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1

Numerical methods in fluid mechanics – an overview

Sobieski Wojciech, Šarler Božidar

Technical Sciences / University of Warmia and Mazury in Olsztyn

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2023

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nr 26(1)

185--218

EN

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.

2

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

Sobieski Wojciech, Trykozko Anna

Technical Sciences / University of Warmia and Mazury in Olsztyn

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2021

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nr 24(1)

83--104

EN

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.

3

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

Sobieski Wojciech, Raoof Amir, Zech Alraune

Technical Sciences / University of Warmia and Mazury in Olsztyn

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2020

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nr 23(1)

25--51

EN

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.

4

Geometry extraction from GCODE files destined for 3D printers

Kiński Wojciech, Sobieski Wojciech

Technical Sciences / University of Warmia and Mazury in Olsztyn

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2020

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nr 23(2)

115--130

EN

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.

5

Fluid flow in the impulse valve of a hydraulic ram

Sobieski Wojciech, Grygo Dariusz

Technical Sciences / University of Warmia and Mazury in Olsztyn

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2019

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nr 22(3)

205--220

EN

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.

6

Modelling heat flow in a heat storage system with the use of the Finite Volume Method

Sobieski Wojciech

Journal of Applied Computer Science

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2019

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Vol. 27, nr 1

27--49

EN

Non-stationary heat flow was analysed in a heat storage system comprising a flat multilayer structure with different parameters and thickness. Concrete was the heat storage material, and water was the transfer medium responsible for supplying and evacuating heat from the storage medium. It was assumed that the modelled heat storage system may be powered by a solar thermal collector. Data were collected over a period of 24 hours, and they were analysed separately for the heat accumulation phase and the heat recovery phase. Calculations were performed in a program developed by the author based on the Finite Volume Method (FVM). The main aim is to illustrate the basic features of the developed numerical code and to find effective methods for evaluating the applicability of the modelled structures for heat storage. Except that, in the paper the possibilities are discussed for the use of the source component of the diffusion equation to describe various phenomena of physical, chemical and biological nature. The present article was motivated by the observation that FVM is currently not applied in the process of designing heat storage systems.