Nonlinear global modes in inhomogeneous mixed convection flows in porous media

Abstract

The aim of this work is to investigate the fully nonlinear dynamics of mixed convection in porous media heated non-uniformly from below and through which an axial flow is maintained. Depending on the choice of the imposed inhomogeneous temperature profile, two cases prove to be of interest: the base flow displays an absolute instability region either detached from the inlet or attached to it. Results from a combined direct numerical simulations and linear stability approach have revealed that in the first case, the nonlinear solution is a steep nonlinear global mode, with a sharp stationary front located at a marginally absolutely unstable station. In the second configuration, the scaling laws for the establishment of a nonlinear global mode quenched by the inlet are found to agree perfectly with the theory. It is also found that in both configurations, the global frequency of synchronized oscillations corresponds to the local absolute frequency determined by linear criterion, even far from the threshold of global instability

Three-dimensional absolute and convective instabilities at the onset of convection in a porous medium with inclined temperature gradient and vertical throughflow

“…Since the publication of the seminal work of Weber (1974) a large number of papers were published that dealt with the natural and forced convection in a horizontal porous layer with inclined temperature gradient. In many studies of convection in a porous medium, the medium is modelled as an extended horizontal saturated porous layer in which the flow motion is induced by either the horizontal or the vertical or inclined temperature and/or salinity gradients, including the Soret effect (see for example Nield 1991Nield , 1994Nield, Manole & Lage 1993;Straughan & Walker 1996;Bahloul, Boutana & Vasseur 2003;Straughan 2004a;Delache, Ouarzazi & Combarnous 2007;Narayana, Murthy & Gorla 2008;Ouarzazi et al 2008 and the references therein). The extended-layer model is employed to facilitate the analysis and, in particular, to make possible the application of analytic treatments such as the treatment of a single monochromatic wave and the stability treatment by using a Fourier transform in space.…”

Onset of Thermal Instabilities in the Plane Poiseuille Flow of Weakly Elastic Fluids: Viscous Dissipation Effects

“…In this case, two types of instabilities can set in (i) buoyancy-driven (thermal) instabilities, which give rise to structures in the form of thermoconvective rolls, and (ii) shear-flow (hydrodynamic) instabilities, which can lead to Tollmien-Schlichting waves at high flow rates. Thermal instabilities were studied in shear flows of Newtonian fluids [5,6], binary fluid mixtures [7,8], as well as fluid-saturated porous media [9,10]. Transient growth mechanisms have also been investigated [11].…”

Weakly nonlinear analysis of viscous dissipation thermal instability in plane Poiseuille and plane Couette flows

“…On the other hand, a vast literature exists on Rayleigh-Bénard-Poiseuille/Couette systems and the interested reader is referred to Nicolas (2002) for a comprehensive review. These systems have recently attracted an increased interest as simple configurations representing open systems to study the transition from convective to absolute instability in Newtonian fluids (Carrière & Monkewitz 1999;Martinand, Carrière & Monkewitz 2006;Ouarzazi et al 2008), in binary fluid mixtures (Hu, Ben Hadid & Henry 2007) and in viscoelastic fluids (Hirata et al 2015;de B. Alves, Hirata & Ouarzazi 2016). Transient growth mechanisms have also been investigated in a Rayleigh-Bénard-Poiseuille system by Biau & Bottaro (2004) in the case of a stable stratification.…”