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On the ROTationality of an inviscid flow: Laplace =/ Euler

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Although the title of this blog article sounds too formal, as if it were a scientific publication, it follows the same idea as most of the previous ones, maintaining more or less a simple explanation of some topics of interest in fluid dynamics, within an acceptable extension. Therefore, I will logically explain why the rotationality remains from the incompressible Navier-Stokes equations (i-NSE) to incompressible Euler (i-Euler) ones after its simplification (from viscous fluid to inviscid flow) and how this concept leads to a better understanding of fluid motion from an alternative vorticity-based perspective. The i-NSE are a set of non-linear partial differential equations (PDEs) that allow approximating the numerical solution for a viscous fluid since they can include all the acting forces such as gravity, pressure, viscous diffusion, and advection (sometimes called convection ) terms. Such equations are mainly described in their velocity-pressure (v-p) formulation, however, they
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An 'inviscid' boundary layer! Is this a bug?! (Part 2)

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Yes, it is! This can be easily demonstrated by visualizing the velocity field directly in Fluent instead of the Results module, where no kind of boundary layer (BL) appears: Video: A visualization bug in the Results module for an inviscid simulation (version: 2024 R2). However, this bug is only present for simulations performed directly by the native inviscid model. Note that not only the lower limit for visualization is affected, but also the maximum (by almost 2 m/s), as if they were two different simulations. At this point, I will not go deeper into this subject, as trying to find the error in the error is nonsense. Even for an AoA case (3 degrees; not converged solution) such a BL evolution remains (see Fig. 4), while in Fluent it does not. I will probably contact someone who can help me understand what is happening with such results...who cares, nobody performs inviscid simulations nowadays! Fig. 4 Velocity contours for the AoA=3 deg. case; a modeled BL is also present. As I jus
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An 'inviscid' boundary layer! Is this a bug?! (Part 1)

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In my opinion, one of the worst ways to justify a physical hypothesis is to perform simulations, especially when they are subject to modeling and approximation rather than the direct solution of equations, which could also be limited by simplifications and assumptions. However, this time I will make use of a commercial tool that is accepted with enough credibility in the field of Computational Fluid Dynamics (CFD) to justify that vorticity can be generated between the interaction of a solid body and an inviscid medium , following the line of previous articles in this blog. To accomplish this task, I have tried to reduce all the steps involved to a minimum, keeping only the essential ones (e.g. I avoided using a viscous model, put the viscosity to zero, and manually set a free-slip wall)*. A two-dimensional simulation in one of the most popular CFD software (based on the finite volume method; FVM), consisting of an inviscid flow past a NACA 0006 airfoil at zero degrees of angle of attac
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Which came first: the chicken or the egg? velocity or pressure?

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The pressure field seems to be the quick answer to almost any question in aerodynamics (and fluid dynamics), from the cause of the lift "force" on an airfoil and wing tip vortices to more specific aspects such as fluid separation or the generation of vorticity on a surface. For example, the term "adverse pressure gradient" (it sounds so smart) is often used by those trying to justify the cause of fluid separation behind an aerodynamic body. According to a recent survey conducted in a LinkedIn CFD group (see Fig. 5), it is clear that two-thirds (36/53) of the participants believe that there is no direct cause-effect between velocity and pressure fields since both are coupled, while the remaining one-third (17/53, including me) mark a causal in one or the other direction (velocity causes pressure or pressure causes velocity). With such disagreement, this uncertainty must be considered an open question. Therefore, in this short blog post, I will try to justify, from b
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Let's talk about vortices, patents and business! 💲

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Once the International Searching Authority (ISA) of the United States Patent and Trademark Office (USPTO) has determined that my international patent application "Full-surface detached vorticity method and system for solving fluid dynamics" (WO/2024/136634) , under the Patent Cooperation Treaty (PCT), meets all three criteria for patentability ( novelty, inventive step, and industrial applicability ), it will be time to make an open offer to exploit such an invention (in the prosecution phase) through a Patent Licensing Agreement (PLA). Fig. 1 The generation of vorticity on surfaces is a purely inviscid mechanism (Morton, 1984, and Terrington et al., 2022). This time I will not write about the technical aspects of the patent (or how wonderful it is! ), since I did that in a previous post:  More patents, less papers (librepenzzzador.blogspot.com) . Now, I want to focus on my business proposal. Since I have some experience as an entrepreneur in engineering ( www. chuteshiut .co
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An "absurd" numerical method that actually works!

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The dynamics of a separated fluid flowing past an object is still a challenging problem in engineering, even in low-speed aerodynamics, where turbulence can be present, making its understanding and solution more difficult. For this reason, some numerical methods have been developed, most of them based on the Eulerian description of the Navier-Stokes equations, by measuring the fluid-flow variables at fixed points defined by a continuous spatial mesh, which in most cases includes several assumptions and empirically based models, to approximate (and artificially close ) the governing equations. In the first place, such methods are relatively computationally expensive, since they calculate the variables in the entire surrounding space, even far away from the object, where their measurement is of little value. Fig. 1 Mesh-based CFD simulation of a parabolic parachute canopy by κ-ω SST turbulence model (Pimentel, 2016). For several decades, the Boundary Element Method (BEM; e.g., panel meth
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10+2 common misconceptions about aerodynamics

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This list is a summary of misinterpretations that I have noticed during the last years as an aeronautical engineer, which from my perspective (and probably in the opinion of the editors and reviewers who have understood and published my research) do not allow to know the fundamental physics of real aerodynamics (and fluid dynamics). As usual in this blog, I try to be concise by explaining each of them in a single paragraph. No more blah, blah, blah, and let's get to the point. Fig. 1 Continuity exists everywhere. Sky and Water (M.C. Escher, 1938). 1. "Ideal flows perfectly attach to the surfaces". Although it is not yet possible to confirm or deny this from an experimental point of view ( the superfluid fountain is not a flow past an object experiment), the Potential Flow Theory (PFT) assumes that an ideal (i.e. incompressible, irrotational, and inviscid; i-i-i) flow will turn around, even with sharp leading edges, to maintain a perfectly attached flow pattern to the bo
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Aerodynamics is just a philosophy: an open critique

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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). The 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)
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