Modelling and shape optimization of an actuator

Bruneau, Charles‐Henri; Chantalat, Frédéric; Iollo, Angelo; Jordi, Bastien; Mortazavi, Iraj

doi:10.1007/s00158-013-0949-y

Cited by 4 publications

(2 citation statements)

References 20 publications

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“…Kevlahan & Ghidaglia [2001], among many other examples, have demonstrated the effectiveness and adaptability of this approach. Brinkman-penalisation has also been employed by Chanta-3 of 28 lat et al [2009], coupled with a level-set technique to express the geometry, and applied by Bruneau et al [2013] to optimise the shape of stirrers. An additional appeal of this method lies in its simple derivation and straightforward numerical implementation.…”

Section: Introductionmentioning

confidence: 99%

Shape optimization of stirring rods for mixing binary fluids

Eggl

Schmid

2020

IMA Journal of Applied Mathematics

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Mixing is an omnipresent process in a wide range of industrial applications, which supports scientific efforts to devise techniques for optimizing mixing processes under time and energy constraints. In this endeavour, we present a computational framework based on nonlinear direct-adjoint looping for the enhancement of mixing efficiency in a binary fluid system. The governing equations consist of the nonlinear Navier–Stokes equations, complemented by an evolution equation for a passive scalar. Immersed and moving stirrers are treated by a Brinkman penalization technique, and the full system of equations is solved using a Fourier-based pseudospectral approach. The adjoint equations provide gradient and sensitivity information which is in turn used to improve an initial mixing strategy, based on shape, rotational and path modifications. We utilize a Fourier-based approach for parameterizing and optimizing the embedded stirrers and consider a variety of geometries to achieve enhanced mixing efficiency. We consider a restricted optimization space by limiting the time for mixing and the rotational velocities of all stirrers. In all cases, non-intuitive shapes are found which produce significantly enhanced mixing efficiency.

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Section: Introductionmentioning

confidence: 99%

Shape optimization of stirring rods for mixing binary fluids

Eggl

Schmid

2020

IMA Journal of Applied Mathematics

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“…Supporting studies, including an asymptotic analysis, are summarized in [12], and applications to high Mach-number flows [13] and turbulent flow past cylinders [14], among many other examples, have demonstrated the effectiveness and flexibility of the approach. A penalization approach has also been taken by [15], coupled with a level-set technique to express the geometry, and applied by [16] to optimize the shape of actuators. The appeal of the penalization method lies in its simple derivation and straightforward numerical implementation.…”

Section: Introductionmentioning

confidence: 99%

A gradient-based framework for maximizing mixing in binary fluids

Eggl

Schmid

2018

Journal of Computational Physics

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A computational framework based on nonlinear direct-adjoint looping is presented for optimizing mixing strategies for binary fluid systems. The governing equations are the nonlinear Navier-Stokes equations, augmented by an evolution equation for a passive scalar, which are solved by a spectral Fourier-based method. The stirrers are embedded in the computational domain by a Brinkmanpenalization technique, and shape and path gradients for the stirrers are computed from the adjoint solution. Four cases of increasing complexity are considered, which demonstrate the efficiency and effectiveness of the computational approach and algorithm. Significant improvements in mixing efficiency, within the externally imposed bounds, are achieved in all cases.

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Geometrical shape optimization in fluid mechanics using FreeFem++

Dapogny

Frey

Omnès

et al. 2018

Struct Multidisc Optim

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In this article, we present simple and robust numerical methods for two-dimensional geometrical shape optimization problems, in the context of viscous flows driven by the stationary Navier-Stokes equations at low Reynolds number. The salient features of our algorithm are exposed with an educational purpose; in particular, the numerical resolution of the nonlinear stationary Navier-Stokes system, the Hadamard boundary variation method for calculating the sensitivity of the minimized function of the domain, and the mesh update strategy are carefully described. Several pedagogical examples are discussed. The corresponding programs are written in the FreeFem++ environment; they are freely available and can easily be elaborated upon to deal with different, or more complex physical situations. 5.5. Energy dissipation around an obstacle 28 6. Conclusion and perspectives 29 Appendix A. Sketch of the proof of Theorem 2.2 31 References 36

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Modelling and shape optimization of an actuator

Cited by 4 publications

References 20 publications

Shape optimization of stirring rods for mixing binary fluids

Shape optimization of stirring rods for mixing binary fluids

A gradient-based framework for maximizing mixing in binary fluids

Geometrical shape optimization in fluid mechanics using FreeFem++

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