• Journal of computational fluids engineering
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• v.11 no.3 s.34
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• pp.37-45
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• 2006

In this study we present the numerical methods that can be used in visualization of the flow and mixing patterns in a cavity driven by a top lid. The basic flow field within the cavity has been obtained by using a simple numerical scheme. The invariant manifold also called unstable manifold was then attained to represent the mixing pattern within the cavity. It was shown that care must be taken in calculating the trajectories of the fluid particles especially near corners of the cavity. The numerical results show excellent agreement with those obtained experimentally by other research group.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.2
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• pp.380-388
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• 1994

Study on the chaotic stirring has been performed numerically and experimentally for a shallow rectangular tank accompanying a vortex shedding. The model is composed of a rectangular tank with a vertical plate with a length half the width of the tank. The tank is subject to a horizontal sinusoidal oscillation. The chaotic stirring was analysed by Poincare sections, unstable manifolds and Lyapunov exponents. As Reynolds number is increased the stirring effect is decreased due to the growth of a regular regions near the lower surface of the tank. In the other hand decrease of Reynolds number gives a weaker vortex shedding resulting in the poorer stirring effect. It was also found that the Lyapunov exponent is the highest at the dimensionless period of 1.3-1.5, which seems to be the best condition for the efficient stirring. The experimental visualization for the deformation of materials exhibits the striation pattern similar to the unstable manifold obtained numerically.

• Journal of the Korean Society for Precision Engineering
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• v.18 no.10
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• pp.161-167
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• 2001

This paper presents an approach to nonlinear engine idle controller and intake manifold absolute pressure(MAP) observer based on mean torque production model. A stable engine idle speed is important in that the unstable engine Idle mode can make engine to drooping or stall state. A sliding fuzzy controller has been designed to control engine idle speed under load disturbance. A sliding observer is also developed to estimate the intake manifold absolute pressure and compared with the actual MAP sensor value. The sliding mode observer has shown good robustness and good tracking performance. The inputs of sliding fuzzy controller are the errors of rpm and MAP. The output is a duty cycle(DC) for driving a idle speed control valve(ISCV).

• International Journal of Automotive Technology
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• v.8 no.2
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• pp.219-224
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• 2007

Recently, atmospheric contaminations has become worse due to the increased number of automobile. The PCV (Positive Crankcase Ventilation) valve acts as a flow control to allow re-combustion of blow-by gas by having it flow from a crankcase to an inlet manifold suction tube. Also, during the fabrication of the PCV valve, micro cracks may occur in the valve body and be extended under operation. The excessive stress distribution and crack initiation on the PCV valve body would bring an unstable blow-by gas flow rate control and would cause valve failure. The purpose of this study is to examine the crack affects on the stress and strain variations on the PCV valve according to the inlet and outlet manifold under differential pressures. From the results, we can explain the behavior of the crack extension for a safe condition of PCV valve.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.2
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• pp.537-547
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• 1995

Numerical study on the chaotic stirring of viscous flow in an alternately driven cavity has been performed. Even under the Stokes-flow assumption, the inherent singularity at the corners made the problem not so easily accessible. With some special treatments to the region near the corners, the biharmonic equation was solved numerically by using the fully implicit method. The velocity field was then used in obtaining the trajectories of passive particles for studying the stirring effect. The three tools developed in the field of the nonlinear dynamics and chaos, that are the Poincare sections, the unstable manifolds, and the Lyapunov exponents, were used in analysing the stirring effect. It was shown that the unstable manifolds obtained in this study well fit the experimental results given by the previous investigators. It is predicted that the best stirring can be obtained when the aspect ratio a is near 0.8 and the dimensionless period T is in the range 4.3 - 4.7.

• Journal of the Korean Mathematical Society
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• v.58 no.5
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• pp.1279-1298
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• 2021

The aim of this paper is to prove the existence of the global attractor of the Cauchy problem for a semilinear degenerate hyperbolic equation involving strongly degenerate elliptic differential operators. The attractor is characterized as the unstable manifold of the set of stationary points, due to the existence of a Lyapunov functional.

• Journal of Advanced Marine Engineering and Technology
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• v.38 no.7
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• pp.806-813
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• 2014

The EGR system being reburned the part of the exhaust gas through intake system indicates more favorable emission characteristics to reduce NOx in a gasoline engine, but the case of inappropriate exhaust gas quantity induced from engine is fallen engine power caused by unstable combustion. In this study, we examined a method to predict EGR ratio according to various engine operation condition based by intake manifold pressure and confirmed such a prediction data through an experimental method. And after having constituted feedback EGR control algorithm in a base with such a prediction data, we acquired qualitatively similar results by having compared data provided through an EGR feedback control experiment with the data which calculated quantity of residual gas for the engine operation condition. Therefore, the applied algorithm and the system for feedback EGR control showed feasibility applied to real electronic control EGR technology.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.6 no.1
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• pp.20-28
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• 1994

A numerical study has been performed on enhancement of heat transfer in a forced convection of the modified driven-cavity flow which was previously found by the author to give a regular or chaotic stirring depending on the parameter value. It is found that for the present case wherein heat is transmitted between fluid and the surrounding walls, the chaotic stirring enhances the heat transfer at high Peclet numbers. The optimal condition of the flow modulation for the best heat transfer can be predicted by purely investigating the hydrodynamic facet, i.e. the stirring effect.

• Journal of applied mathematics & informatics
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• v.38 no.5_6
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• pp.375-406
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• 2020

The anti-predator factor due to fear of predator in eco- epidemiological models has a great importance and cannot be evaded. The present paper consists of a modified Lesli-Gower predator-prey model with contagious disease in the predator population only and also consider the fear effect in the prey population. Boundedness and positivity have been studied to ensure the eco-epidemiological model is well-behaved. The existence and stability conditions of all possible equilibria of the model have been studied thoroughly. Considering the fear constant as bifurcating parameter, the conditions for the existence of limit cycle under which the system admits a Hopf bifurcation are investigated. The detailed study for direction of Hopf bifurcation have been derived with the use of both the normal form and the central manifold theory. We observe that the increasing fear constant, not only reduce the prey density, but also stabilize the system from unstable to stable focus by excluding the existence of periodic solutions.

• Journal of Mechanical Science and Technology
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• v.17 no.10
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• pp.1563-1571
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• 2003

A fast response NO analyzer was applied to investigate the relation between cycle-by-cycle NO emissions and combustion chamber pressure. NO emissions were sampled at an isolated exhaust manifold of 4-stroke spark ignition engine to avoid the interference of exhaust gas from other cylinders. The linear correlation analysis was performed with collected data of NO emissions and combustion chamber pressure with respect to the various air-fuel mixture ratios and engine loads. The sampled data sets were obtained during 200 cycles at each operating condition. The results showed that there was a typical pattern in NO emissions from an exhaust port through a cycle. It was possible to set a block of crank angle in which the linear correlation coefficient between NO emissions and combustion chamber pressure was high. As the engine load increased, NO emissions were more dependent on combustion chamber pressure after TDC. It was also analyzed that the correlation between two parameters with respect to air-fuel mixture ratio tended to increase as mixture went leaner. Furthermore, this correlation coefficient for the mixture near the lean limit seemed to be kept high even though combustion was unstable.