The development of data driven approaches to further turbulence closures

Abstract

The closure of turbulence models at all levels of fidelity is addressed, using unconventional methods that rely on data. The purpose of the thesis is not to present new models of turbulence per se, but rather the main focus is to develop the methodologies that created them. The main tool, Gene Expression Programming, is a versatile evolutionary algorithm. Implementations of the algorithm allow for symbolic regression of scalar and tensor fields and the clustering of data sets. The last two applications are novel algorithms. Scalar field regression is used to construct length scale damping functions for Hybrid RANS/LES. Direct Numerical Simulation snapshots are filtered to mimic Hybrid RANS/LES flow fields and from this new damping functions are created. Two closures are constructed, one from data in a turbulent pipe and another from slices along the classic backward facing step geometry. The new closures are tested for a range of separated flow applications. Tests alongside existing closures of the same class show that both new methods adapt to the local mesh resolution and turbulence level at least as well as other hybrid closures. Tensor field regression is used to construct non-linear stress-strain relationships in a Reynolds-Averaged Navier-Stokes framework. A common two-equation model is modified by including a further term that accounts for extra anisotropy with respect to the Boussinesq approximation. This model term, regressed from time averaged Direct Numerical Simulation data, turns the linear closure into an Explicit Algebraic Stress Model. The training data is taken from the reverse flow region behind a backward facing step. When applied to the classic periodic hills case, the subclass of models generated are found to greatly improve the prediction with respect to the linear model. A subclass of models is created in order to test the ability of the evolutionary algorithm. The deviation from the periodic hills reference data is quantified and used as a metric for model performance. The key finding is that improved performance of the Gene Expression Programming framework corresponded to improved prediction of the periodic hills. The final application of Gene Expression Programming, the clustering of datasets, is used to group Reynolds stress structures into distinct types. Firstly, reference Direct Numerical Simulation data obtained in a turbulent channel is categorised into six distinct groups. These groups are then compared to structures from Hybrid RANS/LES. These groups help to show that Hybrid RANS/LES structures do not correctly capture the near-wall cycle of turbulence. Instead there is an artificial cycle that is characterised by an incorrect buffer layer, defined by tall, long and thin structures. Further, streaky structures lie on the interface between Reynolds-Averaged Navier-Stokes and Large Eddy Simulation. These structures are free to move in the vertical direction and seriously contribute to discrepancies in the second order statistics.

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Identifiers

ORCID for Richard Sandberg: orcid.org/0000-0001-5199-3944

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