| 1. |
- Hellström, J. Gunnar I., et al.
(författare)
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Flow through a hexagonal array of perturbed spheres at low to high Reynolds number
- 2007
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Ingår i: Abstracts of the Second International Conference on Porous Media and its Applications in Science, Engineering and Industry. - : Engineering Conferences International.
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Konferensbidrag (refereegranskat)abstract
- When performing numerical simulations of fluid flow through porous media it is necessary to know when to switch from a creeping flow formulation to a more elaborate laminar description. In the creeping flow regime the Darcy law is sufficient while when inertia-effects become significant it is necessarily to use the full Navier-Stokes equations or at least add a non-linear term to Darcy's law as done in the empirically derived Ergun equation. The latter equation has also turned out to be valid for turbulent flows. It is however not obvious which equation to use at a certain Reynolds number. In order to solve this problem Computational Fluid Dynamics is used to derive the apparent permeability of a hexagonal packed array of spheres. In addition the forces acting on the spheres are derived when a perturbation in the form of a spherically shaped particle is introduced in the pore space. Then simulations are performed at various Reynolds number ranging from the creeping flow region to moderate Reynolds number flows. The simulations are carried out with the commercially available software, ANSYS CFX 11.0, with a particular effort on grid refinement and numerical iteration in order to secure that the errors are sufficiently small. One result is that inertia effects become important already at Reynolds number about 5 for as well the array as the perturbed geometry. As the particle radius increases the shear and normal forces per unit area decreases. In general, these forces increase with Reynolds number. The simulations however show that for some cases the normal forces per unit area decreases and even change sign as Reynolds number increases.
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| 2. |
- Hellström, J. Gunnar I., et al.
(författare)
-
Forces on grains located in model geometry with application to internal erosion in embankment dams
- 2007
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Ingår i: International Symposium on Modern Technology of Dams. ; , s. 375-386
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Konferensbidrag (refereegranskat)abstract
- For a comprehensive understanding of internal erosion in embankment dams it is necessary to elucidate the detailed seepage flow. A neat tool that can be used for this purpose is Computational Fluid Dynamics. With such a tool forces on individual particles can be derived and means to decide when to switch from a creeping flow formulation to a more elaborate laminar description for macroscopic flow simulations can be derived. It can even be decided when the transition from a laminar formulation to a fully turbulent description should take place. In the creeping flow regime a Darcy law formulation is sufficient while when inertia-effects become significant it is necessary to use the Navier-Stokes equations or at least add a non-linear term to Darcy's law as done in the empirically derived Ergun equation. It is, however, not obvious which equation to use at a certain Reynolds number. Hence, Computational Fluid Dynamics is here used to derive the apparent permeability of a hexagonal packed array of spheres. Then, grains are introduced in the pore space between the spheres and forces acting on the grains are derived. It will then be possible to decide at what conditions such particles will start to move, due to flow induced forces, and thereby initiating internal erosion. The simulations are performed at various Reynolds number ranging from the creeping flow region to the transition regime. The software ANSYS CFX 11.0 is applied with particular effort on grid refinement and numerical iteration in order to secure that the numerical errors are sufficiently small. One result is that inertia-effects become important already at a Reynolds number of 10. Another is that the forces acting on the grains can decrease as a function of Reynolds number and can as well be dependent on the geometry of the grains, even though the force per unit area on the array of spheres increases. Interestingly, the direction of the forces on the grains can even be opposite to the main flow direction.
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