A Fundamental Limit on the Heat Flux in the Control of Incompressible Channel Flow

Bewley, Thomas; Ziane, Mohammed

doi:10.1109/tac.2007.906184

Cited by 4 publications

(2 citation statements)

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“…Fundamental performance limitations are notoriously difficult to establish in nonlinear partial differential equation (PDE) systems, as they bound a relevant performance metric of the system over an entire class of possible control inputs. The only other fundamental performance limitation currently proven for the Navier-Stokes equation with boundary controls is related to the minimum heat flux in a channel flow and is given in Bewley & Ziane (2007). Note that, in a related work, Fukagata, Kasagi & Sugiyama (2005) presented (but did not derive) an energy balance relation for pipe flow with interior control forcing and homogeneous boundary conditions; that relation is consistent with the present proof.…”

Section: Discussionsupporting

confidence: 83%

A fundamental limit on the balance of power in a transpiration-controlled channel flow

Bewley

2009

J. Fluid Mech.

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This paper is a direct sequel to Bewley & Aamo (J. Fluid Mech., vol. 499, 2004, pp. 183–196). It was conjectured in that paper, based on the numerical evidence available at that time, that the minimum drag of a constant mass flux channel flow might in fact be that of the laminar flow. This conjecture turned out to be false; Min et al. (J. Fluid Mech., vol. 558, 2006, 309318) discovered a curious control strategy which in fact reduces the time-averaged drag to sub-laminar levels. The present paper establishes rigorously that the power of the control input applied at the walls is always larger than the power saved (due to drag reduction below the laminar level) for any possible control distribution, including that proposed by Min et al. (2006), thus establishing that, energetically (that is accounting for the power saved due to drag reduction and the power exerted by application of the control), the optimal control solution is necessarily to relaminarize the flow.

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Section: Discussionsupporting

confidence: 83%

A fundamental limit on the balance of power in a transpiration-controlled channel flow

Bewley

2009

J. Fluid Mech.

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“…Moreover, thermal fluid dynamics is governed by not only the NavierStokes equations but also the energy equation. Also, the control methodologies for thermal fluid dynamics have been proposed in [7]- [8]. However, mass transport phenomena in thermal fluid systems are governed by the mass transport equation in addition to the continuity, momentum, and energy equations.…”

Section: Introductionmentioning

confidence: 99%

Receding horizon control for mass transport phenomena in thermal fluid systems

Satoh

Hashimoto

Ohtsuka

2014

2014 4th Australian Control Conference (AUCC)

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This paper examines the control problem of mass transport phenomena in thermal fluid systems. The system model considered here is described by the momentum, continuity, energy and mass transport equations. Receding horizon control is one of the most successful control methodologies because of its applicability to a wide range of applications. The objective in this study is to propose a design method of receding horizon controller for mass transport phenomena in thermal fluid systems. The effectiveness of the proposed method is verified by numerical simulations.

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