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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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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.

Transonic --- Aerodynamic modelling --- Preliminary aircraft design --- Full-Potential --- Finite element method --- stabilisation processes --- mesh-dependency --- 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

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By observing some acrobatic maneuvers, one can easily understand that they involve a large amount of various attitudes at a high rate. It is then obvious that higher loads are applied on the structure and thus higher stresses are also found inside the materials. Consequently, a specific aircraft are required. This type of aircraft has to be compliant with a specific standard that guarantees the integrity of the aircraft during this type of flight.

In this way, this master thesis consist in a structural analysis of the extit{Sonaca 200} submitted to aerobatic loads. An estimation of these aerodynamic loads is performed through a panel method software. The latter enables to find the distribution of pressure all over the lifting surfaces. While corresponding stresses in each part of the aircraft are computed by finite element simulations of the whole airplane. The final goal is to determine which parts of the structure have to be reinforced. 

This paper describes all the methodology as well as tools and models used. An example of the results are also presented and interpreted. These developments constitute a preliminary design to motivate future more advanced works.

aircraft structure design --- CFD --- FEM --- Fatigue analysis --- aerobatics --- Ingénierie, informatique & technologie > Ingénierie aérospatiale