High-Frequency Fluctuations in Post-stenotic Patient Specific Carotid Stenosis Fluid Dynamics: A Computational Fluid Dynamics Strategy Study

Figures

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  Figure 1. (a) Patient-specific geometry with flow extensions, where ‘d’ indicates the diameters of CCA, ECA, and ICA. (b) The point P, the slices A, B, C, and D and two perpendicular lines on each slice, with a detail of each slide in (c), indicate where the velocity and pressure were sampled.

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  Figure 2. A typical carotid artery waveform (average 368 mL/min, peak 521 mL/min) was used in this study. Constant flow rate equivalent with peak systolic flow was set as inlet flow for the refinement study in order to allow a more rigorous assessment of grids resolution.

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  Figure 3. The original velocity signal was decomposed in 1000 harmonics and its low-frequency components were separated from the high-frequency components by means of a 16th mode threshold.

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  Figure 4. Top panel: volumetric rendering of the instantaneous velocity magnitude in the common and internal carotid arteries. Bottom panel: enlargement of the box in the top panel, focusing on the stenosis and downstream region. The flow became perturbed already before reaching the stenosis. The flow then accelerates in the stenosis and decelerates once out, causing the jet to break down into turbulent-like structures.

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  Figure 5. The vortical structures in the ICA for the 200K mesh are almost entirely missing. While the 2M and 6M meshes already show some turbulent-like flow features, it is only on the 22M and 50M that these vortical structures are clearly distinct.

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  Figure 6. Time-averaged \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$tke$$\end{document}tke over vertical and horizontal lines on slices A to D for the five meshes in a) and for the four time steps in b).

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  Figure 7. Power spectral density of the numerous meshes (a) and time steps (b) evaluated at point P.

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  Figure 8. Time-averaged SGS viscosity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu_{SGS}$$\end{document}νSGS (upper panel) and resulting turbulent kinetic energy (bottom panel) for the tested SGS models and compared with the reference solution at slice C. The Smagorinsky model is phenotypically different, both in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$tke$$\end{document}tke pattern and magnitude. Although more similar, the Sigma and Dynamic Smagorinsky did not produce the same \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$tke$$\end{document}tke patterns.

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  Figure 9. Time-averaged \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$tke$$\end{document}tke over vertical and horizontal lines on slices A to D for the reference solution and the three SGS models (Smagorinsky, Sigma, Dynamic Smagorinsky).

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  Figure 10. Vortexes in the ICA region was identified by means of the Q-criterion. The breakdown location of the jet and the intensity of flow instabilities of all LES simulations differed from the reference solution.

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  Figure 11. Time-averaged added SGS viscosity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu_{SGS}$$\end{document}νSGS (upper panel), resulting time-averaged \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$tke$$\end{document}tke (middle panel) and its high frequency counterpart \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\widetilde{{tke^{\prime}}}$$\end{document}tke′~ (bottom panel) for the tested SGS models and compared with the pulsatile reference solution on slice C. Both \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}…

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  Figure 12. Comparison of several mesh densities, based on qualitative analysis of the time-averaged turbulent kinetic energy distribution over several slices (A, B, C, D) along the ICA.