Buoyant plane plumes from heated horizontal confined wires and cylinders

Abstract

Two-dimensional computations are reported for timedependent laminar buoyancy-induced flows above a horizontal heated source immersed in an air-filled vessel. Two kinds of heated source were considered: a line heat source, modelled as a heat source term in the energy equation, and a heat-flux cylinder of small diameter. First, comparisons are presented for the results obtained for these two heated sources. Rather large discrepencies between the velocity fields appeared in the conduction regime due to the weak plume motion, while close agreements were found in the boundary layer regime. Nevertheless, same types of bifurcations occur with almost identical frequencies, whatever the Rayleigh number. It is concluded that for dimensions of the enclosures, which largely compared with the cylinder radius, the heat source term model is a promising way to study the behaviour of unsteady plumes owing to its simplicity, flexibility, and low computational costs. Second, transitions to unsteady flows were studied through direct flow simulations for various depths of immersion of a line heat source in the central vertical plane of a vessel. Different routes to chaos were shown to occur according to the aspect ratio of the vessel and the depth of immersion of the line source. Three distinct regimes were detected with different underlying physical mechanisms called natural swaying motion, penetrative convection and Rayleigh-Benard-like convection. The first bifurcations associated with these regimes are supercritical Hopf bifurcation, pitchfork bifurcation and subcritical Hopf bifurcation. Comparisons with experimental results of confined buoyant plumes above heated wires show very good agreement with laminar frequency correlations.

SPH modeling of natural convection around a heated horizontal cylinder: A comparison with experiments

“…The vertical velocity component is very sensitive to small changes in the initial conditions and, therefore it is a convenient parameter to measure the reproducibility of the experiments. The form of the profiles is consistent with a numerical prediction by Lauriat and Desrayaud [3] for laminar buoyancyinduced flows above a horizontal thin cylinder immersed in an air-filled vessel. A non-zero velocity exists close to the cylindrical surface as expected when the pipe behaves as a heat source.…”

“…The main concerns of these studies were first directed to laminar and turbulent natural convection around heated, horizontal cylinders. At small Rayleigh numbers (Ra < 10 4 ), the heat transfer from a horizontal cylinder behaves like a line heat source [2,3,4,5]. For larger Rayleigh numbers (i.e., 10 4 ≤ Ra ≤ 10 8 ), the flow forms a laminar boundary layer around the cylinder [6,7,8,9,10,11,12], while at even higher Rayleigh numbers, the motion of the fluid due to buoyancy is turbulent [13,14,15].…”

“…A number of numerical analyses have been performed to study natural convection from horizontal cylinders enclosed in square and rectangular cavities, using spectral element [17,18], finite-difference [19], finite-element [3,5], and finite-volume [12,20,21] methods. Articles dealing with Smoothed Particle Hydrodynamics (SPH) simulations of natural convection are not abundant in the literature.…”

Laminar free convection induced by a line heat source, and heat transfer from wires at small Grashof numbers

“…Higher-order effects for the far-field behaviour of free convection plumes from line sources on a wall have been considered by Mörwald, Mitsotakis & Schneider (1986). The structure and stability of the buoyant plumes above heated wires and line sources of heat in a bounded region has also been numerically analysed by Desrayaud & Lauriat (1993), Deschamps & Desrayaud (1994) and Lauriat & Desrayaud (1994) using the Boussinesq equations. Their analysis of free convection from heated wires was mainly concerned with the description of the instabilities that lead to a meandering motion of the plume far above the source, which is independent of the details of the flow near the heat source.…”

Appearance of quasiperiodicity within a period doubling route to chaos of a swaying thermal plume

“…The issues of flow stability and bifurcations have been addressed only for long square or rectangular-sectioned cavity with two types of internal source: wires of small diameter and line heat sources [18][19][20][21], and horizontal circular or rectangular cylinders [5,10,[22][23][24][25]. In [18] Desrayaud and Lauriat thoroughly investigated the dynamical behaviour of the buoyant plume arising from a horizontal line source, modeled as a point source in a 2D rectangular cavity with adiabatic side walls and isothermal top and bottom walls.…”