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.

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.

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 On the role of secondary motions in turbulent square duct flow

2018 ◽  
Vol 847 ◽  
Author(s):  
Davide Modesti ◽  
Sergio Pirozzoli ◽  
Paolo Orlandi ◽  
Francesco Grasso
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Streamwise Velocity ◽  
Normal Velocity ◽  
Duct Flow ◽  
Mean Flow ◽  
Square Duct ◽  
The Mean ◽  
Wall Shear

We use a direct numerical simulations (DNS) database for turbulent flow in a square duct up to bulk Reynolds number $Re_{b}=40\,000$ to quantitatively analyse the role of secondary motions on the mean flow structure. For that purpose we derive a generalized form of the identity of Fukagata, Iwamoto and Kasagi (FIK), which allows one to quantify the effect of cross-stream convection on the mean streamwise velocity, wall shear stress and bulk friction coefficient. Secondary motions are found to contribute approximately 6 % of the total friction, and to act as a self-regulating mechanism of turbulence whereby wall shear stress non-uniformities induced by corners are equalized, and universality of the wall-normal velocity profiles is established. We also carry out numerical experiments whereby the secondary motions are artificially suppressed, in which case their equalizing role is partially taken by the turbulent stresses.

Wall shear stress in accelerating turbulent pipe flow

2011 ◽  
Vol 685 ◽  
pp. 440-460 ◽  
Author(s):  
S. He ◽  
C. Ariyaratne ◽  
A. E. Vardy
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Initial Period ◽  
Turbulent Pipe Flow ◽  
Shear Stresses ◽  
Acceleration Rate ◽  
The Mean ◽  
Wall Shear ◽  
Turbulent Wall

AbstractAn experimental study of wall shear stress in an accelerating flow of water in a pipe ramping between two steady turbulent flows has been undertaken in a large-scale experimental facility. Ensemble averaged mean and r.m.s. of the turbulent fluctuations of wall shear stresses have been derived from hot-film measurements from many repeated runs. The initial Reynolds number and the acceleration rate were varied systematically to give values of a non-dimensional acceleration parameter $k$ ranging from 0.16 to 14. The wall shear stress has been shown to follow a three-stage development. Stage 1 is associated with a period of minimal turbulence response; the measured turbulent wall shear stress remains largely unchanged except for a very slow increase which is readily associated with the stretching of existing turbulent eddies as a result of flow acceleration. In this condition of nearly ‘frozen’ turbulence, the unsteady wall shear stress is driven primarily by flow inertia, initially increasing rapidly and overshooting the pseudo-steady value, but then increasing more slowly and eventually falling below the pseudo-steady value. This variation is predicted by an analytical expression derived from a laminar flow formulation. The start of Stage 2 is marked by the generation of new turbulence causing both the mean and turbulent wall shear stress to increase rapidly, although there is a clear offset between the responses of these two quantities. The turbulent wall shear, reflecting local turbulent activities near the wall, responds first and the mean wall shear, reflecting conditions across the entire flow field, responds somewhat later. In Stage 3, the wall shear stress exhibits a quasi-steady variation. The duration of the initial period of nearly frozen turbulence response close to the wall increases with decreasing initial Reynolds number and with increasing acceleration. The latter is in contrast to the response of turbulence in the core of the flow, which previous measurements have shown to be independent of the rate of acceleration.

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.

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