Physiological case
 
Following these works and in parallel to other experimental studies, simulations of unsteady flows are done alike. Several forms of flows are studied : oscillating, simply pulsatory and physiologically pulsatory. These works put into light the importance of of the unsteady character on the dynamics of the flow, and the reliance of the post-stenotic characters on the shape of the flow. These results are interesting as in natural situations, the shape of the debt and particularly the steep of the systolic acceleration depends on the anatomic site which is studied. Considering physiologically pulsed flows, a comparison between numerical and experimental results shows a good concordance.

Following the numerical and experimental studies on unsteady velocity fields, a post-stenotic analysis of the distribution of parietal friction was conducted. According to Ku et al. (1997), experimental measures of the parietal frictions are only estimated and can reveal misevaluation of 20 to 50%, which emphasize the role of numerical simulations. Another point is that the study of the interactions between intimous hyperlasy and parietal friction reveals strong correlation between areas of small values and/or areas of oscillating values of the parietal friction and the intimous thickening. On the opposite, the areas of high parietal friction values are generally spared by the thickening. Still, it is interesting to notice that once the plaques of atheroms are formed, the high values of the friction can lead to complications resulting of the cellular wrench (Giddens et al 1990). Thus, it appears as fundamental to correctly determine the temporal evolution of the parietal friction downstream from an arterial stenosis.

With a view to validate the numerical results, a semi-experimental method was set up. To be preserved from possible mistakes on measures of velocity in lining, a polynomial method, using experimental values of the velocity on the symmetry axis, allows to determine the temporal evolution of the parietal friction in the close downstream from the stenosis. Various shapes of flow have been studied, and the case of a pulsatory flow with a negative part is presented here. On each graph the infinite upstream comportment is presented so that a comparison with a supposed sane artery might be done.

Time evolution of the parietal friction ( Rem=203, v=58 ) downstream from stenosis.

It should be noticed that for the close values downstream from the stenosis, its presence tears the artery in the opposite way as a sane artery does. This comportment lasts during a long part of the cycle : from the appearance of swirling structures (during the acceleration phase) until the phase of flow inversion. This malfunction of the artery corresponds to a field of small negative values of the parietal friction. The global evolution reveals a combination of small negative and oscillating values of the parietal friction during the cycle, which let us suppose the formation of a new intimous thickening downstream from an existing stenosis.

Finally, it is important to observe the evolution of the friction at the stenosis throat. It is known that at this abscisse the parietal friction is very high because of the jet effect caused by the contriction. According to Ku et al. (1997) high values of the parietal friction may activate platelets and induce thromboses which can totally block the flow.

The comparison of the numerical results with those obtained by the semi-experimental method show a good correlation during most of the cycle duration. Still, at the end of the deceleration and at the beginning of the acceleration, qualitative and quantitative differences appear. Considering quality, numerical results show oscillations of the value of the parietal friction which do not appear in the experiments. Experimental results are obtained by taking the average on 40 periods in a volume of measure of about 2 mm3 and a sampling at 0.01s; the results given by a such process can therefore only reveal the phenomena of important scale. On the point of quantity, from z=2.4 cm, the experimental values are lower than the numerical. The process of turbulence can partially explain these differences. The numerical model used is a laminar one which cannot take into account the two types of turbulence induced by such flows. The pulsatory character of the flow actually generates turbulence "in time" at the beginning of deceleration, and turbulence "in space" is generated by the presence of the stenosis itself. The turbulent process implies more dissipation, and so a smaller experimental friction.