• Journal of computational fluids engineering
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• v.13 no.3
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• pp.14-20
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• 2008

In this investigation, flow patterns past two identical nearby spheres at Re=300 were numerically studied. We considered all possible arrangements of the two spheres in terms of the distance between the spheres and, the angle inclined with respect to the main flow direction. It turns out that significant changes in shedding characteristics are noticed depending on how the two spheres are positioned. Collecting all the numerical results obtained, we propose a diagram for flow pattern on the distance vs. angle plane. The perfect geometrical symmetry implied in the flow configuration allows one to use that diagram to identify flow patterns past two identical spheres arbitrarily positioned in physical space with respect to the main flow direction.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.29 no.12 s.243
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• pp.1313-1320
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• 2005

In this investigation, we studied the wake interactions incurred by two nearby spheres at Re=300. We considered all possible arrangements of the two spheres in terms of the distance between the spheres and, the angle inclined with respect to the flow direction. It turns out that significant changes in shedding characteristics are noticed depending on how the two spheres are positioned. In this study, not only quantitative changes in the key physical parameters such as force coefficients and shedding frequencies, but also qualitative changes in shedding patterns are analyzed and reported.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.29 no.2 s.233
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• pp.247-254
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• 2005

A parametric study on the interactions of two spheres aligned in the streamwise direction is carried out using an immersed boundary method. The numerical results for the case of single sphere for the range of $Rs{\le}300$ are in good agreement with other authors' experimental and numerical results currently available. Then, our main investigation is focused on identifying the change of the vortical structures in the presence of a nearby sphere aligned in the streamwise direction for the range $Re{\le}300$. It turns out that significant changes in physical characteristics are noticed depending on how close the two spheres are. In this paper, not only quantitative changes in the key physical parameters such as the force coefficients, but also qualitative changes in vortex structures are reported and analyzed.

• Proceedings of the KSME Conference
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• 2004.11a
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• pp.1418-1423
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• 2004

A parametric study on the interactions of two spheres aligned in the streamwise direction is carried out using an immersed boundary method. The numerical results for the case of single sphere for the range of Re ${\leq}$ 300 are in good agreement with other authors' experimental and numerical results currently available. Then, our main investigation is focused on identifying the change of the vortical structures in the presence of a nearby sphere aligned in the streamwise direction for the range Re ${\leq}$ 220. It turns out that significant changes in physical characteristics are noticed depending on how close the two spheres are. In this paper, not only quantitative changes in the key physical parameters such as the force coefficients, but also qualitative changes in vortex structures are reported and analyzed.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.30 no.5 s.248
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• pp.480-488
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• 2006

Numerical simulations of flow over two spheres placed in a tandem arrangement are conducted to investigate the effect of the inter-sphere spacing on the flow characteristics. The Reynolds numbers considered are 100, 250, 300 and 425, corresponding to steady axisymmetric, steady planar-symmetric, unsteady planar-symmetric, and unsteady asymmetric flows, respectively, in the case of a single sphere. For small inter-sphere spacings, the flow past two spheres is more stable than that past a single sphere. For example, with the spacing of the sphere radius, the flow is steady axisymmetric up to Re=300. However, for relatively large spacings, the flow past two spheres becomes unstable and vortex shedding takes place even at Re=250. The drag coefficient of the rear sphere decreases significantly with decreasing inter-sphere spacing due to reduction of the stagnation pressure, thus being smaller than that of the front sphere. Also, the rear sphere shows large fluctuations of the lift force as compared to the front one in the case of unsteady flow.

• Journal of the Korean Mathematical Society
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• v.54 no.1
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• pp.303-317
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• 2017

An isometry of hyperbolic space can be written as a composition of the reflection in the isometric sphere and two Euclidean isometries on the boundary at infinity. The isometric sphere is also used to construct the Ford fundamental domains for the action of discrete groups of isometries. In this paper, we study the isometric spheres of isometries acting on hyperbolic 4-space. This is a new phenomenon which occurs in hyperbolic 4-space that the two isometric spheres of a parabolic isometry can intersect transversally. We provide one geometric way to classify isometries of hyperbolic 4-space using the isometric spheres.

• Korean Journal of Computational Design and Engineering
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• v.11 no.2
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• pp.97-106
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• 2006

Voronoi diagrams have been known for numerous important applications in science and engineering including CAD/CAM. Especially, the Voronoi diagram for 3D spheres has been known as very useful tool to analyze spatial structural properties of molecules or materials modeled by a set of spherical atoms. In this paper, we present two algorithms, the edge-tracing algorithm and the region-expansion algorithm, for constructing the Voronoi diagram of 3D spheres and applications to protein structure analysis. The basic scheme of the edge-tracing algorithm is to follow Voronoi edges until the construction is completed in O(mn) time in the worst-case, where m and n are the numbers of edges and spheres, respectively. On the other hand, the region-expansion algorithm constructs the desired Voronoi diagram by expanding Voronoi regions for one sphere after another via a series of topology operations, starting from the ordinary Voronoi diagram for the centers of spheres. It turns out that the region-expansion algorithm also has the worst-case time complexity of O(mn). The Voronoi diagram for 3D spheres can play key roles in various analyses of protein structures such as the pocket recognition, molecular surface construction, and protein-protein interaction interface construction.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.9
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• pp.910-914
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• 2007

We present a simple and an inexpensive method for the fabrication of a nano-fluidic filter and a nano-pore micromixer using self-assembly of nano-spheres and surface tension. Colloid-plug was formed by surface tension of liquid in a microchannel to fabricate nanofluidic filter. When colloid is evaporated, nano-spheres in a colloid are orderly stacked by a capillary force. Orderly stacked nano-spheres form 3-D nano-mesh which can be used as a mesh structure of a fluidic filter. We used silica nano-sphere whose diameter is $567{\pm}85nm$, and silicon micro-channel of $50{\mu}m$-diameter. Fabricated nano-fluidic filter in a micro-channel has median pore diameter of 158nm which was in agreement with expected diameter of the nano-pore of $128{\pm}19nm$. A nano-pore micromixer consists of $200\;{\mu}m-wide,\;100\;{\mu}m-deep$ micro-channel and self-assembled nano-spheres. In the nano-pore micromixer, two different fluids had no sooner met together than two fluids begin to mix at wide region. From the experimental study, we completely apply self-assembly of nano-spheres to nano-fluidic devices.

• Korea-Australia Rheology Journal
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• v.19 no.4
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• pp.201-209
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• 2007

The present paper is concerned with non-isothermal spherical Couette flow of Oldroyd-B fluid in the annular region between two concentric spheres. The inner sphere rotates with a uniform angular velocity while the outer sphere is kept at rest. Moreover, the two spherical boundaries are maintained at fixed temperature values. Hence, the fluid is effect by two heat sources; namely, the viscous heating and the temperature gradient between the two spheres. The viscoelasticity of the fluid is assumed to dominate the inertia such that the latter can be neglected. An approximate analytical solution of the energy and momentum equations is obtained through the expansion of the dynamical fields in power series of Nahme number. The analysis show that, the temperature variation due to the external source appears in the zero order solution and its effect extends to the fluid velocity distribution up to present second order. Viscous heating contributes in the first and second order solutions. In contrast to isothermal case, a first order axial velocity and a second order stream function fields has been appeared. Moreover, at higher orders the temperature distribution depends on the gap width between the two spheres. Finally, there exist a thermal distribution of positive and negative values depend on their positions in the domain region between the two spheres.

• Journal of computational fluids engineering
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• v.12 no.4
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• pp.61-67
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• 2007

Numerical simulation of laminar flow over two spheres in a side-by-side arrangement is carried out to investigate the effect of the inter-sphere spacing on the flow characteristics. The Reynolds numbers considered are 100, 250, and 300, covering the steady axisymmetric, steady planar-symmetric, and unsteady planar-symmetric flows in the case of a single sphere. Results show that the drag and lift coefficients and wake structures are significantly modified depending on both the Reynolds number and the spacing between the spheres. At Re=100, the flow is steady planar-symmetric irrespective of the spacing, but it shows some variation according to the spacing at Re=250 and 300. That is, the flow maintains planar symmetry of the single-sphere wake at large spacings, while it loses the symmetry at small spacings due to the generation of new asymmetric vortical structures. It is also shown that the drag and lift coefficients generally increase with decreasing inter-sphere spacing because the high pressure region is formed near the gap between the spheres.