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While powder discharge from hoppers has been well studied, most work has focused on axisymmetric, conical hoppers and plane flow, wedge-shaped hoppers.
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In this study an existing analytical pore-scale model for flow parallel and perpendicular to 1D unidirectional fibres are used and adapted to propose permeability predictions for in-plane and through plane flow in layered 2D fibre arrangements as well as flow through 3D isotropic fibrous porous media.
We derive and implement Green's function based solvers for the channel flow and plane Couette flow geometries.
The fluid flows used in this study are a self-designed quasi-fluid flow problem, stagnation in plane flow (Hiemenz flow), and flow between two concentric cylinders.
The standard ADE scheme, however, is only moderately accurate and is restricted to uniform grids and plane strain flow conditions.
However, the plane flow involving a shock wave moving at constant speed admits a self-similar solution.
With two-dimensional particle image velocimetry (2D-PIV), planar flows can be well examined when there is no out-of-plane (perpendicular to the lightsheet plane) flow motion.
Based on the new method, the plane flow model for stratified turbulent flow in pipe is built.
The plane flow of a layer of incompressible viscous magnetic fluid with constant magnetic permeability under the action of a traveling magnetic field is analyzed.
Berker [1] has defined the 'pseudo plane motions' of the first kind that: if the streamlines in a plane flow are contained in parallel planes but the velocity components are dependent on the coordinate normal to the planes.
For pipe and plane Poiseuille flows, it has been demonstrated that the transition to turbulence for these wall-bounded parallel flows occurs at a consistent value of the energy gradient parameter (Kmax).
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