• Title/Summary/Keyword: diffusivity equation

Search Result 107, Processing Time 0.025 seconds

A Three-Dimensional Galerkin-FEM Model with Density Variation (밀도 변화를 포함하는 3차원 연직함수 전개모형)

  • 이호진;정경태;소재귀;강관수;정종율
    • Journal of Korean Society of Coastal and Ocean Engineers
    • /
    • v.8 no.2
    • /
    • pp.123-136
    • /
    • 1996
  • A three-dimensional Galerkin-FEM model which can handle the temporal and spatial variation of density is presented. The hydrostatic approximation is used and density effects are included by means of conservation equation of heat and the equation of state. The finite difference grids are used in the horizontal plane and a set of linear-shape functions is used for the vertical expansion. The similarity transform is introduced to solve resultant matrix equations. The proposed model was first applied to the density-driven circulation in an idealized basin in the presence of the heat exchange between the air and the sea. The advection terms in the momentum equation were ignored, while the convection terms were retained in the heat equation. Coefficients of the vertical eddy viscosity and diffusivity were fixed to be constant. Calculation in a non-rotating idealized basin shows that the difference in heat capacity with depth gives rise to the horizontal gradient of temperature. Consequently, there is a steady new in the upper layer in the direction of increasing depth with compensatory counter flow .in the lower layer. With Coriolis force, geostrophic flow was predominant due to the balance between the pressure gradient and the Coriolis force. As a test in region of irregular topography, the model is applied to the Yellow Sea. Although the resultant flow was very complex, the character of the flow Showed to be geostrophic on the whole.

  • PDF

The Effects of Temperature and Pressure on the Diffusion of Phenol in Apples (사과 내에서 페놀의 확산에 대한 온도와 증기압의 영향)

  • Park, Hyeon-Ju;Lee, Ki-Won;Chung, Kyong-Hwan;Song, Yo-Soon;Seo, Gon
    • Korean Journal of Environmental Agriculture
    • /
    • v.26 no.1
    • /
    • pp.69-76
    • /
    • 2007
  • The accumulation curves of phenol in the flesh of apples were measured at $5^{\circ}C$, $25^{\circ}C$ and $40^{\circ}C$ when they were exposed to phenol vapor, The effective diffusivities of phenol at the rind and flesh were determined by comparing its experimentally obtained accumulation curves with simulated ones. The simulation was carried out by the non-steady state diffusion rate equation. The diffusion model assumed the consecutive diffusion of phenol at the rind and flesh of apples. The detection time of phenol in the flesh of apples was shortened with increasing temperature, and it accumulated amount also increased rapidly. The estimated effective diffusivity of phenol at the rind of apples increased with temperature as like $1.1{\times}10^{-13}\;m^2/s$ at $5^{\circ}C$, $1.4{\times}10^{-13}\;m^2/s$ at $25^{\circ}C$ and $2.2{\times}10^{-13}\;m^2/s$ at $40^{\circ}C$, but those at the flesh of apples were invariant as $1.5{\times}10^{-10}\;m^2/s$ at this temperature range. The effect of temperature on the diffusivity of phenol was small, but the increase of the vapor pressure of phenol with temperature accelerated the penetration of phenol at the rind, resulting in the rapid accumulation at the flesh of apple.

Burning Characteristics of Nitramine Propellant Embedded with Metal Wires (금속선을 삽입한 니트라민계 추진제의 연소특성)

  • 유지창
    • Journal of the Korean Society of Propulsion Engineers
    • /
    • v.4 no.4
    • /
    • pp.50-58
    • /
    • 2000
  • Burning rate of the matrix propellant($r_{sb}$) and burning rate along the metal wire($r_w$) were measured and analyzed for the HTPB/AP/Al propellant embedded with Ag wire($\phi$0.15mm) according to weight % of RDX(0~20%). Variation of burning rate increment ratio($r_w$/$r_{sb}$) and pressure exponent(n) was studied for the nitramine propellant having 10% RDX embedded with three kinds of metal(Ag, Cu, and Ni-Cr) of which diameter range is between 0.1~0.6mm. Maximum burning rate increment ratio of the nitramine propellant embedded with Ag wire($\phi$0.1mm) was 5.94 at $20^{\cire}C$, 1000 psia, 16.4% faster than that of HTPB/AP propellant, it is because that autoignition temperature of the nitramine propellant was higher than that of HTPB/AP propellant. Standard deviation of absolute ($r_{wc}$/$r_{we}$)/$r_{we}$ calculated by using new empiracal equation composed of four dimensionless groups, is 6.11% less than that calculated by using original empirical equation composed of three dimensionless group. The new empiracal equation is derived from Buckingham pi theorem using the parameters such as thermal diffusivity, melting temperature. wire diameter, propellant sample diameter, frame temperature, autoignition temperature and matrix burning rate which influence on $r_w$.

  • PDF

Development of a High Performance Ocean Model using Julia Language (줄리아 언어를 이용한 고성능 해양모델의 개발)

  • KWON, MIN-SUN;KIM, JONG GU
    • The Sea:JOURNAL OF THE KOREAN SOCIETY OF OCEANOGRAPHY
    • /
    • v.24 no.2
    • /
    • pp.187-207
    • /
    • 2019
  • In order to develop a high performance ocean model, we used Julia, a Just-In-Time compile language, and to obtain the solution of the momentum equation, we made the code to solve the Poisson equation by the Successive Over-Relaxation method. And then we made two models to test Julia calculation codes. First, a simple channel form is modeled to test constant source/sink conditions. Second, the simplified Yellow Sea was modeled to test tidal forcing, Coriolis forces, and the effect of vertical eddy diffusivity coefficients. The model has been tested with a total of eight cases in the two scenarios. As a result of the test, the depth-averaged current speed of the three cases in Scenario 1 converged perfectly to the theoretical value, and that showed well a vertical flow velocity gradient due to the bottom friction. Also, the result of Scenario 2 represented well the amphidromic points of Yellow Sea and the tidal characteristics of mid-western and southwestern coast of Korea. Therefore, it is considered that the ocean model using Julia language has developed successfully, this suggests that the ocean model has come to the stage of successful transition from a classical compile language to a Just-In-Time compile language.

Prediction of Thermal Diffusivities of Meat Products Containing Fish Meat (혼합육 가공품의 열확산도 추정에 관한 연구)

  • LEE Keon-Young;PARK Sang-Min;AN Hee-Woo;CHO Hyun-Duk;HAN Bong-Ho
    • Korean Journal of Fisheries and Aquatic Sciences
    • /
    • v.26 no.1
    • /
    • pp.26-30
    • /
    • 1993
  • To suggest a thermal diffusivity predicting equation for mixed meat products, heat penetration curves of pork products containing filefish meat were plotted in the temperature range of $80.44{\sim}121.03^{\circ}C$, and thermal diffusivities were calculated from the heat penetration curves. The ground pork was mixed with minced filefish meat and some additives such as lard, isolated soy protein, $1.5\%$ of table salt and $2\%$ of polyphosphate to control the composition and texture of products, and then stuffed into a model can. The heat penetration curves were plotted using a thermocouple fixed at the slowest heating point of the can. At constant heating temperature, the thermal diffusivities of the products increased linearly with increasing moisture content. The values of the products with constant moisture content also increased linearly with increasing heating temperature. The thermal diffusivities of the products with moisture content of $51.47{\sim}80.20\%$ could be predicted by following equation: $${\alpha}_p=(3.045+0.59{\cdot}X_w){\cdot}{\alpha}_w+0.0098{\cdot}10^{-6}{\cdot}X_w-0.4287{\cdot}10^{-6},(m^2{\cdot}s^{-1})$$ Maximal differences of the thermal diffusivities predicted with this equation were in the range of ${\pm}0.8\%$ compared with the practical values. This equation and another predicting equation obtained from the previous study for the pork product without fish meat could be simplified as following one equation, and the maximal differences of the thermal diffusivities predicted with this equation for both products with and without fish meat were in the range of less than ${\pm}2.5\%$ $${\alpha}_p=(2.290+0.54{\cdot}X_w){\cdot}{\alpha}_w+0.0024{\cdot}10^{-6}{\cdot}X_w-0.3535{\cdot}10^{-6},(m^2{\cdot}s^{-1})$$

  • PDF

A Kinetic Study on the Hydration Process of Barley Kernels with Various Polishing Yields (도정수율별 보리의 수화공정(水和工程)에 관(關)한 속도론적(速度論的) 연구(硏究))

  • Mok, Chul-Kyoon;Lee, Hyun-Yu;Nam, Young-Jung;Min, Byong-Yong
    • Korean Journal of Food Science and Technology
    • /
    • v.15 no.2
    • /
    • pp.136-140
    • /
    • 1983
  • The hydration characteristics of barley kernels with various polishing yields were investigated at temperatures of $20-60^{\circ}C$ and their sorption kinetics were studied. The moisture gain in initial stage of hydration was directly proportional to square root of hydration time and there was a break point at the moisture gain of 0.45-0.55g $H_2O/g$ solid. The hydration rate was great in order of polishing yield of 50, 70, 95, 90 and 100%, and increased with increasing hydration temperature. The diffusivity of water into barley kernels followed Arrhenius equation, and the activation energies in hydration reaction of polished barley were ranged from 6.9 to 9.5 Kcal/mole and that of non-polished one was 11.6Kcal/mole.

  • PDF

Application of Laser Beam Deflection Technique to Analysis of Stresses Generated during Hydrogen Diffusion through Pd Foil Electrode

  • Han Jeong-Nam;Pyun Su-Il
    • Journal of the Korean Electrochemical Society
    • /
    • v.4 no.2
    • /
    • pp.70-76
    • /
    • 2001
  • The present work describes the capabilities of laser beam deflection (LBD) technique for the analysis of the stresses developed during hydrogen diffusion through Pd foil electrode. First, we explain briefly the elasto-diffusive (Gorsky effect) and diffusion-elastic phenomena. A model for the diffusion-elastic phenomenon is theoretically derived from the solution of the Fick's equation for given initial and boundary conditions, Vegard's second law and Hooke's law. Second, we introduce how to apply the principle of LBD technique to the study on the stresses generated during hydrogen diffusion. From the comparison of the deflection transients numerically calculated with those experimentally measured, we finally discuss the change in the tensile deflection with time in terms of hydrogen concentration profile transient and hydrogen diffusivity.

Analysis of Particle Deposition onto a Heated or Cooled, Horizontal Free-Standing Wafer Surface (가열 또는 냉각되는 수평웨이퍼 표면으로의 입자침착에 관한 해석)

  • 유경훈;오명도;명현국
    • Transactions of the Korean Society of Mechanical Engineers
    • /
    • v.19 no.5
    • /
    • pp.1319-1332
    • /
    • 1995
  • Numerical analysis was performed to characterize the particle deposition behavior on a horizontal free-standing wafer with thermophoretic effect under the turbulent flow field. A low Reynolds number k-.epsilon. turbulence model was used to analyze the turbulent flow field around the wafer, and the temperature field for the calculation of the thermophoretic effect was predicted from the energy equation introducing the eddy diffusivity concept. The deposition mechanisms considered were convection, diffusion, sedimentation, turbulence and thermophoresis. For both the upper and lower surfaces of the wafer, the averaged particle deposition velocities and their radial distributions were calculated and compared with the laminar flow results and available experimental data. It was shown by the calculated averaged particle deposition velocities on the upper surface of the wafer that the deposition-free zone, where the deposition velocite is lower than 10$^{-5}$ cm/s, exists between 0.096 .mu.m and 1.6 .mu.m through the influence of thermophoresis with positive temperature difference of 10 K between the wafer and the ambient air. As for the calsulated local deposition velocities, for small particle sizes d$_{p}$<0.05 .mu.m, the deposition velocity is higher at the center of the wafer than at the wafer edge, whereas for particle size of d$_{p}$ = 2.0 .mu.m the deposition takes place mainly on the inside area of the wafer. Finally, an approximate model for calculating the deposition velocities was recommended and the calculated deposition velocity results were compared with the present numerical solutions, those of Schmidt et al.'s model and the experimental data of Opiolka et al.. It is shown by the comparison that the results of the recommended model agree better with the numerical solutions and Opiolka et al.'s data than those of Schmidt's simple model.

Interpretation of Ammonia Absorption Behavior in Water Turbulent Flow (물 난류에서의 암모니아 흡수 거동 해석)

  • Lee, Sang-Ryong;Park, Jin-Won
    • Journal of the Korea Organic Resources Recycling Association
    • /
    • v.27 no.3
    • /
    • pp.75-80
    • /
    • 2019
  • The article is devoted to the interpretation of ammonia, one of the fine dust precursors, absorption behavior in water turbulent flow. The water flow was considered as a turbulent flow with Reynolds number more than $10^4$, because ammonia gas penetration depth was deeper at turbulent flow compared to laminar flow. For the interpretation, the dimensionless mass transfer governing-equation and the constant physical-properties at room temperature were used. The diffusivity of ammonia in water and the kinematic viscosity of water were $2{\times}10^{-9}m^2/s$ and $1{\times}10^{-6}m^2/s$, respectively. The concentration distribution of ammonia in water was estimated with respect to the position from the point where the water started to be exposed to ammonia. The quantitative distribution as a function of the mixing length was also acquired. The quantitative interpretation may provide the insight how much the turbulent flow was more efficient to remove ammonia rather than the laminar flow.

Moire Interferometry Measurement and Numerical Analysis for Hygroscopic Swelling of Al-Polymer Joint (Al-Polymer 접합체의 흡습팽창에 대한 모아레 간섭 측정 및 수치해석)

  • Kim, Kibum;Kim, Yong-Yun
    • Journal of the Korea Academia-Industrial cooperation Society
    • /
    • v.15 no.6
    • /
    • pp.3442-3447
    • /
    • 2014
  • A simple method to evaluate the hygroscopic characteristics of polymer of microelectronic plastic package is suggested. To evaluate the characteristics, specimens were prepared, and the internally absorbed moisture masses were measured as a function of the absorbing time and calculated numerically. The hygroscopic pressure ratio was calculated by heat transfer analysis supported by commercial FEM code because the hygroscopic diffusion equation has the same form as the heat transfer equation. The moisture masses were then summed by the self developed code. The nonconductive polymers had quite different characteristics for the different lots, even though they were the same products. The absorbed moisture mass variations were calculated for several different characteristics, and the optimal curve of the mass variation close to experimental data was selected, whose solubility and diffusivity were affected by the hygroscopic characteristics of the material. The method can be useful in the industrial fields to quickly characterize the polymer material of the semiconductor package because the fast correspondence is normally required in industry. The weight changes in the aluminum-nonconductive-polymer joint due to moisture absorption were measured. The deformed system was also measured using the Moire Interferometry system and compared with the results of finite element analysis.