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Flow structure analysis and velocity field reconstruction using Reduced Order Method (POD and DMD : application to stirred tank and oscillating bubble plume.

Abstract : In this work, we apply Reduced Order Methods (ROM’s) to perform a mode decomposition of the fluid flow present in two systems widely used in the bio-chemical industry: stirred tanks and bubble columns. This decomposition allows identifying and classifying the fluid flow components according to their dynamical relevance. The most important structures identified correspond to large-scale structures with a high degree of organization known as coherent structures. Subsequently, the classification of results lead to a reconstruction of the fluid flow, the accuracy and computation time involved in the procedure of ROM's were also determined. These parameters are compared with those corresponding to CFD, this comparison shows that ROM's approach implies a lower time cost with a relatively low error.The ROM's chosen are the most recently used for industrial applications: Proper Orthogonal Decomposition (POD) and Dynamical Mode Decomposition (DMD). The implementation of these methods in the baffled stirred tank was approached through two strategies because the simulation of the system (perform in ANSYS/FLUENT) has a fixed mesh zone and a sliding mesh zone.The first strategy is the typical or standard algorithm and the second is a new algorithm not reported in the literature.For the first strategy or typical approach, the POD was applied in the fixed zone and in the rotating zone separately. The results allowed the reconstruction of the mean flow and the trailing vortices generated by the passage of the turbine blades. In this case the velocity fields of the rotating zone were suitably transformed to the rotating reference frame of the turbine before the ROM’s procedure.For the second and novel implementation the POD and DMD were applied directly to the entire simulation domain without separating the respective zones. According findings found, this new proposal also allows the reconstruction of large-scale organized structures (mean flow and trailing vortices in the impeller region). However, for this case it is not possible to perform a physical interpretation of the POD eigenvectors as it is the case for the conventional POD algorithm.The results obtained for the POD and DMD using the proposed approach are equivalent due to the presence of highly periodic fluid flow, such as a similarity is mentioned (but not verified) in the literature.Additionally, the DMD algorithm allows the identification of low-frequency, low-energetic structures associated with macro instabilities identified experimentally and numerically in other published works. The identification of macro-instabilities in simulations through DMD has not been reported in the literature.The numerical data for the stirred tank were generated using the U-RANS turbulence model. The choice of this turbulence model over others available such as Large Eddy Simulation (LES) is due to the objective of generating reconstructed velocity fields to be used in future works for compartmentalization models (CMA) implementations. The CMA models can be fed with mean velocity fields calculated by U-RANS simulations or alternatively reconstructed velocity fields generated by order reduction methods.We also apply POD and DMD to the case of bubble plume in a quasi-2D column. An euler-euler two-fluid model was solved for the bubbly flow and Rij-epsilon approach was tested as turbulence model. From this approach, it was possible to identify the dominant organized structures (low-frequency structures) for both phases employing POD and DMD. The simulation for this case was taken from a database generated by David Laupsien (PhD 2017), using the NEPTUNE CFD code.Finally we briefly address the basic principles necessary for the coupling of CFD with CMA. In this conceptual framework of mixing we implement in the model the particle transport based on the Monte-Carlo approach simulation.
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Submitted on : Wednesday, July 6, 2022 - 5:24:18 PM
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Carlos Luis Mayorga Espinoza. Flow structure analysis and velocity field reconstruction using Reduced Order Method (POD and DMD : application to stirred tank and oscillating bubble plume.. Fluids mechanics [physics.class-ph]. INSA de Toulouse, 2022. English. ⟨NNT : 2022ISAT0006⟩. ⟨tel-03715759⟩

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