The onset of absolute instability of rotating Hagen–Poiseuille flow: A spatial stability analysis

2002 ◽  
Vol 14 (9) ◽  
pp. 3087-3097 ◽  
Author(s):  
R. Fernandez-Feria ◽  
C. del Pino
Keyword(s):  
Stability Analysis ◽  
Poiseuille Flow ◽  
Absolute Instability ◽  
Spatial Stability

Spatial stability and the onset of absolute instability of Batchelor's vortex for high swirl numbers

2007 ◽  
Vol 583 ◽  
pp. 27-43 ◽  
Author(s):  
L. PARRAS ◽  
R. FERNANDEZ-FERIA
Keyword(s):  
Stability Analysis ◽  
Temporal Stability ◽  
Axial Flow ◽  
Reynolds Numbers ◽  
Absolute Instability ◽  
Spatial Stability ◽  
The Past ◽  
Trailing Vortices ◽  
The Stability ◽  
Large Aircraft

Batchelor's vortex has been commonly used in the past as a model for aircraft trailing vortices. Using a temporal stability analysis, new viscous unstable modes have been found for the high swirl numbers of interest in actual large-aircraft vortices. We look here for these unstable viscous modes occurring at large swirl numbers (q > 1.5), and large Reynolds numbers (Re >103), using a spatial stability analysis, thus characterizing the frequencies at which these modes become convectively unstable for different values of q, Re, and for different intensities of the uniform axial flow. We consider both jet-like and wake-like Batchelor's vortices, and are able to analyse the stability for Re as high as 108. We also characterize the frequencies and the swirl numbers for the onset of absolute instabilities of these unstable viscous modes for large q.

Räumliche Stabilitätsanalysen und Globale Stabilitätsnachweise nach DIN EN 1993–1–1/Spatial stability analysis and global stability checks according to DIN EN 1993–1–1

Bauingenieur ◽  
2015 ◽  
Vol 90 (10) ◽  
pp. 469-477
Author(s):  
Josef Szalai ◽  
Achim Rubert ◽  
Ferenc Papp
Keyword(s):  
Stability Analysis ◽  
Global Stability ◽  
Spatial Stability ◽  
Numerische Analyse

Über räumliche Stabilitätsanalysen aus Baustahl mit dünnwandigen vorwiegend offenen Profilen werden die globalen Eigenlösungen (elastische kritische Laststeigerungsfaktoren acr,op und zugehörige Eigenformen) biegetorsionsgefährdeter Gesamtkonstruktionen ermittelt. Anschließend wird die sogenannte “Allgemeine Nachweismethode” von DIN EN 1993–1–1, Abschnitt 6.3.4 benutzt, um Tragfähigkeitsnachweise gegen räumliches Gesamtversagen (Biegedrillknicken) zu führen. Da keine analytischen Lösungen zur exakten Berechnung von acr,op zur Verfügung stehen, ist eine integrierte softwarebasierte Methodik der Stabilitätsanalyse und -nachweise optimal und einfach in der praktischen Anwendung. Sie wird mit der klassischen Ersatzstabmethode für Stabilitätsnachweise einfacher Stabmodelle verglichen, bei der unterschiedliche Berechnungsmodelle zu Schnittgrößenberechnung und Stabilitätsnachweis in der Ebene und den Stabilitätsnachweisen aus der Ebene (ggf. mit entsprechender Software) verwendet werden. Für die numerische Analyse (das ist ein entscheidender Kernpunkt der integrierten Methode und des Nachweises nach 6.3.4) wird die auf der Basis von EC 3 entwickelte Software ConSteel eingesetzt, die ein leistungsfähiges 3D finites Balken-Stützenelement mit zwei Knoten und jeweils sieben Verformungsfreiheitsgraden (inklusive der Verwölbung) verwendet. Mit den beiden Beispielen wird aufgezeigt, dass die Nachweise nach Abschnitt 6.3.4 mit den Einschränkungen des deutschen nationale Anhangs zu übertrieben sicheren und unwirtschaftlichen Ergebnissen führen, dessen Einschränkungen nach Auffassung der Verfasser und [16] nicht empfohlen werden.

scholarly journals Shear instability of an axisymmetric air–water coaxial jet

2018 ◽  
Vol 843 ◽  
pp. 575-600 ◽  
Author(s):  
Jean-Philippe Matas ◽  
Antoine Delon ◽  
Alain Cartellier
Keyword(s):  
Surface Tension ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Convective Instability ◽  
Scaling Laws ◽  
Shear Instability ◽  
Liquid Jet ◽  
Absolute Instability ◽  
Instability Waves

We study the destabilization of a round liquid jet by a fast annular gas stream. We measure the frequency of the shear instability waves for several geometries and air/water velocities. We then carry out a linear stability analysis, and show that there are three competing mechanisms for the destabilization: a convective instability, an absolute instability driven by surface tension and an absolute instability driven by confinement. We compare the predictions of this analysis with experimental results, and propose scaling laws for wave frequency in each regime. We finally introduce criteria to predict the boundaries between these three regimes.

Convective and absolute instabilities in Rayleigh–Bénard–Poiseuille mixed convection for viscoelastic fluids

2015 ◽  
Vol 765 ◽  
pp. 167-210 ◽  
Author(s):  
S. C. Hirata ◽  
L. S. de B. Alves ◽  
N. Delenda ◽  
M. N. Ouarzazi
Keyword(s):  
Rayleigh Number ◽  
Mixed Convection ◽  
Poiseuille Flow ◽  
Flow Direction ◽  
Viscoelastic Fluids ◽  
Newtonian Fluids ◽  
Absolute Instability ◽  
Elastic Regime ◽  
Elasticity Number ◽  
Rayleigh Benard

AbstractThe convective and absolute nature of instabilities in Rayleigh–Bénard–Poiseuille (RBP) mixed convection for viscoelastic fluids is examined numerically with a shooting method as well as analytically with a one-mode Galerkin expansion. The viscoelastic fluid is modelled by means of a general constitutive equation that encompasses the Maxwell model and the Oldroyd-B model. In comparison to Newtonian fluids, two more dimensionless parameters are introduced, namely the elasticity number${\it\lambda}_{1}$and the ratio${\it\Gamma}$between retardation and relaxation times. Temporal stability analysis of the basic state showed that the three-dimensional thermoconvective problem can be Squire-transformed. Therefore, one must distinguish mainly between two principal roll orientations: transverse rolls TRs (rolls with axes perpendicular to the Poiseuille flow direction) and longitudinal rolls LRs (rolls with axes parallel to the Poiseuille flow direction). The critical Rayleigh number for the appearance of LRs is found to be independent of the Reynolds number ($\mathit{Re}$). Depending on${\it\lambda}_{1}$and${\it\Gamma}$, two different regimes can be distinguished. In the weakly elastic regime, the emerging LRs are stationary, while they are oscillatory in the strongly elastic regime. For TRs, it is found that in the weakly elastic regime, the stabilization effect of$\mathit{Re}$is more important than in Newtonian fluids. Moreover, for sufficiently elastic fluids a jump is observed in the oscillation frequencies and wavenumbers for moderate$\mathit{Re}$. In the strongly elastic regime, the effect of the imposed throughflow is to promote the appearance of the upstream moving TRs for low values of$\mathit{Re}$, which are replaced by downstream moving TRs for higher values of $\mathit{Re}$. Moreover, the results proved that, contrary to the case where$\mathit{Re}=0$, the elasticity number${\it\lambda}_{1}$(the ratio${\it\Gamma}$) has a strongly stabilizing (destabilizing) effect when the throughflow is added. The influence of the rheological parameters on the transition curves from convective to absolute instability in the Reynolds–Rayleigh number plane is also determined. We show that the viscoelastic character of the fluid hastens the transition to absolute instability and even may suppress the convective/absolute transition. Throughout this paper, similarities and differences with the corresponding problem for Newtonian fluids are highlighted.

Pulsatile flow in stenotic geometries: flow behaviour and stability

2009 ◽  
Vol 622 ◽  
pp. 291-320 ◽  
Author(s):  
M. D. GRIFFITH ◽  
T. LEWEKE ◽  
M. C. THOMPSON ◽  
K. HOURIGAN
Keyword(s):  
Stability Analysis ◽  
Shear Layer ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Base Flow ◽  
Arterial Stenosis ◽  
Working Fluid ◽  
Absolute Instability ◽  
Straight Tube ◽  
Instability Modes

Pulsatile inlet flow through a circular tube with an axisymmetric blockage of varying size is studied both numerically and experimentally. The geometry consists of a long, straight tube and a blockage, semicircular in cross-section, serving as a simplified model of an arterial stenosis. The stenosis is characterized by a single parameter, the aim being to highlight fundamental behaviours of constricted pulsatile flows. The Reynolds number is varied between 50 and 700 and the stenosis degree by area between 0.20 and 0.90. Numerically, a spectral element code is used to obtain the axisymmetric base flow fields, while experimentally, results are obtained for a similar set of geometries, using water as the working fluid. For low Reynolds numbers, the flow is characterized by a vortex ring which forms directly downstream of the stenosis, for which the strength and downstream propagation velocity vary with the stenosis degree. Linear stability analysis is performed on the simulated axisymmetric base flows, revealing a range of absolute instability modes. Comparisons are drawn between the numerical linear stability analysis and the observed instability in the experimental flows. The observed flows are less stable than the numerical analysis predicts, with convective shear layer instability present in the experimental flows. Evidence is found of Kelvin–Helmholtz-type shear layer roll-ups; nonetheless, the possibility of the numerically predicted absolute instability modes acting in the experimental flow is left open.

Spatial Stability Analysis of Subsonic Jets Modified for Low-Frequency Noise Reduction

AIAA Journal ◽  
2015 ◽  
Vol 53 (8) ◽  
pp. 2335-2358 ◽  
Author(s):  
Ali Uzun ◽  
Farrukh S. Alvi ◽  
Tim Colonius ◽  
M. Yousuff Hussaini
Keyword(s):  
Stability Analysis ◽  
Noise Reduction ◽  
Low Frequency ◽  
Frequency Noise ◽  
Low Frequency Noise ◽  
Spatial Stability
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