Aerodynamic lift and drag breakdown in steady and unsteady flows

The analysis of the aerodynamic force is a crucial aspect for the design of an aircraft. Furthermore, innovative applications like devices inspired by natural flight, windmills, drones etc. also require an accurate analysis of the forces they experience. Design requirements result in more and more complex flows, and different phenomena interaction can change significantly the distribution of the aerodynamic forces. Designers are typically interested in a physical decomposition of the aerodynamic force that allows estimating the contributions of the different phenomena that occur around the body. During last decades, many breakdown methods have been developed in steady flows to decompose aerodynamic drag in order to obtain a decomposition in viscous, wave and lift-induced drag components. Moreover, the recent interest in unsteady aerodynamics requires the physical decomposition of the whole aerodynamic force (lift and drag), with the necessity for the extension of aerodynamic force analysis methods o the unsteady regime. In this dissertation the author analyzes an unconventional aerodynamic force exact expression, valid in compressible unsteady viscous flow. The method links the aerodynamic force generation to local flow variables which are non-zero only in localized zones of the flow, i.e. boundary layers, viscous wakes, shock waves and shock wakes. The application of this theory is focused on the case of Computational Fluid Dynamics (CFD) simulations. The first part of this thesis is dedicated to the analysis of steady flows. A rigorous definition of the lift-induced drag component is proposed and numerically proved. The drag breakdown in profile and lift-induced drag components is analyzed for the flow around an elliptic wing, with the analysis of the lift-induced drag generation. An alternative aerodynamic force expression is then developed to overcome numerical issues that occurs at high transonic regime. A first viscous-wave profile drag breakdown is also proposed. Applications are shown in the case of an airfoil, an elliptic wing, and a realistic transonic aircraft configuration. Comparisons with classical drag breakdown methods are also presented. A discussion on the improvements in the lift-induced drag analysis is provided. Finally to overcome some discrepancies with previous drag breakdown methods a new wave drag definition is derived. The second part of this thesis is focused on the analysis of unsteady flows. A link between present nonlinear theory and classical linear inviscid results is found. This link allows for a new definition of dynamic force derivatives. Present decomposition is applied to incompressible flows around an oscillating flat plate at low and high Reynolds number. In addition, a new mixed inertial-non inertial formula is derived, which allows for more accurate results when dealing with numerical solutions obtained by moving rigid grid methods. The theoretical link allowed for a definition of reversible and irreversible parts of the aerodynamic force in both incompressible and compressible flows. Finally, the method is applied to the analysis of a numerical solution around a pitching airfoil and is validated with a comparison with a recent unsteady drag breakdown method.