• 한국전산유체공학회지
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• 제7권1호
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• pp.10-19
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• 2002

The non-staggered(collocated) grid approach in which all the solution variables are located at the centers of control volumes is very popular for incompressible flow analyses because of its numerical efficiency on the curvilinear or unstructured grids. Rhie and Chow's paper is the first in using non-staggered grid method for SIMPLE algorithm, where pressure weighted interpolation was used to prevent decoupling of pressure and velocity. But it has been known that this non-staggered grid method has stability problems when pressure fields are nonlinear like in natural convection flows. Also Rhie-Chow scheme generates large numerical diffusion near curved walls. The cause of these unwanted problems is too large pressure damping term compared to the magnitude of face velocity. In this study the magnitude of pressure damping term of Rhie-Chow's method is limited to 1∼10% of face velocity to prevent physically unreasonable solutions. The wall pressure extrapolation which is necessary for cell-centered FVM is another source of numerical errors. Some methods are applied in a unstructured FV solver and analyzed in view of numerical accuracy. Here, two natural convection problems are solved to check the effect of the Rhie-Chow's method on numerical stability. And numerical diffusion from Rhie-Chow's method is studied by solving the inviscid flow around a circular cylinder.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2003년도 The Fifth Asian Computational Fluid Dynamics Conference
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• pp.33-34
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• 2003

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2005년도 춘계 학술대회논문집
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• pp.153-158
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• 2005

Numerical simulations of two-dimensional steady incompressible lid-driven flow in a square cavity are presented to verify the validity of a new solution code(PowerCFD) with unstructured grids. The code uses the non-staggered(collocated) grid approach which is very popular for incompressible flow analysis because of its numerical efficiency on the curvilinear or unstructured grids. Solutions are obtained for configurations with a Reynolds number as high as 10,000 with both rectangular and hybrid types of unstructured grid mesh. Interesting features of the flow are presented in detail and comparisons are made with benchmark solutions found in the literature. It is found that the code is capable of producing accurately the nature of the lid-driven cavity flow at high Reynolds numbers.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2003년도 추계학술대회
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• pp.910-915
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• 2003

A Navier-Stokes equation solver for incompressible viscous flows with free surface is developed and tested. This is based upon a fractional time step method and a non-staggered finite volume formulation for unstructured meshes. For time advancement scheme, Adams -Bashforth method for convective term and Crank-Nicolson method for diffusive term are applied. The interface between two fluids with different fluid properties is tracked with Piecewise Linear Interface Calculation(PLIC) Volume-of-Fluid(VOF) methods. Computational results are presented for some test problems: the broken dam, the sloshing in a rectangular tank, the filling of a cylindrical tank.

• 한국전산유체공학회지
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• 제13권3호
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• pp.51-61
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• 2008

The SMAC (Simplified Marker And Cell) algorithm is extended for an application to thermal non-equilibrium two-phase flows in light water nuclear reactors (LWRs). A two-fluid three-field model is adopted and a multi-dimensional unstructured grid is used for complicated geometries. The phase change and the time derivative terms appearing in the continuity equations are implemented implicitly in a pressure correction equation. The energy equations are decoupled from the momentum equations for faster convergence. The verification of the present numerical method was carried out against a set of test problems which includes the single and the two-phase flows. The results are also compared to those of the semi-implicit ICE method, where the energy equations are coupled with the momentum equation for pressure correction.

• 에너지공학
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• 제17권4호
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• pp.218-226
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• 2008

가압 경수로의 주요 기기에서 발생할 수 있는 과도 2상 유동(Two-phase flow) 현상에 대한 해석을 수행하기 위해 원자로 기기 열수력 해석 코드를 개발 중에 있다. 개발중인 기기 열수력 해석 코드는 지배 방정식으로 Two-phase, three-field model을 사용하고 있으며, 복잡한 기하학적 형상의 원자로 기기를 모사하기 위해 비정렬 격자계(Unstructured grid)를 활용하고 있다. 수치해석 기법으로는, 원자로 계통 해석코드 REIAP5가 사용 중이며 대부분의 원자로 내 2상 유동 조건에서 안정적이며 정확하다고 알려진 Semi-implicit 방법을 적용하였다. 그러나 기존의 Semi-implicit 방법은 1차원, 엇갈림격자(Staggered grid)에 대해 개발되었기 때문에 이를 다차원, 비정렬, 비엇갈림 격자(Non-staggered grid)에 적용하기 위해 기존의 Semi-implicit 방법을 수정하였다. 본 논문에서는 수정된 Semi-implicit 방법을 소개하고 이를 이용해 수행한 예비 계산결과를 수록하였다.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2009년 춘계학술대회논문집
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• pp.290-297
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• 2009

가압 경수로의 주요 기기에서 발생할 수 있는 과도 2상 유동(Two-phase flow) 현상에 대한 해석을 수행하기 위해 원자로 기기 열수력 해석 코드를 개발 중에 있다. 개발 중인 기기 열수력 해석 코드는 지배 방정식으로 Two-phase, three-field model을 사용하고 있으며, 복잡한 기하학적 형상의 원자로 기기를 모사하기 위해 비정렬 격자계(Unstructured grid)를 활용하고 있다. 수치해석 기법으로는, 원자로 계통 해석코드 RELAP5가 사용 중이며 대부분의 원자로 내 2상 유동 조건에서 안정적이며 정확하다고 알려진 Semi-implicit 방법을 적용하였다. 그러나 기존의 Semi-implicit 방법은 1차원, 엇갈림격자(Staggered grid)에 대해 개발되었기 때문에, 이를 다차원, 비정렬, 비엇갈림 격자(Non-staggered grid)에 적용하기 위해 기존의 Semi-implicit 방법을 수정하였다. 본 논문에서는 Semi-implicit 방법의 대류항을 이차정확도를 갖도록 확장하였으며, 이차정확도에 의한 수치확산의 감소를 평가하기 위해 수행된 수치시험의 결과를 기술하였다. 이차정확도 및 일차정확도로 계산된 값을 해석해 또는 격자 수렴성 시험을 통해 평가해 본 결과, 이차정확도 계산시 수치 확산의 감소 확인하였다.

• 한국전산유체공학회지
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• 제14권4호
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• pp.13-22
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• 2009

A two-phase (gas and liquid) flow analysis solver, named CUPID, has been developed for a realistic simulation of transient two-phase flows in light water nuclear reactor components. In the CUPID solver, a two-fluid three-field model is adopted and the governing equations are solved on unstructured grids for flow analyses in complicated geometries. For the numerical solution scheme, the semi-implicit method of the RELAP5 code, which has been proved to be very stable and accurate for most practical applications of nuclear thermal hydraulics, was used with some modifications for an application to unstructured non-staggered grids. This paper is concerned with the effects of interpolation schemes on the simulation of two-phase flows. In order to stabilize a numerical solution and assure a high numerical accuracy, the second-order upwind scheme is implemented into the CUPID code in the present paper. Some numerical tests have been performed with the implemented scheme and the comparison results between the second-order and first-order upwind schemes are introduced in the present paper. The comparison results among the two interpolation schemes and either the exact solutions or the mesh convergence studies showed the reduced numerical diffusion with the second-order scheme.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제12권4호
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• pp.249-260
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• 2008

In this work we propose a mixed finite volume method for the Signorini problem which are based on the idea of Keller's finite volume box method. The triangulation may consist of both triangles and quadrilaterals. We choose the first-order nonconforming space for the scalar approximation and the lowest-order Raviart-Thomas vector space for the vector approximation. It will be shown that our mixed finite volume method is equivalent to the standard nonconforming finite element method for the scalar variable with a slightly modified right-hand side, which are crucially used in a priori error analysis.

• 한국자동차공학회논문집
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• 제1권1호
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• pp.1-13
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• 1993

The three-dimensional numerical analysis for in-cylinder flow of four-valve engine without intake port has been successfully computed. These computations have been performed using technique of the general coordinate transformation based on the finite-volume method and body-fitted non-orthogenal grids using staggered control volume and covariant variable as dependent one. Computations are started at intake valve opening and are carried through top-dead-center of compression. A k-$\varepsilon$model is used to represent turbulent transport of momentum. The principal study is the evolution of interaction between mean flow and turbulence and of the role of swirl and tumble in generating near TDC turbulence. Results for three different inlet flow configuration are presented. From these results, complex flow pattern may be effective for promoting combustion in spark-ignition engines and kinetic energy of mean flow near TDC is well converted into turbulent kinetic energy.