In this study, a numerical investigation of the effect of different magnetic fields on ferrofluid... more In this study, a numerical investigation of the effect of different magnetic fields on ferrofluid-fluid mixing processes in a two-dimensional microchannel is performed An improved version of smoothed particle hydrodynamics, SPH, by shifting particle algorithm and dummy particle boundary condition, is implemented to solve numerical continuity, ferrohydrodynamics-based momentum and mass transfer equations. SPH is formulated through the irregular arrangement of the nodes where the fields are approximated using the fifth-order Wendland kernel function. After validating the computational approach, the influence of the number (from one to three) of parallel electrical wires positioned perpendicular to the microchannel on the mixing efficiency is studied for the first time. It has originally been found that the mixing efficiency highly non-linearly depends on the Reynolds number and the number of electrical wires. For Re ≤ 20 the mixing efficiency is almost the same for two and three elect...
Numerical modeling is the approach used most often for studying and optimizing the molten steel f... more Numerical modeling is the approach used most often for studying and optimizing the molten steel flow in a continuous casting mold. The selection of the physical model might very much influence such studies. Hence, it is paramount to choose a proper model. In this work, the numerical results of four turbulence models are compared to the experimental results of the water model of continuous casting of steel billets using a single SEN port in a downward vertical orientation. Experimental results were obtained with a 2D PIV (Particle Image Velocimetry) system with measurements taken at various cut planes. Only hydrodynamic effects without solidification are considered. The turbulence is modeled using the RANS (Realizable k-ε, SST k-ω), hybrid RANS/Scale Resolved (SAS), and Scale Resolved approach (LES). The models are numerically solved by the finite volume method, with volume of fluid treatment at the free interface. The geometry, boundary conditions, and material properties were entir...
This paper describes a primitive variable boundary integral equation solution of the free boundar... more This paper describes a primitive variable boundary integral equation solution of the free boundary problem arising in the steady natural convection of the incompressible Newtonian solid-liquid phase change material. Solution of the coupled mass, momentum, and energy equations in two-dimensions is structured by the fundamental solution of the Laplace equation, straight line geometry and discontinuous linear field boundary elements. The involved domain integrals are treated through the dual reciprocity transformation based on the scaled augmented thin plate splines.
A new one-domain dual reciprocity boundary integral method technique for solving one-phase contin... more A new one-domain dual reciprocity boundary integral method technique for solving one-phase continuum formulation of the convective-diffusive energy equation as appears when treating energy transport in solid-liquid phase change systems is described. Laplace equation fundamental solution weighting, straight line geometry and constant field shape functions on the boundary, Crank-Nicolson time discretization and thin plate splines for transforming the domain integrals into a finite series of boundary integrals are employed. Iterations over the timestep are based on the Voller-Swaminathan scheme, upgraded to cope with the convective term. The technique could be applied to a wide range of solid-liquid phase change problems where finite volume or finite element solvers have been almost exclusively used in the past.
In this paper, a heat transfer problem of continuous casting is solved by two BEM approaches, i.e... more In this paper, a heat transfer problem of continuous casting is solved by two BEM approaches, i.e. front tracking and fixed grid with dual reciprocity. Both techniques are compared and critically evaluated by solving two numerical examples consisting of determining the temperature field and location of phase change front. Good accuracy has been observed.
This paper describes the solution to transient incompressible two-dimensional Navier-Stokes equat... more This paper describes the solution to transient incompressible two-dimensional Navier-Stokes equations in primitive variables by the dual reciprocity boundary element method. The coupled set of mass and momentum equations is structured by the fundamental solution of the Laplace equation. The boundary is discretized into simplest boundary elements with constant field and straight line geometry. Numerical examples include convergence and accuracy studies for the classical driven cavity problem at Re = 100. The performance of thirteen different global approximation functions, based on conicals, thin plate splines, multiquadrics and Gaussians is shown, assessed by comparison with the Ghia-Ghia-Shin finite difference reference solution.
The purpose of the present paper is to predict the grain size of steel during the hot-rolling pro... more The purpose of the present paper is to predict the grain size of steel during the hot-rolling process. The basis represents a macroscopic simulation system that can cope with temperatures, stresses and strains of steel in a complete continuous rolling mill, including reversible pre-rolling and finishing rolling with several tenths of rolling passes. The grain size models, newly introduced in the present paper, are one-way coupled to the macro-scale calculations performed with the slice model assumption. Macroscale solution is based on a novel radial basis function collocation method. This numerical method is truly meshless by involving the space discretization in arbitrarily distributed nodes without meshing. A new efficient node generation algorithm is implemented in the present paper and demonstrated for irregular domains of the slice as they appear in different rolling passes. Multiple grain size prediction models are considered. Grain size prediction models are based on empirica...
In this work a rolling simulation system has been developed for rolling schedules which consists ... more In this work a rolling simulation system has been developed for rolling schedules which consists of multiple reversing rolling mills. A slice model approach is applied where the position of a slice can only be determined by considering total deformation. Each slice is parallel to each other and perpendicular to the rolling direction. The solution of coupled thermal and mechanical models over each slice, at a given time and position, are achieved by a novel meshless Local Radial Basis Function Collocation Method (LRBFCM). Mechanical material model obeys ideal plastic flow rule defined by Von Mises. Unknown fields over the slices are interpolated by a certain number of collocation points distributed over the physical domain and its boundary. A system of equations is solved for each collocation point considering its local neighbouring points in the range between 5 and 7. A non-linear system of equations is solved by direct iteration. Groove geometries of each roll are implemented in a ...
International Journal of Numerical Methods for Heat & Fluid Flow, 2004
This paper describes the solution of a steady‐state natural convection problem in porous media by... more This paper describes the solution of a steady‐state natural convection problem in porous media by the radial basis function collocation method (RBFCM). This mesh‐free (polygon‐free) numerical method is for a coupled set of mass, momentum, and energy equations in two dimensions structured by the Hardy's multiquadrics with different shape parameter and different order of polynomial augmentation. The solution is formulated in primitive variables and involves iterative treatment of coupled pressure, velocity, pressure correction, velocity correction, and energy equations. Numerical examples include convergence studies with different collocation point density and arrangements for a two‐dimensional differentially heated rectangular cavity problem at filtration Rayleigh numbers Ra*=25, 50 and 100, and aspect ratios A=1/2, 1, and 2. The solution is assessed by comparison with reference results of the fine‐mesh finite volume method in terms of mid‐plane velocity components, mid‐plane and...
In this study, a numerical investigation of the effect of different magnetic fields on ferrofluid... more In this study, a numerical investigation of the effect of different magnetic fields on ferrofluid-fluid mixing processes in a two-dimensional microchannel is performed An improved version of smoothed particle hydrodynamics, SPH, by shifting particle algorithm and dummy particle boundary condition, is implemented to solve numerical continuity, ferrohydrodynamics-based momentum and mass transfer equations. SPH is formulated through the irregular arrangement of the nodes where the fields are approximated using the fifth-order Wendland kernel function. After validating the computational approach, the influence of the number (from one to three) of parallel electrical wires positioned perpendicular to the microchannel on the mixing efficiency is studied for the first time. It has originally been found that the mixing efficiency highly non-linearly depends on the Reynolds number and the number of electrical wires. For Re ≤ 20 the mixing efficiency is almost the same for two and three elect...
Numerical modeling is the approach used most often for studying and optimizing the molten steel f... more Numerical modeling is the approach used most often for studying and optimizing the molten steel flow in a continuous casting mold. The selection of the physical model might very much influence such studies. Hence, it is paramount to choose a proper model. In this work, the numerical results of four turbulence models are compared to the experimental results of the water model of continuous casting of steel billets using a single SEN port in a downward vertical orientation. Experimental results were obtained with a 2D PIV (Particle Image Velocimetry) system with measurements taken at various cut planes. Only hydrodynamic effects without solidification are considered. The turbulence is modeled using the RANS (Realizable k-ε, SST k-ω), hybrid RANS/Scale Resolved (SAS), and Scale Resolved approach (LES). The models are numerically solved by the finite volume method, with volume of fluid treatment at the free interface. The geometry, boundary conditions, and material properties were entir...
This paper describes a primitive variable boundary integral equation solution of the free boundar... more This paper describes a primitive variable boundary integral equation solution of the free boundary problem arising in the steady natural convection of the incompressible Newtonian solid-liquid phase change material. Solution of the coupled mass, momentum, and energy equations in two-dimensions is structured by the fundamental solution of the Laplace equation, straight line geometry and discontinuous linear field boundary elements. The involved domain integrals are treated through the dual reciprocity transformation based on the scaled augmented thin plate splines.
A new one-domain dual reciprocity boundary integral method technique for solving one-phase contin... more A new one-domain dual reciprocity boundary integral method technique for solving one-phase continuum formulation of the convective-diffusive energy equation as appears when treating energy transport in solid-liquid phase change systems is described. Laplace equation fundamental solution weighting, straight line geometry and constant field shape functions on the boundary, Crank-Nicolson time discretization and thin plate splines for transforming the domain integrals into a finite series of boundary integrals are employed. Iterations over the timestep are based on the Voller-Swaminathan scheme, upgraded to cope with the convective term. The technique could be applied to a wide range of solid-liquid phase change problems where finite volume or finite element solvers have been almost exclusively used in the past.
In this paper, a heat transfer problem of continuous casting is solved by two BEM approaches, i.e... more In this paper, a heat transfer problem of continuous casting is solved by two BEM approaches, i.e. front tracking and fixed grid with dual reciprocity. Both techniques are compared and critically evaluated by solving two numerical examples consisting of determining the temperature field and location of phase change front. Good accuracy has been observed.
This paper describes the solution to transient incompressible two-dimensional Navier-Stokes equat... more This paper describes the solution to transient incompressible two-dimensional Navier-Stokes equations in primitive variables by the dual reciprocity boundary element method. The coupled set of mass and momentum equations is structured by the fundamental solution of the Laplace equation. The boundary is discretized into simplest boundary elements with constant field and straight line geometry. Numerical examples include convergence and accuracy studies for the classical driven cavity problem at Re = 100. The performance of thirteen different global approximation functions, based on conicals, thin plate splines, multiquadrics and Gaussians is shown, assessed by comparison with the Ghia-Ghia-Shin finite difference reference solution.
The purpose of the present paper is to predict the grain size of steel during the hot-rolling pro... more The purpose of the present paper is to predict the grain size of steel during the hot-rolling process. The basis represents a macroscopic simulation system that can cope with temperatures, stresses and strains of steel in a complete continuous rolling mill, including reversible pre-rolling and finishing rolling with several tenths of rolling passes. The grain size models, newly introduced in the present paper, are one-way coupled to the macro-scale calculations performed with the slice model assumption. Macroscale solution is based on a novel radial basis function collocation method. This numerical method is truly meshless by involving the space discretization in arbitrarily distributed nodes without meshing. A new efficient node generation algorithm is implemented in the present paper and demonstrated for irregular domains of the slice as they appear in different rolling passes. Multiple grain size prediction models are considered. Grain size prediction models are based on empirica...
In this work a rolling simulation system has been developed for rolling schedules which consists ... more In this work a rolling simulation system has been developed for rolling schedules which consists of multiple reversing rolling mills. A slice model approach is applied where the position of a slice can only be determined by considering total deformation. Each slice is parallel to each other and perpendicular to the rolling direction. The solution of coupled thermal and mechanical models over each slice, at a given time and position, are achieved by a novel meshless Local Radial Basis Function Collocation Method (LRBFCM). Mechanical material model obeys ideal plastic flow rule defined by Von Mises. Unknown fields over the slices are interpolated by a certain number of collocation points distributed over the physical domain and its boundary. A system of equations is solved for each collocation point considering its local neighbouring points in the range between 5 and 7. A non-linear system of equations is solved by direct iteration. Groove geometries of each roll are implemented in a ...
International Journal of Numerical Methods for Heat & Fluid Flow, 2004
This paper describes the solution of a steady‐state natural convection problem in porous media by... more This paper describes the solution of a steady‐state natural convection problem in porous media by the radial basis function collocation method (RBFCM). This mesh‐free (polygon‐free) numerical method is for a coupled set of mass, momentum, and energy equations in two dimensions structured by the Hardy's multiquadrics with different shape parameter and different order of polynomial augmentation. The solution is formulated in primitive variables and involves iterative treatment of coupled pressure, velocity, pressure correction, velocity correction, and energy equations. Numerical examples include convergence studies with different collocation point density and arrangements for a two‐dimensional differentially heated rectangular cavity problem at filtration Rayleigh numbers Ra*=25, 50 and 100, and aspect ratios A=1/2, 1, and 2. The solution is assessed by comparison with reference results of the fine‐mesh finite volume method in terms of mid‐plane velocity components, mid‐plane and...
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Papers by Božidar Šarler