Spatiotemporal Structures of Buoyancy-Induced Flow in a Vertical Channel

Abstract

The present investigation deals with the developflU!nl of low-order represeniations of transitional free convection in a vertical channel with discrete heaters. The governing equations are sowed using a spectral element method. Proper orlhogollll1 decomposuion (POD) is applied to extract the most energetic eigenfunctions (and lhe related spatWlemporaJ structures) from time-dependen: numerical solutions of the full model equations at a Groshof number higher than the critical value. Using the computed eigenfunctions in a truncated series expansion, reconstruction of Ihe original flow and temperature fields is aehieved in an optimal way. It is found that almost aUthe flow and temperature fluctuation energy is captured by the first six eigenmodes. A low-dimensional set of nonlinear ordinary differential equations tha: describes the dynamics of lhe flow and temperature fields is also derived. It is found that low-order models based on retaining at least four eigenmodes for eaeh field predict stable, self-sustained oscillations with correct amplitude and frequency.

Transient Natural Convection in Vertical Channels Symmetrically Heated at Uniform Heat Flux

“…A more complete description of natural convective heat transfer between vertical parallel plates should analyze the transient behaviors of the full elliptic equations on an extended computational domain. In the following, a short review of the literature on transient laminar natural convection in vertical channels [17][18][19][34][35][36][37][38][39][40] is given.…”

“…A transient analysis on structures of buoyancy-induced flow in a vertical channel with discrete heaters was accomplished in ref. [39]. A two-dimensional natural convection flow due to periodically spaced heat sources of uniform heat flux and flush mounted on a channel wall was considered.…”

Numerical Investigation of Transient Natural Convection in Air in a Convergent Vertical Channel Symmetrically Heated at Uniform Heat Flux

“…An open cavity with permeable walls, with all the boundaries open to the surroundings, which considered only half of the entire domain, was assumed as a computational domain. It was observed that [21]. A numerical investigation of the transient regime of natural convection in air, in a vertical channel symmetrically heated at uniform heat flux, was carried out in [22].…”

“…Investigation of a symmetrically heated vertical channel, at either uniform temperature or uniform heat flux, is reported in [18][19][20][21][22]. A numerical study with the boundary-layer approximation was carried out in [18].…”