• East Asian mathematical journal
• /
• v.37 no.1
• /
• pp.109-122
• /
• 2021

We establish existence and uniqueness of Green functions for flow velocity of stationary Stokes systems, under a continuity assumption of weak solutions to the system, in a bounded domain such that the divergence equation is solvable there. We also obtain pointwise bounds of the Green functions.

• Journal of the Korean Chemical Society
• /
• v.40 no.6
• /
• pp.409-414
• /
• 1996

The limit of applicability of Navier-Stokes equation to stationary plane shock-waves is examined by using the principle of minimum entropy production of linear irreversible thermodynamics. In order to obtain analytic results, the equation is linearized near the equilibrium of downstream. Results show that the solution of Navier-Stokes equation which fits the boundary condition of far downstream flow is consistent with the thermodynamic requirement within the first order when the solution is expanded around the M=1, where M is the Mach number of upstream speed.

• Bulletin of the Korean Mathematical Society
• /
• v.33 no.3
• /
• pp.343-357
• /
• 1996

• Selected Papers of The Society of Naval Architects of Korea
• /
• v.1 no.1
• /
• pp.45-51
• /
• 1993

By using multiple-scale expansion techniques, the Mach reflection of sinusoidally- modulated nonlinear Stokes waves by a stationary thin wedge has been studied within the framework of potential theory. It is shown that the evolution of diffracted wave amplitude can be described by the Zakharov equation to the loading order and that It reduces to the cubic Schrodinger equation with an additional linear term in the case of stable modulations. Computations are made for the cubic Schrodinger equation for different values of nonlinear and dispersion parameters. Numerical results reflect the experimental findings in terms of the amplitude and width of generated stem waves. Based on the computations it is concluded that the nonlinearity dominates the wave field, while the dispersion does not significantly affect the wave evolution.

• Proceedings of the Korean Society of Propulsion Engineers Conference
• /
• 1996.11a
• /
• pp.27-41
• /
• 1996

In this study the heat transfer and fluid flow of the molten pool in stationary gas tungsten arc welding using argon shielding gas were investigated. Transporting phenomena from the welding arc to the base material surface, such as current density, heat flux, arc pressure and shear stress acting on the weld pool surface, were taken from the simulation results of the corresponding welding arc. Various driving forces for the weld pool convection were considered, self-induced electromagnetic, surface tension, buoyancy, and impinging plasma arc forces. Furthermore, the effect of surface depression due to the arc pressure acting on the molten pool surface was considered. Because fusion boundary has a curved and unknown shape during welding, a boundary-fitted coordinate system was adopted to precisely describe the boundary for the momentum equation. The numerical model was applied to AISI 304 stainless steel and compared with the experimental results.

• Journal of the Society of Naval Architects of Korea
• /
• v.28 no.1
• /
• pp.53-59
• /
• 1991

By employing multiple-scale expansion techniques, the diffraction of sinusoidally-modulated nonlinear Stokes waves by a stationary thin wedge has been studied within the framework of potential theory. It is found that the evolution of diffracted waves can be described by the Zakharov equation to the leading order and it can be replaced by the cubic $Schr\ddot{o}dinger$ equation with an additional linear term for stable modulations. Computations are made for the cubic $Schr\ddot{o}dinger$ equation with different values of nonlinear and dispersion parameters. Numerical results well reflect the experimental findings in the amplitude and width of generated stem waves. It is numerically confirmed that the nonlinearity dominates the wave field, while the dispersion hardly affects the wave evolution, and stem waves are likely to be formed for steep incident waves in the case of stable sinusoidal modulations.

• The KSFM Journal of Fluid Machinery
• /
• v.5 no.3 s.16
• /
• pp.40-45
• /
• 2002

Since the previous cut-and-try design algorithm requires much cost and time, the automated design technique with the CFD and optimum design algorithm has recently been concerned. In this work, the Navier-Stokes equation was solved to gain more detailed viscous flow information of cascade with rotor-stator interactions. The H-grid embedded by O-grid was generated to obtain more accurate solution by eliminating the branch cut of H-grid near airfoil surface. To handle the relative motion of the rotor to the stationary stator, the sliding multiblock method was applied and the cubic-spline interpolation was used on the block interface boundary. To validate present procedure, the time-averaged aerodynamic loads were compared with experimeatal data. A good agreement was obtained. The Modified Method of Feasible Direction (MMFD) was used to carry out the sensitivity analysis of the change of aerodynamic performance by the changes of the cascade geometry. The present optimization of the cascade gave a dramatic reduction of the drag while the lift maintains at the value within the user-specified tolerance.

• Journal of computational fluids engineering
• /
• v.16 no.3
• /
• pp.8-14
• /
• 2011

Although the geometry of circular cylinder is simple, the flow is complicate because of the flow separation and vortex shedding. In spite of many numerical and experimental researches, the flow around a circular cylinder has not been clarified even now. It has been known that the unsteady vortex shedding from a circular cylinder can vibrate and damage a structure. Lock-on phenomenon is very important in the flow around an oscillating circular cylinder. The lock-on phenomenon is that when the oscillation frequency of the circular cylinder is at or near the frequency of vortex shedding from a stationary cylinder, the vortex shedding synchronizes with the cylinder motion. This phenomenon can be recognized by the spectral analysis of the lift coefficient history. At the lock-on region the vortex is shedding by the modulated frequency to the body frequency. However, the vortex is shedding by the mixed frequencies of natural shedding and forced body frequency in the region of non-lock-on. In this paper, it was analyzed the relation between the frequency of rotary oscillating circular cylinder and the vortex shedding frequency.

• Journal of ILASS-Korea
• /
• v.18 no.3
• /
• pp.146-154
• /
• 2013

The flow of a liquid film on spin coating is investigated in the case that the fixed volume of a liquid is placed on the center of a stationary disk. Thin film equations that are well approximated when the characteristic length in the vertical direction is much smaller than that in the radial direction (${\varepsilon}{\ll}1$) and have already been proposed in the work of T.-S. Kim & M.-U. Kim (2009), are used. The differential equation that governs the free surface of a liquid when ${\varepsilon}{\ll}1$ and ${\varepsilon}Re{\ll}1$ is also derived. The basic flow is analyzed using the thin film equations and their results are compared to the results of Navier-Stokes equations.

• 한국전산유체공학회:학술대회논문집
• /
• 1998.11a
• /
• pp.36-41
• /
• 1998

The cross-flow fan performance and its sound noise characteristics are predicted by computational methods. The unsteady incompressible Navier-Stokes equations in moving coordinates are solved by a SMAC method on unstructured triangular meshes, using a sliding mesh technique at the interface between the domain rotating with blades and the rest stationary part. The computationally predicted fan performance was favorably compared with experiment, and some numerical aspects of simulating the cross-flow fan are discussed. With the computed unsteady flow field, aeroacoustic sound noise of the fan is predicted by the Lighthill-Curie equation. The unsteady surface pressure fluctuations on stabilizer enables a prediction of BPF noise of the uniform pitch blade fan quite accurately. The aeroacoustic sound noise characteristics of both uniform and random pitch blade fans are also examined by SPL spectrum analysis.