• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1715-1723
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• 2016

We study the characteristic Jacobi operator ${\ell}={\bar{R}({\cdot},{\xi}){\xi}$ (along the Reeb flow ${\xi}$) on the unit tangent sphere bundle $T_1M$ over a Riemannian manifold ($M^n$, g). We prove that if ${\ell}$ is pseudo-parallel, i.e., ${\bar{R}{\cdot}{\ell}=L{\mathcal{Q}}({\bar{g}},{\ell})$, by a non-positive function L, then M is locally flat. Moreover, when L is a constant and $n{\neq}16$, M is of constant curvature 0 or 1.

• International Journal of Aeronautical and Space Sciences
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• v.17 no.2
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• pp.149-156
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• 2016

The hypersonic flow on the stagnation streamline of a blunt body is analyzed with quasi one-dimensional (1-D) Navier-Stokes equations approximated by adopting the local similarity to the two-dimensional (2-D)/axisymmetric Navier-Stokes equations. The governing equations are solved using the implicit finite volume method. The computational domain is confined from the stagnation point to the shock wave, and the shock fitting method is used to find the shock position. We propose a boundary condition at the shock, which employs the shock wave angle in the vicinity of the stagnation streamline using the shock shape correlation. As a result of numerical computation conducted for the hypersonic flow over a sphere, the proposed boundary condition is shown to improve the accuracy of the prediction of the shock standoff distance. The quasi 1-D Navier-Stokes code is efficient in computing time and is reliable for the flow analysis along the stagnation streamline and the prediction of heat flux at the stagnation point in the hypersonic blunt body flow.

• Journal of computational fluids engineering
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• v.1 no.1
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• pp.123-141
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• 1996

In this paper the upwind flux difference splitting Navier-Stokes method has been applied to study the perfect gas and the equilibrium chemically reacting hypersonic flow over an axisymmetric sphere-cone(5°) geometry. The effective gamma(γ), enthalpy to internal energy ratio was used to couple chemistry with the fluid mechanics for equilibrium chemically reacting air. The test case condition was at altitude(30km) and Mach number(15). The equilibrium shock thickness over the blunt body region was much thinner than that of perfect gas shock. The pressure difference between perfect gas and equilibrium gas was about 3 ∼ 5 percent. The heat transfer coefficient were also calculated. The results were compared with VSL results in order to validate the current numerical analysis. The results from current method were compared well VSL results ; however, not well at near nose. The proper boundary condition and grid system will be studied to improve the solution quality.

• 한국전산유체공학회:학술대회논문집
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• 1995.10a
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• pp.203-212
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• 1995

In this paper the upwind flux difference splitting Navier-Stokes method has been applied to study the perfect gas and the equilibrium chemically reacting hypersonic flow over an axisymmetric sphere-cone($5^{\circ}$) geometry. The effective gamma($\bar{r}$), enthalpy to internal energy ratio was used to couple chemistry with the fluid mechanics for equilibrium chemically reacting air. The test case condition was at altitude(30Km) and Mach number(15). The equilibrium shock thickness over the blunt body region was much thinner than that of perfect gas shock. The pressure difference between perfect gas and equilibrium gas was about $3\sim5$ percent. The skin friction coefficient and heat transfer coefficient were also calculated.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.10
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• pp.2699-2709
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• 1995

This investigation reports on the study of the ambient turbulent effects on the droplet vaporization in the fuel spray combustion. For tractability, this discussion considers a single droplet in an infinite turbulent flow. In this numerical study, the low-Reynolds-number version of k-.epsilon. turbulence model was used to represent the turbulence effects. The set of two-dimensional conservation equations which describe the transport phenomena in turbulent flow using the mean flow quantities including the droplet internal laminar motion, are solved numerically with the finite difference procedure of Patankar(SIMPLER). The evaluation of the computational model is provided by two limiting cases: turbulent flow over the solid sphere and the laminar flow over a liquid drop. The results show that the turbulence effects are noticeable for the vaporization at high turbulence intensity (10-50%) which is encountered in a typical spray. The magnitude of turbulence effects mainly depends on the turbulent intensity. These effects are not sensitive to the Reynolds number in the range of 50 to 200, ambient temperature in the range of 700 to 1000.deg. K and the volatility.

• Journal of the Korea Institute of Military Science and Technology
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• v.4 no.2
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• pp.202-214
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• 2001

In this paper the upwind flux difference splitting Navier-Stokes method has been applied to study quasi one-dimensional nozzle flow and axisymmetric sphere-cone($5^{\circ}$) flow for the perfect gas, the equilibrium and the nonequilibrium chemically reacting hypersonic flow. The effective gamma(${ \tilde{\gamma}}$), enthalpy to internal energy ratio was used to couple chemistry with the fluid mechanics for equilibrium chemically reacting air. The influences of the various altitude(30km, 50km) at Mach number(15.0, 20.0) were investigated. The equilibrium shock position was located farthest downstream when compared with those of perfect gas in a quasi one-dimensional nozzle. The equilibrium shock thickness over the blunt body region was much thinner than that of perfect gas shock.

• Transactions of the Korean Society of Mechanical Engineers
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• v.11 no.2
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• pp.345-353
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• 1987

An analysis is performed to study flow and heat transfer characteristics of mixed free and forced convection about a sphere. Nonsimilar boundary layer equations which are valid over the entire regime of mixed convection are derived in terms of the mixed convection parameter, Gr/Re$^{2}$, through a dimensional analysis. The transformed conservation equations are solved by a finite difference method for the whole range of mixed convection regime. Numerical results for fluids having the Prandtl number 0.7 and 7 are presented. As the mixed convection parameter increases, the local friction coefficient and local heat transfer coefficient increases as well. For small Prandtl number, the friction coefficient is larger, while for large Prandtl number, the heat transfer coefficient is larger. Natural convection effect on the forced flow is more sensitive for small Prandtl number fluid. Flow separation migrates rearward as an increase in the mixed convection parameter. For small Prandtl number, the buoyancy effect is relatively small so that the flow separation occurs earlier.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.9
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• pp.2431-2442
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• 1994

In this paper the efficient space marching Viscous Shock Layer and Parabolized Navier-Stokes method have been applied to study the complex 3-D hypersonic equilibrium chemically reacting flowfilelds over sphere-cone($10^{\circ}$) vehicle at low angles of attack($0^{\circ}~5^{\circ}), Mach 20, and an altitude of 35km. The current bluntbody/afterbody space marching numerical method predicts the complex flowfields accurately and efficiently even on a small computer. The shock thickness from equilibrium air model is thinner than that from the perfect gas model. The windside wall heat-transfer rate, pressure and skin friction force were increased significantly when compared with those of leeside. The CA, CN, CM were increased almost linearly with the angle of attack in this region. The wall pressure, heat transfer, skin friction and axial force coeffient from equilibrium model were much higher than those from perfect gas model. The center of pressure moved forward with the increase of angle of attack.

• Journal of the Korean earth science society
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• v.38 no.3
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• pp.173-181
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• 2017

The stability of the steady Rossby-Haurwitz wave (R-H wave) in the nondivergent barotropic model (NBM) on the sphere was investigated with the normal mode method. The linearized NBM equation with respect to the R-H wave was formulated into the eigenvalue-eigenvector problem consisting of the huge sparse matrix by expanding the variables with the spherical harmonic functions. It was shown that the definite threshold R-H wave amplitude for instability could be obtained by the normal mode method. It was revealed that some unstable modes were stationary, which tend to amplify without the time change of the spatial structure. The maximum growth rate of the most unstable mode turned out to be in almost linear proportion to the R-H wave amplitude. As a whole, the growth rate of the unstable mode was found to increase with the zonal- and total-wavenumber. The most unstable mode turned out to consist of more-than-one zonal wavenumber, and in some cases, the mode exhibited a discontinuity over the local domain of weak or vanishing flow. The normal mode method developed here could be readily extended to the basic state comprised of multiple zonalwavenumber components as far as the same total wavenumber is given.

• Journal of the Korean association of regional geographers
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• v.3 no.1
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• pp.13-34
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• 1997

The impact of a central place on daily living over wide outlying territory has been one of traditional subjects in the field of urban geography. The flow of rural population toward the central city of Chinju characterizes the population movement in Western Kyungnam, where the spillover of urban population into outlying areas, an especially prominent phenomenon in American society, does not occur. The central city of Chinju is supposed to be the most favored settlement area in Western Kyungnam. More than two thousands of teachers. who live in Chinju, cross the city boundary each morning to do their jobs in Western Kyungnam. But only ninety teachers living outside Chinju commute to the workplace in the city. The teachers willingly spend hours commuting each day to enjoy better quality of life in the central city. In fact, the central city of Chinju functions as bedroom communities for many middle-class workers in Western Kyungnam. On the basis of teachers' commuting behavior, four levels of Chinju's urban spheres are identified in Western Kyungnam. As Table-6 and Figure-2 show, the first-order level of Chinju's sphere includes most Myuns of Sanchung/Hadong Guns and some Myuns of Sachun/Gosung Guns. The second-order level comprises Sanchung/Sachun Eubs and many Myuns of Sachun /Gosung Guns. The third-order level is made up of Samchunpo, Hadong/Gosung/Eryung/Namhae/Habchun/Hamyang Eups, and many Myuns of Eryung/Namhae/Habchun Guns. And all of Guchang Gun and most Myuns of Hamyang Gun belong to the fourth-order level of Chinju's sphere. The influence sphere of Metropolitan Chinju is extended farther in the direction of less competition with other metropolises. Such a situation occurs to the west and south of Chinju. Daily commuting, defined as the journeys to and from work, is an excellent indicator for delimiting urban spheres of influence.