A numerical study on turbulent motion in oscillatory pipe flow

Kurzfassung

In this thesis, I studied the turbulent motion in oscillating pipe flow (OP) by means of direct numerical simulation (DNS) techniques. Understanding shear-driven turbulence in oscillating internal flows is of general scientific importance and OP is a canonical test case for this class of problems. Moreover, the major motivation for the addressed topic results from the modelling character of the OP-system to study the respiratory flow in human airways. Using physiological data from the literature I set-up a simplified model of this particular flow problem. A preliminary study with an emphasis on artificial respiration by means of high frequency oscillatory ventilation (HFOV) revealed the following: The clinically relevant Reynolds numbers for typical HFOV scenarios reach maximum values of up to Re = 37000. This is about 26 times higher compared to typical Re in quiet breathing scenarios. The relevant Womersley numbers lie between 0.06 < Wo < 20. Conducting DNS of 21 different OP-scenarios within the identified range of characteristic parameters revealed the following: Depending on the choice of Re and Wo the resulting oscillatory flow is either laminar or conditionally turbulent. In one particular case, a phase asymmetry between positive (turbulent) and negative (laminar) half-cycles is observed. A variation of the boundary conditions showed that this hysteresis is suppressed when the mass flux instead of the pressure drop is prescribed. In general, the turbulent motion in OP is characterised by repeated decay and amplification of local velocity fluctuations. The spatio-temporal behaviour of the flow - e.g. turbulent bursting events, damping, kinetic energy redistribution - depends on Re and Wo as well as on their ratio. By analysing phase-averaged velocity data, it was found that turbulence in OP is in some aspects quite similar but also distinctly different compared to well-understood fully-developed turbulent shear flows. The comparison of the DNS data with theoretical predictions for a laminar OP showed that the onset of turbulence has considerable influence on the oscillating flow. Typical viscous effects of the laminar OP are reduced due to turbulent mixing. The analysis of integral quantities revealed that in some particular cases the onset of turbulence enhances the maximum flow rate (up to 5%) at reduced values of the wall-shear stress (up to 14%).