• Journal of the Mineralogical Society of Korea
• /
• v.13 no.4
• /
• pp.186-195
• /
• 2000

To study phosphate adsorption on kaolinite, $^{31}$ P MAS NMR(magic angle spinning nuclear magnetic resonance spectroscopy)has been used for kaolinite reacted in 0.1 M phosphate solutions at pH’s from 3 to 11. There are at least 3 different forms of phosphate on kaolinite. One is the phosphate physically adsorbed on kaolinite surface (outer-sphere complexes) or species left after vacuum-filtering. The second is the phosphate adsorbed by ligand exchange (inner-sphere complexes), and the third is Al-phosphate precipitates which are pH dependent. Most of the inner-spherer complexes and surface precipitates are mainly on hydroxided Al(aluminol) rather than hydroxided Si(silanol). These are pertinent with the results obtained from the phosphate adsorption experiments on silica gel and ${\gamma}$-Al$_2$O$_3$ as model compounds, respectively. The two peaks with more negative chemical shifts(more shielded) than the ortho-phosphate peak (positive chemical shift) are assigned to be the inner-sphere complexes and surface precipitates. The $^{31}$ P chemical shifts of the Al-phosphate precipitates are more negative than those of inner-sphere complexes at a given pH due to the larger number of P-O-Al linkages per tetrahedron. The chemical shifts of both the inner-sphere complexes and surface precipitates are more negative than those of inner-sphere complexes at a given pH due to the larger number of P-O-Al linkages per tetrahedron. The chemical shifts of both the inner-sphere complexes and surface precipitates become progressively less shielded with increasing pH. For the inner-sphere complexes, decreasing phosphate protonation combined with peak averaging by rapid proton exchange among phosphate tetrahedra with different numbers of protons is though to be the reason for the peak change. The decreasing shielding with increasing pH for surface precipitates is probably due to the decreasing average number of P-O-Al linkages per tetrahedron combined with decreasing protonation like inner-sphere complexes.

• Journal of ILASS-Korea
• /
• v.24 no.4
• /
• pp.171-177
• /
• 2019

This paper describes numerical study of combustion characteristics in CNG(compressed natural gas) DI(direct injection) engine using gaseous sphere injection model. Simulations were conducted using KIVA-3V Release 2 code. Gaseous sphere injection model, which is modified model of liquid fuel injection, was used to simulate the CNG direct injection. Until now, a very fine mesh smaller than the injector nozzle has been required to resolve the gas-jet inflow boundary. However, the gaseous sphere injection model simulates gaseous fuel injection using a coarse mesh. This model injects gaseous spheres as in liquid fuel injection and the gaseous spheres evaporate together without the latent heat of evaporation. Therefore, it does not require a very fine mesh and reduce calculation time. Combustion simulation were performed under various injection timings and injection pressures.

• Communications of the Korean Mathematical Society
• /
• v.13 no.3
• /
• pp.561-577
• /
• 1998

We study (n＋3)-dimensional contact three CR submanifolds of a Riemannian manifold with Sasakian three structure and investigate some characterizations of $S^{4r＋3}$(a) $\times$ $S^{4s＋3}$(b) ($a^2$＋ $b^2$=1, 4(r ＋ s) = n - 3) as a contact three CR sub manifold of a (4m＋3)-dimensional unit sphere.

• Bulletin of the Korean Mathematical Society
• /
• v.51 no.5
• /
• pp.1375-1397
• /
• 2014

In this paper we establish codimension reduction theorem for submanifolds of a (4m+3)-dimensional unit sphere $S^{4m+3}$ with Sasakian 3-structure and apply it to submanifolds of a quaternionic projective space.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.5
• /
• pp.1599-1622
• /
• 2013

We show many examples of curves on the unit 2-sphere $S^2(1)$ in $\mathbb{R}^3$ and the unit 3-sphere $S^3(1)$ in $\mathbb{R}^4$. We study whether its curves are Bertrand curves or spherical Bertrand curves and provide some examples illustrating the resultant curves.

• Journal of the Society of Naval Architects of Korea
• /
• v.54 no.3
• /
• pp.250-257
• /
• 2017

It is desirable to have a way to predict the pressure drag due to various appendages attached to stern. As a mathematical model for these, a sphere and a singularity behind it, both in the uniform flow can be considered. We may use the Butler's sphere theorem to find the Stokes' stream function when the resulting flow is axisymmetric, and then the extended Lagally's theorem to get the force upon the sphere due to the singularity. Assuming the separation distance between the sphere and the singularity is small, the leading order approximation for the force is obtained and it is found out that if the separation distance and the square root of the strength of the dipole are of the same order, the effect of the image of the dipole with respect to the sphere is the most important.

• Wind and Structures
• /
• v.35 no.1
• /
• pp.1-20
• /
• 2022

This research work presents an experimental study's outcomes to reveal the impact of an O-ring on the flow control over a sphere placed in a turbulent boundary layer. The investigation is performed quantitatively and qualitatively using particle image velocimetry (PIV) and dye visualization. The sphere model having a diamater of 42.5 mm is located in a turbulent boundary layer flow over a smooth plate for gap ratios of 0≤G/D≤1.5 at Reynolds number of 5 × 10³. Flow characteristics, including patterns of instantaneous vorticity, streaklines, time-averaged streamlines, velocity vectors, velocity fluctuations, Reynolds stress correlations, and turbulence kinetic energy (), are compared and discussed for a naked sphere and spheres having O-rings. The boundary layer velocity gradient and proximity of the sphere to the flat plate profoundly influence the flow dynamics. At proximity ratios of G/D=0.1 and 0.25, a wall jet is formed between lower side of the sphere and flat plate, and velocity fluctuations increase in regions close to the wall. At G/D=0.25, the jet flow also induces local flow separations on the flat plate. At higher proximity ratios, the velocity gradient of the boundary layer causes asymmetries in the mean flow characteristics and turbulence values in the wake region. It is observed that the O-ring with various placement angles (𝜃) on the sphere has a considerable alteration in the flow structure and turbulence statistics on the wake. At lower placement angles, where the O-ring is closer to the forward stagnation point of the sphere, the flow control performance of the O-ring is limited; however, its impact on the flow separation becomes pronounced as it is moved away from the forward stagnation point. At G/D=1.50 for O-ring diameters of 4.7 (2 mm) and 7 (3 mm) percent of the sphere diameter, the -ring exhibits remarkable flow control at 𝜃=50° and 𝜃=55° before laminar flow separation occurrence on the sphere surface, respectively. This conclusion is yielded from narrowed wakes and reductions in turbulence statistics compared to the naked sphere model. The O-ring with a diameter of 3 mm and placement angle of 50° exhibits the most effective flow control. It decreases, in sequence, streamwise velocity fluctuations and length of wake recovery region by 45% and 40%, respectively, which can be evaluated as source of decrement in drag force.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
• /
• v.36 no.3
• /
• pp.280-285
• /
• 2023

A breakdown voltage and breakdown electric field of the transformer insulating oil of liquid dielectric were studied in uniform electric field and non-uniform electric field and the transformer insulating oil was observed by the process reached breakdown. Insulation performance evaluation of the liquid dielectric was evaluated at the electrode spacing of 2.5 mm under the conditions of domestic and international standards (KS C IEC 60156), so a comparative review was conducted at the electrode spacing of 2.5 mm. When the electrode spacing is 2.5 mm, the average breakdown voltage is 38.5 kV for sphere-sphere electrodes, 26.6 kV for plate-plate electrodes, 22.9 kV for needle-needle electrodes, and 24.3 kV for sphere-needle electrodes. 23.7 kV for the sphere-plate electrode, and 20.7 kV for the needle-plate electrode. From these results, it can be seen that the average value of the breakdown voltage at the electrode spacing of 2.5 mm, in ascending order, is sphere-sphere, plate-plate, sphere-needle, sphere-plate, needle-needle and needle-plate. It was found that the breakdown voltage of the unequal field was lower than that of the equal field.

• Bulletin of the Korean Mathematical Society
• /
• v.59 no.1
• /
• pp.101-110
• /
• 2022

In this article, the notion of *-conformal Ricci soliton is defined as a self similar solution of the *-conformal Ricci flow. A Sasakian 3-metric satisfying the *-conformal Ricci soliton is completely classified under certain conditions on the soliton vector field. We establish a relation with Fano manifolds and proves a homothety between the Sasakian 3-metric and the Berger Sphere. Also, the potential vector field V is a harmonic infinitesimal automorphism of the contact metric structure.

• Journal of the Korean Mathematical Society
• /
• v.54 no.4
• /
• pp.1331-1343
• /
• 2017

A curve ${\gamma}$ immersed in the three-dimensional sphere ${\mathbb{S}}^3$ is said to be a slant helix if there exists a Killing vector field V(s) with constant length along ${\gamma}$ and such that the angle between V and the principal normal is constant along ${\gamma}$. In this paper we characterize slant helices in ${\mathbb{S}}^3$ by means of a differential equation in the curvature ${\kappa}$ and the torsion ${\tau}$ of the curve. We define a helix surface in ${\mathbb{S}}^3$ and give a method to construct any helix surface. This method is based on the Kitagawa representation of flat surfaces in ${\mathbb{S}}^3$. Finally, we obtain a geometric approach to the problem of solving natural equations for slant helices in the three-dimensional sphere. We prove that the slant helices in ${\mathbb{S}}^3$ are exactly the geodesics of helix surfaces.