Global stability map of the flow in a horizontal concentric cylinder forced by natural convection.

Abstract

There are a large number of studies in the literature on natural convection in the annulus between horizontal concentric cylinders. However, not many publications dealing with global stability analysis in this kind of flow have been published. For a fixed diameter ratio L/Di = (Ro − Ri)/2Ri, being Ri and Ro the inner and outer cylinder radii respectively, and assuming Boussinesq approximation, the solution only depends on Prandtl (P r ≡ ν/α) and Rayleigh (Ra ≡ g β L3 (Ti − To)/(ν α)) numbers. A spectral collocation code has been developed to solve the problem by means of Chebyshev and Fourier differentiation matrices for L/Di = 0.8 and it has been validated with classical experimental results. Steady solutions have been sought within the range P r ∈ [1e−2, 1] and Ra ∈ [1e-2, 5e6]. As a result, a steady solution Pr-Ra map (consisting of 149 x 75 points) has been traced, where the different families of similar solutions found are detailed, mainly characterized by presenting single or multiple plumes. In addition, two main double-solution regions have been found.