Shape Of Velocity Profile Research Articles

An MRI-Compatible Hydrodynamic Simulator of Cerebrospinal Fluid Motion in the Cervical Spine.

Develop and test an MRI-compatible hydrodynamic simulator of cerebrospinal fluid (CSF) motion in the cervical spinal subarachnoid space. Four anatomically realistic subject-specific models were created based on a 22-year-old healthy volunteer and a five-year-old patient diagnosed with Chiari I malformation. The in vitro models were based on manual segmentation of high-resolution T2-weighted MRI of the cervical spine. Anatomically realistic dorsal and ventral spinal cord nerve rootlets (NR) were added. Models were three dimensional (3-D) printed by stereolithography with 50-μm layer thickness. A computer controlled pump system was used to replicate the shape of the subject specific in vivo CSF flow measured by phase-contrast MRI. Each model was then scanned by T2-weighted and 4-D phase contrast MRI (4D flow). Cross-sectional area, wetted perimeter, and hydraulic diameter were quantified for each model. The oscillatory CSF velocity field (flow jets near NR, velocity profile shape, and magnitude) had similar characteristics to previously reported studies in the literature measured by in vivo MRI. This study describes the first MRI-compatible hydrodynamic simulator of CSF motion in the cervical spine with anatomically realistic NR. NR were found to impact CSF velocity profiles to a great degree. CSF hydrodynamics are thought to be altered in craniospinal disorders such as Chiari I malformation. MRI scanning techniques and protocols can be used to quantify CSF flow alterations in disease states. The provided in vitro models can be used to test the reliability of these protocols across MRI scanner manufacturers and machines.

Closure relations effects on the prediction of the stratified two-phase flow stability via the two-fluid model

The possibility of predicting the exact long wave linear stability boundary via the two-fluid (TF) model for horizontal and inclined stratified two-phase flow is examined. The application of the TF model requires the introduction of empirical closure relations for the velocity profile shape factors and for the wave induced wall and interfacial shear stresses. The latter are recognized as the problematic closure laws. In order to explore the closure relations effects and to suggest the necessary modifications that can improve the stability predictions of the TF model, the results are compared with the exact long wave solution of the Orr–Sommerfeld equations for the two-plate geometry. It is demonstrated that with the shape factors corrections and the inclusion of wave induced stresses effects, the TF model is able to fully reproduce the exact long wave neutral stability curves. The wave induced shear stresses in phase with the wave slope, which give rise to the so called “sheltering force”, were found to have a remarkable destabilizing effect in many cases of horizontal and inclined flows. In such cases, the sheltering effects must be included in the TF model, otherwise the region of smooth stratified flow would be significantly over predicted. Based on the results of the exact analysis, a simple closure relation for the sheltering term in the TF model is provided.

Pipe flow of a dense emulsion: Homogeneous shear‐thinning or shear‐induced migration?

The flow field of a 70% concentrated noncolloidal o/w emulsion in a pipe has been investigated by means of Particle Image Velocimetry in a matched refractive index medium. At steady state and in laminar regime, the shape of axial velocity profiles is not parabolic and exhibits a shear‐thinning behavior of the dense emulsion, with a flow index of 0.5 and a negligible yield stress (less than 1 Pa). However, instead of a square root law, the pressure drop increases linearly with Um. To explain this apparent inconsistency, two mechanisms of different nature are considered. The first originates from a possible relation between the consistency factor and the drop mean diameter. The second mechanism is shear‐induced migration and leads to the development of a concentration gradient in the pipe cross section. Both mechanisms considered reconcile the experimental data, the apparent local shear‐thinning behavior and the linear evolution of the pressure drop with the flow rate. © 2017 American Institute of Chemical Engineers AIChE J, 2017

Are Urban-Canopy Velocity Profiles Exponential?

Using analyses of data from extant direct numerical simulations and large-eddy simulations of boundary-layer and channel flows over and within urban-type canopies, sectional drag forces, Reynolds and dispersive shear stresses are examined for a range of roughness densities. Using the spatially-averaged mean velocity profiles these quantities allow deduction of the canopy mixing length and sectional drag coefficient. It is shown that the common assumptions about the behaviour of these quantities, needed to produce an analytical model for the canopy velocity profile, are usually invalid, in contrast to what is found in typical vegetative (e.g. forest) canopies. The consequence is that an exponential shape of the spatially-averaged mean velocity profile within the canopy cannot normally be expected, as indeed the data demonstrate. Nonetheless, recent canopy models that allow prediction of the roughness length appropriate for the inertial layer’s logarithmic profile above the canopy do not seem to depend crucially on their (invalid) assumption of an exponential profile within the canopy.

A plane turbulent wall jet on a fully rough surface

The mean velocity field and skin friction characteristics of a plane turbulent wall jet on a smooth and a fully rough surface were studied using Particle Image Velocimetry. The Reynolds number based on the slot height and the exit velocity of the jet was Re= 13,400 and the nominal size of the roughness was k = 0.44mm. For this Reynolds number and size of roughness element, the flow was in the fully rough regime. The surface roughness results in a distinct change in the shape of the mean velocity profile when scaled in outer coordinates, i.e. using the maximum velocity and outer half-width as the relevant velocity and length scales, respectively. Using inner coordinates, the mean velocity in the lower region of the inner layer was consistent with a logarithmic profile which characterizes the overlap region of a turbulent boundary layer; for the rough wall case, the velocity profile was shifted downward due to the enhanced wall shear stress. For the fully rough flow, the decay rate of the maximum velocity of the wall jet is increased, and the skin friction coefficient is much larger than for the smooth wall case. The inner layer is also thicker for the rough wall case. The effects of surface roughness were observed to penetrate into the outer layer and slightly enhance the spread rate for the outer half-width, which was not observed in most other studies of transitionally rough wall jet flows.

Design and testing of a low subsonic wind tunnel gust generator

This paper summarises the design of a gust generator and the comparison between high fidelity numerical results and experimental results. The gust generator has been designed for a low subsonic wind tunnel in order to perform gust response experiments on wings and assess load alleviation. Special attention has been given to the different design parameters that influence the shape of the gust velocity profile by means of CFD simulations. Design parameters include frequency of actuation, flow speed, maximum deflection, chord length and gust vane spacing. The numerical results are compared to experimental results obtained using a hot-wire anemometer and using flow visualisation by means of smoke. Discrepancies have been noticed between CFD and flow measurements but trends compare well and the system is fully functional.

Coarse‐grained debris flow dynamics on erodible beds

AbstractA systematic set of flume experiments is used to investigate the features of velocity profiles within the body of coarse‐grained debris flows and the dependence of the transport sediment concentration on the relevant parameters (runoff discharge, bed slope, grain size, and form). The flows are generated in a 10 m long laboratory flume, initially filled with a layer consisting of loose debris. After saturation, a prescribed water discharge is suddenly supplied over the granular bed, and the runoff triggers a debris flow wave that reaches nearly steady conditions. Three types of material have been used in the tests: gravel with mean grain size of 3 and 5 mm, and 3 mm glass spheres. Measured parameters included: triggering water discharge, volumetric sediment discharge, sediment concentration, flow depth, and velocity profiles. The dynamic similarity with full‐sized debris flows is discussed on the basis of the relevant dimensionless parameters. Concentration data highlight the dependence on the slope angle and the importance of the quasi‐static friction angle. The effects of flow rheology on the shape of velocity profiles are analyzed with attention to the role of different stress‐generating mechanisms. A remarkable collapse of the dimensionless profiles is obtained by scaling the debris flow velocity with the runoff velocity, and a power law characterization is proposed following a heuristic approach. The shape of the profiles suggests a smooth transition between the different rheological regimes (collisional and frictional) that establish in the upper and lower regions of the flow and is compatible with the presence of multiple length scales dictated by the type of contacts (instantaneous or long lasting) between grains.

From Surface Flow Velocity Measurements to Discharge Assessment by the Entropy Theory

A new methodology for estimating the discharge starting from the monitoring of surface flow velocity, usurf, is proposed. The approach, based on the entropy theory, involves the actual location of maximum flow velocity, umax, which may occur below the water surface (dip phenomena), affecting the shape of velocity profile. The method identifies the two-dimensional velocity distribution in the cross-sectional flow area, just sampling usurf and applying an iterative procedure to estimate both the dip and umax. Five gage sites, for which a large velocity dataset is available, are used as a case study. Results show that the method is accurate in simulating the depth-averaged velocities along the verticals and the mean flow velocity with an error, on average, lower than 12% and 6%, respectively. The comparison with the velocity index method for the estimation of the mean flow velocity using the measured usurf, demonstrates that the method proposed here is more accurate mainly for rivers with a lower aspect ratio where secondary currents are expected. Moreover, the dip assessment is found more representative of the actual location of maximum flow velocity with respect to the one estimated by a different entropy approach. In terms of discharge, the errors do not exceed 3% for high floods, showing the good potentiality of the method to be used for the monitoring of these events.

On mixed convection of two immiscible layers with a layer of non-Newtonian nanofluid in a vertical channel

Mixed convection in a vertical parallel plate channel is analyzed with one region filled with Newtonian fluids and another region with non-Newtonian nanofluids. Pseudo-plastic and dilatant fluids are used as working base flow of nanofluids. Power-law modelling is adopted to predict the effect of non-Newtonian behavior on the fluid flow and thermal performance of nanofluids, and the effective kinematic viscosity and thermal conductivity are determined using linear relations as functions of nanoparticle loading parameter. The velocity and temperature fields are investigated, considering the influence of power-law index n(0.6≤n≤1.4) and nanoparticle volume fraction ϕ(0≤ϕ≤4%). Two cases have been paid special attention in the present work, that is, Case I: in the absence of viscous dissipation (Br=0, GR≠0), and Case II: in the absence of buoyancy forces (GR=0, Br≠0) when purely forced convection happens. It is observed that the power-law index has a strong effect on the shape of velocity profile, and on the scale of temperature curves. The results reveal that the power-law effect on both velocity and temperature is more observable in shear-thinning fluids than that in the dilatant flow. These findings demonstrate that, in some potential applications, the shear-thinning fluid should be chosen for its higher effectiveness on fluid driving where the non-Newtonian fluid is used to drive Newtonian flow via interface shear.

Brain strain uncertainty due to shape variation in and simplification of head angular velocity profiles.

Head angular velocity, instead of acceleration, is more predictive of brain strains. Surprisingly, no study exists that investigates how shape variation in angular velocity profiles affects brain strains, beyond characteristics such as peak magnitude and impulse duration. In this study, we evaluated brain strain uncertainty due to variation in angular velocity profiles and further compared with that resulting from simplifying the profiles into idealized shapes. To do so, we used reconstructed head impacts from American National Football League for shape extraction and simulated head uniaxial coronal rotations from onset to full stop. The velocity profiles were scaled to maintain an identical peak velocity magnitude and duration in order to isolate the shape for investigation. Element-wise peak maximum principal strains from 44 selected impacts were obtained. We found that the shape of angular velocity profile could significantly affect brain strain magnitude (e.g., percentage difference of 4.29-17.89% in the whole brain relative to the group average, with cumulative strain damage measure (CSDM) uncertainty range of 23.9%) but not pattern (correlation coefficient of 0.94-0.99). Strain differences resulting from simplifying angular velocity profiles into idealized shapes were largely within the range due to shape variation, in both percentage difference and CSDM (signed difference of 3.91% on average, with a typical range of 0-6%). These findings provide important insight into the uncertainty or confidence in the performance of kinematics-based injury metrics. More importantly, they suggest the feasibility to simplify head angular velocity profiles into idealized shapes, at least within the confinements of the profiles evaluated, to enable real-time strain estimation via pre-computation in the future.

Field-flow fractionation in microfluidic channels of low aspect ratio

ABSTRACTThe shape of the steady-state three-dimensional flow velocity profile established in carrier liquid flowing inside the rectangular cross-sectional channel for field-flow fractionation should be taken into account to optimize the separation. The central parts of this profile in the planes parallel to the main channel walls are flat with almost identical flow velocities which drop down to zero at the side walls. The separated species transported by the flow in the close-to-side walls regions move with lower average velocities compared to the species transported in the central part of the channel and are undesirably broadened. The hydrodynamic splitting of the carrier liquid at the entry of the channel where the sample is injected only into the central part of the channel eliminates the excessive zone broadening. The aspect ratio of the breadth to the thickness of the channel ratio can thus be reduced. The effect of various aspect ratios on the shape of the flow velocity profile is calculated and the results are used to optimize the aspect ratio of microfluidic channels. The experiments carried out by microthermal field-flow fractionation confirmed that the aspect ratio cannot be reduced to a value of 1, proposed by other authors.

Investigation of fluid flow structure in open type cavity under stationary and pulsatile flow conditions

A study of fluid flow in structured channels plays an important role in solving most fluid dynamics problems. The knowledge of the flow structure in separate cavities can be used to intensify mixing in microreactors and microelectrochemical systems (MEMS) as well as to increase heat transfer in heat sinks. Besides, knowledge about fluid flow in micro cavities could be useful to mitigate the symptoms of aneurysms. In this study, a 2D micro-particle image velocimetry (µPIV) system was used to investigate water flow in an open-type microcavity located in a straight, square cross-section (0.5 × 0.5 mm2) microchannel. Two identical micro cavities of the same cross-section as the main channel and the depth of 1 mm are oppositely located in the middle part of the channel. Because of symmetry, the flow structure of the primary vortex was investigated in only one cavity. Measurements were carried out in different planes over the entire height of the cavity at Reynolds number in the range from 100 to 3000. The flow in the channel was stationary and pulsating. Results indicate that flow in the cavity is three-dimensional. This is confirmed by velocity profile shape changes in its different transversal planes. In addition, it is determined that flow structure in the cavity depends on flow regime and flow pulsation characteristics. Velocity distribution shows that in the transverse direction there is the minimum velocity zone corresponding to the centre of the primary vortex generated by the channel flow, also the same zone is observed along the cavity in its axial plane. At low Re, such velocity distribution occurs in pulsating flow earlier than in the case of stationary flow. With increasing Re, velocity distribution in pulsating flow flattens out also more. It means that disturbed flow in the channel accelerates the formation of a stable flow structure in the cavity.

A variable turbulent Prandtl number model for simulating supercritical pressure CO2 heat transfer

In order to predict heat transfer deterioration (HTD) of supercritical pressure fluid correctly and to investigate the HTD mechanism, the effect of turbulent Prandtl number (Prt) on numerical simulation was theoretically analyzed. Based on such analysis, a new turbulent Prt model (TWL model) was proposed. Numerical simulations of the supercritical pressure CO2 heat transfer in vertical heated tubes were conducted with the proposed Prt model as well as two other previous Prt models and two constant Prt numbers. The performance of the new Prt model was validated by comparing with 14 reported heat-transfer experimental data, especially for the HTD cases. The comparison showed that a better prediction of wall temperature can be achieved with the proposed Prt model in most of the validations, especially for the HTD cases. When HTD occurs, turbulent mixing was restrained in the buffer layer since an “M” shape of velocity profile is formed under the buoyancy effect. The maximum predicted Prt value with TWL model also appears in the buffer layer, while the maximum predicted Prt value with other models appear in the viscous sub-layer. Such Prt profile restrains the turbulent mixing contribution to heat transfer further. Although the turbulent mixing contribution is still several times higher than molecular conduction contribution in the buffer layer when HTD occurs, it’s not strong enough to diffuse energy from near wall region to the bulk region.

Two-dimensional effects in counterflow methane flames

The effect of flowfield geometry on flame propagation and extinction of atmospheric CH4/N2/air flames was studied in the counterflow configuration. Laminar flame speeds and extinction strain rates for lean premixed and non-premixed flames were measured in axisymmetric burners producing either uniform or non-uniform axial velocity exit profiles. Particle image velocimetry was used to characterize the two-dimensional flowfield between the burners. The experiments were modeled with a one-dimensional code and a detailed C2 hydrocarbon kinetic model. Laminar flame speeds were found to be insensitive to the burner exit velocity profile shape but extinction measurements were strongly affected. In non-uniform flows, two-dimensional flow field measurements revealed significant radial dependence of flow quantities and high-speed video captured off-center initiation of extinction. Thus, centerline measurements did not represent the extinction state properly, given the direct contradiction to one-dimensional modeling assumptions, and the data was deemed unreliable for kinetic model validation. Flames in uniform flows were found to exhibit minimal radial dependence with extinction initiating at near-centerline locations.

Characterization of Transition to Turbulence for Blood in a Straight Pipe Under Steady Flow Conditions.

Blood is a complex fluid that, among other things, has been established to behave as a shear thinning, non-Newtonian fluid when exposed to low shear rates (SR). Many hemodynamic investigations use a Newtonian fluid to represent blood when the flow field of study has relatively high SR (>200 s-1). Shear thinning fluids have been shown to exhibit differences in transition to turbulence (TT) compared to that of Newtonian fluids. Incorrect prediction of the transition point in a simulation could result in erroneous hemodynamic force predictions. The goal of the present study was to compare velocity profiles near TT of whole blood and Newtonian blood analogs in a straight rigid pipe with a diameter 6.35 mm under steady flow conditions. Rheology was measured for six samples of whole porcine blood and three samples of a Newtonian fluid, and the results show blood acts as a shear thinning non-Newtonian fluid. Measurements also revealed that blood viscosity at SR = 200 s-1 is significantly larger than at SR = 1000 s-1 (13.8%, p < 0.001). Doppler ultrasound (DUS) was used to measure velocity profiles for blood and Newtonian samples at different flow rates to produce Reynolds numbers (Re) ranging from 1000 to 3300 (based on viscosity at SR = 1000 s-1). Two mathematically defined methods, based on the velocity profile shape change and turbulent kinetic energy (TKE), were used to detect TT. Results show similar parabolic velocity profiles for both blood and the Newtonian fluid for Re < 2200. However, differences were observed between blood and Newtonian fluid velocity profiles for larger Re. The Newtonian fluid had blunt-like velocity profiles starting at Re = 2403 ± 8 which indicated transition. In contrast, blood did not show this velocity profile change until Re = 2871 ± 104. The Newtonian fluid had large velocity fluctuations (root mean square (RMS) > 20%) with a maximum TKE near the pipe center at Re = 2316 ± 34 which indicated transition. In contrast, blood results showed the maximum TKE at Re = 2806 ± 109. Overall, the critical Re was delayed by ∼20% (p < 0.001) for blood compared to the Newtonian fluid. Thus, a Newtonian assumption for blood at flow conditions near transition could lead to large errors in velocity prediction for steady flow in a straight pipe. However, these results are specific to this pipe diameter and not generalizable since SR is highly dependent on pipe diameter. Further research is necessary to understand this relation in different pipe sizes, more complex geometries, and under pulsatile flow conditions.

Reversal of Secondary Flows in a Sharp Channel Bend

Field observations of the currents at a bending channel in the Abashiri River in Hokkaido, Japan have revealed an unexpected secondary circulation during flood tide with near-bed and near-surface currents toward the outer and inner banks of the bend, respectively. The direction of these cross-stream currents was reversed at the end of flood tide. The occurrence and shutdown of these observed unexpected secondary circulation were further investigated through the shape of the along-channel velocity profile by using a theoretical solution based on the steady-state momentum equation and the Stokes's second problem for oscillating flow. Also, an advanced numerical model was used to quantify the unexpected secondary flow. It was shown from the theoretical analysis that vertical advection plays a great role in the momentum balance affecting the direction of secondary flows. The typical secondary flow was found to occur throughout ebb tide with a pronounced near-surface maximum velocity profile. Whereas, during flood tide, the longitudinal velocity profile was characterized by a near-bed and mid-depth maximum, resulting an upwelling flow near the outer bank. These findings were reconfirmed by numerical simulations that were conducted for the entire estuary.

The Estimation of Convective Mass Flux from Radar Reflectivities

AbstractCumulus parameterizations in general circulation models (GCMs) frequently apply mass-flux schemes in their description of tropical convection. Mass flux constitutes the product of the fractional area covered by cumulus clouds in a model grid box and the vertical velocity within the cumulus clouds. The cumulus area fraction profiles can be derived from precipitating radar reflectivity volumes. However, the vertical velocities are difficult to observe, making the evaluation of mass-flux schemes difficult. In this paper, the authors develop and evaluate a parameterization of vertical velocity in convective (cumulus) clouds using only radar reflectivities collected by a C-band polarimetric research radar (CPOL), operating at Darwin, Australia. The parameterization is trained using vertical velocity retrievals from a dual-frequency wind profiler pair located within the field of view of CPOL. The parametric model uses two inputs derived from CPOL reflectivities: the 0-dBZ echo-top height (0-dBZ ETH) and a height-weighted column reflectivity index (ZHWT). The 0-dBZ ETH determines the shape of the vertical velocity profile, while ZHWT determines its strength. The evaluation of these parameterized vertical velocities using (i) the training dataset, (ii) an independent wind-profiler-based dataset, and (iii) 1 month of dual-Doppler vertical velocity retrievals indicates that the statistical representation of vertical velocity is reasonably accurate up to the 75th percentile. However, the parametric model underestimates the extreme velocities. The method allows for the derivation of cumulus mass flux and its variability on current GCM scales based only on reflectivities from precipitating radar, which could be valuable to modelers.

Interpreting the inter-model spread in regional precipitation projections in the tropics: role of surface evaporation and cloud radiative effects

In this study, we investigate and quantify different contributors to inter-model differences in regional precipitation projections among CMIP5 climate models. Contributors to the spread are very contrasted between land and ocean. While circulation changes dominate the spread over oceans and continental coasts, thermodynamic changes associated with water vapor increase dominate over inland regions. The inter-model spread in the dynamic component is associated with the change in atmospheric radiative cooling with warming, which largely relates to atmospheric cloud radiative effects. Differences in the thermodynamic component result from the differences in the change in surface evaporation that is explained by decreases in surface humidity and limited surface water availability over land. Secondary contributions to the inter-model spread in thermodynamic and dynamic components result respectively from present-day climatology (owing to the Clausius–Clapeyron scaling) and from the shape of the vertical velocity profile associated with changes in surface temperature gradients. Advancing the physical understanding of the cloud-circulation and precipitation-evaporation couplings and improving their representation in climate models may stand the best chance to reduce uncertainty in regional precipitation projections.

Nonpolar and polar fluid flow through flat nanochannels with amorphous and crystalline walls

The flow of nonpolar and polar fluids through flat nanochannels with amorphous and crystalline boundary walls is investigated by means of molecular dynamics (MD) simulations. It is shown that the fluid polarity and structure of the boundary walls have very strong influences on both the average fluid flow rate and the shape of the fluid velocity profiles. For channels with amorphous boundary walls, the nonpolar fluid flow appears to be faster than the flow of the polar fluid, whereas for channels with crystalline boundary walls, one has the reversed trend. This feature is discussed under the light of the larger self-diffusivity of bulk polar fluids, contrasting with their smaller slip velocities near crystalline walls.

Exponential roughness layer and analytical model for turbulent boundary layer flow over rectangular-prism roughness elements

We conduct a series of large-eddy simulations (LES) to examine the mean flow behaviour within the roughness layer of turbulent boundary layer flow over rough surfaces. We consider several configurations consisting of arrays of rectangular-prism roughness elements with various spacings, aspect ratios and height distributions. The results provide clear evidence for exponential behaviour of the mean flow with respect to the wall normal distance. Such behaviour has been proposed before (see, e.g., Cionco, 1966 Tech. Rep. DTIC document), and is represented as $U(z)/U_{h}=\exp [a(z/h-1)]$, where $U(z)$ is the spatially/temporally averaged fluid velocity, $z$ is the wall normal distance, $h$ represents the height of the roughness elements and $U_{h}$ is the velocity at $z=h$. The attenuation factor $a$ depends on the density of the roughness element distribution and details of the roughness distribution on the wall. Once established, the generic velocity profile shape is used to formulate a fully analytical model for the effective drag exerted by turbulent flow on a surface covered with arrays of rectangular-prism roughness elements. The approach is based on the von Karman–Pohlhausen integral method, in which a shape function is assumed for the mean velocity profile and its parameters are determined based on momentum conservation and other fundamental constraints. In order to determine the attenuation parameter $a$, wake interactions among surface roughness elements are accounted for by using the concept of flow sheltering. The model transitions smoothly between ‘$k$’ and ‘$d$’ type roughness conditions depending on the surface coverage density and the detailed geometry of roughness elements. Comparisons between model predictions and experimental/numerical data from the existing literature as well as LES data from this study are presented. It is shown that the analytical model provides good predictions of mean velocity and drag forces for the cases considered, thus raising the hope that analytical roughness modelling based on surface geometry is possible, at least for cases when the location of flow separation over surface elements can be easily predicted, as in the case of wall-attached rectangular-prism roughness elements.