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TECHNICAL PAPERS: Fluids/Heat/Transport

# Turbulence Modeling in Three-Dimensional Stenosed Arterial Bifurcations

[+] Author and Article Information
J. Banks

Computational Engineering and Design Group,  University of Southampton, Highfield, Southampton SO17 1BJ, U.K.jb17@soton.ac.uk

N. W. Bressloff1

Computational Engineering and Design Group,  University of Southampton, Highfield, Southampton SO17 1BJ, U.K.N.W.Bressloff@soton.ac.uk

1

Corresponding author.

J Biomech Eng 129(1), 40-50 (Jul 28, 2006) (11 pages) doi:10.1115/1.2401182 History: Received May 25, 2005; Revised July 28, 2006

## Abstract

Under normal healthy conditions, blood flow in the carotid artery bifurcation is laminar. However, in the presence of a stenosis, the flow can become turbulent at the higher Reynolds numbers during systole. There is growing consensus that the transitional $k−ω$ model is the best suited Reynolds averaged turbulence model for such flows. Further confirmation of this opinion is presented here by a comparison with the RNG $k−ϵ$ model for the flow through a straight, nonbifurcating tube. Unlike similar validation studies elsewhere, no assumptions are made about the inlet profile since the full length of the experimental tube is simulated. Additionally, variations in the inflow turbulence quantities are shown to have no noticeable affect on downstream turbulence intensity, turbulent viscosity, or velocity in the $k−ϵ$ model, whereas the velocity profiles in the transitional $k−ω$ model show some differences due to large variations in the downstream turbulence quantities. Following this validation study, the transitional $k−ω$ model is applied in a three-dimensional parametrically defined computer model of the carotid artery bifurcation in which the sinus bulb is manipulated to produce mild, moderate, and severe stenosis. The parametric geometry definition facilitates a powerful means for investigating the effect of local shape variation while keeping the global shape fixed. While turbulence levels are generally low in all cases considered, the mild stenosis model produces higher levels of turbulent viscosity and this is linked to relatively high values of turbulent kinetic energy and low values of the specific dissipation rate. The severe stenosis model displays stronger recirculation in the flow field with higher values of vorticity, helicity, and negative wall shear stress. The mild and moderate stenosis configurations produce similar lower levels of vorticity and helicity.

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## Figures

Figure 1

Inflow velocity profile

Figure 2

Computational model and mesh structure

Figure 3

Axial velocity profile comparisons at locations distal to the stenosis at T2. The range for each profile is between 0 and 5u∕Uo.

Figure 4

Turbulence intensity at T2, k−ϵ RNG model. The range for each profile is between 0% and 100%.

Figure 5

Turbulent viscosity at T2, k−ϵ RNG model. The range for each profile is between 0Kam−1s−1 and 0.2kgm−1s−1.

Figure 6

Velocity profiles at T2, k−ϵ RNG model. The range for each profile is between 0u∕U0 and 5u∕U0.

Figure 7

Velocity profiles at T2, k−ω model. The range for each profile is between 0u∕U0 and 5u∕U0.

Figure 8

Turbulence intensity at T2, k−ω model. The range for each profile is between 0% and 40%.

Figure 9

Turbulent viscosity at T2, k−ω model. The range for each profile is between 0kgm−1s−1 and 0.08kgm−1s−1.

Figure 10

Computational model—severe stenosis configuration

Figure 11

Pulse waveform for the common carotid artery

Figure 12

Computational mesh (z=0) for mild stenosis model. The three locations in the sinus bulb used to analyze the velocity profiles are displayed.

Figure 13

Mild stenosis streamwise velocity profiles at M1. The range for each profile is between 0ms−1 and 1ms−1.

Figure 14

Moderate stenosis streamwise velocity profiles at M1. The range for each profile is between 0ms−1 and 1ms−1.

Figure 15

Severe stenosis streamwise velocity profiles at M1. The range for each profile is between 0ms−1 and 1ms−1.

Figure 16

Turbulent viscosity ratio at M1. The range for each profile is between 0 and 0.2.

Figure 17

Turbulent kinetic energy at M1. The range for each profile is between 0ms−1 and 0.0005m2∕s2.

Figure 18

y velocity component flow patterns for M1 (t=0.18s) at y=1D, 2D, and 3D

Figure 19

Negative wall shear stress (streamwise component) at M1 (t=0.18s)

Figure 20

Helicity profiles at M1 (t=0.18s)

Figure 21

Helicity profiles at t=0.25s

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