Parabolic Velocity Distribution Research Articles

Finding the peak velocity in a flow from its doppler spectrum

The signal backscattered by blood cells crossing a sample volume produces a Doppler power spectrum determined by the scatterers¿ velocity distribution. Because of intrinsic spectral broadening, the peak Doppler frequency observed does not correspond to the peak velocity in the flow. Several methods have been proposed for estimating the maximum velocity component--an important clinical parameter--but these methods are approximate, based on heuristic thresholds that can be inaccurate and strongly affected by noise. Reported here is a method of modeling the Doppler power spectrum of a flow, and from that model, determining what Doppler frequency on the descending slope of the power spectrum corresponds to the peak velocity in the insonated flow. It is shown that, for a fully insonated flow with a parabolic velocity distribution, the peak velocity corresponds to the Doppler frequency at the half-power point on that slope. The method is demonstrated to be robust with regard to the effects of noise and valid for a wide range of acquisition parameters. Experimental maximum velocity measurements on steady flows with rates between 100 and 300 mL/min (peak velocity range 6.6 cm/s to 19.9 cm/s) show a mean bias error that is smaller than 1%.

Accuracy and Reproducibility of a Novel Dynamic Volume Flow Measurement Method

In clinical practice, blood volume flow (BVF) is typically calculated assuming a perfect parabolic and axisymmetric velocity distribution. This simple approach cannot account for the complex flow configurations that are produced by vessel curvatures, pulsatility and diameter changes and, therefore, results in a poor estimation. Application of the Womersley model allows compensation for the flow distortion caused by pulsatility and, with some adjustment, the effects of slight curvatures, but several problems remain unanswered. Two- and three-dimensional approaches can acquire the actual velocity field over the whole vessel section, but are typically affected by a limited temporal resolution. The multigate technique allows acquisition of the actual velocity profile over a line intersecting the vessel lumen and, when coupled with a suitable wall-tracking method, can offer the ideal trade-off among attainable accuracy, temporal resolution and required calculation power. In this article, we describe a BVF measurement method based on the multigate spectral Doppler and a B-mode edge detector algorithm for wall-position tracking. The method has been extensively tested on the research platform ULA-OP, with more than 1700 phantom measurements at flow rates between 60 and 750 mL/min, steering angles between 10° and 22° and constant, sinusoidal or pulsed flow trends. In the averaged BVF measurement, we found an underestimation of about −5% and a coefficient of variability (CV) less than 6%. In instantaneous measurements (e.g., systolic peak) the CV was in the range 2%–8.5%. These results were confirmed by a preliminary test on the common carotid artery of 10 volunteers (CV = 2%–11%).

Flow patterns on spectral‐domain optical coherence tomography reveal flow directions at retinal vessel bifurcations

To study intravascular characteristics of flowing blood in retinal vessels using spectral-domain optical coherence tomography (SD-OCT). Examination of selected arterial bifurcations and venous sites of confluence in 25 healthy 11-year-old children recruited as an ad hoc subsample from the population-based, observational Copenhagen Child Cohort 2000 study. The blood stream in retinal arteries maintains a figure-of-8 SD-OCT profile consistent with a laminar flow in concentric sheets and a parabolic velocity distribution up to the point of divergence at arterial bifurcations. In contrast, the blood stream at the site of confluence of two retinal veins remains divided into two parallel sets of sheets with separate velocity distribution for a downstream distance of at least four trunk vessel diameters. Consequently, retinal trunk vessels near bifurcations/confluences have distinctly different internal SD-OCT profiles, a figure-of-8 pattern in arteries and a figure figure-of-88 in veins that can be used to distinguish between the two vessel types. This study verified the hypothesis that directions of blood flow at dichotomous vascular branchings can be determined using SD-OCT. This feature may assist the identification of flow reversal near sites of vascular occlusion, the analysis of blood flow near vascular malformations and the segmentation of retinal SD-OCT images.

Lateral Migration and Nonuniform Rotation of Biconcave Particle Suspended in Poiseuille Flow

A biconcave particle suspended in a Poiseuille flow is investigated by the multiple-relaxation-time lattice Boltzmann method with the Galilean-invariant momentum exchange method. The lateral migration and equilibrium of the particle are similar to the Segré-Silberberg effect in our numerical simulations. Surprisingly, two lateral equilibrium positions are observed corresponding to the releasing positions of the biconcave particle. The upper equilibrium positions significantly decrease with the increasing Reynolds number, whereas the lower ones are almost insensitive to the Reynolds number. Interestingly, the regular wave accompanied by nonuniform rotation is exhibited in the lateral movement of the biconcave particle. It can be attributed to the fact that the biconcave shape in various postures interacts with the parabolic velocity distribution of the Poiseuille flow. A set of contours illustrate the dynamic flow field when the biconcave particle has successive postures in a rotating period.

Abstract 246: Echo Particle Image Velocimetry Generates Wall Shear Stress Biomarkers with Higher Accuracy than Doppler: Clinical Studies on 24 Healthy and 12 Tia Subjects

Wall shear stress (WSS) is an important modulator of vascular disease. We assessed the hypothesis that WSS profiles derived from Echo Particle Image Velocimetry (EchoPIV) are characteristic of vascular conditions such as TIA with superior accuracy to Doppler. We obtained ultrasound images of CCA from 24 healthy and 12 TIA subjects. Doppler provided centerline peak velocity and WSS estimate based on parabolic velocity distribution. Velocity profiles measured by EchoPIV varied from patient to patient and within the cardiac cycle. Curve-fitting to a power law function with an exponent term (n-value) showed that in healthy carotid arteries, a blunt velocity profile is present during systole with an average n-value of 5, whereas during diastole a more parabolic profile with an n-value of 2 is present. Therefore, assuming a fully parabolic velocity distribution for WSS estimation, the basis for Doppler velocimetry, introduces a mean error of 48% during diastole and 98% during systole. EchoPIV offers characterization of WSS profiles; time waveform analysis revealed smoother and fewer number of peaks per cycle for healthy and increased flow pulsatality (reverberations) for TIA (Figure). Echo PIV generated means for phase averaged peak velocity (27.95 vs 16.13 cm/s), WSS (6.45 vs 4.65 Dynes/cm2) and flow rate (0.3179 vs 0.2215 L/min) with standard deviations 3.66 vs 2.35, 2.8 vs 1.74 and 0.0723 vs 0.0744 were significantly different between healthy and TIA subjects respectively (all p < 0.01). Direct measurement of the velocity profile using Echo PIV provides superior estimates of WSS in carotid vessels. TIA populations have compromised hemodynamic variables compared to healthy subjects.

Controls of Wellbore Flow Regimes on Pump Effluent Composition

Where well water and formation water are compositionally different or heterogeneous, pump effluent composition will vary due to partial mixing and transport induced by pumping. Investigating influences of purging and sampling methodology on composition variability requires quantification of wellbore flow regimes and mixing. As a basis for this quantification, analytical models simulating Poiseuille flow were developed to calculate flow paths and travel times. Finite element modeling was used to incorporate influences of mixing. Parabolic velocity distributions within the screened interval accelerate with cumulative inflow approaching the pump intake while an annulus of inflowing formation water contracts uniformly to displace an axial cylinder of pre-pumping well water as pumping proceeds. Increased dispersive mixing forms a more diffuse formation water annulus and the contribution of formation water to pump effluent increases more rapidly. Models incorporating viscous flow and diffusion scale mixing show that initially pump effluent is predominantly pre-pumping well water and compositions vary most rapidly. After two screen volumes of pumping, 94% of pump effluent is inflowing formation water. Where the composition of formation water and pre-pumping well water are likely to be similar, pump effluent compositions will not vary significantly and may be collected during early purging or with passive sampling. However, where these compositions are expected to be considerably different or heterogeneous, compositions would be most variable during early pumping, that is, when samples are collected during low-flow sampling. Purging of two screen volumes would be required to stabilize the content and collect a sample consisting of 94% formation water.

CFD Simulation on Circulation within the Liquid Slug under Gas-Liquid Taylor Flow in Circular Capillary

Computational Fluid Dynamics (CFD) was used to simulate the circulation within the liquid slug on gas-liquid Taylor flow in circular capillaries. The velocity profile within liquid slug was studied, the strength of circulation was considered. The separate influences of the gas bubble velocity， Taylor unit length, capillary diameter and liquid film thickness on the internal circulation in liquid slug were investigated. Parabolic velocity distribution inside liquid was obtained and found to in good agreement with the literature report. The strength of circulation was mainly determined by the gas bubble velocity and the liquid film thickness.

Rapid spectroscopic velocity quantification using periodically oscillating gradients

In this work two spectroscopic methods are described which allow rapid flow velocity quantification in the presence of a parabolic velocity distribution. This method requires only a single excitation and is based on flow encoding by periodically oscillating gradients. In the shown spin echo variant additional refocusing pulses correct for field inhomogeneities. A theoretical model is introduced, which describes the course of the derived spectra even in high flow region, where a significant part of the encoded spins leaves the sensitive area of the coil during data acquisition (outflow-effect). It was demonstrated that both methods can quantify flow velocities within the velocity range of 1 mm / s up to 36 cm / s in the presence of a parabolic flow velocity distribution. The maximum velocity of the parabolic distribution is indicated in this method by a peak in the acquired spectrum from which the velocity could be quantified. Flow velocity quantification by periodically oscillating gradients seems a reasonable and fast alternative to established imaging techniques.

LIMITING MAXIMUM DRAG REDUCTION ASYMPTOTE FOR THE MOMENT COEFFICIENT OF AN ENCLOSED ROTATING DISK WITH FINE SPIRAL GROOVES

In this study, the limiting maximum drag reduction asymptote for the moment coefficient of an enclosed rotating disk with fine spiral grooves in turbulent flow region were obtained analytically. Analysis which were based on an assumption for a simple parabolic velocity distribution of turbulent pipe flow to represent relative tangential velocity, was carried out using momentum integral equations of the boundary layer. For a certain K- parameter the moment coefficient results agree well with experimental results for maximum drag reduction in an enclosed rotating disk with fine spiral grooves and drag reduction ratio approximately was 15 %. Additionally, the experimental results for drag reduction on a rotating disk can be explained well with the analytical results.

Imaging of Single Phase Flow in Porous Media by High Resolution MRI

This paper presents the single flow in porous media to investigate CO2 flow velocity in porous media.We used high resolution MRI to visualize the fluid flow distribution and measure axial mean velocity in porous media.In the experiment, the porous media sample was packed with glass beads, with a porosity of around 0.4. Based the traditional spin echo sequence, we modified the sequence with flow encoding gradients in the flow direction .The sample was saturated. The water flow rates were 1ml/min、2ml/min、3ml/min and 5ml/min,respectively. First, the sequence was calibrated by pipe flow without porous media. As expected, the experimental images show parabolic velocity distribution. The velocity in the centre is high. Then the sample was measured with the same sequence. The images show that the velocity distribution is homogeneous in the porous media. In the boundary of the sample, the velocities are low because of wall-effect. Moreover, the mean velocities calculated from MRI images agree with the real velocities.These errors between calculated velocities and real velocities are small. It may be reduced by changing the experiment conditions.MRI is a useful technology for measuring flow in porous media.

Effect of Rotating Magnetic Field on Two-phase Flow in RH Vacuum Degassing Vessel

Rotating magnetic field is applied in up-leg of RH vessel to promote the removal of non- metallic inclusions of molten steel and to prolong the life of RH equipment. Physical and mathematical models have been developed to understand the two-phase turbulent flow considering the effect of the rotating magnetic field in the RH vacuum degassing vessel. Water model experiments verified that the gas bubbles can be moved toward the central zone of up-leg of RH vessel as the result of density difference between gas bubbles and liquid in the swirling flow. The larger circulation flow rate can be obtained in RH degassing vessel with the effect of swirling flow. A penetrating velocity, which does not change the equation characteristics but changes solution distribution, is proposed to revise the gas volume fraction conservation equation. A revised gas volume fraction conservation equation is successfully used to solve the gas distribution in RH vessel. If there is no swirling flow, the larger upward velocities and maximum of the gas volume fraction appear near wall of up-leg. If the rotating magnetic field is applied in up-leg, the larger upward velocities occur in the central zone of up-leg. These phenomena agree with the experimental observation. When the rotating electromagnetic force is applied, the numerical results showed that a swirling flow may be produced and extended into the vacuum chamber. As the occurrence of swirling flow in upper part of up-leg, the maximum of gas volume fraction moves toward the center zone of up-leg and the upward parabolic velocity distribution is also formed.

Comparison of Hydrodynamics and Mass Transfer in Airlift and Bubble Column Reactors Using CFD

AbstractComputational Fluid Dynamics (CFD) is used to compare the hydrodynamics and mass transfer of an internal airlift reactor with that of a bubble column reactor, operating with an air/water system in the homogeneous bubble flow regime. The liquid circulation velocities are significantly higher in the airlift configuration than in bubble columns, leading to significantly lower gas holdups. Within the riser of the airlift, the gas and liquid phases are virtually in plug flow, whereas in bubble columns the gas and liquid phases follow parabolic velocity distributions. When compared at the same superficial gas velocity, the volumetric mass transfer coefficient, kLa, for an airlift is significantly lower than that for a bubble column. However, when the results are compared at the same values of gas holdup, the values of kLa are practically identical.

1925 二次元平行噴流の特性について

This paper describes characteristic features of flow patterns that were experimentally analyzed in the transision region of the two dimensional parallel jet with parabolic velocity distribution. The asymmetrical vortex street or symmetrical vortex street was observed in the jet of water shot out from the slot into two dimensional flow field. There were the asymmetrical voltex street at low Reynolds number, and symmetrical voltex street at hight Reynolds number determind by the width 2b of slot and the jet velocity U at slot. These results fitted the linear approximation mathmatical model by Euler's kinetic equation and continuity equation.

CVD Process Simulation for TiN, Mo Film Growth Rate Distributions

Growth rate distributions of chemical-vapor-deposited TiN and Mo films in a horizontal tubular reactor were simulated, and the gas flow, heat and mass transfer were analyzed. This study compared calculated results obtained by different models. The parabolic gas velocity distribution at the inlet persisted throughout the reactor, and this tendency was common in models with and without consideration of heat transfer. The temperature difference between the central axis and the reactor wall became larger with the increase of gas velocity. TiN film growth rate distributions were mostly predicted by a model without consideration of heat transfer and gas phase decomposition reactions because the surface reaction rate was the rate limiting process of the film deposition. Mo film growth rates depended more on the partial pressure of H 2 than on that of MoCl 5 , and a large growth rate peak was formed in the distribution at high P H2 . These phenomena were explained by considering the behavior of the intermediate gas species.

Effect of Peclet number on transmission of free and attached radon daughters through a circular tube with concurrent formation and attachment

The present work is devoted to the solution of the steady-state diffusion equation for radon or thoron decay products within a fluid which moves with a parabolic velocity distribution through a circular tube. Taking into consideration axial diffusion, formation and attachment of the decay products to aerosol particles, the concentration distribution of the radioactive decay products was calculated. The transmission rate parameters for both free and attached decay products are given as a function of Peclet number and attachment rate. These parameters, as calculated from the present solution, show considerable dependence on the Peclet number. The obtained theoretical results can be extended to determine experimentally the diffusion coefficient of radioactive gases decay products and attachment rates of small ions to aerosol particles via the two filter method.

Effect of Peclet number on transmission of free and attached radon daughters through a circular tube with concurrent formation and attachment

The present work is devoted to the solution of the steady-state diffusion equation for radon or thoron decay products within a fluid which moves with a parabolic velocity distribution through a circular tube. Taking into consideration axial diffusion, formation and attachment of the decay products to aerosol particles, the concentration distribution of the radioactive decay products was calculated. The transmission rate parameters for both free and attached decay products are given as a function of Peclet number and attachment rate. These parameters, as calculated from the present solution, show considerable dependence on the Peclet number. The obtained theoretical results can be extended to determine experimentally the diffusion coefficient of radioactive gases decay products and attachment rates of small ions to aerosol particles via the two filter method.

Particle collection efficiency of the rotational particle separator

The rotational particle separator is a patented technique for separating solid and/or liquid particles of 0.1 m and larger from gases. The core component is the rotating filter element which consists of a multitude of axially oriented channels which rotate as a whole around a common axis. Particles in the gas flowing in a laminar fashion through the channels are centrifuged towards the outer collecting walls of each individual channel while the purified gas leaves the channels at the exit. Solutions in closed form are presented for the probability that particles of given diameter are separated from the gas. Particle trajectories are governed by centrifugal forces and Stokes drag forces including Cunningham's correction. Solutions are given for channels of the following cross-sectional shapes: concentric rings, circles, triangles and sinusoids. Account has been taken of parabolic (Hagen?Poiseuille type) velocity distributions inside the channels and various distributions of the flow over the assembly of channels. The results compare favourably with measurements executed on six differently sized practical versions of the rotational particle separator.

Interaction of a ribbon's wake with a turbulent shear flow

Furthermore, we define a new Reynolds number based on the diameter of the cylinder and the average speed of fluid flow at the cross section of Jt = 0, • Concluding Remarks The effects of the wall boundaries on the formation of the recirculating flow of the flow past a circular cylinder have been investigated. The computed data reveal that even at a small blockage ratio, such influence is still significant. This implies that care must be exercised when truncations of a flow domain is unavoidable for computational purposes. For a careful numerical study of the flow past a circular cylinder, it seems that the value of B should not exceed 0.05, or even smaller. In addition, it is also noticed that the uniform and parabolic velocity distribution at the upstream boundary do not lead to different centerline velocity profiles at the rear of the cylinder. Therefore, the upstream velocity distribution does not affect Rer because at this stage the Reynolds number is small and the viscous dissipation over the cylinder is strong.

Steady expiratory flow in a model symmetric bifurcation.

A model symmetric bifurcation was employed to simulate steady expiratory flow in the upper part of the human central airways. A two color, two component laser Doppler anemometer was used to measure both the axial flow and the secondary flow at three different Reynolds numbers of 518, 1036, and 2089, corresponding to Dean numbers of 98, 196, and 395. The test section is a symmetric bifurcation of constant cross-sectional area with a branching angle of 70 degrees. The flow rate into the two daughter branches was about the same. Results show that in the junction plane, velocity profiles in the daughter branches are skewed towards the inner walls. In the parent tube, just downstream of the flow divider, the velocity profile is biconcave with a dip at the center but this is rapidly transformed into a velocity peak. In a plane transverse to the bifurcation plane, parabolic velocity distribution was conserved through the daughter branches. In the parent tube, the transverse profiles became flat downstream of the flow divider and developed a defect at the center further downstream towards the end of the parent tube part of the bifurcation. The velocity defect was confined to a small region in the vicinity of the centerline. Helical motion typified by symmetric vortices was observed in the daughter branches. In the parent tube, a set of four vortices induced by the turning of the flow was observed.

Heat transfer and solidification of a laminar liquid flow in a cooled parallel plate channel: The stationary case

A simple numerical model is presented to predict the steady-state ice layers on the cooled walls inside a parallel plate channel for arbitrary entrance velocity profiles. The effect of two different entrance velocity distributions (a parabolic velocity distribution and a slug flow) on the shape of the ice-layers are examined. The quality of an approximative solution given in literature was checked by comparing with the numerical results. For the case of a fully developed parabolic velocity distribution at the entrance of the cooled channel the results are compared with experimental findings of Kikuchi [8]. A generally good agreement was found.