The transitional regime of pulsatile pipe flow

Abstract

The presence of turbulence in the circulatory system is thought to lead to cardiovascular diseases. Despite its importance, turbulence transition in cardiovascular flows is not well understood. In particular, it is unclear which one of the numerous complex features of blood flow (unsteady driving, rheology, flexible walls, complex geometry...) is the dominant one in terms of turbulence transition. The main aim of this thesis is to single out the effects of one of these features: the unsteady driving of the flow. Specifically, the case of a pulsatile driven, Newtonian fluid, in a rigid smooth pipe of circular cross-section is considered, referred to as pulsatile pipe flow. Two main questions are investigated: whether and how laminar pulsatile pipe flows transition to turbulence, and how turbulence behaves once triggered. Pulsatile pipe flows in the transitional regime, with a mean 1000<Re<3000, are considered. Apart from single harmonic pulsations, different waveforms are considered, including waveforms relevant for physiological flows. By combining linear transient growth and stability analyses, it is demonstrated that, at intermediate pulsation frequencies (4<Wo<20) and moderate to high pulsation amplitudes (0.5<A<3), the laminar pulsatile pipe flow is highly susceptible to large disturbance amplification. Coincidentally the blood flow in the human aorta falls in this parameter regime. The underlying mechanisms related to this susceptibility are identified, and their dependence with respect to the flow parameters explored. Additionally, it is shown that, specific features of the driving waveform can enhance these mechanisms. In particular, bulk velocities with steep acceleration/deceleration phases and, counter-intuitively, with longer low velocity phases promote turbulence transition. The turbulence behavior in this broad parametric space is studied with the use of a large number of direct numerical simulations. As part of this thesis a new C-CUDA code was developed in order to perform fast direct numerical simulations. The code outperforms state-of-the-art CPU codes in terms of computing time and computing resources. With the use of a causal analysis, it is shown that turbulence production increases due to the same mechanisms that render the flow susceptible to transition. Finally, a reduced-order model is developed to approximate the behavior of turbulence in pulsatile pipe flow reasonably well. In sum, this thesis describes the way the flow is more likely to transition to turbulence in this parametric regime, and the behavior of turbulence once triggered. The results presented here suggest that blood flow in the larger arteries is susceptible to transition due to the pulsatile beating of our hearts alone.