Implementation of a viscous-inviscid interaction scheme in a finite element full potential solver

During preliminary design of an aircraft, high fidelity simulations are not ideal due to their computational cost. Even, RANS simulations are of the order of hours and are not suitable for rapid modification in the design during early stages. Methods have been developed to lower the computational cost such as the full potential equation. This equation allows to simulate flow in the transonic regime but neglects the viscosity of the fluid. Therefore, the method is not able to predict interesting features such as the stall or an accurate drag coefficient.

The purpose of this master's thesis is to implement a viscous correction into a finite element full potential solver named Flow. A viscous-inviscid interaction scheme has been implemented. The first goal of this work is to define a theoretical model which can handle either incompressible or compressible, attached or separated flows. The viscous formulation is based on the two-equations dissipation integral boundary layer method coupled with a transition formulation of the e^9 type. The viscous solver is coupled to the inviscid solver by a quasi-simultaneous interaction method. This coupling method provides an easy integration without modifying the inviscid solver and allows to compute weak separation regions. The second goal of the thesis is the numerical implementation of the scheme. The fully coupled non linear system of the viscous solver is discretized by a finite-difference method and is resolved by a robust Newton solution procedure. The results presented demonstrates the ability of Flow to predict with accuracy aerodynamic loads and laminar to turbulent transition for attached incompressible and compressible flow cases. Moreover, Flow is able to simulate with accuracy separated or highly compressible flows. However, some limits of Flow are reached by these extreme cases and this work presents them. A concise summary of the main outcomes and few hints for future work are provided in the conclusion.