• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.12
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• pp.2989-2994
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• 2000

A mechanical face seal is a tribo-element intended to control leakage of working fluid at the interface of a rotating shaft and its housing. Leakage of working fluid decreases drastically as the clearance between mating seal faces gets smaller. But the very small clearance may result in an increased reduction of seal life because of high wear and heat generation. Therefore, in the design of mechanical face seals a compromise between low leakage and acceptable seal life is important, ant it present a difficult and practical design problem. A fluid film or sealing dam geometry of the seal clearance affects seal lubrication performance very much, and thereby is optimization is one of the main design consideration. in this study the Reynolds equation for the sealing dam of mechanical face seals is numerically analyzed, using the Galerkin finite element method, which is readily applied to various seal geometries, to give lubrication performances, such as opening force, restoring moment, leakage, and axial and angular stiffness coefficients. Then, to improve the seal performance an optimization is performed, considering various design variables simultaneously. For the tested case the optimization ha successfully resulted in the optimal design values of outer and inner seal radii, coning, seal clearance, and balance radius while satisfying all the operation subjected constraints and design variable side-constraints, and improvements of axial and angular stiffness coefficients by 16.8% and 2.4% respectively and reduction of leakage by 38.4% have been achieved.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.6 no.3
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• pp.302-314
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• 1994

The effects of the inclination of enclosure and partition on natural convective flow and heat transfer were investigated numerically. The enclosure was composed of the lower hot and the upper cold horizontal walls and the adiabatic vertical walls, and a partition was positioned perpendicularly at the mid-height of one vertical insulated wall. The governing equations are solved by using the finite element method with Galerkin method. The computations were performed with the variations of the partition length and Rayleigh number based on the temperature difference between two horizontal walls and the enclosure height with water(Pr=4.95). The effects of the inclination angle of enclosure and partition on the heat transfer within an enclosure were also studied. As the results, the increase of the inclination angle of enclosure rapidly raised the heat transfer rate, while the inclination angle for the maximum Nusselt number was retarded with the increase of the partition length and the decrease of the heat transfer rate became larger in proportion to the increase of the partition length. The Nusselt number obtained by the inclination of partition was smaller than that of the inclination of enclosure. However, the difference of the heat transfer rates was considerably decreased at the longer partition lengths and the trends for the variation of the average Nusselt number were more similar with that of the inclination of enclosure. The upward oriented partition increases the convective heat transfer distinctly in contrast to that of the inclination of enclosure as the partition length increases.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.26 no.12
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• pp.1738-1746
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• 2002

In the FSI (Fluid-Structure Interaction) problems, two different governing equations are to be solved together. One is fur the fluid and the other for the structure. Furthermore, a kinematic constraint should be imposed along the boundary between the fluid and the structure. We use the combined formulation, which incorporates both the fluid and structure equations of motion into a single coupled variational equation so that it is not necessary to calculate the fluid force on the surface of structure explicitly when solving the equations of motion of the structure. A two-dimensional channel flow divided by a Bernoulli-Euler beam is considered and the dynamic response of the beam under the influence of channel flow is studied. The Navier-Stokes equations are solved using a P2P1 Galerkin finite element method with ALE (Arbitrary Lagrangian-Eulerian) algorithm. The internal structural damping effect is not considered in this study and numerical results are compared with a previous work fer steady case. In addition to the Reynolds number, two non-dimensional parameters, which govern this fluid-structure system, are proposed. It is found that the larger the dynamic viscosity and density of the fluid are, the larger the damping of the beam is. Also, the added mass is found to be linearly proportional to the density of the fluid.

• Korean Chemical Engineering Research
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• v.47 no.1
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• pp.72-78
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• 2009

For the electro-discharge machining of an electro-conductive anisotropic composite, an unsteady state formulation was established and solved by Galerkin's finite element method. The distribution of temperature on work piece, the shape of the crater and the material removal rate were obtained in terms of the process parameters. The $12{\times}12$ irregular mesh that was chosen as the optimum in the previous analysis was used for computational accuracy and efficiency. A material having the physical properties of alumina/titanium carbide composite was selected and an electricity with power of 51.4 V and current of 7 A was applied, assuming the removal efficiency of 10 % and the thermal anisotropic factors of 2 and 3. As the spark was initiated the workpiece immediately started to melt and the heat affected zone was formed. The moving boundary of the crater was also identified with time. When the radial and axial conductivities were increased separately, the temperature distribution and the shape of the crater were shifted in the radial and axial directions, respectively. The material removal rate was found to be higher when the conductivity was increased in the radial direction rather than in the axial direction.

• Journal of the Korean earth science society
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• v.38 no.2
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• pp.105-114
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• 2017

Two dimensional finite element method with quadrilateral basis functions was applied to the spherical high order filter on the spherical surface limited area domain. The basis function consists of four shape functions which are defined on separate four grid boxes sharing the same gridpoint. With the basis functions, the first order derivative was expressed as an algebraic equation associated with nine point stencil. As the theory depicts, the convergence rate of the error for the spherical Laplacian operator was found to be fourth order, while it was the second order for the spherical Laplacian operator. The accuracy of the new high order filter was shown to be almost the same as those of Fourier finite element high order filter. The two-dimension finite element high order filter was incorporated in the weather research and forecasting (WRF) model as a hyper viscosity. The effect of the high order filter was compared with the built-in viscosity scheme of the WRF model. It was revealed that the high order filter performed better than the built in viscosity scheme did in providing a sharper cutoff of small scale disturbances without affecting the large scale field. Simulation of the tropical cyclone track and intensity with the high order filter showed a forecast performance comparable to the built in viscosity scheme. However, the predicted amount and spatial distribution of the rainfall for the simulation with the high order filter was closer to the observed values than the case of built in viscosity scheme.

• International Journal of Naval Architecture and Ocean Engineering
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• v.10 no.6
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• pp.692-710
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• 2018

The Three-dimensional (3-D) dynamical behaviors of a fluid-conveying pipe subjected to vortex-induced vibration are investigated with different internal flow velocity ${\nu}$. The values of the internal flow velocity are considered in both subcritical and supercritical regimes. During the study, the 3-D nonlinear equations are discretized by the Galerkin method and solved by a fourth-order Runge-Kutta method. The results indicate that for a constant internal flow velocity ${\nu}$ in the subcritical regime, the peak Cross-flow (CF) amplitude increases firstly and then decrease accompanied by amplitude jumps with the increase of the external reduced velocity. While two response bands are observed in the In-line (IL) direction. For the dynamics in the lock-in condition, 3-D periodic, quasi-periodic and chaotic vibrations are observed. A variety of CF and IL responses can be detected for different modes with the increase of ${\nu}$. For the cases studied in the supercritical regime, the dynamics shows a great diversity with that in the subcritical regime. Various dynamical responses, which include 3-D periodic, quasi-periodic as well as chaotic motions, are found while both CF and IL responses are coupled while ${\nu}$ is beyond the critical value. Besides, the responses corresponding to different couples of ${\mu}_1$ and ${\mu}_2$ are obviously distinct from each other.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.5
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• pp.829-837
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• 1992

This paper presents a new approach for the analysis of hot strip rolling processes. The approach is based on the finite element method and capable of predicting velocity field in the strip, temperature field in the strip, temperature field in the roll, and roll pressure. Basic finite element formulations for heat transfer analysis are described with emphasis on the treatment of numerical instability resulting from a standard Galerkin formulation. Comparison with the theoretical solutions found in the literature is made for the evaluation of the accuracy of the temperature solutions. An iterative scheme is developed for dealing with strong correlations between the metal flow characteristics and the thermal behavior of the roll-strip system. A series of process simulations are carried out to investigate the effect of various process parameters including interface friction, interface heat transfer coefficient, roll speed, reduction in thickness, and spray zone. The results are shown and discussed.

• Smart Structures and Systems
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• v.16 no.1
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• pp.141-162
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• 2015

The magneto-rheological visco-elastomer (MRVE) is used as a smart core to control the stochastic micro-vibration of a sandwich plate with supported mass. The micro-vibration response of the sandwich plate with MRVE core and supported mass under stochastic support motion excitations is studied and compared to evaluate the vibration suppression capability. The effects of the supported mass and localized magnetic field on the stochastic micro-vibration response of the MRVE sandwich plate are taken into account. The dynamic characteristics of the MRVE core in micro-vibration are described by a non-homogeneous complex modulus dependent on vibration frequency and controllable by applied magnetic fields. The partial differential equations for the coupled transverse and longitudinal motions of the MRVE sandwich plate with supported mass are derived from the dynamic equilibrium, constitutive and geometric relations. The simplified ordinary differential equations are obtained for the transverse vibration of the MRVE sandwich plate under localized magnetic fields. A frequency-domain solution method for the stochastic micro-vibration response of sandwich plates with supported mass is developed based on the Galerkin method and random vibration theory. The expressions of frequency-response functions, response power spectral densities and root-mean-square velocity responses of the plate in terms of the one-third octave frequency band are obtained for micro-vibration evaluation. Finally, numerical results are given to illustrate the large response reduction capacity of the MRVE sandwich plate with supported mass under stochastic support motion excitations, and the influences of MRVE parameters, supported mass and localized magnetic field placement on the micro-vibration response.

• Steel and Composite Structures
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• v.44 no.2
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• pp.155-169
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• 2022

In the present paper an analytical model was developed to study the non-linear vibrations of Functionally Graded Carbon Nanotube (FG-CNT) reinforced doubly-curved shallow shells using the Multiple Scales Method (MSM). The nonlinear partial differential equations of motion are based on the FGM shallow shell hypothesis, the non-linear geometric Von-Karman relationships, and the Galerkin method to reduce the partial differential equations associated with simply supported boundary conditions. The novelty of the present model is the simultaneous prediction of the natural frequencies and their mode shapes versus different curvatures (cylindrical, spherical, conical, and plate) and the different types of FG-CNTs. In addition to combining the vibration analysis with optimization algorithms based on the genetic algorithm, a design optimization methode was developed to maximize the natural frequencies. By considering the expression of the non-dimensional frequency as an objective optimization function, a genetic algorithm program was developed by valuing the mechanical properties, the geometric properties and the FG-CNT configuration of shallow double curvature shells. The results obtained show that the curvature, the volume fraction and the types of NTC distribution have considerable effects on the variation of the Dimensionless Fundamental Linear Frequency (DFLF). The frequency response of the shallow shells of the FG-CNTRC showed two types of nonlinear hardening and softening which are strongly influenced by the change in the fundamental vibration mode. In GA optimization, the mechanical properties and geometric properties in the transverse direction, the volume fraction, and types of distribution of CNTs have a considerable effect on the fundamental frequencies of shallow double-curvature shells. Where the difference between optimized and not optimized DFLF can reach 13.26%.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.13 no.7
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• pp.667-678
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• 2002

In this paper, a new radiating structure with a multi-layered two-dimensional metallic disk array was proposed for shaping the flat-topped element pattern. It is an infinite periodic planar array structure with metallic disks finitely stacked above the radiating circular waveguide apertures. The theoretical analysis was in detail performed using rigid full-wave analysis, and was based on modal representations for the fields in the partial regions of the array structure and for the currents on the metallic disks. The final system of linear algebraic equations was derived using the orthogonal property of vector wave functions, mode-matching method, boundary conditions and Galerkin's method, and also their unknown modal coefficients needed for calculation of the array characteristics were determined by Gauss elimination method. The application of the algorithm was demonstrated in an array design for shaping the flat-topped element patterns of $\pm$20$^{\circ}$ beam width in Ka-band. The optimal design parameters normalized by a wavelength for general applications are presented, which are obtained through optimization process on the basis of simulation and design experience. A Ka-band experimental breadboard with symmetric nineteen elements was fabricated to compare simulation results with experimental results. The metallic disks array structure stacked above the radiating circular waveguide apertures was realized using ion-beam deposition method on thin polymer films. It was shown that the calculated and measured element patterns of the breadboard were in very close agreement within the beam scanning range. The result analysis for side lobe and grating lobe was done, and also a blindness phenomenon was discussed, which may cause by multi-layered metallic disk structure at the broadside. Input VSWR of the breadboard was less than 1.14, and its gains measured at 29.0 GHz. 29.5 GHz and 30 GHz were 10.2 dB, 10.0 dB and 10.7 dB, respectively. The experimental and simulation results showed that the proposed multi-layered metallic disk array structure could shape the efficient flat-topped element pattern.