Modeling Bubble Entrainment and Transport for Ship Wakes: Progress Using Hybrid RANS/LES Methods

This article presents progress on modeling bubble entrainment and transport around ships using hybrid Reynolds-averaged Navier-Stokes/large eddy simulation (RANS/ LES) methods. Previous results using a Boltzmann-based polydisperse bubbly flow model show that LES perform better than RANS in predicting transport of bubbles to depth, a very important process to predict bubbly wakes. However, standard DES-type models fail to predict proper turbulent kinetic energy (TKE) and dissipation, needed by bubble entrainment, breakup, and coalescence models. We propose different approaches to obtain TKE and dissipation in LES regions and evaluate them for cases of increasing complexity, including decay of isotropic turbulence, a flat plate boundary layer, and the flow in the wake of the research vessel Athena. An exponential weighted average is used to estimate statistics and obtain the averaged quantities in regions with resolved turbulence. The TKE is satisfactorily predicted in the cases tested. A modified omega equation in the SST model is proposed to implicitly compute the dissipation, showing superior results than the standard DES models, although further improvements are necessary. A hybrid RANS/LES approach is proposed, which focused at conserving total TKE as the flow crosses RANS/LES interfaces, as previously performed for zonal approaches but attempting a DES-like detection of regions suitable for LES, critical for large-scale computations of bubbly flows involving complex geometries. A general form of a dynamic forcing term is derived to transfer the modeled TKE to resolved TKE with a controller to guarantee proper conservation of the energy transferred. It was verified that the model is not sensitive to grid size or time step. Improvements to DDES and the proposed TKE-conserving hybrid RANS/ LES method show encouraging results, although remaining challenges are discussed.