• 대한수학회지
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• 제55권2호
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• pp.253-292
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• 2018

In this paper, we introduce a general Ricci flow system, which is closely linked with the Ricci flow and the renormalization group flow, etc. We prove the short-time existence, the entropy functionals, the higher derivatives estimates and the compactness theorem for this general Ricci flow system on closed Riemannian manifolds. These basic results are useful tools to understand the singularities of this system.

• Wind and Structures
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• 제9권4호
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• pp.315-330
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• 2006

Flow and scalar dispersion around Cheomseongdae are numerically investigated using a three-dimensional computational fluid dynamics (CFD) model with the renormalization group (RNG) $k-{\varepsilon}$ turbulence closure scheme. Cheomseongdae is an ancient astronomical observatory in Gyeongju, Korea, and is chosen as a model obstacle because of its unique shape, that is, a cylinder-shaped architectural structure with its radius varying with height. An interesting feature found is a mid-height saddle point behind Cheomseongdae. Different obstacle shapes and corresponding flow convergences help to explain the presence of the saddle point. The predicted size of recirculation zone formed behind Cheomseongdae increases with increasing ambient wind speed and decreases with increasing ambient turbulence intensity. The relative roles of inertial and eddy forces in producing cavity flow zones around an obstacle are conceptually presented. An increase in inertial force promotes flow separation. Consequently, cavity flow zones around the obstacle expand and flow reattachment occurs farther downwind. An increase in eddy force weakens flow separation by mixing momentum there. This results in the contraction of cavity flow zones and flow reattachment occurs less far downwind. An increase in ambient wind speed lowers predicted scalar concentration. An increase in ambient turbulence intensity lowers predicted maximum scalar concentration and acts to distribute scalars evenly.

• 한국자동차공학회논문집
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• 제4권5호
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• pp.119-129
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• 1996

This study is concerned with the critical evaluation of predicative capability of a k-$\varepsilon$ turbulence model using the Renormalization Group(RNG) theory. The present numerical model for solution of the Navier-Stokes System is based on the modified PISO algorithms. Computations have been performed with the RNG-based K-$\varepsilon$ model for the two-dimensional flow over a backward-facing step, a confined coaxial jet, and a swirling flow in a swirl combustor. Numerical results are compared with experimental data in terms of mean flow velocities, turbulent kinetic energy, and turbulent stresses. Numerical results clearly indicate that the RNG-based K-$\varepsilon$ turbulence model shows a significant improvement over a standard K-$\varepsilon$ model in predicting the turbulent flows with flow separation and swirl.

• 한국대기환경학회지
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• 제21권5호
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• pp.525-535
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• 2005

Using a three-dimensional computational fluid dynamics (CFD) model with the $k-{\varepsilon}$ turbulence closure scheme based on the renormalization group theory, flow regimes in urban street canyons are classified according to the building and street aspect ratios. The transition between skimming flow (SF) and wake interference flow (WIF) is determined with the size of double-eddy circulation generated behind the upwind building. The transition between WIF and isolated roughness flow (IRF) is determined with the flow reattachment distance from the upwind building. The critical aspect ratios at which the flow transition occurs are found and compared with those in previous studies. The results show that the flow-regime classification method used in this study is quite reasonable and that the values of the critical aspect ratios are generally consistent with those in fluid experiments or large-eddy simulation. The regression equation describing a relation between the building and street aspect ratios at the flow-regime transition is presented.

• 한국대기환경학회지
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• 제23권2호
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• pp.214-224
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• 2007

A three-dimensional computational fluid dynamics (CFD) model with the renormalization group (RNG) $k-{\varepsilon}$ turbulence model is used to examine the effects of difference in building height on flow and pollutant dispersion in asymmetric street canyons. Three numerical experiments with different street canyons formed by two isolated buildings are performed. In the experiment with equal building height, a portal vortex is formed in the street canyon and a typical recirculation zone is formed behind the downwind building. In the experiment with the downwind building being higher than the upwind building, the ambient flow comes into the street canyon at the front of the downwind building and incoming flow diverges strongly in the street canyon. Hence, pollutants released therein are strongly dispersed through the lateral sides of the street canyon. In the experiment with the upwind building being higher than the downwind building, a large recirculation zone is formed behind the upwind building, which is disturbed by the downwind building. Pollutants are weakly dispersed from the street canyon and the residue concentration ratio is largest among the three experiments. This study shows that the difference in upwind and downwind building height significantly influences flow and pollutant dispersion in and around the street canyon.

• 대기
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• 제21권1호
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• pp.95-108
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• 2011

The effects of an apartment complex on flow and pollutant dispersion in an urban area are numerically investigated using a computational fluid dynamics (CFD) model. The CFD model is based on the Reynolds-averaged Navier-Stokes equations and includes the renormalization group k-${\varepsilon}$ turbulence model. The geographic information system (GIS) data is used as an input data of the CFD model. Eight numerical simulations are carried out for different inflow directions and, for each inflow direction, the effects of an apartment complex are investigated, comparing the characteristics of flow and dispersion before and after construction of the apartment complex in detail. The observation data of automatic weather system (AWS) is analyzed. The windrose analysis shows that the wind speed and direction after the construction of the complex are quite different from those before the construction. The construction of the apartment complex resulted in the decrease in wind speed at the downwind region. It is also shown that the wind speed increased partially inside the apartment complex due to the channeling effect to satisfy the mass continuity. On the whole, the wind speed decreased at the downwind region due to the drag effect by the apartment complex. As a result, the passive pollutant concentration increased (decreased) near the downwind region of (within) the apartment complex compared with that before the construction.

• 한국자동차공학회논문집
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• 제5권1호
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• pp.87-100
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• 1997

The ability of turbulence model to accurately describe the complex characteristics of the flow field and the fuel spray is of great importance in the optimum design of diesel engine. The numerical simulations of the flow field and the spray characteristics within the combustion chamber of direct injection model entgine are performed to examine the applicability of turbulence model. The turbulence models used are the RNG $\varepsilon$ model and the modified $\varepsilon$ model which included the compressibility effect due to the compression/expansion of the charges. In this study, the predicted results in the quiescent condition of direct injection model engine show reasonable trends comparing with the experimental data of spray characteristics, i. e., spray tip penetration, spray tip velocity. The results of eddy viscosity obtained using the $\varepsilon$ model in the spray region is significantly larger than that obtained using the RNG $\varepsilon$ model. The application of the RNG model seems to have some potential for the simulations of the spray characteristics, e. g., spray tip penetration, spray tip velocity, droplets distribution over the $\varepsilon$ model.

• 한국안전학회지
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• 제10권3호
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• pp.68-80
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• 1995

A series of parametric calculations have been performed in order to investigate the short-term and short-range plume and puff behavior of toxic gaseous and solid pollutant dispersion in an open atmosphere. The simulation is made by the use of the computer program developed by this laboratory, in which a control-volume based finite-difference method is used together with the SIMPLEC algorithm for the resolution of the pressure-velocity coupling appeared In Wavier-Stokes equation. The Reynolds stresses are solved by the standard two-equation k-$\varepsilon$ model modified for buoyancy together with the RNG(Renormalization Group) k-$\varepsilon$ model. The major parameters considered in this calculation are pollutant gas density and temperature, the relative velocity of pollutants to that of the surrounding atmospheric air, and particulate size and density together with the height released. The flow field is typically characterized by the formation of a strong recirculation region for the case of the low density gases such as $CH_4$ and air due to the strong buoyancy, while the flow is simply declining pattern toward the downstream ground for the case of heavy molecule like the $CH_2C1_2$and $CCl_4$, even for the high temperature, $200^{\circ}C$. The effect of gas temperature and velocity on the flow field together with the particle trajectory are presented and discussed in detail. In general, the results are physically acceptable and consistent.

• 한국환경과학회지
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• 제23권7호
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• pp.1223-1232
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• 2014

Density currents have been easily observed in environmental flows, for instance turbidity currents and pollutant plumes in the oceans and rivers. In this study, we explored the propagation dynamics of density currents using the FLOW-3D computational fluid dynamics code. The renormalization group (RNG) $k-{\varepsilon}$ scheme, a turbulence numerical technique, is employed in a Reynold-averaged Navier-Stokes framework (RANS). The numerical simulations focused on two different types of intrusive density flows: (1) propagating into a two-layer ambient fluid; (2) propagating into a linearly stratified fluid. In the study of intrusive density flows into a two-layer ambient fluid, intrusive speeds were compared with laboratory experiments and analytical solutions. The numerical model shows good quantitative agreement for predicting propagation speed of the density currents. We also numerically reproduced the effect of the ratio of current depth to the overall depth of fluid. The numerical model provided excellent agreement with the analytical values. It was also clearly demonstrated that RNG $k-{\varepsilon}$ scheme within RANS framework is able to accurately simulate the dynamics of density currents. Simulations intruding into a continuously stratified fluid with the various buoyancy frequencies are carried out. These simulations demonstrate that three different propagation patterns can be developed according to the value of $h_n/H$ : (1) underflows developed with $h_n/H=0$ ; (2) overflows developed when $h_n/H=1$ ; (3) intrusive interflow occurred with the condition of 0 < $h_n/H$ < 1.

• 대한기계학회논문집B
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• 제21권9호
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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.