• Interaction and multiscale mechanics
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• v.5 no.1
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• pp.27-40
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• 2012

The two-dimensional incompressible flow of a linear viscoelastic fluid we considered in this research has rapidly oscillating initial conditions which contain both the large scale and small scale information. In order to grasp this double-scale phenomenon of the complex flow, a multiscale analysis method is developed based on the mathematical homogenization theory. For the incompressible flow of a linear viscoelastic Maxwell fluid, a well-posed multiscale system, including averaged equations and cell problems, is derived by employing the appropriate multiple scale asymptotic expansions to approximate the velocity, pressure and stress fields. And then, this multiscale system is solved numerically using the pseudospectral algorithm based on a time-splitting semi-implicit influence matrix method. The comparisons between the multiscale solutions and the direct numerical simulations demonstrate that the multiscale model not only captures large scale features accurately, but also reflects kinetic interactions between the large and small scale of the incompressible flow of a linear viscoelastic fluid.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.25 no.1
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• pp.108-116
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• 2001

The vortex tube is a simple device which separates fluid stream into a cold stream and a hot stream without any chemical reaction. The process of energy separation in the vortex tube has caused a great deal of interest. Although many studies on energy separation in the vortex tube using air as the working fluid have been made so far, few experimental studies treated energy separation for incompressible fluid. So, an experimental study for the energy separation in the vortex tube using the water which is essentially an incompressible fluid is presented. When working fluid is the water, the best geometric values of nozzle area ratio and number of nozzle holes are 0.155, 6 respectively. These geometric values are showed by the similar values which are presented by compressible fluid as working fluid. But hot side mass fraction of which maximum temperature drop is happened are different from compressible fluid.

• Proceedings of the KSME Conference
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• 2005.11a
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• pp.43.1-43.1
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• 2005

• Journal of applied mathematics & informatics
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• v.41 no.2
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• pp.401-411
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• 2023

The effects of longitudinal velocity dusty fluid flow in a weak magnetic field are investigated in this paper. An external uniform magnetic field parallel to the flow of dusty fluid influences the flow of dusty fluid. Besides that, the problem under investigation is completely defined in terms of identifying parameters such as longitudinal velocity (u), Hartmann number (M), dust particle interactions β, stock resistance γ, Reynolds number (Re) and magnetic Reynolds number (Rm). While using suitable transformations of resemblance, The governing partial differential equations are transformed into a system of ordinary differential equations. The Hankel Transformation is used to solve these equations numerically. The effects of representing parameters on the fluid phase and particle phase velocity flow are investigated in this analysis. The magnitude of the fluid particle is reduced significantly. The result indicates the magnitude of the particle reduced significantly. Although some of our numerical solutions agree with some of the available results in the literature review, other results differs because of the effect of the introduced magnetic field.

• The Pure and Applied Mathematics
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• v.19 no.2
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• pp.147-169
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• 2012

We introduce a Heaviside-function formulation of the interaction between incompressible two-phase fluid and a non-deformable solid. Fluid and solid interact in two ways : fluid satises the Dirichlet boundary condition imposed by the velocity field of solid, and solid is accelerated by the surface traction exerted by fluid. The two-way couplings are formulated by the Heaviside function to the interface between solid and fluid. The cumbersome treatment of interface is taken care of by the Heaviside function, and the interaction is discretized in a simple manner. The discretization results in a stable and accurate projection method.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.2
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• pp.271-277
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• 2010

We prove the global (in time) vorticity existence for the 2-D Euler equations of a perfect incompressible fluid in $B^0_{{\infty},1}({\mathbb{R}}^2){\cap}L^p({\mathbb{R}}^2)$ with 1 < p < 2. Moreover, we prove that the particle trajectory map X(x, t) satisfies the following estimate: for some positive constant C $${\parallel}X^{\pm1}(\cdot,\;t)-id(\cdot){\parallel}_{B^1_{\infty,1}}{\leq}Ce^{e^{Ct}}$$, where id represents the identity map on ${\mathbb{R}}^2$.

• Journal of the Society of Naval Architects of Korea
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• v.48 no.6
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• pp.581-591
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• 2011

This paper describes the air compressibility effect in the CFD simulation of water impact load prediction. In order to consider the air compressibility effect, two sets of governing equations are employed, namely the incompressible Navier-stokes equations and compressible Navier-Stokes equations that describe general compressible gas flow. In order to describe violent motion of free surface, volume-of-fluid method is utilized. The role of air compressibility is presented by the comparative study of water impact load obtained from two different air models, i.e. the compressible and incompressible air. For both cases, water is considered as incompressible media. Compressible air model shows oscillatory behavior of pressure on the solid surface that may attribute to the air-cushion effect. Incompressible air model showed no such oscillatory behavior in the pressure history. This study also showed that the CFD simulation can capture the formation of air pockets enclosed by water and solid surface, which may be the location where the air compressibility effect is dominant.

• Journal of the Society of Naval Architects of Korea
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• v.48 no.6
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• pp.560-568
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• 2011

In SPH(Smoothed Particle Hydrodynamics) method, the fluid has been assumed that it is weakly compressible to solve the basic equations composed of Navier-Stokes equations and continuity equation. That leads to some drawbacks such as non-physical pressure fluctuations and a restriction as like small time steps in computation. In this study, to improve these problems we assume that the fluid is incompressible and the velocity-pressure coupling problem is solved by a projection method(that is, by ISPH method). The two-dimensional computation results of dam breaking and gravitational wave generation are respectively compared with the results of finite volume method and analytical method to confirm the accuracy of the present numerical computation technique. And, the agreements are comparatively acceptable. Subsequently, the green water simulations of a two-dimensional fixed barge are carried out to inspect the possibility of practical application to ship hydrodynamics, those correspond to one of the violent free surface motions with impact loads. The agreement between the experimental data and the present computational results is also comparatively good.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.393-403
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• 2005

We study the isothermal flow of a dusty viscous incompressible conducting fluid between two types of boundary motions- oscillatory and non-oscillatory, under the influence of gravitational force. Within the frame work of some physically realistic approximations and suitable boundary conditions, closed form solutions were obtained for the velocity profiles and the skin friction of the particulate flow. These results show that for a constant pressure gradient, only the velocity profile of the fluid and the skin friction are unaffected by gravity, while magnetic field is seen to affect both the fluid, particle velocities and the skin friction. Thus, our results are extension of previous results in literature, and graphical demonstration of some these solutions have been presented.

• 한국전산유체공학회:학술대회논문집
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• 2008.08a
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• pp.67.1-67.1
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• 2008