A unified thermodynamic/vortical theory for the aerodynamic force analysis

Aerodynamic force prediction and decomposition into physical constituents is a fundamental research topic, and a clear identification of lift-induced, viscous and wave drag in a generally compressible and dissipative flow is still an open issue. The Lamb vector, cross-product of flow vorticity and velocity, is at the basis of different far-field methods developed in the last decades for the aerodynamic force analysis, as an alternative to the nowadays well-assessed thermodynamic methods. They offer far-field formulations and decompositions of the whole aerodynamic force (drag alone is instead addressed by thermodynamic methods), with identification of local flow structures associated with the force generation. Different exact Lamb-vector-based force formulations were proposed in the past, and the decomposition of total drag into lift-induced and parasite contributions was subject of very recent studies, where new induced drag definitions were proposed for viscous and compressible flows. However, inconsistencies were also reported, raising questions on the physical role of a non-zero induced drag found in two-dimensional flows. Moreover, the separation of parasite drag into viscous and wave drag contributions by Lamb vector field analysis is still questioned. In this doctoral research, the steady flow regime is first addressed. Consistency between lift-induced/parasite drag definitions, and the drag generated in isentropic flow conditions (reversible drag) or due to entropy production (irreversible drag) is analysed. A spurious contribution (related to the streamwise momentum perturbation) is identified, resulting in non-zero induced drag values in two-dimensional flows. A new approach to parasite drag breakdown into viscous and wave contributions is proposed, accounting for the flow entrainement in the viscous wake, and results are compared against predictions obtained using consolidated thermodynamic-based methods and against available results from recent literature. Then investigations are extended to the unsteady regime. Vortical force formulas are extended to the unsteady regime considering inertial or non-inertial frames, viscous or inviscid flows, fixed or moving bodies. An aerodynamic force decomposition is proposed, allowing for Thrust/Drag Bookkeeping (TDB) in two-dimensional viscous and unsteady flows, addressing an open topic in moving wings aerodynamics where no TDB methodology is actually available for oscillating aerofoils in dissipative and compressible flow regime. Unsteady terms are re-formulated in an analytically equivalent expression, which provides higher accuracy in numerical applications. Finally, a new unified thermodynamic/vortical method is developed, where exact Lamb-vector-based formulas are used in combination with a thermodynamic-based calculation of the Lamb vector through Crocco's equation. The resulting hybrid method, which does not require an explicit vorticity calculation, provides results in far better agreement with regards to near-field force data when compared to standard vorticity-based approaches, especially in the presence of shock waves, where inaccuracies of domain integrals involving the Lamb vector were systematically reported by different authors. The proposed unified approach also led to the formulation of a new exact force formula, representing an innovative thermodynamic method, able to compute the total force in generally unsteady viscous and compressible flows (overcoming the limitations of previous thermodynamic methods, which only compute part of the drag force). The new formula is based on a far-field expression of pressure forces on the body (the only ones deserving a phenomenological decomposition) while friction stresses are retained in their standard near-field expression.