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The article explores the impact of deformable surfaces on oscillatory flow in a cylindrical tube, revealing complex secondary time-averaged flows. By analyzing the interaction under a long-wave theory, the research uncovers the exponential decay of oscillatory pressure along the length of a deformable channel, influenced by material properties and flow frequency. The study quantifies time-averaged secondary flow and highlights the interplay between fluid inertia and elastic deformations, offering valuable insights into fluid-structure interactions in diverse systems like cardiovascular physiology and microfluidic device design. [Extracted from the article]

Flow through sudden expansion finds its application in several engineering and biological processes. Though the stability of flow through steady sudden expansion has garnered much attention, little to none is given to the pulsatile flow through sudden expansion. Hence, in the present work we study the influence of inflow pulsatility on flow characteristics in a sudden expansion. The inflow velocity is a sinusoidal waveform that is modulated to encompass a wide range of amplitudes, α, and reduced velocities, Ur. We report four different modes, namely, synchronized growth of the recirculation region (at high Ur), necking and diffusion of the recirculation region (at moderately high Ur), splitting and convection of the recirculation region (at moderate Ur) and inverse growth of the recirculation region (at low Ur). In each mode, the symmetry-breaking critical Reynolds number is obtained through numerical experiments and compared with those of Floquet stability analysis. We found that diffusion and the convection mode of the recirculation region increases the stability of the flow while the inverse growth mode of the recirculation region decreases the same. The effect of the expansion ratio, ER, is also explored, and we found that as ER increases, the absolute stability of flow decreases, but relative stability between the modes remains similar. Finally, we explain the dynamics of the modes by using terms involving the vorticity transport equation. [ABSTRACT FROM AUTHOR]

Various systems of mechanical devices and natural organisms use the repeated expansion and contraction of deformable structures to draw in and blow out fluid. Instead of such deformable continuous structures, a system that consists of multiple discrete bodies can also generate a directional flow through the cooperative movement of the individual bodies. In this study, we numerically investigate the collective effects of a multi-body system composed of eight circular cylinders, each of which oscillates separately in the radial direction to generate thrust. The cylinder array performs cooperative motion regulated by three motion parameters: phase difference, oscillation amplitude and frequency at a low Reynolds number (Re = 10). The phase difference between the cylinders is critical in determining the extent of the directional flow and the time-averaged thrust. The optimal phase difference that yields the maximum time-averaged thrust is consistent, regardless of the oscillation amplitude and frequency. However, the thrust generation performance becomes significantly weaker at a higher Reynolds number (Re = 100). This highlights that the hydrodynamic blockage in gaps between cylinders, which is induced by strong viscous diffusion at the low Reynolds number, is essential for the cooperative force generation of multiple closely spaced bodies. A new dimensionless geometric parameter based on the motion of the array is proposed to characterize the degree of bias in the generated flow and it successfully predicts the trend in the time-averaged thrust at the low Reynolds number with strong hydrodynamic blockage. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Existing theoretical analyses of Faraday waves in Hele-Shaw cells rely on the Darcy approximation and assume a parabolic flow profile in the narrow direction. However, Darcy's model is known to be inaccurate when convective or unsteady inertial effects are important. In this work, we propose a gap-averaged Floquet theory accounting for inertial effects induced by the unsteady terms in the Navier--Stokes equations, a scenario that corresponds to a pulsatile flow where the fluid motion reduces to a two-dimensional oscillating Poiseuille flow, similarly to the Womersley flow in arteries. When gap-averaging the linearised Navier--Stokes equation, this results in a modified damping coefficient, which is a function of the ratio between the Stokes boundary layer thickness and the cell's gap, and whose complex value depends on the frequency of the wave response specific to each unstable parametric region. We first revisit the standard case of horizontally infinite rectangular Hele-Shaw cells by also accounting for a dynamic contact angle model. A comparison with existing experiments shows the predictive improvement brought by the present theory and points out how the standard gap-averaged model often underestimates the Faraday threshold. The analysis is then extended to the less conventional case of thin annuli. A series of dedicated experiments for this configuration highlights how Darcy's thin-gap approximation overlooks a frequency detuning that is essential to correctly predict the locations of the Faraday tongues in the frequency--amplitude parameter plane. These findings are well rationalised and captured by the present model. [ABSTRACT FROM AUTHOR]

Non-stationarity is the rule in the atmospheric boundary layer (ABL). Under such conditions, the flow may experience departures from equilibrium with the underlying surface stress, misalignment of shear stresses and strain rates, and three-dimensionality in turbulence statistics. Existing ABL flow theories are primarily established for statistically stationary flow conditions and cannot predict such behaviours. Motivated by this knowledge gap, this study analyses the impact of time-varying pressure gradients on mean flow and turbulence over urban-like surfaces. A series of large-eddy simulations of pulsatile flow over cuboid arrays is performed, programmatically varying the oscillation amplitude $\alpha$ and forcing frequency $\omega$. The analysis focuses on both longtime-averaged and phase-dependent flow dynamics. Inspection of longtime-averaged velocity profiles reveals that the aerodynamic roughness length $z_0$ increases with $\alpha$ and $\omega$ , whereas the displacement height $d$ appears to be insensitive to these parameters. In terms of oscillatory flow statistics, it is found that $\alpha$ primarily controls the oscillation amplitude of the streamwise velocity and Reynolds stresses, but has a negligible impact on their wall-normal structure. On the other hand, $\omega$ determines the size of the region affected by the unsteady forcing, which identifies the so-called Stokes layer thickness $\delta _s$. Within the Stokes layer, phase-averaged resolved Reynolds stress profiles feature substantial variations during the pulsatile cycle, and the turbulence is out of equilibrium with the mean flow. Two phenomenological models have been proposed that capture the influence of flow unsteadiness on $z_0$ and $\delta _s$ , respectively. [ABSTRACT FROM AUTHOR]

As the queue becomes exhausted, different maintenance tasks can be performed according to the fatigue load and wear degree of the service equipment. At the same time, considering the customer's sensitivity to time delay, the service facility will not completely remain inactive during the maintenance period. To describe this objectively existing phenomenon arising in the waiting line system, we consider a hyper-exponential working vacation queue with a batch renewal arrival process. Through the calculation of the well-structured roots of the associated characteristic equation, the shift operator method in the theory of difference equations and the supplementary variable technique for stochastic modeling plays a central role in the queue-length distribution analysis. Comparison with other ways to analyze queueing models, the advantage of our approach is that we can avoid deriving the complex transition probability matrix of the queue-length process embedded at input points. The feasibility of this approach is verified by extensive numerical examples. [ABSTRACT FROM AUTHOR]

In this study, for the first time, we consider longitudinal motion of the walls during peristalsis in a distensible tube and how this affects backward (or retrograde) flow, i.e. peristaltic reflux. Building on the analytical model developed by Shapiro et al. (J. Fluid Mech. , vol. 37, no. 4, 1969, pp. 799–825) based on lubrication theory, we model peristalsis as a two-dimensional infinite sinusoidal wavetrain. We develop an objective function with high mechanical pumping efficiency and low reflux to find optimal peristalsis conditions. We show that optimal wall longitudinal motion contributes substantially to limiting reflux during peristalsis. The results suggest that the optimal form of wall longitudinal velocity is a linear function of the wall transverse coordinate, moving forward with the wave when the tube is distended and retracting when contracted. Our results are in general agreement with clinical observations of ureteral peristalsis. [ABSTRACT FROM AUTHOR]

Three-dimensional steady-state Arnold–Beltrami–Childress (ABC) flow has a chaotic Lagrangian structure, and also satisfies the Navier–Stokes (NS) equations with an external force per unit mass. It is well known that, although trajectories of a chaotic system have sensitive dependence on initial conditions, i.e. the famous 'butterfly effect', their statistical properties are often insensitive to small disturbances. This kind of chaos (such as governed by the Lorenz equations) is called normal-chaos. However, a new concept, i.e. ultra-chaos, has been reported recently, whose statistics are unstable to tiny disturbances. Thus, ultra-chaos represents higher disorder than normal chaos. In this paper, we illustrate that ultra-chaos widely exists in Lagrangian trajectories of fluid particles in steady-state ABC flow. Moreover, solving the NS equation when $Re=50$ with the ABC flow plus a very small disturbance as the initial condition, it is found that trajectories of nearly all fluid particles become ultra-chaotic when the transition from laminar to turbulence occurs. These numerical experiments and facts highly suggest that ultra-chaos should have a relationship with turbulence. This paper identifies differences between ultra-chaos and sensitivity of statistics to parameters. Possible relationships between ultra-chaos and the Poincaré section, ultra-chaos and ergodicity/non-ergodicity, etc., are discussed. The concept of ultra-chaos opens a new perspective of chaos, the Poincaré section, ergodicity/non-ergodicity, turbulence and their inter-relationships. [ABSTRACT FROM AUTHOR]

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 fromthe nonlinear mechanisms sustaining turbulence. [ABSTRACT FROM AUTHOR]

The linear dynamics of perturbations developing in an infinite channel with compliant walls is investigated for pulsatile flow conditions. Two-dimensional modal perturbations are considered for Womersley-type pulsating base flows and the wall motion is only allowed in the normal direction. It is found that the flow dynamics is mainly governed by four control parameters: the Reynolds number Re, the reduced velocity VR, theWomersley number Wo and the amplitude of the base-flow modulation ?Q. Linear stability analyses are carried out within the framework of Floquet theory, implementing an efficient approach for removing spurious eigenmodes. The characteristics of flow-based (Tollmien-Schlichting) and wall-based (both travelling-wave flutter and divergence) modes are investigated over a large control-parameter space. It is shown that travelling-wave flutter (TWF) modes are predominantly influenced by the reduced velocity and that the Reynolds number has only a marginal effect. The critical reduced velocity (corresponding to onset of linear instability) is demonstrated to depend both on the Womersley number and modulation amplitude for a given set of wall parameters. Similarly to the steady flow case, the Tollmien-Schlichting (TS) mode is also found to be only weakly affected by the flexibility of the wall in pulsatile flow conditions. Finally, the classification given by Benjamin (J. Fluid Mech., vol. 16, 1963, pp. 436-450) is found to be too restrictive in the case of pulsatile base flows. In particular, a new type of mode is identified that shares characteristics of two distinct Floquet eigenmodes: TS and TWF modes. Due to coupling of the different Floquet harmonics, a phenomenon specific to time-periodic base flows, this two-wave mode exhibits a beating over the intracyclic dynamics. [ABSTRACT FROM AUTHOR]

A Lagrangian analysis is performed to measure the rate at which recirculating fluid is replaced (depleted) in pulsatile flows. Based on this approach, we then investigate how depletion is affected in dense suspensions. Experiments are conducted for pure liquid as well as suspensions with volume fractions of $\varPhi =5\,\%$ , 10 % and 20 %. Using Lagrangian tracking and pathline extension techniques, the depletion of the recirculation region is quantified via the trajectories of individual fluid parcels exiting the domain. Pulsatile flows with varying concentrations of hydrogel beads, up to a volume fraction of 20 %, are compared at mean Reynolds numbers of $Re=4800$ , 9600 and 14 400, while the Strouhal number ($St=0.04$ , 0.08 and 0.15) and amplitude ratio ($\lambda =0.25$ , 0.50 and 0.95) are systematically varied. A so-called 'depletion efficiency' is calculated for each test case, which is shown to increase with increasing Strouhal number and amplitude ratio. For most pulsatile cases, periodic vortex formation significantly increases depletion efficiency through enhanced entrainment of recirculating fluid. Conversely, low-amplitude pulsatile flows are dominated by Kelvin–Helmholtz instabilities, which do not penetrate into the recirculation region, and thus their depletion efficiency is markedly lower as a result. The efficiency trends and depletion mechanisms remain virtually unchanged between the pure liquid and each of the suspension concentrations under almost all flow conditions, which forms an unexpected conclusion. The only exception is for low-amplitude and steady flows, where increasing the suspension volume fraction is shown to suppress fluid transport across the shear layer, which in turn slows depletion and decreases the overall depletion efficiency. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The high-Strouhal-number pulsatile flow in a curved pipe is studied numerically. A general force analysis is developed for the bend force, where the new contribution from flow acceleration is identified and analysed. The mechanisms of secondary flow production are studied by extending Hawthorne's (Proc. R. Soc. Lond. A , vol. 206, issue 1086, 1951, pp. 374–387) model to account for viscous effects and applied to assess the distinct contributions from an inviscid stretching and no-slip condition. A detailed comparison is made between the numerical simulations and models for a pipe flow characterised by a volume flux $Q=U_b A |\sin \varOmega _p t|$ (where $U_b$ is the maximum bulk velocity, $\varOmega _p$ is the angular frequency and $A$ is the pipe cross-sectional area). For high-Reynolds-number ($Re_b$) and high-Strouhal-number ($St$), the bend force predictions are in good agreement with the numerical results over a wide range of bend curvature ($R_c/D$ ; where $R_c$ is the bend radius of curvature and $D$ is the pipe diameter) owing to the influence of the streamwise flow acceleration on the pressure field. At high- $St$ , the streamwise vorticity (secondary flow) distribution is steady and close to the low- $St$ case, which is explained using a linear secondary flow model. [ABSTRACT FROM AUTHOR]

Oscillatory flows have the potential to overcome long-standing limitations encountered when using steady flows for inertial focusing due to low particle Reynolds numbers. The periodic displacement generated by oscillatory flow increases the total path length travelled by a suspended particle with no net displacement within a channel or the need for increased channel length. The effects of unsteady inertial forces on inertial focusing, however, have not been thoroughly examined. Here, we present a combined theoretical and experimental study on the effect of Womersley number on inertial focusing in planar pulsatile flows. The migration velocity for a small and weakly inertial particle was evaluated for different oscillation frequencies using the method of matched asymptotics. Using experiments in a custom-built microchannel, we show that oscillatory flows are remarkably efficient for inertial focusing, even at low particle Reynolds numbers. For appropriately selected oscillation amplitude and frequency, inertial focusing is achieved in only a fraction of the channel length (1 % to 10 %) compared to what would be required in a steady flow. We show that the Womersley number influences the equilibrium focusing position and the overall focusing efficiency. In fact, above a critical Womersley number, inertial focusing does not occur despite increasing particle Reynolds number. Lastly, the application of oscillatory inertial focusing for the direct measurement of particle migration velocity is demonstrated. [ABSTRACT FROM AUTHOR]

The two-dimensional laminar flow of a viscous fluid induced by peristalsis due to a moving wall wave has been studied previously for a rectangular channel, a circular tube and a concentric circular annulus. Here, we study peristaltic flow in a non-axisymmetric annular tube: in this case, the flow is three-dimensional, with motions in the azimuthal direction. This type of geometry is motivated by experimental observations of the pulsatile flow of cerebrospinal fluid along perivascular spaces surrounding arteries in the brain, which is at least partially driven by peristaltic pumping due to pulsations of the artery. These annular perivascular spaces are often eccentric and the outer boundary is seldom circular: their cross-sections can be well matched by a simple, adjustable model consisting of an inner circle (the outer wall of the artery) and an outer ellipse (the outer edge of the perivascular space), not necessarily concentric.We use this geometric model as a basis for numerical simulations of peristaltic flow: the adjustability of the model makes it suitable for other applications. We concentrate on the general effects of the non-axisymmetric configuration on the flow and do not attempt to specifically model perivascular pumping. We use a finite-element scheme to compute the flow in the annulus driven by a propagating sinusoidal radial displacement of the inner wall. Unlike the peristaltic flow in a concentric circular annulus, the flow is fully three-dimensional: azimuthal pressure variations drive an oscillatory flow in and out of the narrower gaps, inducing an azimuthal wiggle in the streamlines. We examine the dependence of the flow on the elongation of the outer elliptical wall and the eccentricity of the configuration. We find that the time-averaged volumetric flow is always in the same direction as the peristaltic wave and decreases with increasing ellipticity or eccentricity. The additional shearing motion in the azimuthal direction will increase mixing and enhance Taylor dispersion in these flows, effects that might have practical applications. [ABSTRACT FROM AUTHOR]

The instability and transition to turbulence and its evolution in pulsatile flows, which involve reverse flows and unsteady flow separations, is the primary focus of this experimental work. A piston driven by a programmable DC servo motor was used to set-up a water flow system and provide the pulsation characteristics. Time-resolved particle image velocimetry data were acquired in a refractive index matching set-up by using a continuous wave laser and a high-frame-rate digital camera. The position of the piston was continuously recorded by a laser proximity sensor. Five different experiments were carried out with Reynolds numbers in the range of 535–4825 and Womersley numbers from 11.91 to 23.82. The non-stationarity of the data was addressed by incorporating trend removal methods involving low- and high-pass filtering of the data, and using empirical mode decomposition together with the relevant Hilbert–Huang transform to determine the intrinsic mode functions. This latter method is more appropriate for nonlinear and non-stationary cases, for which traditional analysis involving classical Fourier decomposition is not directly applicable. It was found that transition to turbulence is a spontaneous event covering the whole near-wall region. The instantaneous vorticity profiles show the development of a large-scale ring-like attached wall vortical layer (WVL) with smaller vortices of higher frequencies than the pulsation frequency superimposed, which point to a shear layer Kelvin–Helmholtz (K–H) type of instability. Inflectional instability leads to flow separation and the formation of a major roll-up structure with the K–H vortices superimposed. This structure breaks down in the azimuthal direction into smaller turbulence patches with vortical content, which appears to be the prevailing structural content of the flow at each investigated Reynolds number (Re). At higher Re numbers, the strength and extent of the vortices are larger and substantial disturbances appear in the free stream region of the flow, which are typical of pipe flows at transitional Re numbers. Turbulence appears to be produced at the locations of maximum or minimum vorticity within the attached WVL, in the ridges between the K–H vortices around the separated WVL and the upstream side of the secondary vortex where the flow impinges on the wall. This wall turbulence breaks away into the middle section of the pipe, at approximately Re ≥ 2200, by strong eruptions of the K–H vortices. [ABSTRACT FROM AUTHOR]

The flow in a spherical cavity on a curved round pipe is a canonical flow that describes well the flow inside a sidewall aneurysm on an intracranial artery. Intracranial aneurysms are often treated with a flow-diverting stent (FDS), a low-porosity metal mesh that covers the entrance to the cavity, to reduce blood flow into the aneurysm sac and exclude it from mechanical stresses imposed by the blood flow. Successful treatment is highly dependent on the degree of reduction of flow inside the cavity, and the resulting altered fluid mechanics inside the aneurysm following treatment. Using stereoscopic particle image velocimetry, we characterize the fluid mechanics in a canonical configuration representative of an intracranial aneurysm treated with a FDS: a spherical cavity on the side of a curved round pipe covered with a metal mesh formed by an actual medical FDS. This porous mesh coverage is the focus of Part 2 of the paper, characterizing the effects of parent vessel Re, De and pulsatility, Wo, on the fluid dynamics, compared with the canonical configuration with no impediments to flow into the cavity that is described in Part 1 (Chassagne et al., J. Fluid Mech., vol. 915, 2021, A123). Coverage with a FDS markedly reduces the flow Re in the aneurysmal cavity, creating a viscous-dominated flow environment despite the parent vessel Re > 100. Under steady flow conditions, the topology that forms inside the cavity is shown to be a function of the parent vessel De. At low values of De, flow enters the cavity at the leading edge and remains attached to the wall before exiting at the trailing edge, a novel behaviour that was not found under any conditions of the high-Re, unimpeded cavity flow described in Part 1. Under these conditions, flow in the cavity co-rotates with the direction of the free-stream flow, similar to Stokes flow in a cavity. As De increases, the flow along the leading edge begins to separate, and the recirculation zone grows with increasing De, until, above De ≈ 180, the flow inside the cavity is fully recirculating, counter-rotating with respect to the free-stream flow. Under pulsatile flow conditions, the vortex inside the cavity progresses through the same cycle - switching from attached and co-rotating with the free-stream flow at the beginning of the cycle (low velocity and positive acceleration) to separated and counter-rotating as De reaches a critical value. The location of separation within the harmonic cycle is shown to be a function of both De and Wo. The values of aneurysmal cavity Re based on both the average velocity and the circulation inside the cavity are shown to increase with increasing values of De, while Wo is shown to have little influence on the time-averaged metrics. As De increases, the strength of the secondary flow in the parent vessel grows, due to the inertial instability in the curved pipe, and the flow rate entering the cavity increases. Thus, the effectiveness of FDS treatment to exclude the aneurysmal cavity from the haemodynamic stresses is compromised for aneurysms located on high-curvature arteries, i.e. vessels with high De, and this can be a fluid mechanics criterion to guide treatment selection. [ABSTRACT FROM AUTHOR]

Flow in sidewall cerebral aneurysms can be ideally modelled as the combination of flow over a spherical cavity and flow in a curved circular pipe, two canonical flows. Flow in a curved pipe is known to depend on the Dean number De, combining the effects of Reynolds number Re and of the curvature along the pipe centreline, κ. Pulsatility in the flow introduces a dependence on the Womersley number Wo. Using stereo particle image velocimetry measurements, this study investigated the effect of these three key non-dimensional parameters, by modifying pipe curvature (De), flow rate (Re) and pulsatility frequency (Wo), on the flow patterns in a spherical cavity. A single counter-rotating vortex was observed in the cavity for all values of pipe curvature κ and Reynolds number Re, for both steady and pulsatile inflow conditions. Increasing the pipe curvature impacted the flow patterns in both the pipe and the cavity, by shifting the velocity profile towards the cavity opening and increasing the flow rate in to the cavity. The circulation in the cavity was found to collapse well with only the Dean number, for both steady and pulsatile inflows. For pulsatile inflow, the counter-rotating vortex was unstable and the location of its centre over time was impacted by the curvature of the pipe, as well as Re and Wo in the free stream. The circulation in the cavity was higher for steady inflow than for the equivalent average Reynolds number and Dean number pulsatile inflow, with very limited impact of the Womersley number in the range studied. A second part of this study, that focuses on the changes in fluid dynamics when the intracranial aneurysm is treated with a flow-diverting stent, can be found in this issue (Barbour et al., J. Fluid Mech., vol. 915, 2021, A124). [ABSTRACT FROM AUTHOR]

Laminar flows through pipes driven at steady, pulsatile or oscillatory rates undergo a subcritical transition to turbulence. We carry out an extensive linear non-modal stability analysis of these flows and show that for sufficiently high pulsation amplitudes the stream-wise vortices of the classic lift-up mechanism are outperformed by helical disturbances exhibiting an Orr-like mechanism. In oscillatory flow, the energy amplification depends solely on the Reynolds number based on the Stokes-layer thickness, and for sufficiently high oscillation frequency and Reynolds number, axisymmetric disturbances dominate. In the high-frequency limit, these axisymmetric disturbances are exactly similar to those recently identified by Biau (J. Fluid Mech., vol. 794, 2016, R4) for oscillatory flow over a flat plate. In all regimes of pulsatile and oscillatory pipe flow, the optimal helical and axisymmetric disturbances are triggered in the deceleration phase and reach their peaks in typically less than a period. Their maximum energy gain scales exponentially with Reynolds number of the oscillatory flow component. Our numerical computations unveil a plausible mechanism for the turbulence observed experimentally in pulsatile and oscillatory pipe flow. [ABSTRACT FROM AUTHOR]

Flow pulsatility is ubiquitous in biological and biomedical fluid dynamics. Cardiovascular flow, the most well-studied pulsatile flow, has benefited from decades of fundamental studies of the temporal influences of basic parameter changes in simplified models. A similar approach is employed herein on a relatively unstudied, canonical flow configuration. Using experiments and simulations, we examine highly pulsatile flow over a surface-mounted bluff body. The pulsatile (i.e. with no flow reversal) inflow waveform is sinusoidal, and the inflow pulsation frequency is varied from low-frequency, quasi-steady pulsation to high-frequency pulsatility. A wake regime map encompassing the range of pulsation frequency is created, and a mechanistic explanation of the regimes observed is put forth. Finally, we introduce a non-dimensional parameter applicable to pulsatile flows and point out remarkable similarity to the formation time parameter associated with vortex ring generation, including a similar critical value, despite substantive differences in the flow configurations. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Transient, steady and oscillatory flows in a $180^{\circ }$ curved pipe are investigated both numerically and experimentally to understand secondary flow vortex formation and interactions. The results of numerical simulations and particle image velocimetry experiments are highly correlated, with a low error. To enable simulations in a smaller domain with shorter inlet section, an analytical solution for the unsteady Navier–Stokes equation is obtained with non-zero initial conditions to provide physical velocity profiles for the simulations. The vorticity transport equation is studied and its terms are balanced to find the mechanism of vorticity transfer to structures in the curved pipe. Several vortices are identified via various vortex identification (ID) methods and their results are compared. Isosurfaces of the $\unicode[STIX]{x1D706}_{2}$ vortex ID are used to explain the temporal and spatial evolution of vortices in the curved pipe. Eigenvalues and eigenvectors of the velocity gradient tensor are calculated for the swirling strength vortex ID method, which also determines vortex axis orientation. The classical Lyne vortex in oscillatory flow with an inviscid core is also revisited and its results are compared with the transient and steady flows. These in-depth analyses provide a better understanding and characterization of vortical structures in the curved pipe flow. Our findings show that, although there are some visual similarities between cross-sectional views of steady/transient flows and oscillatory flows, the structure herein designated as Lyne-type vortex detected in the cross-sections (under steady, transient and pulsatile flows) is not the same as the classical Lyne vortex pair (in oscillatory flows). [ABSTRACT FROM AUTHOR]

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 6 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 Xu et 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. [ABSTRACT FROM AUTHOR]

The dynamics of small-amplitude perturbations, as well as the regime of fully developed nonlinear propagating waves, is investigated for pulsatile channel flows. The time-periodic base flows are known analytically and completely determined by the Reynolds number Re (based on the mean flow rate), the Womersley number Wo (a dimensionless expression of the frequency) and the flow-rate waveform. This paper considers pulsatile flows with a single oscillating component and hence only three non-dimensional control parameters are present. Linear stability characteristics are obtained both by Floquet analyses and by linearized direct numerical simulations. In particular, the long-term growth or decay rates and the intracyclic modulation amplitudes are systematically computed. At large frequencies (mainly Wo⩾14), increasing the amplitude of the oscillating component is found to have a stabilizing effect, while it is destabilizing at lower frequencies; strongest destabilization is found for Wo≃7. Whether stable or unstable, perturbations may undergo large-amplitude intracyclic modulations; these intracyclic modulation amplitudes reach huge values at low pulsation frequencies. For linearly unstable configurations, the resulting saturated fully developed finite-amplitude solutions are computed by direct numerical simulations of the complete Navier–Stokes equations. Essentially two types of nonlinear dynamics have been identified: ‘cruising’ regimes for which nonlinearities are sustained throughout the entire pulsation cycle and which may be interpreted as modulated Tollmien–Schlichting waves, and ‘ballistic’ regimes that are propelled into a nonlinear phase before subsiding again to small amplitudes within every pulsation cycle. Cruising regimes are found to prevail for weak base-flow pulsation amplitudes, while ballistic regimes are selected at larger pulsation amplitudes; at larger pulsation frequencies, however, the ballistic regime may be bypassed due to the stabilizing effect of the base-flow pulsating component. By investigating extended regions of a multi-dimensional parameter space and considering both two-dimensional and three-dimensional perturbations, the linear and nonlinear dynamics are systematically explored and characterized. [ABSTRACT FROM AUTHOR]

The analysis of axial dispersion of solute is presented in a pulsatile flow of Casson fluid through a tube in the presence of interfacial mass transport due to irreversible first-order reaction catalysed by the tube wall. The theory of dispersion is studied by employing the generalized dispersion model proposed by Sankarasubramanian & Gill (Proc. R. Soc. Lond. A, vol. 333 (1592), 1973, pp. 115-132). This dispersion model describes the whole dispersion process in terms of three effective transport coefficients, i.e. exchange, convection and dispersion coefficients. In the present study, the effects of yield stress of Casson fluid ιy, wall absorption parameter β, amplitude of fluctuating pressure component e and Womersley frequency parameter α on the dispersion process are discussed under the influence of pulsatile pressure gradient. In a pulsatile flow, the plug flow radius changes during the period of oscillation and it has an effect on the dispersion process. Even with the Casson fluid model also, in an oscillatory flow, for small values of α, the dispersion coefficient K2 is positive, but when the value of α is as large as 3, K2 takes both positive and negative values due to the fluctuations in the velocity profiles. This nature becomes more predominant for ιy, e and β. It is observed that initially, for small time, the amplitude and magnitude of fluctuations of K2 becomes more rapid and increases with time but it decreases after certain time and reaches a non-transient state for large time. Like in the case of Newtonian model, double frequency period for K2 is observed at small time for large values of α with the Casson model for blood. It is seen that critical time for which K2 reaches a non-transient state is independent of ιy and e but is dependent on α. It is also observed that the axial distribution of mean concentration Cm of solute depends on ιy and e But the effect of e and α on Cm is not very significant. This dispersion model in non-Newtonian pulsatile flow can be applied to study the dispersion process in the cardiovascular system and blood oxygenators. [ABSTRACT FROM AUTHOR]

Prosthetic heart valves have been widely used to replace diseased or defective native heart valves. Flow through bileaflet mechanical heart valves (BMHVs) have previously demonstrated complex phenomena in the vicinity of the valve owing to the presence of two rigid leaflets. This study aims to accurately capture the complex flow dynamics for pulsatile flow through a 23 mm St Jude Medical (SJM) Regent™ BMHV. The lattice-Boltzmann method (LBM) is used to simulate pulsatile flow through the valve with the inclusion of reverse leakage flow at very high spatiotemporal resolution that can capture fine details in the pulsatile BMHV flow field. For higher-Reynolds-number flows, this high spatiotemporal resolution captures features that have not been observed in previous coarse resolution studies. In addition, the simulations are able to capture with detail the features of leaflet closing and the asymmetric b-datum leakage jet during mid-diastole. Novel flow physics are visualized and discussed along with quantification of turbulent features of this flow, which is made possible by this parallelized numerical method. [ABSTRACT FROM AUTHOR]

Very little is known about the udder characteristics, partitioning of milk in the mammary gland and efficiency of machine milking in donkeys. This study aimed to evaluate the characteristics of the udder and teats, milk yield in relation to pulsation rates (90, 120 and 150 cycles/min), milk partitioning in the mammary gland, composition of the spontaneously removed and residual milk fractions and milking efficiency. Forty-one healthy Martina Franca jennies in the third month of lactation and routinely milked twice daily were used in three studies. Udder characteristics were evaluated by direct measurements and ultrasonographic scanning. Residual milk was obtained by milking after an oxytocin administration (40 IU i.m.). The prevalent shapes were 'bowl' for udders and 'conical' for teats. After milking the udder characteristics decreased within a range from -11·6% (udder depth) to -25·7% (diameter of teat at the base). The internal structures of the udder resulted as several pockets of ducts empting directly into the teat. The pulsation rate of 120 cycles/min improved (P<0·05) the milk yield in comparison to the 90 and 150 cycles/min, reduced the residual milk fraction, thus improved (P<0·05) milking efficiency. Residual milk composition had higher (P<0·05) fat content and somatic cell count than the spontaneously removed milk fraction. The udders revealed several pockets of ducts empting into the teat instead of a single cisternal cavity and showed a certain compliance. The use of 120 cycles/min pulsation rate improved milking efficiency.

Tetralogy of Fallot is the most common cyanotic congenital heart disease with decreased pulmonary blood flow. Right-to-left shunt and infundibular pulmonary stenosis in this disease lead to a decrease in arterial O(2) saturation. Hypoxia is a strong stimulus for angiogenesis; however, the reason for insufficiency in the pulmonary vascular growth in patients despite chronic arterial hypoxia is still not known. This study was planned considering that the impairment in vascular endothelial growth factor-receptor relationship or the vascular endothelial growth factor-receptor deficiency in the pulmonary vascular bed during development may cause insufficiency of pulmonary vascular growth. A total of 24 patients were grouped as cyanotic - including 13 patients with tetralogy of Fallot - and acyanotic - including 11 patients with left-to-right shunt lesions. During cardiac catheterisation, vascular endothelial growth factor measurements were performed; and oxygen saturations, pressures, and haemoglobin levels were measured. Perioperative lung biopsy for vascular endothelial growth factor receptors was performed in the cyanotic group. Vascular endothelial growth factor of the aorta was higher in the acyanotic group. There was a significant negative correlation between vascular endothelial growth factor levels and aortic O(2) saturation in the cyanotic group (p < 0.05). Vascular endothelial growth factor tissue staining was negative in 11 out of 13 (84.6%) patients. KDR/Flk-1 receptor was positive in four out of 13 (30.7%) patients; Flt-1 receptor was positive in six out of 13 (46.1%) patients. Vascular endothelial growth factor values were found to be lower than those of the acyanotic patients in this study. Low serum vascular endothelial growth factor levels of the cyanotic group, in spite of the hypoxia, demonstrated the importance of studying vascular endothelial growth factor tissue levels and vascular endothelial growth factor receptors in these patients.

Vascular anomalies, extracranial and intracranial arteriovenous malformations as well as glomus jugulare tumour are well known causes of pulsatile tinnitus. Of late, benign intracranial hypertension has been stated to be a more common cause. However, tinnitus arising from and within the internal jugular vein has been reported only infrequently. Previously known as cephalic bruit and essential objective tinnitus, the venous hum tinnitus presents as pulse synchronous unilateral objective tinnitus. Ligation of the internal jugular vein appears to be a successful treatment. Two cases are presented.