• Title/Summary/Keyword: Convective equation

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A Comprehensive Groundwater Modeling using Multicomponent Multiphase Theory: 1. Development of a Multidimensional Finite Element Model (다중 다상이론을 이용한 통합적 지하수 모델링: 1. 다차원 유한요소 모형의 개발)

  • Joon Hyun Kim
    • Journal of Korea Soil Environment Society
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    • v.1 no.1
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    • pp.89-102
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    • 1996
  • An integrated model is presented to describe underground flow and mass transport, using a multicomponent multiphase approach. The comprehensive governing equation is derived considering mass and force balances of chemical species over four phases(water, oil, air, and soil) in a schematic elementary volume. Compact and systemati notations of relevant variables and equations are introduced to facilitate the inclusion of complex migration and transformation processes, and variable spatial dimensions. The resulting nonlinear system is solved by a multidimensional finite element code. The developed code with dynamic array allocation, is sufficiently flexible to work across a wide spectrum of computers, including an IBM ES 9000/900 vector facility, SP2 cluster machine, Unix workstations and PCs, for one-, two and three-dimensional problems. To reduce the computation time and storage requirements, the system equations are decoupled and solved using a banded global matrix solver, with the vector and parallel processing on the IBM 9000. To avoide the numerical oscillations of the nonlinear problems in the case of convective dominant transport, the techniques of upstream weighting, mass lumping, and elementary-wise parameter evaluation are applied. The instability and convergence criteria of the nonlinear problems are studied for the one-dimensional analogue of FEM and FDM. Modeling capacity is presented in the simulation of three dimensional composite multiphase TCE migration. Comprehesive simulation feature of the code is presented in a companion paper of this issue for the specific groundwater or flow and contamination problems.

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Experimental Investigation on the Droplet Entrainment in the Air-Water Horizontal Stratified Flow (물-공기 수평 성층류 유동조건에서 액적이탈 현상에 대한 실험연구)

  • Bae, Byeong Geon;Yun, Byong Jo;Kim, Kyoung Doo;Bae, Byoung Uhn
    • Journal of Energy Engineering
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    • v.24 no.1
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    • pp.114-122
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    • 2015
  • In the high convective gas flow condition, irregular shaped water waves from which droplet entrainment occurs are generated under horizontally stratified two-phase flow condition. KAERI proposed a new mechanistic droplet entrainment model based on the momentum balance equation consisting of the shear stress, surface tension, and gravity forces. However, this model requires correlation or experimental data of several physical parameters related to the wave characteristics. In the present study, we tried to measure the physical parameters such as wave slope, wave hypotenuse length, wave velocity, wave frequency, and wavelength experimentally. For this, an experiment was conducted in the horizontal rectangular channel of which width, height, and length are, respectively, 40 mm, 50 mm, and 4.2 m. In the present test, the working fluids are chosen as air and water. The PIV technique was applied not only to obtain images for phase interface waves but also to measure the velocity field of the water flow. Additionally, we developed the parallel wire conductance probe for the confirmation of wave height from PIV image. Finally, we measured the physical parameters to be used in the validation of new droplet entrainment model.

Study on the Retrieval of Vertical Air Motion from the Surface-Based and Airborne Cloud Radar (구름레이더를 이용한 대기 공기의 연직속도 추정연구)

  • Jung, Eunsil
    • Atmosphere
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    • v.29 no.1
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    • pp.105-112
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    • 2019
  • Measurements of vertical air motion and microphysics are essential for improving our understanding of convective clouds. In this paper, the author reviews the current research on the retrieval of vertical air motions using the cloud radar. At radar wavelengths of 3 mm (W-band radar; 94-GHz radar; cloud radar), the raindrop backscattering cross-section (${\sigma}b$) varies between successive maxima and minima as a function of the raindrop diameter (D) that are well described by Mie theory. The first Mie minimum in the backscattering cross-section occurs at D~1.68 mm, which translates to a raindrop terminal fall velocity of ${\sim}5.85m\;s^{-1}$ based on the Gunn and Kinzer relationship. Since raindrop diameters often exceed this size, the signal is captured in the radar Doppler spectrum, and thus, the location of the first Mie minimum can be used as a reference for retrieving the vertical air motion. The Mie technique is applied to radar Doppler spectra from the surface-based and airborne, upward pointing W-band radars. The contributions of aircraft motion to the vertical air motion are also described and further the first-order aircraft motion corrected equation is presented. The review also shows that the separate spectral peaks due to the cloud droplets can provide independent validation of the Mie technique retrieved vertical air motion using the cloud droplets as a tracer of vertical air motion.

A Study on the Shape and Movement in Dissolved Air Flotation for the Algae Removal (수중조류제거(水中藻類除去)를 위한 가압부상(加壓浮上)에 있어서 기포(氣泡)의 양태(模態)에 관한 연구(研究))

  • Kim, Hwan Gi;Jeong, Tae Seop
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.4 no.4
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    • pp.79-93
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    • 1984
  • The dissolved air flotation(DAF) has been shown to be efficient process for the removal of algae ftom water. The efficiency of DAF can be affected by the volume ratio of pressurized liquid to sample, the pressure pressurized liquid, the contact time, the appropriate coagulant and its amount, the water temperature, the turbulence of reactor, the bubble size and rising velocity etc. The purpose of this paper is to compare the practical bubble rising velocity with the theoretical one, to investigate the adhesion phenomenon of bubbles and floc, and the influence of bubble size and velocity upon the process. The results through theoretical review and experimental investigation are as follows: Ives' equation is more suitable than Stokes' equation in computation of the bubble rising velocity. The collection of bubble and algae floc is convective collection type and resulted from absorption than adhesion or collision. The treatment efficiency is excellent when the bubble sizes are smaller than $l00{\mu}m$, and the turbulence of reactor is small. In the optimum condition of continuous type DAF the volume ratio of pressurized liquid to sample is 15%, the contact time in reactor is 15 minutes, the pressure of pressurized liquid is $4kg/cm^2$ and the distance from jet needle to inlet is 30cm.

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Development and evaluation of a 2-dimensional land surface flood analysis model using uniform square grid (정형 사각 격자 기반의 2차원 지표면 침수해석 모형 개발 및 평가)

  • Choi, Yun-Seok;Kim, Joo-Hun;Choi, Cheon-Kyu;Kim, Kyung-Tak
    • Journal of Korea Water Resources Association
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    • v.52 no.5
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    • pp.361-372
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    • 2019
  • The purpose of this study is to develop a two-dimensional land surface flood analysis model based on uniform square grid using the governing equations except for the convective acceleration term in the momentum equation. Finite volume method and implicit method were applied to spatial and temporal discretization. In order to reduce the execution time of the model, parallel computation techniques using CPU were applied. To verify the developed model, the model was compared with the analytical solution and the behavior of the model was evaluated through numerical experiments in the virtual domain. In addition, inundation analyzes were performed at different spatial resolutions for the domestic Janghowon area and the Sebou river area in Morocco, and the results were compared with the analysis results using the CAESER-LISFLOOD (CLF) model. In model verification, simulation results were well matched with the analytical solution, and the flow analyses in the virtual domain were also evaluated to be reasonable. The results of inundation simulations in the Janghowon and the Sebou river area by this study and CLF model were similar with each other and for Janghowon area, the simulation result was also similar to the flooding area of flood hazard map. The different parts in the simulation results of this study and the CLF model were compared and evaluated for each case. The results of this study suggest that the model proposed in this study can simulate the flooding well in the floodplain. However, in case of flood analysis using the model presented in this study, the characteristics and limitations of the model by domain composition method, governing equation and numerical method should be fully considered.

Nonhydrostatic Effects on Convectively Forced Mesoscale Flows (대류가 유도하는 중규모 흐름에 미치는 비정역학 효과)

  • Woo, Sora;Baik, Jong-Jin;Lee, Hyunho;Han, Ji-Young;Seo, Jaemyeong Mango
    • Atmosphere
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    • v.23 no.3
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    • pp.293-305
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    • 2013
  • Nonhydrostatic effects on convectively forced mesoscale flows in two dimensions are numerically investigated using a nondimensional model. An elevated heating that represents convective heating due to deep cumulus convection is specified in a uniform basic flow with constant stability, and numerical experiments are performed with different values of the nonlinearity factor and nonhydrostaticity factor. The simulation result in a linear system is first compared to the analytic solution. The simulated vertical velocity field is very similar to the analytic one, confirming the high accuracy of nondimensional model's solutions. When the nonhydrostaticity factor is small, alternating regions of upward and downward motion above the heating top appear. On the other hand, when the nonhydrostaticity factor is relatively large, alternating updraft and downdraft cells appear downwind of the main updraft region. These features according to the nonhydrostaticity factor appear in both linear and nonlinear flow systems. The location of the maximum vertical velocity in the main updraft region differs depending on the degrees of nonlinearity and nonhydrostaticity. Using the Taylor-Goldstein equation in a linear, steady-state, invscid system, it is analyzed that evanescent waves exist for a given nonhydrostaticity factor. The critical wavelength of an evanescent wave is given by ${\lambda}_c=2{\pi}{\beta}$, where ${\beta}$ is the nonhydrostaticity factor. Waves whose wavelengths are smaller than the critical wavelength become evanescent. The alternating updraft and downdraft cells are formed by the superposition of evanescent waves and horizontally propagating parts of propagating waves. Simulation results show that the horizontal length of the updraft and downdraft cells is the half of the critical wavelength (${\pi}{\beta}$) in a linear flow system and larger than ${\pi}{\beta}$ in a weakly nonlinear flow system.