• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.49-65
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• 2006

A robust numerical method for a singularly perturbed second-order ordinary differential equation having two parameters with a discontinuous source term is presented in this article. Theoretical bounds are derived for the derivatives of the solution and its smooth and singular components. An appropriate piecewise uniform mesh is constructed, and classical upwind finite difference schemes are used on this mesh to obtain the discrete system of equations. Parameter-uniform error bounds for the numerical approximations are established. Numerical results are provided to illustrate the convergence of the numerical approximations.

• Journal of Mechanical Science and Technology
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• 제16권4호
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• pp.557-563
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• 2002

In this paper, the characteristics of flow and spray motions affected by from piston head configurations were investigated numerically. Calculations were carried out from intake process to the end of compression. GTT (Generalized Tank and Tube method) code, which includes a third order upwind Chakravarthy-Osher TVD scheme and k-$\varepsilon$ turbulence model with fuel spray analysis was used for the calculations. As a results, piston heads with smaller radii of curvature were found to give stronger reverse tumble than those with larger radii of curvature. Similar results are shown in the convection and diffusion of fuel sprays.

• Journal of the Korean Society of Combustion
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• 제22권3호
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• pp.23-28
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• 2017

The fuel and oxidizer mixing process in the shock tube driven section is simulated numerically. The boundary condition is set based on an shock tube experimental condition. The objective is to predict the gas mixing time for experiments. In the experiment, the amount of fuel to be injected is determined in advance. Then, according to duration of fuel injection, 5 cases with the same fuel mass but different fuel mass flow rate are simulated. After fuel is injected into the driven section, the fuel and air will be mixed with each other through convection and diffusion processes. The mixing time is predicted numerically for experiments.

• Environmental Engineering Research
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• 제14권2호
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• pp.126-133
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• 2009

This study investigated the removal characteristics of various micro organic compounds by low-pressure nanofiltration membranes comprised of disinfection by products and pharmaceutically active compounds. The experimental removal of micro organic compounds by low-pressure nanofiltration membranes was compared with the transport model calculations, which consist of diffusion and convection terms including steric hindrance factor. The selected molecule from the disinfection byproducts and pharmaceutical active compounds showed a much lower removal than polysac-charides with a similar molecular size. However,the difference between model calculation and experimental removal of disinfection by-products and pharmaceutically active compounds could be corrected. The correlation of Ks with solute radius was further considered to clarity transport phenomena of micro organic solutes through nanofiltration membranes.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 한국정밀공학회 1996년도 추계학술대회 논문집
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• pp.560-564
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• 1996

In recently, annealing process of cold rolled sheet tend to change to continuous annealing process for improving qualify, saving yield. In the meantime as demand for various kind and small lot of products has been increasing, batch annealing has been appreciated for its small restriction for the operation. So, we tested on the effect for a hydrogen contents of atmospheric gas at annealing furnace. As a result of several investigation. We confirmed for the following characteristics ; improved productivity, uniform heating, improved surface quality, saving energy. Therefore, the use of hydrogen instead of nitrogen as the protective gas, combined with high convection in batch annealing furnaces, has shown that considerable increases in furnace output and material quality are attainable. Owing to the low density, high diffusion and reducing character of hydrogen, a better transfer resulting in uniform material temperatures and improved coil surfaces can be achieved.

• Transactions of the Korean Society of Automotive Engineers
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• 제4권3호
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• pp.130-138
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• 1996

The transient incompressible flow behind the widely-spaced co-axial jet is numerically simulated using the random vortex method(RVM). This numerical approach is based on the Lagrangian approach for the vorticity formulation of the unsteady Navier-Stokes equations, utilizing vortex elements to account for the convection and diffusion processes. The effects of the mass flow rate of an annular air jet and a central fuel jet on the co-axial jet flow dynamics is investigated. To validate the present procedure, the numerical results are compared with the available experimental data the present procedure, the numerical results are compared with the available experimental data in terms of the centerline and off-centerline profiles of the mean axial velocity. Discrepancies between the RVM results and the measurements are discussed in detail.

• Journal of the Korean Society of Clothing and Textiles
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• 제21권8호
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• pp.1387-1395
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• 1997

Effects of the ambient air temperature and the opening position on the pattern of the clothing ventilation of a thermal manikin wearing an impermeable blouse were investigated by the trace gas method. Under an isothermal condition, the ventilation was governed by diffusion, and the ventilation rate through the wrist-openings was greatly affected by the distance from the openings. Under non-isothermal conditions, however, the ventilation was accelerated by the convection driven by the temperature gradient between the clothing microclimate and the surrounding air; the greater the temperature gradient, the greater the ventilation. Even though it was certainly affected by the ambient air temperature, the ventilation rate was more significantly influenced by the position of openings. The ventilation patterns at the arm and the body were distinctive.

• Journal of Korea Foundry Society
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• 제13권6호
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• pp.540-546
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• 1993

The effects of fluid flow on the purification of aluminum were studied. As the revolution rate(N) increased, the size of columnar grain decreased gradually. The concentration of solidified crystal was decreased with increasing distance from chill and revolution rate(N). Distribution boundary layer thickness(${\delta}$) was calculated from the solute distribution obtained in solid experimentally and by use of BPS equation. The value of ${\delta}$ changed from about $60{\mu}m$ at N value of 27rpm to about $15{\mu}m$ at N value of 1000rpm. From this result, high purification was obtained by decreasing the diffusion boundary layer under forced convection.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.141-152
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• 2007

In this paper a numerical method is presented to solve singularly perturbed two points boundary value problems for second order ordinary differential equations consisting a discontinuous source term. First, in this method, an asymptotic expansion approximation of the solution of the boundary value problem is constructed using the basic ideas of a well known perturbation method WKB. Then some initial value problems and terminal value problems are constructed such that their solutions are the terms of this asymptotic expansion. These initial value problems are happened to be singularly perturbed problems and therefore fitted mesh method (Shishkin mesh) are used to solve these problems. Necessary error estimates are derived and examples provided to illustrate the method.

• Structural Engineering and Mechanics
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• 제4권6호
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• pp.589-600
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• 1996

An explicit 4th order time integration scheme for solving the convection-diffusion equation is discussed in this paper. A system of ordinary differential equations are derived first by discretizing the spatial derivatives of the relevant PDE using the finite difference method. The integration of the ODEs is then carried out using a 4th order scheme and a self-adaptive technique based on the spatial grid spacing. For a non-uniform spatial grid, different time step sizes are used for the integration of the ODEs defined at different spatial points, which improves the computational efficiency significantly. A numerical example is also discussed in the paper to demonstrate the implementation and effectiveness of the method.