• Journal of KSNVE
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• v.7 no.3
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• pp.489-498
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• 1997

In this paper, chaotic motions of a curved pipe conveying oscillatory flow are theoretically investigated. The nonliear partial differential equation of motion is derived by Newton's method. The transformed nonlinear ordinary differential equation is a type of Hill's equation, which has the external and parametric excitation with a same frequency. Bifurcation curves of chaotic motion of the piping systems are obtained by applying Melnikov's method. Numerical simulations are performed to demonstrate theoretical results and show the strange attractor of the chaotic motion.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.13 no.2
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• pp.88-95
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• 2001

Transition to chaotic convection is investigated for natural convection of a fluid with Pr=0.1 in a wide-gap horizontal annuls. The unsteady two-dimensional stream-function-vorticity equation is solved with finite difference method. As the Rayleigh number is increased, the steady 'downward flow' bifurcates to a time-periodic flow with a fundamental frequency, and afterwards a period-doubling bifurcation occurs. As the Rayleigh number is increased further, the chaotic flow regime is reached after a sequence of successive Hopf bifurcation to quasi-periodic and chaotic flow regimes. The route to chaos shows the Ruelle-Takens-Newhouse scenario. The flow of chaotic regime displays complex coalescence and separation of eddies in the side and lower region of the annulus.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.25 no.3
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• pp.433-441
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• 2001

Natural convection of a fluid with intermediate Prand시 number of Pr=0.2 in a horizontal annulus is considered, and the bifurcation phenomena and chaotic flows are numerically investigated. The unsteady two-dimensional streamfunction-vorticity equation is solved with finite difference method. The steady downward flow with two counter-rotating eddies bifurcates to a simple periodic flow with a fundamental frequency. And afterwards, second Hopf bifurcation occurs, and a quasi-periodic flow with two incommensurable frequencies appears. However, a new time-periodic flow is established after experiencing quasi-periodic states. As Rayleigh number is increased further, the chaotic flow regime is reached after a sequence of successive Hopf bifurcation to quasi-periodic and chaotic flow regimes. A scenario similar to the Ruelle-Takens-Newhouse scenario of the onset of chaos is observed.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.1
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• pp.63-69
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• 2004

It is of great interest to enhance mixing performance in a microchannel in which the flow is usually characterized as a low Reynolds number (Re) so that good mixing is quite difficult to be achieved in this laminar flow regime. In this regard, we present a new chaotic passive micromixer, named Barrier Embedded Micromixer (BEM), of which the mixing mechanism is based on chaotic flows. In BEM, chaotic flow is induced by periodic perturbation of the velocity field due to periodically inserted barriers along the channel wall while a helical type of flow is obtained by slanted grooves on the bottom surface of the channel in the pressure driven flow. To experimentally compare the mixing performance, a T-microchannel and a microchannel with only slanted grooves were also fabricated. All microchannels were made of PDMS (Polydimethylsiloxane) from SU-8 masters that were fabricated by conventional photolithography. Mixing performance was experimentally characterized with respect to an average mixing intensity by means of color change of phenolphthalein as pH indicator. It was found that mixing efficiency decreases as Re increases for all three micromixers. Experimental results obviously indicate that BEM has better mixing performance than the other two. Chaotic mixing mechanism, suggested in this study, can be easily applied to integrated microfluidic systems , such as Micro-Total-Analysis-System, Lab-on-a-chip and so on.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1996.10a
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• pp.288-294
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• 1996

In this paper, Chaotic motions of a curved pipe conveying oscillatory flow are theoretically investigated. The nonlinear partial differential equation of motion is derived by Newton's method. The transformed nonlinear ordinary differential equation is a type of Hill's equation, which have the parametric and external excitation. Bifurcation curves of chaotic motion of the piping systems are obtained by applying Melnikov's method. Poincare maps numerically demonstrate theoretical results and show transverse homoclinic orbit of the chaotic motion.

• Journal of KSNVE
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• v.6 no.2
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• pp.233-244
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• 1996

In this paper chaotic mothions of a straight pipe conveying oscillatory flow and being subjected to external forces such as earthquake are theoretically investigated. The nonlinear partial differential equation of motion is derived by Newton's method. In this equation, the nonlinear curvature of the pipe and the thermal expansion effects are contained. The nonlinear ordinary differential equation transformed from that partial differential equation is a type of Hill's equations, which have the parametric and external exciation term. This original system is transfered to the averaged system by the averaging theory. Bifurcation curves of chaotic motion of the piping system are obtained in the general case of the frequency ratio, n by applying Melnikov's method. Numerical simulations are performed to demonstrate theorectical results and show strange attactors of the chaotic motion.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.22 no.12
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• pp.1774-1783
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• 1998

The transition from steady laminar to chaotic convection in a glass melting furnace specified by upper surface temperature distribution has been studied by the direct numerical analysis of the two and three-dimensional time dependent Navier-Stokes equations. The thermal instability of convection roll may take place when modified Rayleigh number($Ra_m$) is larger than $9.71{\times}10^4$. It is shown that the basic flows in a glass melting furnace are steady laminar, unsteady periodic, quasi-periodic or chaotic flow. The dimensionless time scale of unsteady period is about the viscous diffusion time, ${\tau}_d=H^2/{\nu}_0$. Through primary and secondary instability analyses the fundamental unsteady feature in a glass melting furnace is well defined as the unsteady periodic or weak chaotic flow.

• 한국전산유체공학회:학술대회논문집
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• 2007.04a
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• pp.53-57
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• 2007

The quality of chaotic mixing in square cavity flow was studied numerically by CFD simulation and particle tracking technique. The chaotic mixing was generated by using time-periodic electro-osmotic flow. Finite Volume Method (FVM) was employed to get the stretching and folding field in cavity domain. With adjusting the initial condition of concentration distribution, the best values of modulation period and Peclet number which gave us good mixing performance was determined precisely. From $Poicar{\acute{e}}section$and Lyapunov exponents for characteristic trajectories we find that mixing performance also depends on modulation period. The higher value of modulation period, the better mixing performance wag achieved in this case. Furthermore, the results for tracking particle trajectories were also compared between using of Bilinear Interpolation and Higher-order scheme. The values of modulation period for obtaining best mixing effect were matched between using FVM and particle tracking techniques.

• Proceedings of the KOSOMBE Conference
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• v.1996 no.11
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• pp.258-262
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• 1996

The physiological systems have nonlinear complex phenomena. Expecially, the flow of capillary blood vessel has a nonlinear dynamic system. Thus, this study analyzes nonlinear characteristics of the flow of capillary blood vessel in physiological systems using chaotic tools(phase space reconstruction, correlation dimension, largest lyapunov exponent). Experimental data have been acquired from examining 10 rabbits. The results of chaotic analysis showed a decreasing largest lyapunov exponent and correlation dimension according to increasement glocose index. And we also know the chaotic behavior.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.24 no.9
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• pp.1210-1218
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• 2000

Thermal convection in a horizontal annulus is considered, and the bifurcation phenomena of flows from time-periodic to chaotic convection are numerically investigated. The unsteady two-dimensional streamfunction-vorticity equation is solved with finite difference method. As Rayleigh number is increased, the steady flow bifurcates to a time-periodic flow with a fundamental frequency, and afterwards a period-tripling bifurcation occurs with further increase of the Rayleigh number. Chaotic convection is established after a period-doubling bifurcation. A periodic convection with period 4 appears after the first chaotic convection. At still higher Rayleigh numbers, chaotic flows reappear.