AIAA Paper: Fully-Parabolized Prediction of Hypersonic Sonic Boom

Abstract: Hypersonic flight-vehicles create shock and expansion waves that propagate through the atmosphere and are observed on the ground as sonic booms. We present a methodology to predict the near-field aerodynamic pressure and sonic boom signature using approximately 1% of the computational cost relative to fully-nonlinear computational fluid dynamics and state-ofthe-art sonic boom propagation solvers. Relative differences in predictions between the present method and the state-of-the-art are approximately 8%. We find that unique physics must be accounted for in the hypersonic regime, which includes viscous, non-equilibrium, and real gas effects. The method is based on the fully-parabolized Navier-Stokes equations, which are solved via marching in the propagation direction to the aerodynamic near-field. The near-field aerodynamic pressure is propagated through the atmosphere to the ground via the waveform parameter method, and is validated with NASA PCBoom and data from the NASA Sonic Boom Workshops. To illustrate the approach, three bodies are analyzed: the Sears-Haack geometry, the HIFiRE-5 hypersonic test vehicle, and a power-law waverider. Global Mach numbers range from 4.0 through 15.0. We find that the viscous stress tensor is essential for accurate hypersonic prediction. For example, viscous effects increase near-field and sonic boom overpressure by 15.7% and 8.49%, respectively for the Sears-Haack geometry. Finally, we show that the divergence of viscous versus inviscid near-field predictions are due to the hypersonic boundary layer.

King, C., Skowron, S., and Miller, S. A. E., “Toward Fully-Parabolized Prediction of Hypersonic Sonic Boom,” 2023 AIAA Aviation Forum, July, AIAA 2023-4167, 2023. DOI: 10.2514/6.2023-4167 [Link via DOI][PDF Preprint][PDF Presentation]

Reflection on Twenty Years Since the Loss of Columbia

Graduate Student Garrison S. Osborne and Steven A. E. Miller
University of Florida Department of Mechanical and Aerospace Engineering

Well before the loss of Columbia, the NASA Office of Technology Assessment wrote, “Shuttle reliability is uncertain, but has been estimated to range between 97 and 99 percent. If the Shuttle reliability is 98 percent, there would be a 50-50 chance of losing an Orbiter within 34 flights … The probability of maintaining at least three Orbiters in the Shuttle fleet declines to less than 50 percent after flight 113,” (1989, CAIB Vol. 1).

The Crew of STS-107 launched aboard the Columbia on a beautiful Florida day, January 16th, 2003, with blue sky, cool 60 deg. F air, and winds of max. 12.3 mph. At 81.7 seconds, a piece of foam protecting the left bipod strut detached due to sudden wind shear and collided with the left-wing leading edge of Columbia. The relative velocity of the foam at impact was nearly 490 mph and damaged a panel.

Foam impact and subsequent spray pattern from CAIB vol. 1. (Source: NASA)

Following ground observations, the NASA Debris Assessment Team used models to estimate damages. They concluded that only slight damage had occurred to the reinforced carbon-carbon paneling and that Columbia would only suffer localized heating during reentry. The limited damage estimates were due in part to poor image angles of the launch and denied requests for high-resolution ground images from the Department of Defense.

Astronauts Colonel Rick Husband; Lt. Colonel Michael Anderson; Commander Laurel Clark; Captain David Brown; Commander William McCool; Dr. Kalpana Chawla; and Colonel Ilan Ramon (Israeli Air Force) conducted three major tasks during the mission: SpaceHab Research Double Module, the Orbital Acceleration Research Experiment, and an Extended Duration Orbiter pallet. Each experiment was concluded and stowed successfully. It was now time for reentry.

Reentry of Columbia began at 8:44 AM, on Feb. 1, 2003. At 7,000 m/s (15,660 mph or Mach 24) and approximately 75 km altitude, heated air entered the breached panel and into the leading wing segment. Inside, flows reached an estimated 2,600 m/s (5816 mph) at 6,000 K (10,340 deg. F), causing a rapid burn-through of the left wing. This event led to the disintegration of Columbia via left wing detachment. As the scheduled landing time of 9:16 AM approached, the realization that Columbia and crew were lost became unavoidably apparent to the American public.

The president addressed the country at 2:04 PM that same day, “… The cause in which they died will continue. Mankind is led into the darkness beyond our world by the inspiration of discovery and the longing to understand. Our journey into space will go on…” One might ask, what is acceptable risk? This is a question the second author often asks his students through these case studies.

The original ideas of the NACA’s spaceplanes have not been forgotten, but commercial and government space agencies still pursue more capsule-based entry and descent. Undoubtably, the loss of Challenger and Columbia strengthened the original approach for spaceflight pioneered by the Mercury and Vostok (USSR) programs. Capsules eliminate risk of thermal protection system damage during launch, a lesson learned from the Columbia disaster.

Today, the loss of Columbia is used as a design, risk, and ethics case study in aerospace departments internationally. The choice to develop novel spacecraft or spaceplanes beyond the capsule concept will be up to the students graduating from aerospace programs today. The choice is their generations to make and will be guided by our legacy.

Acknowledgements: This article is inspired by the lives and dedication to the profession of the STS-107 Columbia Crew and people of NASA. This article is based on a ten-page term paper analysis by graduate student Mr. Garrison Osborne who recently completed Prof. Steve Miller’s Compressible Flow class.

On Seminar with Professor Said Elghobashi

It is more rare to be inspired as time goes on. On occasion, it is a great priveledge to hear a seminar by a world expert in turbulence. In this case at University of Florida, we had Professor Said Elghobashi from University of California Irvine join us for department seminar. He can be credited with creating the first k-$\epsilon$ model for particle laiden flow-fields. I believe the model was calibrated with experiments performed for jet flows using various particle mass fractions. The work is beautiful. When I heard his seminar I felt inspired – in that I was in the presence of a true scholar. I’m thankful for Professor Bala of my department for hosting the speaker, and letting meet with him one-on-one in my office.

Fontenelle on Science

We like to regard as useless what we do not know; it is a kind of revenge; and since mathematics and physics are rather generally unknown, they rather generally pass for useless. The source of their misfortune is plain; they are prickly, wild, and hard to reach ….

Such is the destiny of sciences handled by few. The usefulness of their progress is imperceptible to most people, especially if they are practiced by professions not particularly illustrious.


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, 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,

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.