• 한국연소학회지
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• 제10권3호
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• pp.25-33
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• 2005

Fast-time instability is investigated for diffusion flames with Lewis numbers greater than unity by employing the numerical technique called the Evans function method. Since the time and length scales are those of the inner reactive-diffusive layer, the problem is equivalent to the instability problem for the $Li\tilde{n}\acute{a}n#s$ diffusion flame regime. The instability is primarily oscillatory, as seen from complex solution branches and can emerge prior to reaching the upper turning point of the S-curve, known as the $Li\tilde{n}\acute{a}n#s$ extinction condition. Depending on the Lewis number, the instability characteristics is found to be somewhat different. Below the critical Lewis number, $L_C$, the instability possesses primarily a pulsating nature in that the two real solution branches, existing for small wave numbers, merges at a finite wave number, at which a pair of complex conjugate solution branches bifurcate. For Lewis numbers greater than $L_C$, the solution branch for small reactant leakage is found to be purely complex with the maximum growth rate found at a finite wave number, thereby exhibiting a traveling nature. As the reactant leakage parameter is further increased, the instability characteristics turns into a pulsating type, similar to that for L < $L_C$.

• 한국자동차공학회논문집
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• 제13권3호
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• pp.41-47
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• 2005

This paper deals with a squeal noise in a brake system. It has been proved that the squeal noise is influenced by the angular misalignment of a disk, disk run-out, with the previously experimental study. In this study, a cause of the noise is examined by using FE analysis program(SAMCEF) and numerical analyses with a derived analytical equation of the disk based on the experimental results. The FE analyses and numerical results show that the squeal noise is due to the disk run-out as the experimental results and the frequency component of the noise equals to that of a disk's bending mode arising from the Hopf bifurcation.

• 한국전산유체공학회지
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• 제20권3호
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• pp.47-53
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• 2015

This study performed numerical simulation to elucidate the characteristics of flow past a rectangular cylinder with various values of the aspect ratio(AR) of the cylinder. We calculated the flow field, force coefficients and Strouhal number of vortex shedding depending on the Reynolds number(Re) and the aspect ratio. The $AR{\approx}1$ is preferred for drag reduction, and 0.375$AR{\approx}0$ is recommended if suppression of the lift-coefficient fluctuation and the shedding frequency is desirable. Furthermore the criticality of the Hopf bifurcation is also reported for each AR.

• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.193-207
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• 2010

In this paper, a predator-prey model with stage structure and distributed delay is investigated. Mathematical analyses of the model equation with regard to boundedness of solutions, nature of equilibria, permanence, extinction and stability are performed. By the comparison theorem, a set of easily verifiable sufficient conditions are obtained for the global asymptotic stability of nonnegative equilibria of the model. Taking the product of the per-capita rate of predation and the rate of conversing prey into predator as the bifurcating parameter, we prove that there exists a threshold value beyond which the positive equilibrium bifurcates towards a periodic solution.

• 한국전산유체공학회지
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• 제16권1호
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• pp.1-6
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• 2011

Flow instability is investigated in a two-dimensional channel with thin baffles placed symmetrically in the vertical direction and periodically in the streamwise dircetion. At low Reynolds numbers, the flow is steady and symmetric. Above a critical Reynolds number, the steady flow undergoes a Hopf bifurcation leading to unsteady periodic flow. As Reynolds number further increases, we observe the onset of secondary instability. At high Reynolds numbers, the two-dimensional periodic flow becomes three dimmensional. To identify the onset of secondary instability, we carry out Floquet stability analysis. We obseved the transition to 3D flow at a Reynolds number of about 125. Also, we computed dominant spanwise wavenumbers near the critical Reynolds number, and visualized vortical structures associated with the most unstable spanwise wave.

• 한국전산유체공학회지
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• 제15권3호
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• pp.54-59
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• 2010

A parametric study has been carried out to elucidate the characteristics of channel flow with a streamwise-periodic array of cylinders. This flow configuration is relevant to heat exchanger applications. The presence of cylinders in channel flow causes the attached wall boundary layer to separate, leading to significant change in flow instabilities. There exist two kinds of instabilities; flow undergoes a primary instability (Hopf bifurcation) at a lower Reynolds number, and the unsteady two-dimensional flow becomes unstable to three-dimensional disturbances at a higher Reynolds number. We report here the dependencies of the primary instability as well as the flow characteristics of the subsequent unsteady flow, including flow-induced forces and Strouhal number of vortex shedding, on the distance between the cylinder and the channel wall.

• 대한기계학회논문집B
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• 제25권6호
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• pp.804-810
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• 2001

Transition of flows in natural convection in a horizontal cylindrical annulus is investigated for the fluid with Pr=0.2. The unsteady streamfunction-vorticity equation is solved with finite difference method. As Rayleigh number is increased, the steady crescent-shaped eddy flow bifurcates to a time-periodic flow with like-rotating eddies. After the first Hopf bifurcation, however, a reverse transition from oscillatory to a steady flow occurs by the flow pattern variation. Hysteresis phenomenon occurs between the solution branches of up-scan and down-scan stages, and dual solutions with one steady and one oscillatory flow are found. Overall Nusselt of the flows at the flows at the down-scan stage is greater than that at the up-scan stage.

• 대한수학회지
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• 제44권3호
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• pp.511-523
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• 2007

We consider a two parametric family of the planar systems with the form $\dot{x}=P(x,\;y)+{\in}_1p_1(x,\;y)+{\in}_2p_2(x,\;y)$, $\dot{y}=Q(x,\;y)+{\in}_1p_1(x,\;y)+{\in}_2p_2(x,\;y)$, where the unperturbed equation(${\in}_1={\in}_2=0$) is assumed to have at least one periodic solution or limit cycle. Our aim here is to study the behavior of the system under two parametric perturbations; in fact, using the Poincare-Andronov technique, we impose conditions on the system which guarantee persistence of the periodic trajectories. At the end, we apply the result on the Van der Pol equation ; where, we consider the effect of nonlinear damping on the equation. Also the Hopf bifurcation for the Van der Pol equation will be investigated.

• 대한기계학회논문집B
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• 제25권4호
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• pp.546-553
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• 2001

A Parametric study is numerically carried out for flow fields in a two-dimensional plane channel with thin obstacles(“baffles and blocks”) mounted symmetrically in the vertical direction and periodically in the streamwise direction. The aim of this investigation is to understand how various geometric conditions influence the critical characteristics and pressure drop. A range of BR(the ratio of baffle interval to channel height) between 1 and 5 is considered. Especially when BR is equal to 3, for which the critical Reynolds number turned out to be minimal, we add blocks in the center region in order to study their destabilizing effects on the flows. It is revealed that the critical Reynolds number is further decreased by the presence of the block.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2000년도 춘계학술대회논문집B
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• pp.783-788
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• 2000

Flow fields in two-dimensional plane channels with thin obstacles("baffles and blocks") mounted symmetrically in the vertical direction and periodically in the streamwise direction are studied numerically to understand how various geometric conditions influence the critical Reynolds number and pressure drop. Changing BR(the ratio of channel to baffle interval) from 1:1 to 1.5, we computed the critical Reynolds number and pressure drop. Especially when BR is 1:3, at which the critical Reynolds number turned out to be minimal, we added blocks in the geometry in order to study their destabiliting effects on the flows.