Development of turbulence in steady flow through models of abdominal aortic aneurysms

As part of a general examination of the effects of blood flow patterns on the risk of rupture of abdominal aortic aneurysms, we have investigated steady flow through a series of polyvinyl chloride models of fusiform aneurysms. A series of steady flow rates between 460 ml/min and 2.0 l/min have been delivered through the models, and the resulting flow patterns have been evaluated by color Doppler flow imaging. At low volume flow rates, the pattern of flow through the model is smooth and laminar. At higher flow rates, however, this is replaced by an irregular, fluctuating, and apparently turbulent motion. This finding is consistent with previous clinical observations. Turbulence appears initially at the distal end of the model aneurysm and then spreads proximally to fill the whole model only if the flow rate continues to increase. The onset of irregular, turbulent flow is found to be governed by both the overall flow rate through the model and the model diameter. Critical conditions for the appearance of turbulence are presented and discussed, and the critical value of the Reynolds number for both the initial distal transition and the final full transition is shown to decrease as the size of the model aneurysm increases.