Modeling of high speed erosion with a morphological updating routine

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Abstract

Erosion is a phenomenon present in several industrial processes. In dredging, the jetting of sand in drag heads erodes the sand bed. In construction of offshore infrastructure such as wind turbines, oil and gas production units, marine pipelines, erosion of material near the foundations can put the stability of structures at stake. Furthermore, rivers or even tsunamis are some of the natural phenomena that can be the cause of erosion. C. van Rhee, 2007 and Bisschop et al., 2015, distinguished two regimes for the erosion of sand dependent on the fluid velocity. On one hand, for low flow velocities, 0.5-1m/s, the erosion process is dependent on the size and the density of the sand grains. On the other, for flow velocities >1.5 m/s, the upper layers of sand are sheared. Densely packed sand has a dilatant behaviour to shearing (see image). This dilatant behaviour leads to a drop of pressure in the interior of the sand-bed, creating a hydraulic gradient and forcing water to flow towards the interior of the sand-bed to fill the voids. The hydraulic gradient caused by the drop in pressure acts against the eroding forces adding resistance to the erosion process. This regime is defined as hindered erosion. The improvements in computing power have led to a spread in the use of numerical modelling for industrial purposes. The aim of this thesis is to develop a numerical solver able to model the behaviour of sand-water mixtures with an emphasis on the erosive process. The numerical model was developed in C++ using the Foam-extend 3.2 framework. The sand is modelled using 2 different approaches. It is modelled as a continuum when in suspension and, through the morphological updating routine when settled in a sand-bed. The fluid motion is modelled by a transient incompressible fluid solver (P.I.S.O) using a collocated arrangement of the unknowns. The momentum exchange between suspended sand grains and the fluid is approached by the Boussinesq approximation of the density. The transport of suspended sand is modelled by an advection-diffusion relation, including the hindered settlement effect. The turbulence model is a standard k-ε model. The erosion process is here modelled using the pick-up flux approach (van Rijn, 1984), with a modified stability criterion (θ_cr). X. Lui, 2008 and N. Jacobsen, 2011, corrected the stability criterion calculated from the sand grain properties (θ_(cr,0)) to include the slope effect (θ_slope). For this work, and following the formulation proposed by van Rhee, 2007, the stability criterion will be corrected to include the resistance due to the dilatant behaviour presented previously in this abstract (θ_vR). θ_cr=θ_(cr,0) (θ_slope+θ_vR ) The solver developed was used in two test cases. First, a settling test, with an initial concentration of sand of c=0.3. For this model, the solver shows a good behavior modeling the settling of sediment, nevertheless, the settling velocity is slightly higher than the one seen in the test. In the high speed erosion test, the velocity above the bed varies from 0-6 m/s. The fitting parameter of this model is the bed roughness; which for this test is 1.05 cm. The bed roughness (ks) was fitted to have the same erosion time. The calculated sand-bed height has values similar to the experimental results. The conservation of sediment presents satisfactory results as the error is lower than 1%, for the settling and the erosion test case. The automatic mesh motion presents certain limitations in this specific application. In the settling case an important shrinking of the mesh will lead to instabilities in the calculations of other fields. In the erosion test, the upper row of cells is greatly deformed sacrificing accuracy near the upper boundary. The mesh deformation should be explored more in depth in further studies.