• Title/Summary/Keyword: Dispersion equation

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Transport and Fate of Benzene in a Sandy Soil (사질토양에서의 Benzene의 이동성에 관한 연구)

  • 백두성;김동주
    • Journal of the Korean Society of Groundwater Environment
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    • v.6 no.2
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    • pp.95-100
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    • 1999
  • Hydrocarbon compounds in vadose zone soils caused by adsorption onto the surfaces of solid particles are generally considered to show retardation effect. In this study, we investigated the retardation effect on the transport of Benzene in a sandy soil by conducting batch and column tests. The batch test was conducted by equilibrating dry soil mass with Benzene solutions of various initial concentrations. and by analyzing the concentrations of Benzene in initial and equilibrated solutions using HPLC. The column test consisted of monitoring the concentrations of effluent versus time known as a breakthrough curve (BTC). We used KCl and Benzene solutions with the concentration of 10 g/L and 0.88 g/L as a tracer, and injected them into the inlet boundary of the soil sample as a square pulse type respectively, and monitored the effluent concentrations at the exit boundary under a steady state condition using an EC-meter and HPLC. From the batch test, we obtained a distribution coefficient assuming that a linear adsorption isotherm exists and calculated the retardation factor based on the bulk density and porosity of the column sample. We also predicted the column BTC curve using the retardation factor obtained from the distribution coefficient and compared with the measured BTC of Benzene. The results of the column test showed that i) the peak concentration of Benzene was much smaller than that of KCl and ⅱ) the travel times of peak concentrations for the two tracers were more or less identical. These results indicate that adsorption of Benzene onto the sand panicles occurred during the pulse propagation but the retardation of Benzene caused by adsorption was not present in the studied soil. Comparison of the predicted with the measured BTC of Benzene resulted in a poor agreement due to the absence of the retardation phenomenon. The only way to describe the absolute decrease of Benzene concentration in the column leaching experiment was to introduce a decay or sink coefficient in the convection-dispersion equation (CDE) model to account for an irreversible sorption of Benzene in the aqueous phase.

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Dispersion of Particle Pulse in Human Lung Airway (인체기관지내의 입자펄스 확산 실험)

  • 이진원;이동엽;추경호
    • Journal of Biomedical Engineering Research
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    • v.19 no.5
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    • pp.511-518
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    • 1998
  • In order to develop the aerosol bolus technique which is thought to be a potential tool for probing geometries or abnormalities of small airways, an experimental system of measuring fast time variations of particle concentration in the inhaled and exhaled breathing air was developed. The system generates monodisperse sebacic acrid particles of 1 micron size and 1.2 of geometric standard deviation in high concentration of $10^8$ particles/cc, delivers a short pulse of particles at the controlled instant during inhalation using a solenoid valve, and measures the fast change of particle concentration in using the laser light scattering. Successful operation of the generator and the measuring system was confirmed by smooth concentration profiles in inhalation. It was also confirmed that maintaining a constant breathing rate is essential to stable outputs and any disturbance in flow rate near the mode (maximum concentration) induces a large number of spurious peaks in the exhalation. Experimental data without strict control of breathing flow rate showed a substantial amount of scatter. The measured results showed an improvement in scatter over the existing results. When compared with theoretical predictions from 1-D convective diffusion equation and other experiments, general characteristics of dispersion for several penetration depths showed a good agreement, but there exists some difference in absolute values, which is attributed to the difference in body conditions. Improvements are needed in the theory, especially in relation to correcting for the effect of breathing flow rate.

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Spatial Distribution and Sampling Plan for Pink Citrus Rust Mite, Aculops pelekassi (Acari: Eriophyidae) in Citrus Orchard (감귤원에서 귤녹응애 공간분포 분석과 표본조사법 개발)

  • Song, Jeong-Heub;Hong, Soon-Yeong;Lee, Shin-Chan
    • Korean journal of applied entomology
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    • v.51 no.2
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    • pp.91-97
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    • 2012
  • The dispersion indices, spatial pattern and sampling plan for pink citrus rust mite (PCRM), Aculops pelekassi, monitoring was investigated. Dispersion indices of PCRM indicated the aggregated spatial pattern. Taylor's power law provided better description of variance-mean relationship than Iwao's patchiness regression. Fixed-precision levels (D) of a sequential sampling plan were developed using by Taylor's power law parameters generated from PCRM on fruit sample (cumulated number of PCRM in $cm^2$ of fruit). Based on Kono-Sugino's empirical binomial the mean density per $cm^2$ could be estimated from fruit ratio with more than 12 rust mites per $cm^2$: $ln(m)=4.61+1.23ln[-ln(1-p_{12})]$. To determine the optimal tally threshold, the variance (var(lnm)) for mean (lnm) in Kono-Sugino equation was estimated. The lower and narrow ranged change of variance for esimated mean showed at a tally threshold of 12. To estimate PCRM mean density per $cm^2$ at fixed precision level 0.25, the required sample number was 13 trees, 5 fruits per tree and 2 points per fruit (total 130 samples).

Development of Pollutant Transport Model Working In GIS-based River Network Incorporating Acoustic Doppler Current Profiler Data (ADCP자료를 활용한 GIS기반의 하천 네트워크에서 오염물질의 이송거동모델 개발)

  • Kim, Dongsu
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.29 no.6B
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    • pp.551-560
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    • 2009
  • This paper describes a newly developed pollutant transport model named ARPTM which was designed to simulate the transport and characteristics of pollutant materials after an accidental spill in upstream of river system up to a given position in the downstream. In particular, the ARPTM incorporated ADCP data to compute longitudinal dispersion coefficient and advection velocity which are necessary to apply one-dimensional advection-dispersion equation. ARPTM was built on top of the geographic information system platforms to take advantage of the technology's capabilities to track geo-referenced processes and visualize the simulated results in conjunction with associated geographic layers such as digital maps. The ARPTM computes travel distance, time, and concentration of the pollutant cloud in the given flow path from the river network, after quickly finding path between the spill of the pollutant material and any concerned points in the downstream. ARPTM is closely connected with a recently developed GIS-based Arc River database that stores inputs and outputs of ARPTM. ARPTM thereby assembles measurements, modeling, and cyberinfrastructure components to create a useful cyber-tool for determining and visualizing the dynamics of the clouds of pollutants while dispersing in space and time. ARPTM is expected to be potentially used for building warning system for the transport of pollutant materials in a large basin.

Effects of Velocity Structures on Tracer Mixing in a Meandering Channel (사행수로에서 유속구조가 추적물질의 혼합에 미치는 영향)

  • Seo, Il Won;Park, Sung Won
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.29 no.1B
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    • pp.35-45
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    • 2009
  • In this study, a laboratory experiment has been performed on a S-curved channel with two curved sections. In the experiments, effects of 3-D velocity structures on mixing characteristics of tracer material were investigated. As a result, it was clearly noticed that the primary flow travels taking the shortest course of the meandering channel and has a very ununiform distribution at the bends. The secondary cell which was developing at the first bend disappears at the crossover, and then, at the next bend, secondary cell is re-developing in the opposite direction. The experimental results show that mixing of tracer is significantly affected by the combined action of ununiform primary flow and secondary cell. The ununiform primary flow separates the tracer cloud in the longitudinal direction, and the secondary cell further separates the retarding tracer cloud mainly in the transverse direction. As a result, these complex flow structures cause separation and spreading of tracer cloud both in the longitudinal and in the transverse directions. The measured dimensionless transverse dispersion coefficients calculated using 2-D routing procedure ranges 0.012-0.875, and is generally proportional to width to depth ratio (W/h). The predicted values calculated by the theoretical equation overestimate slightly the measured transverse dispersion coefficients.

Simulation on Contaminant Transport in the Aquifer Affected by River Stage (하천 수위의 영향을 받는 대수층에서 오염원의 이동에 관한 모의실험)

  • 김민환
    • Journal of the Korean Society of Groundwater Environment
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    • v.4 no.1
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    • pp.54-59
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    • 1997
  • The river and groundwater are contaminated by pollution source of a waste landfill and others near river. The contaminant transport and response of aquifer parameters are studied in the aquifer affected by variation of river stage. First, the equation for component of variation velocity with river stage is developed by using the analytical solution of groundwater governing equation. The numerical model which considered component of variation velocity is constructed for the transport of mass by advection and dispersion. In order to verify a numerical scheme, the analytical solution is used. The numerical solution is coincided with the analytical one. Aquifer parameters of Nanjido are used as the data for numerical experiment. Second, the range of aquifer parameters is established in order to reponse contaminant transport in aquifer with river stage. The result of numerical experiment shows that the range of the storage coefficient except hydraulic conductivity and effective porosity is relatively sensitive to the contaminant transport. When the storage coefficient is the order of 10$\^$-2/, the response is very sensitive to the variation of river stage.

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An Analytical Solution for Regular Progressive Water Waves

  • Shin, JangRyong
    • Journal of Advanced Research in Ocean Engineering
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    • v.1 no.3
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    • pp.157-167
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    • 2015
  • In order to provide simple and accurate wave theory in design of offshore structure, an analytical approximation is introduced in this paper. The solution is limited to flat bottom having a constant water depth. Water is considered as inviscid, incompressible and irrotational. The solution satisfies the continuity equation, bottom boundary condition and non-linear kinematic free surface boundary condition exactly. Error for dynamic condition is quite small. The solution is suitable in description of breaking waves. The solution is presented with closed form and dispersion relation is also presented with closed form. In the last century, there have been two main approaches to the nonlinear problems. One of these is perturbation method. Stokes wave and Cnoidal wave are based on the method. The other is numerical method. Dean's stream function theory is based on the method. In this paper, power series method was considered. The power series method can be applied to certain nonlinear differential equations (initial value problems). The series coefficients are specified by a nonlinear recurrence inherited from the differential equation. Because the non-linear wave problem is a boundary value problem, the power series method cannot be applied to the problem in general. But finite number of coefficients is necessary to describe the wave profile, truncated power series is enough. Therefore the power series method can be applied to the problem. In this case, the series coefficients are specified by a set of equations instead of recurrence. By using the set of equations, the nonlinear wave problem has been solved in this paper.

A Parabolic Approximation Model for Wave Deformation Combined Refraction, Diffraction, and Breaking (파랑(波浪)의 굴절(屈折), 회절(回折) 및 쇄파변형(碎波變形)에 관한 포물형근사모형(抛物形近似模型))

  • Lee, Dong Soo;Lee, Jong Sup;Park, II Heum
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.14 no.3
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    • pp.619-633
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    • 1994
  • A wave deformation model for general purpose combined refraction, diffraction, and breaking is developed in the shallow water. A parabolic approximation equation considered a higher order diffraction term is derived from the previous mild slope equation. A wave energy dissipation term due to bottom friction and breaking is introduced from the turbulence model. The Crank-Nicoloson implicit scheme is used in the numerical calculation, then the solutions are compared with the various hydraulic experiment data in the circular, the elliptic shoal, and the surf zone. The wave height decay in the surf zone is sensitively affected by the incident wave steepness, and the wave height variation around the elliptic shoal is well explained by the non-linear dispersion relation and the wave energy dissipation term. The model is also applied to a field coastal area and reasonable results are obtained.

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An Accuracy Improvement in Solving Scalar Wave Equation by Finite Difference Method in Frequency Domain Using 49 Points Weighted Average Method (주파수영역에서 49점 가중평균을 이용한 scalar 파동방정식의 유한차분식 정확도 향상을 위한 연구)

  • Jang, Seong Hyung;Shin, Chang Soo;Yang, Dong Woo;Yang, Sung Jin
    • Economic and Environmental Geology
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    • v.29 no.2
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    • pp.183-192
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    • 1996
  • Much computing time and large computer memory are needed to solve the wave equation in a large complex subsurface layer using finite difference method. The time and memory can be reduced by decreasing the number of grid per minimun wave length. However, decrease of grid may cause numerical dispersion and poor accuracy. In this study, we present 49 points weighted average method which save the computing time and memory and improve the accuracy. This method applies a new weighted average to the coordinate determined by transforming the coordinate of conventional 5 points finite difference stars to $0^{\circ}$ and $45^{\circ}$, 25 points finite differenc stars to $0^{\circ}$, $26.56^{\circ}$, $45^{\circ}$, $63.44^{\circ}$ and 49 finite difference stars to $0^{\circ}$, $18.43^{\circ}$, $33.69^{\circ}$, $45^{\circ}$, $56.30^{\circ}$, $71.56^{\circ}$. By this method, the grid points per minimum wave length can be reduced to 2.5, the computing time to $(2.5/13)^3$, and the required core memory to $(2.5/13)^4$ computing with the conventional method.

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Weighted-averaging Finite-element Method for Scalar Wave Equation in the Frequency Domain (가중평균 유한요소법을 이용한 주파수영역에서의 인공 음향파 합성)

  • Hyun Hye-Ja;Suh Jung-Hee;Min Dong-Joo
    • Geophysics and Geophysical Exploration
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    • v.5 no.3
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    • pp.169-177
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    • 2002
  • We develop the weighted-averaging finite-element method which uses four kinds of element sets. By constructing global stiffness and mass matrices for four kinds of element sets and then averaging them with weighting coefficients, we obtain a new global stiffness and mass matrix. With the optimal weighting coefficients minimizing grid dispersion and grid anisotropy, we can reduce the number of grid points required per wavelength to 4 for a $1\%$ upper limit of error. We confirm the accuracy of our weighted-averaging finite-element method through accuracy analyses for a homogeneous and a horizontal-layer model. By synthetic data example, we reconfirm that our method is more efficient for simulating a geological model than previous finite-element methods.