scholarly journals The stability of developing pipe flow at high Reynolds number and the existence of nonlinear neutral centre modes

2011 ◽  
Vol 684 ◽  
pp. 284-315 ◽  
Author(s):  
Andrew G. Walton
Keyword(s):  
Reynolds Number ◽  
Pipe Flow ◽  
High Reynolds Number ◽  
Pipe Wall ◽  
Fluid Velocity ◽  
Nonlinear Effects ◽  
Neutral Curve ◽  
High Reynolds ◽  
The Stability ◽  
Axisymmetric Disturbances

AbstractThe high-Reynolds-number stability of unsteady pipe flow to axisymmetric disturbances is studied using asymptotic analysis. It is shown that as the disturbance amplitude is increased, nonlinear effects first become significant within the critical layer, which moves away from the pipe wall as a result. It is found that the flow stabilizes once the basic profile has become sufficiently fully developed. By tracing the nonlinear neutral curve back to earlier times, it is found that in addition to the wall mode, which arises from a classical upper branch linear stability analysis, there also exists a nonlinear neutral centre mode, governed primarily by inviscid dynamics. The centre mode problem is solved numerically and the results show the existence of a concentrated region of vorticity centred on or close to the pipe axis and propagating downstream at almost the maximum fluid velocity. The connection between this structure and the puffs and slugs of vorticity observed in experiments is discussed.

scholarly journals Video: DNS of turbulent pipe flow at high Reynolds number

2021 ◽  
Author(s):  
Alessandro Ceci ◽  
Sergio Pirozzoli ◽  
Joshua Romero ◽  
Massimiliano Fatica ◽  
Roberto Verzicco ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Pipe Flow ◽  
High Reynolds Number ◽  
Turbulent Pipe Flow ◽  
High Reynolds

Stability of non-parabolic flow in a flexible tube

1999 ◽  
Vol 395 ◽  
pp. 211-236 ◽  
Author(s):  
V. SHANKAR ◽  
V. KUMARAN
Keyword(s):  
Reynolds Number ◽  
Velocity Profile ◽  
Asymptotic Analysis ◽  
High Reynolds Number ◽  
Reynolds Numbers ◽  
Flexible Tube ◽  
Developing Flow ◽  
Parabolic Flow ◽  
High Reynolds ◽  
The Stability

Flows with velocity profiles very different from the parabolic velocity profile can occur in the entrance region of a tube as well as in tubes with converging/diverging cross-sections. In this paper, asymptotic and numerical studies are undertaken to analyse the temporal stability of such ‘non-parabolic’ flows in a flexible tube in the limit of high Reynolds numbers. Two specific cases are considered: (i) developing flow in a flexible tube; (ii) flow in a slightly converging flexible tube. Though the mean velocity profile contains both axial and radial components, the flow is assumed to be locally parallel in the stability analysis. The fluid is Newtonian and incompressible, while the flexible wall is modelled as a viscoelastic solid. A high Reynolds number asymptotic analysis shows that the non-parabolic velocity profiles can become unstable in the inviscid limit. This inviscid instability is qualitatively different from that observed in previous studies on the stability of parabolic flow in a flexible tube, and from the instability of developing flow in a rigid tube. The results of the asymptotic analysis are extended numerically to the moderate Reynolds number regime. The numerical results reveal that the developing flow could be unstable at much lower Reynolds numbers than the parabolic flow, and hence this instability can be important in destabilizing the fluid flow through flexible tubes at moderate and high Reynolds number. For flow in a slightly converging tube, even small deviations from the parabolic profile are found to be sufficient for the present instability mechanism to be operative. The dominant non-parallel effects are incorporated using an asymptotic analysis, and this indicates that non-parallel effects do not significantly affect the neutral stability curves. The viscosity of the wall medium is found to have a stabilizing effect on this instability.

The effect of rigid rotation on the finite-amplitude stability of pipe flow at high Reynolds number

1984 ◽  
Vol 148 ◽  
pp. 193-205 ◽  
Author(s):  
T. R. Akylas ◽  
J.-P. Demurger
Keyword(s):  
Reynolds Number ◽  
Pipe Flow ◽  
High Reynolds Number ◽  
Finite Amplitude ◽  
Linear Instability ◽  
Rigid Rotation ◽  
Transition To Turbulence ◽  
Neutral Stability ◽  
Axisymmetric Mode ◽  
High Reynolds

A theoretical study is made of the stability of pipe flow with superimposed rigid rotation to finite-amplitude disturbances at high Reynolds number. The non-axisymmetric mode that requires the least amount of rotation for linear instability is considered. An amplitude expansion is developed close to the corresponding neutral stability curve; the appropriate Landau constant is calculated. It is demonstrated that the flow exhibits nonlinear subcritical instability, the nonlinear effects being particularly strong owing to the large magnitude of the Landau constant. These findings support the view that a small amount of extraneous rotation could play a significant role in the transition to turbulence of pipe flow.

Experimental study on high Reynolds number pipe flow

2019 ◽  
Vol 2019.68 (0) ◽  
pp. 217
Author(s):  
Kusano Eisuke ◽  
Noriyuki Furuichi ◽  
Wada Yuki ◽  
Yoshiyuki Tsuji
Keyword(s):  
Experimental Study ◽  
Reynolds Number ◽  
Pipe Flow ◽  
High Reynolds Number ◽  
High Reynolds

1502 Universality of the velocity profile in the high Reynolds number turbulent pipe flow

2015 ◽  
Vol 2015 (0) ◽  
pp. _1502-1_-_1502-2_
Author(s):  
Yuki WADA ◽  
Noriyuki FURUICHI ◽  
Yoshiya TERAO ◽  
Yoshiyuki TSUJI
Keyword(s):  
Reynolds Number ◽  
Velocity Profile ◽  
Pipe Flow ◽  
High Reynolds Number ◽  
Turbulent Pipe Flow ◽  
High Reynolds

A Modified Form of the k-ε Model for Predicting Wall Turbulence

1981 ◽  
Vol 103 (3) ◽  
pp. 456-460 ◽  
Author(s):  
C. K. G. Lam ◽  
K. Bremhorst
Keyword(s):  
Reynolds Number ◽  
Pipe Flow ◽  
Dissipation Rate ◽  
High Reynolds Number ◽  
Present Form ◽  
Wall Turbulence ◽  
Wall Region ◽  
Wall Function ◽  
High Reynolds ◽  
Number Form

The high Reynolds number form of the k-ε model is extended and tested by application to fully developed pipe flow. It is established that the model is valid throughout the fully turbulent, semilaminar and laminar regions of the flow. Unlike many previously proposed forms of the k-ε model, the present form does not have to be used in conjunction with empirical wall function formulas and does not include additional terms in the k and ε equations. Comparison between predicted and measured dissipation rate in the important wall region is also possible.

On the linear stability of spiral flow between rotating cylinders

1982 ◽  
Vol 382 (1782) ◽  
pp. 83-102 ◽  
Keyword(s):  
Reynolds Number ◽  
Numerical Study ◽  
Stability Boundary ◽  
Rotating Cylinders ◽  
Spiral Flow ◽  
Compound Matrix Method ◽  
Compound Matrix ◽  
High Reynolds ◽  
The Stability ◽  
Axisymmetric Disturbances

A numerical study is made of the effects of both axisymmetric and non-axisymmetric disturbances on the stability of spiral flow between rotating cylinders. If we let Ω 1 and Ω 2 be the angular speeds of the inner and outer cylinders, and R 1 and R 2 be their respective radii, then for fixed values of η = R 1 / R 2 and μ = Ω 2 / Ω 1 , the onset of instability depends on both the Taylor number T and the axial Reynolds number R . Here R is based on the gap width between the cylinders and the average axial velocity of the basic flow, while T is based on the average angular speeds of the cylinders. Using the compound matrix method, we have computed the complete stability boundary in the R , T -plane for axisymmetric disturbances with η = 0.95 and μ = 0. We find that, for sufficiently high Reynolds numbers, there are two distinct axisymmetric modes corresponding to the usual shear and rotational instabilities. We have also obtained the stability boundaries for non-axisymmetric disturbances for R ≼ 6000 for η = 0.95 and 0.77 with μ = 0. These last results are found to be in substantial agreement with the experimental observations of Snyder (1962, 1965), Nagib (1972) and Mavec (1973) in the low and moderate axial Reynolds number régimes.

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