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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 v DKUM: 04.08.2017; Ogledov: 915; Prenosov: 365
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Opis: This paper presents a mixed boundary element formulation of the boundary domain integral method (BDIM) for solving diffusion-convective transport problems. The basic idea of mixed elements is the use of a continuos interpolation polynomial for conservative field function approximation and a discontinuous interpolation polynomial for its normal derivative along the boundary element. In this way, the advantages of continuous field function approximation are retained and its conservation is preserved while the normal flux values are approximated by interpolation nodal points with a uniquely defined normal direction. Due to the use of mixed boundary elements, the final discretized matrix system is overdetermined and a special solver based on the least squares method is applied. Driven cavity, natural and forced convection in a closed cavity are studied. Driven caviaty results at Re=100, 400 and 1000 agree better with the benchmark solution than Finite Element Method of Finite Volume Method results for the same grid density with 21 x 21 degrees of freedom. The average Nusselt number values for natural convection ▫$10^3$▫▫$le$▫Ra▫$le$▫▫$10^6$▫ agree better than 0.1% with benchmark solutions for maximal calculated grid desities 61 x 61 degrees for freedom.
Ključne besede: fluid mechanics, incompressible fluid, laminar flow, velocity vorticity formulation, boundary element method, mixed boundary elements
Objavljeno v DKUM: 01.06.2012; Ogledov: 1828; Prenosov: 91
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Opis: The main purpose of this work is to present the use of the Boundary Element Method (BEM) in the analysis of the natural convection in the square porous cavity saturated by the non-Newtonian fluid. The results of hydrodynamic and heat transfer evaluations are reported for the configuration in which the enclosure is heated from a side wall while the horizontal walls are insulated.The flow in the porous medium is modelled using the modified Brinkman extended Darcy model taking into account the non-Darcy viscous effects. The governing equations are transformed by the velocity-vorticity variables formulation enabling the computation scheme to be partitioned into kinematic and kinetic parts. To analyse the effects of the available non-Newtonian viscosity and to evaluate the presented approach, the power law model for shear thinning fluids (n<1), for shear thickening fluids (n>1) and in the limit for the Newtonian fluids (n=1) is considered. Numerical model is tested also for the Carreau model adequate for many non-Newtonian fluids. Solutions for the flow and temperature fields and Nusselt numbers are obtainedin terms of a modified Rayleigh number Ra*, Darcy number Da, and the non-Newtonian model parameters. The agreement between the results obtained with finite difference method is very good indicating that BEM can be efficiently used for solving transport phenomena in saturated porous medium.
Ključne besede: natural convection, non-Newtonian fluid, porous medium, cavity flow, boundary element method, boundary domain integral method
Objavljeno v DKUM: 01.06.2012; Ogledov: 1530; Prenosov: 91
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Opis: A wavelet matrix compression technique was used to solve systems of linear equations resulting from BEM applied to fluid dynamics. The governing equations were written in velocity-vorticity formulation and solutions of the resulting systems of equations were obtained with and without wavelet matrix compression. A modification of the Haar wavelet transform, which can transformvectors of any size, is proposed. The threshold, used for making fully populated matrices sparse, was written as a product of a user defined factor and the average value of absolute matrix elements values. Numerical tests were performed to assert, that the error caused by wavelet compression depends linearly on the factor , while the dependence of the error on the share of thresholded elements in the system matrix is highly non-linear. The results also showed that the increasing non-linearity (higher Ra and Re numbervalues) limits the extent of compression. On the other hand, higher meshdensity enables higher compression ratios.
Ključne besede: fluid mechanics, computational fluid dynamics, boundary element method, wavelet transform, linear systems of equations, velocity vorticity formulation, driven cavity, natural convection, system matrix compression
Objavljeno v DKUM: 01.06.2012; Ogledov: 1843; Prenosov: 91
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Opis: This paper discusses the problem of wave reflection from the fictitious boundary, with particular regard to the higher harmonic modes. This problem occurs when solving the wave equation in exterior domains using an asymptotic local low-order Dirichlet-to-Neumann (DtN) map for computational procedures applied to a finite domain. We demonstrate that the amplitudes of the reflected fictitious harmonics depend on the wave number, the location of the fictitious boundary, as well as on the local DtN operator used in the computations. Moreover, we show that a constant value of the asymptotic local low-order operator cannot sufficiently eliminate the amplitudes of all reflected waves, and that the results are poor especially for higher harmonics. We propose therefore an iterative method, which varies the tangential dependence of the local operator in each computational step. We only discuss some logical and interesting choices for the operators although this method permits several possibilities on how to vary the operator. The method is simple to apply and the presented examples demonstrate that the accuracy is considerably improved by iterations.
Ključne besede: wave motion, infinite domains, fictitious boundary, radiation condition, finite element method, Dirichlet-to-Neumann map
Objavljeno v DKUM: 01.06.2012; Ogledov: 1518; Prenosov: 79
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