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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.

Viscous-inviscid interaction --- Integral boundary layer equations --- Quasi-simultaneous coupling --- Boundary layer --- Ingénierie, informatique & technologie > Ingénierie aérospatiale

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Preliminary aircraft design often relies on solutions of the RANS equations to characterize the flow field in the different conditions of interest. Such a procedure usually comes at the expense of costly computations that can hardly be used routinely in the early stages of the design. To overcome this problematic, inviscid flow models are considered as an alternative since the associated computational time is more interesting. The main drawback of these models is their inability to predict aerodynamic drag or flow separation which is of upmost interest to optimize the aircraft for fuel consumption. Viscous corrections can be used with these flow models and offer a fast tool suited for preliminary design.
This study presents a pseudo-time dependent, two-dimensional interacting boundary layer method for compressible flows in external aerodynamics. An inviscid flow is modeled by an unstructured finite-element, full potential solver suited for transonic flow computations. The flow in the immediate wall vicinity and in the wake is distinguished from the external inviscid flow by its viscosity property and is described by the time-dependent, compressible integral boundary layer equations. Steady-state flow solutions in the boundary layer are obtained on a dedicated mesh through a damped Newton scheme and are interfaced with the inviscid solutions through a quasi-simultaneous coupling method. The eN method is used to capture the laminar to turbulent transition. A pseudo-time marching method is presented with time advancement control and spo- radic numerical information update. Results are presented subsequently for attached and mildly separated flows around a symmetrical airfoil, for high angle of attack and low Reynolds number flows. Transonic capabilities are demonstrated on a supercritical airfoil and compared to RANS solutions which constitute the current reference in the domain. Stable convergence and good agreement with reference results is observed for flows with limited separation regions. Expected limitations are shown when the regime approaches stall. Further possible improvements, such as the use of an inverse method and mesh quality improvements are discussed especially for the transonic regime and results are consequently argued.

Viscous-inviscid interaction --- Coupled IBL --- Boundary layer --- Viscous flow --- Separation bubble --- Turbulent flow --- Turbulence --- Transition --- DARFLO --- Shear-lag equation --- Ingénierie, informatique & technologie > Ingénierie aérospatiale