• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 1998년도 제13차 학술회의논문집
• /
• pp.461-467
• /
• 1998

In spite of significant nonlinearities even in the simplest model, some types of steady-state and dynamic behavior common for nonlinear systems have never been associated with distillation columns. In recent years, multiplicity of steady states has been a subject of much research and is now widely accepted. Subsequently, stability of steady states has been explored. Another phenomenon that. although widely observed in chemical reactors, has not been associated with models of distillation columns is the existence of periodic oscillations. In this article we study the steady-state and dynamic behavior of the azeotropic distillation of the ternary homogeneous system methanol-methyl butyrate-toluene. Our simulations reveal nonlinear behavior not reported in earlier studies. Under certain conditions, the open-loop distillation system shows a sustained oscillation associated with branching to periodic solutions. The limit cycles are accompanied by traveling waves inside the column. Significant underdamped oscillations are also observed over a wide range of product rates.

• 천문학회보
• /
• 제44권2호
• /
• pp.40.3-40.3
• /
• 2019

Our recent observations of the Sun through strong spectral lines have revealed several important properties of the three-minute umbral oscillations inside sunspots -- the oscillations of intensity and Doppler velocity with periods of 2 to 3 minutes. The oscillations usually occur in the form of a time series of oscillation packets each of which lasts 10 to 20 minutes, not as continuous trains. Each oscillation packet is characterized by a singly peaked power spectrum of velocity oscillation. The oscillations propagate in the vertical direction from the photosphere to the corona. In the upper chromosphere, they develop into shocks that eventually collide with the transition region. When shocks propagate along a highly inclined direction, the merging of two successive shocks can take place. Once they enter the corona, they change to linear compressional waves. In the image plane, the three-minute oscillations propagate with high speeds in the transverse direction as well, usually propagating radially outwards from a point, and sometimes accompanying spiraling patterns of Doppler velocity. These observational properties can be theoretically explained by postulating the spatio-temporally localized source of fast MHD waves at a depth of about 2000 km below the surface, the excitation of slow MHD waves via mode conversion near the photosphere, and the resonance of the slow waves in the photospheric layer below the temperature minimum, and the nonlinear development of slow waves in the chromosphere.

• Korean Journal of Mathematics
• /
• 제23권4호
• /
• pp.521-536
• /
• 2015

We investigate the nonlinear motions of discrete loaded cable with different periodic forcing. We present the numerical evidence of the nonlinear motions of the cable by solving initial value problems and obtaining the motions after a long time. There appeared to be various types of nonlinear oscillations over a wide range of frequencies and amplitudes for the periodic forcing term.

• 한국초전도ㆍ저온공학회논문지
• /
• 제23권1호
• /
• pp.1-6
• /
• 2021

Thermoacoustic oscillations (TAOs) could be often observed in liquid helium cryogenic system especially in half-open tubes. These tubes have closed warm end (300K) and open cold end (usually 4.4K). This phenomenon significantly induces additional heat load to cryogenic system and other undesirable effects. This work focuses on using computational fluid dynamics (CFD) method to study TAOs in liquid helium. The calculated physical model, numerical scheme and algorithm, and wall boundary conditions were introduced. The simulation results of onset process of thermoacoustic oscillations were presented and analyzed. In addition, other important characteristics including phase relation and frequency were studied. Moreover, comparisons between experiments and the CFD simulations were made, which demonstrated thevalidity of CFD simulation. CFD simulation can give us a better understanding of onset mechanism of TAOs and nonlinear characteristics in liquid helium cryogenic system.

• Nuclear Engineering and Technology
• /
• 제47권7호
• /
• pp.838-848
• /
• 2015

One of the most important operations in nuclear power plants is load following, in which an imbalance of axial power distribution induces xenon oscillations. These oscillations must be maintained within acceptable limits otherwise the nuclear power plant could become unstable. Therefore, bounded xenon oscillation is considered to be a constraint for the load following operation. In this paper, the design of a sliding mode control (SMC), which is a robust nonlinear controller, is presented.SMCis ameansto control pressurized water nuclear reactor (PWR) power for the load following operation problem in a way that ensures xenon oscillations are kept bounded within acceptable limits. The proposed controller uses constant axial offset (AO) strategy to ensure xenon oscillations remain bounded. The constant AO is a robust state constraint for the load following problem. The reactor core is simulated based on the two-point nuclear reactor model with a three delayed neutron groups. The stability analysis is given by means of the Lyapunov approach, thus the control system is guaranteed to be stable within a large range. The employed method is easy to implement in practical applications and moreover, the SMC exhibits the desired dynamic properties during the entire output-tracking process independent of perturbations. Simulation results are presented to demonstrate the effectiveness of the proposed controller in terms of performance, robustness, and stability. Results show that the proposed controller for the load following operation is so effective that the xenon oscillations are kept bounded in the given region.

• Journal of applied mathematics & informatics
• /
• 제8권1호
• /
• pp.137-149
• /
• 2001

In this paper we consider some nonlinear parabolic partial differential equations with distributed deviating arguments and establish sufficient conditions for the oscillation of some boundary value problems.

• Journal of applied mathematics & informatics
• /
• 제3권2호
• /
• pp.169-182
• /
• 1996

This paper presents the numerical experiment of a dis-cretized loaded cable with periodic forcing. There appeared to be var-ious type of nonlinear oscillations over a wide range of fequencies and amplitudes for the periodic forcing term. The same forcing term can give rise to large or small oscillation by solving initial value problem and observing the solutions after a long time.

• Journal of applied mathematics & informatics
• /
• 제9권2호
• /
• pp.635-643
• /
• 2002

The asymptotic behaviour of the solutions of initial - boundary value problem for a class of nonlinear parabolic differential - functional equations is studied via the method of differential inequalities in order to obtain oscillation criterion for the solutions.

• 대한기계학회논문집B
• /
• 제30권7호
• /
• pp.671-681
• /
• 2006

This study focuses on the development of numerical procedure to analyze the nonlinear combustion instabilities in liquid rocket engine. Nonlinear behaviors of acoustic instabilities are characterized by the existence of limit cycle in linearly unstable engines and nonlinear or triggering instability in linearly stable engines. To discretize convective fluxes with high accuracy and robustness, approximated Riemann solver based on characteristics and Euler-characteristic boundary conditions are employed. The present procedure predicts well the transition processes from initial harmonic pressure disturbance to N-like steep-fronted shock wave in a resonant pipe. Longitudinal pressure oscillations within the SSME(Space Shuttle Main Engine) engine have been analyzed using the pressure-sensitive time lag model to account for unsteady combustion response. It is observed that the pressure oscillations reach a limit cycle which is independent of the characteristics of the initial disturbances and depends only on combustion parameters and operating conditions.

• 한국해양공학회:학술대회논문집
• /
• 한국해양공학회 2003년도 추계학술대회 논문집
• /
• pp.171-176
• /
• 2003

Peristaltic mass transfer of fluid in a channel with standing wall oscillations is analyzed. Averaged nonlinear Navier-Stokes equations of motion are examined for a wide range of Reynolds numbers and external pressure drops. Nonpropogating wall oscillations with relatively big amplitudes essentially increase the liquid flow. Most effective intensifying of mass transfer occurred for low Reynolds numbers.