On innovation and other hoaxes: aiming to the details (Part 2)

Go to the first part: On innovation and other hoaxes: a true story at university (Part 1)

After the development, verification, and validation (v&v) of the last code for massive flow separation, the time has come to explore a three-dimensional low-order panel method. The vortex lattice method (VLM) was chosen because of its simplicity in implementation compared to more complex potential-based schemes, such as the doublet lattice method (DLM). In addition, the VLM has historically provided good agreement with the expected results at the lowest computational cost, although it only allows calculations for zero-thickness bodies or plates, similar to a fabric (e.g., a parachute canopy). Originally, the standard (or single wake) VLM provides a linear solution (for the lift coefficient), since it allows flow separation only along the trailing edge. Historically, such a method has been applied from medium-high (AR>4) to high aspect ratio configurations, such as wings or airplanes, where the aerodynamic effects of the lateral, or wingtip, wakes can be considered negligible.

Fig. 1 The Vortex Lattice Method for solving stability derivatives of a Boeing 737-800. 

Source: Back to basics: Vortex lattice method for stability derivative estimation | aeroscience

Unfortunately, the COVID-19 pandemic arrived in mid-March 2020 and almost all activities (except the essential), including academic ones, were closed. In Spain, as in most of the European countries, this situation was taken very seriously and confined us for about 3 months. Certainly, this situation was too difficult to overcome, especially because of my self-imposed routine for frequent exercise, by jogging, going to the gym, and of course, playing baseball and futsal with friends. I remember going to the farthest ATM to get my money every Saturday afternoon to have an excuse to go out on the street, but always wearing the damn mask...Ah, those were bad times (whisper). During this time, besides watching old western movies, I improved the data post-processing (smoothing of pressures, etc.) of the last two-dimensional code and the implementation, v&v of the steady VLM (compared to Tornado and XFLR5 software), which was a relatively easy task. More interesting for me was to do a paragliding course as soon as the pandemic situation eased!

Video: Paragliding in Ager, Spain (August, 2020).

During the new normal, I asked the university to come back to the office, but I was the only one there. I really liked this situation, because I took a nap every day on a mat next to my desk, which helped to keep calm when things were confusing with coding. At that time I implemented the unsteady VLM (UVLM), based on the well-known book "Low-Speed Aerodynamics" by Professors J. Katz and A. Plotkin. Then I contacted some researchers by e-mail to ask for their verifications, since some small discrepancies appear. Thus, I discovered the finer details of such a method, such as the influence of the parameters on the results, or the lack of wake symmetry as the simulation evolves in time, due to rounding errors; as in previous cases, I always focused on numerical accuracy rather than performance. In addition to the original method, I implemented the vortex stretching calculation and a vortex core model to obtain the most accurate results possible. At this point, if you ask if I have better things to do with my life, yes, I got a girlfriend during that time! 😁

Animation: The Unsteady Vortex Lattice Method for a high AR swept-back flat plate.

The addition of lateral wakes to the steady and unsteady VLM has been studied and published in the 70's and 80's to solve low aspect ratio (LAR) configurations (i.e., AR=1), giving good, if not excellent, agreement for flat plates with experimental data, at least in the low angle of attack (AoA) range. Such additional wakes give the VLM its nonlinear behavior (in terms of the lift component) by adding terms to the influence coefficient matrix or, alternatively, to the right-hand side in the unsteady case, while the flow solution remains, as usual, from a typical linear system of equations. But how does a supposedly inviscid flow solution give perfect agreement with viscous (real) data? (see Fig. 2) Perhaps such a solution is not inviscid at all? If lift is a purely inviscid phenomenon, then according to these results a fundamental question of fluid dynamics has been solved since several decades and nobody noticed! Thus, where is the role of viscosity in lift? Similar questions went through my head while I was implementing, verifying and validating the addition of wing tip wakes to LAR configurations.

Fig. 2 Numerical and visual results for a wake relaxation calculation up to two iterations.

As is always the case in research, there is a lot of work done over several weeks or even months that has never been published, although the results could be of interest, at least to confirm something that was already known, but without further details. This was the case with the wake relaxation calculation for a steady-state VLM for LAR configurations. This task was performed in the context of knowing how wake deformation affects aerodynamic coefficients, as an intermediate step between barely and massively detached flow conditions. From such results it is clear that such wake deformation practically does not affect the aerodynamic coefficients in the low AoA range, thus such results show that the straight wake assumption is a good approximation for solving LAR configurations, at least in this range (see Fig. 2). Further precise analysis between the steady VLM (straight wakes) and UVLM (rolled-up wakes) shows an interesting and convenient fact: the rolled-up case replicates the results obtained by the straight wakes case over the entire AoA range! This could be an interesting topic to explore and uncover, unfortunately it was beyond the scope of my research during this part of the project. Finally, the lateral wakes were implemented in the UVLM code (see Fig. 3). Needless to say, all the activities described were suggested by my advisor, except paragliding!

Fig. 3 Developed rolled-up wake for the Unsteady Vortex Lattice Method (with lateral wakes) for an AR=4 flat plate at an angle of attack.

Go to the third part: On innovation and other hoaxes: first disagreements (Part 3)