Application of the Asymptotic Numerical Method to the Coanda effect study

The phenomenon of jet attachment to a wall by Coanda effect is very important in many industrial applications (sound reduction, bad dispersion of the air in a venlilated room …). In order to control it, it is necessary to know its occurrence according to the various parameters of the flow. In this article the asymptotic numerical method (ANM) is used to study the Coanda effect which occurs in several flow configurations (sudden expansion with or without divergent and open cavity). The ANM is a jast, efficient and robust melhod 10 determine these stalionary bifurcations. The attachement Reynolds numbers oblained with the ANM are compared 10 the results found in the literature. Finally, evolution laws of critical Reynolds numbers according to the various geometrical parameters are proposed.

[1]  T. Mullin,et al.  Nonlinear flow phenomena in a symmetric sudden expansion , 1990, Journal of Fluid Mechanics.

[2]  Jiro Mizushima,et al.  Structural instability of the bifurcation diagram for two-dimensional flow in a channel with a sudden expansion , 2000, Journal of Fluid Mechanics.

[3]  P. Vannucci,et al.  An asymptotic-numerical method to compute bifurcating branches , 1998 .

[4]  H. Okamoto,et al.  Stability of flow in a channel with a suddenly expanded part , 1996 .

[5]  T. Sheu,et al.  Side wall effects on the structure of laminar flow over a plane-symmetric sudden expansion , 2000 .

[6]  Jean-Marc Cadou.  Méthode asymptotique numérique pour le calcul des branches solutions et des instabilités dans les fluides et pour les problèmes d'interaction fluide-structure , 1997 .

[7]  Maurel,et al.  Experimental study of self-sustained oscillations in a confined jet. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[8]  S. J. Kline,et al.  Experimental Investigation of Subsonic Turbulent Flow Over Single and Double Backward Facing Steps , 1962 .

[9]  Cyrille Allery,et al.  Contribution à l'identification des bifurcations et à l'étude des écoulements fluides par des systèmes dynamiques d'ordre faible (P. O. D. ) , 2002 .

[10]  Michel Potier-Ferry,et al.  Traitement des fortes non-linarits par la mthode asymptotique numrique , 1997 .

[11]  B. Braikat,et al.  A high order implicit algorithm for solving instationary non-linear problems , 2002 .

[12]  M. Potier-Ferry,et al.  Résolution des équations de Navier-Stokes et Détection des bifurcations stationnaires par une Méthode Asymptotique-Numérique , 1996 .

[13]  T. Hawa,et al.  A weakly nonlinear analysis of the dynamics of a viscous flow in a symmetric channel with a sudden expansion , 1999 .

[14]  G. Dhatt,et al.  Asymptotic-Newton method for solving incompressible flows , 1997 .

[15]  B. Cochelin,et al.  An Asymptotic Numerical Method for non-linear transient dynamics , 2000 .

[16]  B. Cochelin.  A path-following technique via an asymptotic-numerical method , 1994 .

[17]  J. M. T. Thompson,et al.  The non-linear perturbation analysis of discrete structural systems , 1968 .

[18]  F. Battaglia,et al.  Bifurcation of Low Reynolds Number Flows in Symmetric Channels , 1996 .

[19]  Katsuya Nakagawa,et al.  STEADY AND UNSTEADY FINITE ELEMENT ANALYSIS OF INCOMPRESSIBLE VISCOUS FLUID. , 1976 .

[20]  D. Degani,et al.  Stability and existence of multiple solutions for viscous flow in suddenly enlarged channels , 1990 .

[21]  D. Drikakis.  Bifurcation phenomena in incompressible sudden expansion flows , 1997 .

[22]  Bruno Cochelin,et al.  ANM for stationary Navier–Stokes equations and with Petrov–Galerkin formulation , 2001 .

[23]  F. Durst,et al.  Asymmetric flows and instabilities in symmetric ducts with sudden expansions , 1978, Journal of Fluid Mechanics.