Aerodynamics is just a philosophy

In the context of high Reynolds number aerodynamics, what does it mean to have a "laminar boundary layer" (BL)? How long is it on a wing under normal operating conditions? According to Reynolds number calculations, at best it can be no longer than a few centimeters from the leading edge! (see Fig. 1). So can we talk about a laminar BL in both the physical transition and turbulent regimes, including their instabilities and vortices? What about so-called "laminar airfoils"? Perhaps most of the aerodynamicists (experimentalists, theorists and computationalists) are abusing on oversimplifying things to make everything fit with their own interpretations?

Fig. 1 Surface oil flow visualization of a wing upper surface (AR=3, AoA=0 deg., Re=1E6). Fluid separation region (transition to turbulent BL; ignore the red rectangle) is clearly marked around the top of the wing. Source: "Variable Camber Compliant Wing-Wind Tunnel Testing", C.R. Marks et al. (2015).

Since aerodynamics was originally conceived by pure observation and trial-and-error approaches, some experimentalists hold that such a field will never be replicated by computational simulations or even described by theories, as if the understanding of aerodynamics per se is divine or sacred (in the end, it is nature!). Perhaps they are not wrong at all, since some fundamental aspects in this field, such as the mechanism of lift generation and the role of viscosity in it, have not been revealed by any theory or computational simulation (not even by DNS*), while experimentalists have been designing the first flying devices based on aerodynamic concepts for more than a century, initially based only in experimental tests. However, such a negative way of thinking is a great burden for the understanding of such complex phenomena, since this perspective closes two of the three ways of understanding from a more integral point of view, relegating aerodynamics to a purely empirical knowledge. Moreover, this group seems to forget that by avoiding the solution of aerodynamics from other perspectives, its inherent impracticality, in terms of time and monetary cost to perform physical tests under difficult physical conditions, ceases to be the panacea that it is supposed to be.

Fig. 2 Preliminary inflation test for a semi-flexible wing prototype (designer: C. Pimentel; National Polytechnic Institute, 2013).

A physical phenomenon, or at least a simplified version of it, can be explained and understood through a theoretical description; this is the reason why mathematics has been developed. Undoubtedly, the work of theoreticians cannot be disparaged in any way, since it is the steeping stone on which numerical, analytical and semi-empirical developments are based; without scientifically based theories (and hypotheses), our knowledge hangs in the balance. At this point, arises a crucial aspect: there should be an equilibrium between theory and practical application, especially in the field of engineering, which is focused on solving problems in a relatively efficient way. But how to choose the right amount of simplifications or assumptions in order to obtain a well-justified solution? It is true that oversimplified models need to be applied only under certain specific conditions or to obtain approximate values, which are sometimes sufficient to have a better understanding of the problem to be solved. This is where experience, not only theoretical or numerical, but above all, physical (i.e., hands-on), is crucial to making the right decisions, especially in a practical field like aerodynamics (and fluid dynamics in general). Furthermore, we must remember that all theories are subject to revision as new well-founded hypotheses or ideas arise, especially if the new results are even slightly different from the previous ones. At this point, it is crucial to focus on understanding the fundamentals first in order to construct more complete theories and models; if the foundation is strong, whatever is built upon it will hold.

Fig. 3 General (left) and simplified (right) parachute dynamics scheme. The 2D case is already by itself a simplification of a 3D case (C. Pimentel, 2016).**

Now it is time to write about computationalists. Within this group, two subgroups can be defined: users and developers. The academic users are focused on obtaining, in the best case, a valuable result that will allow them to make "better decisions" (a very trilled phrase) during the design phase, which may be too limited depending on the computational resources available; in the worst case, it is only to obtain a good image or animation for a presentation, full of pretty colors, regardless of whether the solution shows something close to reality, enough for paper publications (e.g., to get a degree) or hundreds of likes in social media (for fun it is OK!). This is not bad, after all, in the end it counts as experience in several tasks to be performed in CFD simulations (modeling of geometries, meshing, selection of parameters and physical models, etc.), which undoubtedly gives valuable knowledge to know all the processes involved, but unfortunately limited for a serious contribution.

On the other hand, industrial users, usually called Computational Aided Engineering (CAE) engineers specialized in CFD, are more involved in following manuals to set the correct options and parameters (e.g., turbulence model coefficients) along the entire simulation process, regardless that they may not have any physical hands-on experience for the particular device or phenomenon they intend to simulate. Even during their hiring process, most CAE-based companies look for knowledge of a particular software rather than understanding of the physics and theory involved, proven skills, or even experience in solving real-world problems. They seem to want people who just follow instructions like machines do (some of them are only hired to perform meshes!); in the near future, such a profile seems to be easily replaceable...Ultimately, CAE engineers are limited by current simulation technology; however, programming skills (and open source codes) could alleviate this situation somewhat.

Fig. 4 Transonic wing fluid simulation (with limited computational resources; C. Pimentel and L. Jiménez, 2018).

Now, about developers...I consider myself to be one of them, especially in the last few years, after having written some (more or less) complex and extended codes in the context of meshless fluid dynamics. Undoubtedly, most of the brilliant minds I have met work in this area, as it combines logical thinking, problem solving (at least in the virtual environment), patience and other skills that only perfectionists (in the good sense of the word) have. However, working in such a rigid language environment is probably the cause that changes (in the long run) their way of thinking about considering alternative forms of solving problems in real life, which inherently reduces creativity and the ability to see problems from a different perspective, becoming the most closed minds I have known: "Things are this way because they have always been this way". This is a common behavior I have observed over the years, even among developers who do research, not just implement code. The big problem I see is that most of the work they do only increases the complexity of the solutions (and, in most cases computational resources), implementing schemes, methods and techniques that are more in line with the tasks of a software developer than a computational fluid dynamics engineer. By the way, before we can be computational (or even aerodynamicist), we must ideally first be fluid dynamicists.

It seems to me that at this point the north is lost, and even artificial intelligence is not solving the underlying problem at this stage (data-driven solutions depend on the quality of that data; the physics must first be solved accurately). A clear example with current conventional CFD methods is that if we compare the results obtained for the same two-dimensional airfoil (under the same operating conditions) using different CFD solutions (e.g., URANS vs. DES) and even turbulence models within the same method, we will always get quite different results, no matter which software is used. I mean, we have not even solved the simplest two-dimensional simulations yet, and the tendency is to make things more complicated. On the other hand, direct numerical simulations (DNS) are still impractical, and the solution seems to increase computational resources to infinity. At this point, even those who are trying to sell the idea that CFD is the solution to everything, know that the raw truth is that it is still an unfinished, untested tool. Note, however, that I am not denying the relevance of CFD (and CAE in general) for industrial applications, even if it is not the perfect tool; some valuable information can be obtained and it helps to solve practical problems.

Fig. 5 Nice view! Detailed programming and analyzing vorticity-based methods (Belgrade, summer 2022).

To close this criticism, I will not talk about what a new wonderful method is the solution for solving everything in aerodynamics and CFD, but about an alternative roadmap that gives more weight to understanding fundamentals first (and boring theories), rather than focusing on efficient code implementations (I am sure that a generic software developer without fluid dynamics or aeronautics background can do almost the same task), leaving aside unjustified simplifications or assumptions, usually applied prematurely and arbitrarily. Probably avoiding thinking only in terms of continuum mechanics (i.e., at the macroscale level) will help in this task; breaking down barriers between physicists and engineers might help in solving the problem (understanding at the mesoscale level could be a good start). Nevertheless, the guiding principle must always be experimental fluid dynamics, i.e. all theories and computational implementations must be subject to reproduce what is measured and observed, not the other way around. This sounds logical, but in current theoretical and computational aerodynamics based on Potential Flow Theory (PFT), it seems out of reality and has been a huge burden to understand aerodynamics because it only works for specific operating conditions (i.e., under perfectly attached flow assumption) and cannot be easily extended to a complex one just by applying some "corrections". On the other hand, solutions based on the Navier-Stokes equations should ideally be independent of semi-empirical models (boundary layer, turbulence, etc.), avoiding the use of external parameters that undoubtedly modify not only the qualitative but also the quantitative results. By the way, looking for other ways to discretize such equations might be a good alternative (e.g., Lagrangian instead of Eulerian description). Perhaps it is not yet possible to obtain a purely numerical solution, at least for the simplest incompressible case (a damned flat plate at the low AoA range!) in aerodynamics? Have we already developed the mathematics to solve/approximate it or not? In the meantime, aerodynamics is still a philosophy and simplified explanations (e.g., for undergraduate students and pilots) must be left aside in the context of a more formal understanding.

Fig. 6 The Full Non-linear Vortex Tube-Vorton Method (C. Pimentel, 2023; Advances in Aerodynamics).

This was an open criticism (not personal: fight ideas, not people), based on my own short experience on what I have seen, heard and felt (about 10 years in engineering), and it should be taken with an open mind. In the end, I am not writing anything that some experts in the field have not said before.

*There is not yet a version of mesh-based direct numerical simulation (DNS) for "solving" inviscid flows (Euler equations). Q:"Who cares about inviscid flows?" A:The fundamentals are there!

**This analysis was performed for a small-perturbation assumption (oscillation angles are exaggerated for better visualization; some forces are hidden to avoid saturation).

"I do not care if thousands disagree with me; anyway, I do not expect anything from them. It is enough to convince the right person".