scholarly journals The effect of pulsation frequency on transition in pulsatile pipe flow

2018 ◽  
Vol 857 ◽  
pp. 937-951 ◽  
Author(s):  
Duo Xu ◽  
Marc Avila
Keyword(s):  
Pipe Flow ◽  
Experimental Studies ◽  
Quantitative Agreement ◽  
Transition To Turbulence ◽  
Pulsation Frequency ◽  
Pipe Length ◽  
Pulsation Amplitude ◽  
Frequency Regime ◽  
Pulsatile Flows ◽  
The Stability

Pulsatile flows are common in nature and in applications, but their stability and transition to turbulence are still poorly understood. Even in the simple case of pipe flow subject to harmonic pulsation, there is no consensus among experimental studies on whether pulsation delays or enhances transition. We here report direct numerical simulations of pulsatile pipe flow at low pulsation amplitude$A\leqslant 0.4$. We use a spatially localized impulsive disturbance to generate a single turbulent puff and track its dynamics as it travels downstream. The computed relaminarization statistics are in quantitative agreement with the experiments of Xuet al. (J. Fluid Mech., vol. 831, 2017, pp. 418–432) and support the conclusion that increasing the pulsation amplitude and lowering the frequency enhance the stability of the flow. In the high-frequency regime, the behaviour of steady pipe flow is recovered. In addition, we show that, when the pipe length does not permit the observation of a full cycle, a reduction of the transition threshold is observed. We obtain an equation quantifying this effect and compare it favourably with the measurements of Stettler & Hussain (J. Fluid Mech., vol. 170, 1986, pp. 169–197). Our results resolve previous discrepancies, which are due to different pipe lengths, perturbation methods and criteria chosen to quantify transition in experiments.

scholarly journals Experimental and theoretical progress in pipe flow transition

2008 ◽  
Vol 366 (1876) ◽  
pp. 2671-2684 ◽  
Author(s):  
A.P Willis ◽  
J Peixinho ◽  
R.R Kerswell ◽  
T Mullin
Keyword(s):  
Pipe Flow ◽  
Quantitative Agreement ◽  
Travelling Wave ◽  
Turbulent Pipe Flow ◽  
Transition To Turbulence ◽  
Reynolds Number Flow ◽  
Threshold Amplitude ◽  
Number Flow ◽  
The Stability ◽  
Laminar State

There have been many investigations of the stability of Hagen–Poiseuille flow in the 125 years since Osborne Reynolds' famous experiments on the transition to turbulence in a pipe, and yet the pipe problem remains the focus of attention of much research. Here, we discuss recent results from experimental and numerical investigations obtained in this new century. Progress has been made on three fundamental issues: the threshold amplitude of disturbances required to trigger a transition to turbulence from the laminar state; the threshold Reynolds number flow below which a disturbance decays from turbulence to the laminar state, with quantitative agreement between experimental and numerical results; and understanding the relevance of recently discovered families of unstable travelling wave solutions to transitional and turbulent pipe flow.

scholarly journals Transition to turbulence in pulsating pipe flow

2017 ◽  
Vol 831 ◽  
pp. 418-432 ◽  
Author(s):  
Duo Xu ◽  
Sascha Warnecke ◽  
Baofang Song ◽  
Xingyu Ma ◽  
Björn Hof
Keyword(s):  
Pipe Flow ◽  
Oscillation Amplitude ◽  
Intermediate Frequency ◽  
Finite Amplitude ◽  
Decay Rates ◽  
Transition To Turbulence ◽  
Pulsation Frequency ◽  
Onset Of Turbulence ◽  
Frequency Regime ◽  
The Impact

Fluid flows in nature and applications are frequently subject to periodic velocity modulations. Surprisingly, even for the generic case of flow through a straight pipe, there is little consensus regarding the influence of pulsation on the transition threshold to turbulence: while most studies predict a monotonically increasing threshold with pulsation frequency (i.e. Womersley number, $\unicode[STIX]{x1D6FC}$), others observe a decreasing threshold for identical parameters and only observe an increasing threshold at low $\unicode[STIX]{x1D6FC}$. In the present study we apply recent advances in the understanding of transition in steady shear flows to pulsating pipe flow. For moderate pulsation amplitudes we find that the first instability encountered is subcritical (i.e. requiring finite amplitude disturbances) and gives rise to localized patches of turbulence (‘puffs’) analogous to steady pipe flow. By monitoring the impact of pulsation on the lifetime of turbulence we map the onset of turbulence in parameter space. Transition in pulsatile flow can be separated into three regimes. At small Womersley numbers the dynamics is dominated by the decay turbulence suffers during the slower part of the cycle and hence transition is delayed significantly. As shown in this regime thresholds closely agree with estimates based on a quasi-steady flow assumption only taking puff decay rates into account. The transition point predicted in the zero $\unicode[STIX]{x1D6FC}$ limit equals to the critical point for steady pipe flow offset by the oscillation Reynolds number (i.e. the dimensionless oscillation amplitude). In the high frequency limit on the other hand, puff lifetimes are identical to those in steady pipe flow and hence the transition threshold appears to be unaffected by flow pulsation. In the intermediate frequency regime the transition threshold sharply drops (with increasing $\unicode[STIX]{x1D6FC}$) from the decay dominated (quasi-steady) threshold to the steady pipe flow level.

On transition of the pulsatile pipe flow

1986 ◽  
Vol 170 ◽  
pp. 169-197 ◽  
Author(s):  
J. C. Stettler ◽  
A. K. M. Fazle Hussain
Keyword(s):  
Steady Flow ◽  
Pipe Flow ◽  
Three Dimensional ◽  
Building Blocks ◽  
Rate Of Change ◽  
Turbulent Pipe Flow ◽  
Dimensional Parameter ◽  
Pipe Length ◽  
The Mean ◽  
The Stability

Transition in a pipe flow with a superimposed sinusoidal modulation has been studied in a straight circular water pipe using laser-Doppler anemometer (LDA) techniques. This study has determined the stability–transition boundary in the three-dimensional parameter space defined by the mean and modulation Reynolds numbers Rem, Remω and the frequency parameter λ. Furthermore, it documents the mean passage frequency Fp of ‘turbulent plugs’ as functions of Rem’ Remω and λ. This study also delineates the conditions when plugs occur randomly in time (as in the steady flow) or phase-locked with the excitation. The periodic flow requires a new definition of the transitional Reynolds number Rer, identified on the basis of the rate of change of Fp with Rem. The extent of increase or decrease in Rer from the corresponding steady flow value depends on λ and Remω. At any Rem and Remω, maximum stabilization occurs at λ ≈ 5. With increasing Remω, the ‘stabilization bandwidth’ of modulation frequencies increases and then abruptly decreases after levelling off. The maximum stabilization bandwidth depends strongly on Rem, decreasing with increasing Rem. Previously reported observations of turbulence during deceleration, followed by a relaminarization during acceleration, can be explained in terms of a new phenomenon: namely, periodic modulation produces longitudinally periodic cells of turbulent fluid ‘plugs’ which differ in structural details from ‘puffs’ or ‘slugs’ in steady transitional pipe flows and are called patches. The length of a patch could be increased continuously from zero to the entire pipe length by increasing Rem. This tends to question the concept that all turbulent plugs (and even the fully-turbulent pipe flow) consists of many identical elementary plugs as basic ‘building blocks’.

Experimental study of the stability and dynamics of a two-dimensional ideal vortex under external strain

2018 ◽  
Vol 848 ◽  
pp. 256-287 ◽  
Author(s):  
N. C. Hurst ◽  
J. R. Danielson ◽  
D. H. E. Dubin ◽  
C. M. Surko
Keyword(s):  
Ideal Fluid ◽  
Experimental Studies ◽  
Quantitative Agreement ◽  
Two Dimensions ◽  
Global Dynamics ◽  
Two Dimensional ◽  
Plasma Dynamics ◽  
Electron Plasmas ◽  
Precise Control ◽  
The Stability

The dynamics of two-dimensional (2-D) ideal fluid vortices is studied experimentally in the presence of an irrotational strain flow. Laboratory experiments are conducted using strongly magnetized pure electron plasmas, a technique which is made possible by the isomorphism between the drift–Poisson equations describing plasma dynamics transverse to the field and the 2-D Euler equations describing an ideal fluid. The electron plasma system provides an excellent opportunity to study the dynamics of a 2-D Euler fluid due to weak dissipation and weak 3-D effects, simple diagnosis and precise control. The plasma confinement apparatus used here was designed specifically to study vortex dynamics under the influence of external flow by applying boundary conditions in two dimensions. Additionally, vortex-in-cell simulations are carried out to complement the experimental results and to extend the parameter range of the studies. It is shown that the global dynamics of a quasi-flat vorticity profile is in good quantitative agreement with the theory of a piecewise-constant elliptical patch of vorticity, including the equilibria, dynamical orbits and stability properties. Deviations from the elliptical patch theory are observed for non-flat vorticity profiles; they include inviscid damping of the orbits and modified stability limits. The dependence of these phenomena on the flatness of the initial profile is discussed. The relationship of these results to other theoretical, numerical and experimental studies is also discussed.

Transition to turbulence in constant-mass-flux pipe flow

1995 ◽  
Vol 289 ◽  
pp. 83-114 ◽  
Author(s):  
A. G. Darbyshire ◽  
T. Mullin
Keyword(s):  
Mass Flux ◽  
Pipe Flow ◽  
Critical Level ◽  
Transition To Turbulence ◽  
Constant Mass ◽  
Critical Amplitude ◽  
Injection Point ◽  
Driven Systems ◽  
The Stability ◽  
Transition Behaviour

We report the results of an experimental study of the transition to turbulence in a pipe under the condition of constant mass flux. The transition behaviour and structures observed in this experiment were qualitatively the same as those described in previous reported studies performed in pressure-driven systems. A variety of jet and suction devices were used to create repeatable disturbances which were then used to test the stability of developed Poiseuille flow. The Reynolds number (Re) and the parameters governing the disturbances were varied and the outcome, whether or not transition occurred some distance downstream of the injection point, was recorded. It was found that a critical amplitude of disturbance was required to cause transition at a given Re and that this amplitude varied in a systematic way with Re. This finite, critical level was found to be a robust feature, and was relatively insensitive to the form of disturbance. We interpret this as evidence for disconnected solutions which may provide a pointer for making progress in this fundamental, and as yet unresolved, problem in fluid mechanics.

scholarly journals Transition of unsteady velocity profiles with reverse flow

1998 ◽  
Vol 374 ◽  
pp. 251-283 ◽  
Author(s):  
DEBOPAM DAS ◽  
JAYWANT H. ARAKERI
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Pipe Flow ◽  
Boundary Layer Thickness ◽  
Reverse Flow ◽  
Boundary Layer Separation ◽  
Velocity Profiles ◽  
Transition To Turbulence ◽  
Unsteady Boundary Layer ◽  
The Stability

This paper deals with the stability and transition to turbulence of wall-bounded unsteady velocity profiles with reverse flow. Such flows occur, for example, during unsteady boundary layer separation and in oscillating pipe flow. The main focus is on results from experiments in time-developing flow in a long pipe, which is decelerated rapidly. The flow is generated by the controlled motion of a piston. We obtain analytical solutions for laminar flow in the pipe and in a two-dimensional channel for arbitrary piston motions. By changing the piston speed and the length of piston travel we cover a range of values of Reynolds number and boundary layer thickness. The velocity profiles during the decay of the flow are unsteady with reverse flow near the wall, and are highly unstable due to their inflectional nature. In the pipe, we observe from flow visualization that the flow becomes unstable with the formation of what appears to be a helical vortex. The wavelength of the instability ≃3δ where δ is the average boundary layer thickness, the average being taken over the time the flow is unstable. The time of formation of the vortices scales with the average convective time scale and is ≃39/(Δū/δ), where Δu=(umax−umin) and umax, umin and δ are the maximum velocity, minimum velocity and boundary layer thickness respectively at each instant of time. The time to transition to turbulence is ≃33/(Δū/δ). Quasi-steady linear stability analysis of the velocity profiles brings out two important results. First that the stability characteristics of velocity profiles with reverse flow near the wall collapse when scaled with the above variables. Second that the wavenumber corresponding to maximum growth does not change much during the instability even though the velocity profile does change substantially. Using the results from the experiments and the stability analysis, we are able to explain many aspects of transition in oscillating pipe flow. We postulate that unsteady boundary layer separation at high Reynolds numbers is probably related to instability of the reverse flow region.

Pulsating pipe flow with large-amplitude oscillations in the very high frequency regime. Part 2. Phase-averaged analysis

2015 ◽  
Vol 766 ◽  
pp. 272-296 ◽  
Author(s):  
M. Manna ◽  
A. Vacca ◽  
R. Verzicco
Keyword(s):  
Pipe Flow ◽  
Experimental Studies ◽  
Turbulence Models ◽  
Turbulent Pipe Flow ◽  
Very High Frequency ◽  
Frequency Regime ◽  
Order Of Magnitude ◽  
Flow Cycle ◽  
Mean Current

AbstractThis paper is the follow-up of a previous study (Manna, Vacca & Verzicco,J. Fluid Mech., vol. 700, 2012, pp. 246–282) that numerically investigated the effects of a harmonic volume forcing on the turbulent pipe flow at a bulk Reynolds number of$\simeq 5900$. There, the investigation was focused on the time- and space-averaged statistics of the first- and second-order moments of the velocity, the vorticity fluctuations and the Reynolds stress budgets in order to study the changes induced on the mean current by the oscillating component. The amplitude of the latter was used as a parameter for the analysis. However, as the flow is inherently unsteady, the phase-averaged statistics are also of interest, and this is the motivation and subject of the present study. Here, we show the variability of the above quantities during different phases of the flow cycle and how they are affected by the amplitude of the oscillation. It is observed that when the ratio of the oscillating to the time-constant velocity component is of the order of one (${\it\beta}\simeq O(1)$), the phase-averaged profiles are appreciably influenced by the pulsation, although only small deviations of the time-averaged counterparts have been documented. In contrast, when that ratio is increased by one order of magnitude (${\it\beta}\simeq O(10)$) the phase- and cycle-averaged quantities differ considerably, especially during the decelerating part of the cycle. In more detail, the amplitude and the phase of all turbulence statistics show significant variations with${\it\beta}$. This variability has important implications in the dynamics and modelling of these flows. Since the data have been obtained by direct numerical simulations and validated by comparisons with experimental studies, the results could be used for validation of codes, testing of turbulence models or measurement procedures.

scholarly journals Performance Evaluation of Heading-and-Winning Machines in the Conditions of Potash Mines

2021 ◽  
Vol 11 (8) ◽  
pp. 3444
Author(s):  
Sergey A. Lavrenko ◽  
Dmitriy I. Shishlyannikov
Keyword(s):  
Energy Efficiency ◽  
Experimental Studies ◽  
Efficiency Coefficient ◽  
Mechanized Method ◽  
Methodological Approaches ◽  
The Stability ◽  
Technical Solutions ◽  
Potash Mine ◽  
Complex Indicators ◽  
Potassium Magnesium

The authors focus on the process of potash ore production by a mechanized method. They show that currently there are no approved procedures for assessing the performance of heading-and-winning machines operating in the conditions of potash mines. This causes difficulties in determining the field of application of heading-and-winning machines, complicates the search for implicit technical solutions for the modernisation of existing models of mining units, prohibits real-time monitoring of the stability of stope-based technological processes and makes it difficult to assess the performance of the services concerning mining enterprises. The work represents an aggregate assessment of the performance of heading-and-winning machines for potash mines by determining complex indicators describing the technological and technical levels of organising the work in stopes. Such indicators are the coefficients of productivity and energy efficiency, respectively. Experimental studies have been carried out in the conditions of the potash mine of the Verkhnekamskoye potassium-magnesium salt deposit to assess the performance of the latest and most productive Ural-20R heading-and-winning machines manufactured in Russia. Using the above methodological approaches, this paper shows that the unsatisfactory technological performance of the studied machine is due to the low productivity of the mine district transport. The average productivity coefficient was 0.29. At the same time, high values of the energy efficiency coefficient show that the productivity of the machine is on par with design conditions.

scholarly journals Extended-State-Observer-Based Super Twisting Control for Pneumatic Muscle Actuators

Actuators ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 35
Author(s):  
Yu Cao ◽  
Zhongzheng Fu ◽  
Mengshi Zhang ◽  
Jian Huang
Keyword(s):  
Control Method ◽  
Experimental Studies ◽  
State Observer ◽  
Extended State Observer ◽  
Extended State ◽  
Pneumatic Muscle ◽  
System States ◽  
The Stability ◽  
Twisting Control ◽  
Muscle Actuators

This paper presents a tracking control method for pneumatic muscle actuators (PMAs). Considering that the PMA platform only feedbacks position, and the velocity and disturbances cannot be observed directly, we use the extended-state-observer (ESO) for simultaneously estimating the system states and disturbances by using measurable variables. Integrated with the ESO, a super twisting controller (STC) is design based on estimated states to realize the high-precision tracking. According to the Lyapunov theorem, the stability of the closed-loop system is ensured. Simulation and experimental studies are conducted, and the results show the convergence of the ESO and the effectiveness of the proposed method.

Stability of Hagen-Poiseuille flow with superimposed rigid rotation

1976 ◽  
Vol 73 (1) ◽  
pp. 153-164 ◽  
Author(s):  
P.-A. Mackrodt
Keyword(s):  
Poiseuille Flow ◽  
Pipe Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Neutral Curve ◽  
Rigid Rotation ◽  
Transition To Turbulence ◽  
Navier Stokes ◽  
Navier Stokes Equations

The linear stability of Hagen-Poiseuille flow (Poiseuille pipe flow) with superimposed rigid rotation against small three-dimensional disturbances is examined at finite and infinite axial Reynolds numbers. The neutral curve, which is obtained by numerical solution of the system of perturbation equations (derived from the Navier-Stokes equations), has been confirmed for finite axial Reynolds numbers by a few simple experiments. The results suggest that, at high axial Reynolds numbers, the amount of rotation required for destabilization could be small enough to have escaped notice in experiments on the transition to turbulence in (nominally) non-rotating pipe flow.

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