposed and occasionally used. The lead-cooled fast reactor is a nuclear reactor design that features a fast neutron spectrum and molten lead or lead-bismuth eutectic coolant. Lead-Bismuth Eutectic or LBE is a eutectic alloy of lead (44.5%) and bismuth (55.5%). Molten lead or lead-bismuth eutectic can be used as the primary coolant because lead and bismuth have low neutron absorption and relatively low melting points.

Melting and boiling points of lead and lead-bismuth eutectic mixture are:

  • lead
    • melting point – 327.5°C
    • boiling point – 1749°C
  • lead-bismuth – eutectic mixture
    • melting point – 123.5°C
    • boiling point – 1670°C
Lead-cooled Fast Reactor (LFR)
Lead-cooled Fast Reactor (LFR).

As compared to sodium-based liquid metal coolants such as liquid sodium or NaK, lead-based coolants have significantly higher boiling points, meaning a reactor can be operated without risk of coolant boiling at much higher temperatures. Lead and LBE also do not react readily with water or air, in contrast to sodium and NaK which ignite spontaneously in air and react explosively with water. Due to its denseness and high atomic number, lead and bismuth are also an excellent gamma radiation shield, while simultaneously being virtually transparent to neutrons.

On the other hand, lead and LBE coolant are more corrosive to steel than sodium or NaK eutectic alloy. This and the very high density of lead puts an upper limit on the velocity of coolant flow through the reactor due to safety considerations. Furthermore, the higher melting points of lead and LBE (327 °C and 123.5 °C respectively) may mean that solidification of the coolant may be a greater problem when the reactor is operated at lower temperatures.

Nusselt Number for Liquid Metal Reactors

A liquid metal cooled reactor is an advanced type of nuclear reactor where the primary coolant is a liquid metal.  Liquid metals can be used as a coolant because they have excellent heat transfer properties and can be employed in low-pressure systems as is the case of sodium-cooled fast reactors (SFRs). The unique feature of metals as far as their structure is concerned is the presence of charge carriers, specifically free electrons, giving them high electrical conductivity, high thermal conductivity. This very high thermal conductivity together with low viscosity causes, that typical heat transfer correlations (e.g. Dittus-Boelter) can not be used.

Thermal Conductivity of Sodium
Liquid sodium is used as a heat transfer fluid in some types of nuclear reactors because it has the high thermal conductivity and low neutron absorption cross section required to achieve a high neutron flux in the reactor. The high thermal conductivity properties effectively create a reservoir of heat capacity which provides thermal inertia against overheating.

thermal conductivity - sodium

See also: Thermal Conductivity

See also: Thermal Conductivity of Metals

Special reference: Thermophysical Properties of Materials For Nuclear Engineering: A Tutorial and Collection of Data. IAEA-THPH, IAEA, Vienna, 2008. ISBN 978–92–0–106508–7.

For liquid metals the Prandtl number is very small, generally in the range from 0.01 to 0.001. This means that the thermal diffusivity, which is related to the rate of heat transfer by conduction, unambiguously dominates. This very high thermal diffusivity results from very high thermal conductivity of metals, which is about 100 times higher than that of water. The Prandtl number for sodium at a typical operating temperature in the Sodium-cooled fast reactors is about 0.004. For this case the thermal boundary layer development is much more rapid than that of the velocity boundary layer (δt >> δ), and it is reasonable to assume uniform velocity throughout the thermal boundary layer.

Heat transfer coefficients for sodium flow through fuel channel are based on the Prandtl number and Péclet number. Pitch-to-diameter (P/D) also enters many calculations of heat transfer in liquid metal reactors. Convective heat transfer correlations are usually presented in terms of Nusselt number versus Péclet number. Typical Péclet number for normal operation are from 150 to 300 in the fuel bundles. As for another flow regimes,  the Nusselt number and a given correlation can be used to determine the convective heat transfer coefficient.

Graber-Rieger Correlation

Nusselt number - Liquid Metal - Graber-Rieger

FFTF Correlation

Nusselt number - Liquid Metal - FFTF

Reactor Physics and Thermal Hydraulics:
  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. Todreas Neil E., Kazimi Mujid S. Nuclear Systems Volume I: Thermal Hydraulic Fundamentals, Second Edition. CRC Press; 2 edition, 2012, ISBN: 978-0415802871
  6. Zohuri B., McDaniel P. Thermodynamics in Nuclear Power Plant Systems. Springer; 2015, ISBN: 978-3-319-13419-2
  7. Moran Michal J., Shapiro Howard N. Fundamentals of Engineering Thermodynamics, Fifth Edition, John Wiley & Sons, 2006, ISBN: 978-0-470-03037-0
  8. Kleinstreuer C. Modern Fluid Dynamics. Springer, 2010, ISBN 978-1-4020-8670-0.
  9. U.S. Department of Energy, THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW. DOE Fundamentals Handbook, Volume 1, 2 and 3. June 1992.
  10. White Frank M., Fluid Mechanics, McGraw-Hill Education, 7th edition, February, 2010, ISBN: 978-0077422417

See above:

Liquid Metals