Axial Flow Component Research Articles

Transverse flow under oscillating stimulation in helical square ducts with cochlea-like geometrical curvature and torsion

The cochlea, situated within the inner ear, is a spiral-shaped, liquid-filled organ responsible for hearing. The physiological significance of its shape remains uncertain. Previous research has scarcely addressed the occurrence of transverse flow within the cochlea, particularly in relation to its unique shape. This study aims to investigate the impact of the geometric features of the cochlea on fluid dynamics by characterizing transverse flow induced by harmonically oscillating axial flow in square ducts with curvature and torsion resembling human cochlear anatomy. We examined four geometries to investigate curvature and torsion effects on axial and transverse flow components. Twelve frequencies from 0.125 Hz to 256 Hz were studied, covering infrasound and low-frequency hearing, with mean inlet velocity amplitudes representing levels expected for normal conversation or louder situations. Our simulations show that torsion contributes significantly to transverse flow in unsteady conditions, and that its contribution increases with increasing oscillation frequency. Curvature alone has a small effect on transverse flow strength, which decreases rapidly with increasing frequency. Strikingly, the combined effect of curvature and torsion on transverse flow is greater than expected from a simple superposition of the two effects, especially when the relative contribution of curvature alone becomes negligible. These findings may be relevant to understanding physiological processes in the cochlea, including metabolite transport and wall shear stress. Further studies are needed to investigate possible implications for cochlear mechanics.

Static Force Characteristic of Annular Gaps – Experimental and Simulation Results

AbstractWe discuss the static characteristics, i.e., the induced force on the rotor, the attitude angle and the pressure difference, of off-centered annular gaps with an axial flow component without cavitation. The paper focuses on turbulent flow inside the annulus. Instead of modeling the inertia effects using the bulk-flow approach, the presented model uses an integro-differential approach in combination with power-law ansatz functions for the velocity profiles and a Hirs’ model to calculate the resulting pressure field. For an experimental validation of the model and comparison to the bulk-flow approach, an annular gap test rig is presented using magnetic bearings to inherently measure the position as well as the force on the rotor induced by the flow field inside the gap. The experimental investigations are performed using three different annuli with three different lengths. The impact of a variation of a modified Reynolds number, the flow number and the preswirl ratio on the resulting force on the rotor, the attitude angle and the pressure difference across the annulus is investigated and compared to the presented model and the bulk-flow approach.

Quasi-equilibrium states for helical vortices with swirl

We present a family of exact equilibrium solutions of the Euler equations consisting of a single helical vortex with an axial flow component along the vortex core. Relations between vorticity, velocity and streamfunction are analytically derived in the inviscid framework and constitute a generalization of relations valid for vortex rings (Batchelor, 1967 An Introduction to Fluid Dynamics. Cambridge University Press). Through Navier–Stokes simulations, it is shown that these relations hold for quasi-steady viscous solutions and become independent of the Reynolds number when sufficiently large. We also elaborate a procedure which generates a quasi-equilibrium with prescribed characteristics (circulation, helix radius, helical pitch, vortex core size, swirl level) and compare the obtained state with the results of an asymptotic theory. Finally, we illustrate how a strong axial flow jeopardizes such an evolution towards a quasi-equilibrium.

Computational fluid dynamic characterization of vertical‐wheel bioreactors used for effective scale‐up of human induced pluripotent stem cell aggregate culture

AbstractBioreactor‐based processes are the method of choice for efficient expansion of cells in a controlled setting. However, induced pluripotent stem cells (iPSCs) have proven to be extremely sensitive to the bioreactor hydrodynamic environment, making the use of suspension bioreactors to produce quality‐assured cells at clinical and commercial scales very challenging. The PBS vertical‐wheel (VW) bioreactor combines radial and axial flow components to produce uniform hydrodynamic force distributions, making it a promising platform to overcome the scale‐up challenges associated with iPSCs. In this study, hydrodynamic characterization through computational fluid dynamics modelling of VW bioreactors was performed. Analysis of these models proved that important volume average hydrodynamic variables could be maintained throughout scale‐up from the 0.1 L to the 15 L VW bioreactor scale. Each bioreactor scale (0.1, 0.5, 3, and 15 L) was modelled at a variety of agitation rates, leading to the generation of scale‐up correlation equations. These equations allow operators to define a working range of hydrodynamic variables at one scale and calculate the corresponding agitation rates at other modelled scales. A suggested operating range of agitation rates was determined for the successful culture of iPSCs in the VW bioreactor at each scale, corresponding to constant volume average energy dissipation rate. Agitation rates from the 0.1 and 0.5 L VW bioreactor scale were experimentally tested to biologically validate the suggested range. High cell‐fold expansion, healthy aggregate morphology, growth, and uniformity were demonstrated for all conditions tested within the suggested working range.

Numerical Investigation of Heat Transfer Enhancement Due to Flow Agitators Between Fins

Abstract The paper investigates the heat transfer characteristics of a channel system consisting of mean axial flow and oscillatory cross flow components. A numerical model has been developed to solve the governing equations associated with the flow. The paper identifies advection, diffusion, and oscillation time scales and intensity of squeezing in the channel as critical parameters controlling system behavior. The total Reynolds number parameter is considered in the paper to understand the combined effect of axial and transverse Reynolds numbers on the Nusselt number. Flow visualization techniques are used to understand the boundary layer changes that occur over an oscillation cycle. Nusselt number is found to increase with a reduction in advection and oscillation time scales. A linear relationship is observed between the Nusselt number and total Reynolds number when the axial and transverse Reynolds numbers are comparable. Nondimensional pressure drop is primarily defined by only two parameters: axial Reynolds number and squeezing fraction. The flow visualization results indicate significant heat transfer enhancement in a small fraction of the oscillation cycle characterized by flow conditions similar to Couette flow.

Effects of Varying Inhalation Duration and Respiratory Rate on Human Airway Flow

Studies of flow through the human airway have shown that inhalation time (IT) and secondary flow structures can play important roles in particle deposition. However, the effects of varying IT in conjunction with the respiratory rate (RR) on airway flow remain unknown. Using three-dimensional numerical simulations of oscillatory flow through an idealized airway model (consisting of a mouth, glottis, trachea, and symmetric double bifurcation) at a trachea Reynolds number (Re) of 4200, we investigated how varying the ratio of IT to breathing time (BT) from 25% to 50% and RR from 10 breaths per minute (bpm) corresponding to a Womersley number (Wo) of 2.41 to 1000 bpm (Wo = 24.1) impacts airway flow characteristics. Irrespective of IT/BT, axial flow during inhalation at tracheal cross-sections was non-uniform for Wo = 2.41, as compared to centrally concentrated distribution for Wo = 24.1. For a given Wo and IT/BT, both axial and secondary (lateral) flow components unevenly split between left and right branches of a bifurcation. Irrespective of Wo, IT/BT and airway generation, lateral dispersion was a stronger transport mechanism than axial flow streaming. Discrepancy in the oscillatory flow relation Re/Wo2 = 2 L/D (L = stroke length; D = trachea diameter) was observed for IT/BT ≠ 50%, as L changed with IT/BT. We developed a modified dimensionless stroke length term including IT/BT. While viscous forces and convective acceleration were dominant for lower Wo, unsteady acceleration was dominant for higher Wo.

Tomography-assisted Doppler photoacoustic microscopy: proof of concept

The previous methods to measure flow speed by photoacoustic microscopy solely focused on either the transverse or the axial flow component, which did not reflect absolute flow speed. Here, we present absolute flow speed maps by combining Doppler bandwidth broadening with volumetric photoacoustic microscopy. Photoacoustic Doppler bandwidth broadening and photoacoustic tomographic images were applied to measure the transverse flow component and the Doppler angle, respectively. Phantom experiments quantitatively demonstrated that ranges of 55° to 90° Doppler angle and 0.5 to 10 mm/s flow speed can be measured. This tomography-assisted method provides the foundation for further measurement in vivo.

Optical coherence tomography velocimetry based on decorrelation estimation of phasor pair ratios (DEPPAIR).

Quantitative velocity estimations in optical coherence tomography requires the estimation of the axial and lateral flow components. Optical coherence tomography measures the depth resolved complex field reflected from a sample. While the axial velocity component can be determined from the Doppler shift or phase shift between a pair of consecutive measurements at the same location, the estimation of the lateral component for in vivo applications is still challenging. One approach to determine lateral velocity is multiple simultaneous measurements at different angles. In another approach the lateral component can be retrieved through repeated measurements at (nearly) the same location by an analysis of the decorrelation over time. In this paper we follow the latter approach. We describe a model for the complex field changes between consecutive measurements and use it to predict the uncertainties for amplitude-based, phase-based and complex algorithms. The uncertainty of the flow estimations follows from a statistical analysis and is determined by the number of available measurements and the applied analysis method. The model is verified in phantom measurements and the dynamic range of velocity estimations is investigated. We demonstrate that phase-based and complex (phasor) based lateral flow estimation methods are superior to amplitude-based algorithms.

Precision analysis and optimization in phase decorrelation OCT velocimetry.

Quantitative flow velocimetry in Optical Coherence Tomography is used to determine both the axial and lateral flow component at the level of individual voxels. The lateral flow is determined by analyzing the statistical properties of reflected electro-magnetic fields for repeated measurements at (nearly) the same location. The precision or statistical fluctuation of the quantitative velocity estimation depends on the number of repeated measurements and the method to determine quantitative flow velocity. In this paper, both a method to determine quantitative flow velocity and a model for the prediction of the statistical fluctuations of velocity estimations are developed to analyze and optimize the estimation precision for phase-based velocimetry methods. The method and model are validated by phantom measurements in a bulk scattering medium as well as in intralipid solution in a capillary. Based on the model, the number of repeated measurements to achieve a certain velocimetry precision is predicted.

Vector Flow Imaging of a Highly Laden Suspension in a Zinc-Air Flow Battery Model.

Flow batteries using suspension electrodes, e.g., zinc-air flow batteries (ZABs), have recently gained renewed interest as potential candidates for grid energy storage or mobile applications. The performance of ZABs depends on the local flow conditions of the suspension in the electrochemical cell, which acts as an electrode. Hence, it is crucial to measure and understand the complex flow characteristics of such solid-liquid suspensions. The investigated suspension electrode is an opaque slurry that consists of microscopic zinc particles and an aqueous potassium hydroxide electrolyte. Commonly, ultrasound Doppler velocimetry is used for flow imaging in opaque fluids. However, due to the high particle concentration in the suspension electrode, strong scattering and wavefront distortions of the ultrasound are introduced. In this paper, we show that this results in an increased measurement uncertainty for Doppler-based velocity estimation. Instead, ultrasound image velocimetry is applied to measure the 2-D and two-component flow field in the zinc-electrolyte suspension. This is possible by adapting the measurement system to the suspension with a calibration setup. The total measurement uncertainties of 4.1% and 2.5% for the axial and lateral flow components are derived from the calibration measurements. For the first time, the flow field of such a suspension could be measured in a scaled fluidic model of a ZAB. The comparison of the estimated flow rates from the velocity profiles showed good agreement to a gravimetric reference. A significant difference in the flow characteristics of a macroscopically homogeneous electrolyte and the same electrolyte loaded with 8 vol.-% zinc particles, i.e., the suspension electrode, was found. Along with the demonstration of the measurement technique for opaque, concentrated suspensions, the measurement data will be used to calibrate and validate numerical models for comparable multiphase fluids.

On the Accuracy of Hemolysis Models in Couette-Type Blood Shearing Devices.

Hemolysis is one of the most challenging issues faced by blood contacting devices. Empirical hemolysis models often relate hemolysis to shear stress and exposure time. These models were generally derived from the experimental results of Couette-type blood shearing devices, with assumption of uniform exposure time and shear stress. This assumption is not strictly valid since neither exposure time nor shear stress is uniform. Hence, this study evaluated the influence of the nonuniform exposure time and rotor eccentricity or run-out on the accuracy of power-law hemolysis models, using both theoretical and CFD analysis. This work first provided a systematic analysis of the flow regime in a typical Couette shearing device, and showed the axial flow component can be regarded as fully developed laminar plane Poiseuille flow. It was found that the influence of nonuniform exposure time is within 4% for several widely used power-law models, which were validated by steady CFD simulations. A theoretical relationship was then built between the rotor run-out and hemolysis. We noticed that the influence of rotor run-out on hemolysis is within 5% for a moderate rotor run-out ratio of 0.2. Next, transient CFD simulations were performed to investigate the influence of rotor run-out on hemolysis with run-out ratios of 0.1 and 0.2. The results showed negligible effects for a moderate run-out ratio of 0.1. However, a run-out ratio of 0.2 led to a significant increase of hemolysis, resulting from back flows induced by the run-out of the rotor. These findings will be of great importance for the improvement of the hemolysis estimation and blood compatibility design.

Vortex-induced vibrations of cylinders bent by the flow

Flexible cylinders exposed to transverse flows may undergo transverse vortex-induced vibrations due to the oscillating lift force imposed by their wake. But the drag on such structures often leads to large in-line deflections that may significantly affect the dynamics through the combined effects of the curvature-induced tension, the local inclination of the cylinder, the non-uniformity of the normal flow profile, and the large axial flow component. In this paper, we investigate the consequences of flow-induced bending on the vortex-induced dynamics of slender cantilever cylinders, by means of numerical simulations. We combine a distributed wake oscillator approach to model the dynamics of the wake with Lighthill’s large-amplitude elongated body theory to account for the effect of the axial flow in the reactive (added mass) force. The use of such reduced order models facilitates the identification of the physical mechanisms at play, including through the linear analysis of the coupled fluid–structure system. We find that the primary consequence of flow-induced bending is the inhibition of single mode lock-in, replaced by a multi-frequency response of the structure, and the reduction of the vibration amplitude, as a result of the broadening of the wake excitation spectrum and of the localization of the energy transfer due to the variations induced in the normal flow profile. We also find that the curvature-induced tension is of negligible influence, but that the axial flow component may on the other hand significantly alter the dynamics owing to the destabilizing effect of the reactive force on the structural modes.

Three-dimensional instabilities and inertial waves in a rapidly rotating split-cylinder flow

The nonlinear dynamics of the flow in a differentially rotating split cylinder is investigated numerically. The differential rotation, with the top half of the cylinder rotating faster than the bottom half, establishes a basic state consisting of a bulk flow that is essentially in solid-body rotation at the mean rotation rate of the cylinder and boundary layers where the bulk flow adjusts to the differential rotation of the cylinder halves, which drives a strong meridional flow. There are Ekman-like layers on the top and bottom end walls, and a Stewartson-like side wall layer with a strong downward axial flow component. The complicated bottom corner region, where the downward flow in the side wall layer decelerates and negotiates the corner, is the epicentre of a variety of instabilities associated with the local shear and curvature of the flow, both of which are very non-uniform. Families of both high and low azimuthal wavenumber rotating waves bifurcate from the basic state in Eckhaus bands, but the most prominent states found near onset are quasiperiodic states corresponding to mixed modes of the high and low azimuthal wavenumber rotating waves. The frequencies associated with most of these unsteady three-dimensional states are such that spiral inertial wave beams are emitted from the bottom corner region into the bulk, along cones at angles that are well predicted by the inertial wave dispersion relation, driving the bulk flow away from solid-body rotation.

Full-scale measurement of wind pressure on the surface of an oscillating circular cylinders

Under wind excitation, many slender structural members with circular cross sections have exhibited large-amplitude vibrations. The nature of some problematic vibrations remains to be fully understood. To investigate the excitation mechanisms that can cause the vibrations, an experimental campaign was conducted to measure simultaneously the wind pressure on the surface of a circular cylinder in the atmospheric boundary layer and the acceleration of this cylinder. The pressure and acceleration measurements were used to investigate the interaction between the cylinder and the turbulent wind in subcritical and critical Reynolds number ranges. The study revealed several effects of turbulence in wind in the atmospheric boundary layer on the critical transition, including the promotion of early critical transition, the attenuation of the single separation bubble, and the early cessation of the coherent vortex shedding. A coherent fluctuating axial flow component in the wake of circular cylinders yawed to the flow, which has been previously observed in wind tunnel tests in smooth flow and postulated to be critical for the onset of dry cylinder vibration at high reduced velocity, was not observed in the present experiment.

Effects of an axial flow component on the Honji instability

This paper is concerned with a numerical study of the three-dimensional Honji instability that can arise in an oscillatory flow impinging on a circular cylinder. It is well known that when the fluid motion far from the cylinder is perpendicular to its axis then the flow is liable to a three-dimensional breakdown via this instability which initially appears as an axially periodic mushroom-like structure attached to the surface of the cylinder. Here the focus is on examining the Honji instability under an oblique inflow. The obliqueness of the free stream is represented by an angle of attack through introducing an axial flow component. It is found that the Honji mode is suppressed by increasing the axial flow component, and when this component is sufficiently large the instability mechanism is no longer operative so that all that remains is a featureless two-dimensional columnar flow. At smaller values of angle of attack, though the Honji structure remains, it is deformed by the axial flow component. The developed two-layer near-cylinder vortical structures can be related to the energy and momentum transfer between the two layers.

Control and optimization of solute transport in a thin porous tube

Predicting the distribution of solutes or particles in flows within porous-walled tubes is essential to inform the design of devices that rely on cross-flow filtration, such as those used in water purification, irrigation devices, field-flow fractionation, and hollow-fibre bioreactors for tissue-engineering applications. Motivated by these applications, a radially averaged model for fluid and solute transport in a tube with thin porous walls is derived by developing the classical ideas of Taylor dispersion. The model includes solute diffusion and advection via both radial and axial flow components, and the advection, diffusion, and uptake coefficients in the averaged equation are explicitly derived. The effect of wall permeability, slip, and pressure differentials upon the dispersive solute behaviour are investigated. The model is used to explore the control of solute transport across the membrane walls via the membrane permeability, and a parametric expression for the permeability required to generate a given solute distribution is derived. The theory is applied to the specific example of a hollow-fibre membrane bioreactor, where a uniform delivery of nutrient across the membrane walls to the extra-capillary space is required to promote spatially uniform cell growth.

Fully resolved numerical simulation of reactive mixing in a T-shaped micromixer using parabolized species equations

This paper introduces and exploits a hybrid numerical approach for fully resolved numerical simulations of reactive mixing in T-shaped microreactors and thereby enables a computational analysis of how chemical reactions interact with convective and diffusive transport. The approach exploits the fast redirection of the flow inside the mixing channel, resulting in a flow field with positive axial flow component everywhere after a short entry zone. This allows handling the axial flow direction as a pseudo-time variable, so that the evolution of the concentration profile can be computed consecutively on successive cross sections, following the main axial flow direction. With this approach the finest length scales, given by the Batchelor length scale, can be resolved for such a reactive mixing process inside a T-microreactor at stationary flow conditions. This allows for a detailed analysis of the mixing state as well as important characteristics of the reactive mixing process like yield and selectivity. The concrete numerical simulations yield local diffusion times inside the reactor, reveal the influence of the strength of the secondary flow on the progress of the chemical reaction and show how local selectivities result from the species transport.

Field Measurements of Mean Velocity Characteristics of a Large-Diameter Swirling Jet

Full-scale field acoustic Doppler velocimeter measurements of the radial, axial, and tangential flow components were undertaken in a large-diameter turbulent swirling jet generated by a raft-mounted axial flow-mixing propeller discharging through a draft tube during isothermal and stratified conditions. The results were compared with classical jet theory and showed significant differences in the zone of flow establishment though similar behavior in the zone where established flow was found. It was concluded that the efflux from the axial flow-mixing propeller could not be described adequately by conventional jet theory due to the jet size and swirling characteristics.

Rossby waves and α-effect

Rossby waves drifting in the azimuthal direction are a common feature at the onset of thermal convective instability in a rapidly rotating spherical shell. They can also result from the destabilization of a Stewartson shear layer produced by differential rotation as expected in the liquid sodium experiment (Derviche Tourner Sodium) working in Grenoble, France. A usual way to explain why Rossby waves can contribute to the dynamo process goes back to Busse [A model of the Geodynamo. Geophys. J. R. Astron. Soc. 1975, 42, 437–459]. In his picture, the flow geometry is a cylindrical array of parallel rolls aligned with the rotation axis. The axial flow component (parallel to the rotation axis) is maximum in the middle of each roll and changes its sign from one roll to the next (case (i)). It is produced by the Ekman pumping at the fluid containing shell boundary. The corresponding dynamo mechanism can be explained in terms of an α-tensor with non-zero diagonal coefficients. It corresponds to the heuristic picture given by Busse (1975). In rapidly rotating objects like the Earth's core (or in a fast rotating experiment), Rossby waves occur in the limit of small Ekman number (). In that case, the main source of the axial flow component is not the Ekman pumping but rather the “geometrical slope effect” due to the spherical shape of the fluid containing shell. This implies that the axial flow component is maximum at the borders of the rolls and not at the centres (case (ii)). If assumed to be stationary, such rolls would lead to zero coefficients on the diagonal of the α-tensor, making the dynamo probably less efficient if possible at all. Actually, the rolls are drifting as a wave, and we show that this drift implies non-zero coefficients on the diagonal of the α-tensor. These new coefficients are, in essence, very different from the ones obtained in case (i) and cannot be interpreted in terms of the heuristic picture of Busse (1975). They were interpreted as higher-order effects in Busse (1975). In addition, we consider rolls not only drifting but also having an arbitrary radial phase shift as expected in real objects.

Coupled flows and oscillations in asymmetric rotating plasmas

Nonlinear coupling among the radial, axial, and azimuthal flows in an asymmetric cold rotating plasma is considered nonperturbatively. Exact solutions describing an expanding or contracting plasma with oscillations are then obtained. It is shown that despite the flow asymmetry the energy in the radial and axial flow components can be transferred to the azimuthal component but not the vice versa, and that flow oscillations need not be accompanied by density oscillations.