Page 223 - Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

194 Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

Δz j G K,i jG K,i

ð p K,in p K,out Þ A f + ς A V ρ g
D h 2 ρ K,i
K,i

_ m K,out G K,out _ m K,in G K,in
X
0
0
¼ + s i, j Δz G u K,i G u K, j (5.6)
ρ K,out ρ K,in i, j i, j
∗
X J
+ s i, j Δz G u ∗
i, j i, j
J
The three terms in the left side are the pressure force, the hydraulic resistance force,
and the body force, respectively. The first two terms in the right side are the momen-
tum flow exiting from and entering into the control volume. The last two terms
describe the interchannel exchange of momentum, caused by the undirected velocity
fluctuation and the directed cross flow. Here, p K,in and p K,out denote the pressure at the
axial inlet and outlet of the control volume, A the cross-sectional area, f the friction
factor, d the hydraulic diameter, ζ the local hydraulic resistance coefficient, G K,i the
axial mass flux in the subchannel i, V the cell volume, ρ the fluid density and g the
gravitational acceleration, and u K,i and u K,j the axial velocities in the subchannels i
and j, respectively. The cross flow velocity is.
∗ ∗
u ¼ u i if G 0 (5.7)
i, j i, j
and
∗ ∗
u ¼ u j if G < 0 (5.8)
i, j i, j

5.2.1.3 Energy conservation
The energy balance is expressed as

Q ¼ E K,out E K,in + E K,int (5.9)

The external source term takes into consideration the heat transfer between the fluid
and the fuel rod surface:

Q ¼ A F α F T F Tð Þ (5.10)

with A F the heat-transfer area, α F the heat-transfer coefficient at the fuel rod surface,
and T the temperature. Similar to the momentum exchange, the interchannel exchange
of energy is caused by the undirected velocity fluctuation and the directed cross flow:

X
0 0
E K,int ¼ s ij Δz G h K,i G h K, j
ij ji
J
X ∗ ∗ X 1
+ s ij Δz G h + (5.11)
ij ij s ij Δz λ eff T i T j
J j l ij