Stern and wake flows over submarine models based on constrained large-eddy simulation

The boundary-layer and near-wake flows of the Submarine Off-body Flow (SUBOFF) bare hull (AFF-1) and fully appended configuration (AFF-8), developed by the Defense Advanced Research Projects Agency (DARPA), are numerically investigated using constrained large-eddy simulations (CLES) method at length-based Reynolds numbers of 1.1−1.2×106. In the CLES method, a Spalart–Allmaras type model is employed to constrain the near-wall mean subgrid-scale (SGS) stresses, while a wall-adapting local eddy-viscosity (WALE) model is selected as the baseline closure to mimic the SGS stresses. Comparisons are made for surface pressure, skin-friction coefficients and boundary-layer thicknesses with SUBOFF measurements and high-resolution simulations. Generally, the CLES method outperforms the WALE model on the same low-resolution grid. The present results manifest that a weakly favorable-pressure-gradient zone upstream of the stern is followed by a strong adverse-pressure-gradient region, in which the boundary layer thickens rapidly while remaining attached, and the stern boundary layer develops an inner-outer double-peak structure in turbulent kinetic energy (TKE). The existence of fins enhances outer-layer turbulence and introduces strong three-dimensionality, providing an upstream origin for the bimodal distribution of TKE observed in the appended wake. In the wake of AFF-1, the velocity deficit exhibits classical self-similar behavior. For AFF-8, the appendages mainly broaden the wake and redistribute outer-layer momentum, so that the decay of centerline velocity deficit remains broadly comparable to that of AFF-1, whereas the establishment of self-similarity is clearly delayed. Further analysis shows that the second-order wake statistics of AFF-8 gradually approach a quasi-stable self-similar state farther downstream.