Spatio-temporal stability analysis of linear arrays of 2D density stratified wakes and jets

2018 ◽  
Vol 30 (11) ◽  
pp. 114103 ◽  
Author(s):  
Jacob Sebastian ◽  
Benjamin Emerson ◽  
J. O’Connor ◽  
Tim Lieuwen
Keyword(s):  
Stability Analysis ◽  
Temporal Stability ◽  
Linear Arrays ◽  
Spatio Temporal

scholarly journals An analytical connection between temporal and spatio-temporal growth rates in linear stability analysis

2013 ◽  
Vol 469 (2156) ◽  
pp. 20130171 ◽  
Author(s):  
Lennon Ó Náraigh ◽  
Peter D. M. Spelt
Keyword(s):  
Stability Analysis ◽  
Landau Equation ◽  
Temporal Stability ◽  
Exact Formula ◽  
Complex Frequency ◽  
Ginzburg Landau ◽  
First Case ◽  
Wake Instability ◽  
Spatio Temporal ◽  
Parameter Values

We derive an exact formula for the complex frequency in spatio-temporal stability analysis that is valid for arbitrary complex wavenumbers. The usefulness of the formula lies in the fact that it depends only on purely temporal quantities, which are easily calculated. We apply the formula in two model dispersion relations: the linearized complex Ginzburg–Landau equation, and a model of wake instability. In the first case, a quadratic truncation of the exact formula applies; in the second, the same quadratic truncation yields an estimate of the parameter values at which the transition to absolute instability occurs; the error in the estimate decreases upon increasing the order of the truncation. We outline ways in which the formula can be used to characterize stability results obtained from purely numerical calculations, and point to a further application in global stability analyses.

scholarly journals Diffusion-flame flickering as a hydrodynamic global mode

2016 ◽  
Vol 798 ◽  
pp. 997-1014 ◽  
Author(s):  
D. Moreno-Boza ◽  
W. Coenen ◽  
A. Sevilla ◽  
J. Carpio ◽  
A. L. Sánchez ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Global Stability ◽  
Diffusion Flames ◽  
Temporal Stability ◽  
Critical Conditions ◽  
Global Mode ◽  
Laminar Jet ◽  
Global Stability Analysis ◽  
Jet Diffusion Flames ◽  
Spatio Temporal

The present study employs a linear global stability analysis to investigate buoyancy-induced flickering of axisymmetric laminar jet diffusion flames as a hydrodynamic global mode. The instability-driving interactions of the buoyancy force with the density differences induced by the chemical heat release are described in the infinitely fast reaction limit for unity Lewis numbers of the reactants. The analysis determines the critical conditions at the onset of the linear global instability as well as the Strouhal number of the associated oscillations in terms of the governing parameters of the problem. Marginal instability boundaries are delineated in the Froude number/Reynolds number plane for different fuel jet dilutions. The results of the global stability analysis are compared with direct numerical simulations of time-dependent axisymmetric jet flames and also with results of a local spatio-temporal stability analysis.

Inertialess temporal and spatio-temporal stability analysis of the two-layer film flow with density stratification

2006 ◽  
Vol 18 (10) ◽  
pp. 104101 ◽  
Author(s):  
J. Hu ◽  
S. Millet ◽  
V. Botton ◽  
H. Ben Hadid ◽  
D. Henry
Keyword(s):  
Stability Analysis ◽  
Film Flow ◽  
Temporal Stability ◽  
Density Stratification ◽  
Layer Film ◽  
Spatio Temporal

scholarly journals Instability regimes in the primary breakup region of planar coflowing sheets

2013 ◽  
Vol 736 ◽  
pp. 150-176 ◽  
Author(s):  
D. Fuster ◽  
J.-P. Matas ◽  
S. Marty ◽  
S. Popinet ◽  
J. Hoepffner ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Convective Instability ◽  
Dynamic Pressure ◽  
Plate Thickness ◽  
Temporal Stability ◽  
Gas Velocity ◽  
Asymptotic Regime ◽  
Primary Breakup ◽  
Spatio Temporal ◽  
The Waves

AbstractThis article investigates the appearance of instabilities in two planar coflowing fluid sheets with different densities and viscosities via experiments, numerical simulation and linear stability analysis. At low dynamic pressure ratios a convective instability is shown to appear for which the frequency of the waves in the primary atomization region is influenced by both liquid and gas velocities. For large dynamic pressure ratios an asymptotic regime is obtained in which frequency is solely controlled by gas velocity and the instability becomes absolute. The transition from convective to absolute is shown to be influenced by the velocity defect induced by the presence of the separator plate. We show that in this regime the splitter plate thickness can also affect the nature of the instability if it is larger than the gas vorticity thickness. Computational and experimental results are in agreement with the predictions of a spatio-temporal stability analysis.

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