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Title: Bifurcation tracking and continuation methods for high Reynolds number compressible flows
Author: Huntley, Samantha
ISNI:       0000 0004 5917 2034
Awarding Body: University of Bristol
Current Institution: University of Bristol
Date of Award: 2015
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The behaviour of flow that is inherently non-linear in nature is dependent on the values of certain parameters. At critical parameter values this can result in a change in stability, known as a bifurcation point. Identification of bifurcation points is necessary to understand these non-linearities and tracking the path of the bifurcation point as it varies with two parameters allows the behavioural response of the system under a range of different conditions to be determined. This thesis ultimately presents a new and innovative, computationally inexpensive method to directly locate and track bifurcation points. It achieves this through the systematic developments made to existing continuation and bifurcation tracking methods. Firstly, an existing numerical continuation method has been extended to allow continuation in shape parameters for compressible turbulent flows at high Reynolds numbers around an aerofoil for the first time. This continuation method used the time-independent form of the system but continuation was also performed on the time-discrete system using the Recursive Projection Method (RPM). This is the first time that RPM has been applied to this type of flow in order to perform continuation. The original time-independent continuation method used a coupled form of the mean-flow and turbulence model equations, however it is commonplace to use a decoupled formulation. The effect of using this decoupled formulation within a continuation method has not before been investigated, and so was implemented to discover whether the assumptions employed to enable a decoupled method are valid throughout the entire parameter range of interest. Results from the application of the newly developed method to flows about aero foils are presented. Results are presented for both the Spalart-Allmaras and Menter SST turbulence model for continuation in shape parameters for the first time. Whilst results are presented using the Spalart-Allmaras turbulence model and a number of different aerofoils that are known to exhibit the flow behaviour of interest for the decoupled continuation, RPM and bifurcation tracking methods. The results show that continuation methods can be used to identify the dependence of equilibrium solutions on geometrical parameters and that these equilibrium solutions provide a good approximation to the time-averaged unsteady values whilst the solution is stable. Furthermore, a decoupled method can be used during the stable region to enable a computationally more efficient continuation method. The Recursive Projection Method allows continuation to be performed with a large time-discrete RANS system. This extends the applicability of the underlying time integration scheme and improves the convergence rate. The results of the bifurcation tracking methods show that they represent a viable option as a means of understanding the dependency of the bifurcation point as two parameters are varied. The novel bifurcation tracking methods developed in this work offer a low-cost way of achieving this.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available