Sheet Flow Test

The sediment transport under oscillatory sheet flow is a challenging yet important topic in coastal engineering. The near-bed sediment transport under waves is largely determined by the sand size and the near-bed oscillatory flow caused by waves[58].

Figure 5.15: Phase-averaged surface elevationη, horizontal velocityu, vertical

velocityw, and turbulent kinetic energy kat selected sections (Part II). Black:

modelling results; red: measurements.

The model is applied to a case with fine sand under sinusoidal oscillatory flow condition. The experiment was performed by O’Donoghue and Wright[57] in the Aberdeen Oscillatory Flow Tunnel. It was 16 m long with a 10 m long glass- sided rectangular test section, 0.75 m high and 0.3 m wide. A 250 mm deep bed of well sorted sand with the median grain size 0.13 mm was placed in the central part of the test section. A sinusoidal oscillatory flow was generated with a period of 6 s and an orbital amplitude of 1.2 m. The flow velocity was measured by an ultrasonic velocity profiler (UVP), which was capable to collect data from several millimetres to approximately 50 mm above the instantaneous bed level. The sediment concentration below the initial bed level was measured by three conductivity concentration meters (CCMs) placed at separate locations along the central line of the tunnel[44]. More details can be found in O’Donoghue and Wright[57] and Li et al.[44].

Figure 5.16: The velocity profile at selected phases. t/T = 0.0, 0.13, 0.25,

0.4, 0.58, 0.66, and 0.96 as indicated in the figure by each line. Black solid lines: modelling results; red dashed lines: measurements.

The computational domain is set as 100mmlong, 100mmhigh, and one cell wide. The mesh resolution is 1 mm. The time step is 1×10−3 _{s. A sand layer of 10}

mm is placed on the bottom initially, and the maximum volume concentration is 0.6. Periodic boundary conditions are employed at the inlet and outlet boundaries for both the fluid phase and the solid phase. To save computational costs, a typical boundary modelling approach is adopted, i.e., an oscillatory body force is used to represent the wave induced pressure term in the flow momentum and this force is assumed to be uniformly distributed across the depth. The oscillatory force term is tuned to meet the experimental set-up. The k−equation large eddy simulation is adopted. The flow starts from an initially stationary status. The simulation reaches stable status after 60 wave cycles and the results hereafter are found converged to be periodical and therefore are used for analysis.

The computed flow velocity profile at selected phases are compared with the mea- surements in Figure 5.16. Overall the agreement between the computed and mea- sured velocity is encouraging. In particular, the velocity profile 15 mm above

(a)t/T = 0 (b)t/T = 1/6

(c) t/T = 1/3 (d) t/T = 1/2

(e) t/T = 2/3 (f) t/T = 5/6

the sandy bed reaches better agreement with the measurements than that be- low this level. The phase lead between the flow in the boundary layer and the outer flow is also captured by the model very well. When approaching peak flow (t/T = 0.25,0.66) and during maximum acceleration (t/T = 0.13,0.58), the agree- ment is better with the measurements than at flow reversal (t/T = 0.96). Most deviations are observed in the region close to the bed, where significant changes occur to the hydrodynamics due to the wave boundary layer process and the sheet flow process.

Employing a particle approach, the model is able to resolve the sand motion at the particle scale. Figure 5.17 shows the particle distribution and the streamwise velocity at selected phases. The velocity contour is generally uniform up in the water column with variations locally. The velocity decreases when approaching the bed. A layered velocity distribution immediately above the bed, i.e., z = 10−15

mm is observed throughout the flow cycle. It is particularly obvious at peak flow (see Figure 5.17b, 5.17c, 5.17e and 5.17f). It demonstrates that the influence of the sandy bed on the flow is well resolved by the model. The particle distribution at peak flow is widespread over the whole water column due to the strong suspension. At flow reversal, particles are entrained high into the water column, and a vortex- shaped distribution is observed in Figure 5.17a and Figure 5.17d. It is noteworthy that Figure 5.17 is the instantaneous particle distribution at selected phases, and the ensemble averaged values are used for comparison against measurements.

To examine the modelling results on sediment motion, the computed sediment concentration profiles are obtained by averaging those values over the length of the computational domain. The sediment concentration profiles at selected phases are compared to the measurements in Figure 5.18 and 5.19. Overall, very good

Figure 5.18: Comparison of the computed and measured sediment concentra-

tion at various flow phases in the first half of a wave cycle. Lines: modelling results; circles: measurements.

agreement is achieved between the computed and measured value, from the high concentration region deep inside the bed up to the low concentration region higher in the water column. However, certain deviations are observed near the bed sur- face, where the deviation can be as large as 500 g/l. It can be caused by the inaccurately resolved flow velocity there, as well as the challenging situation re- garding the active interaction between the flow the sediment dynamics at the bed surface. At layers 1mmdeep in the bed and below, the predicted sediment concen- tration is much better, suggesting the model’s good performance in dealing with a nearly fully packed bed. Also, it can be seen that the model is able to simulate the acceleration induced suspension near the bed, i.e., from t = 0 to t = 1.5 s. The erosion inside the bed is evident and the concentration curve becomes steeper. In the deceleration phase, sediment is settling down with the rise of bed level and the concentration curve becoming less steep (t = 2.7 s and t = 3 s). Both the magnitude and the trend of the concentration agree with the measurements very well, indicating the capability of the model in simulating the particle interaction at very high concentration level.

Figure 5.19: Comparison of the computed and measured sediment concentra-

tion at various flow phases in the second half of a wave cycle. Lines: modelling results; circles: measurements.