• Korean Journal of Mathematics
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• v.27 no.1
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• pp.193-219
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• 2019

The Navier-Stokes equations with variable density are challenging problems in numerical analysis community. We recently built the 2nd order stabilized Gauge-Uzawa method [SGUM] to solve the Navier-Stokes equations with constant density and have estimated theoretically optimal accuracy. Also we proved that SGUM is unconditionally stable. In this paper, we apply SGUM to the Navier-Stokes equations with nonconstant variable density and find out the stability condition of the algorithms. Because the condition is rather strong to apply to real problems, we consider Allen-Cahn scheme to construct unconditionally stable scheme.

• 한국전산유체공학회:학술대회논문집
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• 1996.05a
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• pp.27-32
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• 1996

A previously developed pressure based calculation procedure for incompressible flows was modified and applied to transonic and supersonic flows. It uses pressure as a primary variable in preference to density and body fitted coordinate and non-staggered grid system. The discretized momentum equations were rearranged as a system of equations with respect to covariant velocity components. Three different discretization schemes, QUICK hybrid and first order upwind, were used to approximate the convective terms and compared. Present approach was tested far two transonic flow and one supersonic flow problems. Comparison with previous results show that present approach can be used as a solver for compressible flows.

• The Transactions of the Korean Institute of Electrical Engineers B
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• v.49 no.1
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• pp.9-14
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• 2000

When current flows through a thick conductor such, most of the current flows along outside of the conductor, which is called skin effect. This paper represents a method calculating such a current distribution in the conductor region. The conductor region is divided into some pieces and each piece has its own unknown variable, i.e. current density. The governing equation which expresses Maxwell's equation is combined with the circuit equation with voltage source. The combined equation is solved to obtain current distribution in the conductor. This algorithm is applied to EMC(Electromagnetic Casting) to calculate current density with voltage source.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.2
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• pp.616-623
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• 1996

This paper investigates the linear stability of reacting mixing layers with special emphasis on the existence of multiple unstable modes. The governing equations for laminar flows are from two-dimensional compressible boundary-layer equations. The chemistry is a finite rate single step irreversible reaction with Arrhenius kinetics. For the incompressible reacintg mixing layer with variable density. A necessary condition for instability has been derived. The condition requires that the angular momentum, not the vorticity, to have a maximum in the flow domain. New inflectional modes of instability are found to exist in the outer part of the mixing layer. For the compressible reacting mixing layer, supersonic unstable modes may exist in the abscence of a generalized inflection point. The outer modes at high Mach numbers in the reacting mixing layer are continuations of the inflectional modes of low Mach number flows. However, the generalized inflection point is less important at supersonic flows.

• Proceedings of the KSME Conference
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• 2008.11b
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• pp.2471-2476
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• 2008

Turbulent flow and heat transfer to water at supercritical pressure flowing in vertical pipes is investigated using direct numerical simulation (DNS). A conservative space-time discretization scheme for variable-density flows at low Mach numbers is adopted in the present study to treat steep variations of fluid properties at supercritical pressure just above the thermodynamic critical point. The fluid properties at these conditions are obtained using PROPATH and used in the form of tables in the simulations. The buoyancy influence induced by strong variation of density across the pseudo-critical temperature proved to play an important role in turbulent flow and heat transfer at supercritical state. Depending on the degree of buoyancy influence, turbulent heat transfer may be enhanced or significantly deteriorated, resulting in local hot spots along the heated surface.

• 한국연소학회:학술대회논문집
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• 2000.05a
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• pp.122-132
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• 2000

Computational fluid dynamic simulation is performed for the floating turbulent premixed flames stabilized in stagnation flows of Cho et al. [1] and Cheng and Shepherd [2]. They are both in the wrinkled flamelet regime far from the extinction limit with $u'/S^{0}_{L}$ less than unity. The turbulent flux is given in the first moment closure as a sum of the classical gradient flux due to turbulent motions and the countergradient flux due to thermal expansion. The parameter $N_{B}'s$ are greater than unity with the countergradient flux dominant over the gradient flux. The countergradient flux is assumed to be zero in $\bar{c}<0.05$. The flame surface density is modeled as a symmetric parabolic function with respect to $\bar{c}$. The product of the maximum flame surface density and the mean stretch factor is considered as a tuning constant to match the flame location. Good agreement is achieved with the measured $\tilde{w}$ and $\bar{c}$ profiles along the axis in both flames.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.28 no.11
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• pp.1302-1314
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• 2004

Turbulent heat transfer to $CO_2$ at supercritical pressure flowing in vertical tubes is investigated using direct numerical simulation (DNS). A conservative space-time discretization scheme for variable-density flows at low Mach numbers is adopted in the present study to treat steep variations of fluid properties at supercritical pressure just above the thermodynamic critical point. The fluid properties at these conditions are obtained using PROPATH and used in the form of tables in the simulations. The buoyancy influence induced by strong variation of density across the pseudo-critical temperature proved to play a major role in turbulent heat transfer at supercritical state. Depending on the degree of buoyancy influence, turbulent heat transfer may be enhanced or significantly deteriorated, resulting in local hot spots along the heated surface. Based on the results of the present DNS combined with theoretical considerations, the physical mechanism of this local heat transfer deterioration is elucidated.

• International Journal of Fluid Machinery and Systems
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• v.3 no.4
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• pp.324-331
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• 2010

Cavitation in cryogenic fluids generates substantial thermal effects and strong variations in fluid properties, which in turn alter the cavity characteristics. In order to investigate the cavitation characteristics in cryogenic fluids, numerical simulations are conducted around an axisymmetric ogive in liquid nitrogen and hydrogen respectively. The modified Merkle cavitation model and energy equation which accounts for the influence of cavitation are used, and variable thermal properties of the fluid are updated with software. A good agreement between the numerical results and experimental data are obtained. The results show that vapor production in cavitation extracts the latent heat of evaporation from the surrounding liquid, which decreases the local temperature, and hence the local vapor pressure in the vicinity of cavity becomes lower. The cavitation characteristics in cryogenic fluids are obtained that the cavity seems frothy and the cavitation intense is lower. It is also found that when the fluid is operating close to its critical temperature, thermal effects of cavitation are more obviously in cryogenic fluids. The thermal effect on cavitation in liquid hydrogen is more distinctively compared with that in liquid nitrogen due to the changes of density ratio, vapour pressure gradient and other variable properties of the fluid.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.26 no.10
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• pp.1394-1405
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• 2002

The performance of micro-actuators utilizing radiometric forces are studied numerically. The Knudsen number based on gas density and characteristic dimension is varied from near-continuum to highly rarefied conditions. Direct simulation Monte Carlo(DSMC) calculations have been performed to estimate the performance of the micro-actuators. In the present DSMC method, the variable hard sphere molecular model and no time counter technique are used to simulate the molecular collision kinetics. For simulation of diatomic gas flows, the Borgnakke-Larsen phenomenological model is adopted to redistribute the translational and internal energies.

• Journal of the Korean Society of Propulsion Engineers
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• v.16 no.1
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• pp.55-63
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• 2012

The turbulent flow characteristics in a coaxial injector were investigated by the nonlinear $k-{\varepsilon}-f_{\mu}$ model of Park et al.[1] and large eddy simulation (LES). In order to analyze the geometric effects on the scalar mixing for nonreacting variable-density flows, several recessed lengths and momentum flux ratios are selected at a constant Reynolds number. The nonlinear $k-{\varepsilon}-f_{\mu}$�� model proposed the meaningful characteristics for various momentum flux ratios and recess lengths. The LES results showed the changes of small-scale structures by the recess. When the inner jet was recessed, the development of turbulent kinetic energy became faster than that of non-recessed case. Also, the mixing characteristics were mainly influenced by the variation of shear rates, but the local mixing was changed by the adoption of recess.