Volume 8
Issue 4
Agricultural Engineering
JOURNAL OF
POLISH
AGRICULTURAL
UNIVERSITIES
Available Online: http://www.ejpau.media.pl/volume8/issue4/abs-78.html
USING THE METHODS OF GEOSTATIC FUNCTION AND MONTE CARLO IN ESTIMATING THE RANDOMNESS OF DISTRIBUTION OF A TWO-COMPONENT GRANULAR MIXTURE DURING THE FLOW MIXING
Jolanta Królczyk, Marek Tukiendorf
Department of Agriculture and Forest Technology,
Opole University of Technology, Poland
ABSTRACT
Mixing granular materials has a signficant importance in a lot of industrial branches such as food and agricultural ones. For that reason, it is of extreme importance to get to know the phenomena determining this prcoess. Mixing non-uniform, two-component grnaular structures is a complex phenomenon with a number of factors affecting its course. Obtaining a uniform mixture is dependent on the properties of the elements, type of the mixer as well as the conditions in which the process takes place. The granular structure used in the studies was that of lead – mustard with the relation of diameters d1/d2 = 1.55 and the relation of density ρ1/ρ2 = 8.25. The proportion of volume was 1:9. The components were mixed using the funnel-flow method in a laboratory model of flow mixer. The focus of interest was distribution of tracer (lead) on the surface of particular cross-sections of the mixer obtained by means of successive flows. The first step in estimating the randomness of the quality of the tracer was to use a computer image analysis. An analysing program PATAN was used to this aim, on the basis of which the coefficients of the location of the tracer’s grains were determined on the surface of the container’s segments. The coefficients were next used to analyze the spatial distribution given in program S-PLUS. The estimation of the randomness of distribution of a two-component granular mixture was performed on the basis of geostatic function G(y) and Monte Carlo method. The paper attempts to adapt these methods in the estimation of the share of randomness of the tracer’s distribution. All photographed cross-sections were subjected to analysis. The method based on geostatic function G(y) used for the estimation of relations between the points is based on the distance to the closest neighbour. Monte Carlo method was used paralelly. After a simulation of the coefficients of the tracer’s location and with a definite number of simulations, two lines of reference were obtained: maximum and minimum ones, which were then compared with the line formed on the basis of empirical data. Basing on the suggested statistical method, the purpose of the studies was to determine whether the mixing process is dependent on the properties of the mixed materials or it is a purely random process where the movement of grains is only accidental. It was found out that for the studied structure this process is mainly dependent on the properties of the components. This is testified to by the graphds obtained by means of function G(y) and Monte Carlo method. However, one should not neglect random events in the movement of grains, which is shown in the limits.
Key words: granular materials, granular mixture, geostatic function, Monte Carlo method, computer image analysis.
Jolanta Królczyk
Department of Agriculture and Forest Technology,
Opole University of Technology, Poland
5 Mikołajczyka Street, 45-271 Opole, Poland
Phone: (+48) 77 400 62 64
email: j.krolczyk@po.opole.pl
Marek Tukiendorf
Department of Agriculture and Forest Technology,
Opole University of Technology, Poland
5 Mikołajczyka Street, 45-271 Opole, Poland
Phone: (+48) 77 400 62 64
email: m.tukiendorf@po.opole.pl
Responses to this article, comments are invited and should be submitted within three months of the publication of the article. If accepted for publication, they will be published in the chapter headed 'Discussions' and hyperlinked to the article.