The block of particles in the preceding section is fixed in the flow as an immobile structure. Enlightened by this, bespoke particle clusters can be used to represent porous media or complex geometries. As long as the boundary of a structure or geometry is known, the initialiser code as described in Section 3.5.2 can be adapted to generate a cluster of particles or several clusters to represent a structure with specific porosity and geometry. The porosity value can be easily achieved by assigning the desirable solid volume fraction θs and the critical solid volume
fraction θcs in the model.
A wedge test is performed as a simple demonstration. The wedge with a porosity of 0.42 is fixed in the flow. Flow gets contracted around the wedge and vortices are formed in the lee-wake side (see Figure 4.8). The magnitude of the interphase momentum transfer term and the volume exclusion term are shown is Figure 4.9.
Figure 4.8: Velocity vector field. Red line: the boundary of the wedge.
(a) Magnitude ofSU (b)Magnitude ofTve
Figure 4.9: Magnitude of interphase momentum transfer term and volume
exclusion term.
The distribution patterns of the magnitude of both source terms resemble those in the isolated block tests. Maximum values of both terms are observed at the up- stream corners of the wedge, and the magnitudes inside the wedge are comparable to those in the isolated block tests.
in the flow. On top of that, even if a rigid structure involved in the simulation has movement, for example, a turbine blade, the model can be easily modified to accommodate this need by assigning the desired position or velocity to the particles used to represent this structure. The advantage is obvious in this way that no mesh deformation or complex boundary conditions are needed, neither is special treatment or parameterisation for the movement of a structure in the flow as well as the associated requirement on other configurations. In addition, it is also possible to simulate aggregation or dissolution effect of certain structure or materials where applicable. Because particles are traced on a one-to-one basis, they can be introduced or removed as required withoug influencing the rest of the existing particles.
4.5
Conclusions
The particle motion related implementations are calibrated and validated by per- forming particle falling tests. The modelled particle fall velocity highly agrees with the theoretical value with a discrepancy of only 0.45% and 1.02% for particle
d50 = 2.5 mm and d50 = 0.25 mm, respectively. Considering numerical accuracy limited by truncated errors etc., this agreement is remarkable. The reliability of the numerical implementation concerning particle motion is confirmed.
For conventional modelling approaches with an Eulerian mesh, the mesh resolu- tion, i.e., the grid size is a typical concern for an accurate prediction of hydrody- namics. On top of that, in the coupled Eulerian-Lagrangian model, the parcel size
is required to be smaller than the grid size. Therefore the ratio of the grid spacing to the parcel diameter needs investigation to ensure a reliable prediction. Particle falling tests with various grid spacing ratios to parcel diameter are performed for this purpose. Considering the predicted particle fall velocity and the behaviour of the interphase momentum transfer term and the volume exclusion term, results show that the larger this size ratio is, the better results are achieved. However, a larger size ratio requires much more parcels in one cell, the number of parcels involved in a simulation can be enormous. Taking into account the limit of compu- tational efficiency as well, the ratio of grid size to parcel diameter is recommended to be between three and four.
The hydrodynamic performance with the influence of the solid phase is examined by a series of isolated block tests. The behaviour of the source terms arisen from the introduction of the solid phase is checked, both inside the computational domain and on the boundaries. The interphase momentum transfer term is the dominant source term. With this term on, the flow deceleration inside the isolated block is significant. Flow accelerates around the block and vortices are formed in the wake side. The volume exclusion term has a very minor effect compared to the interphase momentum transfer term, and is therefore negligible. On its own, this term leads to flow acceleration inside the block due to the gradient of fluid volume fraction. In addition, this term is very sensitive to the size ratio of grid spacing to parcel diameter. As the fluid phase is divergence free, this term is not essential to the model, therefore, it is removed hereafter.
When the particles are fixed, the block of particles behaves as an immobile porous medium. From this perspective, the particle initialiser can be used to generate
clusters of particles to represent porous media, rigid structures or complex geome- tries. A simple demonstration with a wedge in the flow is presented. Even when the rigid structure has movement or where aggregation and dissolution effect is necessary, the model can be easily extended to account for those effects.
The influences of the Eulerain grid size on the particle motion and potentially the overall transport process demonstrate that the Euler-Lagrange method has certain weak points that need to be treated carefully. However, these challenges are largely due to the numerical implementation methods, including the interpolation method and the solution algorithms, which can be treated with proper numerical method. On the other hand, the Euler-Lagrange method also demonstrates its advantages in dealing with solid obstacles in the flow by grouping a large number of particles. Usually, special treatments have to be employed in the traditional Eulerian approaches to tackle such difficulties, such as mesh masking etc.
Model Applications
5.1
Introduction
After calibration and validation, the model is applied to a range of experiments in this chapter. The performance of the model regarding the hydrodynamics, sediment transport and scour development will be presented in sequence. Firstly, the model is applied to different hydrodynamic conditions, including steady current and waves. A test of a steady current passing a vertical cylinder by Roulund et al.[70] and a plunging wave breaker experiment by Ting and Kirby[87] are simulated by the model in Section 5.2. Secondly, the model is applied to an oscillatory sheet flow test by O’Donoghue and Wright[56] and O’Donoghue et al.[58] to testify the model’s performance regarding sediment transport in Section
5.3.1. Finally, the model is applied to benchmark scour tests in steady current and waves respectively, including a current-induced pipeline scour case by Mao[50] and a wave-induced scour case by Sumer and Fredsøe[78]. Detailed results regarding the hydrodynamics, turbulence structures and scour development will be presented in Section 5.4.