• Particle and aerosol research
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• v.5 no.3
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• pp.123-131
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• 2009

This paper presents simulation results of particle transport in low-pressure, low-temperature plasma environment. The size dependent transport of particles in the plasma is investigated with a two-dimensional simulation tool developed in-house for plasma chamber analysis and design. The plasma model consists of the first two and three moments of the Boltzmann equation for ion and electron fluids respectively, coupled to Poisson's equation for the self-consistent electric field. The particle transport model takes into account all important factors, such as gravitational, electrostatic, ion drag, neutral drag and Brownian forces, affecting the motion of particles in the plasma environment. The particle transport model coupled with both neutral fluid and plasma models is simulated through a Lagrangian approach tracking the individual trajectory of each particle by taking a force balance on the particle. The size dependant trap locations of particles ranging from a few nm to a few ${\mu}m$ are identified in both electropositive and electronegative plasmas. The simulation results show that particles are trapped at locations where the forces acting on them balance. While fine particles tend to be trapped in the bulk, large particles accumulate near bottom sheath boundaries and around material interfaces, such as wafer and electrode edges where a sudden change in electric field occurs. Overall, small particles form a "dome" shape around the center of the plasma reactor and are also trapped in a "ring" near the radial sheath boundaries, while larger particles accumulate only in the "ring". These simulation results are qualitatively in good agreement with experimental observation.

• Ocean Systems Engineering
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• v.12 no.1
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• pp.63-86
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• 2022

A refined projection-based purely Lagrangian meshfree method is presented towards reliable numerical analysis of fluid flow interactions with saturated/unsaturated porous media of uniform/spatially-varying porosities. The governing equations are reformulated on the basis of two-phase mixture theory with incorporation of volume fraction. These principal equations of mixture are discretized in the context of Incompressible SPH (Smoothed Particle Hydrodynamics) method. Associated with the consideration of governing equations of mixture, a new term arises in the source term of PPE (Poisson Pressure Equation), resulting in modified source term. The linear and nonlinear force terms are included in momentum equation to represent the resistance from porous media. Volume increase of fluid particles are taken into consideration on account of the presence of porous media, and hence multi-resolution ISPH framework is also incorporated. The stability and accuracy of the proposed method are thoroughly examined by reproducing several numerical examples including the interactions between fluid flow and saturated/unsaturated porous media of uniform/spatially-varying porosities. The method shows continuous pressure field, smooth variations of particle volumes and regular distributions of particles at the interface between fluid and porous media.

• Journal of the Korea Concrete Institute
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• v.19 no.6
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• pp.803-810
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• 2007

An analytical method capable of predicting various stress-strain responses in axially loaded concrete confined with FRP (fiber reinforced polymers) composites in a rational manner is presented. Its underlying idea is that the volumetric expansion due to progressive microcracking in mechanically loaded concrete is an important measure of the extent of damage in the material microstructure, and can be utilized to estimate the load-carrying capacity of concrete by considering the corresponding accumulated damage. Following from this, an elastic modulus expressed as a function of area strain and concrete porosity, the energy-balance equation relating the dilating concrete to the confining device interactively, the varying confining pressure, and an incremental calculation algorithm are included in the solution procedure. The proposed method enables the evaluation of lateral strains consecutively according to the related mechanical model and the energy-balance equation, rather than using an empirically derived equation for Poisson's ratio or dilation rate as in other analytical methods. Several existing analytical methods that can predict the overall response were also examined and discussed, particularly focusing on the way of considering the volumetric expansion. The results predicted by the proposed and Samaan's bilinear equation models correlated with observed results with a reasonable degree, however it can be judged that the latter is not capable of predicting the response of lateral strains correctly due to incorporating the initial Poisson's ratio and the final converged dilation rate only. Further, the proposed method seems to have greater benefits in other applications by the use of the fundamental principles of mechanics.

• Solar Energy
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• v.17 no.3
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• pp.59-66
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• 1997

The present study adopted the PTV method for the velocity acquisition. The system consists of an image grabber built-in a personal computer and a laser-based sheet light projector and particle identification softwares. Velocity vectors are obtained, by PTV and they are used as velocity components for Poisson equation for pressure. Related boundary conditions and no-slip condition at solid wall and the linear velocity extrapolation on the upper side of cavity are well examined for the present study. For calculation of pressure, resolution of grid is basically $40{\times}40$ and 2-dimensional uniform mesh using MAC staggered grid is adopted. The result of experiment reveal that, newly suggested measuring method is capable of estimating pressure and velocity distribution of flow field reasonably.

• Steel and Composite Structures
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• v.38 no.2
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• pp.189-211
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• 2021

An analytical solution is presented to analyze the thermoelastoplastic response of a rotating thick-walled cylindrical pressure vessel made of functionally graded material (FGM). The analysis is based on Tresca's yield condition, its associated flow rule and linear strain hardening material behaviour. The uncoupled theory of thermoelasticity is used, and the plane strain condition is assumed. The material properties except for Poisson's ratio, are assumed to vary nonlinearly in the radial direction. Elastic, partially plastic, fully plastic, and residual stress states are investigated. The heat conduction equation for the one-dimensional problem in cylindrical coordinates is used to obtain temperature distribution in the vessel. It is assumed that the inner surface is exposed to an airstream and that the outer surface is exposed to a uniform heat flux. Tresca's yield criterion and its associated flow rule are used to formulate six different plastic regions for a linearly hardening condition. All these stages are studied in detail. It is shown that the thermoelastoplastic stress response of a rotating FGM pressure vessel is affected significantly by the nonhomogeneity of the material and temperature gradient. The results are validated with those of other researchers for appropriate values of the system parameters and excellent agreement is observed.

• Proceedings of the Korea Concrete Institute Conference
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• 2008.11a
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• pp.201-204
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• 2008

The proposed method, capable of predicting various stress-strain responses in axially loaded concrete confined with FRP (Fiber Reinforced Polymers) composites in a rational manner, is based on the fact that the volumetric expansion due to progressive microcracking in mechanically loaded concrete is an important measure of the extent of damage in the material microstructure. The elastic modulus expressed as a function of area strain and concrete porosity, the energy-balance equation relating the dilating concrete to the confining device interactively, the varying confining pressure, and an incremental calculation algorithm are included in the solution procedure. This procedure enables the evaluation of lateral strains consecutively according to the related mechanical model and the energy-balance equation, rather than using an empirically derived equation for Poisson's ratio or dilation rate as in other analytical methods.

• Journal of the Korean Society of Hazard Mitigation
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• v.10 no.1
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• pp.111-117
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• 2010

A three-dimensional numerical model is employed to investigate wave deformation due to a submerged structure. The three-dimensional numerical model solves the spatially averaged Navier-Stokes equations for two-phase flows. The LES(large-eddy-simulation) approach is adopted to model the turbulence effect by using the Smagorinsky SGS(sub-grid scale) closure model. The two-step projection method is employed in the numerical solutions, aided by the Bi-CGSTAB technique to solve the pressure Poisson equation for the filtered pressure field. The second-order accurate VOF(volume-of-fluid) method is used to track the distorted and broken free surface. A simple linear wave is generated on a constant depth and compared with analytical solutions. The model is then applied to study wave deformation due to a submerged structure and the predicted results are compared with available laboratory measurements.

• Journal of the Society of Naval Architects of Korea
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• v.49 no.2
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• pp.196-202
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• 2012

In this study, numerical analysis of viscous flows is carried out based on the unstructured grid. There exist some difficulties in expressing and computing numerical derivatives on the unstructured grid due to lack of the structured characteristics. The general computer algorithms are developed to perform numerical derivatives easily and extended to be applicable to various geometries composed of hybrid meshes. And the optimal method of strongly implicit procedure is newly contrived to accelerate the rate of convergence in solving the pressure Poisson equation. To verify numerical schemes, the driven cavity problems of 2 and 3 dimension are simulated. The numerical results are compared with others and our numerical schemes are shown to be valid.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.5 no.1
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• pp.55-78
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• 2001

Given the anisotropic Poisson equation $-{\nabla}{\cdot}{\mathcal{K}}{\nabla}p=f$, one can convert it into a system of two first order PDEs: the Darcy law for the flux $u=-{\mathcal{K}{\nabla}p$ and conservation of mass ${\nabla}{\cdot}u=f$. A very natural mixed finite volume method for this system is to seek the pressure in the nonconforming P1 space and the Darcy velocity in the lowest order Raviart-Thomas space. The equations for these variables are obtained by integrating the two first order systems over the triangular volumes. In this paper we show that such a method is really a standard finite element method with local recovery of the flux in disguise. As a consequence, we compare two approaches in analyzing finite volume methods (FVM) and shed light on the proper way of analyzing non co-volume type of FVM. Numerical results for Dirichlet and Neumann problems are included.

• Environmental Engineering Research
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• v.11 no.3
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• pp.164-171
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• 2006

Numerical modeling of the flow velocity fields for the near corona wire electrohydrodynamic (EHD) flow was conducted. The steady, two-dimensional momentum equations have been computed for a wire-plate type electrostatic precipitator (ESP). The equations were solved in the conservative finite-difference form on a fine uniform rectilinear grid of sufficient resolution to accurately capture the momentum boundary layers. The numerical procedure for the differential equations was used by SIMPLEST algorithm. The Phoenics (Version 3.5.1) CFD code, coupled with Poisson's electric field, ion transport equations and the momentum equation with electric body force were used for the numerical simulation and the Chen-Kim ${\kappa}-{\varepsilon}$ turbulent model numerical results that an EHD secondary flow was clearly visible in the downstream regions of the corona wire despite the low Reynolds number for the electrode ($Re_{cw}=12.4$). Secondary flow vortices caused by the EHD increases with increasing discharge current or EHD number, hence pressure drop of ESP increases.