Turbulence model adaptability at critical Reynolds numbers and applications in wake control via fairings

The water-drop shaped fairings with varying shape angles are attached to a circular cylinder to achieve wake control and vortex suppression at critical Reynolds numbers. To ensure the capability of Reynolds averaged Navier–Stokes (RANS), detached eddy simulation (DES) and large eddy simulation (LES) models at the critical Reynolds number region, three representative turbulence models are employed: LES with $\sigma$ subgrid-scale (SGS) model, delayed DES model with improved wall-modeling capability (IDDES) and shear stress transport (SST) $k-\omega$ RANS model. These models are utilized to simulate flow around a circular cylinder at Reynolds number $\text{Re}=2.5\times 10^5$. The solver used in this paper is further developed based on the high-resolution algorithm platform for incompressible flow (HRAPIF). The comparative analysis of the results from the three turbulence models has been rigorously validated and investigated. An exhaustive examination of the mean flow field, Reynolds stresses, characteristic lengths, and instantaneous flow fields among the models reveals instructive insights. The IDDES and $\sigma$-LES models predict the hydrodynamic forces, the so-called ‘drag crisis’, alongside the pressure distribution and skin friction coefficient with high precision. The $\sigma$-LES model stands out for its superior accuracy, while the IDDES model is also a viable alternative, offering commendable accuracy with a reduced demand for mesh density. Subsequently, the IDDES model is selected for wake control calculations using fairings with five distinct shape angles ($30^{\circ },45^{\circ },60^{\circ },75^{\circ }$ and $90^{\circ }$) at $\text{Re}=2.5\times 10^5$. In-depth comparisons to the bare cylinder and subcritical results reveal that the wake control effect varies at the critical Reynolds region. The fairing with a 30° shape angle substantially suppresses hydrodynamic forces. The lift coefficient experiences a remarkable decrease of approximately 96%, while the drag coefficient diminishes by about 90%. Concurrently, fairings with angles from 45° to 90° lead to reductions in drag coefficient of 11.6%, 10%, 3% and 4%, respectively. A 75% lowering in the lift force coefficient is found even with a short fairing with shape angle $\alpha =90^{\circ }$, which may be a meaningful instruction to industrial design.