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.

See also: Thermal Conductivity

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 (δ_t >> δ), and it is reasonable to assume uniform velocity throughout the thermal boundary layer.

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

Graber-Rieger Correlation

FFTF Correlation

References:

Reactor Physics and Thermal Hydraulics:

J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
Todreas Neil E., Kazimi Mujid S. Nuclear Systems Volume I: Thermal Hydraulic Fundamentals, Second Edition. CRC Press; 2 edition, 2012, ISBN: 978-0415802871
Zohuri B., McDaniel P. Thermodynamics in Nuclear Power Plant Systems. Springer; 2015, ISBN: 978-3-319-13419-2
Moran Michal J., Shapiro Howard N. Fundamentals of Engineering Thermodynamics, Fifth Edition, John Wiley & Sons, 2006, ISBN: 978-0-470-03037-0
Kleinstreuer C. Modern Fluid Dynamics. Springer, 2010, ISBN 978-1-4020-8670-0.
U.S. Department of Energy, THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW. DOE Fundamentals Handbook, Volume 1, 2 and 3. June 1992.
White Frank M., Fluid Mechanics, McGraw-Hill Education, 7th edition, February, 2010, ISBN: 978-0077422417

See above:

Nusselt Number