Finite Volume Method Approach Research Articles

Numerical simulation of gas migration through engineered and geological barriers for a deep repository for radioactive waste

In this paper a finite volume method approach is used to model the 2D compressible and immiscible two-phase flow of water and gas in heterogeneous porous media. We consider a model describing water...

Numerical determination of permeability of Al–Cu alloys using 3D geometry from X-ray microtomography

In the present study, the permeabilities of Al–15·5 wt-%Cu and Al–19·5 wt-%Cu have been determined numerically by solving the full Navier–Stokes equations on 3D geometries of interdendritic channels obtained by X-ray microtomography. The samples for X-ray microtomography imaging were sectioned from different heights in directionally solidified cylinders in order to obtain a variety of microstructures for each composition. The flow has been solved using a second order accurate finite volume method approach. The effect of employing uniform or unstructured mesh on the calculated permeability has been studied. The Marching–Cube triangulation method was used to extract accurate surfaces for unstructured volume meshing. Calculated values of permeability for this range of solid fractions show partial agreement with previous experiments. Observed deviations are analysed and ultimately attributed to experimental error associated with the difficulties of measuring permeability.

The finite volume method approach to the collapsed dimension method in analyzing steady/transient radiative transfer problems in participating media

With the finite volume formulation (FVM) approach applied to the collapsed dimension method (CDM), this article deals with the application of the CDM to analyze radiative heat transfer problems in a participating medium subjected to a continuous diffuse or a continuous/short-pulse collimated boundary radiative loading. The planar medium contained between diffuse gray boundaries is absorbing, emitting and anisotropically scattering. With three categories of thermal boundary radiative loadings, for the four types of problems considered, the CDM results are compared for a wide range of radiative parameters with that of the FVM.

Lattice Boltzmann Method and Modified Discrete Ordinate Method Applied to Radiative Transport in a Spherical Medium with and without Conduction

This article deals with the application of the modified discrete ordinate method (MDOM) to calculate volumetric radiative information with and without conduction in a concentric spherical enclosure containing a participating medium. With radiative information known from the MDOM, the energy equation of the combined mode transient conduction and radiation heat transfer is formulated and solved using the lattice Boltzmann method (LBM). Without conduction, for pure radiation case, two benchmark problems, representing nonradiative and radiative equilibrium situations are taken up. In the case of non-radiative equilibrium, an isothermal medium is bounded by cold walls and medium is the source of radiation, while in the case of radiative equilibrium, nonisothermal medium is confined between a hot and a cold wall, and the hot (inner sphere) wall is the radiation source. Depending upon the problem, heat flux, energy flow rate, emissive power, and temperature distributions in the medium are calculated for different values of parameters such as the extinction coefficient, the scattering albedo, the conduction-radiation parameter, the boundary emissivity, and the radius ratio. To validate the MDOM and the LBM-MDOM formulations, problems are also solved using the finite volume method (FVM) and the finite-difference method (FDM)–FVM approach, in which the FVM is used to calculate the volumetric radiation and the energy equation is also solved using the FDM. Results of the MDOM, LBM–MDOM, FVM and FDM–FVM are also benchmarked against those available in the literature. MDOM and LBM–MDOM have been found to provide accurate results.

Radiative and Conductive Heat Exchanges in High-Temperature Glass Melt with the Finite-Volume Method Approach. Influence of Several Spatial Differencing Schemes on RTE Solution

ABSTRACT This article is devoted to heat transfer involving radiation and conduction. Considering a nongray, purely absorbing medium, the radiative heat transfer equation (RTE) and the energy balance equation are both solved with the finite-volume method (FVM). The energy equation is coupled to the RTE through the radiative source term. Several differencing scheme efficiencies are discussed for the case of strong opacities. Validation of the model with various benchmarks simulating high-temperature glass melting, including one- and two-dimensional geometries, is achieved.

Magnetohydrodynamic Simulation of DC Arc Plasma under AC Magnetic Field

Direct current (DC) thermal plasma, shape controlled by use of alternative current (AC) magnetic field enables the wide area of thermal treatment and has potentials of applications other than welding. In this paper, the behavior of DC plasma under AC magnetic field imposed perpendicular to the plasma current is discussed experimentally and theoretically by changing various parameters such as plasma electric current, nozzle diameter, argon flow rate and magnetic flux density including its wave form. As the theoretical study, DC plasma was mathematically modeled by use of three dimensional magnetohydrodynamics (MHD) theory and discussed through numerical simulations performed by full finite volume method approach. Then the DC arc plasma motion under sinusoidal AC magnetic field is discussed through MHD analysis. By these experimental and theoretical investigations, the controlling parameters of DC plasma by AC magnetic field have been made clear quantitatively.