On innovation and other hoaxes: the leading edge lifts! (Part 4)
Go to the first part: On innovation and other hoaxes: a true story at university (Part 1)
Most real aerodynamicists, even computationalists, know the typical pressure coefficient (cp) distribution for an airfoil (with positive AoA) in the pre-stall region, where cp tends to increase from the suction side (top) towards the leading edge (LE), typically with a negative peak value. On the other hand, at the frontal stagnation point, such a value must be equal to 1 (for the incompressible case), which no longer coincides with the geometric frontal point of the airfoil, since it is naturally shifted backwards due to its inclination. Obviously, a zero value of cp must be located in such a curved region, i.e. close to the geometric frontal point (see Fig. 1). But what happens if instead of an airfoil we use an "infinitely thin" flat plate? Yes, in the limit of thickness equal to zero, cp must be equal to the difference between the upper and lower side cp's, which have a different value since they depend on the inclination of the plate, so such a LE will contribute to the lift! For those familiar with the Vortex Lattice Method (VLM), this can be easily demonstrated using the Kutta-Zhukovsky (KJ) force calculation: the LE of the plate (through discretized segments) contributes to obtaining the expected numerical results. If we avoid considering such bounded vortex filaments, the lift decreases abruptly, by about half (I vaguely remember that it was exactly half...). In summary, the LE contributes to the lift from a VLM and Potential Flow Theory (PFT) perspective.
The previous explanation of the LE's contribution to the lift was another cause for discussion with my advisor. If I had been him, I probably would have asked for a demonstration instead of doubting the numerical results. After that, I realized that he did not have enough experience with KJ calculations...anyway. But what is the physical significance of the contribution of the plate's LE to the lift? Since the VLM models an attached flow condition due to the discretized bounded circulation at the surface, the LE is not an exception. In fact, the standard VLM models for a rounded LE since it does not allow flow separation along such an edge. On the other hand, a sharp LE should allow flow separation. But what characteristic should such an LE wake have? To answer this question, the lifting surface problem must be explained by its simpler version: a single discretized element (see Fig. 2).
For a single element at AoA, the trailing and lateral wakes are separated as usual (with a positive rotation). If we also add a positive LE wake, no lift can be obtained by the KJ calculation, since no edge contributes to the force (all vortex segment circulations are zero). In such a case, the single element is stalled, regardless of its AoA. The other possibility is to invert its sign (with a negative rotation). This is not an arbitrary choice, but it is a well-justified operation: in general, the circulation or intensity of a detached wake between two discretized bounded elements along the chordwise direction is the difference between the upstream and the downstream circulation (see Fig. 3). If the upstream circulation is zero (because it does not exist), as in the case of an LE bounded element, such a detached wake, which is actually the LE wake, must be inverted to maintain the original relationship. This simple operation gives the VLM the ability to numerically account for an LE wake that remains experimentally attached to the plate within the pre-stall condition.
When I tried to explain the justification for inverting the LE wake sign, my research and results were treated as absurd, especially by my co-advisor, who I personally consider the instigator for my work not being considered for review, although he is not an aerodynamicist but a structurist. Furthermore, he said that he had never seen an internal detached wake model before, for such a reason he questioned the results shown and suggested that they had been manipulated. On the other hand, my advisor, who originally proposed the multiwake model, was practically silent during this presentation. According to his curriculum vitae, the latter should have more experience in practical aerodynamics, but probably only with streamlined configurations like wings. Unfortunately, smooth flow and their modeling are relatively simple to understand compared to separated flow concepts and cannot be applied easily, or in simpler words, a separated flow numerical model cannot be constructed by assumptions and simplifications. At this point, and after many months of development, I presented the numerical results for different configurations, ready to perform simulations for sideslip cases, but both refused to review my research because, according to them, "it lacked theoretical support", and even suggested stop wasting more time and add more equations to make it look like a PhD thesis...😅
As an alternative to continue the research, they both agreed to propose to remove all internal detached wakes to the multiwake model, or in other words, to go back 8 months in time. Of course, I do not accept to continue under these conditions, since such a simplified scheme models a cavity case, sometimes called Kirchhoff-Rayleigh flow, which has a theoretically underestimated drag coefficient (see Fig. 5). As far as I know, no parachute canopy operates under this flow condition (circulation, so vorticity remains attached to the canopy except at the outer edges). Hardly, someone who has no practical experience, especially with separated fluids, could understand that continuity of fluid variables must exist everywhere, and vorticity is not an exception. Simplifications cannot be made before developing the most general model possible, under the idea that it should be solved quickly, for "engineering purposes"; aerodynamics must be respected first. In addition, such a simplified model will increase or decrease the spacing between vortex elements (Lagrangian grid distortion), a negative condition to be avoided in particle-based methods. Maybe I should manipulate the final results by applying some semi-empirical corrections, or worse, multiplying by some arbitrary factor to match the expected results? Semi-empirical corrections, or more politely called turbulence models, destroy the main advantage of vorticity-based methods: the direct solution without any modeling for flow separation, at least theoretically so far.
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