• Journal of computational fluids engineering
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• 제2권1호
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• pp.66-72
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• 1997

Optimum nozzle design exploiting the method of characteristic(M.O.C) has been in application as an efficient design methodology targeting a less weighted and short expansion nozzle. This paper treats the optimum nozzle design and the analysis of the inviscid compressible flow inside. Based on traditional Rao's method, the optimum nozzle design is coded with minor modifications for the identification of the control surface across which the mass flux should be conserved. Internal flow field is simulated numerically by M.O.C and implicit/explicit Taylor-Galerkin finite element method(F.E.M) with the aid of adaptive remeshing to capture the shock wave, hence improve the accuracy. Designed and calculated flow fields due to the separate analyses show that the mass flux predicted by optimum nozzle design with M.O.C is not conserved across the control surface and the sonic line should be located upstream of the nozzle throat. Rao's optimum nozzle design methodology exaggerates the momentum thrust and tends to overemphasize the engine performance loss.

• Korea-Australia Rheology Journal
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• 제21권3호
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• pp.193-200
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• 2009

We present a direct simulation technique for two-dimensional mold-filling simulations of fluids filled with a large number of circular disk-like rigid particles. It is a direct simulation in that the hydrodynamic interaction between particles and fluid is fully considered. We employ a pseudo-concentration method for the evolution of the flow front and the DLM (distributed Lagrangian multipliers)-like fictitious domain method for the implicit treatment of the hydrodynamic interaction. Both methods allow the use of a fixed regular discretization during the entire computation. The discontinuous Galerkin method has been used to solve the concentration evolution equation and the rigid-ring description has been introduced for freely suspended particles. A buffer zone, the gate region of a finite area subject to the uniform velocity profile, has been introduced to put discrete particles into the computational domain avoiding any artificial discontinuity. From example problems of 450 particles, we investigated the particle motion and effects of particles on the flow for both Newtonian and shear-thinning fluid media. We report the prolonged particle movement toward the wall in case of a shear-thinning fluid, which has been interpreted with the shear rate distribution.

• Journal of the Korean Institute of Gas
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• 제7권4호
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• pp.44-52
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• 2003

In this work dynamic heat transfer in a CPFS (cable penetration fire stop) system built in the firewall of nuclear power plants is three-dimensionally investigated to develop a test-simulator that can be used to verify effectiveness of the sealant. Dynamic heat transfer in the fire stop system is formulated in a parabolic PDE (partial differential equation) subjected to a set of initial and boundary conditions. First, the PDE model is divided into two parts; one corresponding to heat transfer in the axial direction and the other corresponding to heat transfer on the vertical planes. The first PDE is converted to a series of ODEs (ordinary differential equations) at finite discrete axial points for applying the numerical method of SOR (successive over-relaxation) to the problem. The ODEs are solved by using an ODE solver In such manner, the axial heat flux can be calculated at least at the finite discrete points. After that, all the planes are separated into finite elements, where the time and spatial functions are assumed to be of orthogonal collocation state at each element. The initial condition of each finite element can be obtained from the above solution. The heat fluxes on the vertical planes are calculated by the Galerkin FEM (finite element method). The CPFS system was modeled, simulated, and analyzed here. The simulation results were illustrated in three-dimensional graphics. Through simulation, it was shown clearly that the temperature distribution was influenced very much by the number, position, and temperature of the cable stream, and that dynamic heat transfer through the cable stream was one of the most dominant factors, and that the feature of heat conduction could be understood as an unsteady-state process.

• KSCE Journal of Civil and Environmental Engineering Research
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• 제26권5B호
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• pp.447-457
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• 2006

This paper presents a numerical model for the simulations of 2D depth-averaged flows. The shallow water equations are solved numerically by the Characteristic Dissipative Galerkin (CDG) finite element method. For validation, the developed model is applied to the hydraulic jump. The computed results are compared with the analytical solution, revealing good agreement. In addition, flow in a contracting channel showing standing waves is simulated. The calculated water surface profile appears to be qualitatively consistent with the observed data. The foregoing results indicate that the model is capable of simulating the abrupt change in flow field. Next, the model is applied to the flow in a $180^{\circ}$ curved channel. The simulated results show that the velocity near the inner bank is faster than that near the outer bank and the water depth near the inner bank is shallower than that near the outer bank. However, the simulated results show that the velocity distribution across the channel is almost uniform in the bend except the reach close to the end of the bend. This is due to the limitation of the governing equations in which the transverse convection of momentum by the secondary flows along a channel bend is not taken into account.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• 제14권5호
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• pp.458-465
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• 2003

In this paper, we analyze the transient electromagnetic response from three-dimensional(3-D) dielectric bodies using a time-domain electric field integral equation formulation. The solution method in this paper is based on the Galerkin＇s method that involves separate spatial and temporal testing procedures. Triangular patch basis functions are used for spatial expansion and testing functions for arbitrarily shaped 3-D dielectric structures. The time-domain unknown coefficients of the equivalent electric and magnetic currents are approximated as an orthonormal basis function set that is derived from the Laguerre functions. These basis functions are also used as the temporal testing. Numerical results involving equivalent currents and far fields computed by the proposed method are presented.

• Korea-Australia Rheology Journal
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• 제16권3호
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• pp.117-128
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• 2004

The effect of molecular parameters on the steady vortex behaviors in the inertial viscoelastic flow past a cylinder has been investigated. FENE-CR model was considered as a constitutive equation. A recently developed iterative solution method (Kim et al., (in press)) was found to be successfully applicable to the computation of inertial viscoelastic flows. The high-resolution computations were carried out to understand the detailed flow behaviors based on the efficient iterative solution method armed with ILU(0) type pre-conditioner and BiCGSTAB method. The discrete elastic viscous split stress-G/streamline upwind Petrov Galerkin (DEVSS-G/SUPG) formulation was adopted as a stabilization method. The vortex size decreased as elasticity increases. However, the vortex enhancement was also observed in the case of large extensibility, which means that the vortex behavior is strongly dependent upon the material parameters. The longitudinal gradient of normal stress was found to retard the formation of vortex, whereas the extensional viscosity played a role in the vortex enhancement. The present results are expected to be helpful for understanding the inertial vortex dynamics of viscoelastic fluids in the flow past a confined cylinder.

• Structural Engineering and Mechanics
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• 제61권2호
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• pp.209-220
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• 2017

The purpose of this paper is to study the geometrically nonlinear free vibration of functionally graded nano/micro beams (FGNBs) based on the modified couple stress theory. For practical applications, some analytical expressions of nonlinear frequencies for FGNBs on a nonlinear Pasternak foundation are developed. Hamilton's principle is employed to obtain nonlinear governing differential equations in the context of both Euler-Bernoulli and Timoshenko beam theories for a comprehensive investigation. The modified continuum theory contains one material length scale parameter to capture the size effect. The variation of two-constituent material along the thickness is modeled using Reddy's power-law. Also, the Mori-Tanaka method as an accurate homogenization technique is implemented to estimate the effective material properties of the FGNBs. The results are presented for both hinged-hinged and clamped-clamped boundary conditions. The nonlinear partial differential equations are reduced to ordinary differential equations using Galerkin method and then the powerful method of homotopy analysis is utilized to obtain the semi-analytical solutions. Eventually, the presented analytical expressions are used to examine the influences of the length scale parameter, material gradient index, and elastic foundation on the nonlinear free vibration of FGNBs.

• Structural Engineering and Mechanics
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• 제68권1호
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• pp.103-119
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• 2018

In the present research, an attempt is made to obtain a semi analytical solution for both nonlinear natural frequency and forced vibration of embedded functionally graded double layered nanoplates with all edges simply supported based on nonlocal strain gradient elasticity theory. The interaction of van der Waals forces between adjacent layers is included. For modeling surrounding elastic medium, the nonlinear Winkler-Pasternak foundation model is employed. The governing partial differential equations have been derived based on the Mindlin plate theory utilizing the von Karman strain-displacement relations. Subsequently, using the Galerkin method, the governing equations sets are reduced to nonlinear ordinary differential equations. The semi analytical solution of the nonlinear natural frequencies using the homotopy analysis method and the exact solution of the nonlinear forced vibration through the Harmonic Balance method are then established. The results show that the length scale parameters give nonlinearity of the hardening type in frequency response curve and the increase in material length scale parameter causes to increase in maximum response amplitude, whereas the increase in nonlocal parameter causes to decrease in maximum response amplitude. Increasing the material length scale parameter increases the width of unstable region in the frequency response curve.

• Journal of the Korean earth science society
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• 제36권5호
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• pp.476-483
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• 2015

The high-order Laplacian-type filter, which is capable of providing isotropic and sharp cut-off filtering on the spherical domain, is essential in processing geophysical data. In this study, a spherical high-order filter was designed by combining the Fourier method with finite difference-method in the longitude and latitude, respectively. The regular grid system was employed in the filter, which has uniform angular spacing including the poles. The singularity at poles was eliminated by incorporating variable transforms and continuity-matching boundary conditions across poles. The high-order filter was assessed using the Rossby-Haurwitz wave, the observed geopotential, and observed wind field. The performance of the filter was found comparable to the filter based on the Galerkin procedure. The filter, employing the finite difference method, can be designed to give any target order of accuracy, which is an important advantage being unavailable in other methods. The computational complexity is represented with 2n-1 diagonal matrices solver with n being the target order of accuracy. Along with the availability of arbitrary target-order, it is also advantageous that the filter can adopt the reduced grid to increase computational efficiency.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• 제14권10호
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• pp.1096-1103
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• 2003

In this paper, we analyze the transient electromagnetic response from three-dimensional(3-D) dielectric bodies using a time-domain PMCHW(Poggio, Miller, Chang, Harrington, Wu) formulation. The solution method in this paper is based on the Galerkin's method that involves separate spatial and temporal testing procedures. Triangular patch basis functions are used for spatial expansion and testing functions for arbitrarily shaped 3-D dielectric structures. The time-domain unknown coefficients of the equivalent currents are approximated by a set of orthonormal basis functions that are derived from the Laguerre polynomials. These basis functions are also used as the temporal testing. Numerical results involving equivalent currents and far fields computed by the proposed method are presented.