On innovation and other hoaxes: a true story at university (Part 1)

This is a true story told in the first person; however, real names are omitted because my goal is not to demonize anyone; fight ideas but not people. However, this situation may soon change as all of those mentioned continue to affect my interests.

It was 2017 when I crossed the Atlantic Ocean for the third time to attend a conference series about computational fluid dynamics (CFD) software that we distribute in my country. The last two times it was to take summer courses at Moscow and Kharkiv/Kharkov aviation institutes, in 2011 (MAI) and 2014 (KhAI), during my bachelor and master programs, respectively. This last time, I took the opportunity to meet my future PhD advisor and co-advisor, whose I contacted some months ago via e-mail to ask for a chance to develop a project related to parachute aerodynamics, a field in which I have some experience, designing, manufacturing and testing small-scale ones for different applications. Everything goes fine, as I presented some CFD simulations performed, by finite volume (FVM) and lattice-Boltzmann (LBM) methods, for a round parachute canopy. We agreed to explore a different approach (Lagrangian), based on vortex methods (VM), due to a computational resource limitation, which was the main goal of the original project.

Fig. 1 Vorticity field behind a round parachute canopy (T10-C model) by Lattice-Boltzmann Method.

Then I came back to Mexico to continue my job as a CFD application engineer for almost a year, looking for the possibility of getting a scholarship for the next Ph.D. call in my country. After fulfilling a huge number of requirements (certifications, legalizations, etc.) to obtain it, I finally crossed the Atlantic for the fourth time in September 2018, ready to start the research. Having some experience living abroad, it was easy to adapt to this new small city, especially since I decided to live close to my workplace, a great advantage to focus on my research during the weekdays. Luckily, I made very good friends there, most of them from my country, the center, and South America, with whom I played futsal every Friday night, sometimes for more than 2 hours! Afterward, we would go out for dinner and a drink, and sometimes to the big city near the sea to celebrate something. It was a good time (before the pandemic)!

Fig. 2 Big city night (January 2019).

During the first two months of my research, I focused on searching the state of the art, which is why I practically wrote the introductory chapter of my dissertation. Meanwhile, I was also allowed to attend some bachelor's and master's courses as a listener, where my advisor and co-advisor taught me to review some topics related to the current research since such a PhD program does not formally include any subject, but pure research. During this time, I noticed a big difference in learning styles between both, if not countries, at least both universities I know: there, learning is based on programming and more computational resources (a more abstract way), while in my country it is based on hands-on (physical practices* and hand-solving; more similar to my experience in Russia and Ukraine). Personally, I think that ideally both ways are not exclusive, and a mix of both is desirable, but in a defined order: first physical understanding and practical experience; then theory and computational resources.

Video 1 Wind tunnel test for a parabolic parachute canopy (scale 1:10) during my bachelor's research (National Polytechnic Institute, 2012).

After the first year, I developed two two-dimensional codes based on the Discrete Vortex Method (DVM), which seems to be the most natural way to perform more complex simulations, such as three-dimensional ones. The first consisted of solving the steady-state case for 'inviscid flow' past an airfoil, represented by a vortex sheet, through a vorticity distribution. The second code was the natural extension of such a steady DVM to the unsteady case: the UDVM. During this development, I avoided using functions and libraries to solve the system of equations. My goal was to explicitly understand how such a complete numerical method works, including the implementation of an algorithm to solve the linear system of equations using, for instance, the Gauss-Jordan technique. I personally think that this approach is desirable for beginners in programming like me then, taking every opportunity to explore how algorithms work in detail; in the end, such a code is no more than a simplified method (under thin airfoil theory concepts) for solving an idealized case: flow past an oscillating airfoil. The challenge at this stage was to implement a vortex merging enhancement (based on a bin-search technique), which is useful for reducing the computational effort due to the calculation of the induced velocity between the discrete vortices (saving up to two-thirds of the total computational time; see video 2). In this case, such an algorithm was provided by my advisor and adapted by me to the current code.  

Video 2. The Unsteady Discrete Vortex Method (based on Low-Speed Aerodynamics).

The next step in this research was to implement the Full Vortex Cloud Method (FVCM), which consists of detaching the vorticity from the entire surface, not only from the trailing edge as in the case of the UDVM. Fortunately, I did not start from scratch, since previous research (within the university) with at least a corresponding code was available. However, such code was written in a relatively slow programming language, but I ported it to a more efficient one originally developed for High-Performance Computing (HPC), a language more than half a century old: Fortran (the same used for the previous codes). Furthermore, I included a missing function that was not present in the previous implementations, useful for accurately accounting for the induced velocity from panels to near-wall vortices by using sub-panels, which greatly improves (smooths) the previous results. However, the main contribution was the implementation of the vortex merging enhancement, which allows to running of longer simulations at high Reynolds numbers (e.g. Re=730,000) with reasonable computational resources at a fraction of the original cost.

Video 3. The Full Vortex Cloud Method with vortex merging enhancement (based on Prof. R.I. Lewis' book).

To be continued...

* By the way, in Mexico we have a supersonic wind tunnel (up to 2.5 Mach) with Schlieren visualization for bachelor's practices!

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