• Journal of the Korean Society of Safety
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• v.18 no.1
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• pp.33-37
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• 2003

The objective of the present work is to examine the variation of cooling characteristics due to the Weber number of droplet on a heated surface. The surface temperatures varied from 72.5 - $106.1^{\circ}C$ on steel and Teflon, when Weber number was 60, 180, 300. The results are as follows; In the case of the same droplet size, the initial temperature of solid increases the indepth temperature of solid more drop. In the case of the same surface temperature, Weber number increases with increasing the cooling effect of droplet. The time-average heat flux increases with increasing the initial temperature of solid and Weber number. The evaporation time decreases with increasing the initial temperature of solid and Weber number.

• Proceedings of the KSME Conference
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• 2000.11b
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• pp.738-744
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• 2000

The breakup behaviors of impinging droplet on a hot surface are studied experimentally. The droplets are produced by the dripping method and the breakup behaviors of liquid droplet are recorded by photographs. Experimental conditions are, droplet diameter di : 2.5, 3.2 [mm], weber number : $30{\sim}140$, surface temperature : $28^{\circ}C(room\;temperature){\sim}450^{\circ}C$. Water is used to liquid. As weber number of droplet increases, a liquid sheet, which is formed after the impingement on a hot surface, is disintergrated by the dynamical effect. But at low weber number, it has effected by thermodynamical effect. The breakup behaviors of droplet are divided into three patterns with weber number and surface temperature, non-disintegration, transition and disintegration region. Further, these boundary values are affected by the hot surface temperature and weber number. SMD of breakup droplets are calculated in according to surface temperatures and weber number. The minium SMD of breakup droplets are observed at weber number 65.49, temperature $250^{\circ}C$ and weber number 99.08, temperature $350^{\circ}C$.

• Journal of applied mathematics & informatics
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• v.33 no.1_2
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• pp.157-172
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• 2015

We introduce a non-Euclidean metric for transportation systems with a defined minimum transportation cost (initial fare) and investigate the continuous single-facility Weber location problem based on this metric. The proposed algorithm uses the results for solving the Weber problem with Euclidean metric by Weiszfeld procedure as the initial point for a special local search procedure. The results of local search are then checked for optimality by calculating directional derivative of modified objective functions in finite number of directions. If the local search result is not optimal then algorithm solves constrained Weber problems with Euclidean metric to obtain the final result. An illustrative example is presented.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.4
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• pp.799-814
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• 2009

A class invariant is the value of a modular function that generates a ring class field of an imaginary quadratic number field such as the singular moduli of level 1. In this paper, using Shimura Reciprocity Law, we compute the Galois actions of some class invariants from the generalized Weber functions $\mathfrak{g}_0,\mathfrak{g}_1,\mathfrak{g}_2$ and $\mathfrak{g}_3$ over quadratic number fields with discriminant $D{\equiv}1$ (mod 12).

• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.213-219
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• 2013

A class invariant is the value of a modular function that generates a ring class field of an imaginary quadratic number field such as the singular moduli of level 1. In this paper, we compute the Galois actions of a class invariant from a generalized Weber function $g_1$ over imaginary quadratic number fields with discriminant $D{\equiv}64(mod72)$.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.921-925
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• 2011

A class invariant is the value of a modular function that generates a ring class field of an imaginary quadratic number field such as the singular moduli of level 1. In this paper, using Shimura Reciprocity Law, we compute the Galois actions of a class invariant from a generalized Weber function $g_2$ over quadratic number fields with discriminant $D{\equiv}21$ (mod 36).

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.853-860
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• 2010

A class invariant is the value of a modular function that generates a ring class field of an imaginary quadratic number field such as the singular moduli of level 1. In this paper, using Shimura Reciprocity Law, we compute the Galois actions of a class invariant from a generalized Weber function $g_2$ over quadratic number fields with discriminant $D{\equiv}-3$ (mod 36).

• Journal of the Korea Academia-Industrial cooperation Society
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• v.17 no.6
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• pp.39-44
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• 2016

Recently, there has been increasing concern regarding the collapse of hydraulic structures due to abnormal climate conditions. Therefore, numerous studies of the collapse of hydraulic structures have been carried out. In particular, the velocity of the propagation of a flood wave-front is important for predicting the inundation safety and establishing an EAP (Emergency Action Plan). Although many hydraulic tests have been conducted for precise predictions of a flood wave-front, the scale effect from downsizing has not considered. In this study, the relationships between surface tension and the concentration of surfactant, between surface tension and the velocity of flood wave propagation, and between surface tension and the Weber Number were derived through hydraulic tests using a surfactant and image analysis equipment. Based on these relations, the modification factor for the scale effect of the front of flood wave propagation was suggested. The results highlight the necessity of a modification factor when the Weber Number is lower than 12.2, but the scale effect can be ignored when the Weber Number over 12.2.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2003.10a
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• pp.168-172
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• 2003

The effects of injection conditions on the droplet sizes resulting from the disintegration of a liquid jet by a fast annular gas stream have been investigated using PDPA. The gas/liquid momentum ratio M = $\rho$$_{g}$ $U_{g}$$^2$/$\rho$$_1$ $U_1$$^2$ and Weber number We = $\rho$$_{g}$ $g^2$ $D_1$/$\sigma$ are selected as key parameters in atomization of shear coaxial spray from the fluid mechanics standpoint. It is revealed that SMD( $D_{32}$) varies inversely with gas/liquid momentum ratio(M), whereas Weber number(We) has little effect on the droplet sizes as gas velocities increase. It is found that gas/liquid momentum ratio is more dominant factor controlling the breakup and atomization process of shear coaxial spray. Finally, an empirical correlation between SMD and injection conditions(i.e. gas/liquid momentum ratio M and Weber number We) is proposed based on the experimental results.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.34 no.6
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• pp.51-58
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• 2006

The spray characteristics of liquid jet injected into subsonic cross-flow were investigated experimentally. Spray trajectories were captured using CCD camera. Droplet sizes were measured using PDPA and Image Express. The nozzle diameter was 0.5 mm, and its length-to-diameter ratios (L/D) ran$4.11{\times}10^6$ged from 1.0 to 6.0. Experimental results indicate that the breakup point is delayed by increasing gas momentum ratio and the penetration length is decreased by increasing Weber number. At low injection angle(${\theta}$ < $90^{\circ}$), Weber number is dominant parameter for trajectories, but at high injection angle(${\theta}$ > $90^{\circ}$), L/D is dominant parameter for trajectories rather than Weber number.