Linear Stability Analysis and Gas Kinetic Scheme (GKS) Simulations of Instabilities in Compressible Plane Poiseuille Flow

The receptivity problem of plane Bingham–Poiseuille flow with respect to weak perturbations is addressed. The relevance of this study is highlighted by the linear stability analysis results (spectra and pseudospectra). The first part of the present paper thus deals with the classical normal-mode approach in which the resulting eigenvalue problem is solved using the Chebychev collocation method. Within the range of parameters considered, the Poiseuille flow of Bingham fluid is found to be linearly stable. The second part investigates the most amplified perturbations using the non-modal approach. At a very low Bingham number (B ≪ 1), the optimal disturbance consists of almost streamwise vortices, whereas at moderate or large B the optimal disturbance becomes oblique. The evolution of the obliqueness as function of B is determined. The linear analysis presented also indicates, as a first stage of a theoretical investigation, the principal challenges of a more complete nonlinear study.

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Linear stability analysis of Poiseuille flow in a rectangular duct

Russian Journal of Numerical Analysis and Mathematical Modelling ◽

10.1515/rnam-2013-0008 ◽

2013 ◽

Vol 28 (2) ◽

Cited By ~ 4

Author(s):

K. V. Demyanko ◽

Yu. M. Nechepurenko

Keyword(s):

Stability Analysis ◽

Linear Stability ◽

Linear Stability Analysis ◽

Poiseuille Flow ◽

Rectangular Duct

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Linear stability analysis of the Poiseuille flow of a stratified non-Newtonian suspension: Application to microcirculation

Journal of Non-Newtonian Fluid Mechanics ◽

10.1016/j.jnnfm.2020.104464 ◽

2021 ◽

Vol 287 ◽

pp. 104464

Author(s):

Lorenzo Fusi ◽

Angiolo Farina ◽

Giuseppe Saccomandi

Keyword(s):

Stability Analysis ◽

Linear Stability ◽

Linear Stability Analysis ◽

Poiseuille Flow

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Linear Stability Analysis for the Wall Temperature Feedback Control of Planar Poiseuille Flows

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.1515325 ◽

2002 ◽

Vol 124 (4) ◽

pp. 617-624

Author(s):

Herve´ Pabiou ◽

Jun Liu ◽

Christine Be´nard

Keyword(s):

Stability Analysis ◽

Feedback Control ◽

Flow Control ◽

Linear Stability ◽

Wall Temperature ◽

Linear Stability Analysis ◽

Poiseuille Flow ◽

Numerical Results ◽

Coupled Equations ◽

Linear Loss

Active control of a planar Poiseuille flow can be performed by increasing or decreasing the wall temperature in proportion to the observed wall shear stress perturbation. In continuation with the work of H. H. Hu and H. H. Bau (1994, Feedback Control to Delay or Advance Linear Loss of Stability in Planar Poiseuille Flow, Proc. R. Soc. London A, 447, pp. 299–312), a linear stability analysis of such a feedback control is developed in this paper. The Poiseuille flow control problem is reduced to a modified Orr-Sommerfeld equation coupled with a heat equation. By solving numerically the coupled equations with a finite element method, many numerical results about the stability of the flow control are obtained. We focus our attention on the interpretation of the numerical results. In particular, the role of two essential parameters—the Prandtl number Pr and the control gain K—is investigated in detail. When Pr>1.31, stabilizing K is negative; while, when Pr<1.31, stabilizing K is positive. And when Pr=1.31, the flow cannot be stabilized by a real K. A comparison between symmetric two-wall control and non-symmetric one-wall control is also made.

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