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Numerical analysis of fluid flow in a vial
Žiga Časar, 2019, magistrsko delo

Opis: 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.
Ključne besede: Lyophilization, Knudsen number, computational fluid dynamics, fluid flow, numerical modeling, slip boundary condition
Objavljeno: 09.07.2019; Ogledov: 550; Prenosov: 105
.pdf Celotno besedilo (2,66 MB)

Analytical solutions for one-dimensional consolidation in unsaturated soils considering the non-Darcy law of water flow
Jiwei Li, Huabin Wang, 2014, izvirni znanstveni članek

Opis: 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.
Ključne besede: unsaturated soil, homotopy analysis method, analytical solutions, non-Darcy law, initial and boundary conditions
Objavljeno: 14.06.2018; Ogledov: 263; Prenosov: 60
.pdf Celotno besedilo (295,39 KB)
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A new solution for shallow and deep tunnels by considering the gravitational loads
Mohammad Reza Zareifard, Ahmad Fahimifar, 2012, izvirni znanstveni članek

Opis: 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.
Ključne besede: ground-response curve, elasto-plastic analysis, boundary condition, axial symmetry, gravitational loads
Objavljeno: 13.06.2018; Ogledov: 473; Prenosov: 56
.pdf Celotno besedilo (406,96 KB)
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Double diffusive natural convection in a horizontal porous layer with the boundary domain integral method
Renata Jecl, Janja Kramer Stajnko, Leopold Škerget, 2009, izvirni znanstveni članek

Opis: We present the boundary-domain integral method, one of the numerical methods for solving the transport phenomena in porous media. The results for the case of double diffusive natural convection in a porous horizontal layer, which is fully saturated with an incompressible fluid, are obtained. Modified Navier-Stokes equations were used to describe the fluid motion in porous media in the form of conservation laws for mass, momentum, energy and species. Several results for different cases of double diffusive natural convection in a porous horizontal layer are presented and compared with some published studies in which calculations with other numerical methods were performed.
Ključne besede: porous media, boundary domain integral method, double diffusive natural convection, Darcy-Brinkman equation
Objavljeno: 06.06.2018; Ogledov: 297; Prenosov: 39
.pdf Celotno besedilo (454,56 KB)
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The use of the mesh free methods (radial basis functions) in the modeling of radionuclide migration and moving boundery value problems
Leopold Vrankar, Franc Runovc, Goran Turk, 2007, izvirni znanstveni članek

Opis: Recently, the mesh free methods (radial basis functions-RBFs) have emerged as a novel computing method in the scientific and engineering computing community. The numerical solution of partial differential equations (PDEs) has been usually obtained by finite difference methods (FDM), finite element methods (FEM) and boundary elements methods (BEM). These conventional numerical methods still have some drawbacks. For example, the construction of the mesh in two or more dimensions is a nontrivial problem. Solving PDEs using radial basis function (RBF) collocations is an attractive alternative to these traditional methods because no tedious mesh generation is required. We compare the mesh free method, which uses radial basis functions, with the traditional finite difference scheme and analytical solutions. We will present some examples of using RBFs in geostatistical analysis of radionuclide migration modeling. The advection-dispersion equation will be used in the Eulerian and Lagrangian forms. Stefan's or moving boundary value problems will also be presented. The position of the moving boundary will be simulated by the moving data centers method and level set method.
Ključne besede: mesh free methods, radial basis functions, finite difference methods, finite elemnt methods, boundary elements methods, geostatistics, Eulerian method, Lagrangian method, level set method
Objavljeno: 18.05.2018; Ogledov: 463; Prenosov: 41
.pdf Celotno besedilo (214,16 KB)
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Lagrangian particle tracking in velocity-vorticity resolved viscous flows by subdomain BEM
Jure Ravnik, Matjaž Hriberšek, Janez Lupše, 2016, izvirni znanstveni članek

Opis: A numerical study of particle motion in a cubic lid driven cavity is presented. As a computational tool, a boundary element based flow solver with a Lagrangian particle tracking algorithm is derived. Flow simulations were performed using an in-house boundary element based 3D viscous flow solver. The Lagrangian particle tracking algorithm is capable of simulation of dilute suspensions of particles in viscous flows taking into account gravity, buoyancy, drag, pressure gradient and added mass. The derived algorithm is used to simulate particle behaviour in a cellular flow field and in a lid driven cavity flow. Simulations of particle movement in a cellular flow field were used to validate the algorithm. The main goal of the paper was to numerically simulate the flow behaviour of spheres of different densities and different diameters, as experimentally observed in work of Tsorng et al.The study of slightly buoyant and non-buoyant particles in a lid driven cavity was aimed at discovering cases when particles leave the primary vortex and enter into secondary vortices, a phenomenon described in the work of Tsorng et al. A parametric study of this phenomenon was preformed. The presented computational results show excellent agreement with experiments, confirming the accuracy of the developed computational method.
Ključne besede: dispersed two phase flow, Lagrangian particle tracking, cellular flow, lid driven cavity, boundary element method
Objavljeno: 04.08.2017; Ogledov: 489; Prenosov: 296
.pdf Celotno besedilo (13,57 MB)
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On the solvability of second-order impulsive differential equations with antiperiodic boundary value conditions
Yepeng Xing, Valery Romanovski, 2008, izvirni znanstveni članek

Opis: We prove existence results for second-order impulsive differential equations with antiperiodic boundary value conditions in the presence of classical fixed point theorems. We also obtain the expression of Green's function of related linear operator in the space of piecewise continuous functions.
Ključne besede: second-order impulsive differential equations, antiperiodic boundary value conditions, Green's function
Objavljeno: 26.06.2017; Ogledov: 631; Prenosov: 313
.pdf Celotno besedilo (241,29 KB)
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Geodetic sets in graphs
Boštjan Brešar, Matjaž Kovše, Aleksandra Tepeh, 2011, samostojni znanstveni sestavek ali poglavje v monografski publikaciji

Opis: Na kratko so povzeti rezultati o geodetskih množicah v grafih. Po pregledu rezultatov iz prejšnjih raziskav se posvetimo geodetskemu številu in sorodnim invariantam v grafih. Podrobno so obravnavane geodetske množice kartezičnih produktov grafov in geodetske množice v medianskih grafih. Predstavljen je tudi algoritmični vidik in povezava z nekaterimi ostalimi koncepti iz teorije konveksnih in intervalskih struktur v grafih.
Ključne besede: matematika, teorija grafov, geodetsko število, geodetska množica, kartezični produkt, medianski graf, mejna množica, mathematics, graph theory, geodetic number, geodetic set, Cartesian product, median graph, boundary set
Objavljeno: 10.07.2015; Ogledov: 321; Prenosov: 20
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Heat diffusion in fractal geometry cooling surface
Matjaž Ramšak, Leopold Škerget, 2012, izvirni znanstveni članek

Opis: In the paper the numerical simulation of heat diffusion in the fractal geometry of och snowflake is presented using multidomain mixed Boundary Element Method. he idea and motivation of work is to improve the cooling of small electronic devices sing fractal geometry of surface similar to cooling ribs. The heat diffusion is ssumed as the only principle of heat transfer. The results are compared to the heat lux of a flat surface. The limiting case of infinite small fractal element is computed sing Richardson extrapolation.
Ključne besede: heat transfer, cooling of electronic devices, boundary element method, fractals
Objavljeno: 10.07.2015; Ogledov: 941; Prenosov: 236
.pdf Celotno besedilo (313,63 KB)
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