Pulsatile Pipe Flow Research Articles

Numerical study of the pulsatile flow and aeroacoustics of straight and curved pipes

From an engineering point of view pulsatile pipe flows, which include the hydrodynamic and acoustic fluctuations, can cause many problems such as vibration, noise and structural fatigue etc. Knowledge of the characteristics of hydrodynamic fluctuations (pseudo sound) and acoustic waves inside pipes particularly those with bends make is crucial to pipeline vibration and noise reduction. Numerical simulation of the pulsatile pipe flows shows challenges especially in curved pipes with different flow modes compounded, and predicting the acoustic fluctuations is even tougher. In this work, the unsteady flows of a straight and curved pipe with a 90° elbow induced by a pulsatile pressure inlet were calculated by Detached Eddy Simulations (DES). The pipe acoustic fields are solved through an acoustic perturbation equation, which takes the time derivative of hydrodynamic pressure as the aeroacoustic source. The characteristics of the flow and sound fields are discussed detailly, and special attention is paid to the influence of the 90° elbow on the curved pipe flow. The results show that the amplitude of hydrodynamic pressure fluctuations decrease almost linearly along the straight pipe, and the 90° elbow has obvious local influence on the flow pressure and velocity especially in the downstream side. The acoustic field is of 1-D standing wave pattern because of the fundamental pulsation frequency lower than the pipe cutoff frequency, and the 90° elbow has only negligible effect on the acoustic field in the flow frequency range.

Turbulent puffs in transitional pulsatile pipe flow at moderate pulsation amplitudes

Turbulent puffs in transitional pulsatile pipe flow at moderate pulsation amplitudes

Time-delayed characteristics of turbulence in pulsatile pipe flow

Direct numerical simulations are performed to study temporal variations of the wall shear stresses and flow dynamics in the turbulent pulsatile pipe flow. The mechanisms, responsible for the paradoxical phenomenon for which the amplitude of the oscillating wall shear stress in the turbulent flow is smaller than that in the laminar flow for the same pulsation conditions, are investigated. It is shown that the delayed response of turbulence in the buffer layer generates a large magnitude of the radial gradient of the Reynolds shear stress near the wall, which counteracts the effect of the oscillating pressure gradient on the change of the streamwise velocity and hence reduces the amplitude of the wall shear stress. Such a delayed response consists of two processes: the delayed development of near-wall streaks and the subsequent energy redistribution from the streamwise velocity fluctuation to the other two co-existing components. This is a dynamical manifestation of the viscoelasticity of turbulent eddies. As the frequency is reduced, the variation of the friction Reynolds number results in a phase-wise variation of the time scale and intensity of the turbulence response, causing the hysteresis of the wall shear stress. Such a phase asymmetry is amplified by the increase of the pulsation amplitude. An examination of the energy spectra reveals that the near-wall streaks are stretched in the streamwise direction during the acceleration phase, and then break up into small-scale structures in the deceleration phase, accompanied by the enhanced dissipation that transforms the turbulent kinetic energy into heat.

Effect of waveform on turbulence transition in pulsatile pipe flow

Pulsatile flow in a straight pipe is a model system for unsteady internal flows in industrial engineering and physiology. In some parameter regimes, the laminar flow is susceptible to helical perturbations, whose transient energy growth scales exponentially with the Reynolds number (Re). In this paper, we link the transient growth of these perturbations to the instantaneous linear instability of the laminar flow. We exploit this link to study the effect of the waveform on turbulence transition by performing linear stability and transient growth analyses of flows driven with different waveforms. We find a higher-energy growth in flows driven with longer low-velocity phases as well as with steeper deceleration and acceleration phases. Finally, we perform direct numerical simulations and show that cases with larger transient growth transition faster to turbulence and exhibit larger turbulence intensities. However, these same cases are also more prone to relaminarisation once turbulence has been established. This highlights that, in pulsatile flows, the linear mechanisms responsible for turbulence transition are distinctly different from the nonlinear mechanisms sustaining turbulence.

Optimal energy growth in pulsatile channel and pipe flows

Pulsatile channel and pipe flows constitute a fundamental flow configuration with significant bearing on many applications in the engineering and medical sciences. Rotating machinery, hydraulic pumps or cardiovascular systems are dominated by time-periodic flows, and their stability characteristics play an important role in their efficient and proper operation. While previous work has mainly concentrated on the modal, harmonic response to an oscillatory or pulsatile base flow, this study employs a direct–adjoint optimisation technique to assess short-term instabilities, identify transient energy-amplification mechanisms and determine their prevalence within a wide parameter space. At low pulsation amplitudes, the transient dynamics is found to be similar to that resulting from the equivalent steady parabolic flow profile, and the oscillating flow component appears to have only a weak effect. After a critical pulsation amplitude is surpassed, linear transient growth is shown to increase exponentially with the pulsation amplitude and to occur mainly during the slow part of the pulsation cycle. In this latter regime, a detailed analysis of the energy transfer mechanisms demonstrates that the huge linear transient growth factors are the result of an optimal combination of Orr mechanism and intracyclic normal-mode growth during half a pulsation cycle. Two-dimensional sinuous perturbations are favoured in channel flow, while pipe flow is dominated by helical perturbations. An extensive parameter study is presented that tracks these flow features across variations in the pulsation amplitude, Reynolds and Womersley numbers, perturbation wavenumbers and imposed time horizon.

Spatiotemporal Intermittency in Pulsatile Pipe Flow.

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 (, ) 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.

Quantifying volume loss of a magnetically localized ferrofluid bolus in pulsatile pipe flow

We report on experiments in a model blood vessel of miscible ferrofluid regions held in place by permanent magnets of different strengths and subject to pulsatile flow at various Womersely numbers of O(10). Using image analysis, we quantify the dependence of ferrofluid volume loss, or “wash away,” rate due to hydrodynamic processes, identifying two distinct regimes. Complementary PIV allows visualization of the flow fields that correlate with volume loss, suggesting that volume loss may be a complex combination of vortex shedding during the primary pulse and re-combination during quiescent phase.

Non-modal transient growth of disturbances in pulsatile and oscillatory pipe flows

Abstract

A direct comparison of pulsatile and non-pulsatile rough-wall turbulent pipe flow

Pulsatile rough-wall turbulent pipe flow is compared against its non-pulsatile counterpart using data obtained from direct numerical simulation. Results are presented at a mean friction Reynolds number of 540 for a set of three geometrically scaled roughness topographies at a single forcing condition, which, based on existing classifications, falls into the current-dominated very-high-frequency regime. By comparing the pulsatile data against an equivalent non-pulsatile dataset (Chan et al. , J. Fluid Mech. , vol. 854, 2018, pp. 5–33), the key differences (and similarities) between the forced and unforced configurations are identified. A major finding of this study is that the flow in the outer region retains its self-similar functional form under pulsatile rough-wall conditions, and, as a result, Townsend’s outer-layer similarity hypothesis holds for the roughness-forcing combinations considered here. On the other hand, the unsteady cases exhibit a rich array of flow physics in the region beneath the roughness crests not observed in the steady case. These differences are examined using a Moody chart, which encapsulates how the hydraulic properties of pulsatile rough-wall pipe flow differ from their non-pulsatile counterpart.

Forcing frequency effects on turbulence dynamics in pulsatile pipe flow

The turbulence dynamics of pulsatile pipe flow are investigated using direct numerical simulation (DNS) at a mean friction Reynolds number of 180. Results are presented for a range of forcing frequencies at a fixed amplitude, which, based on existing classifications, corresponds to the current-dominated regime. This work directs attention towards the phase-variations of single and two-point turbulence statistics, with a particular emphasis on the response of the Reynolds shear stress to systematic changes in the applied forcing frequency. The study has yielded two key outcomes. (i) A new frequency classification procedure for pulsatile turbulent flows (at low-to-moderate friction Reynolds numbers), informed by the Reynolds shear stress frequency co-spectra and the value of the applied forcing frequency. (ii) A detailed account of single- and two-point Reynolds shear stress statistics, in response to high, very-high and ultra-high forcing frequencies in order to study turbulence dynamics in the physical and Fourier domains. Furthermore, the oscillatory velocity field obtained from the DNS data is compared against the laminar Womersley solution in order to assess the interaction (or lack thereof) between the oscillatory velocity field and phase-averaged Reynolds shear stress fluctuations. For the higher frequencies considered in this work, single- and two-point Reynolds shear statistics all enter the so-called “frozen” regime — which occurs as the forcing time-scale becomes smaller than that of the highest-frequency, energy-containing motions in the Reynolds shear stress co-spectra.

The effect of pulsation frequency on transition in pulsatile pipe flow

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.

Pulsatile pipe flow transition: Flow waveform effects

Although transition is known to exist in various hemodynamic environments, the mechanisms that govern this flow regime and their subsequent effects on biological parameters are not well understood. Previous studies have investigated transition in pulsatile pipe flow using non-physiological sinusoidal waveforms at various Womersley numbers but have produced conflicting results, and multiple input waveform shapes have yet to be explored. In this work, we investigate the effect of the input pulsatile waveform shape on the mechanisms that drive the onset and development of transition using particle image velocimetry, three pulsatile waveforms, and six mean Reynolds numbers. The turbulent kinetic energy budget including dissipation rate, production, and pressure diffusion was computed. The results show that the waveform with a longer deceleration phase duration induced the earliest onset of transition, while the waveform with a longer acceleration period delayed the onset of transition. In accord with the findings of prior studies, for all test cases, turbulence was observed to be produced at the wall and either dissipated or redistributed into the core flow by pressure waves, depending on the mean Reynolds number. Turbulent production increased with increasing temporal velocity gradients until an asymptotic limit was reached. The turbulence dissipation rate was shown to be independent of mean Reynolds number, but a relationship between the temporal gradients of the input velocity waveform and the rate of turbulence dissipation was found. In general, these results demonstrated that the shape of the input pulsatile waveform directly affected the onset and development of transition.

A non-dimensional oscillation parameter describing interactive influence of oscillation frequency and velocity amplitude ratio for use in pulsatile flows

Abstract The interactive influences of oscillation frequency and velocity amplitude ratio on onset of transition in pulsatile pipe flow are investigated experimentally in the ranges of time-averaged and oscillating Reynolds numbers of 1019 ± 35 ⩽ Re ta ⩽ 4817 ± 164 and 107 ± 4 ⩽ Re os ⩽ 4261 ± 145 with velocity amplitude ratio of 0.05 ± 0.0017 ⩽ A 1 ⩽ 0.96 ± 0.03 for 227 runs. Oscillation frequency is in the range of 0.1 Hz ⩽ f ⩽ 14 Hz corresponding to Womersley number range of 2.72 ⩽ ω ′ ⩽ 32.21 covering quasi-steady, intermediate and beginning of inertia dominant regimes of pulsatile laminar flow. The onset of transition in laminar pulsatile pipe flow can be retarded up to Re ta , crit = 4817 at ω ′ = 3.85 in the covered experimental range. No more effect of A 1 on Re ta , crit is seen for ω ′ > 8.61 although there is a considerable effect of A 1 on Re os , crit . The effect of ω ′ on Re ta , crit and Re os , crit is not observed for A 1 ω ′ and A 1 are also investigated on Re ta , crit as functions of Re ta , crit = Re ta , crit ( A 1 ω ′ ) and Re ta , crit = Re ta , crit ( ω ′ / A 1 ). The interactive influences of ω ′ and A 1 are not seen on Re ta , crit for ω ′ > 8.61. This shows that the time-periodicity ( ω ′ , A 1 ) does not affect significantly the onset of transition at the beginning of inertia dominant region of pulsatile laminar flow ( ω ′ > 8.61) when compared with their interactive effects in the quasi-steady and intermediate regions ( ω ′ ⩽ 8.61). For flow classification of pulsatile flow at the onset of transition, a new non-dimensional interactive oscillation number, I os = ω ′ / A 1 is proposed. According to this non-dimensional number, the pulsatile flow at the onset of transition can be subclassified such as quasi-steady for I os I os ⩽ 30 and inertia dominant regions of pulsatile pipe flows for I os > 30 considering the effects of both ω ′ and A 1 on contrary to the classifications available in the literature.

Definition of sub-classes in sinusoidal pulsatile air flow at onset of transition to turbulence in view of velocity and frictional field analyses

The definition of the sub-classes in sinusoidal pulsatile pipe flow at the onset of transition to turbulence is given through the analyses of the velocity and the frictional field measurements conducted. For this reason, a systematic experimental study was carried out and the validation of the results was compared with those available in the literature. The time averaged and the oscillating components of the local velocities, U‾ta(r) and |U‾os,1|(r) are measured throughout the pipe cross-section and compared with the theoretical background. A variety of friction factors are also evaluated and the correlations in terms of the functional relationship between dimensionless parameters of λsL/λu,ta=fω′/Reta3/4 are proposed. Therefore the limit between quasi steady and intermediate region, and the limit between intermediate and inertia dominant region in the pulsatile pipe flow are found to be at the magnitudes of ω′/Reta3/4=0.145 and ω′/Reta3/4=1.5, respectively. Laminar pulsatile flows even at onset of transition can be classified as quasi-steady and inertia dominant sub-classes for ω′<5.44 and ω′>27.22, respectively. According to the presented experimental study, the intermediate region can also be divided into two sub-classes for ω′≤8.61 and ω′>8.61 as a result of the velocity and the frictional fields. Furthermore, the relationships among time averaged pressure drop, time averaged mean velocity and time averaged friction factor are investigated and the critical limit of ω′=8.61 is found. A new parameter, normalized pressure drop, ΔP∗ is proposed and a common relationship between ΔP∗ and Reta,critω′ is derived as ΔP∗=f(Reta,critω′) with a mean deviation of ±25%.

An experimental test system for the generation, control and analysis of sinusoidal pulsatile pipe flows (An application case for time dependent flow measurements)

The hardware and software of an experimental test system which has been designed, constructed and operated for the analysis of transitional characteristics of a laminar time-dependent flow field into turbulence with comprehensive uncertainty analysis are the major contents of the paper. Therefore presentation herein aims to offer an application case in terms of time-dependent measurement and data acquisition technology using an electronic digital mass flow control (MFC) unit at laboratory site instead of previously used pressure driven mechanisms. The flow field is a sinusoidal pulsatile one in order to simulate the real practice and to utilize the simplicity in production, control and analysis of oscillation. The previous background and the updated portrait on the transitional pulsatile flow [1,2] are outlined to determine the relevant flow parameters and their critical ranges, the details of the measurement and data acquisition systems and the proposed methodologies. The production of the controlled pulsatile flow and the generated flow characteristics, the methodology for the analysis, accuracy and sensitivity of the measurement and data acquisition chains are given for the purpose. The overall uncertainties of the velocity and pressure measurement chains are found to be ±3.2% and ±1.3%, respectively. The range of the experimental research devised to investigate the interactive influences of oscillation frequency, f and velocity amplitude ratio, A1 in the intermediate and the inertia dominant regions of pulsatile flow field with an emphasis on transition to turbulence is presented via sample measurements of mean velocity and pressure waveforms as solid outputs without going into details on physical aspects of flow dynamics.

An Experimental Review on Microbubble Generation to be Used in Echo-Particle Image Velocimetry Method to Determine the Pipe Flow Velocity

Microbubbles are broadly used as ultrasound contrast agents. In this paper we use a low-cost flow focusing microchannel fabrication method for preparing microbubble contrast agents by using some surface active agents and a viscosity enhancing material to obtain appropriate microbubbles with desired lifetime and stability for any in vitro infusion for velocity measurement. All the five parameters that govern the bubble size extract and some efforts are done to achieve the smallest bubbles by adding suitable surfactant concentrations. By using these microbubbles for the echo-particle image velocimetry method, we experimentally determine the velocity field of steady state and pulsatile pipe flows.

An Updated Portrait of Transition to Turbulence in Laminar Pipe Flows with Periodic Time Dependence (A Correlation Study)

Transition to turbulence in axially symmetrical laminar pipe flows with periodic time dependence classified as pure oscillating and pulsatile (pulsating) ones is the concern of the paper. The current state of art on the transitional characteristics of pulsatile and oscillating pipe flows is introduced with a particular attention to the utilized terminology and methodology. Transition from laminar to turbulent regime is usually described by the presence of the disturbed flow with small amplitude perturbations followed by the growth of turbulent bursts. The visual treatment of velocity waveforms is therefore a preferred inspection method. The observation of turbulent bursts first in the decelerating phase and covering the whole cycle of oscillation are used to define the critical states of the start and end of transition, respectively. A correlation study referring to the available experimental data of the literature particularly at the start of transition are presented in terms of the governing periodic flow parameters. In this respect critical oscillating and time averaged Reynolds numbers at the start of transition; Re os,crit and Re ta,crit are expressed as a major function of Womersley number, $\sqrt {\omega ^\prime } $ defined as dimensionless frequency of oscillation, f. The correlation study indicates that in oscillating flows, an increase in Re os,crit with increasing magnitudes of $\sqrt {\omega ^\prime } $ is observed in the covered range of $1<\sqrt {\omega ^\prime } <72$ . The proposed equation (Eq. 7), ${\rm{Re}}_{os,crit} ={\rm{Re}}_{os,crit} \left( {\sqrt {\omega ^\prime } } \right)$ , can be utilized to estimate the critical magnitude of $\sqrt {\omega ^\prime }$ at the start of transition with an accuracy of ±12 % in the range of $\sqrt {\omega ^\prime } <41$ . However in pulsatile flows, the influence of $\sqrt {\omega ^\prime }$ on Re ta,crit seems to be different in the ranges of $\sqrt {\omega ^\prime } <8$ and $\sqrt {\omega ^\prime } >8$ . Furthermore there is rather insufficient experimental data in pulsatile flows considering interactive influences of $\sqrt {\omega ^\prime } $ and velocity amplitude ratio, A 1. For the purpose, the measurements conducted at the start of transition of a laminar sinusoidal pulsatile pipe flow test case covering the range of 0.21< A 1 <0.95 with $\sqrt {\omega ^\prime } <8$ are evaluated. In conformity with the literature, the start of transition corresponds to the observation of first turbulent bursts in the decelerating phase of oscillation. The measured data indicate that increase in $\sqrt {\omega ^\prime } $ is associated with an increase in Re ta,crit up to $\sqrt {\omega ^\prime } =3.85$ while a decrease in Re ta,crit is observed with an increase in $\sqrt {\omega ^\prime } $ for $\sqrt {{\omega }'} >3.85$ . Eventually updated portrait is pointing out the need for further measurements on i) the end of transition both in oscillating and pulsatile flows with the ranges of $\sqrt {\omega ^\prime } <8$ and $\sqrt {\omega ^\prime } >8$ , and ii) the interactive influences of $\sqrt {\omega ^\prime } $ and A 1 on Re ta,crit in pulsatile flows with the range of $\sqrt {\omega ^\prime } >8$ .

An experimental study of transitional pulsatile pipe flow

The transitional regime of a sinusoidal pulsatile flow in a straight, rigid pipe is investigated using particle image velocimetry. The main aim is to investigate how the critical Reynolds number is affected by different pulsatile conditions, expressed as the Womersley number and the oscillatory Reynolds number. The transition occurs in the region of Re = 2250-3000 and is characterized by an increasing number of isolated turbulence structures. Based on velocity fields and flow visualizations, these structures can be identified as puffs, similar to those observed in steady flow transition. Measurements at different Womersley numbers yield similar transition behavior, indicating that pulsatile effects do not play a role in the regime that is investigated. Variations of the oscillatory Reynolds number also appear to have little effect, so that the transition here seems to be determined only by the mean Reynolds number. For larger mean Reynolds numbers, a second regime is observed: here, the flow remains turbulent throughout the cycle. The turbulence intensity varies during the cycle, but has a phase shift with respect to the mean flow component. This is caused by a growth of kinetic energy during the decelerating part and a decay during the accelerating part of the cycle. Flow visualization experiments reveal that the flow develops localized turbulence at several random axial positions. The structures quickly grow to fill the entire pipe in the decelerating phase and (partially) decay during the accelerating phase.

Transport Phenomena of Solid Particles in Pulsatile Pipe Flow

The transportation mechanism of single solid particles in pulsating water flow in a vertical pipe was investigated by means of videography and numerical simulations. The trajectories of alumina particles were observed experimentally by stereo videography. The particle diameter was 3 mm or 5 mm, and the pipe diameter was 18 mm or 22 mm. The frequency of flow pulsation was less than or equal to 6.67 Hz. It was found that the critical minimum water flux at which the particle can be transported upward depended on the pulsating pattern. Two types of numerical simulations were conducted, namely, one-dimensional simulations for tracking the vertical motion of the solid particles and two-dimensional simulations of the pulsating pipe flows in an axisymmetric coordinate system. The computer simulations of axisymmetric pipe flows revealed that the time-averaged radial velocity profile of water in the pulsating flows was very different from that in steady pipe flows. The motion of the particles is discussed in detail for a better understanding of the physics of the transport phenomena.

Laminarization and Turbulentization in a Pulsatile Pipe Flow

A fluid-flow model which automatically determines the flow regime was used to analyze a timewise-periodic pipe flow. Numerical simulation was employed to implement the model. The range of the instantaneous Reynolds number gave rise to four distinct flow regimes: laminarizing, fully laminar, turbulentizing, and fully turbulent. The period of the imposed harmonic oscillations was varied over a very wide range, and the magnitude of the oscillations was of the same order as that of the steady flow on which the oscillations were superimposed. A large-period limit at which the flow is quasi-steady was identified. The predicted quasi-steady fully developed friction factor for each regime was found to be in excellent agreement with steady-state results applied instantaneously. A metric in the form of the ratio of the turbulence production to turbulence destruction was used to exhibit the turbulence characteristics of each of the four flow regimes. The value of this metric was somewhat different in the laminarization and turbulentization regimes at the same instantaneous Reynolds number. This outcome suggests that the flow has memory.