Implementation of wall functions to bridge the low-Re academic/high-Re industrial gap in large-eddy-simulation predictions

Abstract

Turbulent flows occur over a wide range of scales; this wide range becomes a challenge to resolve all the scales in turbulence for high Reynolds number industrial flows as required by direct numerical simulation (DNS) because the process is prohibitively computationally expensive. Large eddy simulation (LES) resolves the large energy-carrying scales in a turbulent flow, while the smallest scales, which can make up to 90% of the computational effort in DNS, are modelled. Consequently, LES is cheaper computationally than DNS, and a wall-resolved LES is used to investigate the development of heat transfer properties through a 90-deg pipe bend. The heat transfer along the outer wall of the bend is in good agreement with the mass transfer experimental data. However, the traditional correlation between heat and mass transfer breaks down along the inner wall due to the difference in the evolution of the flow and thermal fields. Despite the efficiency gains of LES against DNS, the computational cost remains very high for a fully wall-resolved LES. This work develops a wall function approach that allows for the deliberate reduction of the near-wall grid resolution for LES. A separate but smaller grid, which solves Reynolds-averaged Navier-Stokes equations (RANS) overlaps the near-wall LES domain to support the LES grid, where it is expected to be weak. Two variants of this approach have been tested. The more simple of the two variants, termed the numerical wall function for LES, is similar to the wall-modelled LES devised by Balaras et al. (1996) as the RANS grid computes a wall shear stress to correct the first cell at the wall of the under-resolved LES grid. The numerical wall function makes improvements over the wall-modelled LES by coupling consistent information at the interface between the LES grid and the top boundary of the secondary RANS grid. This procedure enables the computation of the full RANS equations, without simplification as done in traditional wall function approaches, and the specification of any advanced turbulence model in the RANS domain. The numerical wall function has been tested for a plane channel flow and a pipe bend flow. The second variant, which forms the major contribution of this project, has been the development of the subdomain wall function for LES to correct the under-resolved near-wall LES coarse grid beyond the first cell at the wall as is done in traditional wall function approaches. This method has a similar setup to the numerical wall function but uses ideas of the dual-mesh hybrid LES/RANS framework proposed by Xiao and Jenny (2012) to specify a weak source term in the LES momentum equation. The source term acts to readjust the partial mean LES fields in the near-wall near-wall region towards the equivalent fields in the RANS secondary grid. Predictions of the flow through numerous plane channels configurations, and flow through periodic hills and an asymmetric plane diffuser are in excellent agreement with reference data.

Date of Award	1 Aug 2022
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Alistair Revell (Supervisor), Dominique Laurence (Supervisor) & Imran Afgan (Supervisor)