• Tunnel and Underground Space
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• v.13 no.5
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• pp.389-396
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• 2003

It is shown that the cubic law can be modified regarding the steady-state Navier-Stokes equations by using perturbation approximation method for a sinusoidal aperture variation. In order to adopt the perturbation theory, the sinusoidal function needs to be non-dimensionalized for the amplitude and wavelength. Then, the steady-state Navier-Stokes equations can be solved by expanding the non-dimensionalized stream function with respect to the small value of the parameter (the ratio of the mean aperture to the wavelength), together with the continuity equation. From the approximate solution of the Navier-Stokes equations, the basic cubic law is successfully modified for the steady-state condition and a sinusoidal aperture variation. A finite difference method is adopted to calculate the pressure within a fracture model, and the results of numerical experiments show the accuracy and applicability of the modified cubic law. As a result, it is noted that the modified cubic law, suggested in this study, will be used for the analysis of fluid flow through aperture geometry of sinusoidal distributions.

• Economic and Environmental Geology
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• v.52 no.4
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• pp.291-297
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• 2019

Fluid flow through rock fractures has been quantified using equations such as Stokes equations, Reynolds equation (or local cubic law), cubic law, etc. derived from the Navier-Stokes equations under the assumption that linear flow prevails. Therefore, these simplified equations are limited to linear flow regime, and cause errors in nonlinear flow regime. In this study, causal mechanism of nonlinear flow and critical Reynolds number were presented by carrying out fluid flow modeling with both the Navier-Stokes equations and the Stokes equations for a three-dimensional rough-walled rock fracture. This study showed that flow regimes changed from linear to nonlinear at the Reynolds number greater than 10. This is because the inertial forces, proportional to the square of the fluid velocity, increased enough to overwhelm the viscous forces. This tendency was also shown for the unmated (slightly sheared) rock fracture. It was found that nonlinear flow was caused by the rapid increase in the inertial forces with increasing fluid velocity, not by the growing eddies that have been ascribed to nonlinear flow.

• Proceedings of the Korean Geotechical Society Conference
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• 1992.10a
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• pp.55-60
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• 1992

Hydraulically filled ground is formed by the settling of soil grains from the mixture of soil grains and water. It was generally known that the settling speed of the soil grains in governed by Stokes low. In the case of clayed dredged material, the shape of soil grains is not round, the surface of the soil grains is relatively large compared to the weight of soil grains and inter-grain ionic force is relatively large compared to the wight of soil grains. By this reason the settling and consolidation behavior of hydraulically filled quite different from that of Stokes law. This study investigated the settling and consolidation behavior of hydraulically filled materials of Yeochon industrial complex by large scale laboratory settling & consolidation container. The test results showed tat actual settling speed of soil grains in quite large compared to that of Stokes law. It was turned out that this phenomenon was due to the aggregation of soil grains. Also, it was truned out that the void ration and water content after the completion of settling process was 8.7 and 322% respectively. The consolidtion settlement of clayey hydraulic fill material was predicated better by "incremental small strain" consolidation concept than classical Terzaghj's consolidation concept (infinitesimal strain).

• Transactions of the Korean Society of Mechanical Engineers B
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• v.22 no.11
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• pp.1603-1609
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• 1998

Numerical solutions of Stokes flow through periodic arrays of cylinders were sought using Darcy's law and homogenization theory. Drag and lift forces of each cylinder were computed for various attack angles and pitch-to-diameter ratios. It was found that drag force decreased as principal pressure gradient direction deviated from array direction and that drag force increased exponentially as pitch-to-diameter ratio approached unity. Similar tendency was found in lift force except that lift force increased and then decreased in quadratic manner as attack angle varied.

• Korean Journal of Optics and Photonics
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• v.3 no.4
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• pp.266-272
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• 1992

A coherent anti-Stokes Raman spectroscopy (CARS) technique is applied to measure temperature profile in a flame. The CARS signal is obtained with BOXCARS phase matching to get better spatial resolution. A program routine for calculating temperature of the flame from the measured CARS spectra is studied. The routine includes the line broadening mechnism of the molecules described with a modified energy gap (MEG) law by using the perturbation theory. We have found that the temperature profile obtained with the MEG law is properly fit with the results measured with a thermocoulpe and calculated with the adiabatic theory.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.30 no.11 s.254
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• pp.1101-1106
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• 2006

To investigate a relation between fine scale eddies and particle dispersion in a near-wall turbulence, direct numerical simulations of turbulent channel flow laden particle are performed for $Re_{\tau}$=180. The motions of 0,8 million particles are calculated for several particle response times ($t_p$) which is the particle response time based on stokes’ friction law. The number density of particles has a tendency to increase with approaching the near-wall regions ($y^+$<20) except for cases of very small and large particle response times (i.e. $t_p$=0.02 and 15). Near the wall, the behavior and distribution of particles are deeply associated with the fine scale eddies, and are dependent on particle response times and a distance from the wall. The Stokes number that causes preferential distribution in turbulence is changed by a distance from the wall. The influential Stokes number based on the Burgers' vortex model is derived by using the time scale of the fine scale eddies. The influential Stokes number is also dependent on a distance from the wall and shows large value in the buffer layer.

• Journal of the Korean Mathematical Society
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• v.32 no.4
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• pp.869-876
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• 1995

Piezo devices such as piezoceramic patches knwon as collocated rate sensor and actuators are commonly used in control of flexible structure (see, e.g., [1]) and noise reduction. Recently, Ito and Kang ([4]) developed a nonlinear feedback control synthesis for regulating fluid flow using these devices.

• 한국전산유체공학회:학술대회논문집
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• 2002.10a
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• pp.17-22
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• 2002

A numerical solution procedure has been developed to analyze the flow field resulted from the injection of a transverse jet through the divergent flap of a 2DCD nozzle for thrust vector control. The formulation employs the compressible Navier-Stokes equations in conservation law form and a two equation $\kappa-\omega$ turbulence model. Detailed numerical results are presented in this paper for the 2DCD nozzle over a range of secondary to primary injection mass flow ratios and nozzle pressure ratios.

• 한국전산유체공학회:학술대회논문집
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• 2009.11a
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• pp.34-37
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• 2009

Deforming mesh should be used when bodies are deforming or moving relative to each other due to the presence of aerodynamic forces and moments. Also, the flow solver for such a flow problem should satisfy the geometric conservation law to ensure the accuracy of the solutions. In this paper, a RANS(Reynolds Averaged Navier-Stokes) solver including automatic mesh capability using TFI(Transfinite Interpolation) method and GCL is developed and applied to flows induced by oscillating wings with given frequencies. The computations are performed both on deforming meshes and on rigid meshes. The computational results are compared with experimental data, which shows a good agreement.

• Journal of computational fluids engineering
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• v.15 no.1
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• pp.37-45
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• 2010

Deforming mesh should be used when bodies are deforming or moving relative to each other due to the presence of aerodynamic forces and moments. Also, the flow solver for such a flow problem should satisfy the geometric conservation law to ensure the accuracy of the solutions. In this paper, a RANS(Reynolds Averaged Navier-Stokes) solver including automatic mesh capability using TFI(Transfinite Interpolation) method and GCL is developed and applied to flows induced by oscillating wings with given frequencies. The computations are performed both on deforming meshes and on rigid meshes. The computational results are compared with experimental data, which shows a good agreement.