Sidewall and thermal boundary condition effects on the evolution of longitudinal rolls in Rayleigh-Bénard-Poiseuille convection

Abstract

Experimental and numerical studies of steady longitudinal convection rolls that develop in a Poiseuille air flow in a rectangular channel heated from below and cooled from the top are conducted in the range 3500 ≤ Ra ≤ 6000 and 20 ≤ Re ≤ 200.The effect of the lateral vertical walls on the onset and development of the convection cells is investigated by changing the transverse aspect ratio of the channel from 4.7 to 18.4. The influence of the entrance temperature and of adiabatic or conductive thermal boundary conditions at the side and top walls of the channel is also investigated.The scenario of the roll formation is described in details. It results in a symmetric pattern in the form of steady longitudinal rolls with an even number of rolls that depends not only on the aspect ratio but possibly on the inlet temperature of the flow.It is shown that the fully developed pattern is determined by the two rolls nearby each vertical side wall that are triggered just at the entrance of the channel due to the presence of velocity boundary layers adjacent to the walls. It is also shown that the heat conduction in the top horizontal wall of the experimental channel must be taken into account in the numerical simulations so that the experimental wavenumber can be properly depicted.

Harmonic mechanical excitations of steady convective instabilities: A means to get more uniform heat transfers in mixed convection flows?

“…However, it appeared that this DOE had to be modified due to a too much extended study domain and the lack of fit of the computed response surfaces. At large excitation magnitude, flows with ten or twelve wavy rolls were observed (a similar behavior is analyzed in [17,19] for longitudinal roll flows) and, at low excitation frequency, the first harmonic of the excitation frequency was amplified by the flow, instead of its fundamental mode (a similar behavior is also observed experimentally in [23,24] between the longitudinal and wavy rolls determined by a linear stability analysis [8,10].…”

“…As already discussed in [2], this assumption is justified on the basis of the works by Chiu et al (2000) [27] and Wang et al (2003) [28] that show that the flow structure and the heat and mass transfers are little modified when the variations of the physical properties with temperature are not taken into account in simulations of CVD reactors with high temperature differences. Furthermore, the present simulations will be compared with FAST experiments [17,21,23,24] in which the maximum temperature difference, T h -T c , in air flows is 40°C at Ra=10 4 . Thus giving the reference quantities H, U mean , ρU mean 2 , and H/U mean , for the lengths, velocity, pressure and time respectively, and defining the reduced temperature θ=(T-T c )/(T h -T c ), the dimensionless governing equations for continuity, momentum and energy read as follows:…”

“…Furthermore, this Reynolds number range partly covers the one of the APCVD reactors envisaged as application of the present study since in these reactors O(10)≤Re≤O(10 3 ) [2]. The chosen Rayleigh number range, 4800≤Ra≤16300, covers the whole domain studied in the experiments [17,21,23,24] and a part of that covered by the APCVD applications. Indeed, Ra varies between O(10 3 ) and O(10 6 ) according to the temperature levels and the carrier gas used in the APCVD reactors [2].…”

“…Carrière and Monkewitz (1999) [16] showed that this pattern is a convective instability of the basic conductive Poiseuille flow. Mergui et al (2011) [17] and Benderradji et al (2008) [18] demonstrated that these rolls are triggered in real channels of finite transverse aspect ratio just downstream the leading edge of the heated plate and near the vertical walls due to the presence of velocity and temperature boundary layers adjacent to these walls. Ra // *=1728.83, B=10 [19] Ra osc *, B→∞ [8] Ra ≈ *, B→∞ [8] Ra ≈ *, B=10 [10] [8,10,19].…”

“…More precisely, in all this work, Pr=0.71 (air flow) and B=10 to allow experimental and numerical comparisons with the PRB experiments carried out at FAST laboratory [17,21,23,24]. Despite this simplification, the problem remains expensive to solve because one simulation of an unsteady fully-developed threedimensional (3D) PRB flow requires channels of long streamwise aspect ratios (say A = L (length) / H ≈ 200), very large grids of more than 10 7 cells or nodes and, as a consequence, high computational resources.…”