Decomposition and reconstruction of the flow field in a stirred tank using data-driven methods and machine learning

Abstract

The aim of this thesis is to use data-driven and machine learning methods to identify, extract and reconstruct the large scale flow structures in an unbaffled stirred tank. Large scale flow structures have been observed behind the impeller blades and throughout the stirred tank. The origins and characteristics of these are not fully understood, but they have been found to play an important role in the rate of mixing and on products from chemical reactions in stirred tanks.

The computational cost of performing simulations with fine resolution to capture these is often prohibitive. On the other hand, the lack of spatial resolution from experimental measurements means that the latter can also only provide limited information. Data-driven and machine learning methods can be used to combine the strengths of the computational and experimental approaches with the aid of reduced order models.

The derived models can be used at both design and off-design conditions to provide quick estimates of the 3D flow field that can be used both in combination with chemical reaction simulation and for optimisation of mixing. For example, the approaches developed in the present thesis open the possibility to synchronise the reactant injection timing with local instantaneous flow features for more precise control of mixing. However, prior to this work, these models were largely limited to 2D flow problems.

An initial investigation was performed on a stirred tank in transitional flow conditions with Re=600 simulated using Direct Numerical Simulations (DNS). Proper Orthogonal Decomposition (POD) was used to decompose the flow into modes. The first 4 POD modes were found to come in two pairs, accounting for 14%, and 2.6% per mode of the mean Turbulent Kinetic Energy (TKE) respectively. The first pair of modes was found to have a frequency of 1.5F_N and the second 3.0F_N (in the rotating reference frame) where F_N is the impeller rotation frequency. These modes were then reconstructed using the velocity input data from 1 and 6 input points using a system identification algorithm. Good fit values were obtained for both datasets for the first pair of modes for both the base design conditions and the off-design conditions of Re=500 and Re=700. The second pair of modes were also reconstructed reasonably well with 6 input points.

Replacing the velocity input data with pressure data taken at the impeller and outer wall surfaces also allowed good prediction of the temporal evolution of the first two modes. Using 1 or 6 input points on the impeller surface, or 12 points (6 on the impeller surface and 6 on the outer wall) the temporal POD coefficients were reconstructed reasonably well for the base case. The successful application of the estimator to the off-design conditions for the 6 and 12 input point cases showed the robustness of the proposed approach to varying flow conditions.

The velocity POD modes were also used to decompose the pressure field into a time averaged component, and components that are linear and quadratic in terms of the temporal coefficient of the velocity modes. The spectrum of the power number of a single blade was found to have peaks at 1.5F_N and 3.0F_N, corresponding to the first two POD mode pairs. However, when considering the power number computed from 3 adjacent blades or the total power number, these peaks vanished, suggesting that these modes have no effect on the total power number fluctuations. The power number spectrum was noisy but had noticeable peaks at 0.04F_N and 0.43F_N. The former corresponded to the frequency of the 9th POD mode that represented fluctuations in the radial jet emanating from the impeller. The latter peak was not concentrated in a particular mode but was reproduced in the power number computed from the first 300 linear pressure modes.

The impeller speed was then increased to consider fully turbulent fluid flow conditions with a base case Re=30000 and off-design conditions of Re=20000 and Re=40000 modelled using Large Eddy Simulations (LES). The first four modes were again found to come in two pairs with 5.5% and 1% per mode of the TKE respectively and frequencies of 1.4F_N and 0.8F_N in the rotating reference frame. In the inertial frame these were found to correspond to frequencies of 0.6F_N and 0.2F_N respectively. Investigation of their spatial components suggests that these modes are precessing Macro-Instabilities (MIs). In total, 4 algorithms (N4SID, N4SID with a preprocessing POD step on the probe data, and a 1 and 2 hidden layer LSTM Neural Network) were used to reconstruct the first pair of POD modes using velocity data from 1, 2 and 6 input points. The modes were reconstructed well for both the design and off-design conditions by all algorithms with similar fit values. The reconstruction of the second pair of modes using a second set of 6 input points was less successful, with only the N4SID with the preprocessing algorithm giving qualitatively reasonable results.