scholarly journals Spatiotemporal Intermittency in Pulsatile Pipe Flow

Entropy ◽  
2020 ◽  
Vol 23 (1) ◽  
pp. 46
Author(s):  
Daniel Feldmann ◽  
Daniel Morón ◽  
Marc Avila
Keyword(s):  
Pipe Flow ◽  
Transition To Turbulence ◽  
Pulsation Period ◽  
Intermittent Turbulence ◽  
Mean Velocity ◽  
Optimal Perturbation ◽  
Pipe Flows ◽  
Spatiotemporal Intermittency ◽  
The Mean ◽  
Made In

Despite its importance in cardiovascular diseases and engineering applications, turbulence in pulsatile pipe flow remains little comprehended. Important advances have been made in the recent years in understanding the transition to turbulence in such flows, but the question remains of how turbulence behaves once triggered. In this paper, we explore the spatiotemporal intermittency of turbulence in pulsatile pipe flows at fixed Reynolds and Womersley numbers (Re=2400, Wo=8) and different pulsation amplitudes. Direct numerical simulations (DNS) were performed according to two strategies. First, we performed DNS starting from a statistically steady pipe flow. Second, we performed DNS starting from the laminar Sexl–Womersley flow and disturbed with the optimal helical perturbation according to a non-modal stability analysis. Our results show that the optimal perturbation is unable to sustain turbulence after the first pulsation period. Spatiotemporally intermittent turbulence only survives for multiple periods if puffs are triggered. We find that puffs in pulsatile pipe flow do not only take advantage of the self-sustaining lift-up mechanism, but also of the intermittent stability of the mean velocity profile.

scholarly journals Nonlinear waves with a threefold rotational symmetry in pipe flow: influence of a strongly shear-thinning rheology

2017 ◽  
Vol 818 ◽  
pp. 595-622
Author(s):  
Emmanuel Plaut ◽  
Nicolas Roland ◽  
Chérif Nouar
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Nonlinear Waves ◽  
Pipe Flow ◽  
Rotational Symmetry ◽  
Shear Thinning ◽  
Transition To Turbulence ◽  
Mean Velocity ◽  
The Mean ◽  
The One

In order to model the transition to turbulence in pipe flow of non-Newtonian fluids, the influence of a strongly shear-thinning rheology on the travelling waves with a threefold rotational symmetry of Faisst & Eckhardt (Phys. Rev. Lett., vol. 91, 2003, 224502) and Wedin & Kerswell (J. Fluid Mech., vol. 508, 2004, pp. 333–371) is analysed. The rheological model is Carreau’s law. Besides the shear-thinning index $n_{C}$, the dimensionless characteristic time $\unicode[STIX]{x1D706}$ of the fluid is considered as the main non-Newtonian control parameter. If $\unicode[STIX]{x1D706}=0$, the fluid is Newtonian. In the relevant limit $\unicode[STIX]{x1D706}\rightarrow +\infty$, the fluid approaches a power-law behaviour. The laminar base flows are first characterized. To compute the nonlinear waves, a Petrov–Galerkin code is used, with continuation methods, starting from the Newtonian case. The axial wavenumber is optimized and the critical waves appearing at minimal values of the Reynolds number $\mathit{Re}_{w}$ based on the mean velocity and wall viscosity are characterized. As $\unicode[STIX]{x1D706}$ increases, these correspond to a constant value of the Reynolds number based on the mean velocity and viscosity. This viscosity, close to the one of the laminar flow, can be estimated analytically. Therefore the experimentally relevant critical Reynolds number $\mathit{Re}_{wc}$ can also be estimated analytically. This Reynolds number may be viewed as a lower estimate of the Reynolds number for the transition to developed turbulence. This demonstrates a quantified stabilizing effect of the shear-thinning rheology. Finally, the increase of the pressure gradient in waves, as compared to the one in the laminar flow with the same mass flux, is calculated, and a kind of ‘drag reduction effect’ is found.

Experiments on transition to turbulence in an oscillatory pipe flow

1976 ◽  
Vol 75 (2) ◽  
pp. 193-207 ◽  
Author(s):  
Mikio Hino ◽  
Masaki Sawamoto ◽  
Shuji Takasu
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Pipe Flow ◽  
Stokes Parameter ◽  
Angular Frequency ◽  
Transition To Turbulence ◽  
Mean Velocity ◽  
Cross Sectional ◽  
Velocity Amplitude ◽  
Turbulent Flow Regime

Experiments on transition to turbulence in a purely oscillatory pipe flow were performed for values of the Reynolds number Rδ, defined using the Stokes-layer thickness δ = (2ν/ω)½ and the cross-sectional mean velocity amplitude Û, from 19 to 1530 (or for values of the Reynolds number Re, defined using the pipe diameter d and Û, from 105 to 5830) and for values of the Stokes parameter λ = ½d(ω/2ν)½ (ν = kinematic viscosity and ω = angular frequency) from 1·35 to 6·19. Three types of turbulent flow regime have been detected: weakly turbulent flow, conditionally turbulent flow and fully turbulent flow. Demarcation of the flow regimes is possible on Rλ, λ or Re, λ diagrams. The critical Reynolds number of the first transition decreases as the Stokes parameter increases. In the conditionally turbulent flow, turbulence is generated suddenly in the decelerating phase and the profile of the velocity distribution changes drastically. In the accelerating phase, the flow recovers to laminar. This type of partially turbulent flow persists even at Reynolds numbers as high as Re = 5830 if the value of the Stokes parameter is high.

Estimating the value of von Kármán’s constant in turbulent pipe flow

2014 ◽  
Vol 749 ◽  
pp. 79-98 ◽  
Author(s):  
S. C. C. Bailey ◽  
M. Vallikivi ◽  
M. Hultmark ◽  
A. J. Smits
Keyword(s):  
Pipe Flow ◽  
Turbulent Pipe Flow ◽  
Data Sets ◽  
Mean Velocity ◽  
Princeton University ◽  
Best Estimate ◽  
Data Points ◽  
Smooth Pipe ◽  
The Mean ◽  
Hot Wires

AbstractFive separate data sets on the mean velocity distributions in the Princeton University/ONR Superpipe are used to establish the best estimate for the value of von Kármán’s constant for the flow in a fully developed, hydraulically smooth pipe. The profiles were taken using Pitot tubes, conventional hot wires and nanoscale thermal anemometry probes. The value of the constant was found to vary significantly due to measurement uncertainties in the mean velocity, friction velocity and the wall distance, and the number of data points included in the analysis. The best estimate for the von Kármán constant in turbulent pipe flow is found to be $0.40 \pm 0.02$. A more precise estimate will require improved instrumentation.

Identification of Transition to Turbulence in a Highly Accelerated Start-Up Pipe Flow

2005 ◽  
Vol 128 (4) ◽  
pp. 680-686 ◽  
Author(s):  
T. Koppel ◽  
L. Ainola
Keyword(s):  
Pipe Flow ◽  
Laplace Transformation ◽  
Transformation Method ◽  
Transition To Turbulence ◽  
Unsteady Boundary Layer ◽  
Physical Explanation ◽  
Pipe Flows ◽  
Flow Parameters ◽  
Start Up ◽  
Laplace Transformation Method

The transition from a laminar to a turbulent flow in highly accelerated start-up pipe flows is described. In these flows, turbulence springs up simultaneously over the entire length of the pipe near the wall. The unsteady boundary layer in the pipe was analyzed theoretically with the Laplace transformation method and the asymptotic method for small values of time. From the experimental results available, relationships between the flow parameters and the transition time were derived. These relationships are characterized by the analytical forms. A physical explanation for the regularities in the turbulence spring-up time is proposed.

scholarly journals Transition to turbulence in the rotating disk boundary layer of a rotor–stator cavity

2018 ◽  
Vol 848 ◽  
pp. 631-647 ◽  
Author(s):  
Eunok Yim ◽  
J.-M. Chomaz ◽  
D. Martinand ◽  
E. Serre
Keyword(s):  
Boundary Layer ◽  
Similarity Solution ◽  
Rotating Disk ◽  
Transition To Turbulence ◽  
Mean Flow ◽  
Self Similarity ◽  
Mean Velocity ◽  
Global Mode ◽  
Spatial Growth ◽  
The Mean

The transition to turbulence in the rotating disk boundary layer is investigated in a closed cylindrical rotor–stator cavity via direct numerical simulation (DNS) and linear stability analysis (LSA). The mean flow in the rotor boundary layer is qualitatively similar to the von Kármán self-similarity solution. The mean velocity profiles, however, slightly depart from theory as the rotor edge is approached. Shear and centrifugal effects lead to a locally more unstable mean flow than the self-similarity solution, which acts as a strong source of perturbations. Fluctuations start rising there, as the Reynolds number is increased, eventually leading to an edge-driven global mode, characterized by spiral arms rotating counter-clockwise with respect to the rotor. At larger Reynolds numbers, fluctuations form a steep front, no longer driven by the edge, and followed downstream by a saturated spiral wave, eventually leading to incipient turbulence. Numerical results show that this front results from the superposition of several elephant front-forming global modes, corresponding to unstable azimuthal wavenumbers $m$, in the range $m\in [32,78]$. The spatial growth along the radial direction of the energy of these fluctuations is quantitatively similar to that observed experimentally. This superposition of elephant modes could thus provide an explanation for the discrepancy observed in the single disk configuration, between the corresponding spatial growth rates values measured by experiments on the one hand, and predicted by LSA and DNS performed in an azimuthal sector, on the other hand.

Forward and Backward Running Waves in the Arteries: Analysis Using the Method of Characteristics

1990 ◽  
Vol 112 (3) ◽  
pp. 322-326 ◽  
Author(s):  
K. H. Parker ◽  
C. J. H. Jones
Keyword(s):  
Transient Flow ◽  
Impedance Analysis ◽  
Time Domain Analysis ◽  
Mean Velocity ◽  
One Dimensional ◽  
Acceleration And Deceleration ◽  
The Mean ◽  
The One ◽  
Made In

The one-dimensional equations of flow in the elastic arteries are hyperbolic and admit nonlinear, wavelike solutions for the mean velocity, U, and the pressure, P. Neglecting dissipation, the solutions can be written in terms of wavelets defined as differences of the Riemann invariants across characteristics. This analysis shows that the product, dUdP, is positive definite for forward running wavelets and negative definite for backward running wavelets allowing the determination of the net magnitude and direction of propagating wavelets from pressure and velocity measured at a point in the artery. With the linearizing assumption that intersecting wavelets are additive, the forward and backward running wavelets can be separately calculated. This analysis, applied to measurements made in the ascending aorta of man, shows that forward running wavelets dominate during both the acceleration and deceleration phases of blood flow in the aorta. The forward and backward running waves calculated using the linearized analysis are similar to the results of an impedance analysis of the data. Unlike the impedance analysis, however, this is a time domain analysis which can be applied to nonperiodic or transient flow.

Nonasymptotic behavior of developing turbulent pipe flow

1976 ◽  
Vol 54 (3) ◽  
pp. 268-278 ◽  
Author(s):  
J. K. Reichert ◽  
R. S. Azad
Keyword(s):  
Reynolds Number ◽  
Pipe Flow ◽  
Reynolds Numbers ◽  
Peak Position ◽  
Turbulent Pipe Flow ◽  
Shear Stresses ◽  
Mean Velocity ◽  
Inlet Region ◽  
The Mean ◽  
Hot Film

Detailed measurements of mean velocity U profiles, in the inlet 70 diameters of a pipe, show that the development of turbulent pipe flow is nonasymptotic. Experiments were done at seven Reynolds numbers in the range 56 000–15 3000. Contours of U and V fields are presented for two representative Reynolds numbers. A U component peak exceeding the fully developed values has been found to occur along the pipe centerline. The Reynolds number behavior of the peak position has been determined. Hot film measurements of the mean wall shear stresses in the inlet region also show a nonasymptotic development consistent with the mean velocity results.

Similarity in non-rotating and rotating turbulent pipe flows

1999 ◽  
Vol 379 ◽  
pp. 1-22 ◽  
Author(s):  
MARTIN OBERLACK
Keyword(s):  
Reynolds Number ◽  
Scaling Laws ◽  
Stokes Equations ◽  
Scaling Law ◽  
Navier Stokes ◽  
Invariant Solutions ◽  
Mean Velocity ◽  
Navier Stokes Equations ◽  
Pipe Flows ◽  
The Mean

The Lie group approach developed by Oberlack (1997) is used to derive new scaling laws for high-Reynolds-number turbulent pipe flows. The scaling laws, or, in the methodology of Lie groups, the invariant solutions, are based on the mean and fluctuation momentum equations. For their derivation no assumptions other than similarity of the Navier–Stokes equations have been introduced where the Reynolds decomposition into the mean and fluctuation quantities has been implemented. The set of solutions for the axial mean velocity includes a logarithmic scaling law, which is distinct from the usual law of the wall, and an algebraic scaling law. Furthermore, an algebraic scaling law for the azimuthal mean velocity is obtained. In all scaling laws the origin of the independent coordinate is located on the pipe axis, which is in contrast to the usual wall-based scaling laws. The present scaling laws show good agreement with both experimental and DNS data. As observed in experiments, it is shown that the axial mean velocity normalized with the mean bulk velocity um has a fixed point where the mean velocity equals the bulk velocity independent of the Reynolds number. An approximate location for the fixed point on the pipe radius is also given. All invariant solutions are consistent with all higher-order correlation equations. A large-Reynolds-number asymptotic expansion of the Navier–Stokes equations on the curved wall has been utilized to show that the near-wall scaling laws for at surfaces also apply to the near-wall regions of the turbulent pipe flow.

Effect of Initial Constant Acceleration on the Transition to Turbulence in Transient Circular Pipe Flow

2010 ◽  
Vol 132 (11) ◽  
Author(s):  
Manabu Iguchi ◽  
Kazuyoshi Nishihara ◽  
Yusuke Nakahata ◽  
Charles W. Knisely
Keyword(s):  
Reynolds Number ◽  
Pipe Flow ◽  
Time Lag ◽  
Transition To Turbulence ◽  
Circular Pipe ◽  
Constant Acceleration ◽  
Mean Velocity ◽  
Cross Sectional ◽  
Circular Pipe Flow ◽  
The Cross

Experimental investigation is carried out on the transition to turbulence in a transient circular pipe flow. The flow is accelerated from rest at a constant acceleration until its cross-sectional mean velocity reaches a constant value. Accordingly, the history of the flow thus generated consists of the initial stage of constant acceleration and the following stage of constant cross-sectional mean velocity. The final Reynolds number based on the constant cross-sectional mean velocity and the pipe diameter is chosen to be much greater than the transition Reynolds number of a steady pipe flow of about 3000. The transition to turbulence is judged from the output signal of the axial velocity component and its root-mean-square value measured with a hot-wire anemometer. A turbulent slug appears after the cross-sectional mean velocity of the flow reaches the predetermined constant value under every experimental condition. Turbulence production therefore is suppressed, while the flow is accelerated. The time lag for the appearance of the turbulent slug after the cross-sectional mean velocity of the flow reaches the constant value decreases with an increase in the constant acceleration value. An empirical equation is proposed for estimating the time lag. The propagation velocity of the leading edge of the turbulent slug is independent of the constant acceleration value under the present experimental conditions.

scholarly journals Effect of the History of Cross-Sectional Mean Velocity on the Transition to Turbulence in Transient Circular Pipe Flow(Fluids Engineering)

2010 ◽  
Vol 76 (770) ◽  
pp. 1464-1472
Author(s):  
Kazuyoshi NISHIHARA ◽  
Ayumu GOTOU ◽  
Yoshiaki UEDA ◽  
Yasushi SASAKI ◽  
Yusuke NAKAHATA ◽  
...  
Keyword(s):  
Pipe Flow ◽  
Transition To Turbulence ◽  
Circular Pipe ◽  
Mean Velocity ◽  
Cross Sectional ◽  
Circular Pipe Flow ◽  
History Of
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