Page 229 - Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

200 Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

2
D πD
2
π P
2 4
A r ¼ (5.37)
6
In the above model, the same sweeping flow velocity is taken for all the axial level,
independent of the relative position between the wire and the gap. To account the var-
iation of the sweeping flow in the axial location, Wantland (1974) assumed that the
flow direction goes with the helical wire. The maximum sweeping flow velocity
occurs on the position where the wire crosses the gap immediately and the effect
of the wire declines with its position from the gap. For wires far away (more than
60 degrees) from the gap, the sweeping flow due to wires is assumed to be negligible
small. Thus, the following equation is proposed:

∗
G s ij H
ð
ð
ij π D + D W Þs ij ½ 1 + cos 3θފ
¼ C s for θ 60 ° (5.38)
m ij A i 2
The models discussed above were mainly derived with strongly simplified assump-
tions and very limited experimental data. Recently, in the frame of the SESAME pro-
ject, CFD analysis was carried out to study the mechanisms of the sweeping flow and
to find out the dependence of the sweeping flow on various parameters. The results
pointed out the necessity of the improvement in the modeling of sweeping flow
(Wang and Cheng, 2017).
Based on the CFD results combined with mechanistic understanding, a new model
of sweeping flow was proposed by Wang and Cheng (2017). According to this model,
the sweeping flow is considered to be driven by the circumferential pressure differ-
ence that is induced by the wake effect of helical wires. When fluid flows across
the wire, the pressure difference between the upper face and lower side of the wire
drives the fluid flowing across the gap. Based on the principle of force balance, the
resistance force that balances the driving force is the surface friction force. The pres-
sure gradient resulted by the surface friction on the gap position can be estimated by
the friction force equation. The pressure gradient induced by friction should be equal
to the gradient from the driving force. Thus, the following semiempirical correlation
was derived (Wang and Cheng, 2018):

h π i
∗
G s ij H cos θ
ij 3
¼ (5.39)
m ij C H
+

P πP
cos αðÞ 1
D
Fig. 5.9 compares the CFD results, the new model, Eq. (5.39), and the model
of Wantland (Eq. 5.38). It is seen that there is a large discrepancy between the corre-
lation of Wantland and the CFD simulation. The new correlation represents well the
CFD results.