• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.2 no.4
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• pp.268-278
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• 1990

Hydrodynamic stability equations are formulated for natural convection flows adjacent to a heated or cooled, inclined, isothermal surface in pure water at $4^{\circ}C$, where the density variation with temperature becomes nonlinear. The resulting stability equations, when reduced to ordinary differential equations by a similarity transformation, constitute a two-point boundary-value problem, which was solved numerically. It is found from the obtained stability results that the neutral stability curves are systematically shifted to have lower critical Grashof numbers, as the inclination angle of upward-facing plate increases. Also, the nose of the neutral stability curve becomes blunter as the angle increases. It implies that the greater the inclination of the upward-facing plate, the more susceptible of the flow to instability for the wide range of disturbance wave number and frequency.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.2
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• pp.644-653
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• 1991

A wave instability problem is formulated for natural convection flows adjacent to a inclined isothermal surface in pure water near the density extremum. It accounts for the nonparallelism of the basic flow and temperature fields. Numerical solutions of the hydrodynamic stability equations constitute a two-point boundary value problem which are accurately solved using a computer code COLSYS. Neutral stability results for Prandtl number of 11.6 are obtained for various angles of inclination of a surface in the range from-10 to 30 deg. The neutral stability curves are systematically shifted toward modified Grashof number G=0 as one proceeds from downward-facing inclined plate(.gamma.<0.deg.) to upward-facing inclined plate (.gamma.>0.deg.). Namely, an increase in the positive angle of inclination always cause the flows to be significantly more unstable. The present results are compared with the results for the parallel flow model. The nonparallel flow model has, in general, a higher critical Grashof number than does the parallel flow model. But the neutral stability curves retain their characteristic shapes.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.2
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• pp.630-643
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• 1991

The hydrodynamic stability equations are formulated for buoyancy-induced flows adjacent to a vertical, planar, isothermal surface in cold pure water. The resulting stability equations, when reduced to ordinary differential equation by a similarity transformation, constitute a two-point boundary-value(eigenvalue) problem, which was numerically solved for various values of the density extremum parameter R=( $T_{m}$ - $T_.inf./) / ( $T_{o}$ - $T_.inf./). These stability equations have been solved using a computer code designed to accurately solve two-point boundary-value problems. The present numerical study includes neutral stability results for the region of the flows corresponding to 0.0.leq. R. leq.0.15, where the outside buoyancy force reversals arise. The results show that a small amount of outside buoyancy force reversal causes the critical Grashof number $G^*/ to increase significantly. A further increase of the outside buoyancy force reversal causes the critical Grashof number to decrease. But the dimensionless frequency parameter $B^*/ at $G^*/ is systematically decreased. When the stability results of the present work are compared to the experimental data, the numerical results agree in a qualitative way with the experimental data.erimental data.

• Journal of Korean Society for Atmospheric Environment
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• v.12 no.2
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• pp.141-149
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• 1996

Lateral dispersion parameter(.sigma.$_{y}$) which is an important factor in atmospheric dispersion can be estimated byusing wind direction fluctuation(.sigma.$_{\theta}$). In this paper, we studied the characteristics of the .sigma.$_{\theta}$ in the Chunchon basin and calculated the .sig- ma.$_{y}$ by using the .sigma.$_{\theta}$. We could find some characteristics of the .sigma.$_{\theta}$ which showed small value, when the atmospheric condition was in weak unstable (C class) and neutral (D class). Moreover, when the atmospheric stability was neutral, there was no difference of .sigma.$_{\theta}$ with wind speed. On the other hand, .sigma.$_{\theta}$ showed large values at the strong unstable (A class) and strong stable (F class) condition with low wind speed. In this case, the .sigma.$_{\theta}$ increased as long as averaging time due to the long-period wind direction fluctuation by the terrain effect. In the result of calculation of .sigma.$_{y}$, it was smaller than that of pasquill-Gifford curve. Especially, when the atmospheric condition was in a neutral and stable, .sigma.$_{y}$ showed small increment as the downwind distance increased.creased.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.36 no.8
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• pp.857-864
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• 2012

A linear stability analysis of a diffusion flame with radiation heat loss is performed to identify linearly unstable conditions for the Damk$\ddot{o}$hler number and radiation intensity. We adopt a counterflow diffusion flame with unity Lewis number as a model. Near the kinetic limit extinction regime, the growth rates of disturbances always have real eigenvalues, and a neutral stability condition perfectly falls into the quasi-steady extinction. However, near the radiative limit extinction regime, the eigenvalues are complex, which implies pulsating instability. A stable limit cycle occurs when the temperatures of the pulsating flame exceed the maximum temperature of the steady-state flame with real positive eigenvalues. If the instantaneous temperature of the pulsating flame is below the maximum temperature, the flame cannot recover and goes to extinction. The neutral stability curve of the radiation-induced instability is plotted over a broad range of radiation intensities.

• Journal of the Korean Society of Propulsion Engineers
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• v.1 no.2
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• pp.74-83
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• 1997

The definition of burning admittance and conventional n-$\tau$ stability rating technique are combined to investigate the high frequency combustion instabilities inside the cylindrical combustion chamber. Perturbed flow variables are written as the sum of fluctuating and time-averaged mean quantities on the assumption that the terms of the order higher than unity are sufficiently small, hence linearized governing equations could be formulated. Chamber admittances up and downstream of the flame front calculated with appropriate boundary conditions result in the burning admittance and corresponding n-$\tau$ neutral stability curve. Configurational and operational design factors are tested to detect the unstable wave-induced LOX-RP1 combustion instabilities. Operational design factors, e.g. pressure or O/F ratio, appear less influential to drive high frequency instability while the location of the flame front and configurational factors enhance or deteriorate the stabilities strongly. Conclusively, LOX-RP1 combustion inside the cylindrical combustion chamber is apt to be unstable against long residence time and shortened chamber length.

• Bulletin of the Korean Chemical Society
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• v.32 no.1
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• pp.277-280
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• 2011

We studied the relative stability and atomic structure of five $C_{20}^{2+}$ isomers obtained by two-electron ionization of a $C_{20}$ cage (the smallest fullerene). All the isomers are bond-stretch isomers, i.e., they differ in bond length. In particular, in one of the isomers with Ih symmetry, all the bond lengths are equal. Full geometry optimizations of the dipositive ion $C_{20}^{2+}$ were performed using the hybrid density functional (B3LYP/6-31G(d)) methods. All isomers were found to be true minima by frequency analysis at the level of B3LYP/6-31G(d) under the reinforced tight convergence criterion and a pruned (99,590) grid. The zero-point correction energy for the cage bond-stretch isomers was in the increasing order $D_{2h}<C_{2h}<C_2<T_h<I_h$ of $C_{20}^{2+}$. The energy difference among the isomers of cage dipositive ions was less than that among neutral cage isomers. Our results suggest that these isomers show bond-stretch isomerism and that they have an identical spin state and an identical potential energy curve. Although the predominant electronic configurations of the isomers are similar, the frontier orbital characteristics are different, implying that we could anticipate an entirely different set of characteristic chemical reactions for each type of HOMO and LUMO.

• Journal of Korean Neurosurgical Society
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• v.64 no.5
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• pp.776-783
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• 2021

Objective : The purpose of this study was to identify risk factors for distal adding on (AO) or distal junctional kyphosis (DJK) in adolescent idiopathic scoliosis (AIS) treated by posterior spinal fusion (PSF) to L3 with a minimum 2-year follow-up. Methods : AIS patients undergoing PSF to L3 by two senior surgeons from 2000-2010 were analyzed. Distal AO and DJK were deemed poor radiographic results and defined as >3 cm of deviation from L3 to the center sacral vertical line (CSVL), or >10° angle at L3-4 on the posterior anterior- or lateral X-ray at ultimate follow-up. New stable vertebra (SV) and neutral vertebra (NV) scores were defined for this study. The total stability (TS) score was the sum of the SV and NV scores. Results : Ten of 76 patients (13.1%) were included in the poor radiographic outcome group. The other 66 patients were included in the good radiographic outcome group. Lower Risser grade, more SV-3 (CSVL doesn't touch the lowest instrumented vertebra [LIV]) on standing and side bending films, lesser NV and TS score, rigid L3-4 disc, more rotation and deviation of L3 were identified risk factors for AO or DJK. Age, number of fused vertebrae, curve correction, preoperative coronal/sagittal L3-4 disc angle did not differ significantly between the two groups. Multiple logistic regression results indicated that preoperative Risser grade 0, 1 (odds ratio [OR], 1.8), SV-3 at L3 in standing and side benders (OR, 2.1 and 2.8, respectively), TS score -5, -6 at L3 (OR, 4.4), rigid disc at L3-4 (OR, 3.1), LIV rotation >15° (OR, 2.9), and LIV deviation >2 cm from CSVL (OR, 2.2) were independent predictive factors. Although there was significant improvement of the of Scoliosis Research Society-22 average scores only in the good radiographic outcome group, there was no significant difference in the scores between the groups. Conclusion : The prevalence of AO or DJK at ultimate follow-up for AIS with LIV at L3 was 13.1%. To prevent AO or DJK following fusion to L3, we recommend that the CSVL touch L3 in both standing and side bending, TS score is -4 or less, the L3/4 disc is flexible, L3 is neutral (<15°) and ≤2 cm from the midline and the patient is ≥ Risser 2.