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

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.19 no.2
• /
• pp.495-508
• /
• 1995

The self-excited vibrations of airfoil is related to the classical flutter problems, and it has been studied as a system with linear stiffness and small damping. However, since the actual aircraft wing and the many mechanical elements of airfoil type have various design variables and parameters, some of these could have strong nonlinearities, and the nonlinearities could be unexpectedly strong as the parameters vary. This abrupt chaotic behavior undergoes ordered routes, and the behaviors after these routes are uncontrollable and unexpectable since it is extremely sensitive to initial conditions. In order to study the chaotic behavior of the system, three parameters are considered, i.e., free-stream velocity, elastic distance and zero-lift angle. If the chaotic parameter region can be identified from the mathematically modeled nonlinear differential equation system, the designs which avoid chaotic regions could be suggested. In this study, by using recently developed dynamically system methods, and chaotic regions on the parameter plane will be found and the safe design variables will be suggested.

• Journal of computational fluids engineering
• /
• v.11 no.2 s.33
• /
• pp.49-55
• /
• 2006

This study investigates the oscillatory thermal convection of a fluid with Pr=0.02 in a wide-gap horizontal annulus with constant heat flux inner wall. When Pr=0.02, dual steady-state flows are not found. After the first Hopf bifurcation from a steady to a time-periodic flow, five successive period-doubling bifurcations are recorded before chaos. The power spectrum shows the $period-2^4\;and\;2^5$ flows clearly, and a window of period $3{\times}2^3$ flow is found in the chaotic regime. The approximate value of the Feigenbaum number for the last three period-doubling bifurcations is 4.76. The transition route to chaos of the present simulations is consistent with the period-doubling route of Feigenbaum.

• Journal of KSNVE
• /
• v.10 no.5
• /
• pp.849-858
• /
• 2000

In this paper the chaotic out-of-plane vibrations of the uniformly curved pipe with pulsating flow are theoretically investigated. The derived equations of motion contain the effects of nonlinear curvature and torsional coupling. The corresponding nonlinear ordinary differential equation is a type of nonhomogenous Hill's equation . this is transformed into the averaged equation by averaging theorem. Bifurcation curves of chaotic motion are obtained by Melnikov's method and plotted in several cases of frequency ratios. The theoretically obtained results are demonstrated by numerical simulation. And strange attractors are shown.

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

• Journal of computational fluids engineering
• /
• v.9 no.4
• /
• pp.55-63
• /
• 2004

The three-dimensional Stokes flow within a staggered screw channel is obtained by using a finite volume method. The geometry is intended to mimic the single screw extruder having staggered arrangement of flights. The flow solution is then subjected to the analysis of the stirring performance. In the analysis of the stirring performance, the stretching-mapping method developed by the author is employed for calculating the materials' stretching exponents, which are to be used in quantification of the mixing effect. The numerical results Indicate that the staggered geometry gives indeed far much better stirring-performance than the standard (nonstaggered) flight geometry. It was also shown that care must be given to the selection of the basis planes for evaluating the local stretching rate, and it turns out that the best method (H-method) has its basis plane just on the half way between the past and future evolution of fluid particles subjected to the defromation. In evaluating the stretching exponent, the expansion ratio must be considered which is one of the characteristic differences of the actual three-dimensional flows from the two-dimensionmal counterparts. The larger axial pressure-difference causes in general the smaller stirring performance while the flow rate is increased. The smaller channel length also increases the stirring performance.

• Journal of computational fluids engineering
• /
• v.11 no.4 s.35
• /
• pp.101-106
• /
• 2006

In the microfluidic devices the most important thing is mixing efficiency ol various fluids. In this study a newly designed miler is proposed to enhance the mixing effect with the purpose to apply it to microchannel mixing in a short future. This design is composed of a channel with cross baffles periodically arranged on the both bottom and top surfaces ol the channel. To obtain the yow patterns, the numerical computation was performed by using a commercial code, ANSYS CFX 10.0. To evaluate the mixing performance, we computed Lyapunov exponent and obtained Poincare sections. it was shown that our design provides the excellent mixing effect.

• 한국전산유체공학회:학술대회논문집
• /
• 2006.10a
• /
• pp.159-162
• /
• 2006

In the microfluidics devices the most important thing is mixing efficiency of various fluids. In this study a newly designed mixer is proposed to enhance the mixing effect with the purpose to apply it to microchannel mixing in a short future. This design is composed of a channel with cross baffles periodically arranged on the both bottom and top surfaces of the channel. To obtain the flow patterns, the numerical computation was performed by using a commercial code, ANSYS CFX 10.0. To evaluate the mixing performance, we computed Lyapunov exponent and obtained Poincare sections.

• 한국가시화정보학회:학술대회논문집
• /
• 2007.11a
• /
• pp.138-142
• /
• 2007

본 연구는 고점도 유체의 혼합을 위한 교반기 설계의 기초연구로서 스크류 형상의 임펠러(또는 헬리컬 임펠러)를 가지는 교반기 내의 유동과 이에 따른 유체혼합 특성을 수치해석을 통해 가시화한 것이다. 이와 더불어 양호한 혼합효과를 가져다 줄 것으로 예상되는 엇갈림형 스크류 임펠러의 모델을 제안하였다. 수치해석상의 유체는 고점도의 Newton유체로 가정하였으며 임펠러의 회전속도는 6[rpm]으로 아주 작게 하여 저 레이놀즈수(약 Re=3)에서 혼합효과를 연구하였다. 또한 각종 설계 파라미터를 변화시켜 혼합 양상의 차이를 분석하여 설계에 반영하고자 하였다.

• Proceedings of the KIEE Conference
• /
• 2008.07a
• /
• pp.1773-1774
• /
• 2008

유동적 비선형 특성을 보이는 혼돈 시계열에 대한 정확한 예측을 위해 예측 입력으로 차분 데이터를 사용하면 보다 나은 예측이 가능하다. 그러므로 본 논문에서는 상관 해석에 기반한 데이터의 전처리를 통해 적절한 최적 차분 간격 후보군을 선정하고 이들 각각에 대한 TS 퍼지 예측기로 다중 모델을 구성하여 성능 지수 평가에 의해 최적의 퍼지 예측기를 선택하여 예측을 수행하도록 하였으며, TS 퍼지 규칙 후건부에서 결정되는 예측 출력에 상관 해석에 기반한 오차 보정 메거니즘을 추가함으로써 예측 성능을 더욱 향상시킬 수 있도록 하였다.