Reduced-Order Modeling of Turbulent Reacting Flows Using Inertial Manifold Theory

Turbulent flows found in aerodynamics, propulsion, and other energy conversion sys- tems pose an inherent computational challenge for extensive predictive simulations. Over the last few decades, a statistical approach for reduced-order modeling of tur- bulence has become the dominant framework for p...

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Bibliographic Details
Main Author: Akram, Maryam
Format: Dissertation
Language:English
Published: ProQuest Dissertations & Theses 01-01-2021
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Summary:Turbulent flows found in aerodynamics, propulsion, and other energy conversion sys- tems pose an inherent computational challenge for extensive predictive simulations. Over the last few decades, a statistical approach for reduced-order modeling of tur- bulence has become the dominant framework for prediction. However, there exists a range of problems that the statistical approaches are ill-suited for – problems driven not only by the chaoticity in the flow, but also by uncertainty in operating, boundary, or initial conditions. Since tails of the initial flow field distribution may drive transi- tion events, there is a need to develop techniques that do not explicitly rely on the statistical representation of unresolved quantities.The uniqueness of this work lies in the development of reduced-order models that can track distinct trajectories of the dynamical behavior of reacting turbulent flows without invoking ad-hoc assumptions about underlying small-scale turbulent motions or flame structure. Treatment of turbulent flows as finite-dimensional dynamical systems opens new paths for the development of a reduced-order description of such systems. For certain types of dynamical systems, a property known as the inertial manifold (IM) is known to exist, which allows for the dynamics to be represented in a sub-space smaller than the entire state-space. The primary concept in approximate IM (AIM) is that slow dominant dynamical behavior of the system is confined to a low-dimension manifold, and fast dynamics respond to the dynamics on the IM instantaneously. Decomposition of slow/fast dynamics and formulation of an AIM is accomplished by only exploiting the governing equations. Based on this concept, a computational analysis of the use of IMs for modeling reacting turbulent flows is conducted.First, the proposed modeling ansatz has been investigated for canonical turbulent flows. An AIM is constructed for the one-dimensional Kuramoto-Sivashinsky equation and the three-dimensional Navier-Stokes equations to assess different aspects of AIM formulation. An a priori study is conducted to examine the validity of AIM assumptions and to obtain an estimation of the inertial manifold or attractor dimension. Then a reduced-order model is developed and tested over a range of parameters.Second, the theory of IM is extended to the development of reduced-order models of turbulent combustion. Unlike pre-generated manifold-based combustion models, here the combustion trajectory is tracked in a low-dimensional manifold determined in-situ without invoking laminar flame structures or statistical assumptions about the underlying turbulent flow. The AIM performance is assessed in capturing flame behaviors with varying levels of extinction and reignition.
ISBN:9798471105393