Variation Of Mean Velocity Research Articles

Use of Lagrangian statistics for the analysis of the scale separation hypothesis in turbulent channel flow

Turbulence models often involve Reynolds averaging, with a closure providing the Reynolds stress tensor as function of mean velocity gradients, through a turbulence constitutive equation. The main limitation of this linear closure is that it rests on an analogy with kinetic theory. For this analogy to be valid there has to be a scale separation between the mean velocity variations and the turbulent Lagrangian free path whose mean value is the turbulent mixing length. The aim of this work is to better understand this hypothesis from a microscopic point of view. Therefore, fluid elements are tracked in a turbulent channel flow. The flow is resolved by direct numerical simulation (DNS). Statistics on particle trajectories ending on a certain distance y 0 from the wall are computed, leading to estimations of the turbulent mixing length scale and the Knudsen number. Comparing the computed values to the Knudsen number in the case of scale separation, we may know in which region of the flow and to what extent the turbulence constitutive equation is not verified. Finally, a new non-local formulation for predicting the Reynolds stress is proposed.

Sound Generation by a Rotor Interacting with a Casing Turbulent Boundary Layer

A new method for predicting the noise generated by a ducted rotor interacting with inhomogeneous and nonisotropic turbulence has been developed. The analytical formulation used a model of the two-point correlation function of the turbulent velocity in the space–time domain. The study focused on a specific condition where the dominant noise source was the interaction between a rotor and a casing turbulent boundary layer. The axial length scale of this turbulence was found to be large enough to generate unsteady lift that was correlated between multiple rotor blades. This led to tonal sound at the blade passing frequency in the absence of mean velocity variations. The analytical formulation was validated with a set of measurements obtained in a ducted rotor facility. The prediction accurately modeled both the tonal and broadband features of the sound spectra.

On MRI turbulence quantification

Turbulent flow, characterized by velocity fluctuations, accompanies many forms of cardiovascular disease and may contribute to their progression and hemodynamic consequences. Several studies have investigated the effects of turbulence on the magnetic resonance imaging (MRI) signal. Quantitative MRI turbulence measurements have recently been shown to have great potential for application both in human cardiovascular flow and in engineering flow. In this article, potential pitfalls and sources of error in MRI turbulence measurements are theoretically and numerically investigated. Data acquisition strategies suitable for turbulence quantification are outlined. The results show that the sensitivity of MRI turbulence measurements to intravoxel mean velocity variations is negligible, but that noise may degrade the estimates if the turbulence encoding parameter is set improperly. Different approaches for utilizing a given amount of scan time were shown to influence the dynamic range and the uncertainty in the turbulence estimates due to noise. The findings reported in this work may be valuable for both in vitro and in vivo studies employing MRI methods for turbulence quantification.

Rotary inertia and temperature effects on non-linear vibration, steady-state response and stability of an axially moving beam with time-dependent velocity

Free non-linear transverse vibration of an axially moving beam in which rotary inertia and temperature variation effects have been considered, is investigated. The beam is moving with a harmonic velocity about a constant mean velocity. The governing partial-differential equations are derived from the Hamilton's principle and geometrical relations. Under special assumptions, the two partial-differential equations can be mixed to form one integro-partial-differential equation. The multiple scales method is applied to obtain steady-state response. Elimination of secular terms will give us the amplitude of vibration. Additionally, the stability and bifurcation of trivial and non-trivial steady-state responses are analyzed using Routh-Hurwitz criterion. Eventually, numerical examples are presented to show rotary inertia, non-linear term, temperature gradient and mean velocity variation effects on natural frequencies, critical speeds, bifurcation points and stability of trivial and non-trivial solutions.

Spanwise variations in nominally two-dimensional rough-wall boundary layers

Laboratory experiments have been conducted in two separate boundary layer facilities to investigate steady spanwise variations in mean velocity discovered during studies of developing flows over regular arrays of large roughness elements. Regular spanwise variation was found with a steady wavelength, moderated by the growing boundary layer, which was an integer multiple of the repeating unit of roughness. Amplitude variations greater than ±5% in the mean were found over the roughness and greater than ±10% in turbulence quantities. Due to the dominating nature of this phenomena throughout the layer, care should be taken in undertaking local measurements aimed at identifying flow variations caused by roughness heterogeneity.

The relative effects of fuel concentration, residual-gas fraction, gas motion, spark energy and heat losses to the electrodes on flame-kernel development in a lean-burn spark ignition engine

The potential of lean combustion for the reduction in exhaust emissions and fuel consumption in spark ignition engines has long been established. However, the operating range of lean-burn spark ignition engines is limited by the level of cyclic variability in the early-flame development stage that typically corresponds to the 0-5 per cent mass fraction burned duration. In the current study, the cyclic variations in early flame development were investigated in an optical stratified-charge spark ignition engine at conditions close to stoichiometry [air-to-fuel ratio (A = 15] and to the lean limit of stable operation (A/F = 22). Flame images were acquired through either a pentroof window (‘tumble plane’ of view) or the piston crown (‘swirl plane’ of view) and these were processed to calculate the intra-cycle flame-kernel radius evolution. In order to quantify the relative effects of local fuel concentration, gas motion, spark-energy release and heat losses to the electrodes on the flame-kernel growth rate, a zero-dimensional flame-kernel growth model, in conjunction with a one-dimensional spark ignition model, was employed. Comparison of the calculated flame-radius evolutions with the experimental data suggested that a variation in A/F around the spark plug of Φ(A/F) ≈ 4 or, in terms of equivalence ratio Φ, a variation in Φ ≈ 0.15 at most was large enough to account for 100 per cent of the observed cyclic variability in flame-kernel radius. A variation in the residual-gas fraction of about 20 per cent around the mean was found to account for up to 30 per cent of the variability in flame-kernel radius at the timing of 5 per cent mass fraction burned. The individual effect of 20 per cent variations in the ‘mean’ in-cylinder velocity at the spark plug at ignition timing was found to account for no more than 20 per cent of the measured cyclic variability in flame kernel radius. An individual effect of similar level was attributed to the heat losses to the electrodes, and a much lower effect than that, namely 5-10 per cent at most, could be attributed to cyclic variations in spark-energy release traces. Even when the variations in mean velocity were coupled to both the effects of heat losses to the electrodes and spark-energy release variations, the combined effect was found to account for no more than 40-50 per cent of the observed cyclic variability in flame-kernel radius at the 5 per cent mass-fraction burned timing of 40 ° crank angle after ignition timing.

Extinction of a premixed flame by a large variation in axial velocity

Unsteady flame propagation in a tube is examined by introducing a mean velocity variation larger than the burning velocity to a stabilized flame for a period longer than the reaction time scale. In our previous work, stabilized propane–air flames were classified as either one-dimensional or two-dimensional flames. The eventual extinction during the velocity increase was categorized as either acoustic extinction or boundary layer extinction. In this work, the effects of a nonunity Lewis number were estimated through experiments with a methane–air flame; the eventual extinction during the velocity decrease was investigated in more detail; and the growth of the extinction boundary layer was analyzed with a transient one-dimensional model of the flame stretch. In our experiments, the Lewis number did not affect the existence or characteristics of the critical velocity and the characteristic time for boundary layer extinction. An additional critical velocity was found, however, for acoustic extinction when the Lewis number was smaller than unity. In the transient one-dimensional model, the velocity transition along the flame was calculated with a continuity equation and an axial momentum equation. The spatial gradient of the burning velocity and the extinction criterion were simplified with the experimental results and some theoretical studies. The analysis shows that the unsteady flame stretch at the flame edge during a large axial velocity variation is the prevailing cause of the growth of the extinction boundary layer. These results provide some evidence that flame stretch affects the behavior of the flame edge; they also suggest the cause of the finger flame. The findings help explain the unsteady behavior of premixed flames near a flammability limit.

On the origin, frequency and magnitude of macro-instabilities of the flows in stirred vessels

The mean flow and turbulence fields in a fully baffled vessel stirred by a Rushton impeller at three clearances and a pitched-blade turbine at one clearance have been investigated with laser-Doppler anemometry (LDA) to characterise the macro-instabilities (MIs) present in such flows. Time-resolved velocity measurements were made and the frequency content of the velocity recordings was analysed with FFT techniques. The study aims to throw light into the frequency, magnitude, nature and origin of such flow variations, especially in view of the different findings that have been reported in the published literature. The frequency of the MIs was found to be linearly related to the rotational speed of the impeller and to be essentially independent of impeller design. A single fundamental frequency, around 0.015–0.02 N (Hz), where N is the impeller rotational speed, was present for all configurations, together with harmonic frequencies, the prominence of which depended on impeller geometry and/or clearance. The LDA data and direct observations made with laser-sheet flow visualisation indicated clearly that the macro-instability stems from a precessional motion about the vessel axis, similar to the precession encountered in most swirling flows. The results show that MIs, as a mean flow motion superimposed on the flow pattern in the vessel, can result in a broadening of the measured turbulence levels by up to 25%, and a mean velocity variation of up to 0.3 V tip. The findings indicate therefore that it might be necessary and indeed it could be advantageous for improved process prediction to take MI into account in models of the flows in stirred vessels.

Characteristic Regimes of Transitional Separation Bubbles in Unsteady Flow

This experimental investigation deals with transition phenomena of a separated boundary layer under unsteady inlet flow conditions. The main purpose of this investigation is to understand the influence of the rotor-stator interaction in turbomachinery on the subsequent, highly loaded boundary layer. The research project is divided into two phases. In the first phase, which has been completed recently, only the variation of mean velocity caused by upstream blades was simulated in the experiments while the free-stream turbulence intensity was retained at a constant low level. The experiments are carried out in an Eifel-type wind tunnel to investigate the laminar separated boundary layer of a flat plate under oscillating inlet conditions. The adverse pressure gradient, similar to that of turbomachines, is generated by the contoured upper wall. The unsteadiness is produced by a rotating flap located downstream of the test section. The reduced frequency, the amplitude and the mean Reynolds number are varied to simulate the conditions prevailing in turbomachines. In addition to the Kelvin–Helmholtz instability of the separated shear layer, a lower frequency instability was observed. This is frequently referred to as `free shear layer flapping' and results in two distinctly different ways of re-attachment, depending primarily on the Reynolds number. For low momentum thickness Reynolds numbers at the separation point, large-scale vortices locked to the frequency of the unsteady main flow are identified. They originate nearly at the top of the separation bubble and are ejected downstream. A fully turbulent boundary layer develops after these vortices mix out. For higher Reynolds numbers, transition is completed within a short length of the free shear layer and there-attachment region. The characteristic momentum thickness Reynolds number separating these two regimes in unsteady flow is about 125. The Strouhal number (reduced frequency) does not appear to have any significant effect. Based on the experimental results, this behaviour is discussed in some detail.

Experiments on turbulent natural convection in an enclosed tall cavity

Experiments have been undertaken to investigate the natural convection of air in a tall differentially heated rectangular cavity (2.18 m high by 0.076 m wide by 0.52 m in depth). They were performed with temperature differentials between the vertical plates of 19.6°C and 39.9°C, giving Rayleigh numbers based on the width of 0.86×106 and 1.43×106. Under these conditions the flow in the core of the cavity is fully turbulent and property variations with temperature are comparatively small. A previously used experimental rig has been modified, by fitting partially conducting top and bottom walls and outer guard channels, to provide boundary conditions which avoid the inadequately defined sharp changes in temperature gradient and other problems associated with insufficient insulation on nominally adiabatic walls. Mean and turbulent temperature and velocity variations within the cavity have been measured, together with heat fluxes and turbulent shear stresses. The temperature and flow fields were found to be closely two-dimensional, except close to the front and back walls, and anti-symmetric across the diagonal of the cavity. The partially conducting roof and floor provide locally unstable thermal stratification in the wall jet flows there, which enhances the turbulence as the flow moves towards the temperature controlled plates. The results provide a greatly improved benchmark for the testing of turbulence models in this low turbulence Reynolds number flow.

Scalar mixing in the vicinity of two disk turbines and two pitched blade impellers

A LIF line scan system was used to obtain unobtrusive, angle-resolved concentration measurements in the vicinity of four forms of impeller agitating a continuously operated stirred tank. The concentration measurements for the two disc turbines, the Rushton and the `bucket’ impeller revealed strong periodic variations in the radical discharge jet. The measurements for the `bucket’ impeller showed that trailing vortex structures are also generated by curved blades and the trailing vortices of both impellers caused undesired regions of high concentration gradients and fluctuations between blade passages. In the case of the 45- and 60°-pitched blade impeller, periodic concentration variations occurred only in the axial discharge of the impellers and concentration gradients and fluctuations were high close to the blades; this was linked to mean velocity variations between a blade-to-blade passage.

Three-Dimensional Flow Characteristics in the Downstream Region of a Butterfly-Type Valve Used in Air-Conditioning Systems

Oil-film flow visualizations and three-dimensional flow measurements have been conducted in the downstream region of a butterfly-type valve used in air-conditioning systems, with the variation of a disk open angle. The flow visualizations in the flow symmetry plane show that there are a pair of counter-rotating separation/recirculation zones as wall as two jet-like near-wall flows. These flow disturbances are strongly depends on the disk open angle. Based on the flow visualization, a qualitative flow model is suggested in the near-field and downstream region of the valve disk. For a small disk open angle, the mean velocities and turbulent intensities have relatively small values in the near-field of the valve disk, but they do not show uniform distributions even in some downstream region. With an increment of the disk open angle, mean velocity variations and turbulent intensities are greatly increased in the immediate downstream region, but uniform distributions are quickly resumed as departing from the valve disk. The mass flow rate remains nearly constant for the disk open angles less than 30 degrees, meanwhile it strongly depends on the disk open angles between 45 and 75 degrees. The pressure loss is found to be about zero for the disk open angles less than 45 degrees, but is substantially increased for those larger than 75 degrees.

Laminar premixed flame propagation using large axial velocity variation

A stabilization condition for the premixed flame in a tube was investigated, and then a mean velocity variation larger than the burning velocity was introduced to the stabilized flame for a period longer than the reaction time scale in order to examine the unsteady behavior of flame propagation. The stabilized flames were classified into two regimes, a one-dimensional regime and a two-dimensional regime, by both the shape and the mass consumption rate. The magnitude and period of the mean velocity variation were treated as experimental parameters. When the large velocity variation was introduced in the same direction as the initial mean velocity, the extinction behaviors were observed and systematically classified into two groups: extinction by boundary layer and extinction by acoustic instability. We found out that there exists a critical velocity change and a critical time above which the extinction region develops to the center of the tube and extinguishes the flame. With the velocity variation in the opposite direction of the initial mean velocity, the flame was not extinguished near the wall, and the characteristics of the flame propagation were similar to those of earlier studies on flame propagation. The mechanism of the extinction near the wall is explained by the flame stretch theory, which provides a clue to the stretch effects on the finger flame.

Modulation of platelet aggregation after percutaneous transluminal angioplasty of the iliac artery for atherosclerosis obliterans

Background: Platelet aggregation is modulated by blood flow. We investigated whether platelet function is altered during percutaneous transluminal balloon angioplasty in patients with atherosclerosis obliterans. Methods: Blood samples were obtained from the iliac artery in 9 lower limbs of 7 patients undergoing percutaneous balloon angioplasty of the iliac artery. An agonists-induced platelet aggregation test was performed with an aggregometer. Femoral blood flow was measured with a Doppler velocimeter before and after the procedure. Results: Before dilatation, the maximum platelet aggregation rates (± SEM) induced by adenosine phosphate, epinephrine, and arachidonic acid were 54.7% ± 5.8%, 64.8% ± 4.3%, and 60.5% ± 6.1%, respectively. After angioplasty, these values reduced to 36.7% ± 4.1%, 36.1% ± 8.6%, and 40.1% ± 5.0%, respectively (P <.05). The pre-procedural ankle-brachial pressure index, mean flow rate, mean velocity, and shear stress variation were 0.63 ± 0.1, 218.1 ± 32.1 mL/min, 9.4 ± 1.1 cm/sec, and 60.6 ± 17.7 dyne/cm2, respectively. The mean velocity at the stenotic lesion was 215.1 ± 83.9 cm/sec, which was significantly greater than those of the distal artery or after angioplasty (P <.01). Both ankle-brachial pressure index and shear stress variation increased after angioplasty to 0.99 ± 0.07 (P <.05) and 139.8 ± 17.0 (P <.05) dyne/cm2, but the mean flow rate and the mean velocity (198.3 ± 24.5 mL/min and 8.8 ± 1.2 cm/sec after angioplasty) did not change significantly. Conclusions: These results indicate that activated platelet function at a stenosed artery was decreased after angioplasty, possibly because of normalized blood flow with reduction of stenotic lesion.(Surgery 2000;127:87-91)

Taylor dispersion of contaminants due to surface waves

This study addresses the longitudinal dispersive effect due to mass transport induced by progressive surface waves. Lagrangian drift is investigated to be the mechanism creating cross-sectional mean velocity variation, an essential component for Taylor dispersion. The dispersive effect is found to be more significant if the wave height is much larger than where D is the diffusivity and T the wave period. The longitudinal dispersion coefficient with a Stoke drift profile is first established. Subsequently drift profiles with viscous effect are considered and the dispersive effect increases substantially. The coupling of the oscillatory orbital motion of the pollutant particles under linear waves with background diffusion is further examined through a random walk numerical approach. Results show that, despite the possible modulation of the probability density with the wavy surface, the magnitude of the dispersion is not affected by the inclusion of the orbital motion.

Dispersion in Flows with Streamwise Variations of Mean Velocity: Radial Flow

The familiar example of Taylor dispersion in pipe flow is extended to the case of laminar flows with velocity variations in the streamwise direction. The effective dispersivity is shown to depend on the streamwise coordinate. The generic scheme is illustrated by the simple example of radial source (sink) flows in two and three dimensions, and the distinctive results for the two cases are contrasted.

Intraoperative changes of transcranial Doppler velocity: relation to arterial oxygen content and whole-blood viscosity

The association of arterial oxygen content (CaO 2) and viscosity with transcranial Doppler (TCD) blood flow velocity in the middle cerebral artery was studied in 20 adults without cerebrovascular disease undergoing abdominal surgery associated with significant fluctuations in hematology. TCD measurements and arterial blood samples were obtained before and directly after surgery but before blood transfusion. There was an inverse association between baseline mean velocity and CaO 2 ( r = −0.56), hematocrit ( r = −0.50), hemoglobin ( r = −0.51), and high-shear viscosity ( r = −0.46). After intraoperative blood loss, intraindividual fluctuations of TCD measurements, blood oxygenation, and rheologic factors were studied. In multiple regression analysis, changes in CaO 2 had the strongest association with changes in TCD values, accounting for 55% of the variation in mean velocity. Addition of hematocrit and viscosity could not account for more variation in mean velocity than CaO 2 alone.

CHARACTERISTICS OF A DEVELOPING DROPLET - LADEN JET IMPINGING ON A NORMAL WALL

The size-velocity characteristics of a droplet-laden air jet impinging on a normal wall is investigated using a phase-Doppler anemometer. The results of measurements conducted for two jet-exit-to-impingement-wall distances are presented. Experimental data are obtained across the jet at several axial stations covering the first ten jet-exit diameters. The radial variation of droplet mean velocity, rms velocity and skewness coefficient indicates that similarity is not achieved. The rate of spreading of the jet is higher than that noticed in both single-phase flow and previous two-phase flow studies. The presence of the impingement wall does not have a significant effect on the mean velocity distributions for Z/Zi &lt; 0.8. There is an increase in droplet size with increasing distance from the nozzle for Z/D &gt; 4.0. In the early regions of the jet, the water droplet size and velocity are strongly correlated, especially in the core regions. With increasing Z/D, there is no association between size and velocity.

Blood Flow in the Human Optic Nerve Head during Isometric Exercise

Investigating blood flow autoregulation in the optic nerve is important to understand the physiopathology of various ocular diseases such as glaucoma. This investigation requires that one establishes the relationship between optic nerve blood flow and perfusion pressure. Previous work has documented the effect of lowering the perfusion pressure on optic nerve blood flow. The purpose of the present study was to investigate the effect of elevated perfusion pressure on blood flow in this tissue.Laser Doppler flowmetry was applied to measure relative mean velocity, volume and flux of red blood cells in the tissue of the optic nerve head. These parameters were measured in 13 subjects during isometric exercise consisting of squatting.In the range of perfusion pressures from 56±4 to 80±5 mmHg (30±8%), there was no significant variation of mean velocity, volume and flux of red blood cells, but vascular resistance increased by about 50%. Intraocular pressure was increased significantly above baseline at the end of squatting and decreased during recovery.The results suggest that the maintenance of constant blood flow is achieved by an increase in vascular resistance taking place either at the arterioles feeding or at the veins draining the blood from the ONH or at the ophthalmic artery and/or vessels between this artery and the site of LDF measurements. Combining the results of this study with those of a previous one where perfusion pressure was decreased by increasing the intraocular pressure, we show the entire relationship between perfusion pressure and optic nerve blood flow in man.

An experimental investigation of flow parameters inside a spherical swirl pre-chamber of a diesel engine under motoring condition

The main aim of the present investigation is to experimentally study the flow parameters inside a spherical combustion chamber of an indirect injection diesel engine. For this a spherical chamber has been fitted in the cylinder head. Using a constant temperature hot-wire anemometer, measurements have been made under non-firing condition at 400 and 500 rpm during compression stroke. Mean velocity and turbulence intensity values are evaluated from the hot-wire signal. Measurements are made at three axial planes, six angular locations and four radial positions. Large variations of mean velocity and turbulence intensity have been observed within the chamber. From the measurements, the mean velocity and turbulence intensity are found to be maximum at 30° before compression TDC and these values are found to decrease towards the centre of the pre-chamber. The mean velocity and turbulence intensity distribution with respect to various locations and crank angles are presented and discussed.