• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.6
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• pp.1509-1514
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• 1990

To investigate the seal dynamic instability for a misaligned and coned mechanical face seal, the finite difference approximation was employed to solve the modified Reynolds equation for an incompressible fluid and temperature dependent viscosity. Using the solution, the results for axial force, transverse moment, restoring moment, and ratio of the transverse moment and the restoring moment are calculated for the whole range from zero to full angular misalignment. The results indicate that the transverse moment due to the angular misalignment and coning terms affects considerably the dynamic instability of face seals. It is shown that the simplified treatment of Reynolds equation using the narrow seal approximation overestimate the ratio of the transverse moment to the restoring moment especially at touch.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.621-639
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• 2011

The purpose of this paper is to introduce a general iterative process by viscosity approximation method with parallel method to ap-proximate a common element of the set of solutions of a mixed equilibrium problem and of the set of common fixed points of a finite family of $k_i$-strict pseudo-contractions in a Hilbert space. We obtain a strong convergence theorem of the proposed iterative method for a finite family of $k_i$-strict pseudo-contractions to the unique solution of variational inequality which is the optimality condition for a minimization problem under some mild conditions imposed on parameters. The results obtained in this paper improve and extend the corresponding results announced by Liu (2009), Plubtieng-Panpaeng (2007), Takahashi-Takahashi (2007), Peng et al. (2009) and some well-known results in the literature.

• Geomechanics and Engineering
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• v.19 no.1
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• pp.11-20
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• 2019

The use of electrokinetic dissipation method to study the fluid flow law in micro-pores is of great significance to reservoir rock microfluidics. In this paper, the micro-capillary theory was combined with the coupling model of the seepage field and the current field under the excitation of the harmonic signal, and the coupling theory of the electrokinetic effect under the first-order approximation condition was derived. The dissipation equation of electrokinetic dissipation and viscous resistance dissipation and its solution were established by using Green's function method. The physical and mathematical models for the electrokinetic dissipation of reservoir rocks were constructed. The microscopic mechanism of the electrokinetic dissipation of reservoir rock were theoretically clarified. The influencing factors of the electrokinetic dissipation frequency of the reservoir rock were analyzed quantitatively. The results show that the electrokinetic effect transforms the fluid flow profile in the pores of the reservoir from parabolic to wavy; under low-frequency conditions, the apparent viscosity coefficient is greater that one and is basically unchanged. The apparent viscosity coefficient gradually approaches 1 as the frequency increases further. The viscous resistance dissipation is two orders of magnitude higher than the electrokinetic effect dissipation. When the concentration of the electrolyte exceeds 0.1mol/L, the electrokinetic dissipation can be neglected, while for the electrolyte solution (<$10^{-2}M$) in low concentration, the electrokinetic dissipation is very significant and cannot be ignored.

• 한국연소학회:학술대회논문집
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• 2004.11a
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• pp.97-106
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• 2004

Stability of laminar premixed planar flames inclined in gravitational field which generate vorticity is asymptotically examined. The flame structure is resolved by a large activation energy asymptotics and a long wave approximation. The coupling between hydrodynamics and diffusion processes is included and near-unity Lewis number is assumed. The results show that as the flame is more inclined from the horizontal plane it becomes more unstable due to not only the decrease of stabilizing effect of gravity but also the increase of destabilizing effect of rotational flow. The obtained dispersion relation involves the Prandtl number and shows the destabilizing effect of viscosity. The analysis predicts that the phase velocity of unstable flame wave depends on not only the flame angle but also the Lewis number. For relatively short wave disturbances, still much larger than flame thickness, the most unstable wavelength is nearly independent on the flame angle and the flame can be stabilized by gravity and diffusion mechanism.

• Journal of the Korean Society of Combustion
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• v.9 no.4
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• pp.9-21
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• 2004

Stability of laminar premixed planar flames inclined in the gravitational field is asymptotically examined. The flame structure is resolved by a large activation energy asymptotics and a long wave approximation. The coupling between hydrodynamics and diffusion processes is included and near-unity Lewis number is assumed. The results show that as the flame is more inclined from the horizontal plane it becomes more unstable due to not only the decrease of stabilizing effect of gravity but also the increase of destabilizing effect of rotational flow. The obtained dispersion relation involves the Prandtl number and shows the destabilizing effect of viscosity. The analysis predicts that the phase velocity of unstable flame wave depends on not only the flame angle but also the Lewis number. For relatively short wave disturbances, still much larger than flame thickness, the most unstable wavelength is nearly independent on the flame angle and the flame can be stabilized by gravity and diffusion mechanism.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2006.05a
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• pp.525-526
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• 2006

The products designed by human sensibility and ergonomics are given good impression. Especially the touch feeling on the human skin is very useful sensibility for quality of products. Elasticity and viscosity of human skin is very important element in product design based on ergonomics. In this paper, we describe a sophisticated method for measurement of dynamic viscoelasticity characteristics of human skin. For this measurement, we developed a measurement system assembled with load cell, actuator, amplifier and data acquisition system. The $MATLAB^{TM}$ is used to analyze the data and fit a approximation curves.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.21 no.3
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• pp.109-124
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• 2017

The numerical solution of the Stokes equation with discontinuous viscosity and singular force term is challenging, due to the discontinuity of pressure, non-smoothness of velocity, and coupled discontinuities along interface.In this paper, we give an efficient algorithm to solve this problem by employing spectral Legendre and Chebyshev approximations.First, we present the algorithm for a problem defined in rectangular domain with straight line interface. Then it is generalized to a domain with smooth curve boundary and interface by employing spectral element method. Numerical experiments demonstrate the accuracy and efficiency of our algorithm and its spectral convergence.

• Korea-Australia Rheology Journal
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• v.17 no.3
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• pp.131-140
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• 2005

In this work we show the results of our most recent Direct Numerical Simulations (DNS) of turbulent viscoelastic channel flow using spectral spatial approximations and a stabilizing artificial diffusion in the viscoelastic constitutive model. The Finite-Elasticity Non-Linear Elastic Dumbbell model with the Peterlin approximation (FENE-P) is used to represent the effect of polymer molecules in solution, The corresponding rheological parameters are chosen so that to get closer to the conditions corresponding to maximum drag reduction: A high extensibility parameter (60) and a moderate solvent viscosity ratio (0.8) are used with two different friction Weissenberg numbers (50 and 100). We then first find that the corresponding achieved drag reduction, in the range of friction Reynolds numbers used in this work (180-590), is insensitive to the Reynolds number (in accordance to previous work). The obtained drag reduction is at the level of $49\%\;and\;63\%$, for the friction Weissenberg numbers 50 and 100, respectively. The largest value is substantially higher than any of our previous simulations, performed at more moderate levels of viscoelasticity (i.e. higher viscosity ratio and smaller extensibility parameter values). Therefore, the maximum extensional viscosity exhibited by the modeled system and the friction Weissenberg number can still be considered as the dominant factors determining the levels of drag reduction. These can reach high values, even for of dilute polymer solution (the system modeled by the FENE-P model), provided the flow viscoelasticity is high, corresponding to a high polymer molecular weight (which translates to a high extensibility parameter) and a high friction Weissenberg number. Based on that and the changes observed in the turbulent structure and in the most prevalent statistics, as presented in this work, we can still rationalize for an increasing extensional resistance-based drag reduction mechanism as the most prevalent mechanism for drag reduction, the same one evidenced in our previous work: As the polymer elasticity increases, so does the resistance offered to extensional deformation. That, in turn, changes the structure of the most energy-containing turbulent eddies (they become wider, more well correlated, and weaker in intensity) so that they become less efficient in transferring momentum, thus leading to drag reduction. Such a continuum, rheology-based, mechanism has first been proposed in the early 70s independently by Metzner and Lamley and is to be contrasted against any molecularly based explanations.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 1993.04a
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• pp.39-53
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• 1993

The minimum oil film thickness(MOFT) in the connecting-rod bering of a 1.5 liter, L-4, gasoline engine is measured up to 5500 rpm and calculated to study the dynamically loaded engine bearing. Short bearing approximation and Mobility method are used for theoretical analysis of oil film charactrtistics. And cylinder pressure, crank-pin surface temperature and bearing tenp ture are measured as the input data of theoretical analysis. The MOFT are measured by the total capacitance method(TCM). To improve the reliability of the test results, a reasonable detmuuination method of bearing clearance is introduced and used, and the effects of cavitation and aeration on the test results are neglected. The crankshaft is grounded by means of a slip ring. A scissor type linkage system was developed to measure the MOFT and bearing temperature. The effects of engine speed, load and oil viscosity on the measured and calculated minimum oil film thicknesses are investigated at 1500 to 5500 rpm. From the comparison between the measured and calculated MOFT, it is found that a qualitative similarity exists between them, but in all cases, the measured MOFT are smaller than those calculated.

• Journal of computational fluids engineering
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• v.16 no.1
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• pp.22-29
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• 2011

In this study, the glass fiber drawing from a silica preform in the furnace for the optical fiber manufacturing process is numerically simulated by considering the radiative heating of cylindrically shaped preform. The one-dimensional governing equations of the mass, momentum, and energy conservation for the heated and softened preform are solved as a set of the boundary value problems along with the radiative transfer approximation between the muffle tube and the deformed preform shape, while the furnace heating is modeled by prescribing the temperature distribution of muffle tube. The temperature-dependent viscosity of silica plays an important role in formation of preform neck-down profile when the glass fiber is drawn at high speed. The calculated neck-down profile of preform and the draw tension are found to be reasonable and comparable to the actual results observed in the optical fiber industry. This paper also presents the effects of key operating parameters such as the muffle tube temperature distribution and the fiber drawing speed on the preform neck-down profile and the draw tension. Draw tension varies drastically even with the small change of furnace heating conditions such as maximum heating temperature and heating width, and the fine adjustment of furnace heating is required in order to maintain the appropriate draw tension of 100~200 g.