Low-dimensional fluid modelling of a backward facing step using Proper Orthogonal Decomposition
B. E. Thesis, University of New South Wales, (2007)Abstract
Proper Orthogonal Decomposition (POD) is a statistical technique that can be used
to break down large quantities of Computational Fluid Dynamics (CFD) or
experimental data output into an orthogonal modal basis. CFD solutions produce
huge amounts of data for many degrees of freedom, particularly for problems in
turbulence. However, many of the modes of the solution are not statistically
significant. The advantage of POD lies in its ability to identify and isolate only the
principal modes of a solution. This study uses the technique of POD to extract a
reduced order model for a backward facing step flow problem. The low-order
model is calculated using CFD data with a particular Reynolds number for which
the basis is optimal. This study examines the validity of applying a low-
dimensional POD mode to a fluid flow problem with a different Reynolds number
to the one that the model was designed for.
A Direct Numerical Simulation was performed on a BFS at low Reynolds numbers,
and resultant output was used to create a low-dimensional POD model. Using this
model, it was found that the POD model performed well for a range of Reynolds
numbers that were less than the reference number, however the model did not
perform as well for increasing Reynolds number. Additionally, it was found that by
combining data from several cases, the range of applicability of the POD model could be increased.