A dynamically-calibrated adaptive detached-eddy simulation method

Hybrid RANS/LES turbulence models are currently among the most promising high-precision turbulence simulation methods for practical engineering applications. Enhancing their generality and accuracy in predicting complex flows is crucial for accelerating this adoption process. To achieve this goal, this study first theoretically analyzes the apparent equivalence of RANS and LES methods under appropriate conditions. A versatile method for calculating the dynamic filter-scale coefficient is derived, enabling a seamless transition from RANS to LES mode within hybrid RANS/LES models. Furthermore, to address the potential "gray area" problem inherent in these models, an adaptive filter-scale coefficient calculation method suitable for separated flows is constructed using the σ-LES subgrid-scale model. When applied to typical Detached-Eddy Simulation (DES) model and their improved variants, i.e., Delayed Detached-Eddy Simulation (DDES) and Improved Delayed Detached-Eddy Simulation (IDDES) models, this leads to the development of a series of adaptive ADES/ADDES/AIDDES models. The validation of the proposed new model is performed on the open source PHengLEI software platform. Numerical simulations of supersonic base flow and critical high-angle-of-attack flow around a high-lift airfoil confirm that the novel adaptive ADES/ADDES/AIDDES models effectively overcome the "gray area" delay issue in the separated shear layers, thereby improving the accuracy of predictions for the velocity field in recirculation zones, turbulent kinetic energy, and velocity profiles in the complex airfoil boundary layers. The numerical results demonstrate that the adaptive filter-scale coefficient calculation method can significantly enhance the accuracy of hybrid RANS/LES models.