Temporal representation of flow transition and separation using URANS method

In aerodynamics, part of the research focuses on the study and characterization of unsteady phenomena occurring in common flow realizations. Among these, flow transition, separation, and reattachment are of particular relevance. These phenomena exhibit a strong temporal dependence; therefore, an accurate investigation must inherently account for their time-dependent nature. A detailed understanding of such phenomena is fundamental in numerous engineering fields, particularly in motorsports, where local flow control helps to maximize overall vehicle performance. High-fidelity simulations of unsteady turbulent flows require significant computational resources due to the resolution of the complete spectrum of time scales, from the smallest dynamically relevant ones to those associated with the largest energy-containing structures. Several techniques are already widely used and discussed in the literature, such as Large Eddy Simulation and Direct Numerical Simulation, principally used for academic purposes. Alternatively, in an industrial context, computationally more affordable approaches, such as Unsteady Reynolds-Averaged Navier-Stokes equations, can be adopted. However, the need to limit the computational cost of the simulations must not compromise the accuracy of the results. Therefore, a precise and comprehensive description of the underlying physical phenomena must be provided. URANS methods are known to struggle in accurately predicting laminar-turbulent transition and flow separation under adverse pressure gradients, and this is a problem especially in configurations where unsteady phenomena critically influence the overall aerodynamic behavior. The objective of this thesis is to investigate the accuracy of temporal signals provided by URANS methods in flows involving flow transition and turbulent separation and to evaluate potential errors resulting from the choice of time-step and numerical models. The flow configuration investigated is a NACA 4412 airfoil at an angle of attack of 15° immersed in a turbulent free-stream and at a Reynolds number (based on the chord length and the free-stream velocity) Re = 66,000. This configuration is paradigmatic, as it is representative of more complex geometries, such as the flow around a wing or an aerodynamic component of a racing car. The simulation was performed using a URANS approach within the open-source software OpenFOAM employing γ - Reθ model. The results were compared with reference DNS data obtained at the same Reynolds number and for the same geometry. Under these conditions, the flow over the suction side exhibits an initial laminar separation, followed by turbulent reattachment and subsequent final turbulent separation. Through the analysis of wall-bounded quantities —specifically statistics related to pressure fluctuations— the study aimed to identify characteristic trends associated with separation and reattachment phenomena. Regarding the analysis of temporal signals, wall-based data allowed the identification of time-varying extensions of the separation regions, as well as the shrinkage and enlargement dynamics of the laminar bubble. Furthermore, the characteristic frequencies of Kelvin-Helmholtz instabilities within the shear layer and of vortex shedding in the turbulent region were evaluated, together with the assessment of their sensitivity to the chosen time-step. This work clarifies the effect of temporal discretization on the study of transition and turbulent separation phenomena around an airfoil. Furthermore, it assesses the capability of URANS methods to identify flow separation and reattachment zones through the analysis of wall quantities. These results provide useful insight for the simulation of more complex flows, typical of motorsport applications.