The wall shear stress produced by the normal impingement of a jet on a flat surface

A method for the theoretical determination of the wall shear stress under impinging jets of various congurations is presented. Axisymmetric and two-dimensional incompressible jets of a wide range of Reynolds numbers and jet heights are considered. Theoretical predictions from this approach are compared with available wall shear stress measurements. These data are critically evaluated based on the method of measurement and its applicability to the boundary layer under consideration. It was found that impingement-region wall shear stress measurements using the electrochemical method in submerged impinging liquid jets provide the greatest accuracy of any indirect method. A unique wall shear stress measurement technique, based on observing the removal of monosized spheres from well-characterized surfaces, was used to conrm the impinging jet analysis presented for gas jets. The technique was also used to determine an empirical relation describing the rise in wall shear stress due to compressibility eects in impinging high-velocity jets

Wall Orientation and Shear Stress in the Lattice Boltzmann Model

The wall shear stress is a quantity of profound importance for clinical diagnosis of artery diseases. The lattice Boltzmann is an easily parallelizable numerical method of solving the flow problems, but it suffers from errors of the velocity field near the boundaries which leads to errors in the wall shear stress and normal vectors computed from the velocity. In this work we present a simple formula to calculate the wall shear stress in the lattice Boltzmann model and propose to compute wall normals, which are necessary to compute the wall shear stress, by taking the weighted mean over boundary facets lying in a vicinity of a wall element. We carry out several tests and observe an increase of accuracy of computed normal vectors over other methods in two and three dimensions. Using the scheme we compute the wall shear stress in an inclined and bent channel fluid flow and show a minor influence of the normal on the numerical error, implying that that the main error arises due to a corrupted velocity field near the staircase boundary. Finally, we calculate the wall shear stress in the human abdominal aorta in steady conditions using our method and compare the results with a standard finite volume solver and experimental data available in the literature. Applications of our ideas in a simplified protocol for data preprocessing in medical applications are discussed.Comment: 9 pages, 11 figure

Response of hot element flush wall gauges in oscillating laminar flow

The time dependent response characteristics of flush-mounted hot element gauges used as instruments to measure wall shear stress in unsteady periodic air flows were investigated. The study was initiated because anomalous results were obtained from the gauges in oscillating turbulent flows for the phase relation of the wall shear stress variation, indicating possible gauge response problems. Flat plate laminar oscillating turbulent flows characterized by a mean free stream velocity with a superposed sinusoidal variation were performed. Laminar rather than turbulent flows were studied, because a numerical solution for the phase angle between the free stream velocity and the wall shear stress variation that is known to be correct can be obtained. The focus is on comparing the phase angle indicated by the hot element gauges with corresponding numerical prediction for the phase angle, since agreement would indicate that the hot element gauges faithfully follow the true wall shear stress variation

Exploring wall shear stress spatiotemporal heterogeneity in coronary arteries combining correlation-based analysis and complex networks with computational hemodynamics

Atherosclerosis at the early stage in coronary arteries has been associated with low cycle-average wall shear stress magnitude. However, parallel to the identification of an established active role for low wall shear stress in the onset/progression of the atherosclerotic disease, a weak association between lesions localization and low/oscillatory wall shear stress has been observed. In the attempt to fully identify the wall shear stress phenotype triggering early atherosclerosis in coronary arteries, this exploratory study aims at enriching the characterization of wall shear stress emerging features combining correlation-based analysis and complex networks theory with computational hemodynamics. The final goal is the characterization of the spatiotemporal and topological heterogeneity of wall shear stress waveforms along the cardiac cycle. In detail, here time-histories of wall shear stress magnitude and wall shear stress projection along the main flow direction and orthogonal to it (a measure of wall shear stress multidirectionality) are analyzed in a representative dataset of 10 left anterior descending pig coronary artery computational hemodynamics models. Among the main findings, we report that the proposed analysis quantitatively demonstrates that the model-specific inlet flow-rate shapes wall shear stress time-histories. Moreover, it emerges that a combined effect of low wall shear stress magnitude and of the shape of the wall shear stress–based descriptors time-histories could trigger atherosclerosis at its earliest stage. The findings of this work suggest for new experiments to provide a clearer determination of the wall shear stress phenotype which is at the basis of the so-called arterial hemodynamic risk hypothesis in coronary arteries

Boundary Layer Flow Due To A Moving Flat Plate In Micropolar Fluid

The mathematical model for a boundary layer flow due to a moving flat plate in micropolar fluid is discussed. The plate is moving continuously in the positive x-direction with a constant velocity. The governing boundary-layer equations are solved numerically using an implicit finite-difference scheme. Numerical results presented include the reduced velocity profiles, gyration component profiles and the development of wall shear stress. The results obtained, when the material parameter K = 0 (Newtonian fluid) showed excellent agreement with those for viscous fluids. Further, the wall shear stress increases with increasing K. For fixed K, the wall shear, stress decreases and the gyration component increases with increasing values of n, in the range 0>n>1 where n is a ratio of the gyration vector component and the fluid shear stress at the wall

The multi-scale nature of Wall shear stress fluctuations in turbulent Rayleigh-Benard convection

Measurements of wall shear-stress fluctuations on very long timescales ($\ge$ 1900 free-fall time units) are reported for turbulent Rayleigh-Benard (RB) convection in air at the heated bottom plate of a RB cell, 2.5 m in diameter and 2.5 m in height. The novel sensor simultaneously captures the fluctuations of the magnitude and the direction of the wall shear stress vector $\boldsymbol{\tau}(t)$ with high resolution in the slow air currents. The results show the persistence of a tumble-type structure, which is in a bi-stable state as it oscillates regularly about a mean orientation at a timescale that compares with the typical eddy turnover time. The mean orientation can persist almost hundreds of eddy turnovers, until a re-orientation of this structure in form of a slow precession sets in, while a critical weakening of the mean wall shear stress magnitude - respectively the mean wind - is observed. The amplitudes of turbulent fluctuations in the streamwise wall shear-stress $\tau_x$ along mean wind direction reveal a highly skewed Weibull distribution, while the fluctuations happening on larger time scales follow a symmetric Gaussian distribution. Extreme events such as local flow reversals with negative $\tau_x$ are recovered as rare events and correlate with a rapid angular twist of the wall shear-stress vector. Those events - linked to critical points in the skin friction field - correlate with the coincidence of signals at the tails in both probability distributions

Hemodynamic wall shear stress profiles influence the magnitude and pattern of stenosis in a pig AV fistula

Venous stenosis is a significant problem in arteriovenous fistulae, likely due to anatomical configuration and wall shear stress profiles. To identify linkages between wall shear stress and the magnitude and pattern of vascular stenosis, we produced curved and straight fistulae in a pig model. A complete wall stress profile was calculated for the curved configuration and correlated with luminal stenosis. Computer modeling techniques were then used to derive a wall shear stress profile for the straight arteriovenous fistula. Differences in the wall shear stress profile of the curved and straight fistula were then related to histological findings. There was a marked inverse correlation between the magnitude of wall shear stress within different regions of the curved arteriovenous fistula and luminal stenosis in these same regions. There were also significantly greater differences in wall shear stress between the outer and inner walls of the straight as compared to curved arteriovenous fistula, which translated into a more eccentric histological pattern of intima-media thickening. Our results suggest a clear linkage between anatomical configuration, wall shear stress profiles, and the pattern of luminal stenosis and intima-media thickening in a pig model of arteriovenous fistula stenosis. These results suggest that fistula failure could be reduced by using computer modeling prior to surgical placement to alter the anatomical and, consequently, the wall shear stress profiles in an arteriovenous fistula

Fabrication of an in-plane SU-8 cantilever with integrated strain gauge for wall shear stress measurements in fluid flows.

We present a cantilever fabricated from the polymer SU-8 for the measurement of wall shear stress in fluid flows. The pressure induced deflection of the cantilever, measured using a calibrated and integrated nichrome strain gauge, can be related to the wall shear stress on the surface. The initial degree of curvature of the cantilever can be controlled via the exposure dose, which allows a small positive deflection to be achieved, and so minimises the intrusion into the flow. Wind tunnel testing results show a sensitivity greater than 2.5 mV/Pa, with a shear stress of 0.38 Pa and excitation of 1 V

Rôle of contrast media viscosity in altering vessel wall shear stress and relation to the risk of contrast extravasations

Iodinated contrast media (CM) are the most commonly used injectables in radiology today. A range of different media are commercially available, combining various physical and chemical characteristics (ionic state, osmolality, viscosity) and thus exhibiting distinct in vivo behaviour and safety profiles. In this paper, numerical simulations of blood flow with contrast media were conducted to investigate the effects of contrast viscosity on generated vessel wall shear stress and vessel wall pressure to elucidate any possible relation to extravasations. Five different types of contrast for Iodine fluxes ranging at 1.5–2.2 gI/s were modelled through 18 G and 20 G cannulae placed in an ideal vein at two different orientation angles. Results demonstrate that the least viscous contrast media generate the least maximum wall shear stress as well as the lowest total pressure for the same flow rate. This supports the empirical clinical observations and hypothesis that more viscous contrast media are responsible for a higher percentage of contrast extravasations. In addition, results support the clinical hypothesis that a catheter tip directed obliquely to the vein wall always produces the highest maximum wall shear stress and total pressure due to impingement of the contrast jet on the vessel wall

Low wall shear stress predicts subsequent development of wall hypertrophy in lower limb bypass grafts

Background: Venous grafts commonly develop myointimal hyperplasia, which can lead to stenoses and, ultimately, with expression of adhesion molecules, lumenal occlusion. The aim of the present study was to investigate whether wall shear stress measured post-operatively would predict subsequent myointimal hypertrophy in lower limb venous bypass grafts. Methods: Magnetic resonance imaging and ultrasound were performed in a cohort of patients following lower limb venous bypass graft surgery for peripheral arterial disease at baseline (1-2 weeks) and at follow-up (9-12 months). Wall shear stress was determined at baseline using computational fluid dynamics techniques and intima-media thickness along the length of the graft was measured by ultrasound at baseline and follow up. Results: Complete follow-up was possible in eight patients, in whom low wall shear stress at baseline predicted high intima-media thickness. The relationship between wall shear stress (WSS) and intima-media thickness (IMT) was curvilinear with IMT increasing sharply at lower levels of WSS (IMT >1.0 mm at <0.3 Pa). Conclusions: Low wall shear stress is associated with subsequent increase in myointimal thickness in lower limb venous bypass grafts. This is believed to be the first prospective study in humans to demonstrate the relationship between low wall shear stress and myointimal thickening and indicates a likely causative role for low wall shear stress in the development of myointimal hyperplasia. © 2009 Association for Research into Arterial Structure and Physiology.Published versio