Spatio-temporal stability analysis of mixed convection flows in porous media heated from below: Comparison with experiments

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.

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Instability of hydromagnetic Couette flow for hybrid nanofluid through porous media with small suction and injection effects

International Journal of Numerical Methods for Heat &amp Fluid Flow ◽

10.1108/hff-12-2020-0814 ◽

2021 ◽

Vol ahead-of-print (ahead-of-print) ◽

Author(s):

Pascalin Tiam Kapen ◽

Cédric Gervais Njingang Ketchate ◽

DIdier Fokwa ◽

Ghislain Tchuen

Keyword(s):

Magnetic Field ◽

Reynolds Number ◽

Porous Media ◽

Stability Analysis ◽

Volume Fraction ◽

Temporal Stability ◽

Darcy Number ◽

Hybrid Nanofluid ◽

Content Type ◽

The Magnetic Field

Purpose This paper aims to investigate a linear and temporal stability analysis of hybrid nanofluid flow between two parallel plates filled with a porous medium and whose lower plate is fixed and the upper plate animated by a uniform rectilinear motion. Design/methodology/approach The nanofluid is composed of water as a regular fluid, silver (Ag) and alumina (Al2O3) as nanoparticles. The mathematical model takes into account other effects such as the magnetic field and the aspiration (injection/suction). Under the assumption of a low magnetic Reynolds number, a modified Orr–Sommerfeld-type eigenvalue differential equation governing flow stability was derived and solved numerically by Chebyshev’s spectral collocation method. The effects of parameters such as volume fraction, Darcy number, injection/suction Reynolds number, Hartmann number were analyzed. Findings It was found the following: the Darcy number affects the stability of the flow, the injection/suction Reynolds number has a negligible effect, the volume fraction damped disturbances and the magnetic field plays a very important role in enlarging the area of flow stability. Originality/value The originality of this work resides in the linear and temporal stability analysis of hydromagnetic Couette flow for hybrid nanofluid through porous media with small suction and injection effects.

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

Physics of Fluids ◽

10.1063/1.5053773 ◽

2018 ◽

Vol 30 (11) ◽

pp. 114103 ◽

Cited By ~ 2

Author(s):

Jacob Sebastian ◽

Benjamin Emerson ◽

J. O’Connor ◽

Tim Lieuwen

Keyword(s):

Stability Analysis ◽

Temporal Stability ◽

Linear Arrays ◽

Spatio Temporal

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Diffusion-flame flickering as a hydrodynamic global mode

Journal of Fluid Mechanics ◽

10.1017/jfm.2016.358 ◽

2016 ◽

Vol 798 ◽

pp. 997-1014 ◽

Cited By ~ 7

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.

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

Physics of Fluids ◽

10.1063/1.2357026 ◽

2006 ◽

Vol 18 (10) ◽

pp. 104101 ◽

Cited By ~ 20

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

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Hybrid nanofluid flow towards a stagnation point on an exponentially stretching/shrinking vertical sheet with buoyancy effects

International Journal of Numerical Methods for Heat &amp Fluid Flow ◽

10.1108/hff-02-2020-0086 ◽

2020 ◽

Vol ahead-of-print (ahead-of-print) ◽

Cited By ~ 3

Author(s):

Iskandar Waini ◽

Anuar Ishak ◽

Ioan Pop

Keyword(s):

Heat Transfer ◽

Stability Analysis ◽

Mixed Convection ◽

Stagnation Point ◽

Temporal Stability ◽

Hybrid Nanoparticles ◽

Hybrid Nanofluid ◽

Nanofluid Flow ◽

Content Type ◽

Exponentially Stretching

Purpose This paper aims to examine the hybrid nanofluid flow towards a stagnation point on an exponentially stretching/shrinking vertical sheet with buoyancy effects. Design/methodology/approach Here, the authors consider copper (Cu) and alumina (Al2O3) as hybrid nanoparticles while water as the base fluid. The governing equations are reduced to the similarity equations using similarity transformations. The resulting equations are programmed in Matlab software through the bvp4c solver to obtain their solutions. Findings The authors found that the heat transfer rate is greater for Al2O3-Cu/water hybrid nanofluid if compared to Cu/water nanofluid. Besides, the non-uniqueness of the solutions is observed for certain physical parameters. The authors also notice that the bifurcation of the solutions occurs in the downward buoyant force and the shrinking regions. In addition, the first solution of the skin friction and heat transfer coefficients increase with the added hybrid nanoparticles and the mixed convection parameter. The temporal stability analysis shows that one of the solutions is stable as time evolves. Originality/value The present work is dealing with the problem of a mixed convection flow of a hybrid nanofluid towards a stagnation point on an exponentially stretching/shrinking vertical sheet, with the buoyancy effects is taken into consideration. The authors show that two solutions are obtained for a single value of parameter for both stretching and shrinking cases, as well as for both buoyancy aiding and opposing flows. A temporal stability analysis then shows that only one of the solutions is stable and physically reliable as time evolves.

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Fingering instabilities in vertical miscible displacement flows in porous media

Journal of Fluid Mechanics ◽

10.1017/s0022112095001078 ◽

1995 ◽

Vol 288 ◽

pp. 75-102 ◽

Cited By ~ 89

Author(s):

O. Manickam ◽

G. M. Homsy

Keyword(s):

Porous Media ◽

Stability Analysis ◽

Linear Stability ◽

Critical Velocity ◽

Linear Stability Analysis ◽

Miscible Displacement ◽

Stable Region ◽

Miscible Displacements ◽

Flows In Porous Media ◽

Two Fluids

The fingering instabilities in vertical miscible displacement flows in porous media driven by both viscosity and density contrasts are studied using linear stability analysis and direct numerical simulations. The conditions under which vertical flows are different from horizontal flows are derived. A linear stability analysis of a sharp interface gives an expression for the critical velocity that determines the stability of the flow. It is shown that the critical velocity does not remain constant but changes as the two fluids disperse into each other. In a diffused profile, the flow can develop a potentially stable region followed downstream by a potentially unstable region or vice versa depending on the flow velocity, viscosity and density profiles, leading to the potential for ‘reverse’ fingering. As the flow evolves into the nonlinear regime, the strength and location of the stable region changes, which adds to the complexity and richness of finger propagation. The flow is numerically simulated using a Hartley-transform-based spectral method to study the nonlinear evolution of the instabilities. The simulations are validated by comparing to experiments. Miscible displacements with linear density and exponential viscosity dependencies on concentration are simulated to study the effects of stable zones on finger propagation. The growth rates of the mixing zone are parametrically obtained for various injection velocities and viscosity ratios.

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Instability regimes in the primary breakup region of planar coflowing sheets

Journal of Fluid Mechanics ◽

10.1017/jfm.2013.536 ◽

2013 ◽

Vol 736 ◽

pp. 150-176 ◽

Cited By ~ 48

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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