• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.4
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• pp.967-976
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• 1994

A tensor invariant model equation for the turbulent energy dissipation rate is proposed in the present study, which is able to simulate secondary straining effects such as curvature effects without the introduction of additional empirical input. The source term in this model has a combined form of the generation term due to the mean vorticity with the conventional one due to the mean strain rate. An extended low-Reynolds-number $k-\epsilon$ turbulence model involving this new model equation is tested for a turbulent Coutte flow between coaxial cylinders with inner cylinder rotated, which is a well defined example of curved flows. The predicted results indicate that the present model works much better for this flow, compared with previous models.

• Journal of KSNVE
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• v.6 no.2
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• pp.233-244
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• 1996

In this paper chaotic mothions of a straight pipe conveying oscillatory flow and being subjected to external forces such as earthquake are theoretically investigated. The nonlinear partial differential equation of motion is derived by Newton's method. In this equation, the nonlinear curvature of the pipe and the thermal expansion effects are contained. The nonlinear ordinary differential equation transformed from that partial differential equation is a type of Hill's equations, which have the parametric and external exciation term. This original system is transfered to the averaged system by the averaging theory. Bifurcation curves of chaotic motion of the piping system are obtained in the general case of the frequency ratio, n by applying Melnikov's method. Numerical simulations are performed to demonstrate theorectical results and show strange attactors of the chaotic motion.

• Journal of the Korean Society of Propulsion Engineers
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• v.25 no.3
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• pp.42-55
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• 2021

In this study, the effect of nozzle performance according to the selection of the center line equation. Three of S-type nozzles and three of double S-type nozzles were designed using the curve equation and design parameters, and the nozzle shielding performance was evaluated using the shielding ratio definition. In order to analyze the internal flow of the nozzle, the characteristics of the velocity distribution and pressure distribution were studied, and the nozzle performance was evaluated through the total thrust ratio(f) and the nozzle insulation efficiency coefficient(η). On the other hand, the centerline with a sharply change in curvature at the entrance has a low nozzle performance and a high shielding rate. The double S-type nozzle is excellent nozzle performance and shielding rate by using a smooth centerline at the first curvature.

• Imaging Science in Dentistry
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• v.36 no.1
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• pp.55-62
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• 2006

Purpose : To find the cause of root curvature by use of panoramic and lateral cephalometric radiograph. Materials and Methods : Twenty six 1st graders whose mandibular 1st molars .just emerged into the mouth were selected. Panoramic and lateral cephalometric radiograph were taken at grade 1 and 6, longitudinally. In cephalometric radio graph, mandibular plane angle, ramus-occlusal plane angle, gonial angle, and gonion-gnathion distance (Go-Gn distance) were measured. In panoramic radio graph, elongated root length and root angle were measured by means of digital subtraction radiography. Occlusal plane-tooth axis angle was measured, too. Pearson correlations were used to evaluate the relationships between root curvature and elongated length and longitudinal variations of all variables. Multiple regression equation using related variables was computed. Results : The Pearson correlation coefficient between curved angle and longitudinal variations of occlusal plane-tooth axis angle and ramus-occlusal plane angle was 0.350 and 0.401, respectively (p<0.05). There was no significant correlation between elongated root length and longitudinal variations of all variables. The resulting regression equation was $Y=10.209+0.208X_1+0.745X_2$ (Y: root angle, $X_1$: variation of occlusal plane-tooth axis angle, $X_2$: variation of ramus-occlusal plane angle). Conclusion : It was suspected that the reasons of root curvature were change of tooth axis caused by contact with 2nd deciduous tooth and amount of mesial and superior movement related to change of occlusal plane.

• The Journal of the Korea Contents Association
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• v.12 no.3
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• pp.434-441
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• 2012

An analytic solution to the extended mild-slope equation was derived for waves propagating over an axi-symmetric pit. The water depth inside the pit was in proportion to a power of radial distance from the center of pit. The equation was transformed into the ordinary differential equation using the method of separation of variables. The coefficients of differential terms were expressed as an explicit form composing of the phase and group velocities. The bottom curvature and the square of bottom slope terms, which were added to the extended mild-slope equation, were expressed as power series. Finally, using the Frobenius series, the analytic solution to the extended mild-slope equation was derived. The present analytic solution was validated by comparing with the numerical solution obtained from FEM.

• Proceedings of the KSME Conference
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• 2002.08a
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• pp.209-212
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• 2002

Since Berkhoff proposed the mild-slope equation in 1972, it has widely been used for calculation of shallow water wave transformation. Recently, it was extended to give an extended mild-slope equation, which includes the bottom slope squared term and bottom curvature term so as to be capable of modeling wave transformation on rapidly varying topography. These equations were derived by integrating the Laplace equation vertically. In the present study, we develop a finite element model to solve the Laplace equation directly while keeping the same computational efficiency as the mild-slope equation. This model assumes the vertical variation of wave potential as a cosine hyperbolic function as done in the derivation of the mild-slope equation, and the Galerkin method is used to discretize . The computational domain was discretized with proper finite elements, while the radiation condition at infinity was treated by introducing the concept of an infinite element. The upper boundary condition can be either free surface or a solid structure. The applicability of the developed model was verified through example analyses of two-dimensional wave reflection and transmission. .

• Journal of the Korean Mathematical Society
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• v.49 no.3
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• pp.585-604
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• 2012

In this paper we consider the evolution of the rolling stone with a rotationally symmetric nonconvex compact initial surface ${\Sigma}_0$ under the Gauss curvature flow. Let $X:S^n{\times}[0,\;{\infty}){\rightarrow}\mathbb{R}^{n+1}$ be the embeddings of the sphere in $\mathbb{R}^{n+1}$ such that $\Sigma(t)=X(S^n,t)$ is the surface at time t and ${\Sigma}(0)={\Sigma}_0$. As a consequence the parabolic equation describing the motion of the hypersurface becomes degenerate on the interface separating the nonconvex part from the strictly convex side, since one of the curvature will be zero on the interface. By expressing the strictly convex part of the surface near the interface as a graph of a function $z=f(r,t)$ and the non-convex part of the surface near the interface as a graph of a function $z={\varphi}(r)$, we show that if at time $t=0$, $g=\frac{1}{n}f^{n-1}_{r}$ vanishes linearly at the interface, the $g(r,t)$ will become smooth up to the interface for long time before focusing.

• Fashion & Textile Research Journal
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• v.1 no.4
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• pp.387-392
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• 1999

The effects of the ratio of warp diameter to filling diameter (${\beta}$-ratio) and warp thread crash on the crimp factor and the yarn curvature were studied theoretically in this paper. The models of 2/2 twill fabric derived square cloth and sinusoidal curved cloth were used for the theoretical analysis. The crimp factors (C) for the models were given theoretically as follows; (1) Derived square cloth(general equation for b) $$C=\frac{(1+{\beta})({\theta}-sin{\theta})}{(1+{\beta})sin{\theta}+{\alpha}}$$ (2) Sihusoidal curved cloth $$C=\frac{(1+{\beta})sin{\theta}\[1+\{\frac{{\pi}(1-cos{\theta})}{4sin{\theta}}\}^2\]+{\alpha}}{(1+{\beta})sin{\theta}+{\alpha}}-1$$ The curvatures(${\kappa}$) for the models were given theoretically as follows; (1) Derived square cloth $${\kappa}=\frac{2}{d_w+d_f}$$ (2) Sinusoidal curved cloth $${\kappa}=\|{^{\;\;\prime\prime} \atop r}(s)\| \\ where \;s=\frac{p^'}{{\pi}}\(u+\frac{k^2u}{4}+\frac{k^2}{8}sin2u\)$$.

• Interaction and multiscale mechanics
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• v.1 no.3
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• pp.369-379
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• 2008

A combined stochastic diffusion and mean-field model is developed for a systematic study of the grain growth in a pure single-phase polycrystalline material. A corresponding Fokker-Planck continuity equation is formulated, and the interplay/competition of stochastic and curvature-driven mechanisms is investigated. Finite difference results show that the stochastic diffusion coefficient has a strong effect on the growth of small grains in the early stage in both two-dimensional columnar and three-dimensional grain systems, and the corresponding growth exponents are ~0.33 and ~0.25, respectively. With the increase in grain size, the deterministic curvature-driven mechanism becomes dominant and the growth exponent is close to 0.5. The transition ranges between these two mechanisms are about 2-26 and 2-15 nm with boundary energy of 0.01-1 J $m^{-2}$ in two- and three-dimensional systems, respectively. The grain size distribution of a three-dimensional system changes dramatically with increasing time, while it changes a little in a two-dimensional system. The grain size distribution from the combined model is consistent with experimental data available.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 1998.04a
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• pp.13-13
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• 1998

A simple model of the tip leakage flow models of the rotor downstream flow is developed, based on Lakshminarayana's theoretical concept on the tip clearance flow and the experimental data published in open literature. And new spanwise distribution models of deviation angle and pressure loss coefficient due to the tip leakage flow are formulated for use in association with the streamline curvature method as a through flow analysis. Combining these new models and previous deviation and loss models due to secondary flow, a robust streamline curvature method is established for flow analysis of single-stage, subsonic axial turbines with wide ranges of turning angle, aspect ratio and blading type. At the exit from rotor rows, the flow variables are mixed radially according to a spanwise transport equation. The proposed streamline curvature method is tested against a forced vortex type turbine as well as a free vortex type one. The results show that the spanwise variations of flow angle, axial velocity and loss coefficients at rotor exit are predicted with good accuracy, being comparable to a steady three-dimensional Navier-Stokes analysis. This simple and fast flow analysis is found to be very useful for the turbine design at the initial design phase.