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Model applications

This section provides examples of the application of the present model (scourFoam) and comparisons with studies to demonstrate its prediction capabilities against experimental data. Firstly, the model’s predictive capability is tested in 2D using the data of Alper Oner et al. (2008) and Mao (1986) and then it is applied to simulate the 3D scour around a complex foundation using the data of Tavouktsoglou et al. (2016).

D scour application

The model is applied to simulate scour under a horizontal pipeline. Firstly, the study of Alper Oner et al. (2008) was used to test the model’s prediction in hydrodynamics around the pipeline. To verify the ability of scourFOAM to predict current induced scour, the benchmark test of Mao (1986) has been simulated.

5.1.1 Hydrodynamics

The experiment of Alper Oner et al. (2008) involves detailed measurements of flow over a cylinder at different elevations above a fixed bed. The model was applied to one of the tests in which the cylinder was placed above the bed without any gap. The water depth was kept at 0.32 m and a steady current with a speed of 0.197 m/s was introduced at the inlet. The cylinder has a diameter of 50 mm The model is set up as shown in Figure 2 with the same parameters in the laboratory experiment. To simulate the flow-structure- sediment interaction, an 8 cm deep sediment rectangular sediment pit was introduced at the bottom while forcing a zero velocity condition on the bed particles to ensure the bed is immobile. The time step was set at 5 x 10'4 s and a mesh size of 5 mm was used in all three directions. The computed vertical profile of the stream-wise flow velocity was compared with the measured data at -1.5D. ID, 0.5D, OD, 0.5D, ID and 1.5D in Figure 3 where the zero level corresponds to the bed surface. It can be seen clearly that the agreement between the model results and measurements are very good at all sites. The computed velocity vertical profile inside the bed (z < 0) also shows the effects of particle on fluid motion, which shows that the interaction produces a good resistance to the flow dynamics near the bed surface.

5.1.2 Scour around 2D pipe

The model is applied to steady current-induced live-bed scour beneath a pipeline, using a benchmark laboratory test carried out by Mao (1986). According to Mao (1986), the water

Comparison of computed and measured horizontal flow velocity in Alper Oner et al. (2008) test

Figure 3: Comparison of computed and measured horizontal flow velocity in Alper Oner et al. (2008) test.

Comparison of computed and measured bed level at t = 1.5 min

Figure 4: Comparison of computed and measured bed level at t = 1.5 min.

depth was set as 0.35 m and pipeline diameter as 0.1 m. The computational domain is 1.6 m long, 0.5 m deep and one cell wide. At the upstream inlet boundary the prescribed flow velocity of 0.5 m/s is distributed across the depth. At the downstream outlet boundary a zero gradient condition is assigned to the variables in the flow module. The particles were allowed to leave the domain when they moved out of the computational area. The bottom of the channel was specified as a wall with a sediment pit in the middle of the domain, taking up 14D in length and 8 cm in depth. The sediment particles with median diameter (d-,o) of 36 mm were distributed inside the pit initially with the pipeline lying on the surface at the middle of this section (see Figure 2). The top boundary is specified as a zero pressure boundary open to the atmosphere. The two side boundaries in the cross-flow direction are treated as periodic to eliminate any side boundary effects. The time-step was specified as 2 x 10'4 s and a uniform mesh size of 5 mm was used in all three directions. Similar to the hydrodynamic test, the mesh around the pipeline is split to resolve the structure. In total the computational mesh comprised of 11,000 cells. The total number of particles exceeds 10,000 in the simulation.

Figure 4 shows the computed scour profile with the dots denoting the measured data at 1.5 min. The shape of the scour hole, the maximum scour depth, and the maximum deposition point in the downstream are all captured by the model. The downstream deposition area at x/D = 1.75 is slightly over predicted, which can be partly attributed to the complex flow structures of the wake vortices that are not strong enough near the bed surface to transport the particles away. Overall, the agreement is very good, which demonstrates the capability of scourFOAM in simulating the scour process over a live bed condition.

It should be noted that in the previous studies, e.g., Yeganeh-Bakhtiary et al. (2013), Zanganeh et al. (2012), Yeganeh-Bakhtiary et al. (2011), Liang and Cheng (2005b), Zhao and Fernando (2007), a gap between the pipeline and bed together with an arbitrary bed profile just underneath the structure are needed in the model in order to initiate the scouring process, due to the inability in dealing with particle-fluid interactions. However, in the present study, the pipeline is placed directly onto the particles on the bed surface without any gap. The initiation of the onset of scour is through the motion of individual particles under the influence of the flow hydrodynamics and the pressure difference between the upstream and downstream sides of the pipeline. Figure 5 details the onset of scouring and the surrounding flow dynamics for the first 1.2 s period at every 0.1 s interval. It can be seen that in the initial 0.5 s there is almost no disturbance in the bed upstream of the structure due to the low flow speed above the bed surface. On the contrary, the flow downstream is marked by the growing vortices which start to erode the bed in the immediate wake of the pipeline from 0.2 s onwards. With the strong flow velocity and vortex shedding, the deformation in the bed surface downstream of the pipeline (x>lD) has already become visible in the initial 0.4 s although the magnitude is small. The bed region between 0.1D and 0.2D also

Computed bed level change at different time steps

Figure 5: Computed bed level change at different time steps.

rises initially with piping taking place. Subsequently, the particles underneath the pipeline between -0.1D and 0.1D start moving along the pipeline perimeter and then towards the downstream side. It is noted that at the upstream of the pipeline, the flow decelerates and forms small vortices beneath the pipeline and the bed surface, which pushes the flow going into the bed. Downstream of the pipeline, the coherent flow structure is generated behind the pipeline and propagates along the bed surface, interacting with the sediment at the bed surface as they touch down and advect downstream.

The results clearly demonstrate the effectiveness of the method used in scourFOAM in dealing with particle motion within the high concentration region, i.e., a nearly fully packed bed. At the same time, these results also suggest that the initiation of the onset of scour is largely driven by the seepage flow within the bed. The bed liquefaction under these fluid-

Computed tunnel erosion at various stages

Figure 6: Computed tunnel erosion at various stages.

particle interactions are the primary driver for further scour, rather than the amplified shear stress. To a large extent , this indicates the necessity to include sub-surface flow information into practical modelling of sediment transport and scour.

Figure 6 shows the subsequent development of the scouring from 1.5 s to 12 s. At t = 1.5 s, a layer with low sediment concentration is visible at the bed surface connecting the upstream and downstream side of the pipeline, forming a very narrow pathway for the particles underneath the pipe. Subsequently, a slope underneath the pipe at the upstream side gradually develops from about 3 s, which encourages flow separation and vortice formation in front of the pipeline. Meanwhile, the transported particles also form a mound of deposition immediately behind the pipeline. From 4.5 s, the gap between the bed surface upstream and the pipeline increases (-1D < x < OD), which allows water to flow under the structure and accelerate in the narrow pathway. The mixture of water and sand can move via this channel towards the downstream side more easily and feed into the mound on the immediate downstream side. Gradually the tunnel erosion stage starts. A jet of water and sand mixture is observed in the pathway underneath the pipe at 6 s, and the vortices in the lee-wake side are affected due to the presence of the mound. After that, the pathway keeps developing (see Figure 6), and the bed underneath the pipe is being eroded and transported downstream. In the later tunnel erosion stage, the pathway develops into a scour hole and the mound downstream grows significantly as shown in the figure.

Figure 7 presents the computed flow velocity vector distribution at the later stage of tunnel erosion and during the development phase of the scour hole. At the later stage of tunnel erosion (15 s), the gap between the pipeline and the underlying bed is still small, and the flow is largely deflected over the structure, generating a small vortex in front of the pipeline and larger lee-wake shedding behind. The gap expands, part of the flow diverges under the pipeline and accelerates as a jet, shooting out on the lee side, causing a vortex to

Computed erosion at development stage of the scour hole

Figure 7: Computed erosion at development stage of the scour hole.

form higher up in the water column, immediately behind the pipeline increasing in size and leading to the generation of a vortex close to the bed at x = 2-3D. As the scour develops further, the jet increases in strength leading to lee-wake vortex shedding higher in the water column. The mound of sediment deposit also gradually increases in size and eventually suppresses the near-bed vortex behind the structure within a distance of 2D.

The computed instantaneous flow velocity vector distribution at lee-wake erosion, t = 1.5 min is presented in Figures 6-8. In general, the flow field at the upstream side of the pipeline remains undisturbed up to -2D. However, noticeable interactions between the fluid flow and particles at the bed surface are visible in this region corresponding to the sediment motion under live-bed conditions. From this point further downstream, the flow field is clearly influenced by the presence of the pipeline and sediment particles. As the flow approaches the pipeline, the main flow is separated with acceleration above and beneath the pipeline. The scour hole beneath the pipeline has already formed and the flow acceleration between the bed and the pipeline develops with little restriction. The accelerated flow under the pipeline propagates downstream to around 2D before reattaching with the flow from above. Further downstream, the lee-wake vortices form and propagate on the downstream side (x > 3D). Between the lee-wake vortices and the bed, the flow is hindered by the bed, particularly in the region of the sediment mound at x = 1.8D (1.5D < x < 3D).

In addition, the free surface becomes perturbed due to the complex flow structures as shown in the figure. As the flow accelerates at x = -ID, the surface dips and subsequently

Velocity field in the vicinity of the pipeline at t = 1.5 min

Figure 8: Velocity field in the vicinity of the pipeline at t = 1.5 min.

fluctuates as vortex shedding takes place in the lee-wake region until about x = 5D where the surface starts to recover to the inflow level. In this particular case, the Froude number Fr is computed to be above 0.2 and free surface variation is expected. By resolving the free surface, the internal flow field can adjust more realistically and timely as the bed profile evolves. This is particularly important for the case with large Froude numbers in order to resolve the flow field correctly and hence improve the accuracy of the scour predictions as discussed above.

5.1.3 Wave induced scour under a pipe

To test model performance under waves, a wave induced scour test around a horizontal pipe was reproduced numerically based on the physical experiments conducted by Sumer and Fredspe (1990). For the test, the water depth was 0.4 m, the wave period (T) was 1.22 s and the bottom orbital velocity was 0.24 m/s. The pipe diameter was 0.03 m resulting in a КС =11. The sediment particles with median diameter of 0.18 mm were distributed inside the pit initially with the pipeline lying on the surface at the middle of this section. For the simulation the mesh resolution was 0.15 cm, and the time step 1 x 10"4 s. The critical solid volume fraction was set at 0.65, with an initial bed fraction of 0.649.

The bed profile at 0.5 min and 1 min is compared to the measurements of Sumer and Fredspe (1990) in Figure 9. The bed surface is plotted as the isoline of the solid volume fraction at 0.6. The overall scour pattern is well captured as seen in these two figures, where the gentle bed slopes on both sides of the pipe are well reproduced. The scour profile is also in good agreement with the measurements. At t = 0.5 min, small fluctuations are observed in the bed surface between x = -10 cm and x = 10 cm, which illustrates that the bed in the model responds immediately to the flow field fluctuations due to vortex shedding from the wave pipe interaction. As time progresses further (t = 1 min), the scour hole beneath the pipe becomes deeper which reduces the flow acceleration under the pipe alongwith the scour rate. Overall, the model predicts the scour depth under the pipe with good accuracy, even though the maximum scour depth at t = 1 min is slightly underestimated.

 
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