A geometric model for non-equilibrium turbulence

Abstract

This thesis presents a geometric framework for implicit large-eddy simulation (iLES) of turbulent boundary layers. By embedding the Navier-Stokes equation within a non-Euclidean manifold, an implicit description is generated in which the sub-grid stress tensor is replaced by an effective metric tensor. The manifold reframes the turbulence modelling problem, offering a novel, resolution-independent mathematical structure that connects locally universal, inertial behaviour of turbulence with the non-universal, tensor structure of general conditions. The result is a model which is strictly local, simplifying the resultant modelling problem, ensuring minimal sensitivity to the specific inhomogeneity and anisotropy of particular flow conditions, and removing reliance upon both empirical assumptions and data.
The method functions as a unified wall and sub-grid scale model which is validated across zero- and adverse-pressure-gradient (APG) flat plate boundary layers, and a NACA4412 aerofoil case. Accurate prediction of mean velocity profiles is achieved without adjustment and the method performs robustly across a large range of resolution regimes. The results confirm that the framework achieves its aim of minimising conditions-sensitivity, while maintaining accuracy in a diverse range of conditions.
Limitations remain particularly in the representation of boundary layer tripping/transition, which leaves minor issues in the prediction of specific Reynolds stress component under history-dependent APG conditions. Nonetheless, the results demonstrate that geometric iLES provides a promising alternative to the classical methodology. The work provides a unique foundation for implicit turbulence models to be equipped with the rich tensor structure that facilitates descriptions of general conditions. This contribution is particularly relevant for the predictive simulation of turbulence under general APG conditions where statistical behaviour is strongly non-universal/problem-dependent and where equilibrium assumptions crucial to the classical, explicit description break down.

More information

Identifiers

ORCID for James Alexander Leetch: orcid.org/0009-0001-7963-0202

ORCID for Bharath Ganapathisubramani: orcid.org/0000-0001-9817-0486

Catalogue record

Export record