Convection in a rotating, horizontal cylinder with radial and normal gravity forces

Abstract

Convection driven by radial and normal gravity forces in a rotating, horizontal cylinder is examined. The cylinder is subjected to uniform volumetric heating and constant-temperature wall cooling. The parameters are the radial-gravity and normal-gravity Rayleigh numbers, Rar and Rag (with Rar, Rag ≤ 106), the rotational Reynolds number, Re = 2Ω r02/v (0 ≤ Re ≤ 250), and the Prandtl number (Pr = 7). Critical conditions for the radial-gravity rest state correspond to a two-cell flow in the azimuthal plane with Rar,c = 13738. Finite-amplitude transient and steady flows are obtained with a Galerkin finite element method for Rayleigh number ratios in the range 0.1 ≤ Rar/Rag ≤ 100. When radial gravity dominates the flows tend to be multicellular and, during transients, initial high-wavenumber forms evolve to lower-wavenumber forms. When normal gravity dominates the flows are bicellular. When radial and normal gravity forces are comparable, in the presence of rotation, complex time-dependent motions occur and the largest rates of fluid circulation and heat transfer are observed.

Convective Motion and Heat Transfer in a Slowly Rotating Fluid Quasi-Sphere With Uniform Heat Source and Axial Gravity

“…(10), see also Eqs. (12) and (13). It is observed that for Ra=10 and Ra=l x 10'^, the influence of rotation on the maximum temperature (and therefore on the Nu number) is negligible.…”

“…The goal of these studies has been to have a better insight into the physics of different heat transfer phenomena appearing in nuclear reactors, such as (i) the cooling of the lower plenum of light water reactors pressure vessels, (ii) the thermal behavior of pressurized water reactors vessel lower head, and (iii) the post accident heat removal in liquid metal fast breeder reactors [6][7][8]. Few papers dealing with the subject of nonrotating, terrestrial axial gravity fleld, nonsteady natural convection in heat-generating fluids enclosed in spherical containers (a situation which commonly appear in processes such as fermentation and certain exothermic chemical reactions) have been published in the literature [9][10][11][12][13][14][15][16]. Heinrich and Pepper [17] and Pepper and Heinrich [18], investigated numerically (by using a finite element model to solve in a Cartesian coordinate system the nonsteady, three-dimensional, incompressible fluid flow equations), the stability of the flow, driven by a terrestrial axial gravity field, within a spherical enclosure subjected to differential heating and cooling on the surface.…”

Natural convection in a horizontal cylinder with axial rotation

“…Foluso and Torrance [16] present a detailed study of a cylinder subjected to radial and normal gravity fields with uniform volumetric heating and an isothermal outer boundary. When the effects of rotation and buoyancy are comparable, they observe complex time-dependent flows, but when rotation dominates, the flow assumes a solid body rotation and the temperature field approaches that of pure conduction.…”

Second order nonlinear spatial stability analysis of compressible mixing layers

“…A procedure that is often used to study stability, for example in Ladeinde and Torrance, 15 consists of an exact, closed-form analysis for the linear problem followed by a purely numerical calculation of the nonlinear or finite amplitude components. Although this procedure allows the computation of very strong flows, complete details of the departure from linearity, which are often of interest, cannot be obtained from such methods.…”