A unified thermodynamic/Lamb-vector-based analysis of the aerodynamic force

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 and decomposition, as an alternative to the nowadays well-assessed thermodynamic methods. We here propose a mixed approach, where exact Lamb-vector-based force formulas are used in combination with a thermodynamic-based calculation of the Lamb vector through Crocco's equation. In computational fluid dynamics, this way of calculating the Lamb vector, therefore, inherits from the numerical form of the flow momentum equation and discretely satisfies the local (and integral) momentum balance on which far-field methods rely. The resulting hybrid method, which does not require an explicit vorticity calculation, provides results in far better agreement with regard 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. In addition, it overcomes the limitations of previous thermodynamic methods, which only compute the drag force.