Influence of a white noise at channel inlet on the parallel and wavy convective instabilities of Poiseuille-Rayleigh-Bénard flows

Abstract

Nicolas, Zoueidi, and Xin Phys. Fluids 24, 084101 (2012) used to make thin coatings on heated substrates from gaseous components.

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

“…A few examples, established experimentally, theoretically and numerically, for different Prandtl numbers and aspect ratios, can be found in [6][7][8][9] in the case of pure fluids. In the case of air PRB flows (Pr=0.7), a complete stability diagram at B≥10 is presented in [10]. It is partially reproduced in Fig.…”

“…1). This instability is observed for sufficiently high Reynolds numbers (typically for Re>O (10) in air) and for Rayleigh numbers above a critical value varying between 1708 and 2000 when B>2 [9]. Carrière and Monkewitz (1999) [16] showed that this pattern is a convective instability of the basic conductive Poiseuille flow.…”

“…In the current paper, we focus on the wavy instability. The time linear stability analysis of longitudinal rolls against wavy rolls has been extended by Kato and Fujimura (2001) [20], Xin et al (2006) [19] and [10] to channels of finite transverse aspect ratio. Previous experimental [21] and numerical [10,22] studies showed that the wavy pattern can develop in the channel only if a perturbation is imposed and maintained into the longitudinal roll flow, meaning that the wavy rolls result from a convective instability of the longitudinal rolls.…”

“…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]. Ra // * is the transition curve between the basic Poiseuille flow and the longitudinal rolls.…”

“…A numerical study by Nicolas et al (2008) [2] has already shown that the presence of wavy rolls generated by harmonic mechanical excitations could homogenize the growth rate and the thickness of the deposited thin solid layers in APCVD (Atmospheric Pressure CVD) reactors. [10] conducted a numerical study to characterize the saturated wavy roll flows by maintaining a random excitation, a white noise on the transverse velocity components, at the channel inlet. It has been shown that, depending on the Reynolds and Rayleigh numbers and on the excitation amplitude, the spanwise displacement magnitude of the wavy rolls can be large on a large extent of the domain suggesting that this configuration could potentially be interesting to homogenize the heat and mass transfers in CVD reactors.…”