Introduction to sodium technology Physical properties of sodium K.S. Rajan Professor, School of Chemical & Biotechnology SASTRA University Joint Initiative of IITs and IISc Funded by MHRD Page 1 of 6
Table of Contents 1 COOLANT FOR FAST REACTORS... 3 1.1 THERMAL CONDUCTIVITY... 3 1.2 VISCOSITY... 4 1.3 SPECIFIC HEAT... 4 1.3 COMPARISON OF PROPERTIES OF COOLANTS... 6 2 REFERENCE/ADDITIONAL READING... 6 Joint Initiative of IITs and IISc Funded by MHRD Page 2 of 6
In this lecture, we shall focus on some key aspects of sodium technology with special reference to the thermo-physical characteristics of sodium and comparison with other coolants At the end of this lecture, the learners will be able to (i) relate the thermo-physical properties of sodium as a function of temperature (ii) compare the thermo-physical properties of sodium to those of other coolants (iii) list the advantages of sodium as coolant for fast reactors 1 Coolant for fast reactors During the development of fast reactor technology, one of the biggest challenges was the identification of an appropriate coolant. The fact that the common coolant like water whose characteristics are well-known and related technologies well-established is unsuitable for use in fast reactors required the development of related technologies for handling, pumping and monitoring of sodium in fast reactor. Considering the use of sodium in large volumes at high temperatures compounded the difficulty of the task. To begin with, let us look at the thermophysical properties of sodium as a function of temperature. This is important as the sodium is repeatedly heated and cooled for several cycles in a nuclear reactor. 1.1 Thermal conductivity It is considered the far-most important property of a coolant. Coolants with higher thermal conductivity are more effective as coolants compared to those with lower thermal conductivity. The dependence of thermal conductivity of a material on temperature depends on the degree with the molecules of material are strongly bound to. Thermal conductivity of gases increases with temperature due to increase in thermal energy that increases the molecular velocity. In liquids, the temperature dependence of thermal conductivity depends on the viscosity also. For low-viscous liquids, thermal conductivity increases with temperature while those for high-viscous liquids decrease with temperature. The temperature dependence of thermal conductivity of sodium can be predicted satisfactorily by the following equation: Joint Initiative of IITs and IISc Funded by MHRD Page 3 of 6
k!!" = 92.951 5.8087x10!! T + 11.7274x10!! T! (1) In Eq. (1), temperature has to be substituted in C. 1.2 Viscosity This is one of the transport properties and influences momentum, heat and mass transfer. The pressure drop for flow of any fluid flowing through a conduit is dependent on the viscosity of fluid. Higher pressure drops while pumping fluids of higher viscosity is attributed to the increased dissipation of energy due to viscous drag. Hence under the circumstances where there is a limitation for the maximum permissible pressure drop, this manifests as a limitation on the maximum velocity of the fluid. For fluids with higher viscosities, the onset of turbulence occurs only at higher velocities. The boundary layer thickness is also influenced by the fluid viscosity. Hence, fluids of lower viscosity are preferable for cooling applications also. Viscosity of liquids normally decreases with temperature due to the weakening of intermolecular forces of attraction. The viscosity of liquid sodium is related to its temperature as follows: log!" μ Pas = 2.4892 +!!".!"! In Eq. (2), temperature has to be substituted in K. 0.4925log!" T (2) 1.3 Specific heat It is defined as the amount of heat required to increase the temperature of unit mass of a substance by 1 K. In simple terms, the magnitude to which the temperature of coolant increases upon receiving a fixed rate of heat flow from a source depends on the specific heat of coolant. Higher specific heat is preferable for a coolant, as its temperature would increase only at a smaller rate. This would ensure the availability of sufficient driving force (temperature of hot stream - temperature of coolant) for heat transfer. Specific heat of sodium is related to temperature as: c!!!"# = 1436.715 0.5805T + 4.6273x10!! T! (3) Density as a function of temperature is given as follows: Joint Initiative of IITs and IISc Funded by MHRD Page 4 of 6
ρ!"!! = 950.0483 0.2298T 14.6045x10!! T! + 5.6377x10!! T! (4) T in Eqs. (3) & (4) needs to be used in C. Example 1: Determine the thermal conductivity and specific heat of liquid sodium at 300 C. Solution: Recall Eq. (1) k W mk = 92.951 5.8087x10!! T + 11.7274x10!! T! Substituting T=300 in Eq. (1), we get the thermal conductivity of liquid sodium at 300 C as 76.58 W/mK Recall Eq. (3) for specific heat J c! kgk = 1436.715 0.5805T + 4.6273x10!! T! Substituting T=300 in Eq. (3), we get the specific heat of liquid sodium at 300 C as 1304.2 J/kgK Example 2: Determine the viscosity and density of liquid sodium at 300 C. Recall Eq. (2), log!" μ Pas = 2.4892 + 220.65 T 0.4925log!" T Substituting T=573 K in Eq. (2), we get the viscosity of liquid sodium at 300 C as 0.345 cp Recall Eq. (4), ρ kg m! = 950.0483 0.2298T 14.6045x10!! T! + 5.6377x10!! T! Substituting T=300 C in Eq. (4), we get the density of liquid sodium at 300 C as 880 kg/m 3 Joint Initiative of IITs and IISc Funded by MHRD Page 5 of 6
1.3 Comparison of properties of coolants Table 1* shows the comparison of properties of materials that are considered to be potential candidates for use in fast reactors as coolant. Table 1. Comparison of properties of potential coolants for fast reactors Property Sodium Lead Lead- Helium Bismuth Eutectic Melting point ( C) 97.8 327.4 123.5 4 Boiling point 892 1737 1670 - Density @ 300 C (kg/m 3 ) 880 10500 10300-267 Specific heat @ 300 C (J/kgK) 1300 160 146 5200 Volumetric heat capacity @ 300 C (MJ/m 3 K) 1.14 1.68 1.50 0.0009 Thermal conductivity @ 300 C (W/mK) 76 16 11 0.238 Viscosity @ 300 C (cp) 0.34 2.25 1.7 0.031 *Ref: www.ne.doe.gov/pdffiles/sodiumcoolant_nrcpresentation.pdf A higher difference between boiling point and melting point is desirable, to ensure that the coolant remains in the liquid state even in cases of temperature fluctuations. Though Lead-Bismuth eutectic would qualify as the ideal coolant on this account, a coolant seldom reaches temperatures as high as 1670 C due to material constraints with clad and other structural materials. Hence for fast reactors, sodium with a boiling point of 892 C and melting point of 97.8 C gives a margin of about 795. The high specific heat of helium is an advantage. However, the density of helium is very low and its as coolant requires use of high pressures to reduce the volume. The coolant velocity required is also too high of the order of 100 m/s. This coupled with lowest thermal conductivity among the coolants makes it the least preferred coolant. Sodium is superior to other metal-based coolants owing to its higher specific heat, higher thermal conductivity and lower viscosity. Sodium is the cheapest of the metalbased coolants. All these point to choice of sodium as ideal candidate for fast reactor coolant. 2 Reference/Additional reading 1. www.ne.doe.gov/pdffiles/sodiumcoolant_nrcpresentation.pdf 2. Sodium Fast Reactor Design: Fuels, Neutronics, Thermal-Hydraulics, Structural Mechanics and Safety, in: Vol. 21, Handbook of Nuclear Engineering, Dan Gabriel Cacucu (Ed. In Chief), Springer Joint Initiative of IITs and IISc Funded by MHRD Page 6 of 6