Data-driven fluid dynamics

Lead Research Organisation: Imperial College London
Department Name: Dept of Aeronautics

Abstract

The aim of this project is to harness the power of statistical analysis to maximise the information we obtain about the dynamics of a fluid flow. In fluid dynamics, simulations and experiments are often carried out with the intention of obtaining as much information about the velocity field as possible. However, fluid flows are difficult to study and control. Having a simplified model of a flow can lead to better understanding of its governing physics and can also be utilised to facilitate flow control.
The main focus of this project is to develop tools for reduced-order modelling and flow feature identification based on data obtained from experiments or numerical simulations. To this end various statistical and optimisation based tools including modal analysis, graph theory, pattern recognition and machine learning will be used. In this project we try to see the extent to which these tools can be used to maximise the amount of information one can extract from the data, despite the limitations of the experimental methods used to acquire them. We also investigate the best ways to model the dynamics of the flow and the extent to which a model based on such analysis can be relied on, in applications such as flow control and state estimation. As a dataset captures certain information about the flow, we also explore the possibility of using these methods to design an experiment such that it maximises the captured information.
The findings of this project can be used in any field where acquiring large datasets is easier than discovering or simplifying the governing equations of the system.

Publications

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Beit-Sadi M (2021) Data-driven feature identification and sparse representation of turbulent flows in International Journal of Heat and Fluid Flow

Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/R512540/1 01/10/2017 31/03/2022
2090966 Studentship EP/R512540/1 01/11/2017 30/04/2021 Mohammad Beit-Sadi
 
Description In fluid dynamics, like many other fields, it is often the case that collecting experimental data is easier than running computationally expensive simulations. There are many techniques for developing a reduced-order-model, ROM, of the underlying dynamical system through analysing the collected data. The ROM can then be utilised for control or estimation purposes. Such techniques include dynamic mode decomposition, DMD, and optimal mode decomposition, OMD, which are shown to be closely related to Koopman analysis.These algorithms extract, out of experimental or numerical data, a finite number of dynamic modes, each of which is associated with an eigenvalue. A finite dimensional, linear ROM of the underlying, possibly nonlinear, dynamical system is then developed using those modes and eigenvalues. The outputs of DMD or OMD, i.e. the modes and eigenvalues, are dependent on the prescribed dimension of the reduced-order-model. Often however, only a few of these modes will be of interest to the practitioner and as such, they may use a statistic to measure the significance of each mode.

So far we have devised an algorithm which, using the graph-theoretic notion of maximal-clique and the inherent non-orthogonal property of such dynamic modes, identifies clusters of modes that are associated with the same underlying physical feature. This will then lead to a significantly more sparse representation of the underlying flow. Applying the algorithm on snapshots of the flow-field from a variety of flows, it is observed that one advantage of the graph-theoretical approach is that the sparse representation of the underlying flow is not limited to those features which are the most energetic in the captured data. Instead, the algorithm also identifies flow features which may not be very energetic, but are dynamically relevant.

Preliminary results were published and presented at the 11th International Symposium on Turbulence and Shear Flow Phenomena (TSFP11) in Southampton, UK, in July 2019 (http://www.tsfp-conference.org/proceedings/2019/103.pdf). Subsequently, this work was invited to be submitted for publication as a journal article as part of a special issue of the International Journal of Heat and Fluid Flow. This work is in preparation for submission in late March 2019.
Exploitation Route Our algorithm can be used in conjunction with any variant DMD or OMD, and any measure of significance for the modes. These techniques have been used in a variety of fields and have been shown to be capable of effectively modelling systems with quasi-periodic behaviour. Therefore, any practitioner devising a model using the said techniques, could benefit from utilising this algorithm to analyse the similarity between the modes. The code for the algorithm and all relevant functions will be made available on the internet.
Sectors Aerospace, Defence and Marine,Digital/Communication/Information Technologies (including Software),Financial Services, and Management Consultancy,Security and Diplomacy

URL http://www.tsfp-conference.org/proceedings/2019/103.pdf