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Início - ICHMT DL Ano atual Arquivos Comitê executivo Centro Internacional para Transferência de Calor e Massa

Direct numerical simulation of transient turbulence in a stenosed carotid artery

DOI: 10.1615/ICHMT.2009.TurbulHeatMassTransf.580
page 3

Leopold Grinberg
Division of Applied Mathematics Brown University Providence, RI 02912, USA

Alexander Yakhot
Mechanical and Aerospace Engineering Princeton University; Department of Mechanical Engineering, Ben-Gurion University, Beersheva 84105, Israel

George Em Karniadakis
Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912, USA


Atherosclerotic plaques inside an arterial wall result in a local occlusion of the artery lumen - a stenosis. The stenosis may trigger transition to turbulence and the onset of turbulence downstream of severe occlusions has been observed in the laboratory experiments. Flow in a stenosed carotid artery has been studied experimentally and numerically by many authors. We have performed model-free three-dimensional direct numerical simulations (DNS) of flow through a carotid artery. A geometric model of the carotid artery was obtained from in-vivo MRA images shown in figure. In this study, we apply the Proper Orthogonal Decomposition (POD) to analyze pulsatile transitional laminar-turbulent flows in a carotid arterial bifurcation. We use high-accuracy DNS results to demonstrate the possibility of analyzing transient turbulence in a stenosed carotid artery by POD. Specifically, we use a mesh with 22,441 tetrahedral elements of 7 variable size, and eights-order polynomial approximation (P = 8) within each element, corresponding to 24,685,100 degrees of freedom per one variable. The total number of quadrature points in the computational domain was above 37 millions. Our simulations confirm that a turbulent state appears during the systolic phase of the cardiac cycle and is localized in the post-stenotic region, with relaminarization occurring further downstream of the stenosis. The possibility to extend the POD analysis to routine clinical tests carried out by ultrasound medical imaging techniques has been analyzed and discussed.
For detection of turbulence in time and space, time traces of instantaneous axial velocity have been monitored along the ICA at several axial stations indicated in Fig. 2(left). From Fig.2c, the flow disturbances, as they appear during the cardiac cycle, reveal that the turbulent state appears during the systolic phase and is localized in the post-stenotic region, with re-laminarization occurring farther downstream. To link the transition process to the time frame of the cardiac circle, in Fig. 2(right bottom plot) we also show the physiological flow rate waveforms in the common and internal carotid arteries (CCA and ICA, respectively) imposed in our calculations. The waveform curves consist of a brief systolic phase (acceleration and deceleration) and a longer diastolic phase with some increase in flow rate around t ≈ 0.55. As follows from the time traces in Fig. 2c, the early turbulent activity in the post-stenotic region begins at the mid-acceleration phase of the cardiac cycle. In the early part of deceleration there is intense turbulent activity; past the mid-deceleration phase, the intensities die out and the flow begins to relaminarize; an exception is a short-term oscillation at t ≈ 0.55. The transient turbulent regime lasts about 90% of a systole time, i.e., about 0.15 seconds or nearly 17% of the cardiac circle.

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