Low-order dynamical modeling and intelligent control of thermo-fluid systems via proper orthogonal decomposition.

In the present investigation, low-order dynamical models of transitional thermo-fluid systems in complex configurations have been developed. Proper orthogonal decomposition (POD) has been applied to supercritical oscillatory solutions, obtained by solving the flow governing partial differential equations (PDEs) with a spectral element method at Reynolds numbers, {dollar}Re\sb{o}{dollar} and Grashof numbers, {dollar}Gr\sb{o},{dollar} higher than the critical values, {dollar}Re\sb{c}{dollar} and {dollar}Gr\sb{c}.{dollar} POD enables us to extract the empirical eigenfunctions, to compress the data and to identify the organized spatio-temporal (coherent) structures. Low-order models (LOMs) consisting of reduced number of nonlinear ordinary differential equations (ODEs) are derived for isothermal and nonisothermal transitional flow in a grooved channel and transitional free convective flow in a vertical channel using the computed empirical eigenfunctions as basis functions and applying Galerkin projection (GP). The ability of the reduced models to describe the dynamics of the flow and temperature field at \"design\" and \"off-design\" conditions is studied. The developed LOMs are used to investigate stability and bifurcation behavior of the dynamical systems, to explore possible routes to chaos and active and passive intelligent flow control ideas using artificial neural networks (ANNs).;For fixed values of Prandtl number, Pr, the eigenvalues, eigenfunctions and spatio-temporal structures depend on the variation of the flow controlling parameters of Reynolds number, Re in forced convective case, and Grashof number, Gr in free convective case. The eigenfunctions associated with the largest eigenvalues are the modes that contain the largest fraction of the total flow and temperature fluctuation \"energy\" and explain the dynamical attributes of the thermo-fluid systems. The dynamical spatio-temporal structures of the thermo-fluid systems under investigation are identified as travelling waves. The accuracy of the developed low-order dynamical models strongly depends on the number of modes retained in the series expansion. For the range of {dollar}430\le Re\le 1050{dollar} and {dollar}22500\le Gr\le 30000{dollar} studied, at least four modes for velocity and four modes for temperature are required to predict self-sustained oscillations in time at \"design\" conditions. Close to the \"design\" conditions, the LOM predictions are in excellent agreement with the full model results, capturing the short and long-time nonlinear dynamical behavior of the thermo-fluid systems. Far from the \"design\" conditions, the LOMs exhibit different routes to chaos depending on the order of truncation (number of modes retained). Ranges of Reynolds and Grashof numbers for which quasi-periodic, period-doubling and intermittent bifurcations exist have been determined by numerically solving the resulting ODEs. The developed LOMs of transitional isothermal flow system in a grooved channel are used to efficiently train an artificial neural network (ANN), resulting in accurate ANN-based low-order dynamical models. Low-order modeling has the potential of becoming very useful tool for transitional and turbulent flow systems in the study of coherent structure dynamics, bifurcation and flow stability, and in exploring ideas in the context of intelligent flow control schemes with the use of ANNs.