scholarly journals Subcritical and supercritical bifurcations in axisymmetric viscoelastic pipe flows

2021 ◽  
Vol 929 ◽  
Author(s):  
Dongdong Wan ◽  
Guangrui Sun ◽  
Mengqi Zhang
Keyword(s):  
Pipe Flow ◽  
Landau Equation ◽  
Polymer Concentration ◽  
Weissenberg Number ◽  
Transition To Turbulence ◽  
Solution Viscosity ◽  
Critical Conditions ◽  
Nonlinear Phenomena ◽  
Theoretical Understanding ◽  
Pipe Flows

Axisymmetric viscoelastic pipe flow of Oldroyd-B fluids has been recently found to be linearly unstable by Garg et al. (Phys. Rev. Lett., vol. 121, 2018, 024502). From a nonlinear point of view, this means that the flow can transition to turbulence supercritically, in contrast to the subcritical Newtonian pipe flows. Experimental evidence of subcritical and supercritical bifurcations of viscoelastic pipe flows have been reported, but these nonlinear phenomena have not been examined theoretically. In this work, we study the weakly nonlinear stability of this flow by performing a multiple-scale expansion of the disturbance around linear critical conditions. The perturbed parameter is the Reynolds number with the others being unperturbed. A third-order Ginzburg–Landau equation is derived with its coefficient indicating the bifurcation type of the flow. After exploring a large parameter space, we found that polymer concentration plays an important role: at high polymer concentrations (or small solvent-to-solution viscosity ratio $\beta \lessapprox 0.785$ ), the nonlinearity stabilizes the flow, indicating that the flow will bifurcate supercritically, while at low polymer concentrations ( $\beta \gtrapprox 0.785$ ), the flow bifurcation is subcritical. The results agree qualitatively with experimental observations where critical $\beta \approx 0.855$ . The pipe flow of upper convected Maxwell fluids can be linearly unstable and its bifurcation type is also supercritical. At a fixed value of $\beta$ , the Landau coefficient scales with the inverse of the Weissenberg number ( $Wi$ ) when $Wi$ is sufficiently large. The present analysis provides a theoretical understanding of the recent studies on the supercritical and subcritical routes to the elasto-inertial turbulence in viscoelastic pipe flows.

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.

Predicting Drag Reduction in Turbulent Pipe Flow With Relaxation Time of Polymer Additives

2018 ◽  
Author(s):  
Xin Zhang ◽  
Xili Duan ◽  
Yuri Muzychka ◽  
Zongming Wang
Keyword(s):  
Experimental Data ◽  
Relaxation Time ◽  
Drag Reduction ◽  
Pipe Flow ◽  
Polymer Concentration ◽  
Weissenberg Number ◽  
Turbulent Pipe Flow ◽  
Dimensionless Number ◽  
Polymer Additives ◽  
Dilute Solution

This paper presents an experimental study on drag reduction induced by PEO (Polyethylene oxide) in a fully turbulent pipe flow. The objective of this work is to develop a correlation to predict drag reduction using the relaxation time of the polymer additives under dilute solution conditions, i.e., the polymer concentration is less than the overlap concertation. This paper discusses the meaning of relaxation time of polymers, and why the Weissenberg number, a dimensionless number that is related to the relaxation time and shear rate, is independent on the concentration in the dilute solution. Experimental data of drag reduction in a pipe flow are obtained from measurements using a flow loop. A correlation to predict drag reduction with the Weissenberg number and polymer concentration is established and a good agreement is shown between the predicted values and experimental data. The new correlation using the Weissenberg number and polymer concentration is shown to cost less to develop than one using the Reynolds number, in which larger pipes or higher flow rates are required.

Rapid Transition to Turbulence in Pipe Flows Accelerated From Rest

2003 ◽  
Vol 125 (6) ◽  
pp. 1072-1075 ◽  
Author(s):  
David Greenblatt ◽  
Edward A. Moss
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Laminar Boundary Layer ◽  
Pipe Flow ◽  
Velocity Profiles ◽  
Transition To Turbulence ◽  
Acceleration Phase ◽  
Pipe Flows ◽  
Rapid Transition ◽  
Rapid Deceleration

Rapid transition to turbulence in a pipe flow, initially at rest, was achieved by temporally accelerating the flow and then sharply decelerating it to its final Reynolds number. The acceleration phase was characterized by the growth of a laminar boundary layer close to the wall. The subsequent rapid deceleration resulted in inflectional velocity profiles near the wall, followed immediately by transition to turbulence. The time taken to transition was significantly less than the time to transition in a pipe flow monotonically accelerated to the same Reynolds number. Transition is intrinsically different to that observed in oscillatory pipe flows, but is qualitatively similar to pipe flows decelerated to rest.

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 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 Perspective on the Response of Turbulent Pipe Flows to Strong Perturbations

Fluids ◽  
2021 ◽  
Vol 6 (6) ◽  
pp. 208
Author(s):  
Liuyang Ding ◽  
Tyler Van Buren ◽  
Ian E. Gunady ◽  
Alexander J. Smits
Keyword(s):  
Pipe Flow ◽  
Abrupt Change ◽  
Pipe Wall ◽  
Surface Condition ◽  
Initial Response ◽  
Body Of Revolution ◽  
Future Directions ◽  
Pipe Flows ◽  
Roughness Elements ◽  
Pipe Geometry

Pipe flow responds to strong perturbations in ways that are fundamentally different from the response exhibited by boundary layers undergoing a similar perturbation, primarily because of the confinement offered by the pipe wall, and the need to satisfy continuity. We review such differences by examining previous literature, with a particular focus on the response of pipe flow to three different kinds of disturbances: the abrupt change in surface condition from rough to smooth, the obstruction due to presence of a single square bar roughness elements of different sizes, and the flow downstream of a streamlined body-of-revolution placed on the centerline of the pipe. In each case, the initial response is strongly influenced by the pipe geometry, but far downstream all three flows display a common feature, which is the very slow, second-order recovery that can be explained using a model based on the Reynolds stress equations. Some future directions for research are also given.

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.

scholarly journals Pipe flow with large particles and their impact on the transition to turbulence

2020 ◽  
Vol 5 (11) ◽  
Author(s):  
Martin Leskovec ◽  
Fredrik Lundell ◽  
Fredrik Innings
Keyword(s):  
Pipe Flow ◽  
Transition To Turbulence ◽  
Large Particles

Effect of viscoelasticity on the soft-wall transition and turbulence in a microchannel

2017 ◽  
Vol 812 ◽  
pp. 1076-1118 ◽  
Author(s):  
S. S. Srinivas ◽  
V. Kumaran
Keyword(s):  
Molecular Weight ◽  
Reynolds Number ◽  
Reynolds Stress ◽  
Mass Fraction ◽  
Rectangular Cross Section ◽  
Pure Water ◽  
Polymer Concentration ◽  
Wall Turbulence ◽  
Solution Viscosity ◽  
Soft Wall

The modification of soft-wall turbulence in a microchannel due to small amounts of polymer dissolved in water is experimentally studied. The microchannels are of rectangular cross-section with height ${\sim}$160 $\unicode[STIX]{x03BC}\text{m}$, width ${\sim}$1.5 mm and length ${\sim}$3 cm, with three walls made of hard polydimethylsiloxane (PDMS) gel, and one wall made of soft PDMS gel with an elasticity modulus of ${\sim}$18 kPa. Solutions of polyacrylamide of molecular weight $5\times 10^{6}$ and mass fraction up to 50 ppm, and of molecular weight $4\times 10^{4}$ and mass fraction up to 1500 ppm, are used in the experiments. In all cases, the solutions are in the dilute limit below the critical overlap concentration, and the solution viscosity does not exceed that of water by more than 10 %. Two distinct types of flow modifications are observed below and above a threshold mass fraction for the polymer, $w_{t}$, which is ${\sim}$1 ppm and 500 ppm for the solutions of polyacrylamide with molecular weights $5\times 10^{6}$ and $4\times 10^{4}$, respectively. At or below $w_{t}$, there is no change in the transition Reynolds number, but there is significant turbulence attenuation, by up to a factor of 2 in the root-mean-square velocities and a factor of 4 in the Reynolds stress. When the polymer concentration increases beyond $w_{t}$, there is a decrease in the transition Reynolds number and in the intensity of the turbulent fluctuations. The lowest transition Reynolds number is ${\sim}$35 for the solution of polyacrylamide with molecular weight $5\times 10^{6}$ and mass fraction 50 ppm (in contrast to 260–290 for pure water). The fluctuating velocities in the streamwise and cross-stream directions are lower by a factor of 5, and the Reynolds stress is lower by a factor of 10, in comparison to pure water.

scholarly journals Dynamics of viscoelastic pipe flow at low Reynolds numbers in the maximum drag reduction limit

2019 ◽  
Vol 874 ◽  
pp. 699-719 ◽  
Author(s):  
Jose M. Lopez ◽  
George H. Choueiri ◽  
Björn Hof
Keyword(s):  
Drag Reduction ◽  
Turbulent Flows ◽  
Pipe Flow ◽  
Domain Size ◽  
Reynolds Numbers ◽  
Weissenberg Number ◽  
Pipe Length ◽  
Low Reynolds Numbers ◽  
Maximum Drag Reduction ◽  
Low Reynolds

Polymer additives can substantially reduce the drag of turbulent flows and the upper limit, the so-called state of ‘maximum drag reduction’ (MDR), is to a good approximation independent of the type of polymer and solvent used. Until recently, the consensus was that, in this limit, flows are in a marginal state where only a minimal level of turbulence activity persists. Observations in direct numerical simulations at low Reynolds numbers ($Re$) using minimal sized channels appeared to support this view and reported long ‘hibernation’ periods where turbulence is marginalized. In simulations of pipe flow at $Re$ near transition we find that, indeed, with increasing Weissenberg number ($Wi$), turbulence expresses long periods of hibernation if the domain size is small. However, with increasing pipe length, the temporal hibernation continuously alters to spatio-temporal intermittency and here the flow consists of turbulent puffs surrounded by laminar flow. Moreover, upon an increase in $Wi$, the flow fully relaminarizes, in agreement with recent experiments. At even larger $Wi$, a different instability is encountered causing a drag increase towards MDR. Our findings hence link earlier minimal flow unit simulations with recent experiments and confirm that the addition of polymers initially suppresses Newtonian turbulence and leads to a reverse transition. The MDR state on the other hand results at these low$Re$ from a separate instability and the underlying dynamics corresponds to the recently proposed state of elasto-inertial turbulence.

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