Multiple buoyancy driven flows in a vertical cylinder heated from below
Abstract
The structure of axisymmetric buoyancydriven convection in a vertical cylinder heated from below is probed by finite element solution of the Boussinesq equations coupled with computedimplemented perturbation techniques for detecting and tracking multiple flows and for determining flow stability. Results are reported for fluids with Prandtl number of one and for cylinders with aspect ratio (Lambda) (defined as the height to radius of the cylinder) between 0.5 and 2.25. Extensive calculations of the neutral stability curve for the static solution and of the nonlinear motions along the bifurcating flow families show a continuous evolution of the primary cellular motion from a single toroidal cell to two and three cells nested radially in the cylinder, instead of the sharp transitions found for a cylinder with shearfree sidewalls. The smooth transitions in flow structure with Rayleigh number and lambda are explained by nonlinear connectivity between the first two bifurcating flow families formed either by a secondary bifurcation point for Lambda or = Lambda * approximately 0.80 or by a limit point for Lambda Lambda *. The transition between these two modes may be described by the theory of multiple limit point bifurcation.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 February 1983
 Bibcode:
 1983STIN...8427001Y
 Keywords:

 Axisymmetric Flow;
 Buoyancy;
 Computational Fluid Dynamics;
 Cylindrical Shells;
 Forced Convection;
 Rayleigh Number;
 Aspect Ratio;
 Boussinesq Approximation;
 Finite Element Method;
 Flow Stability;
 Fluid Filled Shells;
 Microgravity Applications;
 Space Commercialization;
 Two Dimensional Flow;
 Vertical Distribution;
 Fluid Mechanics and Heat Transfer