• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1261-1269
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• 2023

For a fixed parametrization of a curve in an orientable two-dimensional Riemannian manifold, we introduce and investigate a new frame and curvature function. Due to the way of defining this new frame as being the time-dependent rotation in the tangent plane of the standard Frenet frame, both these new tools are called flow.

• 한국전산유체공학회:학술대회논문집
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• 1997.10a
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• pp.131-135
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• 1997

Effect of wall curvature on flow characteristics is studied for mildly and strongly curved duct flows. The ducts are S-shaped, and the flow is partially blocked at the rear of the downstream. The presence of blockage in combination with curvature generates secondary flows on the concave surface; the magnitude of the secondary flow being dependent on the degree of wall curvature. Objectives are to compare the flow structures for mild and strong cases and to illuminate the changes in flow structure as the flow turns. Sensitivity on numerical solutions due to different inflow boundary conditions is also examined.

• Journal of the Korean Mathematical Society
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• v.50 no.4
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• pp.829-845
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• 2013

In this paper, we firstly establish a family of curvature invariant conditions lying between the well-known 2-nonnegative curvature operator and nonnegative curvature operator along the Ricci flow. These conditions are defined by a set of inequalities involving the first four eigenvalues of the curvature operator, which are named as 3-parameter ${\lambda}$-nonnegative curvature conditions. Then a related rigidity property of manifolds with 3-parameter ${\lambda}$-nonnegative curvature operators is also derived. Based on these, we also obtain a strong maximum principle for the 3-parameter ${\lambda}$-nonnegativity along Ricci flow.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.9
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• pp.2223-2236
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• 1995

0The fields of turbomachinery and electrical generators provide many examples of flow through rotating internal passages. At the practicing Reynolds number, most of the flow motion is three dimensional and highly turbulent. The proper understanding for the characteristics of these turbulent flow is necessary for the design of thermo-fluid machinery of a good efficiency. The flow characteristics in the rotating duct with curvature are very complex in practice due to the curvature and rotational effect of the duct. The understanding of the effect of the curvature on the structure and rotational effect of the duct. The understanding of the effect of the curvature on the structure of turbulence in the curved passage and the characteristics of the flow in a rotating radial straight channel have been well studied separately by many workers. But the combined effects of curvature and rotation on the flow have not been well understood inspite of the importance of the phenomena in the practical design process. In this study, the characteristics of a developing turbulent flow in a square sectioned 90.deg. bend rotating at a constant angular velocity are measured by using hot-wire anemometer to seize the rotational effects on the flow characteristics. As the results of this study, centrifugal forces associated with the curvature of the bend and Coriolis forces and centripetal forces associated with the rotational affect directly both the mean motion and the turbulent fluctuations.

• East Asian mathematical journal
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• v.38 no.3
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• pp.331-338
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• 2022

In this paper, we prove that the first nonzero eigenvalues λ₁ of the Laplacian and the p-Laplacian are decreasing along the inverse mean curvature flow with forced term in Euclidean space.

• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.2119-2139
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• 2017

Here, certain Ricci flow for Finsler n-manifolds is considered and deformation of Cartan hh-curvature, as well as Ricci tensor and scalar curvature, are derived for spaces of scalar flag curvature. As an application, it is shown that on a family of Finsler manifolds of constant flag curvature, the scalar curvature satisfies the so-called heat-type equation. Hence on a compact Finsler manifold of constant flag curvature of initial non-negative scalar curvature, the scalar curvature remains non-negative by Ricci flow and blows up in a short time.

• Bulletin of the Korean Mathematical Society
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• v.58 no.4
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• pp.877-884
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• 2021

We prove that if a compact convex hypersurface of ℝⁿ⁺¹ has almost maximal extinction time when it is evolved by the mean curvature flow, then it must be nearly round in the C⁰-norm.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.22 no.8
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• pp.1173-1182
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• 1998

A throughflow analysis program for axial flow turbines is constructed, which can handle not only the two-dimensional multi-streamline (streamline curvature) method but also the one-dimensional mean line method. Calculations are performed for single stage and multi-stage axial flowturbines. For a wide operating range, the performance and flow field calculated by the present streamline curvature method are close enough to the test data. It is also revealed for the single stage turbine that the present analysis leads to far better correspondence with the experiment than other researchers" throughflow analyses. A special focus is put on the comparison of the results between the streamline curvature analysis and the mean line analysis. It is found that the mean line analysis can not predict the performance for highly off-designed conditions as accurately as the streamline curvature method, which shows the importance of considering the spanwise variation of loss and flow.

• 한국전산유체공학회:학술대회논문집
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• 2009.04a
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• pp.97-103
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• 2009

A numerical study of the flow characteristics inside a U-type circular tube is carried out in this paper. The numerical simulations carried out by using a Navier-Stokes code which is commercially available. Before detailed numerical simulations, validation of present numerical approach is made by comparing numerical solutions with experimental data. Numerical simulations are performed to study the effect of curvature on the flow characteristics inside a U-type tube. Numerical solutions show that a significant effect on the secondary flow structure in the cross section of the tube, especially in the curved section is shown when the curvature ratio, ratio of curvature to tube diameter, is smaller than about 3.5. As the curvature ratio decreases below 3.5, a counter rotating vortex is found below the primary vortex in the cross section of the tube. Another dramatic change of the flow structure is the formation of streamwise separation zone when the curvature ratio is decreased below 1.25.

• Journal of computational fluids engineering
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• v.14 no.3
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• pp.105-114
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• 2009

A numerical study of the flow characteristics inside a U-type circular tube is carried out in this paper. The numerical simulations carried out by using a Navier-Stokes code which is commercially available. Before detailed numerical simulations, validation of present numerical approach is made by comparing numerical solutions with experimental data. Numerical simulations are performed to study the effect of curvature on the flow characteristics inside a U-type tube. Numerical solutions show that a significant effect on the secondary flow structure in the cross section of the tube, especially in the curved section is shown when the curvature ratio, ratio of curvature to tube diameter, is smaller than about 3.5. As the curvature ratio decreases below 3.5, a counter rotating vortex is found below the primary vortex in the cross section of the tube. Another dramatic change of the flow structure is the formation of streamwise separation zone when the curvature ratio is decreased below 1.25.