Near-wall modelling in Eulerian–Eulerian simulations

Abstract

The near-wall region in turbulent Eulerian–Eulerian (E–E) simulations has hitherto received little to no attention. A standard approach to modelling this region is through the employment of single-phase wall-functions in the fluid-phase and it is unclear whether such an approach is capable of capturing the turbulent fluid-particle interaction in the near-wall region. In order to both investigate and alleviate E–E models reliance on single-phase wall-functions we propose an E–E elliptic relaxation model to account for the near-wall non-homogeneity which arises in wall-bounded flows. The proposed model is derived within an E–E framework and enables the full resolution of the boundary layer and arbitrary wall sensitivity. The model is then compared against the conventional kf−εf turbulence model with standard single-phase wall-functions. Additionally, the modelling is compared against a low-Re number turbulence model. The elliptic relaxation model is implemented within the open-source CFD toolbox OpenFOAM, applied to a vertical downward-facing channel and validated against the benchmark experimental data of Kulick et al. [1]. Model results show marked improvements over the conventional turbulence model across mean flow and turbulence statistics predictions. The use of conventional single-phase wall functions were shown to negatively impede on the prediction of the velocity covariance coupling term and as a result the particle fluctuation energy. Moreover, this also lead to an underestimation of the near-wall volume fraction accumulation. Finally, the elliptic relaxation model, E-E model and accompanying validation cases are made open-source.