2007
DOI: 10.1063/1.2424490
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Suppression of Rayleigh-Bénard convection with proportional-derivative controller

Abstract: 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 ons… Show more

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Cited by 13 publications
(10 citation statements)
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“…In this work, we show that RL methods can be successfully applied for controlling a Rayleigh-Bénard system at fixed Rayleigh number reducing (or suppressing) convective effects. Considering a 2D proof-of-concept setup, we demonstrate that RL can significantly outperform state-of-the-art linear methods [13] when allowed to apply (small) temperature fluctuations at the bottom plate (see setup in Figure 1). In particular, we target a minimization of the time-averaged Nusselt number (Equation 5), aiming at reducing its instantaneous counterpart:…”
Section: Ra = Gα(t Hmentioning
confidence: 93%
“…In this work, we show that RL methods can be successfully applied for controlling a Rayleigh-Bénard system at fixed Rayleigh number reducing (or suppressing) convective effects. Considering a 2D proof-of-concept setup, we demonstrate that RL can significantly outperform state-of-the-art linear methods [13] when allowed to apply (small) temperature fluctuations at the bottom plate (see setup in Figure 1). In particular, we target a minimization of the time-averaged Nusselt number (Equation 5), aiming at reducing its instantaneous counterpart:…”
Section: Ra = Gα(t Hmentioning
confidence: 93%
“…Однако, как только дело касается физического эксперимента, возникает большая проблема. Например, в работе [22] эксперимен-тально изучалось управление конвекцией Рэлея-Бенара в вертикальном цилиндре, заполненном маслом с очень большим значением числа Пранд-тля (для увеличения инертности системы и увели-чения времени принятия решения контроллером). Контроль осуществлялся с помощью системы не-скольких десятков точечных нагревателей, распре-деленных по дну цилиндра, которые могли вклю-чаться и выключаться в зависимости от сигнала, формируемого системой термопар в центре ци-линдра.…”
Section: рис 3 карта режимов конвекции на плоско-сти числа рэлея (Runclassified
“…Or and Kelly [25] showed that the weakly nonlinear flow properties in the Rayleigh-Bénard-Marangoni problem can be altered by linear and nonlinear proportional feedback control processes and the stabilization of the basic state can be achieved. Remillieux et al [26] delineated the mechanism that lead to oscillatory Rayleigh-Bénard convection in the presence of large controller gains and the application of derivative controller to suppress oscillatory convection. Recently, Hashim and Siri [27] and Siri and Hashim [28,29] applied Bau's [21] feedback control strategy to Marangoni instability in a rotating fluid layer.…”
Section: Introductionmentioning
confidence: 99%