• Title/Summary/Keyword: k-$\varepsilon$ equations

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A Study of Applicability of a RNG $k-\varepsilon$ Model (RNG $k-\varepsilon$ 모델의 적용성에 대한 연구)

  • Yang, Hei-Cheon;Ryou, Hong-Sun;Lim, Jong-Han
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.21 no.9
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    • pp.1149-1164
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    • 1997
  • In this study, the applicability of the RNG k-.epsilon. model to the analysis of the complex flows is studied. The governing equations based on a non-orthogonal coordinate formulation with Cartesian velocity components are used and discretized by the finite volume method with non-staggered variable arrangements. The predicted results using the RNG k-.epsilon. model of three complex flows, i.e., the flow over a backward-facing step and a blunt flat plate, the flow around a 2D model car are compared to these from the standard k-.epsilon. model and experimental data. That of the unsteady axisymmetric turbulent flow within a cylinder of reciprocating model engine including port/valve assembly and the spray characteristics within a chamber of direct injection model engine are compared to these from the standard k-.epsilon. model and experimental data. The results of reattachment length, separated eddy size, average surface pressure distribution using the RNG k-.epsilon. model show more reasonable trends comparing with the experimental data than those using the modified k-.epsilon. model. Although the predicted rms velocity using the modified k-.epsilon. model is lower considerably than the experimental data in incylinder flow with poppet valve, predicted axial and radial velocity distributions at the valve exit and in-cylinder region show good agreements with the experimental data. The spray tip penetration predicted using the RNG k-.epsilon. model is more close to the experimental data than that using the modified k-.epsilon. model. The application of the RNG k-.epsilon. model seems to have some potential for the simulations of the unsteady turbulent flow within a port/valve-cylinder assembly and the spray characteristics over the modified k-.epsilon. model.

A Comparative Study of 2-Dimensional Turbulence Models for Thermal Discharge (2차원 온배수 난류모형의 비교연구)

  • Choi, Hung-Sik
    • Journal of Korea Water Resources Association
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    • v.32 no.3
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    • pp.225-235
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    • 1999
  • For a comparative evaluation of three turbulence models in the analyses of thermal discharge behavior into a crossflow, a 2-dimemsional near-field numerical model is developed. The selected models are k-$\varepsilon$ and k-ι turbulence models as a 2-equation turbulence model and a 4-equation turbulence model in which the transport equations for mean of the temperature fluctuation squared and its dissipation rate for the consideration of buoyancy production and turbulent heat flux terms are added to a k-$\varepsilon$ turbulence model. The developed models are applied to a steady flow in an open channel with simple geometry and the numerical results agree with the existing experimental data. Numerical results of buoyancy induced gravitational lateral spreading by 4-equation turbulence model agree with the experimental data better than those of 2-quation turbulence models. The flow patterns by 4 and 2-equation turbulence models are similar.

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Numerical Study for the Performance Analysis and Design of a Crossflow- Type Forced Draft Cooling Tower

  • Choi, Young-Ki;Kim, Byung-Jo;Lee, Sang-Yun;Lee, Jung-Hee
    • International Journal of Air-Conditioning and Refrigeration
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    • v.8 no.1
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    • pp.1-13
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    • 2000
  • A numerical study for performance analysis of a crossflow-type forced draft cooling tower has been performed based on the finite volume method with non-orthogonal body fitted, and non-staggered grid system. For solving the coupling problem between water and air, air enthalpy, moisture fraction, water enthalpy, and water mass balance equations are solved with Navier-Stoke's equations simultaneously. For the effect of turbulence, the standard k-$\varepsilon$ turbulent model is implied in this analysis. The predicted result of the present analysis is compared with the experimental data and the commercial software result to validate the present study. The predicted results show good agreement with the experimental data and the commercial software result. To investigate the influence of the cooling tower design parameters such as approach, range and wet bulb temperature, parametric studies are also performed.

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Ground-Motion Prediction Equations based on refined data for dynamic time-history analysis

  • Moghaddam, Salar Arian;Ghafory-Ashtiany, Mohsen;Soghrat, Mohammadreza
    • Earthquakes and Structures
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    • v.11 no.5
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    • pp.779-807
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    • 2016
  • Ground Motion Prediction Equations (GMPEs) are essential tools in seismic hazard analysis. With the introduction of probabilistic approaches for the estimation of seismic response of structures, also known as, performance based earthquake engineering framework; new tasks are defined for response spectrum such as the reference criterion for effective structure-specific selection of ground motions for nonlinear time history analysis. One of the recent efforts to introduce a high quality databank of ground motions besides the corresponding selection scheme based on the broadband spectral consistency is the development of SIMBAD (Selected Input Motions for displacement-Based Assessment and Design), which is designed to improve the reliability of spectral values at all natural periods by removing noise with modern proposed approaches. In this paper, a new global GMPE is proposed by using selected ground motions from SIMBAD to improve the reliability of computed spectral shape indicators. To determine regression coefficients, 204 pairs of horizontal components from 35 earthquakes with magnitude ranging from Mw 5 to Mw 7.1 and epicentral distances lower than 40 km selected from SIMBAD are used. The proposed equation is compared with similar models both qualitatively and quantitatively. After the verification of model by several goodness-of-fit measures, the epsilon values as the spectral shape indicator are computed and the validity of available prediction equations for correlation of the pairs of epsilon values is examined. General consistency between predictions by new model and others, especially, in short periods is confirmed, while, at longer periods, there are meaningful differences between normalized residuals and correlation coefficients between pairs of them estimated by new model and those are computed by other empirical equations. A simple collapse assessment example indicate possible improvement in the correlation between collapse capacity and spectral shape indicators (${\varepsilon}$) up to 20% by selection of a more applicable GMPE for calculation of ${\varepsilon}$.

Numerical Simulation of Mean Flows and Turbulent Structures of Partly-Vegetated Open-Channel Flows using the Nonlinear k-ε Model (비선형 k-ε 모형을 이용한 부분 식생 개수로 흐름의 평균흐름 및 난류구조 수치모의)

  • Choi, Seongwook;Choi, Sung-Uk;Kim, Taejoon
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.34 no.3
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    • pp.813-820
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    • 2014
  • This study presents a numerical modeling of mean flow and turbulence structures of partly-vegetated open-channel flows. For this, Reynolds-averaged Navier-Stokes equations with vegetation drag terms are solved numerically using the non-linear k-${\varepsilon}$ model. The numerical model is applied to laboratory experiments of Nezu and Onitsuka (2001), and simulated results are compared with data from measurement and computations by Kang and Choi's (2006) Reynolds stress model. The simulation results indicate that the proposed numerical model simulates the mean flow well. Twin vortices are found to be generated at the interface between vegetated and non-vegetated zones, where turbulence intensity and Reynolds stress show their maximums. The model simulates the pattern of the Reynolds stress well but under-predicts the intensity of Reynolds stress slightly.

Design Optimization of A Multi-Blade Centrifugal Fan with Navier-Stokes Analysis and Response Surface Method (삼차원 Navier-Stokes 해석과 반응면기법을 이용한 원심다익송풍기의 최적설계)

  • Seo, Seoung-Jin;Kim, Kwang-Yong
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.27 no.10
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    • pp.1457-1463
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    • 2003
  • In this paper, the response surface method using three-dimensional Navier-Stokes analysis to optimize the shape of a multi-blade centrifugal fan, is described. For numerical analysis, Reynolds-averaged Navier-Stokes equations with standard k - c 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 this 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.

Numerical Calculation of Viscous Flows for Two HSVA Tankers (HSVA 두 탱커 선형에 대한 점성유동 계산)

  • Kwak, Young-Ki
    • Journal of Ocean Engineering and Technology
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    • v.13 no.2 s.32
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    • pp.138-146
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    • 1999
  • The viscous flow around a ship hull is calculated by the use of RANS(Reynolds-averaged Navier-Stokes) solver. Reynolds stresses are midelled by using the k-${epsilon}$ turbulence model and the law is applied near the body. Body fitted corrdinates are introduced for the treatment of the complex boundary of the ship hull form and the governing equations in the physical domain transformed into ones in the computational domain. The transformed equations are numerically solved by an employment of FVM(Finite Volume Method). SIMPLE(Semi-Implicit Pressure Linked Equation) method is adopted in the calculation of pressure and the solution of the sidcretized equation is obtained by the line-by-line method with the use of TDMA(Tri-Diagonal Matrix Algorithme). To assure the proprietty of this computing method, HSVA tanker and Dyne hull are calculated ar both model and ship scale Reynolds number. Their reaults of pressure distributions on fore and aft body, axial velocity contours and transverse velocity velocity vectors and viscous resistance coefficients are compared with other's experiments and calculations.

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Three-dimensional analysis of the flow through an axial-flow fan (축류송풍기의 삼차원 유동장 해석)

  • Kim, Gwang-Yong;Kim, Jeong-Yeop;Jeong, Deok-Su
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.21 no.4
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    • pp.541-550
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    • 1997
  • Computational and experimental investigations on the three-dimensional flowfield through an automotive cooling fan are carried out in this work. Steady, incompressible, three-dimensional, turbulent flow through a rotating axial-flow fan is analyzed with Reynolds averaged Navier-Stokes equations and standard k-.epsilon. turbulence model. The governing equations are discretized with finite-volume approximations in non-orthogonal curvilinear coordinates. Computational static pressures on the casing wall agree well with the experimental data which are measured in this work. And, they are sensitive to the change of tip clearance. The flowfield is not significantly affected by the thickness of the blade. The k-.omega. model gives the static pressure rise on the casing wall which is similar to that with the k-.epsilon. model.

A study of the spatial amplification of the Type II instability for the Rotating-disk flow (회전원판 유동의 제2형 불안정성 공간증폭에 관한 이론적 연구)

  • Lee, Yun-Yong;Lee, Kwang-Won;Hwang, Young-Kyu
    • Proceedings of the KSME Conference
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    • 2001.11b
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    • pp.481-486
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    • 2001
  • The hydrodynamic instability of the three-dimensional boundary layer on a rotating disk introduces a periodic modulation of the mean flow in the form of stationary cross flow vortices. Detailed numerical values of the growth rates, neutral curves and other characteristics have been calculated for the Type II-instabilities. Presented are the neutral stability results concerning the two instability modes by solving new linear stability equations reformulated not only by considering whole convective terms but by correcting some errors in the previous stability equations. The present stability results are agree with the previously known ones within reasonable limit. The spatial amplification contours have been calculated for the moving disturbance wave, whose azimuth angle is between $\varepsilon=-10^{\circ}$ and $-20^{\circ}$. The transition flow of the moving disturbance wave will be developed at $\varepsilon=-15^{\circ}$ and Re=352 corresponding at the growth rates n = 5.8 from the spatial amplification contours.

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Numerical Calculations of Three-dimensional Viscous Flows over a stern by the Semi-Elliptic Equations (준타원형 방정식에 의한 선미에서의 3차원 점성유동의 수치계산)

  • Shin-Hyoung,Kang;Keon-Je,Oh
    • Bulletin of the Society of Naval Architects of Korea
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    • v.26 no.1
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    • pp.11-23
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    • 1989
  • A computer code has been developed to simulate three-dimensional viscous flows over a ship-stern. Semi-elliptic forms of Reynolds equations are adopted and numerically generated body-fitted coordinate systems are used to resolve complex geometries of the ship-hull. A standard form of $k-\varepsilon$ turbulence model is adopted for evaluation of the Reynolds stresses. Turbulent flows on a model with 3:1 elliptic sections and the SSPA-720 container ship model are predicted by using the code. Calculated pressure distributions of hull-surfaces and mean velocity distributions are generally in good agreements with measured values in wind-tunnels. But turbulent kinetic energies tend to be over-estimated near the stern in comparison with measured data.

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