Master thesis and internship[BR]- Master's thesis : Investigation of various transonic stabilisation techniques for full potential flows calculation in DARTFlo[BR]- Integration Internship

Abstract

The preliminary aircraft design is often performed based on low-fidelity aerodynamic models facilitating the evaluation of best-suited aircraft configurations thanks to low computational costs and reasonable accuracy at this early design stage. The Full Potential equation, based on the inviscid and isentropic assumptions, has demonstrated its ability to meet those requirements. However, the mathematical nature of this partial differential equation highlights that when the flow switches from subsonic to supersonic, it converts from elliptic to hyperbolic. This flow physics change needs to be reflected in the numerical implementation. DARTFlo, a full-potential solver, is implemented based on a physicsdependent solution experiencing mesh-dependency. Thenceforward, the present thesis aims at characterising the mesh-dependency of this physics-dependent solution and to propose alternatives to withdraw it. The current physics-dependent implementation is studied through a mesh convergence analysis in three different test cases to characterise the mesh-dependency. The analysis relies on two comparison axes, the first is a study of global flow parameters and the second treats the problem from a local point of view. The three test cases are constructed to study the behaviour of each solution in different situations. The original DARTFlo implementation illustrates its mesh-dependency by local flow parameters which do not converge with respect to the mesh refinement as well as by instabilities appearing in the supersonic zones when the mesh is highly refined. In parallel, three alternatives are derived and compared with the original implementation to assess their improvements in removing the mesh-dependency problem. The first alternative demonstrates improved mesh convergence and enables to partially remove the results mesh-dependency according to the case studied. However, the two others do not reveal to act on the mesh-dependency of the physics-dependent solutions.