Dynamic and Stability of Wake Vortices

The aim of this internship is to characterize the formation and near-field evolution of wing-tip vortices over a range of Reynolds and Mach numbers by means of Unsteady Reynolds-Averaged Navier–Stokes (URANS) simulations. In particular, we seek steady solutions of the URANS equations, i.e., RANS solutions corresponding to equilibrium states of the flow. These computed flows will constitute the base states of the global stability analyses, in which turbulence is accounted for through a linearized Spalart–Allmaras model. The quality of these base flows will directly determine the reliability of the stability predictions.

The first part of the internship will be devoted to getting to grips with generic URANS solvers on a reference wing-tip vortex configuration for which detailed experimental data are available. Particular attention will be paid to the meshing strategy, since the vortex core is a thin region of intense rotation that must be resolved over long downstream distances.

The second part will consist of a parametric study of wing configurations at several Reynolds and Mach numbers. Beyond computing the flows, the student will analyse the physics of the vortices: roll-up of the vortex sheet, downstream evolution of circulation, core radius and axial velocity, and sensitivity of the vortex core to turbulence modelling. The computed vortices will be compared to analytical models such as the Batchelor vortex, in order to extract the parameters governing their stability (swirl number, axial velocity deficit or excess) and to position each configuration with respect to known instability criteria from literature.

Looking ahead, at the end of the project, the resulting database of converged RANS equilibrium solutions will serve as base states for the first global stability analyses.

Therefore, the goals of this internship can be summarised as follows:

• Getting to grips with the URANS solvers and the CFD mesh generation software (ANSYS ICEM, Gmsh or similar).
• Validating the numerical set-up on a reference wing-tip vortex case against experimental and numerical data.
• Computing the flow around wings at several Reynolds and Mach numbers on dedicated meshes.
• Providing the RANS base flows for the global stability analysis tools.