Controlling chaos in a thermal convection loop

Wang, Yuzhou; Singer, Jonathan P.; Bau, Haim H.

doi:10.1017/s0022112092003501

Cited by 133 publications

(63 citation statements)

References 12 publications

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“…The instabilities related to this problem have been studied among others by Straughan [27,28], Govender [29][30][31], Vanishree and Siddheshwar [32], Mohammad et al [33], Ahmad and Ress [34], Noghrehabadi et al [35], number for the transition from a motionless solution (trivial stationary point) to steady convection (nontrivial stationary point). Numerical, computational 22,23]; Vadasz and Olek [8][9][10][11]), as well as experimental results (Wang et al [42], Yuen and Bau [43]) show that the transition from steady convection to chaos occurs at subcritical values of Rayleigh number, i.e. at R ≤ R o .…”

Section: Introductionmentioning

confidence: 93%

Instability and Route to Chaos in Porous Media Convection

Vadász

2017

Fluids

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A review of the research on the instability of steady porous media convection leading to chaos, and the possibility of controlling the transition from steady convection to chaos is presented. The governing equations consisting of the continuity, the extended Darcy, and the energy equations subject to the assumption of local thermal equilibrium and the Boussinesq approximation are converted into a set of three nonlinear ordinary differential equations by assuming two-dimensional convection and expansion of the dependent variables into a truncated spectrum of modes. Analytical (weak nonlinear), computational (Adomian decomposition) as well as numerical (Runge-Kutta-Verner) solutions to the resulting set of equations are presented and compared to each other. The analytical solution for the transition point to chaos is identical to the computational and numerical solutions in the neighborhood of a convective fixed point and deviates from the accurate computational and numerical solutions as the initial conditions deviate from the neighborhood of a convective fixed point. The control of this transition is also discussed.

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Section: Introductionmentioning

confidence: 93%

Instability and Route to Chaos in Porous Media Convection

Vadász

2017

Fluids

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“…Experiments show that when the difference in temperature between the top and the bottom of the loop is large enough, the fluid exhibits unstable motion which may also be chaotic (see [6,9,10]). We consider the problem of boundary control for this two-dimensional thermal fluid flow problem as in [5].…”

Section: Controller Reduction For Pde Systemsmentioning

confidence: 99%

A Computational Environment for Design of Aerospace Systems

Burns¹

2000

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“…Using ideas borrowed from linear and nonlinear control theory, one can alter the bifurcation structure of the convective motion in a thermal convection loop heated from below and cooled from above in theory and experiment. [8][9][10][11][12] Briefly, with the aid of various controllers, it is possible to delay the transition from a no-motion to a motion state, suppress the naturally occurring chaotic advection, stabilize otherwise nonstable periodic orbits embedded in the chaotic attractor, render subcritical bifurcation supercritical, and induce chaos under conditions in which the flow normally would be laminar. The thermal convection loop can be viewed as a low-dimension analog of the RB convection.…”

Section: Introductionmentioning

confidence: 99%

Suppression of Rayleigh-Bénard convection with proportional-derivative controller

2007

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We study theoretically (linear stability) and experimentally the use of proportional and derivative controllers to postpone the transition from the no-motion state to the convective state in a circular cylinder heated from below and cooled from above. The heating is provided with an array of individually controlled actuators whose power is adjusted in proportion to temperatures measured in the cylinder's interior. As the proportional controller's gain increases, so does the critical Rayleigh number for the onset of convection. Relatively large proportional controller gains lead to oscillatory convection. The oscillatory convection can be suppressed with the application of a derivative controller, allowing further increases in the critical Rayleigh number. The experimental observations are compared with theoretical predictions. We study theoretically ͑linear stability͒ and experimentally the use of proportional and derivative controllers to postpone the transition from the no-motion state to the convective state in a circular cylinder heated from below and cooled from above. The heating is provided with an array of individually controlled actuators whose power is adjusted in proportion to temperatures measured in the cylinder's interior. As the proportional controller's gain increases, so does the critical Rayleigh number for the onset of convection. Relatively large proportional controller gains lead to oscillatory convection. The oscillatory convection can be suppressed with the application of a derivative controller, allowing further increases in the critical Rayleigh number. The experimental observations are compared with theoretical predictions.

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Controlling chaos in a thermal convection loop

Cited by 133 publications

References 12 publications

Instability and Route to Chaos in Porous Media Convection

Instability and Route to Chaos in Porous Media Convection

A Computational Environment for Design of Aerospace Systems

Suppression of Rayleigh-Bénard convection with proportional-derivative controller

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