Andrzej F. Nowakowski

The hydrodynamics of a hydrocyclone based on a three-dimensional multi-continuum model

Abstract The concept and principles of applying a multi-continuum model for calculating a hydrocyclone performance is presented. In this model the carrying liquid is described as one continuum, and each particle fraction, with its characteristic size is described as a separate continuum. Particle–particle and particle–fluid interactions derived from a lubrication theory and a collision theory are discussed. A set of governing partial differential equations consisting of mass and momentum conservation equations together with constitutive expressions is discussed. These equations were discretized by applying an unstructured grid consisting of tetrahedral elements. A numerical solver based on a finite element method combined with a segregated approach is described. The numerical approach is subject to ongoing research.

Investigation of Swirling Flow Structure in Hydrocyclones

Three-dimensional simulations of incompressible fluid flow within hydrocyclones have been performed using the developed numerical technique. The computational approach, based on the finite element method, has the capability to deal with the complex geometry of the head entry part of the hydrocyclone. The boundary conditions represent forces and are efficiently incorporated into the numerical formulation. Such formulation has not been used before for hydrocyclone simulation. Three different swirling angles were investigated and the simulations were carried out for fluids with different properties. The numerical results clearly indicate the presence of an asymmetrical flow not only close to the entrance region, but also in the conical part of hydrocyclone. The different methods for modelling the particle distribution are also discussed.

Experimental study of a turbulent pipe flow through a fractal plate

We study flows forced through plates in a circular wind-tunnel. The plates are based on different iterations of a pattern which would correspond to the generation of a fractal object. Two types of patterns are considered: one leading to an orifice with a fractal perimeter, the other to a fractal equivalent of a perforated plate. We propose this approach as a systematic way to introduce scales forcing and construct a scale by scale multiscale flow. For the sake of comparison we also consider simple orifice plates having a different number of sharp edges but which are based on a single scale geometry (monoscale orifices). In terms of analysis we focus on the pressure drop across the plate as in terms of engineering application this is the most salient effect of the plate multiscale generation. We measure the pressure recovery as a function of the distance from the plate. We also use hotwire anemometry to understand the action of the fractal-based plate on the flow and measure velocity statistics on the pipes axis. We found that as far as pressure drop recovery is concerned, it is not always necessary to choose large numbers of iteration for the fractal pattern. However, the velicity statistics can remember the order of the fractal generation over a long distance. In certain cases it would require a very long pipe to quantify the full recovery from the fractal-generated turbulent flow.

The fractional Laplacian as a limiting case of a self-similar spring model and applications to n-dimensional anomalous diffusion

AbstractWe analyze the “fractional continuum limit” and its generalization to n dimensions of a self-similar discrete spring model which we introduced recently [21]. Application of Hamilton’s (variational) principle determines in rigorous manner a self-similar and as consequence non-local Laplacian operator. In the fractional continuum limit the discrete self-similar Laplacian takes the form of the fractional Laplacian

Wave Propagation in Quasi-continuous Linear Chains with Self-similar Harmonic Interactions: Towards a Fractal Mechanics

- ( - \Delta )^{\tfrac{\alpha } {2}}

Analysis, Design, and Modeling of a Rotary Vane Engine (RVE)

with 0 < α < 2. We analyze the fundamental link of fractal vibrational features of the discrete self-similar spring model and the smooth regular ones of the corresponding fractional continuum limit model in n dimensions: We find a characteristic scaling law for the density of normal modes ∼

Lattice fractional Laplacian and its continuum limit kernel on the finite cyclic chain

\omega ^{\tfrac{{2n}} {\alpha } - 1}

A fractional generalization of the classical lattice dynamics approach

with a positive exponent

Predominant location of coronary artery atherosclerosis in the left anterior descending artery. The impact of septal perforators and the myocardial bridging effect

\tfrac{{2n}} {\alpha } - 1 > n - 1

The Role of Septal Perforators and “Myocardial Bridging Effect” in Atherosclerotic Plaque Distribution in the Coronary Artery Disease

being always greater than n−1 characterizing a regular lattice with local interparticle interactions. Furthermore, we study in this setting anomalous diffusion generated by this Laplacian which is the source of Lévi flights in n-dimensions. In the limit of “large scaled times” ∼ t/rα >> 1 we show that all distributions exhibit the same asymptotically algebraic decay ∼ t-n/α → 0 independent from the initial distribution and spatial position. This universal scaling depends only on the ratio n/α of the dimension n of the physical space and the Lévi parameter α.