Roulund et al.[70] conducted a rough rigid bed experiment with a vertical circular pile in a steady current. A pile of a diameter D = 0.536 m was sealed along its perimeter on a rigid bed covered by a single layer of crushed stones, the rough- ness height of which was k = 0.7 cm. It was conducted in a 28 m long and 4 m
wide flume. The water depth was maintained at 0.54 m. The approach velocity was 0.326 ms−1, which was obtained from the integration of the velocity profile. Only velocity measurements were carried out in this test. The measurements were conducted using a two-component DANTEC “pen-size” laser-Doppler anemome- ter (LDA) in the plane of symmetry upstream and downstream of the pile. The focal length of the “pen-size” probe with a specially built adaptor was 8cm. The measurement volume (dx×dy ×dz) was 1.5 mmÖ 0.12 mmÖ 0.12 mm[70].
Figure 5.1: Refined mesh around the pile.
The model is set up according to the experimental configuration to verify the model’s accuracy in the computed hydrodynamics, particularly the flow velocity. The computational domain is 7mlong, 1mdeep, and 3mwide, consisting of 224, 45 and 112 cells in each direction respectively. The pile is placed in the middle of the domain. Regular grid size varying from 2 cm to 3.125 cmcovers the whole domain. Finer mesh down to mm scale is used around the pile (see Figure 5.1) and near the bed. The time step is set at 1×10−4 s. Figure 5.2 is a sketch of the computational domain, where water is in red, and air is in blue. A steady current of 0.326ms−1 is imposed on the inlet boundary[29]. Zero normal gradient of the velocity is applied at the outlet boundary. The slip condition is used on the front and back wall. Zero velocity is imposed on the bottom and pile surface. The pressure gradient is calculated according to the velocity such that it provides the correct flux on each boundary. The k−ε turbulence model is employed. k and ε
are set as constant values with a 10% turbulence intensity.
The test starts with a uniform streamwise velocity 0.326 ms−1 in the flow. The flow field reaches steady status aftert = 20s. Figure 5.3 shows the computed free surface. Only very slight variations are observed around the pile perimeter at the free surface, apart from which, the free surface is level. This is because compared to the computational domain, the pipe diameter is not very large: the computational domain is approximately 13D long and 6Dwide, which is big enough for the flow to adjust to the presence of the pile.
Figure 5.3: The developed free surface. Red: water; blue: air.
The streamwise velocity distribution at the free surface, the middle depth of the flow and near the bed surface are presented in Figure 5.4. The flow deceleration in front of the pile and in the wake side, acceleration on the two sides of the pile are captured by the model. At the free surface and the middle depth, the streamwise velocity distribution is similar to each other except that at the middle depth the acceleration zone is even larger, and the deceleration in the immediate wake is stronger. At the bed surface, the acceleration zones on the two sides of the pile shrink into a horseshoe shaped area, while the deceleration areas expand toward both the upstream and the downstream side. Further downstream, not only the flow near the centreline has a lower velocity, two low velocity spots (approximately 0.15 ms−1) are also observed near the front and back wall.
The vertical velocity distribution at these three layers are shown in Figure 5.5. The pattern at each layer is very similar to each other. A downflow is identified at one
(a) Free surface
(b) Middle depth
(c) Bed surface
Figure 5.4: Streamwise velocity (m/s) distribution at the free surface (A), the middle depth of the flow (B), and near the bed (C).
upstream quarter of the pile perimeter. Correspondingly, on the other upstream side, the vertical velocity is upward. The non-zero regions at the upstream side of the pile expand slightly from the free surface to the bed surface. In the downstream side, two non-zero spots are observed at the middle depth and near the bed surface. The negative velocity spot is on the same streamline as the positive region at the upstream quarter of the pile, and the positive velocity spot aligns with the negative region at the pile perimeter. These two spots are also larger near the bed surface than those at the middle depth.
The streamwise velocity at different vertical layers is presented in Figure 5.6. From top panel to the bottom, the distance from the bed increases. Overall, the mod- elling results agree with the measurements very well. Particularly, it is seen that the further the layer is away from the bed, the more accurate the modelling results are. The streamwise velocity in front of the pile is predicted accurately at the layer 4.3cm and above. At layers z = 1.3 mm and z = 2.3 mm, the predicted velocity between x/D = −2 and x/D = −1 agrees well with measurements. However, it is over-predicted when approaching the pile, i.e., within 0.5D distance from the pile perimeter. The maximum deviation of the modelling results from the mea- surements is observed at x/D = −0.87 with an over-prediction of 0.15 m/s at
z = 1.3 cm and 0.1 m/s at z = 2.3 cm. This can be due to the deficiencies in the boundary condition imposed on the bed surface, for example, the wall func- tion involved in the turbulence model. The grid size being not fine enough near the bed can also be a possible error source. However, the accuracy is considered acceptable in current study considering the challenging situation close to the bed. Apart from that, the deviation of the modelling results stays within 0.01 m/s in most areas, even at locations very close to vertical pile. At the downstream side, the deceleration within 0.5D distance from the pile and the acceleration between 1D and 2D away from pile are all captured very well by the model. Deviations
(a) Free surface
(b) Middle depth
(c) Bed surface
Figure 5.5: Vertical velocity (m/s) distribution at the free surface (A), in the middle depth of the flow (B), and near the bed (C).
are mainly less than 0.04m/s. The good agreement with the measurements at the downstream side is observed at each vertical layer. In the numerical simulation by Roulund et al.[70], the deviations at the downstream side can be larger than 0.06m/s, which can be caused by the exclusion of the free surface effect in their model. The better results at the downstream side produced by the present model demonstrate well the importance of the free surface effect.
In addition, the three-dimensional feature captured by the model is also seen in Figure 5.6. At the upstream side, the flow deceleration starts at different distances from the pile at each layer. From the bed to the free surface, the beginning point of flow deceleration is observed at approximately 4.5D, 4D, 3D and gradually converges to 2D in front of the pile perimeter. It confirms quantitatively the capability of the model to resolve the full three dimensional features.
The results suggest that the model is able to capture complex flow field around the structure, which is particularly important to the present study. The small deviation from the measurements near the bed surface may potentially affect the particle motion if present. A more delicate treatment of the near wall turbu- lence could be a solution to further improvement. However, considering the small difference in magnitude, it should not cause significant effects.
−6 −5 −4 −3 −2 −1 0 1 2 −0.2 0 0.2 0.4 z=1.3 cm Vertical pile −6 −5 −4 −3 −2 −1 0 1 2 −0.2 0 0.2 0.4 z=2.3 cm Vertical pile −6 −5 −4 −3 −2 −1 0 1 2 −0.2 0 0.2 0.4 z=4.3 cm u (m/s) Vertical pile −6 −5 −4 −3 −2 −1 0 1 2 −0.2 0 0.2 0.4 z=9.3 cm Vertical pile −6 −5 −4 −3 −2 −1 0 1 2 −0.2 0 0.2 0.4 z=19.3 cm x/D Vertical pile
Figure 5.6: Streamwise velocity in the plane of symmetry at different vertical
layers. The level height z is measured from the bed. Solid line: modelling
results; asterisks: measurements.