Fluid flows around an obstacle generate vortices which, in turn, generate lift forces on the obstacle. Therefore, even in a perfectly symmetric framework equilibrium positions may be asymmetric. We show that this is not the case for a Poiseuille flow in an unbounded 2D channel, at least for small Reynolds number and flow rate. We consider both the cases of vertically moving obstacles and obstacles rotating around a fixed pin.
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Denis Bonheure 1 ; Giovanni P. Galdi 2 ; Filippo Gazzola 3
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@article{CRMATH_2020__358_8_887_0,
author = {Denis Bonheure and Giovanni P. Galdi and Filippo Gazzola},
title = {Equilibrium configuration of a rectangular obstacle immersed in a channel flow},
journal = {Comptes Rendus. Math\'ematique},
pages = {887--896},
publisher = {Acad\'emie des sciences, Paris},
volume = {358},
number = {8},
year = {2020},
doi = {10.5802/crmath.95},
language = {en},
}
TY - JOUR AU - Denis Bonheure AU - Giovanni P. Galdi AU - Filippo Gazzola TI - Equilibrium configuration of a rectangular obstacle immersed in a channel flow JO - Comptes Rendus. Mathématique PY - 2020 SP - 887 EP - 896 VL - 358 IS - 8 PB - Académie des sciences, Paris DO - 10.5802/crmath.95 LA - en ID - CRMATH_2020__358_8_887_0 ER -
%0 Journal Article %A Denis Bonheure %A Giovanni P. Galdi %A Filippo Gazzola %T Equilibrium configuration of a rectangular obstacle immersed in a channel flow %J Comptes Rendus. Mathématique %D 2020 %P 887-896 %V 358 %N 8 %I Académie des sciences, Paris %R 10.5802/crmath.95 %G en %F CRMATH_2020__358_8_887_0
Denis Bonheure; Giovanni P. Galdi; Filippo Gazzola. Equilibrium configuration of a rectangular obstacle immersed in a channel flow. Comptes Rendus. Mathématique, Volume 358 (2020) no. 8, pp. 887-896. doi : 10.5802/crmath.95. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.95/
[1] The differentiability of the drag with respect to the variations of a Lipschitz domain in a Navier-Stokes flow, SIAM J. Control Optimization, Volume 35 (1997) no. 2, pp. 626-640 | DOI | MR | Zbl
[2] Eight(y) mathematical questions on fluids and structures, Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei, Mat. Appl., Volume 30 (2019) no. 4, pp. 759-815 | DOI | MR | Zbl
[3] An Introduction to the Mathematical Theory of the Navier-Stokes Equations: Steady-State Problems, Springer, 2011 | Zbl
[4] Lift and sedimentation of particles in the flow of a viscoelastic liquid in a channel, Free and moving boundaries (Lecture Notes in Pure and Applied Mathematics), Volume 252, Chapman & Hall/CRC, 2007 | MR | Zbl
[5] Mathematical models for suspension bridges. Nonlinear structural instability, MS & A Modeling, Simulation and Applications, 15, Springer, 2015 | Zbl
[6] Steady Navier–Stokes equations in planar domains with obstacle and explicit bounds for unique solvability, Arch. Ration. Mech. Anal., Volume 238 (2020) no. 3, pp. 1283-1347 | DOI | MR | Zbl
[7] Shape Variation and Optimization: A Geometrical Analysis, EMS Tracts in Mathematics, 28, European Mathematical Society, 2018 | Zbl
[8] Inertial migration of rigid spheres in two-dimensional unidirectional flows, J. Fluid Mech., Volume 65 (1974), pp. 365-400 | Zbl
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