Numerical simulation of the instabilities of a 2D collapsible channel flow

Liu, Haofei (2010) Numerical simulation of the instabilities of a 2D collapsible channel flow. PhD thesis, University of Glasgow.

Abstract

Collapsible channel flows that originated from physiological applications have many intriguing dynamic system behaviours. In this thesis, the stability of a two-dimensional collapsible channel flow is studied numerically. Three approaches are adopted to investigate the fluid-structure interaction problem: an in-house Finite Element Method (FE) based Fluid-Beam model (FBM), a commercial FE based code, ADINA, and an eigensolver derived from the FBM (linear analysis). Two types of inlet boundary conditions are considered. One is the flow-driven system where the inlet flow rate is specified, and the other is the pressure-driven where the pressure drop is given. It turns out that these two systems yield very different dynamical features even though the steady solutions are the same. For the flow-driven system, a range of steady solutions are studied with both zero and non-zero initial wall tension by means of both FBM (using initial stress configuration) and ADINA (equipped with both initial strain and initial stress configurations). As expected, the FBM agrees with ADINA when using the initial stress configuration, but not when the initial strain configuration is adopted. This established the importance of the initial configuration. The effects of different wall thicknesses on the steady wall performance have also been shown as significant. Fully-coupled unsteady simulations have also been performed with FBM (Bernoulli-Euler beam) and ADINA (Timoshenko beam) to demonstrate significant influences of modelling assumptions on the dynamical behaviour. In addition to unsteady simulations, linear stability analysis is also carried out to identify the critical parameter values that occur when the system is in the neutrally stable state. Using the faster Fourier transform, the unsteady results are then compared with the linear stability analysis results. Excellent agreements are achieved in terms of frequencies of modes of instabilities. Finally, we focus on the dynamical behaviour of collapsible channel flows in a pressure-driven system, and the differences with those of the flow-driven system (Luo et al. 2008). It is found that the stability structure for the pressure-driven system is no longer cascade as in the flow-driven case. Instead, the mode-1 instability is the dominating unstable mode in the pressure-driven system. In the pressure drop and wall stiffness space, neutrally stable mode-2 curve is completely enclosed by the mode-1 neutral curve, and there is no purely mode-2 unstable solution in the parameter space investigated. Interesting mode-switch is also observed. By analysing the energy budgets at the neutral stable points, we confirmed that in the high tension region (on the upper branch of the mode-1 neutral curve), the stability mechanism is the same as that of Jensen & Heil (2003). Namely, self-excited oscillations can grow by extracting kinetic energy from the mean flow, with exactly two thirds of the net kinetic energy flux dissipated by the dissipations and the remainder balanced by increased dissipation in the mean flow. However, the mechanism doesn’t apply for the lower branch of the mode-1 neutral curve. In addition, energy balance changes further for the mode-2 curves in the flow-driven system. It is clear that different mechanisms are operating in different regions of the parameter space, and for different boundary conditions.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Subjects: Q Science > QA Mathematics > QA76 Computer software; T Technology > TJ Mechanical engineering and machinery
• Colleges/Schools: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Supervisor's Name: Luo, Prof. Xiaoyu
• Date of Award: 2010
• Depositing User: Mr Haofei Liu
• Unique ID: glathesis:2010-1827
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 21 May 2010
• Last Modified: 10 Dec 2012 13:47
• URI: https://theses.gla.ac.uk/id/eprint/1827