A unified Thermodynamic/Vortical theory for the Aerodynamic Force analysis

The Lamb vector 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, with identification of local flow structures associated with the force generation.In this doctoral research, 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. 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, while friction stresses are retained in their standard near-field expression.