Geoscience Reference
In-Depth Information
1
m
3
α
22
α
22
I
2
(6.87)
b
s
2
b
s
2
m
)
α
21
α
21
U
s
D
yy
=−
ρ
+
1
α
21
α
22
IU
s
+
(
m
+
2
+
Note that the dispersion transports can also be derived using the logarithmic law
and another helical flow model. The dispersion terms can be treated as additional
source terms in the momentum equations (6.75) and (6.76).
Physically, the helical flow transfers the upper layer of water, which has stronger
momentum, toward the outer bank and the lower layer of water, which has weaker
momentum, toward the inner bank, and thus shifts the main flow to the outer bank
in the bend. If this effect is ignored, the main flow in a curved channel may not be
simulated correctly. Fig. 6.14 shows the simulated flow patterns in a 270
◦
bend, and
Fig. 6.15 compares the measured and simulated velocities at six cross-sections. The
flow was measured by Steffler (1984) in a flume with a flat bed and a rectangular
cross-section. The flume width was 1.07m, the radius of curvature at the centerline
was 3.66m, and the bed slope was 0.00083. The Manning
n
was 0.0125. The inflow
discharge was 0.0235m
3
s
−
1
, and the water depth at the outlet was 0.061m. The
simulations were conducted with and without consideration for the dispersion effects
in the depth-averaged momentum equations (Wu and Wang, 2004a). The parameters
β
I
and
λ
t
were evaluated as 2.0 and 3.0, respectively, using the measurement data of
secondary flow velocity. It can be seen that when the helical flow effect is not taken
into account, the calculated main flow is along the inner wall over the entire bend;
and when the helical flow effect is considered, the main flow shifts from the inner wall
to the outer wall and the accuracy of the simulated flow velocities is much improved.
Figure 6.14
Calculated velocity contours without and with helical flow effect in Steffler's 270
◦
bend
(Wu and Wang, 2004a).
