• Journal of the Chungcheong Mathematical Society
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• v.20 no.3
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• pp.261-267
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• 2007

We show the existence of the positive solution for the system of the following nonlinear wave equations with Dirichlet boundary conditions $$u_{tt}-u_{xx}+av^+=s{\phi}_{00}+f$$, $$v_{tt}-v_{xx}+bu^+=t{\phi}_{00}+g$$, $$u({\pm}\frac{\pi}{2},t)=v({\pm}\frac{\pi}{2},t)=0$$, where $u_+=max\{u,0\}$, s, $t{\in}R$, ${\phi}_{00}$ is the eigenfunction corresponding to the positive eigenvalue ${\lambda}_{00}=1$ of the eigenvalue problem $u_{tt}-u_{xx}={\lambda}_{mn}u$ with $u({\pm}\frac{\pi}{2},t)=0$, $u(x,t+{\pi})=u(x,t)=u(-x,t)=u(x,-t)$ and f, g are ${\pi}$-periodic, even in x and t and bounded functions in $[-\frac{\pi}{2},\frac{\pi}{2}]{\times}[-\frac{\pi}{2},\frac{\pi}{2}]$ with $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}f{\phi}_{00}=\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}g{\phi}_{00}=0$.

• 한국전산유체공학회:학술대회논문집
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• 1998.05a
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• pp.156-161
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• 1998

This describes a numerical method for predicting the incompressible unsteady laminar three-dimensional flows of fluid behaviour with free-surface. The elliptic differential equations governing the flows have been linearized by means of finite-difference approximations, and the resulting equations have been solved via a fully-implicit iterative method. The free-surface is defined by the motion of a set of marker particles and interface behaviour was investigated by way of a 'Lagrangian' technique. Using the GALA concept of Spalding, the conventional mass continuity equation is modified to form a volumetric or bulk-continuity equation. The use of this bulk-continuity relation allows the hydrodynamic variables to be computed over the entire flow domain including both liquid and gas regions. Thus, the free-surface boundary conditions are imposed implicitly and the problem formulation is greatly simplified. The numerical procedure is validated by comparing the predicted results of a periodic standing waves problems with analytic solutions or experimental results from the literature. The results show that this numerical method produces accurate and physically realistic predictions of three-dimensional free-surface flows.

• Journal of computational fluids engineering
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• v.18 no.2
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• pp.85-92
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• 2013

In this study, we consider heat transfer enhancement in laminar channel flow by means of an infinite streamwise array of equispaced identical circular cylinders. This flow configuration can be regarded as a model representing a micro channel or an internal heat exchanger with cylindrical vortex generators. A numerical parametric study has been carried out by varying Reynolds number based on the bulk mean velocity and the cylinder diameter, and the gap between the cylinders and the channel wall. An immersed boundary method was employed to facilitate to implement the cylinders on a Cartesian grid system. No-slip condition is employed at all solid boundaries including the cylinders, and the flow is assumed to be periodic in the streamwise direction. Also, the Prandtl number is fixed as 0.7. For thermal boundary conditions on the solid surfaces, it is assumed that heat flux is constant on the channel walls, while the cylinder surfaces remain adiabatic. The presence of the circular cylinders arranged periodically in the streamwise direction causes a significant topological change of the flow, leading to heat transfer enhancement on the channel walls. The Nusselt number averaged on the channel wall is presented for the wide ranges of Reynolds number and the gap. A significant heat transfer enhancement is noticed when the gap is larger than 0.8, while the opposite is the case for smaller gaps. More quantitative results as well as qualitative physical explanations are presented to justify the effectiveness of varying the gap to enhance heat transfer from the channel walls.

• Korean Journal of Mathematics
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• v.19 no.3
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• pp.331-342
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• 2011

We consider the multiplicity of the solutions for a class of a system of critical growth beam equations with periodic condition on t and Dirichlet boundary condition $$\{u_{tt}+u_{xxxx}=av+\frac{2{\alpha}}{{\alpha}+{\beta}}u_{+}^{{\alpha}-1}v_{+}^{\beta}+s{\phi}_{00}\;\;in\;(-\frac{\pi}{2},\;\frac{\pi}{2}){\times}R,\\u_{tt}+v_{xxxx}=bu+\frac{2{\alpha}}{{\alpha}+{\beta}}u_{+}^{\alpha}v_{+}^{{\beta}-1}+t{\phi}_{00}\;\;in\;(-\frac{\pi}{2},\;\frac{\pi}{2}){\times}R,$$ where ${\alpha}$, ${\beta}$ > 1 are real constants, $u_+=max\{u,0\}$, ${\phi}_{00}$ is the eigenfunction corresponding to the positive eigenvalue ${\lambda}_00=1$ of the eigenvalue problem $u_{tt}+u_{xxxx}={\lambda}_{mn}u$. We show that the system has a positive solution under suitable conditions on the matrix $A=\(\array{0&a\\b&0}\)$, s > 0, t > 0, and next show that the system has another solution for the same conditions on A by the linking arguments.

• Journal of the Korean Society of Visualization
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• v.19 no.2
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• pp.26-31
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• 2021

The spanwise growth of turbulence structures in turbulent pipe flow was investigated using the direct numerical simulation data of Re_𝜏 = 544, 934 and 3008. Two-point correlations and pre-multiplied energy spectra of streamwise velocity fluctuations were examined along the spanwise direction. The arclength direction is defined as r𝛳, which is useful for an analogy with the spanwise direction for channels or boundary layers; here, r and 𝛳 are the radial distance from the core and the azimuthal angles, respectively. Both analyses showed that the arclength scales increased with increasing the wall-normal distance. It showed that the coherent structures were confined in the core region due to the crowding effect of a circular pipe geometry. The pipe flow simulation could describe a realistic geometrical flow along the azimuthal direction, unlike the simulations of turbulent channel or boundary layer flow using periodic boundary conditions along the spanwise direction. The present results provided the spanwise organization of energy-containing motions over a broad range of scales in turbulent pipe flow.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.3
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• pp.311-318
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• 2003

The present work evaluates the effects of mixing vane shape on the flow structure and heat transfer downstream of mixing vane in a subchannel of fuel assembly. by obtaining velocity and pressure fields. turbulent intensity. flow-mixing factors. heat transfer coefficient and friction factor using three-dimensional RANS analysis. Four different shapes of mixing vane. which were designed by the authors were tested to evaluate the performances in enhancing the heat transfer. Standard k-$\varepsilon$ model is used as a turbulence closure model. and. periodic and symmetry conditions are set as boundary conditions. The flow blockage ratio is kept constant. but the twist angle of mixing vane is changed. The results with three turbulence models were compared with experimental data.

• 한국전산유체공학회:학술대회논문집
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• 2002.05a
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• pp.79-87
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• 2002

The present work analyzed the effect of mixing vane shape on the flow structure and heat transfer downstream of mixing vane in a subchannel of fuel assembly, by obtaining velocity and pressure fields, turbulent intensity, flow-mixing factors, heat transfer coefficient and friction factor using three-dimensional RANS analysis. NJl5, NJ25, NJ35, NJ45, which were designed by the authors, were tested to evaluate the performances in enhancing the heat transfer. Standard $\kappa-\epsilon$ model is used as a turbulence closure model, and, periodic and symmetry conditions are set as boundary conditions. The flow blockage ratio is kept constant, but the twist angle of mixing vane is changed. The results with three turbulence models( $\kappa-\epsilon$, $\kappa-\omega$, RSM) were compared with experimental data.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.25 no.3
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• pp.373-380
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• 2001

In this study, a single Taylor bubble and a train of Taylor bubbles rising in a vertical tube were simulated numerically. A finite difference method was used to solve the mass and momentum equations for the liquid-gas region. The liquid-gas interface was captured by a level set function which is defined a signed distance from the interface. For a train of Taylor bubbles repeated periodically in space, the periodic conditions were imposed at the boundaries normal to the gravitational direction and the pressure boundary conditions were iteratively determined so that the computed flow rate should be equal to a given flow rate. Based on the numerical simulation, the calculated shape and rise velocity of a Taylor bubble were found to be in good agreement with the experimental data reported in the literature.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2004.11a
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• pp.210-211
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• 2004

The effect of oscillating on the unsteady laminar flow past a circular cylinder is numerically investigated in the present study. Our study is to analyze the vortex formation behind a circular cylinder for different rotary oscillation conditions. And then we are study to portray the unsteady dynamics of wake flows. We decide lock-on region by observing the phase switching phenomena We classify the vortex formation patterns in the primary lock-on region The present study is to identify the quasi-periodic state around lock-on region. At the boundary between lock-on and non-lock-on the shedding frequency is bifurcated. After the bifurcation, one frequency follow the forcing frequency ($S_f$) and the other returns to the natural shedding frequency ($St_0$). In the quasi-periodic state, the variation of magnitudes and relevant phase changes of $C_L$ with forcing phase are examined.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.5
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• pp.632-639
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• 2004

In this paper, an inverse problem of glass forming process is studied to determine a number of unknown heat transfer coefficients which are imposed as boundary conditions. An analysis program for transient heat conduction of axi-symmetric dimension is developed to simulate the forming and cooling process. The analysis is repeated until it attains periodic state, which requires at least 30 cycles of iteration. Measurements are made for the temperatures at several available time and positions of glass and moulds in operation. Heat removal by the cooling water from the plunger is also recorded. An optimization problem is formulated to determine heat transfer coefficients which minimize the difference between the measured data and analysis results. Significant time savings are achieved in finite difference based sensitivity computation during the optimization by employing distributed computing technique. The analysis results by the optimum heat transfer coefficients are found to agree well with the measured data.