• Title/Summary/Keyword: ${\kappa}-{\varepsilon}$ Model

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Wave Breaking of Sinusoidal Waves in the Surf Zone (쇄파대에서 정현파의 쇄파)

  • Hwang, Jong-Kil;Kim, Young-Taek;Cho, Yong-Sik
    • Journal of Korea Water Resources Association
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    • v.37 no.6
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    • pp.461-466
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    • 2004
  • This study presents a combined experimental and numerical effort to investigate wave breaking of sinusoidal waves in a surf zone. Numerical predictions are verified by comparing to laboratory measurements. The model solves the Reynolds equations and$textsc{k}$-$\varepsilon$ models for the turbulence analysis. To track the free surface displacement, the volume of fluid method is employed. As the height of incident wave increases, the wave breaking occurs at a closer point of the slope in the numerical model and laboratory experiments with the same depth and period. When a wave breaking occurs, the ratio of wave height becomes larger, with the same wave height and depth, as the period increases.

Numerical Analysis of Turbulent Carbon Dioxide Flow and Heat Transfer under Supercritical State in a Straight Duct with a Square Cross-Section (초임계상태 이산화탄소의 정사각 단면 직덕트 내 난류유동 및 열전달의 전산해석)

  • 최영돈;주광섭;김용찬;김민수
    • Korean Journal of Air-Conditioning and Refrigeration Engineering
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    • v.14 no.12
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    • pp.1004-1013
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    • 2002
  • Turbulent carbon dioxide flows and cooling heat transfers under supercritical state in a straight duct with a square cross-section are numerically analyzed employing low Reynolds number $\kappa-\varepsilon$ model and algebraic stress model. The flow is assumed to be (quasi-incompressible. Predicted Nusselt number and friction factor are compared with the experimental data, Blasius correlation for friction factor and Dittus-Boelter correlation for Nusselt number. Computational results for the Fanning's friction factor agree well with the all Rohsenow and Choi's correlation, Liou and Hwang's experimental data and Blasius correlation. The results obtained by algebraic stress model agree more with the Liou and Hwang's experimental data, while the results obtained by low Reynolds number $\kappa-\varepsilon$ model agree more with Blasius correlation. In the computation of Nusselt number, Dittus-Boelter correlation can not exactly fit the computational results. Therefore we propose the new correlation$Nu=0.053Re^{0.73}Pr^{0.4}$for the turbulent cooling heat transfer of carbon dioxide under supercritical state.

Numerical Simulation of Particle Deposition on a Wafer Surface (웨이퍼 표면상의 입자침착에 관한 수치 시뮬레이션)

  • 명현국;박은성
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.17 no.9
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    • pp.2315-2328
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    • 1993
  • The turbulence effect of particle deposition on a horizontal free-standing wafer in a vertical flow has been studied numerically by using the low-Reynolds-number k-.epsilon. turbulence model. For both the upper and lower surfaces of the wafer, predictions are made of the averaged particle deposition velocity and its radial distribution. Thus, it is now possible to obtain local information about the particle deposition on a free-standing wafer. The present result indicates that the particle deposition velocity on the lower surface of wafer is comparable to that on the upper one in the diffusion controlled deposition region in which the particle sizes are smaller than $0.1{\mu}m$. And it is found in this region that, compared to the laminar flow case, the averaged deposition velocity under the turbulent flow is about two times higher, and also that the local deposition velocity at the center of wafer is high equivalent to that the wafer edge.

Design Optimization of A Multi-Blade Centrifugal Fan with Navier-Stokes Analysis (삼차원 Navier-Stokes 해석을 이용한 원심다익송풍기의 최적설계)

  • Seo, Seoung-Jin;Kim, Kwang-Yong
    • Proceedings of the KSME Conference
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    • 2003.04a
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    • pp.2157-2161
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    • 2003
  • In this paper, the response surface method using three-dimensional Navier-Stokes analysis to optimize the shape of a forward-curved blades centrifugal fan, is described. For numerical analysis, Reynolds-averaged Navier-Stokes equations with standard k-e turbulence model are transformed into non-orthogonal curvilinear coordinate system, and are discretized with finite volume approximations. Due to the large number of blades in forward-curved blades centrifugal fan, the flow inside of the fan is regarded as steady flow by introducing the impeller force models for economic calculations. Linear Upwind Differencing Scheme(LUDS) is used to approximate the convection terms in the governing equations. SIMPLEC algorithm is used as a velocity-pressure correction procedure. Design variables, location of cur off, radius of cut off, expansion angle of scroll and width of impeller were selected to optimize the shapes of scroll and blades. Data points for response evaluations were selected by D-optimal design, and linear programming method was used for the optimization on the response surface. As a main result of the optimization, the efficiency was successfully improved. It was found that the optimization process provides reliable design of this kind of fans with reasonable computing time

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Fluid Flow Characteristics in the Aquaculture Tank for a Breeding Fish

  • Jeong, Hyo-Min;Chung, Han-Shik;Kim, Se-Hyun;Choi, Seuk-Cheun;Bae, Kang-Youl
    • Journal of Mechanical Science and Technology
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    • v.18 no.12
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    • pp.2265-2272
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    • 2004
  • The aquaculture tank is used for breeding fish in sea water which was pumped up to land. The flow characteristics in the aquaculture were investigated with varying the tank geometry and flow rate. The numerical analysis has been employed for calculating the velocity and temperature distributions in a water tank of rectangular type. The finite volume method and SIMPLE algorithm with 3-dimensional standard $\kappa$-$\varepsilon$ turbulence model were used for the numerical analysis. For comparison with experimental results, the PIV system was applied to visualize the flow patterns quantitatively. The numerical results showed good agreements with the experimental results. The mean velocity and temperature versus aquarium depth were represented for various circulating flow rates. Especially, the aquaculture environment is recommended that the aquarium depth has to be d=0.5 m, and this case is the condition of higher velocity and temperature in winter season.

A Numerical Analysis of Flow through Open Channel Constrictions using Turbulence Model (난류모델을 이용한 개수로 급축소부 흐름의 수치해석)

  • Choe, Heung-Sik
    • Journal of Korea Water Resources Association
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    • v.30 no.3
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    • pp.201-210
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    • 1997
  • To analyze the flow through open-channel constrictions using $\kappa$-$\varepsilon$ turbulence mode, a numerical model is developed. The simulated results agree well with existing experimental data which attributes to the adequate input of turbulent eddy-viscosity by turbulence model. A stream function and velocity distributions enable the analysis of flow characteristics at the downstream of constriction. Turbulent eddy viscosities over channel are spatially varied with stream pattern. For the evaluation of rapidly varied flow, the eddy-viscosity input by turbulence model is required instead of the empirical effective viscosity to solve a shallow water equation.

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Computational Analysis of Three-Dimensional Turbulent Flow Around Magnetically Levitated Train Configurations in Elevated Track Proximity (고가궤도에 근접한 자기부상열차 형상 주위의 3차원 난류유동에 대한 수치해석)

  • Maeng, J.S.;Yang, S.Y.
    • Transactions of the Korean Society of Automotive Engineers
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    • v.2 no.1
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    • pp.9-25
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    • 1994
  • In the present study, the Reynolds-averaged Navier-Stokes equations, together with the equations of the $k-{\varepsilon}$ model of turbulence, were solved numerically in a general body-fitted coordinate system for three-dimensional turbulent flows around the six basic shapes of the magnetically levitated train(MAGLEV). The numerical computations were conducted on the MAGLEV model configurations to provide information on shapes of this type very near the elevated track at a constant Reynolds number of $1.48{\times}10^{6}$ based on the body length. The coordinate system was generated by numerically solving a set of Poisson equations. The convective transport equations were discretized using the finite-analytic scheme which employed analytic solutions of the locally-linearized equations. A time marching algorithm was employed to enable future extensions to be made to handle unsteady and fully-elliptic problems. The pressure-velocity coupling was treated with the SIMPLER-algorithm. Of particular interests were wall effect by the elevated track on the aerodynamic forces and flow characteristics of the six models calculated. The results indicated that the half-circle configuration with extended sides and with smooth curvature of sides was desirable because of the low aerodynamic forces and pitching moment. And it was found that the separation bubble was occured at wake region in near the elevated track.

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Analysis of Hydraulic effects on Piers and Transverse Overflow Type Structures in Urban Stream (도시하천의 교각 및 횡단 월류형 구조물에 의한 수리영향 분석)

  • Yoon, Sun-Kwon;Chun, Si-Young;Kim, Jong-Suk;Moon, Young-Il
    • Journal of Korea Water Resources Association
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    • v.41 no.2
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    • pp.197-212
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    • 2008
  • Recently, stream flow analysis has been accomplished by one or two dimensional equations and was applied by simple momentum equations and fixed energy conservations which contain many condition limits. In this study, FLOW-3D using CFD (Computational Fluid Dynamics) was applied to stream flow analysis which can solve three dimensional RANS (Reynolds Averaged Navier-Stokes Equation) control equation to find out physical behaviors and the effect of hydraulic structures. Numerical simulation accomplished those results was compared by using turbulence models such as ${\kappa}-{\varepsilon}$, RNG (Renormalized Group) ${\kappa}-{\varepsilon}$ and LES (Large Eddy Simulation). Numerical analysis results have been illustrated by the turbulence energy effects, velocity of flow, water level pressure and eddy flows around the piers and transverse overflow type structures. These results will be able to used by basis data that catch hold of effects on long-term bed elevation changes, sediment accumulations, scours and water aggravations by removal of obsolete transverse over flow type structures in urban stream.

Plume Structure Analysis of an Axisymmetric Supersonic Micro-nozzle at the Various Pressure Ratios (압력비가 변할 때 축대칭 초음속 노즐의 플룸 구조 해석)

  • Kwon, Soon-Duk;Kim, Sung-Cho;Kim, Jeong-Soo;Choi, Jong-Wook;Kim, Yong-Sseok
    • Proceedings of the KSME Conference
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    • 2007.05b
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    • pp.2862-2867
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    • 2007
  • The steady non-reacted compressible flow field in a symmetric micro-thruster, which is used for the accurate attitude control of a satellite, is analyzed varying the nozzle pressure ratio (NPR) to investigate the plume characteristics. The nozzle throat diameter is 0.06 inch and the area ratio is 56. The recirculation region is found just behind the normal shock at the several NPRs due to the locally adverse pressure gradient along the nozzle centerline when the environmental pressure is atmospheric. This phenomenon, the cause of flow loss, is similar to the flow behind a blunt body. As NPR increases the location of Mach disk, characteristics of the normal shock, moves downstream and its strength increases. The Mach number distribution appears in a wave-type patter after the normal shock because oblique shocks are reflected on the shock boundaries especially when NPRs are very high.

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Numerical Study of Periodic Turbulent Flow for a Pipe with an Orifice Ring (오리피스 링이 부착된 원관내 주기적인 난류운동에 대한 수치해석)

  • 맹주성;양시영;서현철
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.17 no.9
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    • pp.2294-2303
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    • 1993
  • This paper investigated the characteristics of the turbulent incompressible flow past the orifice ring in an axi-symmetric pipe. The flow field was the turbulent pulsatile flow for Reynolds number of $2{\times}10^{5}$ which was defined based on the maximum velocity and the pipe diameter at the inlet, with oscillating frequence $(f_{os})=1/4{\pi}$ which was considered as quasi-steady state frequence. In the present investigation, finite analytic method was used to solve the governing equations in Navier Stokes and turbulent transport formulations. Particularly at high Reynolds number and low oscillation frequency, the effects of orifice ring on the flow were numerically investigated. The separation zone behind the orifice ring during the acceleration phase was found to be decreased. However, during the deceleration phase, the separation behind the orifice ring for pulsatile flow continuously grow to a size even larger than that in steady flow. The pressure drop in steady flow was found to be constant and always positive while for pulsatile flow the pressure drop change with time. And large turbulent kinetic energy, dissipation rate were found to be located in the region where the flow passes through the orifics ring. The maximum turbulent kinetic energy, generally occurs along the shear layer where the velocity gradient is large.