• Korean Chemical Engineering Research
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• 제50권3호
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• pp.522-526
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• 2012

수직 고체하강관에서 고체하강속도를 측정할 수 있는 편리한 실험방법을 제시하였으며 Geldart 분류 A, B, D 입자를 사용하여 수직관의 직경 및 입자특성 변화에 따른 고체하강속도를 측정 및 고찰하였다. 초기 입자 장입량 변화에 따른 고체하강속도의 변화는 크지 않았으며 고체하강관 직경이 증가함에 따라 고체흐름속도, 고체순환속도 및 고체하강속도가 증가하는 경향을 나타내었다. 특히 고체하강속도의 경우 모든 입자에 대해 하강관의 직경이 증가함에 따라 직선적으로 증가하는 경향을 나타내었으며, Geldart 분류 A 및 B 입자와 Geldart 분류 D 입자의 결과가 확실하게 구별되는 경향을 나타내었다. 측정된 고체하강속도를 바탕으로 Geldart 분류 A 및 B 입자계와 D 입자계에 대한 고체하강속도 상관식을 제시하였으며 측정값과 유사한 값을 예측할 수 있었다.

• 대한기계학회논문집B
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• 제21권9호
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• pp.1165-1173
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• 1997

The steady state close-contact melting phenomenon occurring between a phase change material and an isothermally heated flat plate with relative motion is investigated analytically, in which the effects of vertical convection in the liquid film and solid-liquid density difference are incorporated simultaneously. Not only the scale analysis is conducted to estimate a priori qualitative dependence of system variables on characteristic parameters, but also an analytical solution to a set of simplified model equations is obtained to specify the effects under consideration. These two results are consistent with each other, in that the vertical convection affects both the solid descending velocity and the film thickness, and that the density difference alters only the solid descending velocity. While the effect of vertical convection can be characterized conveniently by a newly introduced temperature gradient factor which asymptotically approaches the unity/zero with decreasing/increasing the Stefan number, that of density difference is represented by the liquid-to-solid density ratio. It is shown that the solid descending velocity depends linearly on the density ratio, and that the ratios of solid descending velocity, film thickness and friction coefficient to the conduction solution are proportional to 3/4, 1/4 and -1/4 powers of the temperature gradient factor, respectively. Also, established is the fact that the effect of convection can be legitimately neglected in the analysis for the range of the Stefan number less than 0.1.

• 대한기계학회논문집B
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• 제21권12호
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• pp.1710-1719
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• 1997

An approximate analytical solution for the initial transient process of close-contact melting occurring between a phase change material kept at its melting temperature and an isothermally heated flat surface is derived. The model is so developed that it can cover both rectangular and circular cross-sectional solid blocks. Normalization of simplified model equations in reference to the steady solution enables the solution to be expressed in a generalized form depending on the liquid-to-solid density ratio only. A selected result shows an excellent agreement with the previously reported numerical data, which justifies the present approach. The solution appears to be capable of describing all the fundamental characteristics of the transient process. In particular, dependence of the solid descending velocity oft the density ratio at the early stage of melting is successfully resolved. The effects of other parameters except the density ratio on the transient behaviors are efficiently represented via the steady solution implied in the normalized result. A simple approximate method for estimating the effect of convection on heat transfer across the liquid film is also proposed.

• Coupled systems mechanics
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• 제7권4호
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• pp.407-420
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• 2018

In solid-liquid two phase flow, the knowledge of how descending solid particles affected by the presence of downstream wall is important. This work studies at what interstitial distance the velocity of a vertically descending sphere is affected by a downstream wall as a consequence of wall-modified hydrodynamic forces through a validated dynamic model. This interstitial distance-the hydrodynamic coupling distance ${\delta}_c-is$ found to decay monotonically with the approach Stokes number St which compares the particle inertia to viscous drag characterized by the quasi-steady Stokes' drag. The scaling relation ${\delta}_c-St-1$ decays monotonically as literature below the value of St equal to 10. However, the faster diminishing rate is found above the threshold value from St=10-40. Furthermore, an empirical relation of ${\delta}_c-St$ shows dependence on the drop height which clearly indicates the non-negligible effect of unsteady hydrodynamic force components, namely the added mass force and the history force. Finally, we attempt a fitting relation which embedded the particle acceleration effect in the dependence of fitting constants on the diameter-scaled drop height.

• 대한기계학회논문집B
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• 제23권8호
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• pp.945-956
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• 1999

This work reports a set of approximate analytical solutions describing the initial transient process of close-contact melting between a rectangular parallelepiped solid and a flat plate on which either constant temperature or constant heat flux is imposed. Not only relative motion of the solid block tangential to the heating plate, but also the density difference between the solid and liquid phase is incorporated in the model. The thin film approximation reduces the force balance between the solid weight and liquid pressure, and the energy balance at the melting front into a simultaneous ordinary differential equation system. The normalized model equations admit compactly expressed analytical solutions which include the already approved two-dimensional solutions as a subset. In particular, the normalized liquid film thickness is independent of all pertinent parameters, thereby facilitating to define the transition period of close-contact melting. A unique behavior of the solid descending velocity due to the density difference is also resolved by the present solution. A new geometric function which alone represents the three-dimensional effect is introduced, and its properties are clarified. One of the representative results is that heat transfer is at least enhanced at the expense of the increase in friction as the cross-sectional shape deviates from the square under the same contact area.

• 대한기계학회논문집B
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• 제22권12호
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• pp.1726-1734
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• 1998

This paper focuses on the unsteady close-contact melting phenomenon occurring between a phase change material kept at its melting temperature and a flat surface on which constant heat flux is imposed. Based on the same simplifications and framework of analysis as the case of constant surface temperature, an approximate analytical solution which depends only on the liquid-to-solid density ratio is successfully derived. In order to keep consistency with the known solution procedure, both the dimensionless wall heat flux and the Stefan number are properly redefined. The obtained solution proves to agree quite well with the published numerical data and to be capable of resolving the fundamental features of unsteady close-contact melting, especially in the presence of the solid-liquid density difference. The density ratio directly affects the film growth rate and the initial value of solid descending velocity, thereby controlling the duration of unsteady process. The effects of other parameters can be evaluated readily from the steady solution which is implied in the normalized result. Since the dimensionless surface temperature for the present boundary condition increases from zero to unity along the evolution path of the liquid film thickness, the unsteady process lasts longer than that for the case of isothermal heating.