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Research Papers

# Comparison of LES of Steady Transitional Flow in an Idealized Stenosed Axisymmetric Artery Model With a RANS Transitional Model

[+] Author and Article Information
F. P. P. Tan, N. B. Wood

Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom

G. Tabor

School of Engineering, Mathematics and Physical Sciences, University of Exeter, North Park Road, Exeter EX4 4QF, United Kingdom

X. Y. Xu1

Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdomyun.xu@imperial.ac.uk

1

Corresponding author.

J Biomech Eng 133(5), 051001 (Apr 07, 2011) (12 pages) doi:10.1115/1.4003782 History: Received September 09, 2010; Revised March 07, 2011; Posted March 09, 2011; Published April 07, 2011; Online April 07, 2011

## Abstract

In this study, two different turbulence methodologies are investigated to predict transitional flow in a 75% stenosed axisymmetric experimental arterial model and in a slightly modified version of the model with an eccentric stenosis. Large eddy simulation (LES) and Reynolds-averaged Navier–Stokes (RANS) methods were applied; in the LES simulations eddy viscosity subgrid-scale models were employed (basic and dynamic Smagorinsky) while the RANS method involved the correlation-based transitional version of the hybrid $k-ε/k-ω$ flow model. The RANS simulations used 410,000 and 820,000 element meshes for the axisymmetric and eccentric stenoses, respectively, with $y+$ less than 2 viscous wall units for the boundary elements, while the LES used 1,200,000 elements with $y+$ less than 1. Implicit filtering was used for LES, giving an overlap between the resolved and modeled eddies, ensuring accurate treatment of near wall turbulence structures. Flow analysis was carried out in terms of vorticity and eddy viscosity magnitudes, velocity, and turbulence intensity profiles and the results were compared both with established experimental data and with available direct numerical simulations (DNSs) from the literature. The simulation results demonstrated that the dynamic Smagorinsky LES and RANS transitional model predicted fairly comparable velocity and turbulence intensity profiles with the experimental data, although the dynamic Smagorinsky model gave the best overall agreement. The present study demonstrated the power of LES methods, although they were computationally more costly, and added further evidence of the promise of the RANS transition model used here, previously tested in pulsatile flow on a similar model. Both dynamic Smagorinsky LES and the RANS model captured the complex transition phenomena under physiological Reynolds numbers in steady flow, including separation and reattachment. In this respect, LES with dynamic Smagorinsky appeared more successful than DNS in replicating the axisymmetric experimental results, although inflow conditions, which are subject to caveats, may have differed. For the eccentric stenosis, LES with Smagorinsky coefficient of 0.13 gave the closest agreement with DNS despite the known shortcomings of fixed coefficients. The relaminarization as the flow escaped the influence of the stenosis was amply demonstrated in the simulations, graphically so in the case of LES.

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## Figures

Figure 1

Geometries of the idealized axisymmetric (solid line) and eccentric (dashed line) stenosed tubes. The side view (x-z plane) on the left of the figure shows some of the axial positions used for the comparison of flow parameters while front view (x-y plane) shows the offset of the eccentric stenosis axis from the main axis.

Figure 2

Time-averaged vorticity magnitude contours of the axisymmetric stenosis model comparing results of SST-Transitional flow model and two LES flow models as listed in Table 1. Results for each flow model are shown in the x-z plane (Sm0.1: Cs=0.100; dSm: dynamic Smagorinsky).

Figure 3

Instantaneous vorticity magnitude contours of the axisymmetric stenosis model comparing results of two LES flow models as listed in Table 1. Results for each flow model are shown in the x-z plane (Sm0.1: Cs=0.100; dSm: dynamic Smagorinsky).

Figure 4

Axial velocity profiles at several axial locations of the axisymmetric stenosis model for DNS (16) and Frankel (private communication, 2009), SST-Transitional, and two LES flow models as listed in Table 1. Experimental data of Ahmed and Giddens (5) are shown for comparison.

Figure 5

Turbulence intensity (Tu) profiles at several axial locations of the axisymmetric stenosis model for SST-Transitional and two LES flow models as listed in Table 1. Experimental data of Ahmed and Giddens (5) are shown for comparison.

Figure 6

Normalized eddy viscosity (νt/ν) contours from dSm in the x-z plane of the axisymmetric stenosis model at different time-points, (a)–(j), with an initial time of 0.05 s, time interval of 0.05 s, and contour levels of 0–0.10.

Figure 7

Normalized eddy viscosity (νt/ν) contours from dSm in the x-z plane of the axisymmetric stenosis model at different time-points, (a)–(d), with an initial time of 0.5 s, time interval of 0.50 s, and contour levels of 0–0.10 from dSm, showing the quasi-steady nature of the turbulent zone from 0.50 s onward.

Figure 8

Time-averaged vorticity magnitude contours of the eccentric stenosis model comparing results of (a) DNS and RANS SST simulation by Varghese (18) and (b) SST-Tran flow model and several LES flow models as listed in Table 2. Results for each flow model are shown in the order of x-z plane and y-z plane.

Figure 9

Instantaneous vorticity magnitude contours of the eccentric stenosis model comparing results of (a) DNS and Fluent LES simulation by Varghese (18) and (b) several LES flow models as listed in Table 2. Results for each flow model are shown in the order of x-z plane and y-z plane.

Figure 10

Axial velocity profiles at several axial locations on the x-z plane (y=0) of the eccentric stenosis model for DNS, SST-Tran, and LES flow models as listed in Table 2

Figure 11

Time-averaged vorticity magnitude contours of the eccentric stenosis model comparing results of LES computations with different inlet fluctuation levels (0.0001 and 1%). Results for each model are shown in the order of x-z plane and y-z plane.

Figure 12

Axial velocity profiles at several axial locations on the x-z plane (y=0) of the eccentric stenosis model comparing results of LES computations with different inlet fluctuation levels (0.0001 and 1%)

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