• Journal of Advanced Marine Engineering and Technology
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• v.22 no.4
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• pp.436-444
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• 1998

Applicability of the RNG k-$\varepsilon$ model to the analysis of unsteady axisymmetric turbulent flow of a reciprocating engine including port/valve assembly is studied numerically. The governing equations based on non-orthogonal including port/valve assembly is studied numerically. The governing equations based on a non-orthogonal coordinate formulation with Cartesian velocity components are used and discretised by the finite volume method with non-staggered variable arrangements. The predicted results using the RNG k-$\varepsilon$ model of the unsteady axisymmetric turbulent flow within a cylinder of reciprocating model engine including port/valve assembly are compared to these from the modified k-$\varepsilon$ model and experimental data. Using the RNG k-$\varepsilon$ model seems the have some potential for the simulations of the unsteady turbulent flow within a port/valve-cylinder assembly over the modified k-$\varepsilon$model.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.15 no.2
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• pp.80-85
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• 2003

This paper describes the generation and maximum run-up heights of cnoidal waves with varying periods by the numerical model. The model solves the Reynolds equations and the k-epsilon equations for the turbulent analysis. To track free surface displacements, the volume of fluid(VOF) method is employed. It is shown that profiles of the numerically generated cnoidal waves agree well with analytical solutions. The computed maximum run-up heights are compared with laboratory measurements and those of the boundary element method. The present model provides more agreeable results to laboratory measurements that the boundary element model.

• Bulletin of the Korean Mathematical Society
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• v.51 no.5
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• pp.1299-1324
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• 2014

We prove the existence of uniform attractors $\mathcal{A}_{\varepsilon}$ in the space $H^1(\mathbb{R}^N){\cap}L^p(\mathbb{R}^N)$ for the following non-autonomous nonclassical diffusion equations on $\mathbb{R}^N$, $$u_t-{\varepsilon}{\Delta}u_t-{\Delta}u+f(x,u)+{\lambda}u=g(x,t),\;{\varepsilon}{\in}(0,1]$$. The upper semicontinuity of the uniform attractors $\{\mathcal{A}_{\varepsilon}\}_{{\varepsilon}{\in}[0,1]}$ at ${\varepsilon}=0$ is also studied.

• Nuclear Engineering and Technology
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• v.5 no.1
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• pp.30-37
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• 1973

The Nishitani's equations for impedance of anodic oxide films have been derived based on a p-i-n model under the assumption of $\omega$$\varepsilon$$\rho$$_{ο}$<<4$\pi$<<$\omega$$\varepsilon$$\rho$$_{\omega}$, where $\omega$ is angular frequency, $\varepsilon$ is dielectric constant, and $\rho$$_{ο}$ and $\rho$$_{\omega}$ are the resistivity of the interface region and the intrisic region of the anodic oxide film, respectively. Since it is not possible to evaluate all parameters in the equations, however, any clear physical picture cannot be obtained from the equations. Therefore, the equations are modified under the assumption of $\omega$$\tau$$_{\omega}$>>1 and In(1+$\omega$$^2$$\tau$$_{ο}$$^2$)<<1, where $\tau$$_{\omega}$=$\varepsilon$$\rho$$_{\omega}$(4$\pi$) and $\tau$$_{ο}$=$\varepsilon$$\rho$$_{ο}$/(4$\pi$). The modified equations are then used to explain the change in the frequency characteristics of anodic oxide films when they are heated. The change in impedance of anodic oxide films when they are heated is attributed mainly to the increase in the diffusion layer and to the decrease in the resistivity of anodic oxide films.s.

• Proceedings of the KSME Conference
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• 2000.11b
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• pp.428-433
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• 2000

The characteristics of unsteady heat transfer and boundary layer flow in the SSME turbine rotor passage are investigated with LRN $k-{\varepsilon}$ turbulence model. The unsteady flow and heat transfer in a rotor blade passage as a result of wake/blade interaction is modeled by the inviscid/boundary-layer flow approach. The relevant governing equations are discretized to a system of finite different equations by means of a BTBCS implicit method. These equations have been solved numerically, for the velocity and temperature fields using TDMA method. Heat flux on the blade surface and flow parameters in the rotor passage are calculated with wake interaction. Numerical results show that velocity, pressure, turbulent kinetic energy and heat flux on the blade surface are varied periodically by wake passing.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.5 no.4
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• pp.357-368
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• 1993

With the assumption of the diffusion dominated flow, a numerical model has been developed for undertow and turbulence structure under the breaking wave by using the $textsc{k}$-$\varepsilon$ turbulence model. Undertow is a strong mean current which moves seqwards below the level of wave trough in the surf zone. The turbulence, generated by wave breaking in the roller, spreads and dissipates downwards. The governing equations are composed of the equation of motion with the period-averaged shear stress due to waves; $textsc{k}$- and $\varepsilon$-equations with the turbulence energy Production due to wave breaking. They are discretised by the three-level fully implicit scheme, which can be solved by using Thomas algorithm. The model gives good agreements with measurements except for the station that is closest to the breaking point.

• 한국방재학회:학술대회논문집
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• 2007.02a
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• pp.159-162
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• 2007

The numerical efforts are presented for investigation of irregular waves passing a slit cassion and a warock block breakwater. In the numerical model, the Reynolds equations are solved by a finite difference method and $k-\varepsilon$ model is employed for the turbulence analysis. To track the free surface displacement, the volume of fluid method(VOF) is employed. Numerical predictions of reflection and transmission coefficients are compared with those of the warock block breakwater with the slit caisson. Energy dissipation and seawater exchange rates of the slit caisson are better than those of the warock block breakwater.

• Proceedings of the KSME Conference
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• 2000.11b
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• pp.573-578
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• 2000

Flow through turbine flow meter is simulated by solving the incompressible Navier-Stockes equations. The solution method is based on the pseudocompressibility approach and uses an implicit-upwind differencing scheme together with the Gauss-Seidel line relaxation method. The equations are solved steadily in rotating reference frames and the centrifugal force and tile Coriolis force are added to the equation of motion. The standard $k-{\varepsilon}$ model is employed to evaluate turbulent viscosity. At first the stability and accuracy of the program is verified with the flow through a square duct with a $90^{\circ}$ bend and on the flat plate.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.7 no.2
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• pp.287-297
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• 1995

In this study, the geometry consists of a two-dimensional rectangular enclosure with localized heating from below. The size and the location of the heater on the floor has been varied, and one of the vertical walls remains at a low temperature simulating a cold window. The governing equations for momentum, energy and continuity, which are coupled with turbulent equations have been solved using a finite volume method. A low Reynolds number $k-{\varepsilon}$ model has been incorporated to solve the turbulent kinetic energy and the dissipation rate. The heat transfer characteristics and the thermal environmental characteristics of the room have been obtained for various system parameters in a room with a partially heated floor.

• Communications for Statistical Applications and Methods
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• v.8 no.1
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• pp.153-158
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• 2001

A central limit theorem is obtained for stationary linear process of the form -Equations. See Full-text-, where {$\varepsilon$$_{t}$} is a strictly stationary sequence of linearly positive quadrant dependent random variables with E$\varepsilon$$_{t}$=0, E$\varepsilon$$^2$$_{t}$<$\infty$ and { $a_{j}$} is a sequence of real numbers with -Equations. See Full-text- we also derive a functional central limit theorem for this linear process.ocess.s.