A Priori Tests of Models for the Mean and for the Fluctuating Wall Shear Stress in Flows with Separation

2004 ◽  
pp. 125-132
Author(s):  
H.-J. Kaltenbach
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
A Priori ◽  
The Mean ◽  
Wall Shear

scholarly journals Branching exponent heterogeneity and wall shear stress distribution in vascular trees

2001 ◽  
Vol 280 (3) ◽  
pp. H1256-H1263 ◽  
Author(s):  
Kelly L. Karau ◽  
Gary S. Krenz ◽  
Christopher A. Dawson
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Coefficient Of Variation ◽  
Vessel Diameter ◽  
Mean Value ◽  
Heterogeneous Distribution ◽  
Uniform Shear ◽  
The Mean ◽  
Wall Shear ◽  
Stress Dependent

A bifurcating arterial system with Poiseuille flow can function at minimum cost and with uniform wall shear stress if the branching exponent ( z) = 3 [where z is defined by ( D 1) z = ( D 2) z + ( D 3) z ; D 1 is the parent vessel diameter and D 2 and D 3 are the two daughter vessel diameters at a bifurcation]. Because wall shear stress is a physiologically transducible force, shear stress-dependent control over vessel diameter would appear to provide a means for preserving this optimal structure through maintenance of uniform shear stress. A mean z of 3 has been considered confirmation of such a control mechanism. The objective of the present study was to evaluate the consequences of a heterogeneous distribution of z values about the mean with regard to this uniform shear stress hypothesis. Simulations were carried out on model structures otherwise conforming to the criteria consistent with uniform shear stress when z = 3 but with varying distributions of z. The result was that when there was significant heterogeneity in z approaching that found in a real arterial tree, the coefficient of variation in shear stress was comparable to the coefficient of variation in z and nearly independent of the mean value of z. A systematic increase in mean shear stress with decreasing vessel diameter was one component of the variation in shear stress even when the mean z = 3. The conclusion is that the influence of shear stress in determining vessel diameters is not, per se, manifested in a mean value of z. In a vascular tree having a heterogeneous distribution in zvalues, a particular mean value of z (e.g., z = 3) apparently has little bearing on the uniform shear stress hypothesis.

scholarly journals Selectin-mediated rolling of neutrophils on immobilized platelets

Blood ◽  
1993 ◽  
Vol 82 (4) ◽  
pp. 1165-1174 ◽  
Author(s):  
SM Buttrum ◽  
R Hatton ◽  
GB Nash
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Shape Change ◽  
Vascular Occlusion ◽  
Rolling Velocity ◽  
Cell Shape Change ◽  
Cell Velocity ◽  
The Mean ◽  
Wall Shear

Abstract Interaction between neutrophils and platelets at the site of vascular damage or in ischaemic tissue may promote thrombosis and/or vascular occlusion. To study this interaction, we have developed a novel technique that allows visualization of adhesion of flowing neutrophils to immobilized, activated platelets. The total number of adherent neutrophils decreased with increasing wall shear stress in the range 0.05 to 0.4 Pa. Although a proportion of the adherent neutrophils were stationary, most were rolling with a velocity greater than 0.4 micron/s. The percentage of rolling cells increased with increasing wall shear stress, but the mean rolling cell velocity was nearly independent of shear stress. Adhesion of neutrophils was nearly abolished by treatment of the platelets with antibody to P-selectin, or by treatment of neutrophils with either neuraminidase, dextran sulfate, or EDTA. Studies with a series of antibodies to L-selectin (TQ-1, Dreg- 56, LAM1–3, and LAM1–10) suggested that this molecule was one neutrophil ligand for rolling adhesion. Thus, sialylated carbohydrate on neutrophils appears essential for P-selectin-mediated adhesion, and a proportion of this ligand may be presented by L-selectin. Treatment of the neutrophils with N-formyl-methionyl-leucyl-phenylalanine decreased the number of rolling cells, and increased the rolling velocity, possibly due to shedding of neutrophil ligand(s) and/or cell shape change. In vivo, immobilized platelets could play an important role in promoting attachment of neutrophils to vessel walls, eg, by slowing neutrophils so that integrin-mediated immobilization could occur.

Wall friction and velocity measurements in a double-frequency pulsating turbulent flow

2016 ◽  
Vol 788 ◽  
pp. 521-548 ◽  
Author(s):  
L. R. Joel Sundstrom ◽  
Berhanu G. Mulu ◽  
Michel J. Cervantes
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Low Frequency ◽  
Turbulent Pipe Flow ◽  
Oscillating Flow ◽  
Base Case ◽  
Mean Flow ◽  
Double Frequency ◽  
The Mean ◽  
Wall Shear

Wall shear stress measurements employing a hot-film sensor along with laser Doppler velocimetry measurements of the axial and tangential velocity and turbulence profiles in a pulsating turbulent pipe flow are presented. Time-mean and phase-averaged results are derived from measurements performed at pulsation frequencies ${\it\omega}^{+}={\it\omega}{\it\nu}/\bar{u}_{{\it\tau}}^{2}$ over the range of 0.003–0.03, covering the low-frequency, intermediate and quasi-laminar regimes. In addition to the base case of a single pulsation imposed on the mean flow, the study also investigates the flow response when two pulsations are superimposed simultaneously. The measurements from the base case show that, when the pulsation belongs to the quasi-laminar regime, the oscillating flow tends towards a laminar state in which the velocity approaches the purely viscous Stokes solution with a low level of turbulence. For ${\it\omega}^{+}<0.006$, the oscillating flow is turbulent and exhibits a region with a logarithmic velocity distribution and a collapse of the turbulence intensities, similar to the time-averaged counterparts. In the low-frequency regime, the oscillating wall shear stress is shown to be directly proportional to the Stokes length normalized in wall units $l_{s}^{+}~(=\sqrt{2/{\it\omega}^{+}})$, as predicted by quasi-steady theory. The base case measurements are used as a reference when evaluating the data from the double-frequency case and the oscillating quantities are shown to be close to superpositions from the base case. The previously established view that the time-averaged quantities are unaffected by the imposition of small-amplitude pulsed unsteadiness is shown to hold also when two pulsations are superposed on the mean flow.

Wall Shear Stress in Turbulent Pipe Flow

2009 ◽  
Author(s):  
Roland Gårdhagen ◽  
Jonas Lantz ◽  
Fredrik Carlsson ◽  
Matts Karlsson
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Turbulent Flows ◽  
Intima Media Thickness ◽  
Elevated Risk ◽  
Laminar Flows ◽  
Turbulent Pipe Flow ◽  
Mean Flow ◽  
The Mean ◽  
Wall Shear

Low and/or oscillatory Wall Shear Stress (WSS) has been correlated with elevated risk for increased intima media thickness and atherosclerosis in several studies during the last decades [1, 2]. Most of the studies have addressed laminar flows, in which the oscillations mainly are due to the pulsating nature of blood flow. Turbulent flows however show significant spatial and temporal fluctuations although the mean flow is steady.

Temporal and Spatial Variations of Wall Shear Stress in the Entrance Region of Microvessels

2015 ◽  
Vol 137 (6) ◽  
Author(s):  
Othmane Oulaid ◽  
Junfeng Zhang
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Stable State ◽  
Entrance Region ◽  
Channel Inlet ◽  
Long Distance ◽  
The Mean ◽  
Temporal And Spatial ◽  
Wall Shear ◽  
Cell Free Layer

Using a simplified two-dimensional divider-channel setup, we simulate the development process of red blood cell (RBC) flows in the entrance region of microvessels to study the wall shear stress (WSS) behaviors. Significant temporal and spatial variation in WSS is noticed. The maximum WSS magnitude and the strongest variation are observed at the channel inlet due to the close cell-wall contact. From the channel inlet, both the mean WSS and variation magnitude decrease, with a abrupt drop in the close vicinity near the inlet and then a slow relaxation over a relatively long distance; and a relative stable state with approximately constant mean and variation is established when the flow is well developed. The correlations between the WSS variation features and the cell free layer (CFL) structure are explored, and the effects of several hemodynamic parameters on the WSS variation are examined. In spite of the model limitations, the qualitative information revealed in this study could be useful for better understanding relevant processes and phenomena in the microcirculation.

Direct simulation of turbulent swept flow over a wire in a channel

2010 ◽  
Vol 651 ◽  
pp. 165-209 ◽  
Author(s):  
R. RANJAN ◽  
C. PANTANO ◽  
P. FISCHER
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Axial Flow ◽  
Separated Flow ◽  
Mean Flow ◽  
Sweep Angle ◽  
Wire Axis ◽  
The Mean ◽  
The Wire ◽  
Wall Shear

Turbulent swept flow over a cylindrical wire placed on a wall of a channel is investigated using direct numerical simulations. This geometry is a model of the flow through the wire-wrapped fuel pins, the heat exchanger, typical of many nuclear reactor designs. Mean flow along and across the wire axis is imposed, leading to the formation of separated flow regions. The Reynolds number based on the bulk velocity along the wire axis direction and the channel half height is 5400 and four cases are simulated with different flowrates across the wire. This configuration is topologically similar to backward-facing steps or slots with swept flow, except that the dominant flow is along the obstacle axis in the present study and the crossflow is smaller than the axial flow, i.e. the sweep angle is large. Mean velocities, turbulence statistics, wall shear stress and instantaneous flow structures are investigated. Particular attention is devoted to the statistics of the shear stress on the walls of the channel and the wire in the recirculation zone. The flow around the mean reattachment region, at the termination of the recirculating bubble, does not exhibit the typical decay of the mean shear stress observed in classical backward-facing step flows owing to the presence of a strong axial flow. The evolution of the mean wall shear stress angle after reattachment indicates that the flow recovers towards equilibrium at a rather slow rate, which decreases with sweep angle. Finally, the database is analysed to estimate resolution requirements, in particular around the recirculation zones, for large-eddy simulations. This has implications in more complete geometrical models of a wire-wrapped assembly, involving hundreds of fuel pins, where only turbulence modelling can be afforded computationally.

scholarly journals Wind Tunnel Measurements of Surface Shear Stress on an Isolated Dune Downwind a Bridge

2020 ◽  
Vol 10 (11) ◽  
pp. 4022 ◽  
Author(s):  
Wenbo Wang ◽  
Hongchao Dun ◽  
Wei He ◽  
Ning Huang
Keyword(s):  
Shear Stress ◽  
Wind Tunnel ◽  
Wall Shear Stress ◽  
Sand Dune ◽  
Bridge Pier ◽  
Surface Shear Stress ◽  
Surface Shear ◽  
Windward Slope ◽  
The Mean ◽  
Wall Shear

As part of a comprehensive environmental assessment of the Dun-Gel railway project located in Dunhuang city, Gansu Province, China, a wind tunnel experiment was proposed to predict surface shear stress changes on a sand dune when a bridge was built upstream it. The results show that the length of the wall shear stress shelter region of a bridge is about 10 times of the bridge height (H). In the cases that the interval of the bridge and sand dune (S) is less than 5 H, normalized wall shear stress on the windward crest is decreased from 1.75 (isolated dune) to 1.0 (S = 5.0 H, measured downwind bridge pier) and 1.5 (S = 5.0 H, measured in the middle line of two adjacent bridge piers). In addition, the mean surface shear stress in the downstream zone of the sand dune model is reduced by the bridge pier and is increased by the bridge desk. As for the fluctuation of surface shear stress ( ζ ) on the windward crest, ζ decreases from 1.3 (in the isolated dune case) to 1.2 (in the case S = 5.0 H, measured just downwind the pier) and increases from 1.3 (in the isolated dune case) to 1.6 (in the cases S = 5.0 H, in the middle of two adjacent piers). Taking the mean and fluctuation of surface shear stress into consideration together, we introduce a parameter ψ ranging from 0 to 1. A low value indicates deposition and a high value indicates erosion. On the windward slope, the value of ψ increases with height (from 0 at toe to 0.98 at crest). However, in the cases of S = 1.5 H, ψ is decreased by the bridge in the lower part of the sand dune at y = 0 and is increased at y = L/2 compared with the isolated dune case. In other cases, the change of ψ on the windward slope is not as prominent as in the case of S = 1.5 H. Downstream the sand dune, erosion starts in a point that exists between x = 10 H and 15 H in all cases.

Supplementary Boundary-Layer Approximations for Turbulent Flow

1989 ◽  
Vol 111 (4) ◽  
pp. 420-427 ◽  
Author(s):  
L. C. Thomas ◽  
S. M. F. Hasani
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Pressure Gradient ◽  
Adverse Pressure Gradient ◽  
Boundary Layer Flows ◽  
Mean Velocity ◽  
Wide Range ◽  
The Mean ◽  
Wall Shear

Approximations for total stress τ and mean velocity u are developed in this paper for transpired turbulent boundary layer flows. These supplementary boundary-layer approximations are tested for a wide range of near equilibrium flows and are incorporated into an inner law method for evaluating the mean wall shear stress τ0. The testing of the proposed approximations for τ and u indicates good agreement with well-documented data for moderate rates of blowing and suction and pressure gradient. These evaluations also reveal limitations in the familiar logarithmic law that has traditionally been used in the determination of wall shear stress for non-transpired boundary-layer flows. The calculations for τ0 obtained by the inner law method developed in this paper are found to be consistent with results obtained by the modern Reynolds stress method for a broad range of near equilibrium conditions. However, the use of the proposed inner law method in evaluating the mean wall shear stress for early classic near equilibrium flow brings to question the reliability of the results for τ0 reported for adverse pressure gradient flows in the 1968 Stanford Conference Proceedings.

Near-Wall Measurements in Turbulent Boundary Layers Using Laser Doppler Anemometry

2002 ◽  
Author(s):  
T. Gunnar Johansson ◽  
Luciano Castillo
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Pressure Gradient ◽  
Laser Doppler Anemometry ◽  
Reynolds Numbers ◽  
Mean Velocity ◽  
The Mean ◽  
Wall Shear ◽  
Near Wall

Near wall measurements have been performed in a zero pressure gradient turbulent boundary layer at low to moderate local Reynolds numbers using Laser-Doppler Anemometry in order to investigate how accurately the wall shear stress can be determined. Also, scaling problems are particularly difficult at low Reynolds numbers since they involve simultaneous influences of both inner and outer scales and this is most clearly observed in the near-wall region. In order to fully describe the zero pressure gradient turbulent boundary layer at low to moderate local Reynolds numbers it is necessary to accurately measure a number of quantities. These include the mean velocity and Reynolds stresses, and their spatial derivatives all the way down to the wall (y+∼1). Integral parameters that need to be measured are the wall shear stress and boundary layer thickness, particularly the momentum thickness. Problems with the measurement of field properties get worse close to a wall, and they get worse for increasing local Reynolds number. Three different approaches to measure the wall shear stress were examined. It was found that small measurement errors in the mean velocity close to the wall significantly reduced the accuracy in determining the wall shear stress by measuring the velocity gradient at the wall. The constant stress layer was found to be affected by the advection terms. However, it was found that taking the small pressure gradient into account and improving on the spatial resolution in the outer part of the boundary layer made the momentum integral method reliable.

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