Convective instability in sedimentation: Linear stability analysis

We study the destabilization of a round liquid jet by a fast annular gas stream. We measure the frequency of the shear instability waves for several geometries and air/water velocities. We then carry out a linear stability analysis, and show that there are three competing mechanisms for the destabilization: a convective instability, an absolute instability driven by surface tension and an absolute instability driven by confinement. We compare the predictions of this analysis with experimental results, and propose scaling laws for wave frequency in each regime. We finally introduce criteria to predict the boundaries between these three regimes.

Download Full-text

Convective instability of reaction fronts: Linear stability analysis

European Journal of Applied Mathematics ◽

10.1017/s095679259800357x ◽

1998 ◽

Vol 9 (5) ◽

pp. 507-525 ◽

Cited By ~ 2

Author(s):

V. A. VOLPERT ◽

A. I. VOLPERT

Keyword(s):

Stability Analysis ◽

Linear Stability ◽

Linear Stability Analysis ◽

Convective Instability ◽

Eigenvalue Problems ◽

Transport Coefficients ◽

Stability Boundary ◽

New Approaches ◽

Reaction Fronts ◽

The Stability

The paper is devoted to convective instability of reaction fronts. New approaches are developed to study some eigenvalue problems arising in chemical hydrodynamics. For gaseous combustion in the case of equality of transport coefficients, a linear stability analysis of an upward propagating front is carried out. A minimax representation of the stability boundary is obtained.

Download Full-text

Characterisation of a Wavy Convective Instability in Poiseuille-Rayleigh-Be´nard Flows: Linear Stability Analysis and Non Linear Numerical Simulations Under Random Excitations

2010 14th International Heat Transfer Conference, Volume 7 ◽

10.1115/ihtc14-22256 ◽

2010 ◽

Author(s):

Xavier Nicolas ◽

Shihe Xin ◽

Noussaiba Zoueidi

Keyword(s):

Stability Analysis ◽

Numerical Simulations ◽

Linear Stability ◽

Linear Stability Analysis ◽

Convective Instability ◽

Random Excitation ◽

Time Development ◽

Direct Numerical Simulations ◽

Channel Inlet ◽

Non Linear

The aim of the present paper is to characterize a secondary convective instability of Poiseuille-Rayleigh-Be´nard (PRB) mixed convection flows in air that takes the shape of wavy thermoconvective rolls, for 70≤Re≤300 and 3000<Ra<15000. At first, the linear stability analysis by Clever and Busse [JFM, 1991] in the case of PRB flows between two infinite plates is extended to the case of confined channels with a 10 transversal aspect ratio. In the second part, using 3D non linear direct numerical simulations, the space and time development of the chaotic wavy rolls obtained by maintaining a permanent random excitation at channel inlet is analyzed. As the perturbation is designed to cover all the modes, it is possible to detect the modes that are naturally amplified by the flow and those that are damped. It is shown that the wavy roll characteristics obtained in this way vary a lot with Ra increasing and stabilize for Ra>3Ra*. Comparisons with the experiments by Pabiou et al. [JFM, 2005] are proposed.

Download Full-text

Soret-driven thermosolutal convection induced by inclined thermal and solutal gradients in a shallow horizontal layer of a porous medium

Journal of Fluid Mechanics ◽

10.1017/s0022112008002619 ◽

2008 ◽

Vol 612 ◽

pp. 1-19 ◽

Cited By ~ 49

Author(s):

P. A. LAKSHMI NARAYANA ◽

P. V. S. N. MURTHY ◽

RAMA SUBBA REDDY GORLA

Keyword(s):

Porous Medium ◽

Stability Analysis ◽

Linear Stability ◽

Linear Stability Analysis ◽

Convective Instability ◽

Galerkin Approximation ◽

Hadley Circulation ◽

Horizontal Layer ◽

Thermosolutal Convection ◽

The Stability

The stability of Soret-driven thermosolutal convection in a shallow horizontal layer of a porous medium subjected to inclined thermal and solutal gradients of finite magnitude is investigated theoretically by means of a linear stability analysis. The horizontal components of these gradients induce a Hadley circulation, which becomes unstable when vertical components are sufficiently large. We employed a two-term Galerkin approximation for various modes of instability. The effect of the Soret parameter on the mechanism of instability of the thermosolutal convection is investigated. Results are presented for various values of the governing parameters of the flow. It is observed that the Soret parameter has a significant effect on convective instability and this is discussed.

Download Full-text