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1.
Fluid flow simulation with an ▫$ℋ^2$▫ -accelerated boundary-domain integral method
Jan Tibaut, Jure Ravnik, M Schanz, 2024, original scientific article

Abstract: The development of new numerical methods for fluid flow simulations is challenging but such tools may help to understand flow problems better. Here, the Boundary-Domain Integral Method is applied to simulate laminar fluid flow governed by a dimensionless velocity–vorticity formulation of the Navier–Stokes equation. The Reynolds number is chosen in all examples small enough to ensure laminar flow conditions. The false transient approach is utilized to improve stability. As all boundary element methods, the Boundary-Domain Integral Method has a quadratic complexity. Here, the ℋ2 -methodology is applied to obtain an almost linear complexity. This acceleration technique is not only applied to the boundary only part but more important to the domain related part of the formulation. The application of the ℋ2 -methodology does not allow to use the rigid body method to determine the singular integrals and the integral free term as done until now. It is shown how to apply the technique of Guigiani and Gigante to handle the strongly singular integrals in this application. Further, a parametric study shows the influence of the introduced approximation parameters. For this purpose the example of a lid driven cavity is utilized. The second example demonstrates the performance of the proposed method by simulating the Hagen–Poiseuille flow in a pipe. The third example considers the flow around a rigid cylinder to show the behavior of the method for an unstructured grid. All examples show that the proposed method results in an almost linear complexity as the mathematical analysis promisses.
Keywords: boundary-domain integral method, velocity–vorticity, adaptive cross approximation, modified helmholtz equation, Yukawa potential, fast multipole method, ℋ-structure
Published in DKUM: 28.11.2024; Views: 0; Downloads: 4
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2.
Experimental advances in nanoparticle-driven stabilization of liquid-crystalline blue phases and twist-grain boundary phases
George Cordoyiannis, Marta Lavrič, Vasileios Tzitzios, Maja Trček, Ioannis Lelidis, George Nounesis, Samo Kralj, Jan Thoen, Zdravko Kutnjak, 2021, review article

Abstract: Recent advances in experimental studies of nanoparticle-driven stabilization of chiral liquid-crystalline phases are highlighted. The stabilization is achieved via the nanoparticles’ assembly in the defect lattices of the soft liquid-crystalline hosts. This is of significant importance for understanding the interactions of nanoparticles with topological defects and for envisioned technological applications. We demonstrate that blue phases are stabilized and twist-grain boundary phases are induced by dispersing surface-functionalized CdSSe quantum dots, spherical Au nanoparticles, as well as MoS2 nanoplatelets and reduced-graphene oxide nanosheets in chiral liquid crystals. Phase diagrams are shown based on calorimetric and optical measurements. Our findings related to the role of the nanoparticle core composition, size, shape, and surface coating on the stabilization effect are presented, followed by an overview of and comparison with other related studies in the literature. Moreover, the key points of the underlying mechanisms are summarized and prospects in the field are briefly discussed.
Keywords: liquid crystals, nanoparticles, quantum dots, reduced-graphene oxide, calorimetry, microscopy, blue phases, twist-grain boundary phases, disclination lines, screw dislocations
Published in DKUM: 09.08.2024; Views: 97; Downloads: 9
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3.
A coupled point particle two-phase heat and mass transfer model for dispersed flows based on Boundary Element Methods
Timi Gomboc, Matej Zadravec, Jure Ravnik, Matjaž Hriberšek, 2024, published scientific conference contribution

Abstract: In dispersed multiphase flow processes we encounter coupled heat, mass and momentum transfer between the disoersed and the continuous phase. In the context of the subdomain Boundary Domain Integral Method (BDIM) solution of the Navier-Stokes equations a two-way coupling model is presented based on the use of the elliptic fundamental solution and the Dirac delta function properties which leads to accurate evaluation of the heat and mass point particle source impacts on the continuous (air) phase. In addition, the two-phase flow case under consideration is extended to the case of porous spherical particle drying with internal moving drying front, which is solved by the Boundary Element Method (BEM).
Keywords: heat transfer, mass transfer, Boundary Element Methods
Published in DKUM: 01.07.2024; Views: 113; Downloads: 15
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4.
Vial wall effect on freeze-drying speed
Matjaž Ramšak, Matjaž Hriberšek, 2024, original scientific article

Abstract: The vial wall thermal conductivity and thickness effect on freeze-drying speed is simulated. A 2D axisymmetric numerical simulation of Mannitol freeze-drying is employed using the boundary element method. The originality of the presented approach lies in the simulation of heat transfer in the vial walls as an additional computational domain in contrast to the typical methodology without a vial wall. The numerical model was validated using our measurements and the measurements from the literature. Increasing the glass vial thickness from 1 mm to 2 mm has been found as the major factor in primary drying time, increasing the gravimetrical Kv up to 20 % for all the simulated chamber pressures. The effect of thermal conductivity was simulated using a polymer and aluminium vial replacing the standard glass vial of the same thickness. The polymer vial‘s decreased Kv value is 5.6 % at a low chamber pressure of 50 mTorr, and 12.2 % at 400 mTorr, which is in excellent agreement with the experiment. Using higher conductivity materials, for example, aluminium, only 3.7 % and 2.3 % Kv increase were computed for low and high chamber pressures respectively.
Keywords: freeze-drying, lyophilization speedup, vial heat conductivity, vial wall thickness, boundary element method
Published in DKUM: 16.04.2024; Views: 264; Downloads: 28
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5.
6.
Fractal geometry as an effective heat sink
Matjaž Ramšak, 2022, original scientific article

Abstract: "How long is the coast of Britain?" was the question stated by Mandelbrot. Using smaller and smaller rulers the coast length limits to infinity. If this logic is applied to the fractal heat sink geometry, infinite cooling capacity should be obtained using fractals with mathematically infinite surface area. The aim of this article is to check this idea using Richardson extrapolation of numerical simulation results varying the fractal element length from one to zero. As expected, the extrapolated heat flux has a noninfinite limit. The presented fractal heat sink geometry is non-competitive to the straight fins.
Keywords: fractal heat sink, LED cooling, CPU cooling, conjugate heat transfer, laminar flow, boundary element method, Koch snowflake
Published in DKUM: 14.07.2023; Views: 653; Downloads: 17
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7.
Validation of boundary element method for assessment of weld joints accounting for notch stress : magistrsko delo
Rok Skerbiš, 2022, master's thesis

Abstract: Robust, automated mesh generation on arbitrary weld joint geometries, using finite element method (FEM) is a problematic task. It was previously discovered, that an arbitrary weld joint geometry can be parameterized inside a CAD environment [1], however when it comes to domain discretization and boundary conditions assignment, the parameterized approach becomes too demanding inside FEM. This results in long FEM model preparation times and sometimes in problems with the parametric model itself, which leads to a need for an additional numerical method - boundary element method (BEM), which overcomes this issue and is beneficial in this case. BEM is a numerical method, that in addition to other applications finds a use in the elasto-mechanic problems, where the only concern is the boundary of the considered geometric domain. Since notch stress calculations of weld joints fall into this category, their calculation can be carried out with it. Since there is not much available information on whether or not such calculations are a suitable alternative for the currently used FEM, this thesis had to be confirmed through a structured and step by step procedure. First, a notch mesh quality study has been made, then other entities followed. It was discovered that BEM is applicable to the problem and capable of calculating results with sufficient quality. Furthermore, the parameter driven approach and automated calculation provide for additional advantageous potentials.
Keywords: weld joint, boundary element method, finite element method, spatial discretization, notch stress
Published in DKUM: 02.11.2022; Views: 549; Downloads: 0
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8.
Numerical analysis of fluid flow in a vial : [master thesis]
Žiga Časar, 2019, master's thesis

Abstract: Lyophilization or freeze-drying is a widely used process in the pharmaceutical and food industry. In the process the solvent will be removed under extreme conditions of low temperature and low system pressures, whereby sublimation happens, the transition from the solid phase to the gas phase, with skipping the liquid phase, which happens bellow the triple point. This study focuses on numerical modeling at the start of the process, the so called primary drying. For this stage the highest mass flow rates of vapor are typical, since the driving force of the process is the pressure difference between the sublimation front and surrounding area. In this stage the non-bonded solvent is removed. Because of the extreme conditions the typical computational fluid dynamics approach is not suitable anymore and has to be corrected. One way to do this is to use additional models for fluid behavior at the solid wall. The study focuses on the influence of different boundary conditions on the solid wall, No-Slip, Free Slip and Maxwell Slip, and their effect on fluid flow inside the vial. A quantitative and qualitative comparison of the results is presented.
Keywords: Lyophilization, Knudsen number, computational fluid dynamics, fluid flow, numerical modeling, slip boundary condition
Published in DKUM: 09.07.2019; Views: 1570; Downloads: 203
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9.
Analytical solutions for one-dimensional consolidation in unsaturated soils considering the non-Darcy law of water flow
Jiwei Li, Huabin Wang, 2014, original scientific article

Abstract: Analytical solutions were derived for the non-linear, one-dimensional consolidation equations for unsaturated soils. The governing equations with a non-homogeneous mixed-boundary condition were presented, in which the water flow was assumed to be governed by a non-Darcy law, whereas the air flow followed the Darcy law. The non-Darcy law was actually the non-linear, flux-gradients relationship. The consolidation equations were thus present in a strong, non-linear way. In order to analytically solve the equation, a homotopy analysis method (HAM) was introduced in the study, which is an analytical technique for nonlinear problems. Firstly, a governing equation in a dimensionless form was derived for a one-dimensional consolidation under unsaturated soils. The method was then used for a mapping technique to transfer the original nonlinear differential equations to a number of linear differential equations. These differential equations were independent with respect to any small parameters, and were convenient for controlling the convergence region. After this transferring, a series solution to the equations was then obtained using the HAM by selecting the linear operator and the auxiliary parameters. Meanwhile, comparisons between the analytical solutions and the results of the finite-difference method indicate that the analytical solution is more efficient. Furthermore, our solutions indicate that the dissipation of air pressure is much faster than that of water pressure, and the values for the threshold gradient I have obvious effects on the dissipation values of the excess pore-water pressure, but no significant effect on that of the excess pore-air pressure.
Keywords: unsaturated soil, homotopy analysis method, analytical solutions, non-Darcy law, initial and boundary conditions
Published in DKUM: 14.06.2018; Views: 1471; Downloads: 112
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10.
A new solution for shallow and deep tunnels by considering the gravitational loads
Mohammad Reza Zareifard, Ahmad Fahimifar, 2012, original scientific article

Abstract: A new, elasto-plastic, analytical-numerical solution, considering the axial-symmetry condition, for a circular tunnel excavated in a strain-softening and Hoek–Brown rock mass is proposed. To examine the effect of initial stress variations, and also the boundary conditions at the ground surface, the formulations are derived for different directions around the tunnel. Furthermore, the effect of the weight of the plastic zone is taken into account in this regard. As the derived differential equations have no explicit analytical solutions for the plastic zone, the finite-difference method (FDM) is used in this study. On the other hand, analytical expressions are derived for the elastic zone. Several illustrative examples are given to demonstrate the performance of the proposed solution, and to examine the effect of various boundary conditions. It is concluded that the classic solutions, based on the hydrostatic far-field stress, and neglecting the effect of the boundary conditions at the ground surface, give applicable results for a wide range of practical problems. However, ignoring the weight of the plastic zone in the analyses can lead to large errors in the calculations.
Keywords: ground-response curve, elasto-plastic analysis, boundary condition, axial symmetry, gravitational loads
Published in DKUM: 13.06.2018; Views: 1214; Downloads: 199
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