Wojciech Sobieski

University of Warmia and Mazury in Olsztyn · Department of Mechanics and Basic Machine Design

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 c...

The paper presents a comparative analysis of tortuosity calculations in two types of 2D random geometries: with non-overlapping circles and with overlapping squares. Both geometries were converted to binary geometries with different resolution. Next, simulations involving the Lattice Boltzmann Method were performed to obtain velocity fields in a po...

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 paper describes the so-called Waterfall Algorithm, which may be used to calculate a set of parameters characterising the spatial structure of granular porous media, such as shift ratio, collision density ratio, consolidation ratio, path length and minimum tortuosity. The study is performed for 1800 different two-dimensional random pore structur...

The article presents the results of experimental studies investigating the conditions during the filling and start-up of a water ram based on changes in pressure in the working zone and the pressure zone. The test stand is described, and measurements are conducted in three configurations: (a) when the system is filled with water (with the delivery...

Prezentacja dotyczy podstaw obsługi pakietu OpenFOAM. W kolejnych punktach omówiono dokładnie przykład „Cavity”, dostępny w katalogu przykładów bezpośrednio po zainstalowaniu programu. Poszczególne elementy opatrzono komentarzami i wyjaśnieniami.

Prezentacja dotyczy podstaw obsługi pakietu OpenFOAM. W kolejnych punktach omówiono przeróbki przykładu „Cavity” (zobacz pierwsza prezentacja), mające sprawdzić, czy wszystkie elementy tworzenia modelu zostały zrozumiane.

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 sam...

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...

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 fro...

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 e...

In the article, the tortuosity in randomly generated 2D pore structures with various porosity and size of a structural element forming the solid body is investigated. Two different numerical methods are applied: the Lattice Boltzmann Method and the self-developed algorithm, the so-called Path Searching Algorithm. The first method serves to calculat...

The article proposes functions linking the standard deviation of a particle distribution in a porous bed consisting of spherical particles with various parameters characterising the spatial structure of the bed. The porosity, the inner surface, the specific surface and the geometrical tortuosity were analysed. In the first stage, a set of virtual b...

A short presentation of the so-called Path Tracking Method developed by me in 2009.

Tortuosity is one of the most elusive parameters of porous media. The fundamental question is whether it may be computed from the geometry only or the transport equations must be solved first. Elimination of the transport equations would significantly decrease the computation time and memory consumption and thus allow investigating larger samples....

Prezentacja zawiera podstawowe informacje o Metodzie Gazu Sieciowego oraz opis autorskiej implementacji tej metody w przestrzeni 2D w języku Fortran.

The paper presents details of discretisation of a thermal diffusion equation in one-dimensional space in terms of the Finite Volume Method. In the following sections, the method of space discretisation is discussed along with the approximation of a spatial derivative, matrix notation of a system of equations, special cases, approximation of three t...

The paper presents the results of a fractal analysis of the cross-sections of a porous mineral deposit consisting of spherical elements which formed a spatial system with varying porosity (0.4 to 0.95). The virtual deposit was generated using the Discrete Element Method in the YADE code by means of the so-called Radius Expansion Method. The fractal...

In the paper, functions describing different porosity-tortuosity relations were collected, and then the tortuosity values were calculated for a one granular bed consisting of spherical particles with normal distribution of diameters. Information about the bed porosity and particle sizes was obtained from measurements conducted for an artificial gra...

This paper presents the results of experimental research of the phenomena occurring in water ram during a single cycle of its operation. Apart from a brief introduction and description of the test stand and data recording system, the work includes a broad interpretation of the obtained results. Based on the pressure waveforms recorded in two charac...

A new methodology for modeling fluid flow through porous beds consisting of spherical or quasi-spherical particles is proposed. The proposed approach integrates the Discrete Element Method (DEM) with Computational Fluid Dynamics (CFD) techniques. A porous bed was first modeled using the DEM to quantify its pore structure, including the number, coor...

The article is related to a computational method of obtaining the geometric tortuosity in granular beds, i.e. polydisperse beds consisting of spherical or quasi-spherical particles, freely distributed in the 3D space. The main aim is to show a new way of calculating two-dimensional tortuosity distribution in the plane perpendicular to the chosen di...

This paper presents the results of fractal analysis of a set of virtual porous beds with a porosity ranging from 0.4 to 0.95 (Fig. 1). These beds were generated by the so-called growing particle method with the use of the Discrete Element Method, in a space of dimensions l • l • 2l, where l is the characteristic dimension of the computational space...

In the article, a new way for obtaining a set of geometrical parameters of granular porous beds is presented, if the data on the locations and sizes of all particles is available. The input data were prepared with the use of Discrete Element Method. The other way for acquiring the input data may be the application of Computed Tomography (CT) and Im...

The content of this article is a direct continuation of the prior experimental works on the topic of cloud cavitation in Venturis. The results of the experimental tests were used to create a set of characteristics for three types of Venturis. The article has two aims: 1) verification of the similarity between the characteristics obtained and report...

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 tw...

This article presents results of the experimental measurements of the cavitation phenomena in a Venturi tube with water as the working medium. Three variants of such tube were tested. Angles of converging and diverging sections are equal to 45o and 45o, 30o and 60o, 45o and 60o, respectively. In every case the throat diameter is equal to 3 mm and t...

The comprehensive picture of cavitation phenomenon in a small venturi is obtained through a comparison of the results of numerical simulations and experimental measurements. The experimental data give information about the intensity of cavitation cloud at specified cross-sections behind the right edge of cavitation inducer. The evaluation of vapour...

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 b...

Streszczenie: W artykule przedstawiono rozważania dotyczące opływu liniowej palisady profili kołowych powietrzem przy zmiennej prędkości przepływu. Pokazano prostą i praktyczną metodę określania liczby Strouhala, bez konieczności wykonywania kosztownych eksperymentów. Po wyznaczeniu liczby Strouhala dla jednej prędkości, można ją następnie wykorzys...

W artykule przedstawiono szczegółowo zasadę działania urządzenia zwanego taranem wodnym oraz omówiono etapy jego pracy w odniesieniu do zjawiska uderzenia hydraulicznego, stanowiącego podstawę działania tego typu urządzeń. W poszczególnych punktach opisano historię taranów wodnych, klasyczną teorię uderzenia hydraulicznego opracowaną w roku 1889 pr...

Modeling of real physical processes by numerical methods is highly time-consuming and requires significant computational capacity. In some cases, tens or even hundreds of hours of highpower computing are needed to virtually model a real process that lasts one second. Processes that take many hours, such as drying, pose an even greater challenge. Th...

The results of a numerical simulation of a spouted bed grain dryer based on the Eulerian Multiphase Model are presented. The influence of various model parameters on the height of the fountain forming in the drying chamber was analyzed. The following computer model parameters were considered: air inlet velocity, grain size and density, and the lowe...

This article presents a numerical method for determining tortuosity in porous beds consisting of randomly packed spherical particles. The calculation of tortuosity is carried out in two steps. In the first step, the spacial arrangement of particles in the porous bed is determined by using the discrete element method (DEM). Specifically, a commercia...

Forchheimer’s equation, considered to be a nonlinear extension of the linear Darcy’s law, applies to a broader range of velocities for flows through porous media. In this article, we examine sensitivity of the Forchheimer model to permeability κ and a nonlinear coefficient β, using both experimental and computational data for validation. In additio...

This article reviews the formulas determining the drag coefficient of spherical particles moving in a fluid system in the context of numerical modeling of spouted bed grain dryers. The study describes several formulas that have been implemented in code Fluent 6.3, in a simulation model of a spouted bed based on the Eulerian multiphase model. The ar...

The article presents the derivation of the basic balance equations in form characteristic of the Finite Volume Method. In the following sections the origin of the balance equation of momentum, mass and energy is presented. Next, the conservation equations in vector form are described. The Finite Volume Method is used in Computational Fluid Mechanic...

The paper proposes a new concept to use the diffusion equation for heat flow estimation in a composting process. Only general ideas are described , without the full mathematical model and without experiments. The lack of the detailed description stems from the fact that such an approach was not (as it seems) used earlier, and the details are to be...

This article discusses the key aspects of developing a simulation model of a spouted bed grain dryer for an analysis of fluid dynamics. The following aspects have been analyzed: selection of computational space, type of geometry and computational grid, configuration of the mathematical model (based on the Eulerian multiphase model) through the sele...

The article presents two mathematical models designed for the numerical modeling of fluid flow through stationary and non-stationary porous beds, so called Porous Media Model and Eulerian Multiphase Model. After a brief description, both models are illustrated with several examples of their use. All examples were made in the package ANSYS Fluent. A...

We propose an algorithm for upscaling of flow with inertia within a multiscale framework ranging from porescale (microscale) to lab scale (mesoscale). In particular, we solve Navier-Stokes equations over complex pore geometries and average their solutions to get flow parameters at mesoscale. For periodic geometries, this is exactly the idea of homo...

This article presents the concept of applying numerical models for the purpose of validating experimental results. Validation may apply to the values obtained directly from experiments or the follow-up methods of data processing. The discussed concept is illustrated by sample numerical calculations of heat flow through a single-layer wall. The stud...

Raport zawiera opis prac wykonanych podczas tworzenia programu komputerowego służącego do obliczania długości drogi płynu w ośrodku porowatym składających się ze sfer o znanych średnicach i położeniu. W raporcie przedstawiono wyjaśnienie najważniejszych pojęć, rozważania dotyczące sposobu rozwiązania problemu oraz liczne wątki związane z implementa...

The report describes the process of developing a computer program for calculating tortuosity in a porous medium consisting of spheres with a known diameter and position. It explains the key concepts, possible solutions to the problem and various issues related to the implementation of the developed method. Specific problems are described in success...

This article presents the results of spouted bed grain dryer simulation tests where barley grain was the working medium and analyzes the influence of the model describing momentum exchange between components of the fluid–solid type mix on the dynamics of the fluidized bed and height of the fountain characteristic for that type of devices. The Euler...

This article presents considerations pertaining to two aspects of numerical modeling of fluid-solid type systems based on the Gidaspow drag model (key part of the Eulerian multiphase model). The first aspect pertains to the so-called switch function; the characteristics of this function are generalized in the article, new computation formulas are g...

The article presents a computer model of an actual spouted-bed grain dryer, which was experimentally verified as far as the bed dynamics are concerned at both qualitative and quantitative levels. Following verification, a study concerning the response of the simulation model to changes in values of its parameters was carried out. As a consequence,...

The article presents results of numerical studies based on the Finite Volumes Method and concerning determination of the computer model parameters influence on the fountain height in the spouted bed grain dryer. The paper proposes the so-called sensitivity coefficient for determining the model sensitivity level to changes in specific parameters des...

A study was performed to determine the drying characteristics and quality of barley grain dried in a laboratory scale spouted-bed dryer at 30, 35, 40, and 45°C and an inlet air velocity of 23 m/s−1, and in an IR-convection dryer under an infrared radiation intensity of 0.048, 0.061, 0.073, and 0.107 W cm−2 at an air velocity of 0.5 m/s−1. The resul...

The paper presents a mathematical model of three-component flow of the liquid-liquid vapor-gas type including the mass exchange between the liquid and its vapor. The model is implemented in the Multi Flower 2D calculation package and used for computer simulations of flows with cavitation. An algorithm for model implementation, basic tests and an ex...

The paper presents the results of computer simulations carried out on a spouted bed. The sensitivity of the Eulerian Multiphase Model to changes in the parameters of a computer model was analyzed. The aim of this work was to develop a database that would contribute to achieving quantitative conformity of the results of numerical calculations to exp...

The paper describes results of a numerical simulations of air flow in a turned off, 2D channel with the plain nozzle. Simulations are based on an earlier experiment, carried out by Dyban, Mazur and Epik (1971). In the featured channel it has been observed several bifurcation forms, depending on the flow velocity and geometry relations. Basing on th...

The paper describes a numerical attempt to model the operation of an air-air ejector by means of a commercial numerical code. The obtained results are compared with the results of a laboratory experiment – particularly in relation to the diffuser of the modelled ejector. The substantial discrepancies between the performance characteristics obtained...

Due to limitations of the state-of-the-art turbulent combustion models, and insufficient information about the inlet and boundary conditions required for the CFD analysis of engine combustors an original approach has been formulated at the Thermo-Chemical Power Department. We have combined our in-house code COM-GAS based on 0D modelling of a whole...