토양 오염원의 이동에 관한 연구 (감쇠항이 있는 3차원 이송-확산 방정식의 수치모형 개발)

김상준 한국수자원학회 2012 한국수자원학회논문집 Vol.45 No.2

오염물질의 이동 현상을 모의하기 위하여, 감쇠항이 있는 3차원 이송-확산 방정식의 수치모형이 개발되었다. 개발된 모형은 유한차분 모형으로서 시간단계의 가중치 α를 포함하는 음해법(implicit finite difference method)과, 반복법인 Gauss-Seidel SOR(successive over relaxation)이 사용되었다. 모형은 보다 단순화된 가정 하에서 존재하는 두 가지의 해석적인 해와 비교되었다. 그 결과 Peclet number가 5~20 이하에서는 수치 분산의 영향이 크지 않았고 작은 오차 범위 내에서 해석적인 해와 동일하였다. 또한 가중치 α의 변화에 대한 모형의 거동은 Crank-Nicolson 모형(α=0.5)이 fully-implicit 모형(α= 1)보다 해석적인 해에 접근함을 보여주었다. 모형의 검증과 실효성 제고를 위하여, mass balance를 검토하였다. 즉, 이송, 확산 및 감쇠항 각각에 대한 질량 이동을 산출하였으며, 그 결과 질량 이동의 계산 오차는 약 3% 이내였다. 본 모형은 감쇠 과정이 수반되는 3차원 이송-확산의 농도분포와 질량이동을 산출할 수 있으며 다양한 경계 조건을 설정함으로서 현장조건을 반영할 수 있다. 그러나 본 모형은 고정 격자를 기반으로 하는 유한차분 모형이므로 Peclet number가 비교적 작게 나타날 수 있는 토양 및 지하수계의 오염물질 이동 등의 문제에서 유용하게 적용될 수 있을 것으로 사료된다. To simulate the transport of pollutant, a numeric model for the advection-diffusion equation with the decay term is developed. This is finite-difference model using the implicit method (with the weight factor α) and Gauss-Seidel SOR(successive over-relaxation). This model is compared to the analytical solutions (of simpler dimensional or boundary conditions), and in the condition of Peclet number < 5∼20, the result shows stable condition, and Crank-Nicolson method (α=0.5) shows the more accurate results than fully-implicit method (α=1). The mass of advection, diffusion and decay is calculated and the error of mass balance is less than 3%. This model can evaluate the 3-D concentrations of the advection-diffusion and decay problems, but this model uses only the finite-difference method with the fixd grid system, so it can be effectively used in the problems with small Peclet numbers like the pollutant transport in groundwater.

COMPARISON OF FLUX AND RESIDENT CONCENTRATION BREAKTHROUGH CURVES IN STRUCTURED SOIL COLUMNS

Kim, Dong-Ju Korean Society of Soil and Groundwater Environment 1997 지하수토양환경 Vol.2 No.2

오염물질 이동현상 연구에서는 침출수 혹은 잔존수농도 형태가 사용되는데 이의 선택은 모니터링 방법에 의존하게 된다. 파과곡선 실험에서 모니터링 농도 형태에 관한 선택은 임의적이며, 각 농도 형태에서 얻어진 운송 파라미터들은 동등하며 다공성매질의 수리적 특성을 각각 대표하는 것으로 알려져왔다. 그러나, 현장상태의 구조적 발달을 보이는 토양에서는 농도 형태별 운송계수의 동등성이 의문시 된다. 본 연 구에서는 불교란 현장시료(직경 20cm, 높이 20cm)에 대하여 두가지 농도 형태에 의한 파과곡선 실험을 시행하므로써 모니터링 방법에 따른 농도 형태와 그에 따른 운송 파라미터들을 비교분석 하였다. 침출수 농도와 잔존수 농도는 토양상부에서 20cm와 loom 떨어진 지점에서 EC-meter와 TDR 을 이용하여 각각 측정하였다. 연구결과, 침출수 농도는 잔존수 농도보다 첨두농도가 훨씬 높게 그리고 첨두농도의 운송시간이 짧게 나타났음을 알 수 있었다. 따라서 침출수농도곡선으로부터 추정된 운송파 라미터들은 잔존수농도곡선으로부터 추정된 수치들과 상당한 차이를 보였으며 그 차이는 CLT 모델보다 CDE 모델에서 더 크게 나타났다. 특히 CDE 모델에서는 침출수곡선으로부터 도출된 계수값들이 잔존수곡선으로부터 도출된 계수값들보다 훨씬 크게 나타났다. 이는 구조토양내에 존재하고 있는 대공극을 통한 오염물질 우회통과와 평형조건에서의 CDE 모델이 연구대상토양에서의 오염물질 이동현상을 표현하는데 부적합하였기 때문인 것으로 사료된다. 분자 분산에 대한 동수리학적 확산의 비와 Peclet number와의 상관관계를 나타내는 도표영역에서 두가지 농도는 모두 역학적 확산이 오염물질 운송을 좌우하는 영역에 속하였다. 그러나 분자분산은 토양내 대공극부분보다 matrix 부분에서의 오염물질 확산에 더 많은 기여를 하는 것으로 나타났으며 이는 공극유속과 확산계수사이에 존재하는 비선형성에 기인하기 때문인 것으로 사료된다. In many solute transport studies, either flux or resident concentration has been used. Choice of the concentration mode was dependent on the monitoring device in solute displacement experiments. It has been accepted that no priority exists in the selection of concentration mode in the study of solute transport. It would be questionable, however, to accept the equivalency in the solute transport parameters between flux and resident concentrations in structured soils exhibiting preferential movement of solute. In this study, we investigate how they differ in the monitored breakthrough curves (BTCs) and transport parameters for a given boundary and flow condition by performing solute displacement experiments on a number of undisturbed soil columns. Both flux and resident concentrations have been simultaneously obtained by monitoring the effluent and resistance of the horizontally-positioned TDR probes. Two different solute transport models namely, convection-dispersion equation (CDE) and convective lognormal transfer function (CLT) models, were fitted to the observed breakthrough data in order to quantify the difference between two concentration modes. The study reveals that soil columns having relatively high flux densities exhibited great differences in the degree of peak concentration and travel time of peak between flux and resident concentrations. The peak concentration in flux mode was several times higher than that in resident one. Accordingly, the estimated parameters of flux mode differed greatly from those of resident mode and the difference was more pronounced in CDE than CLT model. Especially in CDE model, the parameters of flux mode were much higher than those of resident mode. This was mainly due to the bypassing of solute through soil macropores and failure of the equilibrium CDE model to adequate description of solute transport in studied soils. In the domain of the relationship between the ratio of hydrodynamic dispersion to molecular diffusion and the peclet number, both concentrations fall on a zone of predominant mechanical dispersion. However, it appears that more molecular diffusion contributes to the solute spreading in the matrix region than the macropore region due to the nonliearity present in the pore water velocity and dispersion coefficient relationship.

공간적 상관길이와 유효수직응력의 효과에 따른 거친 단일 균열내의 용질이동특성에 관한 수치적 연구

정우창(Jeong Woochang) 한국지반환경공학회 2009 한국지반환경공학회논문집 Vol.10 No.1

본 연구에서는 유효수직응력의 영향을 받고 있으며, 공간적으로 상관된 간극분포를 포함하고 있는 단일 균열 내에서의 용질이동에 대한 공간적 거동을 수치적으로 분석하였다. 분석결과 단일 균열에서의 용질이동은 간극분포의 공간적 상관정도와 적용된 유효수직응력에 크게 영향을 받는 것으로 나타났다. 공간적 상관길이가 증가함에 따라 용질입자의 평균이동시간은 감소하였으며, 또한 용질이동에 대한 굴곡도와 Peclet 수(유체흐름에 의한 용질의 이송율과 분자확산율과의 관계를 나타내는 무차원 수)가 감소하는 경향을 나타내었다. 이는 공간적 상관길이가 증가할수록 단일 균열 내의 간극분포가 용질입자의 이동에 유리하다는 것을 의미한다. 그러나 유효수직응력이 증가할수록 용질입자의 평균이동시간과 굴곡도는 증가하는 경향을 나타냈으며, Peclet 수는 감소하는 경향을 나타냈다. 이는 유효수직응력이 증가할수록 접촉면의 증가로 인해 한 두 개의 상대적으로 큰 국부유량을 가지는 유로를 따라 이동하기 때문인 것으로 판단된다. 또한 본 연구에서 용질이동에 대한 모의된 결과에 근거하여 공간적 상관길이에 따른 유효 수직응력과 용질의 평균이동시간과의 관계를 나타내는 지수형태의 상관식을 제안하였다. This study is to analyze numerically the spatial behaviors of the solute transport in a spatially correlated variable-aperture fracture under the effective normal stress conditions. Numerical results show that the solute transport in a fracture is strongly affected by the spatial correlation length of apertures and applied effective normal stress. According to increasing spatial correlation length, the mean residence time of solute is decreased and the tortuosity and Peclet number (is a dimensionless number relating the rate of advection of a flow to its rate of diffusion) is also decreased. These results mean that the geometry of the aperture distribution is favorable to the solute transport as the spatial correlation length is increased. However, according to the applied effective normal stress is increased, the mean residence time and tortuosity have a tendency to increase but the Peclet number is decreased. The main reason that the Peclet number is decreased, is that the solute is displaced by one or two channels with relatively higher local flow rate due to the increment of contact areas by increasing effective normal stress. Moreover, based on numerical results of the solute transport in this study, the exponential-type correlation formulae between the mean residence time and the effective normal stress are proposed.

Extended Graetz Problem Including Axial Conduction and Viscous Dissipation in Microtube

Jeong Ho-Eyoul,Jeong Jae-Tack The Korean Society of Mechanical Engineers 2006 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.20 No.1

Extended Graetz problem in microtube is analyzed by using eigenfunction expansion to solve the energy equation. For the eigenvalue problem we applied the shooting method and Galerkin method. The hydrodynamically isothermal developed flow is assumed to enter the microtube with uniform temperature or uniform heat flux boundary condition. The effects of velocity and temperature jump boundary condition on the microtube wall, axial conduction and viscous dissipation are included. From the temperature field obtained, the local Nusselt number distributions on the tube wall are obtained as the dimensionless parameters (Peclet number, Knudsen number, Brinkman number) vary. The fully developed Nusselt number for each boundary condition is obtained also in terms of these parameters.

Shooting method applied to porous rotating disk: Darcy-Forchheimer flow of nanofluid

Muzamal Hussain,Humaira Sharif,Mohamed A. Khadimallah,Abir Mouldi,Hassen Loukil,Mohamed R. Ali,Abdelouahed Tounsi Techno-Press 2023 Advances in nano research Vol.14 No.3

The characteristics of motile microorganism and three dimensional Darcy-Forchheimer nanofluid flow by a porous rotatable disk with heat generation/absorption is reported. Thermophoretic and Brownian motion aspects are included by utilizing Buongiorno model. Moreover, slip conditions are considered on velocity, thermal, concentration and microorganism. Shooting procedure is implemented to find the numerical results of physical quantities are evaluated parametrically. The different physical parameters like heat sink/source parameter, thermal, Brownian number, thermophoresis parameter, concentration, Peclet number, bioconvected Lewis number, microorganism on concentration and density of motile microorganism distributions is considered. Graphs of concentration and microorganism are plotted to examine the influence of distinct prominent flow parameters.

탄화수소/수소/일산화탄소-공기의 예혼합화염에서 층류화염전파속도와 화염안정성

Tran Manh Vu,송원식(Won Sik Song),박정(Jeong Park),이기만(Kee Man Lee) 한국연소학회 2011 한국연소학회지 Vol.16 No.2

To investigate cell formation in hydrocarbon/hydrogen/carbon monoxide-air premixed flames, the outward propagation and cellular instabilities were experimentally studied in a constant pressure combustion chamber at room temperature and elevated pressures. Unstretched laminar burning velocities and Markstein lengths of the mixtures were obtained by analyzing high-speed schlieren images. In this study, hydrodynamic and diffusional-thermal instabilities were evaluated to examine their effects on flame instabilities. The experimentallymeasured unstretched laminar burning velocities were compared to numerical predictions using the PREMIX code. Effective Lewis numbers of premixed flames with methane addition decreased for all of the cases; meanwhile, effective Lewis numbers with propane addition increased for lean and stoichiometric conditions and increased for rich and stoichiometric cases for hydrogen-enriched flames. With the addition of propane, the propensity for cell formation significantly was diminished, whereas cellular instabilities for hydrogen-enriched flames were promoted. However, similar behavior of cellularity was obtained with the addition of methane to the reactant mixtures.

Separation of $\Phi$X HAE III DNA with Electrochromatography

Park, Young G. The Korean Society for Biotechnology and Bioengine 2000 Biotechnology and Bioprocess Engineering Vol.5 No.5

Experimental and theoretical works were performed for the separation of large polyelectrolytes such as DNA in the column packed with gel particles under an electric field. This paper shows how intraparticle convection effects the separation of DNAs in the column because DNAs quickly oriented through the pores in the field direction. Dimensionless transient mass balance equations were derived considering diffusion and electrophoretic convection. The separation criteria is theoretically studied using two different Peclet numbers in the fluid and solid phases and these criteria were verified uing two different DNAs by electrophoretic mobilities measured experimentally, showing how the separation position of DNAs varies in the column according to values of Pe(sub)f/Pe(sub)g of individual DNA. Governing equations are simultaneously solved by operator theoretic and characteristic methods to yield the column response.

고속 가스-부상 FE 윤활해석

이안성(An Sung Lee),이동환(Dong Whan Lee),나언주(Uhn Joo Na) 한국트라이볼로지학회 2003 한국트라이볼로지학회 학술대회 Vol.36 No.-

In high-speed gas-levitation applications a high compressibility number often brings a numerical difficulty in predicting generated pressure profiles by causing erroneous sudden pressure overshootings and oscillations in the trailing-edge. To treat the problem, in this study an exact exponential high-order shape function is introduced in the FE lubrication analyses. It is, shown by various examples that the high-order shape function scheme can subdue successfully pressure overshootings and oscillations.

EFDC 모형을 이용한 댐 붕괴류 수치모의 및 매개변수 민감도 분석

장철 ( Chul Jang ),송창근 ( Chang Geun Song ) 한국안전학회(구 한국산업안전학회) 2016 한국안전학회지 Vol.31 No.4

In this study, a series of numerical simulation of dam break flow was conducted using EFDC model, and input conditions including cell size, time step, and turbulent eddy viscosity were considered to analyze parameter sensitivity. In case of coarse mesh layout, the propagated length of the shock wave front was △χ longer than that of other mesh layouts, and the velocity results showed jagged edge, which can be cured by applying fine grid mesh. Turbulent eddy viscosity influenced magnitude of the maximum velocity passing through gate up to 20% and the cell Peclet number less than 2.0 ensured no numerical oscillations.

에탄 열분해 반응이 동반된 관형 반응기에서의 열전달 및 화학반응 특성 연구

신찬영(C.Y. Shin),안준(J. Ahn) 한국전산유체공학회 2016 한국전산유체공학회지 Vol.21 No.1

Thermal cracking is commonly modeled as plug flow reaction, neglecting the lateral gradients present. In this paper, 2-dimensional computational fluid dynamics including turbulence model and molecular reaction scheme are carried out. This simulation is solved by means of coupled implicit scheme for stable convergence of solution. The reactor is modeled as an isothermal tube, whose length is 1.2 m and radius is 0.01 m, respectively. At first, The radial profile of velocity and temperature at each point are predicted in its condition. Then the bulk temperature and conversion curve along the axial direction are compared with other published data to identify the reason why discussed variations of properties are important to product yield. Finally, defining a new non-dimensional number, Effect of interaction with turbulence, heat transfer and chemical reaction are discussed for design of thermal cracking furnace.