1 edition of **On the stability of plane Poiseuille flow** found in the catalog.

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- 16 Currently reading

Published
**1976** .

Written in English

- Aeronautics

The Physical Object | |
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Pagination | p. ; |

ID Numbers | |

Open Library | OL25389187M |

-L~m. flows, there have been two recent studies of the stability of plane Poiseuille flow of viscoelastic liquids. In the first of these studies, Walters/ using an integral constitutive equa-tion of the type proposed by Oldroyd,2 developed a modified version of the Orr-Sommerfeld equation, and later Chan Man. In the classical hydrodynamic stability theory (see, e.g., [26, 27]), the base flow is obtained as a simple one-dimensional steady solution of the equations of motion (e.g., a plane Poiseuille flow is obtained as a steady one-dimensional solution of the Navier-Stokes equations). The stability of plane Poiseuille flow in a channel forced by a wavelike motion on one of the channel walls is investigated. The amplitude epsilon of this forcing is taken to be small. The most dangerous modes of forcing are by: 4.

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Stability Analysis of a Plane Poisseuille Flow. Course Project: Water Waves and Hydrodynamic Stability Matthias Steinhausen. Matthias Steinhausen –Plane Poiseuille Flow 2. Pressure-driven flow between two resting plates Scaled velocity profile (only On the stability of plane Poiseuille flow book y): 𝑈 = 𝑈∗.

𝑈𝐶𝑙. We present a detailed study of the linear stability of plane Couette-Poiseuille flow in the presence of a cross-flow. The base flow is characterised by the. We present a detailed study of the linear stability of the plane Couette–Poiseuille flow in the presence of a crossflow.

The base flow is characterized by the crossflow Reynolds number R inj and the dimensionless wall velocity 's transformation may be applied to the linear stability equations and we therefore consider two-dimensional (spanwise-independent) perturbations.

Calhoun: The NPS Institutional Archive DSpace Repository Theses and Dissertations Thesis and Dissertation Collection On the stability of plane Poiseuille flow. Part of the International Centre for Mechanical Sciences book series (CISM, volume 74) Abstract In this section we use the local potential technique to investigate the linear stability of a steady plane Poiseuille flow of an incompressible by: 1.

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The stability of a two-dimensional Couette-Poiseuille flow is investigated. The primary unidirectional flow is between two infinite parallel plates, one of.

which moves relative to the other. The results On the stability of plane Poiseuille flow book the case of Poiseuille flow. The main topic of this thesis is the stability of incompressible plane Couette ﬂow and pipe Poiseuille ﬂow.

Plane Couette ﬂow is the stationary ﬂow between two inﬁnite parallel plates, moving in opposite directions at a constant speed, and pipe Poiseuille ﬂow is the stationary ﬂow in an inﬁnite circular pipe, driven by a constantFile Size: KB.

PLANE DISTURBANCE OF PLANE POISEUILLE FLOW HE equations of motion of a homogeneous in-compressible viscous Quid in two dimensions u~ider hydrostatic pressure between two planes at y= ~b are satisfied, to the first order in e by the stream function (y' 4=UoI — y I+ (exp[— in(x — 't)5v(y) (3b') +exp[in(x ct)5P— (y)}, where c and q are complex and c and g their complexFile Size: KB.

In the present work, the stability of a plane Poiseuille flow forced by spanwise oscillations is studied via the instantaneous linear stability theory (LST).

For streamwise Poiseuille flow and a spanwise Stokes layer, the superposition of these two linearly Cited by: 1. This article is concerned with the linear stability of a plane Poiseuille flow of two viscoelastic fluids. Both fluids follow an Oldroyd-B differential constitutive equation.

This law introduces the difference of normal stress σ x,x −σ y,y considered as the characteristic feature of viscoelasticity of polymeric fluid. Stability under infinitesimal disturbances is investigated by the means of generalized Orr–Sommerfeld Cited by: The stability of a two-dimensional Couette-Poiseuille flow is investigated.

The primary unidirectional flow is between two infinite parallel plates, one of which moves relative to the other. The results for the case of Poiseuille flow agree with.

Stability of plane Poiseuille ﬂow of a Bingham ﬂuid through a deformable neo-Hookean channel Ramkarn Patne and V. Shankar * Department of Chemical Engineering, Indian Institute of Technology, KanpurIndia (Received 27 December ; published 5 August ) We study the linear stability of plane Poiseuille ﬂow of a Bingham ﬂuid File Size: 1MB.

Changes occur in amplitude and in character much as would be observed in a laboratory experiment. The classical paradox of stability of Poiseuille flow to low amplitude disturbances at all Reynolds numbers is studied and contrasted to plane‐Poiseuille flow. The amplitude dependence of stability is Cited by: 8.

Nishioka M, Iida S, Ichikawa Y () An experimental investigation of the stability of plane Poiseuille flow. J Fluid Mech – ADS CrossRef Google Scholar Orszag SA () Accurate solution of the Orr–Sommerfeld stability : Andrey V.

Boiko, Alexander V. Dovgal, Genrih R. Grek, Victor V. Kozlov. i.e., in a plane Poiseuille flow, the pressure gradient is a constant along the flow direction. This pressure gradient is the driving force for the flow. Let. ()dp dx1≡−α, so that a positive α corresponds to the case where the pressure decreases along the flow direction.

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.

Linear Stability Analysis for "Plane Poiseuille flow" Disclaimer. This software is published for academic and non-commercial use only. Content. Small thesis about the theory and the schemes used.

MATLAB code for the "Plane Poiseuille Flow" problem. Presentation in PDF and PPTX format. E-mail contact: [email protected] Stability of two superposed fluids of different viscosity in plane Poiseuille flow is studied numerically. Conditions for the growth of an interfacial wave are identified.

The analysis extends Yih’s results [J. Fluid Mech. 27, ()] for small wavenumbers to large wavenumbers and accounts for differences in density and thickness ratios, as well as the effects of interfacial tension and Cited by: Rousset, Franc¸ois, Bourgin, Patrick, and Palade, Liviu-Iulian.

"Stability Analysis of a Plane Poiseuille Flow of Multilayered Viscoelastic Fluids: An Energetic Approach." Proceedings of the ASME Fluids Engineering Division Summer Meeting.

Volume 1: Symposia, Parts A and B. Houston, Texas, USA. June 19–23, pp. : Franc¸ois Rousset, Patrick Bourgin, Liviu-Iulian Palade.

An Internet Book on Fluid Dynamics COUETTE AND PLANAR POISEUILLE FLOW Couette and planar Poiseuilleﬂow are both steady ﬂows between two inﬁnitely long, parallel plates a ﬁxed distance, h, apart as sketched in Figures 1 and 2.

The diﬀerence is that in Couette ﬂow one of the plates Figure 1: Couette ﬂow. Figure 2: Planar Poiseuille Size: 97KB. We study the linear stability of Plane Poiseuille flow of an elastoviscoplastic fluid using a revised version of the model proposed by Putz and Burghelea (A.M.V.

Putz, T.I. Burghelea, Rheol. Acta 48 () –). The evolution of the. Download PDF: Sorry, we are unable to provide the full text but you may find it at the following location(s): (external link). For plane Poiseuille flow, it has been shown that the flow is unstable (i.e.

one or more eigenvalues has a positive imaginary part) for some when > = and the neutrally stable mode at = having =. To see the stability properties of the system, it is customary to plot a dispersion curve, that is, a plot of the growth rate () as a function of the wavenumber.

The stability of Poiseuille flow in channels with walls grooved in the streamwise direction is investigated numerically. In the framework of physically justified scaling of velocity and length, an analysis of energy and linear critical Reynolds numbers was carried out in a practically important range of groove heights, sharpness and by: 4.

stability of a viscoelastic ﬂow without externally-imposed heating have not been considered. In this paper, we examine the stability of Non-Newtonian plane Couette and Poiseuille ﬂow with viscous heating, and the de nition diagrams for these two ﬂows are given in Figures 1(a) and 1(b), respectively.

[Figure 1 about here.]. American Institute of Aeronautics and Astronautics Sunrise Valley Drive, Suite Reston, VA Cited by: 2. A proof by Petrov [10] that plane Couette flow and plane Poiseuille flow are always stable with respect to infinitesimal disturbances is examined and found to be based on a set of incomplete functions, thus rendering the proof by: 4.

Books. AIAA Education Series; Library of Flight; Linear Spatial Stability of the Plane Poiseuille Flow. LEONG ; 17 May | AIAA Journal, Vol. 12, No. 11 On a Proof by Petrov of the Stability of Plane Couette Flow and Plane Poiseuille Flow. SIAM Journal on Applied Mathematics, Vol.

17, No. by: The effect of transverse magnetic field on the stability of plane Poiseuille and Couette flow between two parallel flat plates is investigated for Oldroyd-B fluid. The classical Orr–Sommerfeld analysis is extended to electrically conducting fluid for Oldroyd-B model, assuming that the magnetic Prandtl number is sufficiently by: The stability of plane Poiseuille flow to periodic disturbances of finite amplitude was reinvestigated by the use of 55 harmonics instead of five in the Orr-Sommerfeld expansion, but all the (20) overtones in each harmonic were dropped.

The fundamental mode was chosen as the one of lowest phase velocity c r, so as to enhance the wall by: 7.

The three cases are then re-examined for shear-wave stability, and the results compared with those for confined plane Poiseuille flow. The comparison serves to indicate the vestiges of shear waves in the free-surface flow, and to give a sense of unity in the understanding of the stability of both flows.

The stability of the plane Poiseuille flow is analyzed using a thermodynamic formalism by considering the deterministic Navier– Stokes equation with Gaussian random initial data. A unique critical Reynolds number, Rec ≈2, atwhich theprobability of observing puffs in the solution changes from 0 to 1, is numerically demon-Cited by: 8.

The linear stability of a plane compressible laminar (Poiseuille) flow sandwiched between two semi-infinite elastic media was investigated with the aim of explaining the excitation of volcanic tremors. Our results show that there are several regimes of instability, and the nature of stability significantly depends on the symmetry of oscillatory fluid and solid by: 3.

For that purpose we study the linear stability response to very long waves of a three-layer phase Poiseuille flow with an inner thin layer which represents the interphase. Although this fact is an approximation, it nevertheless takes into account the Cited by: 2. Similar conclusion of the linear theory is also available for the Plane Couette (PC) flow [1].

For the Plane Poiseuille (PP) flow, known estimate of the threshold Reynolds number made on the base of the linear theory more than five times greater than the value obtained in the experiment [].

The instability of shear flows, of which the Poiseuille flow is a canonical example, is among the most classical and most challenging problems in fluid mechanics, and a huge amount of effort has been devoted to it (1 –13).The most definitive advance has been the recent experimental work by Avila et al.

(): By measuring the puff decaying and splitting times, they obtained an estimate for the Cited by: 8. The upper most neutral stability curve (solid line) corresponds to the purely oscillatory flow and as the parameter Γh increases monotonically the critical conditions move to smaller wavenumbers across the plot, asymptoting towards the neutral curve for the plane Poiseuille flow, the dotted line located on the left-hand side of the plot with Cited by: The stability of the viscous flow between two parallel horizontal plates due to a constant reduced pressure gradient in a system rotating about a vertical axis is studied.

The critical value of the Reynolds number R, based on the reduced pressure gradient, is a function of a dimensionless rotation parameter T, the Taylor number. A numerical solution of the eigenvalue problem shows that (i) the. It is shown that linear instability of plane Couette flow can take place even at finite Reynolds numbers Re > Re{sub th} ≈which agrees with the experimental value of Re{sub th} ≈ ± 5 [16, 17].

This new result of the linear theory of hydrodynamic stability is obtained by abandoning. Linear Stability Analysis for Plane-Poiseuille Flow of an Elastoviscoplastic ﬂuid with internal microstructure Miguel Moyers-Gonzáleza∗, Teodor I. Burghelea b and Julian Makc aDepartment of Mathematics and Statistics University of Canterbury, Private BagChristchurch,NZ bInstitute of Polymer Materials.The stability of plane Poiseuille flow to periodic disturbances of finite amplitude was investigated by expanding each harmonic of the solution in terms of the Orr-Sommerfeld eigenfunctions with coefficients which are functions of time.When a cross-flow is present, increasing the strength of the electric field in the high- $\mathit{Re}$ Poiseuille flow yields a more unstable flow in both modal and non-modal stability analyses.