Applications of modal decomposition algorithms to dynamic estimation and reconstruction of fluid flows

Abstract

In this thesis, modal decomposition algorithms are utilised to construct reduced-order models of the fluid flows with applications to estimator design and extraction of the dynamical information from the irregularly sampled data.

A particular implementation of such algorithms, the Optimal Mode Decomposition (OMD), is used to construct the estimator frameworks for bluff body flows, more specifically past a circular cylinder and bullet-shaped object. Estimator design is motivated by feedback flow control applications in which online knowledge of the system is paramount. Reduced order models are constructed and combined with stochastic estimation techniques using Moving Horizon Estimation (MHE) algorithm to achieve accurate representations of primary oscillatory and transient features of the cylinder flow across all of its dynamically distinct regimes. The designed estimator is subsequently extended to turbulent flow past a three-dimensional axisymmetric bluff body by introducing rotation-dependent framework. This is able to approximate the main oscillatory features of the flow despite the dynamical complexity of the system.

Furthermore, an extension to the OMD algorithm is introduced, referred to as the is-OMD algorithm, which allows modal decomposition techniques to be applied to vector-valued signal, such as an ensemble of PIV snapshots, sampled at random time instances. A mapping between underlying time-resolved snapshots and known measurements is defined and data is projected onto a low-order subspace. Subsequently, dynamical characteristics, such as frequencies and growth rates, are approximated by iteratively solving two optimisation sub-problems: consecutively updating a reduced-order dynamical model, then subsequently approximating the `missing' data at intermediate snapshots between the known values. The methodology is demonstrated on three dynamical systems: a synthetic sinusoid, the cylinder wake at Re = 60 and turbulent flow past an axisymmetric bullet-shaped body. In all cases the algorithm is shown to correctly identify the characteristic frequencies and oscillatory structures present in the flow from downsampled data ensemble.