Wall Shear Stress Measurements Research Articles

Wall shear stress calculation in ascending aorta using phase contrast magnetic resonance imaging. Investigating effective ways to calculate it in clinical practice

Introduction There is growing evidence that atherosclerosis, as well as endothelial biology, depend on arterial wall shear stress (WSS). Several methods of WSS calculation with varying degrees of complexity have been proposed. This study aimed at investigating whether the most straightforward and easier to apply of these methods give comparable results in clinical practice. Methods Complete velocity encoding measurements using phase contrast magnetic resonance imaging were performed in 20 patients at a level perpendicular to the long axis of the ascending aorta approximately 2 cm above the aortic valve. WSS was calculated at this location on maximum systole. MR imaging was accomplished on a 1.5 T scanner. Four methods were applied to calculate WSS; three of them are based on the predictions of Poiseuille's theory of flow, while the last one is based on calculations resulting by the application of the definition of WSS. Results WSS calculated with the above mentioned methods was found to be in the range 4.2 ± 1.8 to 3.5 ± 1.7 dynes/m 2. The velocity profile at the site of measurements can be described with a parabolic equation of the form u = a r 2 + b r + c with an average r 2 = 0.83, which is in good agreement with Poiseuille's theory of flow. Comparison of the results shows no statistically significant differences between WSS measurements calculated with these methods. Discussion The four methods are equivalent in calculating WSS at the ascending aorta when blood flow velocities have a good parabolic distribution.

In vivo blood flow and wall shear stress measurements in the vitelline network

The wall shear stress plays a key role in the interaction between blood flow and the surrounding tissue. To obtain quantitative information about this parameter, velocity measurements are required with sufficient spatial (and temporal) resolution. We present a methodology for the determination of the wall shear stress in vivo in the vitelline network of a chick embryo. Velocity data is obtained by microscopic particle image velocimetry using correlation ensemble averaging; the latter is used to increase the signal-to-noise ratio of the measurements. The temporal evolution of the pulsatile flow is reconstructed by sorting the image pairs based on a phase estimate. From these flow measurements, the wall shear stress can be derived either directly from the magnitude of the gradients or from fits to velocity profiles. Both methods give results that are in good agreement with each other, while the former method is significantly easier to implement. For more accurate studies, the full three-dimensional velocity field may be required. It is demonstrated how this velocity field can be obtained by scanning the measurement volume.

Role of Ultrasonic Shear Rate Estimation Errors in Assessing Inflammatory Response and Vascular Risk

Atherosclerotic lesions preferentially originate in arterial regions that experience low wall shear stress (WSS) and reversing flow patterns. Therefore, routinely monitoring arterial WSS may help to identify the potential sites of early atherosclerosis. A new noninvasive ultrasonic method implemented with coded excitation techniques was utilized to improve WSS estimation accuracy and precision by providing high spatial and temporal resolution. WSS measurement errors were quantified in a model system by scanning a linearly varying WSS field (0.3 to 1.9 Pa) within a flow chamber. A 13-bit optimal code (Opt) was found to be most effective in reducing bias and standard deviation in WSS estimates down to ∼10% and ∼8%. The measurement errors slowly increased with input WSS for all imaging pulses. The expression of endothelial cellular adhesion molecules vascular cell adhesion molecule-1 (VCAM-1) and endothelial-leukocyte adhesion molecule-1 (E-selectin) was investigated over a similar shear range (0 to 1.6 Pa) to study the impact of relating shear-mediated cellular adhesion molecule (CAM) expression to inaccuracies in WSS measurements. We quantified this influence as the prediction error, which accounts for the ultrasonic measurement errors and the sensitivity of CAM expression within certain shear ranges. The highest prediction errors were observed at WSS <0.8 Pa, where CAM expression is most responsive to WSS. The results emphasize the importance of minimizing estimation errors, especially within low shear regions. Preliminary two-dimensional in vivo shear imaging is also presented to provide information about the spatial heterogeneity in arterial WSS distribution. (E-mail: mfi@uiuc.edu)

Velocity profile and wall shear stress of saccular aneurysms at the anterior communicating artery

It has recently been shown that the aspect ratio (dome/neck) of an aneurysm correlates well with intraaneurysmal blood flow. Aneurysms with an aspect ratio larger than 1.6 carry a higher risk of rupture. We examined the effect of aspect ratio (AR) on intra-aneurysmal flow using experimental models. Flow visualization with particle imaging velocimetry and measurement of wall shear stress using laser Doppler anemometry were performed on three different aneurysm models: AR 0.5, 1.0, and 2.0. Intraaneurysmal flow consists of inflow, circulation, and outflow. Rapid inflow impinged on the distal neck creating a stagnant point. Rapid flow and maximum wall shear stress were observed in the vicinity of the stagnant point. By changing the Reynold's number, the stagnant point moved. By increasing the AR of the aneurysm, vortices inside the aneurysm sac closed and very slow flow was observed, resulting in very low shear stress markedly at a Reynold's number of 250, compatible with the diastolic phase. In the aneurysm model AR 2.0, both rapid flow at the neck and vortices inside the aneurysm are sufficient to activate platelets, making a thrombus that may anchor on the dome where very slow flow takes place. Hemodynamics in aneurysms larger than AR 2.0 definitely contribute to thrombus formation.

A108 オリフィス下流における流れ加速型腐食の評価 : 1. 流れ場の計測と数値解析(配管減肉(FAC),OS6 保全・設備診断技術(1),一般講演,地球温暖化防止と動力エネルギー技術)

In this study, in order to evaluate the effects of flow field on corrosion rate due to flow accelerated corrosion (FAC), an orifice flow was measured and calculated. The diameter of pipe is 50 mm and that of the orifice is 24.3 mm, and flow velocity in a water loop was set at 2.41 m/s. Flow field was measured by laser Doppler velocimetry (LDV) and particle image velocimetry (PIV), and compared with a calculation for the same flow conditions. Measurements of wall shear stress downstream of the orifice was also planed. The calculated velocity distributions of standard k- agreed qualitatively with PIV data and quantitatively with LDV data. Instantaneous flow field measured by PIV showed vortices around the jet from the orifice and some of them reached near the pipe wall.

Highly Magnifying PTV Measurement for Drag Reducing Turbulent Structure in a Microbubble Flow Channel

The phenomenon of the drag reduction effect with microbubble has been studied experimentally. We revealed the drag reduction effect by using two types of bubbles which are generated in tap water and that with surfactant. We have approached by wall shear stress measurement and flow visualization by using Highly Magnifying PTV with telecentric lens. In both bubble flows, the experiments have been carried out with the Reynolds number ranging from 10 000 to 50 000 and void fraction up to 0.04. In condition of drag reduction effect observed, injecting bubble diameter was 0.6-1.3 mm and the ejection and sweep event were reduced by bubble injection and Reynolds stress was decreased.

A method for estimating wall friction in turbulent wall-bounded flows

We describe a simple method for estimating turbulent boundary layer wall friction using the fit of measured velocity data to a boundary layer model profile that extends the logarithmic profile all the way to the wall. Two models for the boundary layer profile are examined, the power-series interpolation scheme of Spalding and the Musker profile which is based on the eddy viscosity concept. The performance of the method is quantified using recent experimental data in zero pressure gradient flat-plate turbulent boundary layers, and favorable pressure gradient turbulent boundary layers in a pipe, for which independent measurements of wall shear are also available. Between the two model profiles tested, the Musker profile performs much better than the Spalding profile. Results show that the new procedure can provide highly accurate estimates of wall shear with a mean error of about 0.5% in friction velocity, or 1% in shear stress, an accuracy that is comparable to that from independent direct measurements of wall shear stress. An important advantage of the method is its ability to provide accurate estimates of wall shear not only based on many data points in a velocity profile but also very sparse data points in the velocity profile, including only a single data point such as that originating from a near-wall probe.

Mean wall-shear stress measurements using the micro-pillar shear-stress sensor MPS3

A new sensor to measure the mean turbulent wall-shear stress in turbulent flows is described. The wall-shear stress sensor MPS3 has been tested in a well-defined fully developed turbulent pipe flow at Reynolds numbers Reb based on the bulk velocity Ub and the pipe diameter D in the range of Reb = 10 000–20 000. The results demonstrate a convincing agreement of the mean wall-shear stress obtained with the new sensor technique with analytical and experimental results from the literature. The sensor device consists of a flexible micro-pillar that extends from the wall into the viscous sublayer. Bending due to the exerting fluid forces, the pillar-tip deflection serves as a measure for the local wall-shear stress. The sensor concept, calibration techniques, the achievable accuracy and error estimates, the fields of application and the sensor limits will be discussed. Furthermore, a first estimate of the pillar dynamic response will be derived showing the potential of the sensor to also measure the turbulent fluctuating wall-shear stress.

Numerical study of influence of inlet turbulence parameters on turbulence intensity in the flow domain: Incompressible flow in pipe system

The prediction of cleaning in pipe-lines is important for equipment manufacturers, who wish to optimize designs with respect to hygienic performance. Degree of cleaning correlates with the level of fluctuations in the signal recorded in discrete points during wall shear stress measurements using an electrochemical method. For optimization of process equipment with respect to cleaning, the levels of local fluctuations across entire surfaces are needed. Trends of fluctuations in the geometries used can be predicted using computational fluid dynamics (CFD). Two sensitivity studies were carried out to investigate the robustness of the CFD predictions: one with the zone of interest located two 90° bends and a straight pipe with a length to diameter ratio of 14:8 downstream of the inlet (full geometry) and one with only a straight pipe with a length to diameter ratio of 1:7 between the inlet and the zone of interest (shortened geometry). Both studies having a fully developed turbulent velocity inlet profile with changing turbulence parameters: turbulence intensity 0.01-30 per cent and turbulence length scale 7.5-30 per cent of inlet pipe diameter. For the full geometry no sensitivity in the fluctuation profile trend estimated by use of CFD was found, whereas for the shortened geometry a great sensitivity in the estimated fluctuation profile trend when changing inlet conditions was seen. In the process Star-CD and Fluent (used in the present study) were compared and showed comparable predictions of turbulence intensity.

Electrodiffusion diagnostics of laminar flows using the delay-time method

Electrodiffusion diagnostics are widely used for measurement of local wall shear stresses in liquid flows. At present, this method requires special electrolytes, so the applications are limited to laboratory conditions. Another problem concerns the dependence of the limiting diffusion current on the electrode surface state and on the bulk concentration of the electroactive species. In this paper, it is shown that the delay time between generation of the electroactive species and their detection on the downstream electrode, is directly related to the local wall shear stress value. Thus, the measurements of the delay-time open a new way for the study of near-wall hydrodynamics. This new method has been confirmed experimentally using an electrolyte containing the conventional hexacyanoferrate(III/II) redox couple, as well as with the chlorine (chloric(I))/chloride couple in an electrolyte similar to seawater.

In vivo wall shear stress measurements using phase-contrast MRI

There is growing evidence to suggest that endothelial biology and atherosclerosis depend on arterial wall shear stress (WSS). We review the existing literature on in vivo measurements of WSS in healthy individuals using phase-contrast MRI, which is a promising, noninvasive technique for determinating various blood flow characteristics. WSS data exist for the following arteries: carotid, brachial, aorta and femoral. Measured values indicate that WSS is site specific, a finding which opposes the notion that physiological WSS values are maintained at a constant magnitude in all parts of the arterial system. Among the WSS values obtained at the same site by different investigators there is qualitative agreement; however, differences exist in absolute values mainly due to the dependence on the method used to obtain WSS values from velocity data.

Photogrammetry in Oil-Film Interferometry

Theapplication of photogrammetry to the measurement of skin friction using oil-film interferometry isdiscussed. Oil-film interferometry and photogrammetry are first described to justify the need for photogrammetry, and then the method is applied to two flows. The results indicate that when model curvature is high or the camera-to-model distanceisshort,largeuncertainties(oftheorderof10%)inskinfrictioncanbeintroducedifphotogrammetryisnot applied. For most applications demanding high-accuracy skin-friction measurements, approaches such as those described in this article should be considered. HEmeasurementofwallshearstressinaerodynamictestinghas increased significantly in the last decade. The increased use is primarily a result of the growth of image-based oil-film interferometry, which provides measurements of the mean wall shear stress that can be obtained relatively quickly and with good accuracy. The technique has been applied to simple laboratory flows as well as in large wind tunnels. Accompanying the increased use of oil-film interferometry has been a demand for higher accuracy and less time-intensive analysis. One way that these two issues can be addressedisthroughtheuseofphotogrammetry.Althoughthisisthe case, photogrammetry has only been applied to oil-film interferometry in a few cases (e.g., Zilliac [1]), and an in-depth discussion of its importance has not been presented. The use of photogrammetry to facilitate oil-film interferometry measurement of skin friction is the focus of this paper. The theory behind photogrammetry is presented, and specific issues related to oil-film interferometry are discussed. Specific examples of oil-film interferometry measurements that include photogrammetry are then provided. From these example cases, it is clear that photogrammetry reduces and quantifies geometric/imaging bias errors, and it substantially simplifies the handling of geometry in the analysis process. With uncertainty analyses of oil-film interferometry indicatingaccuraciesof2–3%whenperformedwithcare[2,3],these geometric/imaging bias errors become increasingly important if that level of accuracy is to be maintained in complex geometries. Althoughaparticularanalysismethodfordeterminingthewallshear stress from the fringe patterns obtained using oil-film interferometry isusedheretodemonstratetheapplicationofphotogrammetry,itwas simply chosen for convenience. The photogrammetry method discussed here can be used by other oil-film interferogram-analysis approaches to improve the geometry handling.

Dynamic response of micro-pillar sensors measuring fluctuating wall-shear-stress

We present in this paper test results of flexible micro-pillars and pillar arrays for wall shear stress measurements in flows with fluctuating wall shear stress such as unsteady separated flows or turbulent flows. Previous papers reported on the sensing principle and fabrication process. Static calibrations have shown this sensor to have a maximum nonlinearity of 1% over two orders of wall-shear-stress. For measurements in flows with fluctuating wall shear stress the dynamic response has been experimentally verified in an oscillating pipe flow and compared to a calculated response based on Stokes’ and Oseen’s solution for unsteady flow around a cylinder. The results demonstrate good agreement under the given boundary conditions of cylindrical micro-pillars and the limit of viscous Stokes-flow around the pillar. Depending on the fluid and pillar geometry, different response curves result ranging from a flat low-pass filtered response to a strong resonant behavior. Two different methods are developed to detect the frequency content and the directional wall shear stress information from image processing of large sensor films with arrays of micro-pillars of different geometry. Design rules are given to achieve the optimal conditions with respect to signal-to-noise ratio, sensitivity and bandwidth for measurements in turbulent flows.

Approach to an asymptotic state for zero pressure gradient turbulent boundary layers

Flat plate turbulent boundary layers under zero pressure gradient at high Reynolds numbers are studied to reveal appropriate scale relations and asymptotic behaviour. Careful examination of the skin-friction coefficient results confirms the necessity for direct and independent measurement of wall shear stress. We find that many of the previously proposed empirical relations accurately describe the local Cf behaviour when modified and underpinned by the same experimental data. The variation of the integral parameter, H, shows consistent agreement between the experimental data and the relation from classical theory. In accordance with the classical theory, the ratio of Delta and delta asymptotes to a constant. Then, the usefulness of the ratio of appropriately defined mean and turbulent time-scales to define and diagnose equilibrium flow is established. Next, the description of mean velocity profiles is revisited, and the validity of the logarithmic law is re-established using both the mean velocity profile and its diagnostic function. The wake parameter, Pi, is shown to reach an asymptotic value at the highest available experimental Reynolds numbers if correct values of logarithmic-law constants and an appropriate skin-friction estimate are used. The paper closes with a discussion of the Reynolds number trends of the outer velocity defect which are important to establish a consistent similarity theory and appropriate scaling.

Measurement of wall shear stress in an in vitro model of cerebral aneurysm at pulsatile flow(1D2 Cardiovascular Mechanics II)

Measurement of wall shear stress in an in vitro model of cerebral aneurysm at pulsatile flow(1D2 Cardiovascular Mechanics II)

Skin friction reduction by large air bubbles in a horizontal channel flow

Microbubble and air film methods are believed to be applicable to skin friction reduction in ships. Small bubbles are dispersed into the turbulent boundary layer in the former case, and wide air layers cover the wall surface in the latter case. Previous studies did not specifically address the intermediate case between the microbubble and air film conditions. This study is concerned with the possibility and mechanism of drag reduction using relatively large air bubbles compared to the boundary layer thickness in a horizontal turbulent channel flow. The relationship between local skin friction and the bubble’s interfacial structure is investigated by synchronizing the measurement of wall-shear stress with the image acquisition of bubbles. The bubble sizes range from 2 to 90 mm approximately. As a result, a negative correlation between the local skin friction and the local void fraction is confirmed by the time-resolved measurement. A new observation is the fact that the local skin friction decreases drastically in the rear part of individual large bubbles, and rapidly increases after the bubble’s rear interface passes. This characteristic underlies the bubble-size dependency of the average skin friction in the intermediate bubble size condition.

Mean-Average Wall Shear Stress Measurements in the Common Carotid Artery

In this study we determined mean-average wall shear stress values in the common carotid artery and assessed if there is a difference in mean-average WSS between: 1) patients with bilateral carotid bifurcation disease and 2) similar-aged volunteers with no evidence of disease. Sixteen patients with bilateral disease of the carotid bifurcation, and 8 volunteers were included in the study. Magnetic resonance phase velocity mapping was used to determine velocity, flow, vessel cross-sectional dimensions, and mean-average WSS in the common carotid artery in both the patients and volunteers. Mean-average WSS in the common carotid artery was 7.5 +/- 2.5 dynes/cm2 in patients and 8.0 +/- 4.1 dynes/cm2 in volunteers. There was no significant difference in mean-average WSS, average velocity, peak velocity, flowrate, or vessel diameter in the common carotid artery between patients and volunteers.

Diabetes and distal access location are associated with higher wall shear rate in feeding artery of PTFE grafts

Surgical creation of permanent vascular access for haemodialysis leads to considerable haemodynamic changes. They could be implicated in the pathogenesis of access complications, which limit access survival, especially in diabetics. Physiologically, the relation between arterial diameter and blood velocity is maintained by wall shear stress (WSS), which is directly related to both blood viscosity and wall shear rate (WSR = blood velocity/internal diameter). Because of methodological difficulties, WSR is used as a measure of WSS. Extremely high values of WSS might induce hypercoagulable states, which might contribute to access thrombosis. We performed a study, which was aimed to (i) describe WSR values in feeding arteries of various polytetrafluoroethylene access types and (ii) prove that diabetic patients have higher WSR than non-diabetics. A linear-array 11 MHz probe of SONOS 5500 (Phillips, USA) was used to obtain blood velocity and internal diameter in the feeding arteries of radial or brachial polytetrafluoroethylene grafts. WSR was calculated as 4 x blood velocity/internal diameter. We compared observed values of WSR according to feeding artery (radial vs brachial artery) and according to diabetic status using unpaired t-test. We included 106 patients (58 non-diabetic and 48 diabetic) in the study. WSR was significantly higher in radial arteries compared with brachial arteries independent of diabetes status. Diabetic subjects had significantly higher WSR in both radial and brachial arteries. Diabetes mellitus and distal vascular access creation are associated with higher WSR in the feeding artery. This could be of relevance in the pathogenesis of access complications, e.g. thrombosis, and thus lower patency rates in diabetic patients.

Direct Numerical Simulation of Turbulent Flow Around a Rotating Circular Cylinder

Abstract Turbulent flow around a rotating circular cylinder has numerous applications including wall shear stress and mass-transfer measurement related to the corrosion studies. It is also of interest in the context of flow over convex surfaces where standard turbulence models perform poorly. The main purpose of this paper is to elucidate the basic turbulence mechanism around a rotating cylinder at low Reynolds numbers to provide a better understanding of flow fundamentals. Direct numerical simulation (DNS) has been performed in a reference frame rotating at constant angular velocity with the cylinder. The governing equations are discretized by using a finite-volume method. As for fully developed channel, pipe, and boundary layer flows, a laminar sublayer, buffer layer, and logarithmic outer region were observed. The level of mean velocity is lower in the buffer and outer regions but the logarithmic region still has a slope equal to the inverse of the von Karman constant. Instantaneous flow visualization revealed that the turbulence length scale typically decreases as the Reynolds number increases. Wavelet analysis provided some insight into the dependence of structural characteristics on wave number. The budget of the turbulent kinetic energy was computed and found to be similar to that in plane channel flow as well as in pipe and zero pressure gradient boundary layer flows. Coriolis effects show as an equivalent production for the azimuthal and radial velocity fluctuations leading to their ratio being lowered relative to similar nonrotating boundary layer flows.

A linear state-space representation of plane Poiseuille flow for control design: a tutorial

A method for the incorporation of wall transpiration into a model of linearised plane Poiseuille flow is presented, with the aim of producing a state-space model suitable for the development of feedback control of transition to turbulence in channel flow. The system state is observed via wall shear-stress measurements and controlled by wall transpiration. The streamwise discretisation in the linearised model is by Fourier series and the wall-normal discretisation is by a Chebyshev polynomial basis, which is modified to conform to the control boundary conditions. This paper is intended as a tutorial on the addition of boundary control to a spectral model of a fluid continuum, to form a state-space model, as used in the emerging multidisciplinary field of flow control by means of Microelectrical Machines (MEMs). The ultimate aim of such flow control is the reduction of skin-friction drag on moving bodies.