MODIFICATION OF THE PATHFINDER ALGORITHM FOR CALCULATING GRANULAR BEDS WITH VARIOUS PARTICLE SIZE DISTRIBUTIONS

K e y w o r d s: PathFinder code, porous media, granular beds, tortuosity. A b s t r a c t This paper discusses a new approach to analyzing fluid flow through a granular bed. The analysis involves the determination of a set of geometric parameters characterizing a granular bed based on information about the location and diameter of all bed particles. The above task has been achieved with the use of the PathFinder numeric code developed by the authors. The study proposes a new algorithm for calculating the parameters of granular beds composed of spherical particles with various diameters in the PathFinder program. The algorithm has been verified with the use of independent tools and implemented in the new version of the PathFinder code. The modified algorithm's effect on flow path tortuosity has been analyzed. Path length is used to determine tortuosity, a key parameter of pore geometry that is difficult to calculate. Comparative calculations were performed in a granular bed generated by the Discrete Element Method in the PFC 3D program

Geometry extraction from GCODE files destined for 3D printers

The paper presents a method of conversion of GCODE files designed for additive manufacturing in 3D printers to a format which may be conveniently visualized. In the investigations three different 3D models were created: a) shell model (a casing); b) solid model (a gear); c) model with curvilinear elements (a screw). All these models were converted to GCODE files. Next the reverse engineering was applied and GCODE files were converted to points sets. These points represent particular locations of the print head. In the developed algorithm the linear interpolation was added to obtain intermediate points between locations of the print head for longer sections. The final part shows an attempt of applying Poisson Surface Reconstruction in order to obtain the original geometry. The main motivation to develop a new software resulted from the observation that sometimes the original solid model is no longer available, while there is a need to change some geometry details or settings before production stage

Calculating the Binary Tortuosity in DEM-Generated Granular Beds

In this paper, a methodology of calculating the tortuosity in three-dimensional granular beds saved in a form of binary geometry with the application of the A-Star Algorithm and the Path Searching Algorithm is presented. The virtual beds serving as examples are prepared with the use of the Discrete Element Method based on data of real, existing samples. The obtained results are compared with the results described in other papers (obtained by the use of the Lattice Boltzmann Method and the Path Tracking Method) as well as with the selected empirical formulas found in the literature. It was stated in the paper that the A-Star Algorithm gives values similar (but always slightly underestimated) to the values obtained via approaches based on the Lattice Boltzmann Method or the Path Tracking Method. In turn, the Path Searching Algorithm gives results in the same value range as popular empirical formulas and additionally it is approximately two times faster than the A-Star Algorithm

Fluid flow in the impulse valve of a hydraulic ram

The paper presents the results of a study investigating the equilibrium of forces acting on the closing element of the impulse valve in a water ram at the end of the acceleration stage. Acceleration is one of the three main stages in the working cycle of a water ram. In the first part of the paper, we estimated water velocity based on our earlier experimental measurements. We also calculated the minimum force required for closing the impulse valve. The second part of the paper discusses two variants of a numerical model, which was developed in ANSYS Fluent to determine the resultant hydrodynamic pressure and, consequently, the forces acting on the head of the impulse valve at the end of the acceleration stage. The main aim of this research was to verify the applicability of numerical modeling in water ram studies. The present study was motivated by the fact that Computational Fluid Dynamics is very rarely applied to water rams. In particular, we have not found any numerical studies related to the equilibrium of forces acting on the closing element of the impulse valve in a water ram

Numerical methods in fluid mechanics – an overview

The article presents in a review way the most important numerical methods used in modern fluid mechanics. The individual chapters discuss Finite Difference Method, Finite Volume Method, Lattice Boltzmann Method, Discrete Element Method and Smoothed Particle Hydrodynamics. The aim of the article is to familiarize the reader with the most important concepts, features and mathematical equations used in particular methods. The article is intended mainly for people who want to get acquainted with the current possibilities of numerical modelling in the field of broadly understood fluid mechanics. The material is intended to facilitate the decision on how to implement the planned play research

The Use of the Inverse Problem Methodology in Analysis of Fluid Flow Through Granular Beds With Non-Uniform Grain Sizes

The pressure drop during water flow through two gravel beds with 2-8 and 8-16 [mm] grain size was measured across a wide range of filtration velocities, and the optimal method for calculating the coefficients for Darcy’s law and Forchheimer’s law was selected. The laws and the experimental data were used to develop a computational program based on the Finite Element Method (FEM). The results were compared, and errors were analyzed to determine which law better describes flow data. Various methods of measuring porosity and average grain diameter, representative of the sample, were analyzed. The data were used to determine the limits of applicability of both laws. The study was motivated by the observation that computational formulas in the literature produce results that differ by several orders of magnitude, which significantly compromises their applicability. The present study is a continuation of our previous research into artificial granular materials with similarly sized particles. In our previous work, the results produced by analytical and numerical models were highly consistent with the experimental data. The aim of this study was to determine whether the inverse problem methodology can deliver equally reliable results in natural materials composed of large particles. The experimental data were presented in detail to facilitate the replication, reproduction and verification of all analyses and calculations

Time consumption in calculations of hydraulic and geometrical tortuosity in granular beds

Tortuosity is one of the most elusive parameters of porous media due to its subjective estimation. Here, we compare two approaches for obtaining the tortuosity in granular porous media to investigate their capabilities and limitations. First, we determine the hydraulic tortuosity based on the calculated components of the velocity field obtained from flow simulations using the Lattice Boltzmann Method (LBM). Second, we directly determine the geometric tortuosity by making use of the Path Tracking Method (PTM) which only requires the geometric properties of the porous medium. In both cases, we apply the same geometrical structure which is a virtually generated 3D granular bed using the discrete element method consisting of 50 particles. Our results show that the direct PTM is much faster and more precise than the indirect approach based on the calculated velocity field. Therefore, PTM may provide a tool for calculating tortuosity for large 3D granular systems where indirect methods are limited due to the required computational power and time. While LBM considers various routes across the porous media implicitly, PTM identifies them explicitly. As a result, PTM requires a statistical post-processing. As an advantage, this can provide further information than just domain scale average values

Review of numerical models of cavitating flows with the use of the homogeneous approach

The focus of research works on cavitation has changed since the 1960s; the behaviour of a single bubble is no more the area of interest for most scientists. Its place was taken by the cavitating flow considered as a whole. Many numerical models of cavitating flows came into being within the space of the last fifty years. They can be divided into two groups: multi-fluid and homogeneous (i.e., single-fluid) models. The group of homogenous models contains two subgroups: models based on transport equation and pressure based models. Several works tried to order particular approaches and presented short reviews of selected studies. However, these classifications are too rough to be treated as sufficiently accurate. The aim of this paper is to present the development paths of numerical investigations of cavitating flows with the use of homogeneous approach in order of publication year and with relatively detailed description. Each of the presented model is accompanied by examples of the application area. This review focuses not only on the list of the most significant existing models to predict sheet and cloud cavitation, but also on presenting their advantages and disadvantages. Moreover, it shows the reasons which inspired present authors to look for new ways of more accurate numerical predictions and dimensions of cavitation. The article includes also the division of source terms of presented models based on the transport equation with the use of standardized symbols