Mean Flow Direction Research Articles

Computation in the rabbit aorta of a new metric – the transverse wall shear stress – to quantify the multidirectional character of disturbed blood flow

Spatial variation of the haemodynamic stresses acting on the arterial wall is commonly assumed to explain the focal development of atherosclerosis. Disturbed flow in particular is thought to play a key role. However, widely-used metrics developed to quantify its extent are unable to distinguish between uniaxial and multidirectional flows. We analysed pulsatile flow fields obtained in idealised and anatomically-realistic arterial geometries using computational fluid dynamics techniques, and in particular investigated the multidirectionality of the flow fields, capturing this aspect of near-wall blood flow with a new metric – the transverse wall shear stress (transWSS) – calculated as the time-average of wall shear stress components perpendicular to the mean flow direction. In the idealised branching geometry, multidirectional flow was observed downstream of the branch ostium, a region of flow stagnation, and to the sides of the ostium. The distribution of the transWSS was different from the pattern of traditional haemodynamic metrics and more dependent on the velocity waveform imposed at the branch outlet. In rabbit aortas, transWSS patterns were again different from patterns of traditional metrics. The near-branch pattern varied between intercostal ostia, as is the case for lesion distribution; for some branches there were striking resemblances to the age-dependent patterns of disease seen in rabbit and human aortas. The new metric may lead to improved understanding of atherogenesis.

Different-scale convective structures in a cooled liquid layer with a horizontal shear flow

The paper is concerned with three-dimensional different-scale convective structures arising in a thin liquid layer cooled from above and subjected to a horizontal shear flow produced by tangent wind stresses on a free surface. In accord with the previous experiment the region of moderately large Grashof and Marangoni numbers and not too large Reynolds numbers is examined. The problem is solved numerically using a spectral method constructed on the basis of a spectral representation of the standard equations governing the gravity-capillary convection. Spectral decomposition with periodicity condition along the horizontal coordinates together with discretization in the vertical direction is used. The planeforms obtained in a horizontal subsurface section of vertical velocity field are analyzed. The mechanism of formation of coherent different-scale structures arising due to surface cooling and thermocapillarity effects is elucidated and the cell-to-roll transition occurring with the increase of horizontal flow velocity is studied. Roll patterns containing longitudinal (aligned in the mean flow direction) basic rolls and predominantly transversal small-scale rolls are revealed. The problem of upflow and downflow cells in question is discussed and the agreement of the computational results with the available experimental data is confirmed.

An example of solute spreading in nonstationary, bounded geological formations

We analyze the impact of a linear trend in the mean log-conductivity on the transport of a conservative tracer in a bounded domain. The effects of such a linear trend on solute transport were analyzed in depth for unbounded domains (Rubin and Seong, Water Resour Res 30(11):2901–2911, 1994; Indelman and Rubin, Water Resour Res 31(5):1257–1265, 1995; Water Resour Res 32(5):1257–1265, 1996), whereas studies concerning this special case of medium nonstationarity in finite domains usually focus on head or flow statistics (Guadagnini et al., Stoch Environ Res Risk Assess, 17:394–407, 2003). In this study both ensemble and effective plume moments are provided for an instantaneous release of a solute through a linear source normal to the mean flow direction, by taking into account different sizes of the source. The analysis involving a steady velocity field spatially nonstationary is developed by using the stochastic finite element method. Results show that ensemble moments are affected by increasing trends both parallel and normal to the mean flow direction, but the impact on effective plume moments is very different. A parallel trend does not seem to influence the effective second moments; while a normal trend, although modifies the transverse effective moment only weakly, strongly increases the longitudinal one, especially for large initial sizes of the source. Furthermore, the increase of the particle displacement variance produced by a parallel trend in the finite domain disagrees with the results obtained in an unbounded domain, due to the boundary conditions here considered making both head and velocity moments nonstationary and nonsymmetric.

Vortex Shedding in a Tandem Circular Cylinder System With a Yawed Downstream Cylinder

This investigation examines the flow produced by a tandem cylinder system with the downstream cylinder yawed to the mean flow direction. The yaw angle was varied from α=90deg (two parallel tandem cylinders) to α=60deg; this has the effect of varying the local spacing ratio between the cylinders. Fluctuating pressure and hot-wire measurements were used to determine the vortex-shedding frequencies and flow regimes produced by this previously uninvestigated flow. The results showed that the frequency and magnitude of the vortex shedding varies along the cylinder span depending on the local spacing ratio between the cylinders. In all cases the vortex-shedding frequency observed on the front cylinder had the same shedding frequency as the rear cylinder. In general, at small local spacing ratios the cylinders behaved as a single large body with the shear layers separating from the upstream cylinder and attaching on the downstream cylinder, this caused a correspondingly large, low frequency wake. At other positions where the local span of the tandem cylinder system was larger, small-scale vortices began to form in the gap between the cylinders, which in turn increased the vortex-shedding frequency. At the largest spacings, classical vortex shedding persisted in the gap formed between the cylinders, and both cylinders shed vortices as separate bodies with shedding frequencies typical of single cylinders. At certain local spacing ratios two distinct vortex-shedding frequencies occurred indicating that there was some overlap in these flow regimes.

Model-Based Correction of Velocity Measurements in Navigated 3-D Ultrasound Imaging During Neurosurgical Interventions

In neurosurgery, information of blood flow is important to identify and avoid damage to important vessels. Three-dimensional intraoperative ultrasound color-Doppler imaging has proven useful in this respect. However, due to Doppler angle-dependencies and the complexity of the vascular architecture, clinical valuable 3-D information of flow direction and velocity is currently not available. In this work, we aim to correct for angle-dependencies in 3-D flow images based on a geometric model of the neurovascular tree generated on-the-fly from free-hand 2-D imaging and an accurate position sensor system. The 3-D vessel model acts as a priori information of vessel orientation used to angle-correct the Doppler measurements, as well as provide an estimate of the average flow direction. Based on the flow direction we were also able to do aliasing correction to approximately double the measurable velocity range. In vitro experiments revealed a high accuracy and robustness for estimating the mean direction of flow. Accurate angle-correction of axial velocities were possible given a sufficient beam-to-flow angle for at least parts of a vessel segment . In vitro experiments showed an absolute relative bias of 9.5% for a challenging low-flow scenario. The method also showed promising results in vivo, improving the depiction of flow in the distal branches of intracranial aneurysms and the feeding arteries of an arteriovenous malformation. Careful inspection by an experienced surgeon confirmed the correct flow direction for all in vivo examples.

Breakthrough of contaminant plumes in saturated volcanic rock: implications from the Yucca Mountain site

AbstractThis manuscript addresses the topic of transverse dispersion and its impact on the behavior of the saturated zone below Yucca Mountain, a site that had been proposed for a US nuclear waste repository. Guided by a review of relevant observations of dispersion in similar formations, this study evaluates the importance of uncertainty in dispersion, particularly dispersion transverse to the mean transport direction, on metrics of interest to the Yucca Mountain risk assessment. Although as expected, larger values of transverse dispersivity lead to greater spreading of the plume in directions orthogonal to the mean flow direction, a corresponding sensitivity is not observed to the travel time statistics of the breakthrough curve at the compliance boundary. Thus, when a risk assessment is based on contaminant mass flux at compliance well or ‘fence line’ downstream from the source, as in the Yucca Mountain case, transverse dispersion may be of secondary importance to other parameters that more directly impact travel times. This result is in contrast to systems in which reactive transport processes are important to the attenuation of the plume, in which case transverse dispersion and mixing may be expected to play a dominant role in controlling the reaction rates and contaminant concentrations in the plume.

Large-eddy simulation of passive scalar dispersion in an urban-like canopy

AbstractResults from large-eddy simulations of short-range dispersion of a passive scalar from a point source release in an urban-like canopy are presented. The computational domain is that of a variable height array of buildings immersed in a pressure-driven, turbulent flow with a roughness Reynolds number ${\mathit{Re}}_{\tau } = 433$. A comparative study of several cases shows the changes in plume behaviour for different mean flow directions and source locations. The analysis of the results focuses on utilizing the high-fidelity datasets to examine the three-dimensional flow field and scalar plume structure. The detailed solution of the flow and scalar fields within the canopy allows for a direct assessment of the impact of local features of the building array geometry. The staggered, skewed and aligned arrangements of the buildings with respect to the oncoming flow were shown to affect plume development. Additional post-processing quantified this development through parameters fundamental to reduced-order Gaussian dispersion models. The parameters include measures of concentration decay with distance from the source as well as plume trajectory and spread. The horizontal plume trajectory and width were found to be more sensitive to source location variations, and hence local geometric features, than vertical plume parameters.

Autocatalytic reaction fronts inside a porous medium of glass spheres.

We analyze experimentally chemical wave propagation in the disordered flow field of a porous medium. The reaction fronts travel at a constant velocity that drastically depends on the mean flow direction and rate. The fronts may propagate either downstream and upstream but, surprisingly, they remain static over a range of flow rate values. Resulting from the competition between the chemical reaction and the disordered flow field, these frozen fronts display a particular sawtooth shape. The frozen regime is likely to be associated with front pinning in low velocity zones, the number of which varies with the ratio of the mean flow and the chemical front velocities.

Dissipation element analysis in experimental and numerical shear flow

Tomographic particle-image velocimetry (TPIV) measurements and direct numerical simulations (DNS) are performed to analyze the small and large scale structure of channel flow data, i.e., the fields of the fluctuations of the three velocity components and the turbulent kinetic energy, respectively, are investigated by dissipation element analysis which is a new method to gain statistical information from turbulent scalar fields based on distinct, space-filling elements.In the inertial range, the conditional mean of the experimental turbulent kinetic energy difference reveals a scaling in the range of the expected characteristic 2/3-Kolmogorov scaling. This is in excellent agreement with the numerical results from the channel flow DNS and comparative data from the DNS of a homogeneous shear flow. Furthermore, the shape of the marginal pdfs of the normalized element length and the scalar difference, i.e., the linear rise and the exponential decay, is shown to agree with the findings from the associated DNS. On average, the dissipation elements possess an orientation over a certain bandwidth in the mean flow direction.

Upstream-facing convex surfaces: Bedrock bedforms produced by fluvial bedload abrasion

Bedrock bedforms are a common sight in many bedrock river channels but few process-form linkages have been established for the myriad of forms recognised in the literature. Direct observations from bedrock channels on rates and distributions of erosion involved in bedrock bedform development are rare because of difficulties in making observations in these high-energy environments. Upstream-facing convex surfaces (UFCS) are common in bedrock rivers and are partnered with downstream-facing surfaces. We have made observations of bedrock morphology, aspect, and surface texture of UFCSs in bedrock river channels exposed at low river stage in Taiwan. A distinct contrast in morphology and surface texture exists between upstream- and downstream-facing surfaces. On a millimetre scale of observation, UFCSs have a three-dimensional, brittle fracture-dominated, granular surface texture but on a decimetre to metre scale have an overall convex form. Downstream-facing surfaces, in contrast, have millimetre to micrometre scale rugosity characterised by smooth polished surfaces that on a centimetre to metre scale are concave or undulating with intricately sculpted features. A curvilinear topographic feature, or crest line, marks the change in slope, aspect, and surface textures between upstream- and downstream-facing surfaces and is orientated approximately perpendicular to the reach azimuth and therefore mean flow direction. We used a system of removable datums and terrestrial laser scanning to monitor the three-dimensional erosion of nine bedforms at sites in the Liwu River, Taiwan, over a period of one year (2007–2008). All sites had an asymmetric distribution of erosion with higher rates of erosion on upstream-facing surfaces and minor to undetectable erosion on downstream-facing surfaces, with local complexity. The crest line mapped the boundary between relatively high and low erosion rates between the upstream-facing and downstream-facing surfaces respectively. Observations from unscaled flume experiments show that bedload particles transit a flow obstacle by travelling up the upstream-facing surface, where erosion is focused, and hop over the top of the obstacle. Our field and flume observations indicate that UFCSs observed in natural rivers are produced by bedload abrasion, which by being decoupled from the flow can only impact the stoss surface to any significant extent. Micropitting found on polished downstream-facing surfaces indicate that they are dominantly formed by suspended load abrasion. The aspect of a surface, its position in a channel cross section, the topography of the channel upstream, and the local topography of the bedrock bedform are significant controls on the location and magnitude of abrasion by bedload and resultant surface textures because of their effect on steering a bedload particle stream. The high erosion rates observed indicate that abrasion by bedload is the controlling process in the formation of this variety of bedrock bedform and possibly the channel at large in this setting.

External Mean Flow Effects on Sound Transmission Through Acoustic Absorptive Sandwich Structure

A theoretical model is developed to investigate the influence of external mean flow on sound transmission through an infinite double-leaf panel filled with porous sound absorptive materials. The sound transmission process in the porous material is described by using the equivalent fluid model, while fluid-structure coupling conditions are employed to ensure displacement continuity at fluid-structure interfaces. In order to verify the theoretical model, the model predictions are compared with existing experimental results. Numerical investigations are subsequently performed to quantify how a set of systematic parameters affect the sound transmission loss. It is demonstrated that the porous material affects the transmission loss in terms of both the absorption effect and the damping effect. Besides, thematerial loss factor and the thickness of the face plates also have an influence on the coincidence dip of the transmission loss curve. At frequencies below the coincidence frequency, the mean flow increases the transmission loss values due to the added damping effect of themean flow, whilst shifts the coincidence frequency upward because of the refraction effect of the mean flow. In addition, the coincidence frequency decreases with increasing azimuth angle between the sound incident direction and mean flow direction.

Experimental Study of Polymer Flooding in Fractured Systems Using Five-Spot Glass Micromodel: The Role of Fracture Geometrical Properties

Water flooding is being widely used in the petroleum industry and has been considered as a simple inexpensive secondary recovery method. But in fractured formations, existence of fracture system in reservoir rock induces an adverse effect on oil recovery by water flooding. Polymer flooding has been successfully applied as an alternative enhanced oil recovery method in fractured formations. But, the role of fracture geometrical properties on macroscopic efficiency of polymer flooding is not yet well-understood, especially in fractured five-spot systems. In this work five-spot glass micromodel, because of micro-visibility, ease of multiple experimentations and also presence of the unexplored issues, was used to experimentally investigate the influence of fracture geometrical characteristics such as fracture orientation, fracture spacing, fracture overlap and etc on the macroscopic efficiency of polymer flooding. The tests were performed on the fractured models which are initially saturated with the crude oil at fixed flow rate conditions and in a horizontally mounting. The results revealed that the macroscopic efficiency of polymer flooding depends on fracture geometrical properties. Fracture orientation showed more imposing effect than other fracture geometrical properties, and fracture with 45 degree inclination to the mean flow direction, gives greatest oil recovery factor. Large spacing fractures give more recovery than small spacing ones and in case of overlapping, fractures with less overlapping help polymer to better propagate which could be related to their greater effective fracture length. This pre-called effect could be responsible to show how continuity and width to length ratio of fractures affect recovery factor, less fracture discontinuity as well as more length to width ratio of fracture give more swept zone. Also, increasing number of fractures decreases oil recovery factor. The results of this work can be helpful to better understanding the role of fracture geometrical properties on macroscopic efficiency of polymer flooding in five-spot fractured systems.

Energy flow model for thin plate considering fluid loading with mean flow

Energy Flow Analysis (EFA) has been developed to predict the vibration energy density of system structures in the high frequency range. This paper develops the energy flow model for the thin plate in contact with mean flow. The pressure generated by mean flow affects energy governing equation and power reflection–transmission coefficients between plates. The fluid pressure is evaluated by using velocity potential and Bernoulli's equation, and energy governing equations are derived by considering the flexural wavenumbers of a plate, which are different along the direction of flexural wave and mean flow. The derived energy governing equation is composed of two kinds of group velocities. To verify the developed energy flow model, various numerical analyses are performed for a simple plate and a coupled plate for several excitation frequencies. The EFA results are compared with the analytical solutions, and correlations between the EFA results and the analytical solutions are verified.

Comment on “Comparison of Fickian and temporally nonlocal transport theories over many scales in an exhaustively sampled sandstone slab” by Elizabeth Major et al.

Comment on “Comparison of Fickian and temporally nonlocal transport theories over many scales in an exhaustively sampled sandstone slab” by Elizabeth Major et al.

Local flow field of a surface-mounted finite circular cylinder

The local flow field and near-wake region of a surface-mounted finite circular cylinder were studied experimentally in a low-speed wind tunnel using particle image velocimetry (PIV). The cylinder was mounted normal to a ground plane and was partially immersed in a flat-plate turbulent boundary layer. Four finite circular cylinders of aspect ratios AR=9, 7, 5 and 3 were tested at a Reynolds number of ReD=4.2×104. At the location of the cylinder, the boundary layer thickness relative to the cylinder diameter was δ/D=1.6. PIV velocity field measurements were made in a vertical plane parallel to the mean flow direction on the flow centerline (the symmetry plane), within five diameters upstream and downstream of the cylinder, and also above the free end. Above the free end of the cylinder, flow separation from the leading edge leads to the formation of a mean recirculation zone on the free-end surface. The point of reattachment of the flow onto the free-end surface moves towards the trailing edge as the cylinder aspect ratio is decreased. Large regions of elevated turbulence intensity and Reynolds shear stress are found above the free end. In the near-wake region, the large recirculation zone contains a vortex immediately behind and below the free end; this vortex was found for all four aspect ratios. A second vortex is found behind the cylinder near the cylinder-wall junction; this vortex was not observed for the cylinder of AR=3, indicating a distinct wake structure for this cylinder.

Analysis of the anisotropy of group velocity error due to spatial finite difference schemes from the solution of the 2D linear Euler equations

SUMMARY Numerical differencing schemes are subject to dispersive and dissipative errors, which in one dimension, are functions of a wavenumber. When these schemes are applied in two or three dimensions, the errors become functions of both wavenumber and the direction of the wave. For the Euler equations, the direction of flow and flow velocity are also important. Spectral analysis was used to predict the error in magnitude and direction of the group velocity of vorticity–entropy and acoustic waves in the solution of the linearised Euler equations in a two-dimensional Cartesian space. The anisotropy in these errors, for three schemes, were studied as a function of the wavenumber, wave direction, mean flow direction and mean flow Mach number. Numerical experiments were run to provide confirmation of the developed theory. Copyright © 2012 John Wiley & Sons, Ltd.

Large-Eddy Simulation of Atmospheric Boundary-Layer Flow Over Fluvial-Like Landscapes Using a Dynamic Roughness Model

A recently developed dynamic surface roughness model (Anderson and Meneveau, J Fluid Mech 679:288–314, 2011) for large-eddy simulation (LES) of atmospheric boundary-layer flow over multi-scale topographies is applied to boundary-layer flow over several types of fluvial-like landscapes. The landscapes are generated numerically with simulation of a modified Kardar–Parisi–Zhang equation (Passalacqua et al., Water Resour Res 42:WOD611, 2006). These surfaces possess the fractal-like channel network and anisotropic features often found in real terrains. The dynamic model is shown to lead to accurate flow predictions when the surface-height distributions exhibit power-law scaling (scale invariance) in the prevalent mean flow direction. In those cases, the LES provide accurate predictions (invariant to resolution) of mean velocity profiles. Conversely, some resolution dependence is found for applications in which the landscape’s streamwise spectra do not exhibit pure power-law scaling near wavenumbers corresponding to the LES grid resolution.

Separation of nanoparticles by flow past a patterned substrate

Motivated by the problem of efficiently separating nanoparticles of different character held in solution, we investigate trajectory deflection and particle trapping in flows of nanoparticle suspensions past patterned surfaces. We consider rigid atomistic particles suspended in a viscous liquid solvent and driven by a pressure gradient through a channel, one side of which has a pattern of alternating stripes which attract or repel the particles. We first consider van der Waals forces alone, where the wall interaction is obtained by summing over semi-infinite slabs of material having a Lennard-Jones interaction with or without an attractive term, yielding a force field with nontrivial three-dimensional spatial variation. This wall interaction can either trap particles on the attractive stripes or deflect the trajectories of mobile particles away from the direction of mean flow. Using molecular dynamics simulations we determine the motion of particles of different sizes in this potential, and observe distinct but modest deflections of several degrees from the direction of the imposed fluid flow. The effects of electrostatic interactions are considered by decorating the particles and walls with opposite charges, resulting in significantly more trapping and larger deflection angles. We use Langevin simulations to treat the motion of larger particles in the van der Waals case, and again observe particle trapping and deflection, although the numerical details of the results differ from the molecular dynamics simulations. In the Langevin case we are furthermore able to obtain bounds on the deflection angle from an analysis of the associated Fokker-Planck equation. We conclude that patterned surfaces deflect particle trajectories to a degree depending on their size, and may be used as a vector chromatography separation technique.

Flow velocity statistics for uniform flow through 3D anisotropic formations

Groundwater flow through anisotropic heterogeneous formations is investigated using statistical moments of velocity. Uniform flow of constant mean velocity takes place in a random hydraulic conductivity field, which is modeled using the multi-indicator model, used here as an alternative to the common multi-Gaussian model. The mean flow direction is aligned with the long axis of anisotropy. A collection of non-overlapping oblate spheroids of random hydraulic conductivity is placed using a periodic packing in a matrix of hydraulic conductivity K0. Self-consistent (SC) argument is used to calculate approximate analytical solutions of the velocity. The methodology is applied to a medium with random inclusions of normally distributed log-permeability Y=lnK. Closed-form expressions for both average velocity and its variance were obtained, while higher order moments (up to fourth), velocity autocorrelation and integral scales are computed by numerical quadratures. In case when anisotropy is absent, the solutions converge to those developed for isotropic media by Fiori et al. (2003) [14]. The solutions are checked using extensive three-dimensional numerical simulations. The main effect of anisotropy is to increase the variance of the longitudinal velocity and to reduce the variance of the transverse and vertical components. Surprisingly, the growth of the vertical velocity variance with heterogeneity σY2 is not always monotonous. Classic first-order solutions generally overpredict the growth trends of the velocity variance with heterogeneity. Analysis of skewness and kurtosis suggests that the velocity probability density function (pdf) is generally far from Gaussian, except for weakly heterogeneous formations. The deviation from Gaussianity increases with increased anisotropy for all velocity components. The velocity autocorrelation function is weakly dependent on σY2, as confirmed by the numerical simulations.

FIVE-SPOT INJECTION/PRODUCTION WELL LOCATION DESIGN BASED ON FRACTURE GEOMETRICAL CHARACTERISTICS IN HEAVY OIL FRACTURED RESERVOIRS DURING MISCIBLE DISPLACEMENT: AN EXPERIMENTAL APPROACH

Mapping fracture characteristics by using seismic acquisition and processing is important not only to identify sweet spots, but also to optimize production, especially for unconventional heavy oil reservoirs. In this experimental work we used five-spot micromodels initially saturated with heavy oil to find the optimum well locations during first-contact miscible displacement. The experiments were performed at a fixed injection rate on fractured micromodels with various patterns. The optimum location for injection/production wells was found in the pattern where fractures make an angle of 45° with the mean flow direction. Moreover, oil recovery was increased with the density, length, level of scattering, and discontinuity of fractures. The analysis of the experimentally measured recovery curve revealed that there are three distinct stages for each displacement. The efficiency of the first stage was found to be dominated by dispersion and diffusion. However, the recovery of the second stage was significantly affected by the fracture orientation. The displacement efficiency of the third stage was controlled by solvent dispersion, which is at maximum for the pattern with higher density, length, scattering, and discontinuity of fractures. Saturation monitoring showed that the fracture geometrical characteristics strongly affected the splitting, spreading, and shielding of the produced fingers and solvent front shape and consequently affected the recovery factor. As a result, five-spot micromodels can be used to investigate the optimum location of injection/production wells during miscible displacements in fractured heavy oil reservoirs.