k-corrective frozen PANS: A data-driven stochastic closure turbulence model

Abstract

Studies revolving around data-driven methods have been on a rise in recent years to improve highly modelled methods such as the two-equation turbulence models of Reynolds-averaged Navier-Stokes (RANS). Similarly, such data-driven methods are implemented into partially-averaged Navier-Stokes (PANS). PANS is a young bridging method that fulfils the requirements of bridging methods set by Speziale [1]. It can be adjusted according to the fraction of a flow field that is desired by the user to be resolved and modelled by changing the value of fk, a parameter that takes a value between 0 and 1. In this thesis, PANS is extended via a combination of two data-driven methods: k−corrective frozen RANS [2] and data-driven stochastic closure simulation (DSCS) [3]. The k−corrective frozen RANS method aims to correct for the model errors in the k−equation and the anisotropy of the Reynolds
stress tensor derived from the Boussinesq approximation. While DSCS also aims to correct for the anisotropy of the Reynolds stress tensor, it considers that PANS solves for the unresolved part of the flow field and thus corrects for the unresolved anisotropy. While PANS and the two data-driven methods have independently been proved to work as they were theoretically desired, combining these ideas has not yet been attempted. As any turbulence kinetic energy solving RANS turbulence model can be developed into PANS form, the k − ω SST model was chosen for the best initial prediction. This SST model for PANS is extensively derived and then reformulated to produce the target correction terms. The correction terms are analysed at various values of fk and they show good agreements with fk.