A general methodology for investigating flow instabilities in complex geometries: application to natural convection in enclosures

• Published in: International journal for numerical methods in fluids 2001-09, Vol.37 (2), p.175-208
• Main Authors: Gadoin, E., Le Quéré, P., Daube, O.
• Format: Article
• Language: English
• Subjects: Arnoldi-Krylov method; Buoyancy-driven instability; Convection and heat transfer; Eigenvalues and eigenfunctions; Exact sciences and technology; flow instabilities; Fluid dynamics; Fundamental areas of phenomenology (including applications); Heat convection; Hydrodynamic stability; natural convection; Navier Stokes equations; Newton's method; numerical algorithms; Physics; Turbulent flows, convection, and heat transfer
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/fld.173

This paper presents a general methodology for studying instabilities of natural convection flows enclosed in cavities of complex geometry. Different tools have been developed, consisting of time integration of the unsteady equations, steady state solving, and computation of the most unstable eigenmodes of the Jacobian and its adjoint. The methodology is validated in the classical differentially heated cavity, where the steady solution branch is followed for vary large values of the Rayleigh number and most unstable eigenmodes are computed at selected Rayleigh values. Its effectiveness for complex geometries is illustrated on a configuration consisting of a cavity with internal heated partitions. We finally propose to reduce the Navier–Stokes equations to a differential system by expanding the unsteady solution as the sum of the steady state solution and of a linear combination of the leading eigenmodes. The principle of the method is exposed and preliminary results are presented. Copyright © 2001 John Wiley & Sons, Ltd.