Thermosolutal Marangoni effects on the inclined flow of a binary liquid with variable density. I. Linear stability analysis

2016 ◽  
Vol 1 (8) ◽  
Author(s):  
J. P. Pascal ◽  
S. J. D. D'Alessio
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Variable Density ◽  
Binary Liquid ◽  
Marangoni Effects ◽  
Inclined Flow

Variable density and viscosity, miscible displacements in horizontal Hele-Shaw cells. Part 1. Linear stability analysis

2013 ◽  
Vol 721 ◽  
pp. 268-294 ◽  
Author(s):  
L. Talon ◽  
N. Goyal ◽  
E. Meiburg
Keyword(s):  
Growth Rate ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Stokes Equations ◽  
Variable Density ◽  
Local Concentration ◽  
Miscible Displacements ◽  
Instability Modes ◽  
Finger Tip

AbstractA computational investigation of variable density and viscosity, miscible displacements in horizontal Hele-Shaw cells is presented. As a first step, two-dimensional base states are obtained by means of simulations of the Stokes equations, which are nonlinear due to the dependence of the viscosity on the local concentration. Here, the vertical position of the displacement front is seen to reach a quasisteady equilibrium value, reflecting a balance between viscous and gravitational forces. These base states allow for two instability modes: first, there is the familiar tip instability driven by the unfavourable viscosity contrast of the displacement, which is modulated by the presence of density variations in the gravitational field; second, a gravitational instability occurs at the unstably stratified horizontal interface along the side of the finger. Both of these instability modes are investigated by means of a linear stability analysis. The gravitational mode along the side of the finger is characterized by a wavelength of about one half to one full gap width. It becomes more unstable as the gravity parameter increases, even though the interface is shifted closer to the wall. The growth rate is largest far behind the finger tip, where the interface is both thicker, and located closer to the wall, than near the finger tip. The competing influences of interface thickness and wall proximity are clarified by means of a parametric stability analysis. The tip instability mode represents a gravity-modulated version of the neutrally buoyant mode. The analysis shows that in the presence of density stratification its growth rate increases, while the dominant wavelength decreases. This overall destabilizing effect of gravity is due to the additional terms appearing in the stability equations, which outweigh the stabilizing effects of gravity onto the base state.

scholarly journals Self-sustained oscillations in variable-density round jets

2007 ◽  
Vol 582 ◽  
pp. 341-376 ◽  
Author(s):  
JOSEPH W. NICHOLS ◽  
PETER J. SCHMID ◽  
JAMES J. RILEY
Keyword(s):  
Stability Analysis ◽  
Mach Number ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Diffusion Flames ◽  
Density Ratio ◽  
Variable Density ◽  
Transition To Turbulence ◽  
Absolute Instability ◽  
Low Mach Number

The stability properties of round variable-density low-Mach-number jets are studied by means of direct numerical simulation (DNS) and linear stability analysis. Fully three-dimensional DNS of variable-density jets, with and without gravity, demonstrate that the presence of buoyancy causes a more abrupt transition to turbulence. This effect helps to explain differences between normal gravity and microgravity jet diffusion flames observed in the laboratory.The complete spectrum of spatial eigenmodes of the linearized low-Mach-number equations is calculated using a global matrix method. Also, an analytic form for the continuous portion of this spectrum is derived, and used to verify the numerical method. The absolute instability of variable-density jets is confirmed using Brigg's method, and a comprehensive parametric study of the strength and frequency of this instability is performed. Effects of Reynolds number, the density ratio of ambient-to-jet fluid (S1), shear-layer thickness and Froude number are considered. Finally, a region of local absolute instability is shown to exist in the near field of the jet by applying linear stability analysis to mean profiles measured from DNS.

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