• Proceedings of the KSME Conference
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• 2003.04a
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• pp.1851-1856
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• 2003

A new Lagrangian stochastic dispersion model is developed by combining the GLM(generalized Langevin model) and the elliptic relaxation method. Under the physically plausible assumptions a simple analytical solution of elliptic relaxation is obtained. To compare the performance of our model with other model, the statistics of particle velocity as well as concentration are investigated. Numerical simulation results show good agreement with available experimental data.

• Nuclear Engineering and Technology
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• v.36 no.3
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• pp.248-262
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• 2004

Turbulence models are separately assessed for a three dimensional thermal-hydraulic analysis of the integral reactor SMART. Seven models (mixing length, k-l, standard $k-{\epsilon},\;k-{\epsilon}-f{\mu},\;k-{\epsilon}-v2$, RRSM, and ERRSM) are investigated for flat plate channel flow, rotating channel flow, and square sectioned U-bend duct flow. The results of these models are compared to the DNS data and experiment data. The results are assessed in terms of many aspects such as economical efficiency, accuracy, theorization, and applicability. The standard $k-{\epsilon}$ model (high Reynolds model), the $k-{\epsilon}-v2$ model, and the ERRSM (low Reynolds models) are selected from the assessment results. The standard $k-{\epsilon}$ model using small grid numbers predicts the channel flow with higher accuracy in comparison with the other eddy viscosity models in the logarithmic layer. The elliptic-relaxation type models, $k-{\epsilon}-v2$, and ERRSM have the advantage of application to complex geometries and show good prediction for near wall flows.

• Journal of Power System Engineering
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• v.2 no.3
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• pp.21-26
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• 1998

Numerical simulations for various fluid flows require enormous computing time during iterations. In order to solve this problem, several techniques have been proposed. A SOR method is one of the effective methods for solving elliptic equations. However, it is very difficult to find the optimum relaxation factor, the value of this factor for practical problems used to be estimated on the basis of expertise. In this paper, the implication of the relaxation factor are translated into fuzzy control rules on the basis of the expertise of numerical analysers, and fuzzy controller incorporated into a numerical algorithm. From two cases of study, Poisson equation and cavity flow problem, we confirmed the possibility of computational acceleration with fuzzy logic and qualitative reasoning in numerical simulations. Numerical experiments with the fuzzy controller resulted in generating a good performance.

• The Magazine of the Society of Air-Conditioning and Refrigerating Engineers of Korea
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• v.10 no.3
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• pp.185-219
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• 1981

To analyze two dimensional incompressible laminar natural convection in a rectangular enclosure heated from below and cooled by a horizontal ceiling and two vertical walls, he primitive Navier-Stokes equations and the energy equation were solved numerically in time dependent form by a marker and cell method. A successive over-relaxation method for the elliptic portion of the problem and an explicit method for the parabolic portion were applied for the range of Grashoff number of $5{\times}10^3\;to\;5{\times}10^4$ to get the transient and steady state dimensionless temperature and velocity profiles. For the range of aspect ratio $L/H{\leqq}2.4$ in which only a pair of convection rolls exists mean Nusselt number calculated are as follows : $$N_{NU}0.89\;N_{Gr}^{0.2}(H/L)^{0.45}$$ By path lines drawn by marker particle trajectories roll number of cellular motion were observed for various aspect ratio of the enclosure.

• Journal of Mechanical Science and Technology
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• v.18 no.7
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• pp.1140-1149
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• 2004

The absorption characteristics of water vapor into a LiBr-H$_2$O solution flowing down on finned inclined surfaces are numerically investigated in order to study the absorbing performances of different surface shapes of finned tubes as an absorber element. A three-dimensional numerical model is developed. The momentum, energy, and diffusion equations are solved simultaneously using a finite difference method. In order to obtain the temperature and concentration distributions, the Runge-Kutta and the Successive over relaxation methods are used. The flat, circular, elliptic, and parabolic shapes of the tube surfaces are considered in order to find the optimal surface shapes for absorption. In addition, the effects of the fin intervals and Reynolds numbers are studied. The results show that the absorption mainly happens near the fin tip due to the temperature and concentration gradient, and the absorbing performance of the parabolic surface is better than those of the other surfaces.

• Proceedings of the Korea Society for Energy Engineering kosee Conference
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• 1995.11a
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• pp.50-55
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• 1995

향상되어진 93-PCGC-2는 기존의 PCGC-2와 같이 미분탄 연소를 포함하는 다양한 반응성흐름과 비반응성 흐름을 설명하기 위해 2차원 정상상태 모델로 제시되어 졌다. 93-PCGC-2는 실린더형의 축 대칭계에 응용되어질 수 있고, 난류(Turbulence)는 유체역학식과 연소기구 양쪽을 위해 고려되어졌으며, 불연속 세로좌표 방법(Discrete Ordinates Method)을 이용하여 기체, 벽 및 입자들로부터의 복사열(Radiation)을 모사하였다. 입자상은 입자 무리들의 평균 경로들을 따라 해석하는 Lagrangian계의 해석법으로 모델화되어졌다. 석탄의 팽윤(Swelling)과 촤의 반응성에 관한 부모델과 더불어 새롭게 일반화된 석탄 탈휘발화 부모델 (FG-DVC)도 첨가되어졌다. 비균일 반응기구는 확산과 화학반응 둘 모두를 고려하였다. 주요 기상반응은 국부 순간 평형을 가정하여 모델화하였다. 그래서 반응속도는 혼합의 난류속도에 의해 제한되어진다. Thermal NOx과 Fuel NOx의 유한속도 화학론(Finite Rate Chemstry)에 대한 부모델은 화학반응속도론와 난류성의 통계치를 통합하여 만들어져 있다. 기상은 반복적인 line-by-line기교에 의해 풀려지는 elliptic partial differential equation으로 묘사되어진다. 수치적인 안정을 고려하기 위해 under-relaxation이 이용되어졌다. 이렇게 코드화된 93-PCGC-2는 연소를 위해 모사되어졌다. 또한 더 나아가 이 수치모델의 활용범위는 미분탄의 가스화에도 활용되어질 것으로 기대되어진다.

• Journal of computational fluids engineering
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• v.16 no.4
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• pp.39-46
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• 2011

A numerical study of a turbulent natural convection in an enclosure with the lattice Boltzmann method (LBM) is presented. The primary emphasis of the present study is placed on investigation of accuracy and numerical stability of the LBM for the turbulent natural convection flow. A HYBRID method in which the thermal equation is solved by the conventional Reynolds averaged Navier-Stokes equation method while the conservation of mass and momentum equations are resolved by the LBM is employed in the present study. The elliptic-relaxation model is employed for the turbulence model and the turbulent heat fluxes are treated by the algebraic flux model. All the governing equations are discretized on a cell-centered, non-uniform grid using the finite-volume method. The convection terms are treated by a second-order central-difference scheme with the deferred correction way to ensure accuracy and stability of solutions. The present LBM is applied to the prediction of a turbulent natural convection in a rectangular cavity and the computed results are compared with the experimental data commonly used for the validation of turbulence models and those by the conventional finite-volume method. It is shown that the LBM with the present HYBRID thermal model predicts the mean velocity components and turbulent quantities which are as good as those by the conventional finite-volume method. It is also found that the accuracy and stability of the solution is significantly affected by the treatment of the convection term, especially near the wall.

• The Transactions of the Korea Information Processing Society
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• v.2 no.4
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• pp.535-542
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• 1995

In this paper we present two preconditioners for solving large sparse linear systems arising from elliptic partial differential equations on massively parallel machines, such as the CM-5. Most massively parallel machines do heavily rely on the message-passing for the interprocessor communications. but according to the current manufacturing standards the cost of communications is very high compared to that of floating point arithmetic computations. Due to this we need an algorithm which minimizes the amount of interprocessor communication on the massively parallel machines. We will show that Block SOR(Successive Over Relaxation) method coupled with the multi-coloring technique is one of such preconditioner on the massively parallel machines, by conducting experiments in the CM-5. Also, we implemented the ADI(Alternation Direction Implicit) method in the CM-5, which has been conventionally one of the most powerful parallel preconditioner. Our experiment shows that Block SOR method coupled with the multi-coloring technique could yield a speedup with 50% efficiency with the range of number of processors form 16 to 512 for a matrix with dimension 512x512. On the other hand, the ADI method shows a very poor performance.

• The KIPS Transactions:PartA
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• v.10A no.2
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• pp.137-140
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• 2003

Recently, CG (Conjugate Gradient) scheme for the optimization of the Rayleigh quotient has been proven a very attractive and promising technique for interior eigenvalues for the following eigenvalue problem, Ax＝λx (1) The given matrix A is assummed to be large and sparse, and symmetric. Also, the method is very amenable to parallel computations. A proper choice of the preconditioner significantly improves the convergence of the CG scheme. We compare the parallel preconditioners for the computation of the interior eigenvalues of a symmetric matrix by CG-type method. The considered preconditioners are Point-SSOR, ILU (0) in the multi-coloring order, and Multi-Color Block SSOR (Symmetric Succesive OverRelaxation). We conducted our experiments on the CRAY­T3E with 128 nodes. The MPI (Message Passing Interface) library was adopted for the interprocessor communications. The test matrices are up to $512{\times}512$ in dimensions and were created from the discretizations of the elliptic PDE. All things considered the MC-BSSOR seems to be most robust preconditioner.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.24 no.2
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• pp.204-213
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• 2000

This study deals with jet impingement, which is extensively used in the process industries to achieve intense heating, cooling or drying rates and also widely employed as a test flow for turbulent models due to its complex flow configuration, on a flat plate by numerical methods. In this calculation, the finite volume method was employed to solve the Navier-stokes equation based on the non-orthogonal coordinate with non-staggered variable arrangement. To get a better understanding for the fluid flow and heat transfer characteristics of the turbulent jet impingements, $k-{\varepsilon}-{\overline{v^{'2}}}$ turbulent model was adapted and compared with the experimental data and the result of standard $k-{\varepsilon}$ turbulent model. Numerical calculations were carried out with various flow rates, nozzle to plate distances. In the case of the axisymmetric jet impingement on a flat plate, $k-{\varepsilon}-{\overline{v^{'2}}}$ turbulent model showed better agreement with the experimental data than the standard $k-{\varepsilon}$ turbulent model in the prediction of the mean velocity profiles, the turbulent velocity profiles. the turbulent shear stress and the heat transfer rate. The highest heat transfer rate can be obtained when the impingement occurs within the potential core..