Page 226 - Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

Subchannel analysis for LMR 197

where a, b, and n are coefficients. In the past, experimental studies were carried out
using different liquid metals, that is, sodium-potassium (NaK), mercury, LBE, and
sodium. The molecular Prandtl number of NaK, mercury, and LBE is close to each
other, that is, in the range 0.01–0.03, whereas the Prandtl number of sodium is much
smaller, about 0.006. Based on the experimental heat-transfer data in NaK, Skupinski
et al. (1965) pointed out that the following equation gave the best agreement with the
test data:

Nu ¼ 4:82 + 0:0185 Pe 0:827 (5.24)

Sleicher et al. (1973) investigated experimentally local heat-transfer coefficients
in NaK flows in a pipe at different boundary conditions, that is, uniform heat flux
and uniform wall temperature. It was found that in the case with uniform wall
temperature, heat-transfer coefficients are lower than that in the case with uni-
form heat flux. The following equation was suggested for uniform heat flux
conditions:

Nu ¼ 6:3+0:0167 Pe 0:85 Pr 0:08 (5.25)

Heat-transfer tests in LBE pipe flow were reported by Ibragimov et al. (1960). Based
on the wall surface temperature measurement, a good agreement was obtained
between the test data and the following correlation:

Nu ¼ 4:5+0:014 Pe 0:8 (5.26)

A huge number of test data in mercury, NaK, LBE, and Na were collected by the
scientists of the former Soviet Union. Recently, Kirillov and Ushakov (2001)
recommended the following correlation for LBE flows:

Nu ¼ 4:5+0:018 Pe 0:8 (5.27)

Fig. 5.8 compares the Nusselt number calculated with different correlations men-
tioned above. As seen, large deviation occurs among these correlations.
The discrepancy between the heat-transfer correlations was mainly caused by the
discrepancy in the experimental datasets used for the derivation of the correlations.
Checking the large number of heat-transfer test datasets available in the open litera-
ture, it was pointed out by Kirillov (1962) that experimental data on heat transfer to
liquid metals often do not agree with each other. The reasons for the discrepancy have
so far not been clear.
A systematic assessment of different correlations was made by Cheng et al. (2006).
Based on the comparison with test data and CFD results, the following equation was
proposed:

Nu ¼ A +0:018 Pe 0:80 (5.28)