Aerodynamic Force Breakdown in Reversible and Irreversible Components by Vortex Force Theory

Full-Aircraft Energy-Based Force Decomposition Applied to Boundary-Layer Ingestion

“…A promising approach to addressing the lift induced drag decomposition challenge, is through the use of vortex force methods [3,[18][19][20][21]. In primarily tackling the difficulty of applying entropy-based decomposition methods to unsteady flows, Marongiu and Tognaccini [22] adopted the theory of Wu [23] and Wu et al [24] to develop an alternative decomposition method which is based around the vortex force associated with integrals of the Lamb vector.…”

“…However, an important advantage of the vortex force approach, is that it enables the unambiguous calculation of lift-induced drag from numerical solutions [18], thereby providing a more rigorous definition in response to Spalart's [17] concerns whilst avoiding the difficulties of Trefftz plane positioning in entropybased methods because of rapid vortex decay downstream of the aircraft. Subsequently, further development saw the inclusion of compressibility correction term, which allowed for full decomposition of lift from drag with its wave, profile and lift-induced components in 2D and 3D flows [3,[19][20][21]. Although vortex force methods appear to provide an elegant solution to lift-induced drag calculations and have been applied to wing-body configurations, they have not yet been developed for full-aircraft decompositions where the propulsion system is included within the flow domain and interacts aerodynamically with the airframe.…”

“…† It is important to note that F B and F P are not intended to represent a division between drag and thrust respectively. Instead, they are simply convenient for referring back to the integrals they represent in Eq (21). and for distinguishing between unpowered and powered configurations, where F P represents additional terms due to additional flux surfaces or body forces used to simulate a propulsor.…”

Compressibility Correction to Kutta–Joukowski and Maskell Formulas Using Vortex-Force Theory

“…and no lift [16,[20][21][22]. F τ is neglected in practice [23], F ρl is the vortex force and F m ρ is an integral containing the density gradient in compressible flows.…”

“…Mele and Tognaccini [16] numerically emphasized that the incompressible Kutta-Joukowski theorem still holds in transonic and supersonic regimes suggesting that F m ρ is nothing but a compressibility correction to F ρl [20]. Besides, Kang et al [22] established a link with Maskell's formula by subtracting F S e to the total far-field drag.…”