scholarly journals Modal and non-modal linear stability of Poiseuille flow through a channel with a porous substrate

2019 ◽  
Vol 75 ◽  
pp. 29-43 ◽  
Author(s):  
Souvik Ghosh ◽  
Jean-Christophe Loiseau ◽  
Wim-Paul Breugem ◽  
Luca Brandt
Keyword(s):  
Linear Stability ◽  
Poiseuille Flow ◽  
Porous Substrate ◽  
Flow Through

scholarly journals Onset of Thermal Instabilities in the Plane Poiseuille Flow of Weakly Elastic Fluids: Viscous Dissipation Effects

Fluids ◽  
2021 ◽  
Vol 6 (12) ◽  
pp. 432
Author(s):  
Silvia C. Hirata ◽  
Mohamed Najib Ouarzazi
Keyword(s):  
Linear Stability ◽  
Viscous Dissipation ◽  
Viscoelastic Fluid ◽  
Poiseuille Flow ◽  
Hydrodynamic Instability ◽  
Plane Poiseuille Flow ◽  
Volumetric Heating ◽  
Fluid Elasticity ◽  
Different Temperatures ◽  
Elastic Fluids

The onset of thermal instabilities in the plane Poiseuille flow of weakly elastic fluids is examined through a linear stability analysis by taking into account the effects of viscous dissipation. The destabilizing thermal gradients may come from the different temperatures imposed on the external boundaries and/or from the volumetric heating induced by viscous dissipation. The rheological properties of the viscoelastic fluid are modeled using the Oldroyd-B constitutive equation. As in the Newtonian fluid case, the most unstable structures are found to be stationary longitudinal rolls (modes with axes aligned along the streamwise direction). For such structures, it is shown that the viscoelastic contribution to viscous dissipation may be reduced to one unique parameter: γ=λ1(1−Γ), where λ1 and Γ represent the relaxation time and the viscosity ratio of the viscoelastic fluid, respectively. It is found that the influence of the elasticity parameter γ on the linear stability characteristics is non-monotonic. The fluid elasticity stabilizes (destabilizes) the basic Poiseuille flow if γ<γ* (γ>γ*) where γ* is a particular value of γ that we have determined. It is also shown that when the temperature gradient imposed on the external boundaries is zero, the critical Reynolds number for the onset of such viscous dissipation/viscoelastic-induced instability may be well below the one needed to trigger the pure hydrodynamic instability in weakly elastic solutions.

scholarly journals The temporal evolution of neutral modes in the impulsively started flow through a circular pipe and their connection to the nonlinear stability of Hagen–Poiseuille flow

2002 ◽  
Vol 457 ◽  
pp. 339-376 ◽  
Author(s):  
ANDREW G. WALTON
Keyword(s):  
Poiseuille Flow ◽  
Multiple Scales ◽  
Stability Boundary ◽  
Circular Cross Section ◽  
Flow Characteristics ◽  
Internal Flow ◽  
Bypass Transition ◽  
Flow Through ◽  
High Reynolds ◽  
Wave Limit

The linear stability of the impulsively started flow through a pipe of circular cross-section is studied at high Reynolds number R. A crucial non-dimensional time of O(R7/9) is identified at which the disturbance acquires internal flow characteristics. It is shown that even if the disturbance amplitude at this time is as small as O(R−22/27) the subsequent evolution of the perturbation is nonlinear, although it can still be followed analytically using a multiple-scales approach. The amplitude and wave speed of the nonlinear disturbance are calculated as functions of time and we show that as t → ∞, the disturbance evolves into the long-wave limit of the neutral mode structure found by Smith & Bodonyi in the fully developed Hagen–Poiseuille flow, into which our basic flow ultimately evolves. It is proposed that the critical amplitude found here forms a stability boundary between the decay of linear disturbances and ‘bypass’ transition, in which the fully developed state is never attained.

Linear stability of rotating Hagen-Poiseuille flow

1981 ◽  
Vol 108 ◽  
pp. 101-125 ◽  
Author(s):  
Fredrick W. Cotton ◽  
Harold Salwen
Keyword(s):  
Reynolds Number ◽  
Angular Velocity ◽  
Linear Stability ◽  
Poiseuille Flow ◽  
Neutral Stability ◽  
Unstable Region ◽  
Azimuthal Index ◽  
Expansion Technique ◽  
Simple Scaling

Linear stability of rotating Hagen-Poiseuille flow has been investigated by an orthonormal expansion technique, confirming results by Pedley and Mackrodt and extending those results to higher values of the wavenumber |α|, the Reynolds number R, and the azimuthal index n. For |α| [gsim ] 2, the unstable region is pushed to considerably higher values of R and the angular velocity, Ω. In this region, the neutral stability curves obey a simple scaling, consistent with the unstable modes being centre modes. For n = 1, individual neutral stability curves have been calculated for several of the low-lying eigenmodes, revealing a complicated coupling between modes which manifests itself in kinks, cusps and loops in the neutral stability curves; points of degeneracy in the R, Ω plane; and branching behaviour on curves which circle a point of degeneracy.

Sign in / Sign up

Export Citation Format

Share Document