Wall shear stress in the Navier-Stokes equation: A commentary

Wall pressure distribution and shear stress fields for pulsatile laminar flow in a 90-degree bifurcation with rectangular cross sections are evaluated using the results of the numerical solution of the Navier-Stokes equation. The extent of the adverse pressure gradient on the bottom wall of the main duct and the upstream wall of the branch closely correlate to the behavior of the two dynamic recirculation zones which are formed on these two walls. Multiple zones of high and low shear stresses at various sites in the bifurcation are observed. The extent of the fluctuations of the maximum and minimum shear stress is identified. Next-to-the-wall laser Doppler anemometer velocity measurements are used to estimate the shear stress distribution on the walls. In general, qualitative agreement between the experimental and computed wall shear stress values is observed. The variation of the wall shear stress in the vicinity of the branch is discussed in light of the highly perturbed flow field.

Download Full-text

An Experiment on the Pulsatile Flow at Transitional Reynolds Numbers—The Fluid Dynamical Meaning of the Blood Flow Parameters in the Aorta

Journal of Biomechanical Engineering ◽

10.1115/1.2895505 ◽

1993 ◽

Vol 115 (4A) ◽

pp. 412-417 ◽

Cited By ~ 2

Author(s):

Masahide Nakamura ◽

Wataru Sugiyama ◽

Manabu Haruna

Keyword(s):

Blood Flow ◽

Shear Stress ◽

Wall Shear Stress ◽

Pressure Gradient ◽

Pulsatile Flow ◽

Reynolds Numbers ◽

Navier Stokes ◽

Human Aorta ◽

Navier Stokes Equation ◽

Wall Shear

An experiment on the fully developed sinusoidal pulsatile flow at transitional Reynolds numbers was performed to evaluate the basic characteristics of the wall shear stress. In this experiment, the wall shear stress was calculated from the measured section averaged axial velocity and the pressure gradient by using the section averaged Navier-Stokes equation. The experimental results showed that the ratio of the amplitude of the wall shear stress to the amplitude of the pressure gradient had the maximum value when the time averaged Reynolds number was about 4000 and the Womersley number was about 10. As this condition is close to the blood flow condition in the human aorta, it is suggested that the parameter of the aorta has an effect to increase the amplitude of the wall shear stress acting on the arterial wall.

Download Full-text

Preliminary Computational Hemodynamics Study of Double Aortic Aneurysms under Multistage Surgical Procedures: An Idealised Model Study

The Scientific World JOURNAL ◽

10.1155/2013/601470 ◽

2013 ◽

Vol 2013 ◽

pp. 1-9

Author(s):

Yosuke Otsuki ◽

Nhat Bui Minh ◽

Hiroshi Ohtake ◽

Go Watanabe ◽

Teruo Matsuzawa

Keyword(s):

Shear Stress ◽

Aortic Aneurysm ◽

Wall Shear Stress ◽

Aortic Aneurysms ◽

Average Pressure ◽

Navier Stokes Equation ◽

Staged Surgery ◽

Continuity Equations ◽

Wall Shear ◽

Average Wall Shear Stress

Double aortic aneurysm (DAA) falls under the category of multiple aortic aneurysms. Repair is generally done through staged surgery due to low invasiveness. In this approach, one aneurysm is cured per operation. Therefore, two operations are required for DAA. However, post-first-surgery rupture cases have been reported. Although the problems involved with managing staged surgery have been discussed for more than 30 years, investigation from a hemodynamic perspective has not been attempted. Hence, this is the first computational fluid dynamics approach to the DAA problem. Three idealized geometries were prepared: presurgery, thoracic aortic aneurysm (TAA) cured, and abdominal aortic aneurysm (AAA) cured. By applying identical boundary conditions for flow rate and pressure, the Navier-Stokes equation and continuity equations were solved under the Newtonian fluid assumption. Average pressure in TAA was increased by AAA repair. On the other hand, average pressure in AAA was decreased after TAA repair. Average wall shear stress was decreased at the peak in post-first-surgery models. However, the wave profile of TAA average wall shear stress was changed in the late systole phase after AAA repair. Since the average wall shear stress in the post-first-surgery models decreased and pressure at TAA after AAA repair increased, the TAA might be treated first to prevent rupture.

Download Full-text

Effect of reverse flow on the pattern of wall shear stress near arterial branches

Journal of The Royal Society Interface ◽

10.1098/rsif.2011.0108 ◽

2011 ◽

Vol 8 (64) ◽

pp. 1594-1603 ◽

Cited By ~ 10

Author(s):

A. Kazakidi ◽

A. M. Plata ◽

S. J. Sherwin ◽

P. D. Weinberg

Keyword(s):

Shear Stress ◽

Wall Shear Stress ◽

Steady Flow ◽

Stokes Equations ◽

Reverse Flow ◽

Side Branch ◽

Navier Stokes ◽

Wall Region ◽

Wall Shear ◽

Near Wall

Atherosclerotic lesions have a patchy distribution within arteries that suggests a controlling influence of haemodynamic stresses on their development. The distribution near aortic branches varies with age and species, perhaps reflecting differences in these stresses. Our previous work, which assumed steady flow, revealed a dependence of wall shear stress (WSS) patterns on Reynolds number and side-branch flow rate. Here, we examine effects of pulsatile flow. Flow and WSS patterns were computed by applying high-order unstructured spectral/hp element methods to the Newtonian incompressible Navier–Stokes equations in a geometrically simplified model of an aorto-intercostal junction. The effect of pulsatile but non-reversing side-branch flow was small; the aortic WSS pattern resembled that obtained under steady flow conditions, with high WSS upstream and downstream of the branch. When flow in the side branch or in the aortic near-wall region reversed during part of the cycle, significantly different instantaneous patterns were generated, with low WSS appearing upstream and downstream. Time-averaged WSS was similar to the steady flow case, reflecting the short duration of these events, but patterns of the oscillatory shear index for reversing aortic near-wall flow were profoundly altered. Effects of reverse flow may help explain the different distributions of lesions.

Download Full-text

Numerical Modeling of Soil Erosion with Three Wall Laws at the Soil-Water Interface

Civil Engineering Journal ◽

10.28991/cej-2021-03091742 ◽

2021 ◽

Vol 7 (9) ◽

pp. 1546-1556

Author(s):

Hatim El Assad ◽

Benaissa Kissi ◽

Rhanim Hassan ◽

Parron Vera Miguel Angel ◽

Rubio Cintas Maria Dolores ◽

...

Keyword(s):

Shear Stress ◽

Wall Shear Stress ◽

Soil Water ◽

Clay Soil ◽

Stokes Equations ◽

Navier Stokes ◽

Water Interface ◽

Navier Stokes Equations ◽

Modeling Software ◽

Wall Shear

In the area of civil engineering and especially hydraulic structures, we find multiple anomalies that weakens mechanical characteristics of dikes, one of the most common anomalies is erosion phenomenon specifically pipe flow erosion which causes major damage to dam structures. This phenomenon is caused by a hole which is the result of the high pressure of water that facilitate the soil migration between the two sides of the dam. It becomes only a question of time until the diameter of the hole expands and causes destruction of the dam structure. This problem pushed physicist to perform many tests to quantify erosion kinetics, one of the most used tests to have logical and trusted results is the HET (hole erosion test). Meanwhile there is not much research regarding the models that govern these types of tests. Objectives: In this paper we modeled the HET using modeling software based on the Navier Stokes equations, this model tackles also the singularity of the interface structure/water using wall laws for a flow turbulence. Methods/Analysis: The studied soil in this paper is a clay soil, clay soil has the property of containing water more than most other soils. Three wall laws were applied on the soil / water interface to calculate the erosion rate in order to avoid the rupture of such a structure. The modlisitation was made on the ANSYS software. Findings: In this work, two-dimensional modeling was carried of the soil.in contrast of the early models which is one-dimensional model, the first one had shown that the wall-shear stress which is not uniform along the whole wall. Then using the linear erosion law to predict the non-uniform erosion along the whole length. The previous study found that the wall laws have a significant impact on the wall-shear stress, which affects the erosion interface in the fluid/soil, particularly at the hole's extremes. Our experiment revealed that the degraded profile is not uniform. Doi: 10.28991/cej-2021-03091742 Full Text: PDF

Download Full-text

Triple-deck and direct numerical simulation analyses of high-speed subsonic flows past a roughness element

Journal of Fluid Mechanics ◽

10.1017/jfm.2015.281 ◽

2015 ◽

Vol 774 ◽

pp. 311-323 ◽

Cited By ~ 7

Author(s):

G. Mengaldo ◽

M. Kravtsova ◽

A. I. Ruban ◽

S. J. Sherwin

Keyword(s):

Numerical Simulation ◽

Shear Stress ◽

Wall Shear Stress ◽

Direct Numerical Simulation ◽

Pressure Gradient ◽

Stokes Equations ◽

Roughness Element ◽

Navier Stokes ◽

Longitudinal Pressure Gradient ◽

Wall Shear

This paper is concerned with the boundary-layer separation in subsonic and transonic flows caused by a two-dimensional isolated wall roughness. The process of the separation is analysed by means of two approaches: the direct numerical simulation (DNS) of the flow using the Navier–Stokes equations, and the numerical solution of the triple-deck equations. Since the triple-deck theory relies on the assumption that the Reynolds number ($\mathit{Re}$) is large, we performed the Navier–Stokes calculations at $\mathit{Re}=4\times 10^{5}$ based on the distance of the roughness element from the leading edge of the flat plate. This $\mathit{Re}$ is also relevant for aeronautical applications. Two sets of calculation were conducted with the free-stream Mach number $\mathit{Ma}_{\infty }=0.5$ and $\mathit{Ma}_{\infty }=0.87$. We used different roughness element heights, some of which were large enough to cause a well-developed separation region behind the roughness. We found that the two approaches generally compare well with one another in terms of wall shear stress, longitudinal pressure gradient and detachment/reattachment points of the separation bubbles (when present). The main differences were found in proximity to the centre of the roughness element, where the wall shear stress and longitudinal pressure gradient predicted by the triple-deck theory are noticeably different from those predicted by DNS. In addition, DNS predicts slightly longer separation regions.

Download Full-text

Wall Shear Stress Estimates in Coronary Artery Constrictions

Journal of Biomechanical Engineering ◽

10.1115/1.2894104 ◽

1992 ◽

Vol 114 (4) ◽

pp. 515-520 ◽

Cited By ~ 17

Author(s):

L. H. Back ◽

D. W. Crawford

Keyword(s):

Shear Stress ◽

Coronary Artery ◽

Wall Shear Stress ◽

Shape Function ◽

Stokes Equations ◽

Navier Stokes ◽

Simple Method ◽

Navier Stokes Equations ◽

Wall Shear

Wall shear stress estimates from laminar boundary layer theory were found to agree fairly well with the magnitude of shear stress levels along coronary artery constrictions obtained from solutions of the Navier Stokes equations for both steady and pulsatile flow. The relatively simple method can be used for in vivo estimates of wall shear stress in constrictions by using a vessel shape function determined from a coronary angiogram, along with a knowledge of the flow rate.

Download Full-text