• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1999.03b
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• pp.253-256
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• 1999

The Streamline Upwind Petrov-Galerkin(SUPG) finite element method is used to solve the two-dimensional laminar and turbulent flow. The flow is simulated by averaged Navier-Stokes equations with a penalty function approach and the lograithmic(k-$\varepsilon$) turbulent model is employed to take into account its turbulent behavior. The near-wall viscous sub-layer model is employed to approach the dominant viscous effects in the near wall zones. To find a good-enough initial guess of the Newton-Raphson iteration solving Nonlinear Matrix the Incremental method is considered for momentum and the Incomplete logarithmic turbu-lent equations for Turbulence. The validation of our method is investigated in comparision with published experimental data.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.14 no.6
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• pp.1357-1363
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• 1994

A Monte-Carlo simulation model is developed to predict size distribution produced by the coalescence of air bubbles in turbulent shear f1ow. The simulation consists of generating a population of air bubbles into the initial positions at each time step and tracking them by simulating motions and checking collisions. The radial displacement of air bubbles in the simulation model is produced by numerically solving an advective diffusion equation. Longitudinal displacements are generated from the logarithmic flow velovity distribution and the bubble rise velocity. Collision of air bubbles for each time step is detected by a geometric test using their relative positions at the beginning of the time step and relative displacements during the time step. At the end of the time step, the total number of bubbles, their positions, and sizes are updated. The computer program is coded such that minimum storages for sizes and positions of bubbles are required.

• Journal of the Society of Naval Architects of Korea
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• v.47 no.5
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• pp.647-655
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• 2010

In this paper, a numerical study is carried out for super-pipe, flat plate and axisymmetric body flows to investigate a validity of using wall function and high $y_1^+$ in calculation of high Reynolds number flow. The velocity profiles in boundary layer agree well with the law of the wall. And it is found that the range of $y^+$��which validated the logarithmic law of the wall grows with increasing Reynolds number. From the result, an equation is suggested that can be used to estimate a maximum $y^+$ value of validity of the log law. And the slope(1/$\kappa$) of the log region of the numerical result is larger than that of experimental data. On the other hand, as $y_1^+$ is increasing, both the friction and the pressure resistances tend to increase finely. When using $y_1^+$ value beyond the range of log law, the surface shear stress shows a significant error and the pressure resistance increases rapidly. However, when using $y_1^+$ value in the range, the computational result is reasonable. From this study, the use of the wall function with high value of $y_1^+$ can be justified for a full scale Reynolds number ship flow.