scholarly journals Nonlinear stability analysis of Darcy’s flow with viscous heating

2016 ◽  
Vol 472 (2189) ◽  
pp. 20160036 ◽  
Author(s):  
Michele Celli ◽  
Leonardo S. de B. Alves ◽  
Antonio Barletta
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Viscous Dissipation ◽  
Nonlinear Stability ◽  
Linear Stability Analysis ◽  
Integral Transform ◽  
Internal Heat ◽  
Neutral Stability ◽  
Nonlinear Stability Analysis ◽  
Rate Analysis

The nonlinear stability of a rectangular porous channel saturated by a fluid is here investigated. The aspect ratio of the channel is assumed to be variable. The channel walls are considered impermeable and adiabatic except for the horizontal top which is assumed to be isothermal. The viscous dissipation is acting inside the channel as internal heat generator. A basic throughflow is imposed, and the nonlinear convective stability is investigated by means of the generalized integral transform technique. The neutral stability curve is compared with the one obtained by the linear stability analysis already present in the literature. The growth rate analysis of different unstable modes is performed. The Nusselt number is investigated for several supercritical configurations in order to better understand how the system behaves when conditions far away from neutral stability are considered. The patterns of the neutrally stable convective cells are also reported. Nonlinear simulations support the results obtained by means of the linear stability analysis, confirming that viscous dissipation alone is indeed capable of inducing mixed convection. Low Gebhart or high Péclet numbers lead to a transient overheating of the originally motionless fluid before it settles in its convective steady state.

Fluid Dynamic Instabilities in Drawn Fibers

1989 ◽  
Vol 172 ◽  
Author(s):  
Charles Thompson ◽  
Arun Mulpur
Keyword(s):  
Stability Analysis ◽  
Numerical Solution ◽  
Linear Stability ◽  
Nonlinear Equations ◽  
Viscoelastic Fluid ◽  
Nonlinear Stability ◽  
Linear Stability Analysis ◽  
Fluid Dynamic ◽  
Nonlinear Stability Analysis ◽  
Zeroth Order

AbstractThe nonlinear stability analysis of viscoelastic fibers is presented. The molten fiber is modeled as a Maxwellian viscoelastic fluid and the zeroth order equations governing its behavior given. Linear stability analysis is performed to determine the influence of winder speed and impedance as well as viscosity and elasticity. The results of numerical solution of the nonlinear equations are given.

Three Dimensional Film Stability and Draw Resonance

2012 ◽  
Vol 134 (10) ◽  
Author(s):  
Zahir U. Ahmed ◽  
Roger E. Khayat
Keyword(s):  
Stability Analysis ◽  
Eigenvalue Problem ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Physical Mechanism ◽  
Three Dimensional ◽  
Neutral Stability ◽  
Film Stability ◽  
New Approach ◽  
Draw Resonance

In order to understand the effects of inertia and gravity on draw resonance and on the physical mechanism of draw resonance in three-dimensional Newtonian film casting, a linear stability analysis has been conducted. An eigenvalue problem resulting from the linear stability analysis is formulated and solved as a nonlinear two-point boundary value problem to determine the critical draw ratios. Neutral stability curves are plotted to separate the stable/unstable domain in different appropriate parameter spaces. Both inertia and gravity stabilize the process and the process is more unstable to two- than to three-dimensional disturbances. The effects of inertia and gravity on the physical mechanism of draw resonance have been investigated using the eigenfunctions from the eigenvalue problem. A new approach is introduced in order to evaluate the traveling times of kinematic waves from the perturbed thickness at the take-up, which satisfies the same stability criterion illustrating the general stability of the system.

Washing wedges: capillary instability in a gradient of confinement

2016 ◽  
Vol 790 ◽  
pp. 619-633 ◽  
Author(s):  
Ludovic Keiser ◽  
Rémy Herbaut ◽  
José Bico ◽  
Etienne Reyssat
Keyword(s):  
Surface Tension ◽  
Stability Analysis ◽  
Linear Stability ◽  
Viscous Dissipation ◽  
Linear Stability Analysis ◽  
Theoretical Description ◽  
Oil Droplets ◽  
Bulk Viscous ◽  
Open Question ◽  
Wetting Liquid

We present experimental results on the extraction of oil trapped in the confined region of a wedge. Upon addition of a more wetting liquid, we observe that oil fingers develop into this extracting liquid. The fingers eventually pinch off and form droplets that are driven away from the apex of the wedge by surface tension along the gradient of confinement. During an experiment, we observe that the size of the expelled oil droplets decreases as the unstable front recedes towards the wedge. We show how this size can be predicted from a linear stability analysis reminiscent of the classical Saffman–Taylor instability. However, the standard balance of capillary and bulk viscous dissipation does not account for the dynamics found in our experiments, leaving as an open question the detailed theoretical description of the instability.

An extended car-following model considering the low visibility in fog on a highway with slopes

2019 ◽  
Vol 30 (11) ◽  
pp. 1950090
Author(s):  
Jinhua Tan ◽  
Li Gong ◽  
Xuqian Qin
Keyword(s):  
Stability Analysis ◽  
Numerical Simulations ◽  
Traffic Flow ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Neutral Stability ◽  
Car Following ◽  
Low Visibility ◽  
Car Following Model ◽  
The Stability

To depict the effect of low-visibility foggy weather upon traffic flow on a highway with slopes, this paper proposes an extended car-following model taking into consideration the drivers’ misjudgment of the following distance and their active reduction of the velocity. By linear stability analysis, the neutral stability curves are obtained. It is shown that under all the three road conditions: uphill, flat road and downhill, drivers’ misjudgment of the following distance will change the stable regions, while having little effect on the sizes of the stable regions. Correspondingly, drivers’ active reduction of the velocity will increase the stability. The numerical simulations agree well with the analytical results. It indicates that drivers’ misjudgment contributes to a higher velocity. Meanwhile, their active reduction of the velocity helps mitigate the influences of small perturbation. Furthermore, drivers’ misjudgment of the following distance has the greatest effect on downhill and the smallest effect on uphill, so does drivers’ active reduction of the velocity.

Linear stability of a two-fluid interface for electrohydrodynamic mixing in a channel

2007 ◽  
Vol 583 ◽  
pp. 347-377 ◽  
Author(s):  
F. LI ◽  
O. OZEN ◽  
N. AUBRY ◽  
D. T. PAPAGEORGIOU ◽  
P. G. PETROPOULOS
Keyword(s):  
Stability Analysis ◽  
Electric Field ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Neutral Stability ◽  
Surface Charges ◽  
Two Fluids ◽  
Long Wave ◽  
Normal Electric Field ◽  
Two Fluid

We study the electrohydrodynamic stability of the interface between two superposed viscous fluids in a channel subjected to a normal electric field. The two fluids can have different densities, viscosities, permittivities and conductivities. The interface allows surface charges, and there exists an electrical tangential shear stress at the interface owing to the finite conductivities of the two fluids. The long-wave linear stability analysis is performed within the generic Orr–Sommerfeld framework for both perfect and leaky dielectrics. In the framework of the long-wave linear stability analysis, the wave speed is expressed in terms of the ratio of viscosities, densities, permittivities and conductivities of the two fluids. For perfect dielectrics, the electric field always has a destabilizing effect, whereas for leaky dielectrics, the electric field can have either a destabilizing or a stabilizing effect depending on the ratios of permittivities and conductivities of the two fluids. In addition, the linear stability analysis for all wavenumbers is carried out numerically using the Chebyshev spectral method, and the various types of neutral stability curves (NSC) obtained are discussed.

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