Low Reynolds number turbulence modeling of blood flow in arterial stenoses

Moderate and severe arterial stenoses can produce highly disturbed flow regions with transitional and or turbulent flow characteristics. Neither laminar flow modeling nor standard two‐equation models such as the $k$ ‐ $\varepsilon$ turbulence ones are suitable for this kind of blood flow. In order to analyze the transitional or turbulent flow distal to an arterial stenosis, authors of this study have used the Wilcox low‐ $\mathit{Re}$ turbulence model. Flow simulations were carried out on stenoses with 50, 75 and 86% reductions in cross‐sectional area over a range of physiologically relevant Reynolds numbers. The results obtained with this low‐ $\mathit{Re}$ turbulence model were compared with experimental measurements and with the results obtained by the standard $k$ ‐ $\varepsilon$ model in terms of velocity profile, vortex length, wall shear stress, wall static pressure, and turbulence intensity. The comparisons show that results predicted by the low‐ $\mathit{Re}$ model are in good agreement with the experimental measurements. This model accurately predicts the critical Reynolds number at which blood flow becomes transitional or turbulent distal an arterial stenosis. Most interestingly, over the $\mathit{Re}$ range of laminar flow, the vortex length calculated with the low‐ $\mathit{Re}$ model also closely matches the vortex length predicted by laminar flow modeling. In conclusion, the study strongly suggests that the proposed model is suitable for blood flow studies in certain areas of the arterial tree where both laminar and transitional/turbulent flows coexist.