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An efficient method of tortuosity estimation

Sobieski W.

Archives of Mechanics

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2022

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Vol. 74, nr 1

39--64

EN

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 pore space. Based on the obtained velocity fields, Hydraulic tortuosity and streamline tortuosity were calculated, based on the obtained velocity fields, for all considered cases. Hydraulic tortuosity was calculated with the methodology proposed by Koponen et al., whereas streamline tortuosity was determined with the use of a new iterative algorithm. Two variants of the algorithm were proposed. Additionally, the obtained results were compared with selected formulas from the literature. The study demonstrated that calculations of streamlines exiting local inlet velocity maxima are a good alternative to calculations where all possible streamlines are taken into account. Computation time was significantly shorter and estimation quality was comparable.

2

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.

3

Optimized implementation of lattice Boltzmann method in ARUZ

Jabłoński Grzegorz, Kupis Joanna

International Journal of Microelectronics and Computer Science

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2018

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Vol. 9, nr 2

79--84

EN

The paper presents the optimized implementation of the Lattice Boltzmann method on ARUZ, a massively parallel FPGA-based simulator located in Lodz, Poland. Compared to previous publications, a performance improvement of 46% has been achieved on D2Q9 lattice due to overlapping of communication with computation. The presented approach is suitable also for other cellular automata-based simulations. Extrapolation of results from the single ARUZ board suggests, that LBM simulation of 1080 × 480 lattice on 18 panels of ARUZ would reach the performance of 302 · 103 MLUPS (Million Lattice Updates per Second). This implementation has been compared to the classical supercomputer solution, giving much better power efficiency (3000 MLUPS/kW vs. 1280 MLUPS/kW, respectively).

4

Granica laminarnego przepływu wody w obsypce żwirowej studni eksploatacyjnej

Matyka M., Mądrala M.

Przegląd Geologiczny

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2017

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Vol. 65, nr 11/2

1334--1338

EN

Structural changes of aquifers, resulting from a higher velocity of water entering a screen, may occur in the zone around wells ’ screen. Well discharge rate equations assume a laminar flow and agreement with the Darcy s law. Thus, the admissible velocity of water entering the screen should not exceed a certain limit. In this research, the microstructure of water flow velocity in the well s filter pack was studied. We took a picture of the internal structure of the aquifer s pore media in an in situ undisturbed soil sample. Because of the lack of a clear definition of the characteristic length scale in the Reynolds number, we propose to use additionally n - a dimensionless value describing the distribution of kinetic energy in the system - as a criterion for changing the flow nature. We based the study on numerical simulations offluid flow in pore space. We used the Lattice-Boltzmann Method (LBM) to simulate water flow in the filtered zone. We find that in a real porous system of the filter pack with a porosity of n = 0.49, as opposed to highly porous material at n = 0.9, the values of n increase with the decreasing and increasing Reynolds number. The distribution of the velocity field in the analyzed sections also shows the formation ofprivileged waterflow paths and the formation ofvortex structures for high flow velocities.

5

Application of the Lattice Boltzmann Method to the flow past a sphere

Kajzer A., Pozorski J.

Journal of Theoretical and Applied Mechanics

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2017

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Vol. 55 nr 3

1091--1099

EN

The results of fully resolved simulations and large eddy simulations of bluff-body flows obtained by means of the Lattice Boltzmann Method (LBM) are reported. A selection of Reynolds numbers has been investigated in unsteady laminar and transient flow regimes. Computed drag coefficients of a cube have been compared with the available data for validation purposes. Then, a more detailed analysis of the flow past a sphere is presented, including also the determination of vortex shedding frequency and the resulting Strouhal numbers. Advantages and drawbacks of the chosen geometry implementation technique, so called “staircase geometry”, are discussed. For the quest of maximum computational effi- ciency, all simulations have been carried out with the use of in-house code executed on GPU.

6

The application of high level synthesis for implementation of lattice Boltzmann method in ARUZ

Jabłoński G., Kupis J.

International Journal of Microelectronics and Computer Science

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2017

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Vol. 8, nr 1

36--42

EN

The paper presents the implementation results of D2Q9 Lattice Boltzmann method on ARUZ, a massively parallel FPGA-based simulator built in Lodz, Poland in 2015, optimized for execution of the Dynamic Lattice Liquid algorithm. The results of tests on a single ARUZ board indicate, that the LBM simulation of 864 × 384 lattice on 18 panels of ARUZ would reach the performance of 206 · 103 MLUPS (Million Lattice Updates per Second).