Aeroacoustic and Aerodynamic Interaction Effects Between eVTOL Rotors

My student presented his MS thesis on the aerodynamics and aeroacoustics of rotors.

Abstract: Electric vertical take-off and landing (eVTOL) aircraft are characterized by their unconventional wing and electric rotor configurations, which involve both side-by-side and tandem rotor configurations. These configurations create unique aerodynamic and aeroacoustic flow-fields. We numerically investigate the interaction effects between rotor pairs as well as their individual and combined acoustic radiation. We examine horizontal rotor spacing, rotor tilt angles, and forward flight effects. Performance is characterized by thrust coefficient, sound pressure level (SPL) at the blade passage frequency (BPF), and overall sound pressure level (OASPL). This study is performed with a mid-fidelity aerodynamic solver, DUST, which is used to predict the aerodynamic flow-field. The tonal acoustic pressure at observer positions is predicted via the Farassat F-1A formulation of the Ffowcs-Williams and Hawkings equation utilizing the aerodynamic flow-field. The configurations studied show strong aerodynamic interaction effects in thrust, as well as out-of-plane acoustic radiation from the aft rotor. Predictions of thrust and noise are validated via experimental measurement. As rotor separation decreases, we observe that aft rotor thrust decreases and BPF SPL increases. The most forward rotor, however, is marginally impacted by the interactions.

Coelho, Gustavo Resende, “Aeroacoustic and Aerodynamic Interaction Effects Between eVTOL Rotors,” M.S. Aerospace Engineering, Thesis, May 2023. [PDF][PDF Presentation]

On Infinity by Euler

We may here deduce from it a few consequences that are extremely curious, and worthy of attention. The fraction $\frac{1}{\infty}$ represents the quotient resulting from the division of the dividend 1 by the divisor $\infty$. Now, we know, that if we divide the dividend 1 by the quotient $\frac{1}{\infty}$, which is equal to nothing, we obtain again the divisor $\infty$ : hence, we acquire a new idea of infinity ; and learn that it arises from the division of 1 by 0 ; so that we are thence authorised in saying, that 1 divided by 0 expresses a number infinitely great, or $\infty$.

Euler, Elements of Algebra

Teller on Uncertainty

… we have a radioactive substance that emits, on the average, a particle, an alpha particle, once every second on the average. Now, here I have a counter, and I close that counter, so it won’t count, except that I open it for half a second. If, in that half a second, a particle arrives, the probability is one half, then the same apparatus that I have already used can be coupled into other apparatus that will open a horrible door, which will let out some poison, which will kill the cat.

So, the quantum mechanical description is a probability distribution. After an hour, with the cat, the probability of cat being alive, one half, being dead, one half. And the correct description, I don’t know.

Now, here comes our observer, and looks. And his looking will either result in killing the cat for good, or for reviving it. And this finishes, Schrödinger …

I have no objection to any of this except that I say, I don’t need to look.

Prof. Edward Teller

On Large Language Models (AI) and Aerospace Education

Artificial intelligence (AI) is changing all aspects of our lives, much like the internet did when it became widely available to consumers in the mid-1990s. There are many discussions about how the AI revolution has affected different areas, including the workplace, art, culture, writing, and academics. Recently, the “ChatGPT: Optimizing Language Models for Dialogue” has been making significant impacts in these areas.

The development of large language models was initiated at Google, where they were working on creating algorithms for text translation (e.g. English to French). This model was later published in an academic paper, and companies like OpenAI quickly adapted the approach. For a technically minded audience, I would recommend the free article at Ars Technica (Jan, 2023, https://arstechnica.com/gadgets/2023/01/the-generative-ai-revolution-has-begun-how-did-we-get-here) to understand the algorithms. Despite initial skepticism, OpenAI is now receiving billions of dollars in investment from companies such as Microsoft.

As a professor at the University of Florida, which is at the forefront of integrating AI technology in research and teaching, I have seen firsthand the impact of AI in the classroom. The University of Florida has the world’s largest NVIDIA-based supercomputer, which has been instrumental in advancing AI research.

However, many of my colleagues at the university are concerned about the effect AI is having on students’ understanding of the material. These concerns are not limited to the University of Florida and are being discussed at universities across the United States. These discussions at University of Florida and some other regional and local universities within the United States are detailed in the New York Times (Jan, 2023, https://www.nytimes.com/2023/01/16/technology/chatgpt-artificial-intelligence-universities.html).

In my class this semester, my graduate students are required to write a ten-page term paper in the style of an AIAA Journal article. I’ve noticed improvements in their writing, but at the same time, I’ve also noticed a decline in their understanding of the material compared to previous years I’ve taught the class. I suspect that they are using a transform algorithm to assist with their writing. The question remains, how should we respond if our goal is to teach critical thinking (as discussed in my article in the previous NASA Newsletter)?

The genie of language generation and AI is out of the bottle. AI and its use will not leave the classroom, workplace, or industry, even if rules are made against it. This is a new revolution that is happening. In my class, I have instructed the students to include a new section under Acknowledgements in their term papers. They must specify exactly how they used AI, if they chose to do so, to aid in their writing. AI should not be used to write a term paper in a university, but it can help revise and guide the writing. Perhaps, this is the most ethical approach to take.

The question of whether humans can differentiate between AI-generated and human-written content remains to be seen.

Codex Arundel

While reading Leonardo da Vinci’s Codex Arundel last evening, I noticed that the Codex had less scholars examining it relative to others. The fluid dynamics of da Vinci have been extensively studied, with entire dissertations dedicated to the subject. I came across a curious drawing that exhibited turbulent flow. The text is written backward in Italian, which is his typical style. Recently, Caltech conducted gravity experiments based on da Vinci’s calculations and were able to determine the constant and coefficient of gravity with great accuracy. This is remarkable, and it makes me wonder whether it is possible to replicate or test some of da Vinci’s ideas regarding turbulent flow. This would be an interesting historical project, but acquiring funding for such a project may be a challenge within the university system. Attached is the scan I took of the particular field in the Codex. This is not the usual drawing that people show when they talk about da Vinci’s turbulence.

Additional Thoughts on Pressure

I am obsessed with pressure, particularly the internal pressure of fluids. Unlike viscosity, it is absent of frictional forces, and it is a key driving force in both human behavior and aerospace flows. Pressure is an essential component of a perfect fluid and appears on the right-hand side of the Navier-Stokes equations. Without pressure, fluid flow is boring, and people cannot move forward. Pressure can manifest internally, like a fluid, or externally, on our boundaries. However, I prefer to derive my motivation from within, like intrinsic (motivation) pressure. Think of the poor fluid parcel or person moving only to external forces that they know nothing about (see Laplace).

A simplified semi-empirical model for long-range low-frequency noise propagation in the turbulent atmosphere

My student, Dr. Tianshu Zhang, and myself recently published a modified long range acoustic propagation model that handles turbulence in the atmosphere. The abstract is

We present a semi-empirical long-range low-frequency acoustic propagation model, which accounts for atmospheric turbulence. Ostashev and Wilson’s scattering model is combined with a ray-theory based refraction model to account for turbulent scattering and refraction via a turbulent absorption coefficient. The coefficient is ascertained via integration of scattered energy. The model is formulated, calibrated, and validated via corresponding experiments conducted within the National Science Foundation Boundary Layer Wind Tunnel. The predictions of the newly proposed ‘bridging model’ match the wind tunnel experimental data with an average error of 11.9%. Example predictions are shown to quantify the effect of turbulent kinetic energy and turbulent integral length scale on long-range infrasound propagation. To demonstrate the approach, we present predictions of the propagation of noise from a tornado and a nonlinear wave.

DOI: 10.1016/j.apacoust.2023.109256 [link]

Caverns of the Wind

Silent are the caverns of the wind,
But within them, a secret lies pinned
Like Pandora's box, locked up tight
Holding within, a glimmer of light

For in these tunnels, dreams did reside
And hope for the future, they did provide
But like Pandora's box, they were lost
Their secrets stolen, at a great cost

Deformed fluid parcels, in motion they flow
Deviate from Euclidean laws, their movements aglow
Silent now, in the hidden caverns of the wind
But now there is no way in, the temple of the wind

Stolen by the East, left in their wake
Our dreams destroyed, our future at stake
But in the field, a sign remains
"Here they dreamed in the caverns of the wind"

The Tempest

In the skies above, a tempest swirls,
Its winds, a cascade of power unfurled.
Turbulence, a beast with might so true,
Its roars, a symphony in shades of blue.

The winds, the rain, the lightning’s bright gleam,
A show of strength, a testament supreme.
Turbulence, cascade, and acoustics play,
A performance, unmatched, in skies so grey.

So let us pause, and witness nature’s might,
A performance of beauty, a breathtaking sight.
For turbulence, cascade, and acoustics bring,
A reminder of the power, the majesty of spring.

After listening to Purcell’s The Tempest for years in my office.