Linear Instability of Asymmetric Flow in Channels

Fu, Tao

doi:10.1063/1.1692913

Cited by 9 publications

(7 citation statements)

References 2 publications

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“…This was done for a range of the parameters (a, BJ. The results agree with those of Fu & Joseph (1970) and are illustrated in figure 1. As a check, the eigenvalue c, was also computed from the adjoint problem (7.5) using the conditions (5.12).…”

Section: )supporting

confidence: 87%

Subcritical bifurcation of plane Poiseuille flow

Chen

Joseph

1973

J. Fluid Mech.

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We apply the perturbation theory which was recently developed and justified by Joseph & Sattinger (1972) to determine the form of the time-periodic solutions which bifurcate from plane Poiseuille flow. The results a t lowest significant order seem to be in good agreement with those following from the formal perturbation method of Stuart (1960) as extended by Reynolds & Potter (1967). Given the numerical results of the present calculation, the rigorous theory guarantees that the only time-periodic solution which bifurcates from laminar Poiseuille flow is a two-dimensional wave. The wave which bifurcates at the lowest Reynolds number exists, but it is unstable when its amplitude is small. Solutions which escape the small domain of attraction of laminar Poiseuille flow snap through this unstable time-periodic solution with a small amplitude to solutions of larger amplitudes.

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Section: )supporting

confidence: 87%

Subcritical bifurcation of plane Poiseuille flow

Chen

Joseph

1973

J. Fluid Mech.

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“…Considering the numerical solution of the Navier-Stokes equation and the least squares fit of flow parameters, Kachuma and Sobey [9] showed the existence of a flow region after the barrier/step where the above model's basic flow (Equation (9) with β 1 = β 2 = 0) fits well to true longitudinal velocity. Our approximated mean flow solution U(y) is similar to the polynomial-type solution suggested by Fu and Joseph [11] for asymmetric flow in channels. When σ 1 = σ 2 = 0, the limiting flow is plane Poiseuille in a slipper channel [31], and in addition, if β 1 = β 2 = 0, then it is plane Poiseuille in a rigid channel (with U(y) = 3 2 (1 − y 2 )).…”

Section: Mean Velocity Profilementioning

confidence: 53%

“…The mean velocity field of the fully developed flow at that particular position can be approximated by U = (U(y), 0), which satisfies the condition U(y) = ∓β i U y (y) at the walls (y = ±1). Hereat, following the formulation of Fransson and Alfredsson [8], Kachuma and Sobey [9] and Fu and Joseph [11], we have considered a typical mean velocity profile, which takes into account the effects of asymmetry together with wall slip and is given by…”

Section: Mean Velocity Profilementioning

confidence: 99%

Relative Effects of Asymmetry and Wall Slip on the Stability of Plane Channel Flow

Ghosh

2017

Fluids

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The effect of wall velocity slip on the stability of a pressure-driven two-dimensional asymmetric channel flow is examined by considering Navier slip condition on the channel walls. The two-parameter families of mean velocity profiles are considered to approximate the underlying asymmetric basic flow. Competing effects of skewness and maximum velocity on the stability of the flow are explored for a range of model parameters. The Orr-Sommerfeld system of the asymmetric flow is solved using a Chebyshev spectral collocation method for both symmetric and non-symmetric type slip boundary conditions. Numerical results indicate that moderate asymmetry in the basic flow has a significant role on the stability of the Poiseuille-kind parallel/nearly parallel flows. Wall slip shows a passive control on the instability of the asymmetric flow by increasing or decreasing the critical Reynolds number and the set of unstable wave numbers. The stabilizing/destabilizing effect of slip velocity on the flow instability is weak or strong depending on the presence of velocity slip at the upper or lower wall. Velocity slip has a profound grip on the flow behaviour by changing the shear rate inside the perturbed flow.

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“…Gad-el-Hak (2002), Babenko and Kozlov (1972) and Fu and Joseph (1970) reported that although compliant materials can stabilize different types of instabilities, they might cause other types of instabilities such as hydro-and aero-elastic instabilities. In fact, it was noticed by researchers that stable fluid flows inside rigid channels became unstable in deformable channels.…”

Section: Introductionmentioning

confidence: 99%

Implications of inertia for hydroelastic instability of Herschel-Bulkley fluids in plane Poiseuille flow

Jafargholinejad

Najafi

2018

jtam

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This study investigates the effects of inertia on the hydroelastic instability of a pressure-driven Herschel-Bulkley fluid passing through a two-dimensional channel lined with a polymeric coating. The no-viscous hyperelastic polymeric coating is assumed to follow the two-constant Mooney-Rivlin model. In this work, analytical basic solutions are determined for both the polymeric gel and the fluid at very low Reynolds numbers. Next, the basic solutions are subjected to infinitesimally-small, normal-mode perturbations. After eliminating the nonlinear terms, two 4-th order differential equations are obtained. The equations with appropriate boundary conditions are then numerically solved using the shooting method. The results of the solution show that the inertia terms in the perturbed equations destabilize the pressure-driven Herschel-Bulkley fluid flow. The investigation reveals that the elastic parameter has a stabilizing effect on the flow. Also, based on the obtained results, the yield stress, depending on the power-law index, has a stabilizing or destabilizing effect on the flow. Since in this work the inertia terms are included in the pertinent governing equations, therefore, the results of this study are much more realistic and reliable than previous works in which inertia terms were absent. In addition, unlike the previous works, the present study considers both the shear-thinning and shear-thickening types of fluids. Hence, the results of this work embrace all the fluids which obey the Herschel-Bulkley model.

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Linear Instability of Asymmetric Flow in Channels

Cited by 9 publications

References 2 publications

Subcritical bifurcation of plane Poiseuille flow

Subcritical bifurcation of plane Poiseuille flow

Relative Effects of Asymmetry and Wall Slip on the Stability of Plane Channel Flow

Implications of inertia for hydroelastic instability of Herschel-Bulkley fluids in plane Poiseuille flow

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