A production term study of delayed detached eddy simulation for turbulent near wake based on proper orthogonal decomposition

In this study, we investigate the distribution of turbulent kinetic energy (TKE) in the near wake of a circular cylinder in a turbulent flow. Numerical calculations were performed using the delayed detached eddy simulation method, incorporating two different production terms for TKE: one in its original form and the other with the Kato-Launder correction term. Our results demonstrate that the turbulence model utilizing the Kato-Launder correction term exhibits a strong correlation between TKE and the vorticity field, which is related to the calculations of mean velocity, velocity fluctuation, and other parameters that are in closer agreement with direct numerical simulation and experimental values. By employing the proper orthogonal decomposition technique, we extract and reconstruct three significant modes within the flow: the shear layer mode, vortex shedding mode, and near-wake bubble mode. The findings reveal that the Kato-Launder correction term offers a more detailed portrayal closer to the real flow physics. Conversely, the original form of the TKE production term exhibits an uneven energy distribution among the three modes and affects the role of the diffusion term within the flow. This leads to a less accurate representation of the vortex shedding mode and an excessive diffusion effect in the near-wake bubble mode. Finally, possible modifications of the turbulence model in this problem are given to enhance the portrayal of these characteristics. This work presents an analytical framework that enables a comprehensive analysis of turbulence models, providing valuable physical insights and guidance for improvement.