An experimental investigation is made into the effects of forced wall motion on hemodynamic simulations and into transitional behaviors and instability of oscillatory input flows through elastic tubes. A novel mechanism allows active control and feedback over the pressure on the tube exterior. By comparing the pressure within and outside the tube and modifying the exterior pressure accordingly, the tube is inflated in a controlled manner without altering the input flow. Thus, both input flow rate and wall motion waveforms may be specified for a single experiment. Two distinct experimental series were performed: the first examined the effects of wall motion on physiological flows in regions prone to atherosclerosis, and the second series examined the effects of wall motion on transitional behaviors in oscillatory flows. In both cases, particle image velocimetry (PIV) was used to obtain quantitative velocity data from the flow field.
For the first of these experimental series, the flow rate and arterial wall motion are replicated for two physiological regions that are particularly susceptible to atherosclerotic deposits: the abdominal aorta and the coronary arteries. Wall shear stress, cross-sectional velocity profiles, and energy spectra are used to analyze the flow fields and address questions of the effects of accurate wall motion simulation, the possibility of transitional behaviors in these physiological settings, and the hemodynamic effects of implanted stents.
Flows through the coronary arteries were characterized by a low value of the Sexl-Womersley parameter [special characters omitted], where r is the tube radius, n the angular velocity of the input flow, and ν the kinematic viscosity. Because of this low periodicity, the cross-sectional velocity profiles were found to be nearly parabolic throughout the waveform, and wall motion affected the amplitude of the cross-sectional profiles but had little effect on the shape. In contrast, flows in the abdominal aorta occur at a much higher Sexl-Womersley number, and imposed physiological wall motion is found to introduce reverse flow near the wall that is not present if the tube is instead allowed to move freely. Additionally, work done in stented coronary geometries showed reduced wall shear stress downstream of simulated drug-eluting stents as opposed to traditional stents, suggesting a possible mechanism of complication.
In the second series of experiments, sinusoidal input flow is driven through a compliant silicone model in a series of experiments to investigate the effects of wall motion. In these experiments, the tube wall is deformed sinusoidally with an amplitude of approximately ten percent of its radius. Experiments are conducted using varying values of the parameters α and [special characters omitted] where Δx is the cross-stream averaged periodic displacement of a fluid particle undergoing pulsatile motion. The transitional behavior of these flows is analyzed via their energy spectra, and their stability and wall shear stress behaviors are examined under varied offsets between the timing of the wall motion waveform and the flow rate waveform.
At the lowest value of β studied, namely β = 240, it was found that the energy spectrum was independent of phase for α = 10.6, whereas for smaller values of α or higher values of β, a strong phase-dependence was observed in the energy spectrum of the flow, with the energy values peaking twice with each wave period. This continuously unstable behavior at high α is found to be in good agreement with the locations of instability predicted by applying the Fjørtoft condition to an elastic tube flow theory. Additionally, in experiments conducted with a phase offset between the sinusoidal input flow and the sinusoidal wall motion, it was found that wall shear stress oscillates in phase with the wall motion, and that the distinct two-peak cycle of the energy spectrum is disrupted as the offset grows.