• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.527-548
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• 2021

In this paper we prove the existence of global weak solutions, the exponential stability of a stationary solution and the existence of a global attractor for the three-dimensional convective Brinkman-Forchheimer equations with finite delay and fast growing nonlinearity in bounded domains with homogeneous Dirichlet boundary conditions.

• Journal of computational fluids engineering
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• v.3 no.1
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• pp.73-81
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• 1998

The effect of vertical or horizontal throughflow on natural convection in horizontal porous layer was investigated. The computations were performed by employing Darcy-Brinkman-Forchheimer equation to consider the effect of inertia and viscous effect. The patterns of streamlines and isotherms are observed by changing the strength of throughflow. The vertical throughflow stabilizes the natural convection in porous layer. It also disturbs the developing vertical and horizontal velocity component of natural convection cell and increases the critical modified Rayleigh number. The horizontal throughflow influences the stabilization of natural convection in porous layer much more than the vertical throughflow. And it changes a stable convection into a oscillatory convection.

• Journal of Mechanical Science and Technology
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• v.17 no.10
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• pp.1583-1596
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• 2003

A study of forced convection in a circular pipe with a partially filled porous medium was numerically investigated. The Brinkman-Forchheimer extension of the Darcy model was used to analyze the and temperature distribution in the porous medium. Our study includes two types of porous layer configurations: (1) a layer attached at the tube wall extending inward towards the centerline and (2) a layer at the centerline extending outward. The effect of several parameters, such as Darcy number, effective viscosity, effective thermal conductivity, and inertia parameter, as well as the effect of geometric parameters, were investigated.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.37 no.8
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• pp.759-765
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• 2013

This study proposes the characteristics of the pressure drop in a compressible fluid through porous media for application to a porous injector in a liquid rocket engine in order to improve the uniformity of the drop size distribution and the mixing performance of shear coaxial injectors. The fluid through the porous media is a Non-Darcy flow that shows a Nonlinear relation between the pressure drop and the velocity at high speed and high mass flow rate. The pressure drop of the Non-Darcy flow can be derived using the Forchheimer equation that includes the losses of viscous and inertia resistance. The permeability and Ergun coefficient represented as a function of the pressure drop and pore size can be applied to the porous injector, where the fluid through the porous media is compressible. A generalized correlation between the pressure drop in relation to the pore size was derived.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.18 no.4
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• pp.372-382
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• 2006

Most of the conventional breakwaters impermeable breakwaters which block seawater exchange between the outside and inside of the harbors. The blocking of seawater exchange may cause pollution of water in harbors. To solve the water pollution problem, various kinds of seawater exchange breakwaters have been proposed. Their types can be classified into the current type which uses tidal current, and the overtopping type which uses the wave energy. The overtopping type breakwaters require a discharge coefficient to calculate the rate of overtopping into the harbor. The present study is to compute the rate of overtopping with introduction of a correct discharge coefficient and to evaluate the effect of the overtopping type breakwater on the water qualify inside a harbor. The rate of overtopping was computed by using Forchheimer formula with time dependent mild-slope equation for various wave conditions. The formula has been generally used to calculate the overflow discharge in steady state river flows. The discharge coefficient, which is the key parameter of the calculation, was determined by a series of hydraulic model tests. The present scheme was applied to the seawater exchange section of the western breakwater of Jeju New Harbor's and the efficiency of that section was examined. The calculated results showed that the rate of overtopping into the harbor reached about $27.5m^3/s$ in the wave condition (wave height 3.7 m, wave period 8.5s, and wave direction NNW).

• Journal of The Korean Society of Agricultural Engineers
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• v.55 no.6
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• pp.145-154
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• 2013

Recently, damage occurrence by wind erosion has been increasing in society. In times past, such problems only took place in desert area ; however, in recent years, the wind erosion problem is spreading out to agricultural land. Wind erosion in agricultural land can cause loss of loam soils, the disturbance of the photosynthesis of the crop fields and serious economic losses. To overcome the mentioned problems, installation of windbreak fence can be recommended which function as disturbing strong wind and wind erosion. However, there is still no proper guideline to install the windbreak fence and the installation used to rely on the intuition of the workers due to the lack of related studies. Therefore, this study measured the aerodynamic resistance of screens of the windbreak fence using the apparatus for testing screens. The apparatus for testing screens was designed to measure pressure loss around the screen. Measured pressure loss by wall friction compensated for pressure loss to calculate the aerodynamic resistance of screens. The result of pressure loss by regression analysis derived the aerodynamic coefficient of Darcy-Forchheimer equation and power law equation. The aerodynamic resistance was constant regardless of the overlapped shape when the screen was overlapped into several layers. Increasing the number of layers of the screen, internal resistance increased significantly more, and pressure loss caused by the screen also increased linearly when the wind speed was certain conditions, but permeability had no tendency. In the future, the results of this study will be applied to the computational fluid dynamics simulation. The simulation models will be also validated in advance by wind tunnel experiments. It will provide standard of a design for constructing windbreak fence.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.21 no.1
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• pp.30-38
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• 2009

In recent years, there's been strong demand for coastal structures that have a permeability that serves water affinity and disaster prevention from wave attack. The aim of this study is to examine the wave transformation, including wave run-up that propagates over the coastal structures with a steep slope. A numerical model based on the nonlinear shallow water equation, together with the unsteady nonlinear Darcy law for fluid motion in permeable underlayer and laboratory measurements was carried out in terms of the free surface elevations and fluid particle velocities for the cases of regular and irregular waves over 1:5 impermeable and permeable slopes. The numerical results were used to evaluate the application and limitations of the PBREAK numerical model. The numerical model could predict the cross-shore variation of the wave profile reasonably, but showed less accurate results in the breaking zone that the mass and momentum influx is exchanged the most. Except near the wave crest, the computed depth averaged velocities could represent the measured profile below the trough level fairly well.

• Journal of the Korean Electrochemical Society
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• v.2 no.2
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• pp.98-105
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• 1999

In the present study, buoyant force and its stabilizing effects in an electrostatic field were examined systematically in order to reduce the effect of natural convection with thermal stratification in a horizontal fluid-saturated porous layer. The correlation of ionic mass transport induced by double-diffusive convection in a horizontal porous layer has been derived theoretically. And the theoretical model was examined by electrochemical experiments. The theoretical correlation for mass transport which is satisfying Forchheimer's flow equation and based on the micro-turbulence model is derived as a function of soltual Darcy-Rayleigh number, thermal Darcy-Rayleigh number and Lewis number. In the experiment, the mass transport of copper ions in $CuSO_4-H_2SO_4$ solution is measured by electrochemical technique. By assembling theoretical correlation and experimental results, the mass transport correlation induced by double-diffusive convection is proposed as $$Sh=\frac{0.03054(Rs_D-LeRa_D)^{1/2}}{1-3.8788(Rs_D-LeRa_D)^{-1/10}}$$ The present correlation looks flirty reasonable with comparing experimental results, and very promising for the applications of its prototype into various systems involving heat transfer as well as mass transfer, in order to control the effects of natural convection effectively.

• Journal of Korea Water Resources Association
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• v.31 no.3
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• pp.223-234
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• 1998

Recently, the interests of the construction of the permeable submerged breakwaters have been increased to preserve and to improve the coastal environment, and to control the incident waves and littoral transport. It is very important to predict the wave transformation precisely over the permeable submerged breakwaters. This study discusses nonlinear wave transformation and characteristics by using BEM based on the frequency domain method of the 3rd-order Stokes waves. The Dupuit-Forchheimer formula is applied to the analysis of the fluid resistance of rubble stones, and the equation about equivalent linear frictional coefficient is newly modified based on the Lorentz's condition for the equivalent work. The numerical results are compared with the experimental ones for verification. These two results give a close agreement each other. It is confirmed that the present method of the 3rd-order Stokes waves estimates more precisely than that of the 2nd-order Stokes waves.

• Korean Chemical Engineering Research
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• v.53 no.6
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• pp.814-817
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• 2015

A new ionic mass transfer correlation is derived for the fluid-saturated, horizontal porous layer. Darcy-Forchheimer model is used to explain characteristics of fluid motion. Based on the microscales of turbulence a backbone mass transfer relation is derived as a function of the Darcy-Rayleigh number, $Ra_D$ and the porous medium Schmidt number, $Sc_p$. For the Darcy's limit of $Sc_p{\gg}Ra_D$, the Sherwood number, Sh is a function of $Ra_D$ only. However, for the region of high $Ra_D$, Sh can be related with $Ra_DSc_p$. Based on the present backbone equation and the electrochemical mass transfer experiments which are electro plating or electroless plating, the new ionic mass transfer correlation is suggested in the porous media.