Page 232 - Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

Subchannel analysis for LMR 203

Introducing Eqs. (5.40), (5.47), and (5.49) into Eqs. (5.44)–(5.46) yields

0

m ¼ f m β u ij ρ ρ s ij △z (5.50)
i
j
ij

M ¼ f M β u ij ρ u i ρ u j s ij △z (5.51)
0
ij i j

H ¼ f H β u ij ρ h i ρ h j s ij △z (5.52)
0
ij i j
Comparison of Eqs. (5.50)–(5.52) with Eqs. (5.41)–(5.43) gives
β ¼ f m β (5.53)
m
β ¼ f M β (5.54)
M
β ¼ f H β (5.55)
H
The three correction factors f m ,f M , and f H are unknown but may be determined by
performing CFD simulations. Taking the transversal enthalpy exchange as example,
the heat quantity transferred through the gap via the turbulent fluctuation is

0
0
H ¼ q s ij △z (5.56)
ij ij
0
q ij is the so-called turbulent heat flux and computed with the CFD simulation. Com-
bining Eq. (5.56) with Eq. (5.52) gives

q 0
ij
f H ¼ (5.57)
β u ij ρ h i ρ h j
i
j
All the parameters in the right side of Eq. (5.57) can be obtained from the CFD sim-
ulation. Thus, the correction factor f H can also be derived from the CFD simulation.
Shen et al. (2015) pointed out that the correction factor for effective mixing coefficient
for enthalpy f H is much smaller than 1.0.
As soon as the correction factor f H is known, the effective turbulent mixing length
of energy l i,h is determined by Eq. (5.49). Assuming that there is a linear dependence
of both density and enthalpy on the temperature, that is, the thermal expansion coef-
ficient and the specific heat are constant, the distribution of density and enthalpy in
the subchannels is the same. Thus, it is reasonable to assume that the effective
turbulent mixing length of mass l t,m is thesameasthe effectiveturbulentmixing
length of energy l t,H .WithhelpofEq. (5.50), the correction factor of mass f m is then
determined.
The correction factor of momentum f M can be determined by a similar way as the
correction factor of energy. Analog to Eq. (5.57), the momentum exchange across the
gap due to turbulent fluctuation is given: