Can vorticity only be generated along external separation lines? (May-2022)
In the scope of Potential Flow Theory, specifically in the Vortex Lattice Method (3D; inviscid flow past a shell-body), it has been widely accepted "by default" that flow detachment (and thus, vorticity generation) occurs only from trailing and lateral (wing tips) edges, which seems to be a crude simplification that limits its application range. Such an approach avoids that partially or massive flow detachment can be precisely solved (through spatially precise shedding vorticity), since current simplified models consider vorticity embedded on the entire plate, considering a zero vorticity assumption just behind it (no flow perturbation), a more than questionable physical behavior. From this approach, even the boundary layer could be treated as a kind of detached flow but "damped" due the fluid viscosity, which exists on the entire surface not only along the external edges! (at low AoAs; viscous regime).
Fig. 1 A hurricane is a kind of vortex. Source: https://th.bing.com...
Physically, the internal vorticity generation (rectangular plate case, exemplified for simplification purposes) must be explained as a "vorticity interconnection" due to a transport mechanism (chordwise and spanwise) through the external vorticity generated from its edges; it means the vorticity cannot be cutted off suddenly due to the continuity assumption on the (numerically discretized) shell-body; the same analogy applies for temperature distribution or structural stresses applied along the plate's edges. About this, in a recent private communication, emeritus Prof. Joseph Katz (San Diego State University; SDSU) says: "...vorticity is shear - and shear can be generated by the interaction of local streams - that was the argument used in my student dissertation way back then.", which should be a physical justification to include internal wake detachment in the understanding that conservation of mass is satisfied due to the fact that the distance between all discretized elements is considered infinitesimal (zero flux across the plate; see Fig. 2).
Fig. 2 The Full Multi-wake Vortex Lattice Method (FMVLM; Pimentel, 2020-2021)
The previous fact constitutes the main rejection by most reviewers, calling it "unjustifiable" or "nonphysical", However, Prof. Katz faced the same criticism in the 80s while conducting a thesis focused on solving parachute aerodynamics via vortex methods; he supports the detached vorticity generation on surface hypothesis, but he thinks that it must also be proved theoretically. In fact, in a recent publication called "Vorticity generation and conservation on generalised interfaces in three-dimensional flows" [1], it is shown theoretically that vorticity is generated at a vortex sheet (shell-body) due to the difference in flow velocities between its two faces, being a purely inviscid mechanism.
On the other hand, the numerical justification seems to have already been proved through a full multi-wake model [2]. From such a model's viewpoint, no internal detached wakes (or detached wakes with null circulation) means that circulation strengths between neighboring discretized elements on the surface are equal, resulting in a perfectly constant pressure distribution on the plate, which does not match what is physically expected.
Animation 1: The full Vortex Cloud Method (VCM; Lewis, 1991).
As an analogy, from a numerical point of view, in the (unsteady) Full Vortex Cloud Method (see previous animation), the vorticity is shed from each discretized element along the bidimensionally represented surface, obtaining satisfactory results for the massive detached flow condition behind a bluff-body (e.g., a bidimensional cylinder). Since the unsteady case represents a series of steady solutions obtained at a discretized time step, the extension to 3D must be done in a straightforward manner, which means by proposing a (full non-linear) model that allows to detach vorticity on the entire (tridimensional) surface, not only along some separation lines [3] (see the next animation). Any tridimensional simplified model (by only detaching external vortices, even including the leading edge vortex; LEV) could increase the Lagrangian grid distortion (in the scope of the 3D vortex methods), which most probably (to be determined yet) leads to inaccurate results (aerodynamic loads and coefficients calculation), despite its lower computational cost. It should be remembered that a "simple" case such as the flow past a quadrangular thin flat plate has not been solved yet in a precise way (by a previous research) through vortex methods, even in the pre-stall condition where turbulence effects could be neglected (the simplest condition to solve).
Animation 2: The Full Non-linear Vortex Tube-Vorton Method (FTVM; Pimentel, 2023).
By the way, a straight wakes' model (called "Only External Wakes"; OEW in [2]) shows an acceptable fit for lift but an overestimated drag along the analyzed AoA range. In the 2D case, the Kirchhoff-Rayleigh inviscid separated (perpendicular to the plate) flow shows an underestimated drag coefficient. According to "An Introduction to Fluid Dynamics" (K. Batchelor, 1967), it is solving a "cavity flow" with vacuum behind the plate, or in other words, no vorticity modeled just behind it; thus, by analogy to 3D, the OEW would also be modeling a cavity case!!! (see Fig. 3)
Fig. 3 Perpendicular flow past a flat plate. Black zone represents a cavity region.
This text was originally written in May, 2022 on the Researchgate.net portal, but it has been adapted for this format.
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