Flow Instability through a Curved Duct with Square Cross Section

Abstract

Flow instability through a curved duct with square cross section is numerically studied by using the spectral method over a wide range of the Dean number 0≤Dn≤5000 for the curvature δ= 0.1. A temperature difference is applied between the vertical sidewalls for the Grashof number Gr=100, where the outer wall is heated and the inner wall is cooled. After a comprehensive survey over the parametric ranges, two branches of asymmetric steady solutions are obtained by the Newton-Raphson iteration method. Linear stability of the steady solutions is then investigated. It is found that only the first branch is linearly stable in a couple of interval of Dn while the other branch is linearly unstable. Steady values of the Nusselt numbers, Nu, are also calculated for two differentially heated vertical sidewalls. When there is no stable steady solution, time evolution of Nu is obtained and it is found in the unstable region the flow undergoes through various flow instabilities, if Dn is increased.

Key words: Curved square duct; Steady solutions; Time evolution; Dean number; Nusselt number

GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 29 (2009) 71-85 

DOI: http://dx.doi.org/10.3329/ganit.v29i0.8517