# Numerical Study of Partial Dam-Break Flow with Arbitrary Dam Gate Location Using VOF Method
## 3 Results and Discussions
### Effect of Initial Water Stage, Breach Size and Position of Dam Gate on Hydraulic Characteristics
#### 3.2.1 Dynamics and Structure of Dam-Break Wave Inside Reservoir
In addition, when breach size increases, the highest value of near-bed \(v\) velocity increases and its position is further than the central line of the dam, because kinetic energy dissipation increases at the dam gate. In contrast, the 3 models 7A, 8A and 9A witness these values at the larger part of the reservoir, because a portion of the reservoir's water moves to the reservoir's outlet, unlike models 7B, 8B, 9B. Hence, with the same breach width, maximum transverse \(v\)-velocity of cases A are greater than those of cases B (Figure 8). Figure 8: Distribution of transverse \(v\) velocity near dam site at \(t=1.5\) s.  
Figure 7: Depth–average velocity profiles at central line of dam gate at \(t=1.5\) s.  
The dominant difference of water depth probes at the dam gate's center yielded by the 6 scenarios is at normal peak points (Figure 9). Symmetrical dam breach provides a higher peak value of water depth than the asymmetrical one, although the lowest value of hump is independent of this factor. When breach size increases, the gradient of the water surface hydrograph increases. Besides temporal variation of near-bed velocity, components \(u\) and \(w\) at the center of the outlet do not depend on the dam gate's position, (Figure 10). In \(x\) direction, gate width \(b=25\) cm generates the maximum horizontal \(u\) velocity of 2 m/s, while the larger breach sizes, 50 cm and 75 cm, produce smaller values. Vertical component \(w\) is negative and nearly dismissed in all simulated times. This point is different with [28] when 4 breach sizes showed both negative and positive values of \(w\). The reason may be due to the small ratio range \(b/B\), from 0.08 to 0.25, in comparison with the larger range of (0.3 \(\div\) 1.0) in the aforementioned work. Additionally, transverse velocity \(v\) approximately equals zero when the reservoir's mouth is symmetrical, while the harmonic trend of this value is seen in models 7A, 8A and 9A. Figure 10: Near–bed velocity component profiles at the center of dam gate. Black solid line—asymmetrical dam gate; Red dotted line—symmetrical dam gate. Figure 9: Water depth profiles at the center of dam gate. Solid line: cases 7A, 8A, 9A; dot line: cases 7B, 8B, 9B. Vorticity components \(w_{x}\), \(w_{y}\), \(w_{z}\) represent the rate at which a fluid element rotates around its pivot axis [28]. The major effect of the opening gate's location is observed in both values \(w_{x}\) and \(w_{z}\). Negative value of horizontal vorticity \(w_{x}\) and positive value of vertical vorticity \(w_{z}\) present counterclockwise and clockwise rotations in models 7A, 8A and 9A during dam-peak time (Figure 11). While these values are negligible, due to the symmetrical dam's mouth, it means there is no rotational flow formed in both \(x\) and \(z\) directions. Conversely, regarding time variation, clockwise \(w_{y}\) vorticity slightly depends on the position of the dam gate in the first 5 s period, except at the end of this period. Magnitude of \(w_{y}\) increases rapidly from \(b\) = 25 cm to b = 75 cm. Vortex cores are centers of swirling flow where the velocity is parallel to the vorticity [33]. This parameter is very effective in identifying local rotational flow structures. The \(f_{x}\)-vortex core represents centers of swirling flow around pivot \(x\) axis. Figure 12 illustrates this index at \(t\) = 1.5 s in 6 cases 7A, 8A, 9A and 7B, 8B, 9B and shows that swirling flow occurs at the left side of the reservoir, which is near the mouth of the dam in all asymmetrical dam gate cases. When the opening width is larger, vortex core strength is greater. In contrast, the opposite trend occurs in the symmetrical dam gate. Swirling flow is indicated at two corners near the cross section of the dam, but its area is smaller when dam width is larger. Figure 11: Near–bed vorticity components at the center of dam site. Black solid line: cases 7A, 8A, 9A; red dotted line: cases 7B, 8B, 9B.