On the stability of Poiseuille flow of a Bingham fluid

1994 ◽  
Vol 263 ◽  
pp. 133-150 ◽  
Author(s):  
I. A. Frigaard ◽  
S. D. Howison ◽  
I. J. Sobey
Keyword(s):  
Yield Stress ◽  
Poiseuille Flow ◽  
Linear Instability ◽  
Bingham Fluid ◽  
Additional Parameter ◽  
Two Dimensional ◽  
Plane Poiseuille Flow ◽  
Bingham Number ◽  
The Stability ◽  
Drilling Muds

The stability to linearized two-dimensional disturbances of plane Poiseuille flow of a Bingham fluid is considered. Bingham fluids exhibit a yield stress in addition to a plastic viscosity and this description is typically applied to drilling muds. A non-zero yield stress results in an additional parameter, a Bingham number, and it is found that the minimum Reynolds number for linear instability increases almost linearly with increasing Bingham number.

scholarly journals The stability of thermally stratified plane Poiseuille flow

1968 ◽  
Vol 33 (1) ◽  
pp. 21-32 ◽  
Author(s):  
K. S. Gage ◽  
W. H. Reid
Keyword(s):  
Poiseuille Flow ◽  
Richardson Number ◽  
Three Dimensional ◽  
Complete Analysis ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Plane Poiseuille Flow ◽  
Spiral Flow ◽  
Tollmien Schlichting ◽  
The Stability

In studying the stability of a thermally stratified fluid in the presence of a viscous shear flow, we have a situation in which there is an important interaction between the mechanism of instability due to the stratification and the Tollmien-Schlichting mechanism due to the shear. A complete analysis has been carried out for the Bénard problem in the presence of a plane Poiseuille flow and it is shown that, although Squire's transformation can be used to reduce the three-dimensional problem to an equivalent two-dimensional one, a theorem of Squire's type does not follow unless the Richardson number exceeds a certain small negative value. This conclusion follows from the fact that, when the stratification is unstable and the Prandtl number is unity, the equivalent two-dimensional problem becomes identical mathematically to the stability problem for spiral flow between rotating cylinders and, from the known results for the spiral flow problem, Squire's transformation can then be used to obtain the complete three-dimensional stability boundary. For the case of stable stratification, however, Squire's theorem is valid and the instability is of the usual Tollmien—Schlichting type. Additional calculations have been made for this case which show that the flow is completely stabilized when the Richardson number exceeds a certain positive value.

A two-dimensional-three-component model for spanwise rotating plane Poiseuille flow

2019 ◽  
Vol 880 ◽  
pp. 478-496 ◽  
Author(s):  
Shengqi Zhang ◽  
Zhenhua Xia ◽  
Yipeng Shi ◽  
Shiyi Chen
Keyword(s):  
Reynolds Number ◽  
Poiseuille Flow ◽  
Reynolds Shear Stress ◽  
Streamwise Velocity ◽  
Channel Height ◽  
Neutral Stability ◽  
Two Dimensional ◽  
Plane Poiseuille Flow ◽  
Rotation Numbers ◽  
3C Model

Spanwise rotating plane Poiseuille flow (RPPF) is one of the canonical flow problems to study the effect of system rotation on wall-bounded shear flows and has been studied a lot in the past. In the present work, a two-dimensional-three-component (2D/3C) model for RPPF is introduced and it is shown that the present model is equivalent to a thermal convection problem with unit Prandtl number. For low Reynolds number cases, the model can be used to study the stability behaviour of the roll cells. It is found that the neutral stability curves, critical eigensolutions and critical streamfunctions of RPPF at different rotation numbers ($Ro$) almost collapse with the help of a rescaling with a newly defined Rayleigh number $Ra$ and channel height $H$. Analytic expressions for the critical Reynolds number and critical wavenumber at different $Ro$ can be obtained. For a turbulent state with high Reynolds number, the 2D/3C model for RPPF is self-sustained even without extra excitations. Simulation results also show that the profiles of mean streamwise velocity and Reynolds shear stress from the 2D/3C model share the same linear laws as the fully three-dimensional cases, although differences on the intercepts can be observed. The contours of streamwise velocity fluctuations behave like plumes in the linear law region. We also provide an explanation to the linear mean velocity profiles observed at high rotation numbers.

Lateral Migration of Large and Small Droplets Suspended in Channel Flow

2013 ◽  
Author(s):  
Masato Makino ◽  
Masako Sugihara-Seki
Keyword(s):  
Numerical Simulation ◽  
Channel Flow ◽  
Poiseuille Flow ◽  
Size Difference ◽  
Two Dimensional ◽  
Lateral Migration ◽  
Plane Poiseuille Flow ◽  
Surface Tensions ◽  
Segregation Behavior ◽  
The Mean

In order to investigate the effect of the size differences between suspended particles on the segregation behavior in channel flow of multicomponent suspensions, we conduct a two-dimensional numerical simulation for suspensions of fluid droplets of two different sizes subjected to a plane Poiseuille flow. The large and small droplets are assumed to have equal surface tensions and equal internal viscosities. The temporal evolutions of the lateral positions of the large and small droplets relative to the channel centerline are computed for various size ratios and area ratios of the large and small droplets. It is found that the small droplets tend to migrate toward the channel walls with increasing fraction of the large droplets and that the mean lateral positions of the large droplets are always closer to the channel centerline compared to the mean lateral positions of the small droplets, which represent the margination of the small droplets and the segregation of the droplets caused by the size difference. These trends are enhanced as the size ratio of large and small droplets is increased.

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