• Transactions of the Korean Society of Mechanical Engineers B
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• v.39 no.5
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• pp.415-423
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• 2015

In this study, we present a grid refinement model in the lattice Boltzmann method (LBM) for two-dimensional incompressible fluid flow. That is, the model combines the desirable features of the lattice Boltzmann method and stream function-vorticity formulations. In order to obtain an accurate result, very fine grid (or lattice) is required near the solid boundary. Therefore, the grid refinement model is used in the lattice Boltzmann method for stream function-vorticity formulation. This approach is more efficient in that it can obtain the same accurate solution as that in single-block approach even if few lattices are used for computation. In order to validate the grid refinement approach for the stream function-vorticity formulation, the numerical simulations of lid-driven cavity flows were performed and good results were obtained.

• Proceedings of the Korean Nuclear Society Conference
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• 1995.10a
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• pp.480-486
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• 1995

Turbulent flow field in a subchannel of bare rod bundles has been numerically simulated using the control volume based finite element method. Launder & Ying model of Reynolds stress and Lam & Bremhorst low-Reynolds number model are implemented in k-$\varepsilon$ equations and momentum equations. Secondary flows are simulated using the stream function and vorticity approach. The control volume based finite element method enable to use the upwind scheme (donor cell scheme). Sensitivity of the constants in the models are studied, and proper values are found to get the close result to the measured flow distributions.

• The Korean Journal of Rheology
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• v.2 no.1
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• pp.33-45
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• 1990

This study analyzes the planar 4:1 contraction flow of viscoelastic fluids with retardation time using finite volume method. To consider separately the elasticity effect of the viscoelastic fluid without shear thinn-ing effect, Oldroyd B liquid model is adopted for the numerical simulation. Instead of the stream function-vorticity formulation, SIMPLER algorithm with staggered grid system which incorporates primitive variable has been introduced in discretizing the momentum equations. An upwind corrected scheme has been used in discetizing the constitutive equations for the non-Newtonian part of the stress. The size of the corner vortex is shown to be slightly influenced by the Weissenberg number. However as the Weissenberg number is increased the chang-ing of the vortex shape agrees qualitatively well with some experimental studies.

• Journal of the Korean Society of Safety
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• v.10 no.2
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• pp.56-63
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• 1995

A simulation of contaminant dispersion in a water reservoir has been done using 2-D finite difference method(FDM). The steady state velocity field of the reservoir was computed using stream function-vorticity formulation of Wavier-Stokes equation and continuity equation. Based on the computed steady state velocity field, the transient convective diffusion equation of the contaminant dispersion was computed. For the 1m$\times$1m reservoir model with inlet and outlet attached, it was shown that the center of circulation located toward right. For the numerical values of v =0.01($\textrm{cm}^2$/s) and D=0.6($\textrm{cm}^2$/s) and the flow of 50($\textrm{cm}^3$/s ), it was determined that the outflow had to be shut down in 18 seconds to prevent from severe pollution. Also the required time was computed to be 6 seconds for the inflow of 100 ($\textrm{cm}^3$/s). The result of this study is considered, hopefully, to be useful for the design of the water reservoir systems that are the subjects to various contamination.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.6 no.2
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• pp.93-101
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• 1986

The behavior of a plane buoyant jet discharged vertically upward into a stagnant uniform environment is analyzed by continuity, momentum transport equation by numerical scheme. The governing equations are solved by finite difference method employing stream function and vorticity transport and Prandtl's turbulent model. Results for centerline velocities and temperatures, temperature distribution and flow pattern in receiving environment due to buoyant jet in the range of discharge densimetric Froude number of 4 to 32 show good agreement with published data. Spreading rate and dispersion ratio, which are required in integral type analysis of whole range of buoyant jet and have not been obtained yet, are derived in terms of discharge densimetric Froude number and vertical distance from source.

• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.3
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• pp.541-550
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• 1988

Natural convection in a square enclosure was investigated numerically for low prandtl number fluids using Finite Element Method. In case of Ra=10$^{4}$, 10$^{5}$ and 10$^{6}$ the temperature gradient decreases gradually at the lower end of the hot wall(or at the upper end of the cold wall) as prandtl number decreases in the range of 0.01 .leq. Pr .leq. 10. Maximum heat transfer occurs at a somewhat higher point from the lower end of hot wall(or at somewhat lower point from the upper end of the cold wall) and it draws near to the lower end of the hot wall(or draws near to the upper end of the cold wall) with increasing prandtl number. The flow in the enclosure appears as an Unicell Pattern for Ra .leq. 10$^{4}$ and secondarily flows(or tertiary flows) appears in the core region for Ra .geq. 10$^{5}$ . The line joining the center of secondary cells skewes in a clockwise direction as the Prandtl number decreases.