Wall Shear Stress Vector Research Articles

Wall-shear stress fluctuations in a supersonic turbulent boundary layer over an expansion corner

The effect of wall expansion on the structural and statistical characteristics of wall-shear stress (WSS) fluctuations was investigated by direct numerical simulations of a supersonic turbulent boundary layer over a sharp expansion corner with various deflection angles (β = 00, 20, 50 and 100). It is found that the two-dimensional fields of WSS are characterised as streamwise-elongated streaky structures being aligned in the spanwise direction, resembling low- and high-speed streaks in the buffer region of the flow. Due to the relaminarization effect, these WSS steaks experience a sudden weakening shortly after the expansion corner, but present gradual regrowth with their length scales even exceeding those of the flat-plate case in the far downstream. A strong streamwise-alignment of the instantaneous WSS vector is evident in the case of the largest deflection angle, suggesting a distinct reduction of the intermittency in the relaminarization process. Furthermore, the characteristic time scale of the spanwise component of WSS is quasi-invariant to the expansion effect, while the peak frequency of the streamwise component increases with the increase of the deflection angle.

Fluctuations of the wall shear stress vector in a large-scale natural convection cell

We report first experimental data of the wall shear stress in turbulent air flow in a large-scale Rayleigh–Bénard experiment. Using a novel, nature-inspired measurement concept [C. H. Bruecker and V. Mikulich, PLoS One 12, e0179253 (2017)], we measured the mean and fluctuating part of the two components of the wall shear stress vector at the heated bottom plate at a Rayleigh number Ra = 1.58 × 1010 and a Prandtl number Pr = 0.7. The total sampling period of 1.5 h allowed us to capture the dynamics of the magnitude and the orientation of the vector over several orders of characteristic timescales of the large-scale circulation. We found the amplitude of short-term (turbulent) fluctuations to be following a highly skewed Weibull distribution, while the long-term fluctuations are dominated by the modulation effect of a quasi-regular angular precession of the outer flow around a constant mean, the timescale of which is coupled to the characteristic eddy turnover time of the global recirculation roll. Events of instantaneous negative streamwise wall shear occur when rapid twisting of the local flow happens. A mechanical model is used to explain the precession by tilting the spin moment of the large circulation roll and conservation of angular momentum. A slow angular drift of the mean orientation is observed in a phase of considerable weakening of mean wind magnitude.

Experimental and numerical flow analysis through arteries with stent using particle image velocimetry and computational fluid dynamics method

In the paper, an experimental and numerical flow through various kind of arteries is considered. The flow analyses are carried out on the research set up using Particle Image Velocimetry Method (PIV). The individual components of the research set up are discussed and the measurement methodology is explained. The work consists of two parts. The first one is focused on modelling numerical simulation of the stent installation procedure using an expandable balloon and the flow domain design methodology is described. In the final part, an experimental flow test on an artificial silicone vessel (diameter 3.2 mm) with a stent is performed. The results of the experimental tests are compared with a corresponding numerical simulation. The paper presents numerical simulation for two different flow domains and the results obtained from the experimental tests. In both, the experimental tests and numerical simulation, the pulsatile time dependent flow and pressure characteristic are used. Hemodynamic parameters such as the time average wall shear stress (TAWSS) and velocity vector distribution are analysed. The flow was studied at four Reynolds number values (1223; 2257; 3198; 3762) for the straight vessel and at two values for the vessel containing a stent (1223, 2257). A diameter of the vessel was 3.2 mm. Pulsating blood flow based on the data from the experimental test was analysed. During the numerical simulation it was verified which regions of the vessel had TAWSS values below 0.4 Pa. A satisfactory correlation between outcomes of the numerical simulation and the experimental test was obtained. The flow analysis is conducted in ANSYS Fluent software. Additionally, the methodology for defining the velocity profile at the entrance is presented, in order to form the velocity profile in the first step of analysed cases. The study shows possibility to create a new research set up capable of testing various clinical cases of varying pressure values in the setup, or testing the effects of vessel geometrical changes, which allows observing an influence of those parameters on the fluid flow characteristic. As the analysis for the stent has shown, the regions of low TAWSS values are located in a close proximity to the stent struts.

A Eulerian method to analyze wall shear stress fixed points and manifolds in cardiovascular flows.

Based upon dynamical systems theory, a fixed point of a vector field such as the wall shear stress (WSS) at the luminal surface of a vessel is a point where the vector field vanishes. Unstable/stable manifolds identify contraction/expansion regions linking fixed points. The significance of such WSS topological features lies in their strong link with "disturbed" flow features like flow stagnation, separation and reversal, deemed responsible for vascular dysfunction initiation and progression. Here, we present a Eulerian method to analyze WSS topological skeleton through the identification and classification of WSS fixed points and manifolds in complex vascular geometries. The method rests on the volume contraction theory and analyzes the WSS topological skeleton through the WSS vector field divergence and Poincar[Formula: see text] index. The method is here applied to computational hemodynamics models of carotid bifurcation and intracranial aneurysm. An in-depth analysis of the time dependence of the WSS topological skeleton along the cardiac cycle is provided, enriching the information obtained from cycle-average WSS. Among the main findings, it emerges that on the carotid bifurcation, instantaneous WSS fixed points co-localize with cycle-average WSS fixed points for a fraction of the cardiac cycle ranging from 0 to [Formula: see text]; a persistent instantaneous WSS fixed point confined on the aneurysm dome does not co-localize with the cycle-average low-WSS region. In conclusion, the here presented approach shows the potential to speed up studies on the physiological significance of WSS topological skeleton in cardiovascular flows, ultimately increasing the chance of finding mechanistic explanations to clinical observations.

Measurements of the wall-shear stress distribution in turbulent channel flow using the micro-pillar shear stress sensor MPS3

This study investigates the wall-shear stress (WSS) distribution in turbulent channel flow at friction Reynolds numbers of Reτ=860 and 1300 using the micro-pillar shear-stress sensor (MPS3). The probability density functions and the joint probability density functions of the wall-shear stress vectors indicate that the intermittency of the flow increases for higher Reynolds numbers. Extreme events occurring at the wall, such as wall-normal velocity spikes and backflow events, are detected and analyzed based on the wall-shear stress patterns. The events representing the wall-normal spikes are conditionally sampled from the wall-normal velocity component, which is determined from the local wall-shear stress gradients. The results show that the negative velocity spikes tend to co-occur with strong streamwise wall-shear stress motions, and that the positive spikes are likely to accompany large spanwise motions. Rare backflow events are detected from the wall-shear stressdistribution for both Reynolds numbers, serving as an experimental evidence of near-wall flow reversal events in turbulent channel flow. The diameter of the detected backflow region is approximately 20 viscous units. The data confirm the results from previous numerical studies. The wall-normal velocity spikes and the backflow events are likely to be three-dimensional, suggesting an energy and momentum transfer between the viscous sublayer and the outer part of the turbulent channel flow.

Hodge decomposition of wall shear stress vector fields characterizing biological flows.

A discrete boundary-sensitive Hodge decomposition is proposed as a central tool for the analysis of wall shear stress (WSS) vector fields in aortic blood flows. The method is based on novel results for the smooth and discrete Hodge–Morrey–Friedrichs decomposition on manifolds with boundary and subdivides the WSS vector field into five components: gradient (curl-free), co-gradient (divergence-free) and three harmonic fields induced from the boundary, which are called the centre, Neumann and Dirichlet fields. First, an analysis of WSS in several simulated simplified phantom geometries (duct and idealized aorta) was performed in order to understand the nature of the five components. It was shown that the decomposition is able to distinguish harmonic blood flow arising from the inlet from harmonic circulations induced by the interior topology of the geometry. Finally, a comparative analysis of 11 patients with coarctation of the aorta (CoA) before and after treatment as well as 10 control patients was done. The study shows a significant difference between the CoA patients before and after the treatment, and the healthy controls. This means a global difference between aortic shapes of diseased and healthy subjects, thus leading to a new type of WSS-based analysis and classification of pathological and physiological blood flow.

Investigation on wall shear stress measurement in supersonic flows with shock waves using shear-sensitive liquid crystal coating

Wall shear stress (skin friction) is one of the fundamental surface quantities in aerodynamics but its measurement remains challenging. This paper studies the measurement of wall shear stress vector fields in supersonic flows with shock waves using the shear-sensitive liquid crystal coating (SSLCC) technique. A previously developed SSLCC technique was improved and used for the measurement of wall shear stresses in a supersonic jet flow. Experimental results show that the flow structures including shock waves in the supersonic jet flow were visualized by the SSLCC technique; furthermore, the shear stress vector field over a planar surface induced by the supersonic jet flow was measured by the SSLCC technique. The shock waves and the compression-expansion repetitions in the supersonic jet flow were captured, respectively, by analysing the shear direction field and the skin friction line pattern. This work demonstrates the capabilities of the SSLCC technique to visualize and measure wall shear stresses in supersonic flows with complex shock waves.

Clear Detection of Thin-Walled Regions in Unruptured Cerebral Aneurysms by Using Computational Fluid Dynamics

Thin-walled regions (TIWRs) within cerebral aneurysms have a high risk of rupture during surgical manipulation. Previous reports have demonstrated specific changes in the parameters of computational fluid dynamics in TIWRs; however, they have not been fully evaluated. We identified and investigated a novel parameter, wall shear stress vector cycle variation (WSSVV), with user-friendly software that could predict TIWRs. Twelve unruptured cerebral aneurysms were analyzed. TIWRs were defined as reddish areas compared with the normal-colored parent artery on intraoperative views. The position and orientation of these clinical images were adjusted to match the WSSVV color maps. TIWRs and thick-walled regions (TKWRs) were marked and compared with the corresponding regions on WSSVV maps. The default images obtained from WSSVV imaging required appropriate maximum color bar value (MCBV) adjustment for predicting TIWRs. Sensitivity and specificity analyses were performed by changing the MCBV from 300 to 700 at intervals of 100. With the optimal MCBV, the WSSVV values were quantitatively compared. All of the selected 18 TIWRs and 16 TKWRs corresponded to low- and high-value regions of the WSSVV color maps at the adjusted MCBV, respectively. The mean optimal MCBV was 483.3 ± 167.50 (range, 300-700). According to receiver operating characteristic analysis, the best MCBV for predicting TIWRs was 500 (highest sensitivity, 0.89; specificity, 0.94). Under this condition, the quantitative values of the computational fluid dynamics color maps for TIWRs and TKWRs were significantly different (P < 0.01). Low WSSVV values may indicate TIWRs within cerebral aneurysms.

Wall Shear Stress Directional Abnormalities in BAV Aortas: Toward a New Hemodynamic Predictor of Aortopathy?

The bicuspid aortic valve (BAV) generates wall shear stress (WSS) abnormalities in the ascending aorta (AA) that may be responsible for the high prevalence of aortopathy in BAV patients. While previous studies have analyzed the magnitude and oscillatory characteristics of the total or streamwise WSS in BAV AAs, the assessment of the circumferential component is lacking despite its expected significance in this highly helical flow environment. This gap may have hampered the identification of a robust hemodynamic predictor of BAV aortopathy. The objective of this study was to perform a global and component-specific assessment of WSS magnitude, oscillatory and directional characteristics in BAV AAs. The WSS environments were computed in the proximal and middle convexity of tricuspid aortic valve (TAV) and BAV AAs using our previous valve-aorta fluid-structure interaction (FSI) models. Component-specific WSS characteristics were investigated in terms of temporal shear magnitude (TSM) and oscillatory shear index (OSI). WSS directionality was quantified in terms of mean WSS vector magnitude and angle, and angular dispersion index (Dα). Local WSS magnitude and multidirectionality were captured in a new shear magnitude and directionality index (SMDI) calculated as the product of the mean WSS magnitude and Dα. BAVs subjected the AA to circumferential TSM overloads (2.4-fold increase vs. TAV). TAV and BAV AAs exhibited a unidirectional circumferential WSS (OSI < 0.04) and an increasingly unidirectional longitudinal WSS between the proximal (OSI > 0.21) and middle (OSI < 0.07) sections. BAVs generated mean WSS vectors skewed toward the anterior wall and WSS angular distributions exhibiting decreased uniformity in the proximal AA (0.27-point increase in Dα vs. TAV). SMDI was elevated in all BAV AAs but peaked in the proximal LR-BAV AA (3.6-fold increase vs. TAV) and in the middle RN-BAV AA (1.6-fold increase vs. TAV). This analysis demonstrates the significance of the circumferential WSS component and the existence of substantial WSS directional abnormalities in BAV AAs. SMDI abnormality distributions in BAV AAs follow the morphotype-dependent occurrence of dilation in BAV AAs, suggesting the predictive potential of this metric for BAV aortopathy.

Is there a role for computational fluid dynamics (CFD) in neurovascular compression syndrome?

Abstract Introduction - CFD uses complex algorithms to predict flow of fluids through a tube &amp; also predicts its impact on walls. It is increasingly being used for prediction of aneurysmal wall thickness, flow, wall shear stress and to decide clip strategy. This is an experimental study, which analyses use of CFD in neurovascular compression syndrome and probable future applications. We analysed CFD findings in 12 cases retrospectively to know fluid dynamics of vessels and its implications. Methodology - Twelve patients - 7 cases of trigeminal neuralgia and 5 of hemifacial spasm who were to be treated by MVD, were enrolled. CFD i.e. WSSv (wall shear stress vector), WSSm (magnitude), SL (stream line) and Pressure, was done in all prospectively. Results - CFD of superior cerebellar artery, anterior inferior cerebellar artery and vertebral artery was done in each case at the contact site and immediate pre + post contact location. Comparitively High WSSm correlated maximally at nerve vessel contact junction (NVCj) and also high SL at the NVCj comparing with nerve vessel contact proximal (NVCp), WSSv showed wide variations and pressure change was in-conclusive. Conclusion - At contact site, the high WSSm&amp; SL might be a reliable indicator of a neurovascular conflict zone. To conclusively validate the findings we need large number of patients and control group.

Measurement of Wall Shear Stress in High Speed Air Flow Using Shear-Sensitive Liquid Crystal Coating.

Wall shear stress is an important quantity in fluid mechanics, but its measurement is a challenging task. An approach to measure wall shear stress vector distribution using shear-sensitive liquid crystal coating (SSLCC) is described. The wall shear stress distribution on the test surface beneath high speed jet flow is measured while using the proposed technique. The flow structures inside the jet flow are captured and the results agree well with the streakline pattern that was visualized using the oil-flow technique. In addition, the shock diamonds inside the supersonic jet flow are visualized clearly using SSLCC and the results are compared with the velocity contour that was measured using the particle image velocimetry (PIV) technique. The work of this paper demonstrates the application of SSLCC in the measurement/visualization of wall shear stress in high speed flow.

Measurement of surface shear stress vector beneath high-speed jet flow using liquid crystal coating

The shear-sensitive liquid crystal coating (SSLCC) technique is investigated in the high-speed jet flow of a micro-wind-tunnel. An approach to measure surface shear stress vector distribution using the SSLCC technique is established, where six synchronous cameras are used to record the coating color at different circumferential view angles. Spatial wall shear stress vector distributions on the test surface are obtained at different velocities. The results are encouraging and demonstrate the great potential of the SSLCC technique in high-speed wind-tunnel measurement.

Shear Stress Vector Measurement Using a Circular Sublayer Plate with Multiple Pressure Taps

A local wall shear-stress vector measurement technique has been developed using a thin circular plate, referred to as a sublayer plate, which is attached to the wall in the sublayer of a near-wall turbulent flow. The pressure difference between the leading and trailing edges of the plate is correlated to the known wall shear stress obtained in the fully developed turbulent channel flow. A circular sublayer plate surrounded by eight pressure taps is designed to measure the wall shear-stress vector. The curvature of the round edge of the circular plate slightly reduces the sensitivity to the wall shear-stress magnitude in comparison with a rectangular plate. The circular plate can successfully detect the flow direction over a wide-range flow angle. The circular plate with eight pressure taps has a higher resolution in the measurement of the wall shear vector for a small angle of attack using the ratio of the pressure differences at two taps adjacent to the tap showing the maximum stagnation pressure.

Wall shear stress fixed points in cardiovascular fluid mechanics

Complex blood flow in large arteries creates rich wall shear stress (WSS) vectorial features. WSS acts as a link between blood flow dynamics and the biology of various cardiovascular diseases. WSS has been of great interest in a wide range of studies and has been the most popular measure to correlate blood flow to cardiovascular disease. Recent studies have emphasized different vectorial features of WSS. However, fixed points in the WSS vector field have not received much attention. A WSS fixed point is a point on the vessel wall where the WSS vector vanishes. In this article, WSS fixed points are classified and the aspects by which they could influence cardiovascular disease are reviewed. First, the connection between WSS fixed points and the flow topology away from the vessel wall is discussed. Second, the potential role of time-averaged WSS fixed points in biochemical mass transport is demonstrated using the recent concept of Lagrangian WSS structures. Finally, simple measures are proposed to quantify the exposure of the endothelial cells to WSS fixed points. Examples from various arterial flow applications are demonstrated.

Non-intrusive measurement of wall shear stress in flow channels

Flow shear stress measurement plays an important role in the characterization of macro and microfluidic systems. Many currently used wall shear sensors quantify local shear stress with the use of fluid-disruptive probes, unless installed accurately flush to the channel surface. Non-intrusive shear stress measurement systems capable of quantifying the shear stress vector field in larger areas are highly desirable. The present study reports on non-intrusive direct measurement of wall shear stress under pressure-driven fluid flows with the use of particle imaging velocimetry and Fourier transform traction cytometry. This method uses the known mechanical properties of a soft substrate strained under the flow to quantify the shear stress field. Under fully developed pressure-driven laminar flows of different flow rates in a rectangular channel, the average magnitude of wall shear stress thus obtained matched with the theoretical results obtained for Poiseuille flow. The major advantage of this method is the direct experimental characterization of wall shear stress vector field without disruption of the flow itself. The method shows promise in the characterization of shear flow in diverse areas such as aerospace and bioengineering.

Computational Fluid Dynamics Analysis and Correlation with Intraoperative Aneurysm Features.

There are many controversies about computational fluid dynamics (CFD) findings and aneurysm initiation, growth, and ultimate rupture. The aim of our work was to analyze CFD data in a consecutive series of patients and to correlate them with intraoperative visual aneurysm findings. Hemoscope software (Amin, Ziosoft Corporation, Minato ward, Tokyo, Japan) was used to process images from 17 patients who underwent clipping of 18 aneurysms. Pressure (P), wall shear stress (WSS) gradient and vectors, normalized WSS, and streamlines (SL) direction and velocity were assessed. CFD data were compared to intraoperative visual findings. A total of 39 aneurysm wall areas were assessed. Red, thin aneurysm wall areas were more often associated with low WSS. However, the association of low WSS with high P, diverging WSS vectors, direct impact of SL, and high SL velocity more frequently matched with yellow, atherosclerotic aneurysm walls. Low WSS alone is not sufficient to determine the thickness of an aneurysm wall. Its association with other parameters might enable one to distinguish preoperatively atherosclerotic, thick areas (high P, diverging WSS vectors, high flow velocity) from thin areas with higher rupture risk (parallel WSS vectors, lower flow velocity). The changing balance between these parameters can modify the features and the risk of rupture of aneurysm wall over time.

A mathematical modelling on the effect of high intensity magnetic fields on pulsatile blood flow in human arteries

An attempt is made to investigate whether the static magnetic field (SMF) employed in magnetic resonance imaging (MRI) have any adverse effect on the hemodynamic wall parameters in large arteries or not. With the intention of addressing the controversy in the safety issues during MRI exposure, haemodynamics and pathology of large arteries, such as brachial, femoral and pulmonary artery, are compared by varying the intensity of SMF from high to ultrahigh. To be more medically accurate physiological pressure gradient waveforms taken from cardiology literature were digitised and adequate number of harmonics were extracted in order to represent them as Fourier series. All the medically relevant parameters related to endothelial functioning are significantly affected during the time of exposure to ultrahigh intensity SMF, irrespective of the fact whether the artery is closer or away from the heart. In such fields, the fluctuation of Wall Shear Stress (WSS) vector in pulmonary artery is too severe as inferred from oscillatory shear index (OSI) values. The common hypothesis that low WSS and high OSI colocate is not acceptable both in the absence and the presence of magnetic field. It is also inferred that relative residence time can be considered as a single robust metric to predict the pathogenesis of vascular diseases when OSI is moderate. It is felt that more research is necessary, especially to clarify many existing contradictory results in this regard. The controversial reports in the literature of SMF motivated us to mathematically investigate the possible adverse effects of ultrahigh SMFs on pulsatile blood flow in large human arteries and find the maximum intensity of SMF up to which the blood flow and other medically relevant parameters are not significantly affected.

3D axial and circumferential wall shear stress from 4D flow MRI data using a finite element method and a laplacian approach.

To decompose the 3D wall shear stress (WSS) vector field into its axial (WSSA ) and circumferential (WSSC ) components using a Laplacian finite element approach. We validated our method with in silico experiments involving different geometries and a modified Poiseuille flow. We computed 3D maps of the WSS, WSSA , and WSSC using 4D flow MRI data obtained from 10 volunteers and 10 patients with bicuspid aortic valve (BAV). We compared our method with the centerline method. The mean value, standard deviation, root mean-squared error, and Wilcoxon signed rank test are reported. We obtained an error <0.05% processing analytical geometries. We found good agreement between our method and the modified Poiseuille flow for the WSS, WSSA , and WSSC . We found statistically significance differences between our method and a 3D centerline method. In BAV patients, we found a 220% significant increase in the WSSC in the ascending aorta with respect to volunteers. We developed a novel methodology to decompose the WSS vector in WSSA and WSSC in 3D domains, using 4D flow MRI data. Our method provides a more robust quantification of WSSA and WSSC in comparison with other reported methods. Magn Reson Med 79:2816-2823, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Local wall shear stress measurements with a thin plate submerged in the sublayer in wall turbulent flows

A local wall shear stress measurement technique has been developed using a thin plate, referred to as a sublayer plate which is attached to the wall in the sublayer of a near-wall turbulent flow. The pressure difference between the leading and trailing edges of the plate is correlated to the known wall shear stress obtained in the fully developed turbulent channel flow. The universal calibration curve can be well represented in dimensionless form, and the sensitivity of the proposed method is as high as that of the sublayer fence, even if the sublayer fence is enveloped by the linear sublayer. The results of additional experiments prove that the sublayer plate has fairly good angular resolution in detecting the direction of the local wall shear stress vector.

Wall shear stress and near-wall flows in the stenosed femoral artery

Stenotic artery hemodynamics are often characertised by metrics including oscillatory shear index (OSI) and residence time (RT). This analysis was conducted to clarify the link between the near-wall flow behaviour and these resultant flow metrics. A computational simulation was conducted of a stenosed femoral artery, with an idealised representative geometry and a physiologically realistic inlet profile. The overall flow behaviour was characterised through consideration of the axial flow, which was non-dimensionalised against mean flow velocity. The OSI and RT metrics, which are a useful indicator of likely atherosclerotic sites, were explained through a discussion of the WSS values at different time points, the velocity behaviour and velocity profiles, with a particular focus on the near-wall behaviour which influences wall shear stress and the transient evolution of the wall shear stress. While, the stenosis throat experiences high values of wall shear stress, the smooth flow through this contracted region results in low variation in wall shear stress vectors and limited opportunity for any particle stasis. However, regions were noted distal and proximal (though to a lesser extent), where the change in recirculation zones over the cycle created highly elevated regions of both OSI and RT.