Assessment of Hybrid RANS-LES and WALE Formulations for Wake and Resistance Prediction of the BB2 Submarine

Abstract

Submarine hydrodynamics presents unique challenges in accurately predicting flow separation, wake structure, and resistance due to complex geometry and turbulent behaviour at high Reynolds (Re) numbers. Traditional Reynolds-Averaged Navier-Stokes (RANS) approaches are often limited in resolving unsteady flow structures and turbulence in the near and far regions. To address these limitations, hybrid RANS-LES models such as Detached Eddy Simulation (DES) and Large Eddy Simulation (LES) offer improved performance in capturing near-wall vortical structures. The capturing of turbulent vortices and wake structures significantly contributes to conduct hydrodynamic noise analysis. Detailed resolution and understanding of these coherent structures help minimize hydroacoustic signatures, essential for submarines' stealth characteristics. Based on prior studies, Breuer et al. (2003) reported that RANS failed to capture unsteady vortex shedding, producing only steady results even in 3D simulations. In contrast, DES and LES successfully resolved asymmetric shedding across different grid resolutions. Spalart (2009) reported that DES is more effective than RANS or LES for high Re flows, although it suffers from challenges related to ambiguous grids and nonmonotonic grid refinement behaviour. Whereas Liang \& Xue (2014) found that DES predicts tip vortex flow characteristics more accurately than RANS-SA and can capture complex 3D vortex structures. In addition, Guilmineau et al. (2018) demonstrated that the IDDES model accurately predicts recirculation bubbles and aligns more closely with experimental data for flow prediction. Long et al. (2021) confirmed the capability of DDES in simulating cavitating flows around hydrofoils and marine propellers. Lungu (2022) highlighted the efficiency and accuracy of the hybrid IDDES-SST model in DARPA submarine simulations. Zhang et al. (2023) also noted that URANS struggles with resolving small-scale turbulence structures, whereas IDDES is better suited for predicting complex phenomena such as ship air wake asymmetry. Nevertheless, capturing the unsteadiness and turbulence fluctuations scales is extremely challenging because the cell size requirements should suit each turbulence model employed. Thus, as a continuation of the prior work of Abidin et al. (2024), the unsteady simulation with high mesh resolution at $U_m=1.8235$ m/s and Re of $3.6\times 10^6$ to generate the asymmetrical wake dynamic and vortical structure. The current research expands the methodology by parameterizing the meshes and numerical scheme based on Taylor microscale refinement with respect to the characteristic length of (L, B and D) of submarine, particularly focusing on hybrid turbulence model and WALE to observe the ability to resolve turbulence in the wake region. The transient simulations were performed initially using wall-resolved mesh (76x10^6 cells) at y^+ < 5 and then wall-modelled mesh (56x10^6 to 74x10^6 cells) at y^+ > 30, which produced notably different and more detailed results (vortices and turbulence fluctuation) than previous steady-state RANS simulations without risking the accuracy of quantity of interest (global resistance).