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Compact data-based models for scalar transport in reoriented flows

Chemical Engineering Research and Design, ISSN: 0263-8762, Vol: 213, Page: 95-112
2025
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Article Description

This study develops a computationally efficient (“compact”) data-based predictive model for the evolution of diffusive/reactive scalar fields (e.g. temperature or chemical species) in reoriented flows (i.e. unsteady laminar flows consisting of arbitrary reorientations of a steady base flow). Its backbone is a base-flow model that can predict scalar evolutions for any initial field, which is beyond existing data-based models. The principal contributions to current model capabilities are a compact base-flow model that (i) can handle arbitrary initial fields – facilitating control of scalar transport via arbitrary flow reorientations (offering a potent actuation mechanism compared to far slower alternatives such as e.g. thermal actuators at the boundary) – and (ii) admits efficient and easy identification from data generated by standard (commercial) CFD solvers. The proposed data-based modelling thus enables advanced process control in a wide range of practical (engineering) flows and is demonstrated for a representative flow: fast heating of a cold fluid in the 2D unsteady Rotated Arc Mixer (RAM). The model relies on Dynamic Mode Decomposition (DMD) of CFD temperature data for the base flow due to its particular suitability for scalar transport problems subject to arbitrary initial conditions (essential for applications to reoriented flows). DMD has a key advantage over other methods here by (besides being solely data-based and free of a pre-defined modelling structure) enabling step-wise identification of the model from data sets that each incorporate part of the degrees of freedom (DOFs) of the initial state. The step-wise identification, crucial for the proposed method, is extremely costly, though, since the (for reoriented flows arbitrary) initial states (“input space”) and the spatial distribution of evolving states (“state space”) each have O(105−106) DOFs for standard CFD. Data and model reduction in space by projection of these states on a basis of orthogonal (Fourier–Chebyshev) polynomials with exponential convergence properties substantially reduces the input and state spaces to O(102) and O(103−104) DOFs, respectively, upon permitting an “engineering tolerance” of O(1%) in the state representation and thus makes system identification (from standard CFD data) practicable. Decisive in this respect is that the polynomial bases are a priori defined (as opposed to common POD-based reduction methods) and thereby enable systematic generation of sufficiently rich training data for a drastically reduced number of DOFs. Compact models so obtained accurately and efficiently predict the evolving temperature field within the RAM for arbitrary switching protocols and thus indeed pave the way to advanced process control.

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