Equilibrium configuration of a rectangular obstacle immersed in a channel flow

Denis Bonheure; Giovanni P. Galdi; Filippo Gazzola

doi:10.5802/crmath.95

Partial Differential Equations, Fluid Mechanics

Equilibrium configuration of a rectangular obstacle immersed in a channel flow

Denis Bonheure ¹; Giovanni P. Galdi ² ; Filippo Gazzola ³

¹Département de Mathématique – Université Libre de Bruxelles, Belgium
²Department of Mechanical Engineering – University of Pittsburgh, USA
³Dipartimento di Matematica – Politecnico di Milano, Italy

Comptes Rendus. Mathématique, Volume 358 (2020) no. 8, pp. 887-896

Abstract

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.

Received: 2020-04-21
Revised: 2020-06-30
Accepted: 2020-08-06
Published online: 2020-12-03

DOI: 10.5802/crmath.95

Classification: 35Q30, 35A02, 46E35, 31A15

Author's affiliations:

Denis Bonheure ¹ ; Giovanni P. Galdi ² ; Filippo Gazzola ³

¹ Département de Mathématique – Université Libre de Bruxelles, Belgium
² Department of Mechanical Engineering – University of Pittsburgh, USA
³ Dipartimento di Matematica – Politecnico di Milano, Italy

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

@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},
     year = {2020},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {8},
     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

References
Cited by

[1] Juan Antonio Bello; Enrique Fernández-Cara; Jérôme Lemoine; Jacques Simon 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 | MR | DOI | Zbl

[2] Denis Bonheure; Filippo Gazzola; Gianmarco Sperone 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 | MR | DOI | Zbl

[3] Giovanni P. Galdi An Introduction to the Mathematical Theory of the Navier-Stokes Equations: Steady-State Problems, Springer, 2011 | Zbl

[4] Giovanni P. Galdi; Vincent Heuveline 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] Filippo Gazzola Mathematical models for suspension bridges. Nonlinear structural instability, MS & A Modeling, Simulation and Applications, 15, Springer, 2015 | Zbl

[6] Filippo Gazzola; Gianmarco Sperone 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] Antoine Henrot; Michel Pierre Shape Variation and Optimization: A Geometrical Analysis, EMS Tracts in Mathematics, 28, European Mathematical Society, 2018 | Zbl

[8] B. P. Ho; L. Gary Leal Inertial migration of rigid spheres in two-dimensional unidirectional flows, J. Fluid Mech., Volume 65 (1974), pp. 365-400 | Zbl

Cited by Sources:

Comments - Policy