Perpendicular ultrasound velocity measurement by 2D cross correlation of RF data. Part A: validation in a straight tube

An ultrasound velocity assessment technique was validated, which allows the estimation of velocity components perpendicular to the ultrasound beam, using a commercially available ultrasound scanner equipped with a linear array probe. This enables the simultaneous measurement of axial blood velocity and vessel wall position, rendering a viable and accurate flow assessment. The validation was performed by comparing axial velocity profiles as measured in an experimental setup to analytical and computational fluid dynamics calculations. Physiologically relevant pulsating flows were considered, employing a blood analog fluid, which mimics both the acoustic and rheological properties of blood. In the core region (|r|/a < 0.9), an accuracy of 3 cm s⁻¹ was reached. For an accurate estimation of flow, no averaging in time was required, making a beat to beat analysis of pulsating flows possible.     

Roughness induced forced convective laminar-transitional micropipe flow: energy and exergy analysis

Variable fluid property continuity, Navier–Stokes and energy equations are solved for roughness induced forced convective laminar-transitional flow in a micropipe. Influences of Reynolds number, heat flux and surface roughness, on the momentum-energy transport mechanisms and second-law of thermodynamics, are investigated for the ranges of Re = 1–2,000, Q = 5–100 W/m² and ε = 1–50 μm. Numerical investigations put forward that surface roughness accelerates transition with flatter velocity profiles and increased intermittency values (γ); such that a high roughness of ε = 50 μm resulted in transitional character at Re _tra = 450 with γ = 0.136. Normalized friction coefficient (C _f^*) values showed augmentation with Re, as the evaluated C _f^* are 1.006, 1.028 and 1.088 for Re = 100, 500 and 1,500, respectively, at ε = 1 μm, the corresponding values rise to C _f^* = 1.021, 1.116 and 1.350 at ε = 50 μm. Heat transfer rates are also recorded to rise with Re and ε; moreover the growing influence of ε on Nusselt number with Re is determined by the Nu _ε=50 μm/Nu _ε=1 μm ratios of 1.086, 1.168 and 1.259 at Re = 500, 1,000 and 1,500. Thermal volumetric entropy generation values decrease with Re and ε in heating; however the contrary is recorded for frictional volumetric entropy generation data, where the augmentations in are more considerable when compared with the decrease rates of      

Probability distribution functions for small scale turbulence

The exact expression for the probability distribution function (pdf),P(Δu_r), of a velocity difference Δu_r, over a distancer, in incompressible fluid turbulence, obtained from the Navier-Stokes equations, is used as a basis for deriving approximate profiles forP(Δu_r). These approximate forms are deduced from an approximate factorisation of the underlying functional probability distribution of the flow field, in which the individual factors capture different physical effects.P(Δu_r) is represented as the integral, with respect to the spatially averaged dissipation rateε _r, of the product of the conditionalpdf of Δu_r givenε _r, and thepdf ofε _r. The approximation yields the latter as a log-Poissonpdf, while the conditionalpdf is found to be a Gaussian for a transverse increment, and the product of a Gaussian and a cubic polynomial for a longitudinal increment. This approximation is equivalent to the refined similarity hypothesis coupled with the log-Poisson distribution, and it possesses the characteristic features ofP(Δu_r), including symmetric profiles for transverse increments, asymmetric profiles for longitudinal increments, and the development of pronounced non-Gaussian features at small separations. The associated scaling exponents for longitudinal and transverse structure functions are shown to be identical, in this approximation, and to assume the log-Poisson form.     

Pulsatile entrance flow in curved pipes: effect of various parameters

This paper presents the results of an experimental study on the developing pulsatile flow in curved pipes with a long, straight pipe upstream. In order to examine the dependence of flow-field development on the governing parameters, LDV measurements were conducted systematically for six cases of flow, where the Womersley number α was varied from 5.5 to 18, the mean Dean number D _m was 200 and 300, the flow rate ratio η was 0.5 and 1, and the curvature radius ratio Rc was 10 and 30. Peculiar flow phenomena, such as flow reversal for all values of α and a depression in the axial velocity profile for α = 10, were analyzed by decomposing the axial velocity into a time-mean and a varying component, as well as by obtaining the bias of their profiles. The velocity distributions abruptly change with the phase at turn angles Ω of 15–30°, corresponding to the nondimensional axial length z′ ≅ 1–2 from the bend entrance, and their development along the pipe axis is the most complicated for the flow at a moderate α of 10 and large η of 1. The entrance length in the case of pulsatile flow is shorter than that for steady flow with the same flow rate as the maximum pulsatile flow rate.     

Synchronized analysis of an unsteady laminar flow downstream of a circular cylinder centred between two parallel walls using PIV and mass transfer probes

Experiments are carried out in the wake of a cylinder of d _c  = 10 mm diameter placed symmetrically between two parallel walls with a blockage ratio r = 1/3 and a Reynolds number varying between 75 ≤ Re ≤ 277. Particle image velocimetry is exerted to obtain the instantaneous velocity components in the cylinder wake. A snapshot proper orthogonal decomposition (POD) is also applied to these PIV results in order to extract the dominant modes through the implementation of an inhomogeneous filtering of these different snapshots, apart from an interpolation to estimate the wall shear rate at the lower wall downstream the cylinder. Mass transfer circular probes are placed at the lower wall downstream this obstacle so as to further determine the time evolution of the wall shear rate, by bringing the inverse method to bear on the convective-diffusion equation. Comparisons between the two synchronized techniques demonstrate that electrochemical method can give more accurate information about the coherent structures present in the flow and about the interaction of the von Kármán vortices with the walls of the tunnel as well. The comparison between the two measurement techniques in the flow regions concerns the spatiotemporal evolutions of the wall shear rate obtained from PIV measurements and the wall shear rate using mass transfer probes. Discrepancy between the PIV measurements and the electrochemical ones near the wall, where the secondary vortices P ₁′ are generated at wall, are caused by a PIV bias and a limitations of the singular mass transfer probes.     

Investigation of the specific mass flow rate distribution in pipes supplied with a pulsating flow

A pulsating flow is typical of inlet and exhaust pipes of internal combustion engines and piston compressors. Unsteady flow phenomena are especially important in the case of turbocharged engines, because dynamic effects occurring in the exhaust pipe can affect turbine operation conditions and performance.One of the basic parameters describing the unsteady flow is a transient mass flow rate related to the instantaneous flow velocity, which is usually measured by means of hot-wire anemometers. For the flowing gas, it is more appropriate to analyze the specific mass flow rate φ_m = ρv, which takes into account also variations in the gas density. In order to minimize the volume occupied by measuring devices in the control section, special double-wire sensors for the specific mass flow rate (CTA) and temperature (CCT) measurement were applied. The article describes procedures of their calibration and measurement. Different forms of calibration curves are analyzed as well in order to match the approximation function to calibration points. Special attention is paid to dynamic phenomena related to the resonance occurring in a pipe for characteristic frequencies depending on the pipe length. One of these phenomena is a reverse flow, which makes it difficult to interpret properly the recorded CTA signal. Procedures of signal correction are described in detail. To verify the measurements, a flow field investigation was carried out by displacing probes radially and determining the profiles of the specific mass flow rate under the conditions of a steady and pulsating flow. The presence and general features of a reverse flow, which was identified experimentally, were confirmed by 1-D unsteady flow calculations.     

Full-field measurements of flow through a scaled metal foam replica

Open-celled foam geometries show great promise in heat/mass transfer, chemical treatment, and enhanced mixing applications. Flow measurements on these geometries have consisted primarily of observations of the upstream and downstream effects the foam has on the velocity field. Unfortunately, these observations give little insight into the flow inside the foam. We have performed quantitative flow measurements inside a scaled replica of a metal foam, ϕ = 0.921, D _Cell = 2.5 mm, by Magnetic Resonance Velocimetry to better understand the fluid motion inside the foam and give an alternative method to determine the foam cell and pore sizes. Through these 3-D, spatially resolved measurements of the flow field for a cell Reynolds number of 840, we have shown that the transverse motion of the fluid has velocities 20–30% of the superficial velocity passing through the foam. This strong transverse motion creates and dissipates streamwise jets with peak velocities 2–3 times the superficial velocity and whose coherence length is strongly correlated to the cell size of the foam. This complex fluid motion is described as “mechanical mixing” and is attributed to the geometry of the foam. A mechanical dispersion coefficient, D _M, was formed which demonstrates the transverse dispersion of this geometry to be 14 times the kinematic viscosity and 10 times the thermal diffusivity of air at 20°C and 1 atm.     

Near-field tip vortex behind a swept wing model

The near-field flow structure of a tip vortex behind a sweptback and tapered NACA 0015 wing was investigated and compared with a rectangular wing at the same lift force and Re=1.81×10⁵. The tangential velocity decreased with the downstream distance while increased with the airfoil incidence. The core radius was about 3% of the root chord c _r, regardless of the downstream distance and α for α<8°. The core axial velocity was always wake-like. The core Γ_c and total Γ_o circulation of the tip vortex remained nearly constant up to x/c _r=3.5 and had a Γ_c/Γ_o ratio of 0.63. The total circulation of the tip vortex accounted for only about 40% of the bound root circulation Γ_b. For a rectangular wing, the axial flow exhibited islands of wake- and jet-like velocity distributions with Γ_c/Γ_o=0.75 and Γ_o/Γ_b=0.70. For the sweptback and tapered wing tested, the inner region of the tip vortex flow exhibited a self-similar behavior for x/c _r≥1.0. The lift force computed from the spanwise circulation distributions agreed well with the force-balance data. A large difference in the lift-induced drag was, however, observed between the wake integral method and the inviscid lifting-line theory.     

On hot-wire diagnostics in Rayleigh–Taylor mixing layers

Two hot-wire flow diagnostics have been developed to measure a variety of turbulence statistics in the buoyancy driven, air-helium Rayleigh–Taylor mixing layer. The first diagnostic uses a multi-position, multi-overheat (MPMO) single wire technique that is based on evaluating the wire response function to variations in density, velocity and orientation, and gives time-averaged statistics inside the mixing layer. The second diagnostic utilizes the concept of temperature as a fluid marker, and employs a simultaneous three-wire/cold-wire anemometry technique (S3WCA) to measure instantaneous statistics. Both of these diagnostics have been validated in a low Atwood number (A _t  ≤ 0.04), small density difference regime, that allowed validation of the diagnostics with similar experiments done in a hot-water/cold-water water channel facility. Good agreement is found for the measured growth parameters for the mixing layer, velocity fluctuation anisotropy, velocity fluctuation p.d.f behavior, and measurements of molecular mixing. We describe in detail the MPMO and S3WCA diagnostics, and the validation measurements in the low Atwood number regime (A _t  ≤ 0.04). We also outline the advantages of each technique for measurement of turbulence statistics in fluid mixtures with large density differences.     

The interfacial crack between two dissimilar elastic-plastic materials

This paper presents an exact asymptotic analysis on the interfacial crack between two dissimilar elastic-plastic materials. These two materials have identical hardening exponent (n ₁=n ₂) but different hardening coefficient (α₁ ≠ α₂). Two groups of the near-crack-tip fields have been obtained, which not only satisfy the continuity of both tractions (σ_θ, τ_rθ) and displacements (u _r ,u _θ) on the interface, but also meet the traction free conditions on the crack faces. The first group of fields have the mode mixityM ^P quite close toM ^P =1 (MODE I) within the whole range 0 ≤ α₁/α₂ < ∞. As for the second group of fields, which is only obtained within the narrow range 0.9 ≤ α₁/α₂ ≤ 1, it is found that the mode mixity changes sharply with the ratio value α₁/α₂. The project supported by National Natural Science Foundation of China     

Comparison of turbulent channel and pipe flows with varying Reynolds number

Single normal hot-wire measurements of the streamwise component of velocity were taken in fully developed turbulent channel and pipe flows for matched friction Reynolds numbers ranging from 1,000 ≤ Re _τ ≤ 3,000. A total of 27 velocity profile measurements were taken with a systematic variation in the inner-scaled hot-wire sensor length l ⁺ and the hot-wire length-to-diameter ratio (l/d). It was observed that for constant l ⁺ = 22 and l/d >~200l/d \gtrsim 200, the near-wall peak in turbulence intensity rises with Reynolds number in both channels and pipes. This is in contrast to Hultmark et al. in J Fluid Mech 649:103–113, (2010), who report no growth in the near-wall peak turbulence intensity for pipe flow with l ⁺ = 20. Further, it was found that channel and pipe flows have very similar streamwise velocity statistics and energy spectra over this range of Reynolds numbers, with the only difference observed in the outer region of the mean velocity profile. Measurements where l ⁺ and l/d were systematically varied reveal that l ⁺ effects are akin to spatial filtering and that increasing sensor size will lead to attenuation of an increasingly large range of small scales. In contrast, when l/d was insufficient, the measured energy is attenuated over a very broad range of scales. These findings are in agreement with similar studies in boundary layer flows and highlight the need to carefully consider sensor and anemometry parameters when comparing flows across different geometries and when drawing conclusions regarding the Reynolds number dependency of measured turbulence statistics. With an emphasis on accuracy, measurement resolution and wall proximity, these measurements are taken at comparable Reynolds numbers to currently available DNS data sets of turbulent channel/pipe flows and are intended to serve as a database for comparison between physical and numerical experiments.     

Phase-resolved flow characteristics between two shrouded co-rotating disks

Flow characteristics in the interdisk midplane between two shrouded co-rotating disks were experimentally studied. A laser-assisted particle-laden flow-visualization method was used to identify the qualitative flow behaviors. Particle image velocimetry was employed to measure the instantaneous flow velocities. The flow visualization revealed rotating polygonal flow structures (hexagon, pentagon, quadrangle, triangle, and oval) existing in the core region of the interdisk spacing. There existed a difference between the rotating frequencies of the polygon and the disks. The rotating frequency ratio between the polygonal flow structure and the disks depended on the mode shapes of the polygonal core flow structures—0.8 for pentagon, 0.75 for quadrangle, 0.69 for triangle, and 0.6 for oval. The phase-resolved flow velocities relative to the bulk rotation speed of the polygonal core flow structure were calculated, and the streamline patterns were delineated. It was found that outside the polygonal core flow structure, there existed a cluster of vortex rings—each side of the polygon was associated with a vortex ring. The radial distributions of the time-averaged and phase-resolved ensemble-averaged circumferential and radial velocities were presented. Five characteristic regions (solid-body rotation region, hub-influenced region, buffer region, vortex region, and shroud-influenced region) were identified according to the prominent physical features of the flow velocity distributions in the interdisk midplane. In the solid-body rotation region, the fluid rotated at the angular velocity of the disks and hub. In the hub-influenced region, the circumferential flow velocity departed slightly from the disks’ angular velocity. The circumferential velocities in the hub-influenced and vortex regions varied linearly with variation of radial coordinates. The phase-resolved ensemble-averaged relative radial velocity profiles in the interdisk midplane at various phase angles exhibited grouping behaviors in three ranges of polygon phase angles (θ = 0 and α/2, 0 < θ < α/2, and α/2 < θ < α) because three-dimensional flow induced similar flow patterns to appear in the same range of polygon phase angles.     

An experimental investigation of moderate reynolds number flow in a T-Channel

An experimental investigation of water flow in a T-shaped channel with rectangular cross section (20 × 20 mm inlet ID and 20 × 40 mm outlet ID) has been conducted for a Reynolds number Re range of 56–422, based on inlet diameter. Dynamical conditions and the T-channel geometry of the current study are applicable to the microscale. 2-D planar particle imaging velocimetry (PIV) and laser-induced fluorescence (LIF) were used in multiple locations of the T-channel to investigate local dynamical behaviors. Steady symmetric and asymmetric flow regimes predicted in the literature, which is largely numerical, are experimentally verified. Unsteady flow regimes, which are numerically predicted to occur at higher Re but have not yet been experimentally characterized, are also examined, and real-time LIF results illuminate the evolution of unsteady structure. Experimental data of the present resolution and scope are not presently available for unsteady flow regimes. Time scales are presented for unsteady flow regimes, which are found to exhibit periodic behavior and to occur for Re  ≥ 195. An unsteady symmetrical regime is identified for Re ≥ 350 that is detrimental to mixing. Momentum fields and dynamical behaviors of all flow regimes are characterized in detail, such that published mixing trends may be better understood. Results of all experimental trials were used to construct a regime map. A symmetric topology is found to be dominant for Re from 56 to 116, when flow is steady, and 350 to 422, when flow is characterized by unsteady stagnation-point oscillation in the T-channel junction. Asymmetric flow, which is positively indicated for mixing, is dominant for Re between 142 and 298, and the fluid interface exhibits both steady (two standing vortices) and unsteady (shear-layer type roll-up) behaviors. This result is based on multiple experiments and suggests a practical operating range of 142  ≤ Re ≤ 298 where asymmetric flow is highly likely to experimentally occur. The identification of an upper limit on Re,  beyond which mixing appears negatively impacted by a more symmetrical momentum field, is practically important as pressure drops on the microscale are significant.     

Streamwise evolution of an inclined cylinder wake

The streamwise evolution of an inclined circular cylinder wake was investigated by measuring all three velocity and vorticity components using an eight-hotwire vorticity probe in a wind tunnel at a Reynolds number Re_d of 7,200 based on free stream velocity (U _∞) and cylinder diameter (d). The measurements were conducted at four different inclination angles (α), namely 0°, 15°, 30°, and 45° and at three downstream locations, i.e., x/d = 10, 20, and 40 from the cylinder. At x/d = 10, the effects of α on the three coherent vorticity components are negligibly small for α ≤ 15°. When α increases further to 45°, the maximum of coherent spanwise vorticity reduces by about 50%, while that of the streamwise vorticity increases by about 70%. Similar results are found at x/d = 20, indicating the impaired spanwise vortices and the enhancement of the three-dimensionality of the wake with increasing α. The streamwise decay rate of the coherent spanwise vorticity is smaller for a larger α. This is because the streamwise spacing between the spanwise vortices is bigger for a larger α, resulting in a weak interaction between the vortices and hence slower decaying rate in the streamwise direction. For all tested α, the coherent contribution to [`(v<sup>2</sup>)] \overline{{v^{2}}} is remarkable at x/d = 10 and 20 and significantly larger than that to [`(u²)] \overline{{u^{2}}} and [`(w<sup>2</sup>)]. \overline{{w^{2}}}. This contribution to all three Reynolds normal stresses becomes negligibly small at x/d = 40. The coherent contribution to [`(u²)] \overline{{u^{2}}} and [`(v²)] \overline{{v^{2}}} decays slower as moving downstream for a larger α, consistent with the slow decay of the coherent spanwise vorticity for a larger α.     

Heat transfer by laminar flow in a vertical and horizontal pipe with twisted-tape inserts

 This article presents the results of laboratory research on heat exchange while heating water in horizontal and vertical tubes with twisted-tape inserts. The scope of the research: 70 ≤ Re ≤ 4000 3.6 ≤ Pr ≤ 5.9 8.6 ≤ Gz ≤ 540 The research was held for three cases: – horizontal experimental tube – vertical experimental tube, the direction of flow according to the free convection vector – vertical experimental tube, the direction of flow not in accordance with the free convection vector For such cases the correlation equation was defined Nu_T=f(Gz; y), Nu = f(Gz) and the proportion Nu_T/Nu was analysed. Received on 30 March 2000     

Hydromagnetic free convection flow with induced magnetic field effects

An exact solution is presented for the hydromagnetic natural convection boundary layer flow past an infinite vertical flat plate under the influence of a transverse magnetic field with magnetic induction effects included. The transformed ordinary differential equations are solved exactly, under physically appropriate boundary conditions. Closed-form expressions are obtained for the non-dimensional velocity (u), non-dimensional induced magnetic field component (B _x ) and wall frictional shearing stress i.e. skin friction function (τ _x ) as functions of dimensionless transverse coordinate (η), Grashof free convection number (G _r ) and the Hartmann number (M). The bulk temperature in the boundary layer (Θ) is also evaluated and shown to be purely a function of M. The Rayleigh flow distribution (R) is derived and found to be a function of both Hartmann number (M) and the buoyant diffusivity parameter (ϑ ^*). The influence of Grashof number on velocity, induced magnetic field and wall shear stress profiles is computed. The response of Rayleigh flow distribution to Grashof numbers ranging from 2 to 200 is also discussed as is the influence of Hartmann number on the bulk temperature. Rayleigh flow is demonstrated to become stable with respect to the width of the boundary layer region and intensifies with greater magnetic field i.e. larger Hartman number M, for constant buoyant diffusivity parameter ϑ ^*. The induced magnetic field (B _x ), is elevated in the vicinity of the plate surface with a rise in free convection (buoyancy) parameter G _r , but is reduced over the central zone of the boundary layer regime. Applications of the study include laminar magneto-aerodynamics, materials processing and MHD propulsion thermo-fluid dynamics.     

Experimental study on interfacial area transport of a vertical downward bubbly flow

In relation to the development of the interfacial area transport equation, local flow measurements of vertical downward air–water flows in a pipe with an inner diameter of 50.8 mm were performed at three axial locations of z/D=6.50, 34.0, and 66.5 as well as ten radial locations from r/R=0 to r/R=0.9 using a multi-sensor probe. In the experiment, the superficial liquid velocity and the void fraction ranged from –0.620 m/s to –2.49 m/s and from 0.21% to 8.4%, respectively. The dependence of the interfacial area transport on the liquid velocity, void fraction, and bubble size is discussed in detail.     

Optimal design of angled rib turbulators in a cooling channel

In the present study, an optimal design for enhancement of heat transfer and thermal performance for a stationary channel with angled rib turbulators was investigated to find the most suitable rib geometry. Among various design parameters, two design variables, rib angle of attack (α) and pitch-to-rib height (p/e), were chosen. The ranges of two design variables were set as 30° ≤ α ≤ 80° and 3.0 ≤ p/e ≤ 15.0. Approximations for design of the best rib turbulators were obtained using the advanced response surface method with functional variables. The second-order response surfaces (or correlations) within the ranges of two design variables were completed by this method. As for the optimized results, maximum averaged heat transfer value was obtained at α = 53.31° and p/e = 6.50, while the highest thermal performance value was presented at α = 54.67° and p/e = 6.80.     

A numerical study of non-isothermal turbulent coaxial jets

In this work, we propose to study non isothermal air–air coaxial jets with two different approaches: parabolic and elliptic approaches. The standard k−ε model and the RSM model were applied in this study. The numerical resolution of the equations governing this flow type was carried out for: the parabolic approach, by a “home-made” CFD code based on a finite difference method, and the elliptic approach by an industrial code (FLUENT) based on a finite volume method. In forced convection mode (Fr = ∞), the two turbulence models are valid for the prediction of the mean flow. But for turbulent sizes, k−ε model gives results closer to those achieved in experiments compared to RSM Model. Concerning the limit of validity of the parabolic and elliptic approaches, we showed that for velocities ratio r lower than 1, the results of the two approaches were satisfactory. On the other hand, for r > 1, the difference between the results became increasingly significant. In mixed convection mode (Fr ≅ 20), the results obtained by the two turbulence models for the mean axial velocity were very different even in the plume region. For the temperature and the turbulent sizes the two models give satisfactory results which agree well with the correlations suggested by the experimenters for X ≥ 20. Thus, the second order model with σ _t = 0.85 is more effective for a coaxial jet study in a mixed convection mode.