Investigation of flow through a computationally generated packed column using CFD and additive layer manufacturing

Preprint submitted to Computers and Chemical Engineering 18 March 2014. © The AuthorsThe version of record is available from the publisher via doi:10.1016/j.compchemeng.2014.04.005.When analysing packed beds using CFD approaches, producing an accurate geometry is often challenging. Often a computational model is produced from non-invasive imaging of the packed bed using 3d MRI or μ-CT. This work pioneers the exact reverse of this, by creating a physical bed from the computational model using Additive Layer Manufacturing (ALM). The paper focuses on both experimental analysis and computational analysis of packed columns of spheres. A STL file is generated of a packed column formed using a Monte-Carlo packing algorithm, and this is meshed and analysed using Computational Fluid Dynamics. In addition to this, a physical model is created using ALM on a 3d printer. This allows us to analyse the identical bed geometry both computationally and experimentally and compare the two. Pressure drop and flow patterns are analysed within the bed in detail. © 2014 Elsevier Ltd

Finite Boolean Algebras for Solid Geometry using Julia's Sparse Arrays

The goal of this paper is to introduce a new method in computer-aided geometry of solid modeling. We put forth a novel algebraic technique to evaluate any variadic expression between polyhedral d-solids (d = 2, 3) with regularized operators of union, intersection, and difference, i.e., any CSG tree. The result is obtained in three steps: first, by computing an independent set of generators for the d-space partition induced by the input; then, by reducing the solid expression to an equivalent logical formula between Boolean terms made by zeros and ones; and, finally, by evaluating this expression using bitwise operators. This method is implemented in Julia using sparse arrays. The computational evaluation of every possible solid expression, usually denoted as CSG (Constructive Solid Geometry), is reduced to an equivalent logical expression of a finite set algebra over the cells of a space partition, and solved by native bitwise operators.Comment: revised version submitted to Computer-Aided Geometric Desig

Radon Transform in Finite Dimensional Hilbert Space

Novel analysis of finite dimensional Hilbert space is outlined. The approach bypasses general, inherent, difficulties present in handling angular variables in finite dimensional problems: The finite dimensional, d, Hilbert space operators are underpinned with finite geometry which provide intuitive perspective to the physical operators. The analysis emphasizes a central role for projectors of mutual unbiased bases (MUB) states, extending thereby their use in finite dimensional quantum mechanics studies. Interrelation among the Hilbert space operators revealed via their (finite) dual affine plane geometry (DAPG) underpinning are displayed and utilized in formulating the finite dimensional ubiquitous Radon transformation and its inverse illustrating phase space-like physics encoded in lines and points of the geometry. The finite geometry required for our study is outlined.Comment: 8page