Third M.I.T. Conference on Computational Fluid and Solid Mechanics June 14–17, 2005  

Computational stability study of 3D flow in a differentially heated 8:1:1 cavity

Andrew G. Salinger*
Computational Sciences Department, Sandia National Laboratories†, Albuquerque, NM 87185, USA

  Full Text
The critical Rayleigh number Racr of the Hopf bifurcation that signals the limit of steady flows in a differentially heated 8:1:1 cavity is computed. The two-dimensional analog of this problem was the subject of a comprehensive set of benchmark calculations that included the estimation of Racr [1]. In this work we begin to answer the question of whether the 2D results carry over into 3D models. For the case of the 2D model being extruded for a depth of 1, and noslip/no-penetration and adiabatic boundary conditions placed at these walls, the steady flow and destabilizing eigenvectors qualitatively match those from the 2D model. A mesh resolution study extending to a 20-million unknown model shows that the presence of these walls delays the first critical Rayleigh number from 3.06 × 105 to 5.13 × 105 .

Keywords:  Flow instabilities; Stability analysis; Eigenvalues; Bifurcation; Finite element; Incompressible flow; CFD; Natural convection; Thermal cavity

* Tel.: + 1 (505) 845 3523; E-mail:
† Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed-Martin Company, for the United States Department of Energy under Contract DE-AC04-94AL85000.