Analytical Closed-Form Solution of the Navier-Stokes Equations for the Aerodynamic Near-field and Sonic Boom from Axisymmetric Bodies

I completed my Acoustical Society work and returned to the United States.

Abstract: An analytical closed-form solution is presented for the aerodynamic near-field and ground signature from an axisymmetric body with a low thickness ratio. The Navier-Stokes equations are formulated as a boundary value problem that incorporates the incoming ambient flow-field and the aerodynamic properties on the body surface. The shape of the aerodynamic body is defined as a product of generalized functions. A direct solution for the density of the aerodynamic near-field, represented as a function of both space and time, is proposed through the integration of the Navier-Stokes equations in a generalized functional form. Pressure, temperature, velocity, and Mach number are then derived in the near-field. The methodology, being fully nonlinear, surpasses the traditional F-function, impulse, and hypersonic similarity theories originally developed for near-field prediction. The presentation outlines the major steps in deriving the analytical solution and provides predictions from an aerodynamic body in the near-field, along with the associated ground signature. The methodology is focused on aerodynamic bodies operating at high-speeds, ranging from the supersonic to the hypersonic regime. This research is supported by the Defense Advanced Research Project Agency, under Grant Number W911NF-21-1-0342.

Miller, S. A. E., “Analytical Closed-Form Solution of the Navier-Stokes Equations for the Aerodynamic Near-field and Sonic Boom from Axisymmetric Bodies,” Acoustical Society of America, Sydney, Australia, Dec. 4-8, 2023.

Acknowledgements: Research was sponsored by the Defense Advanced Research Project Agency (DARPA) and the Army Research Office and was accomplished under Grant Number W911NF-21-1-0342. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Office or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein.

Remembering Stephen Jurczyk

https://everloved.com/life-of/stephen-jurczyk/obituary/

It seems just like yesterday that I was at NASA Langley working for a short time under then Director Stephen G. Jurczyk. He passed away just recently on Thanksgiving of 2023. He helped propel my career in the later stages of my time at Langley. One thing that I appreciated a lot about Stephen Jurczyk was that he came up through the organization as an engineer. Not all NASA administrators or SES are engineers nowadays. I appreciated this fact about him, because I felt that he could understand the needs of the research staff of the center. Reading books like Engineer in Charge gave me a deep appreciate of the history of NASA, and also gave me a viewpoint that the leaders of NASA should be first and foremost learned people of science. Unfortunately, this is not so much the case today. I’m hopeful that future leaders of NASA come from backgrounds in engineering especially, instead of political appointees with degrees in economics or finance.

Another important lesson is that one should try and depart love ones with kind words, because one never knows when will be the last time someone says goodbye.

Toward Exascale Computation for Turbomachinery Flows

Citation: Yuhang Fu, Weiqi Shen, Jiahuan Cui, Yao Zheng, Guangwen Yang, Zhao Liu, Jifa Zhang, Tingwei Ji, Fangfang Xie, Xiaojing Lv, Hanyue Liu, Xu Liu, Xiyang Liu, Xiaoyu Song, Guocheng Tao, Yan Yan, Paul Tucker, Steven Miller, Shirui Luo, Seid Koric, and Weimin Zheng, “Toward Exascale Computation for Turbomachinery Flows,” Gordon Bell, High Performance Computing, Networking, Storage and Analysis (SC ’23). Association for Computing Machinery, Article 4, 2023. pp. 1-12. DOI: 10.1145/3581784.3627040 [Open Access Link via DOI]

The screenshot of Q-criteria iso-surface colored with velocity magnitude, with background contoured by pressure gradient to visualize the shock wave and pressure propagation.

Abstract: A state-of-the-art large eddy simulation code has been developed to solve compressible flows in turbomachinery. The code has been engineered with a high degree of scalability, enabling it to effectively leverage the many-core architecture of the new Sunway system. A consistent performance of 115.8 DP-PFLOPs has been achieved on a high-pressure turbine cascade consisting of over 1.69 billion mesh elements and 865 billion Degree of Freedoms. By leveraging a high-order unstructured solver and its portability to large heterogeneous parallel systems, we have progressed towards solving the grand challenge problem outlined by NASA, which involves a time-dependent simulation of a complete engine, incorporating all the aerodynamic and heat transfer components.

Updates on Tsien

I was able to find additional interesting pictures for my page on Tsien. One is with Adolf Busemann, father of swept wings and German / NASA Langley Scientist. Others are interesting like his home in Beijing. I’m currently reviewing a biography, and will make a note when finisihed.

National Air and Space Museum’s Journey Toward 2025

Appearing next month in the NASA Alumni Newsletter.

Walking on the Washington, D.C. Mall is an inspiring experience for all citizens. One might be inspired by the many memories and great institutions of our American people. Nestled as one of the most visited museums of the world is the National Air and Space Museum, just southwest of our Nation’s Capital. The museum had a partial reopening on October 14, 2022, with the west wing of its building unveiling eight new and renovated galleries. However, the east wing remains closed for renovation. The next phase of the renovation, which includes the east wing, is scheduled to be completed in 2025.

I have traveled to D.C. and have seen the entirety of the previous exhibits on display. Like many in the aerospace profession, every time I go to D.C. I visit the museum. I love seeing the new exhibits. The best part of the museum is not the exhibits themselves, but watching people from all over the world who are amazed. Here, people say, ‘we did that?’ often expressing surprise at what was accomplished in the approximately last 120 years of flight.

What is new in the western third of the museum includes:

  1. Destination Moon: This exhibition features numerous icons of space history, such as the Apollo 11 command module Columbia and Neil Armstrong’s Apollo 11 spacesuit, both of which have undergone extensive conservation in recent years.
  2. Jackie Cochran’s T-38: On display is a Northrop T-38A Talon flown by aviator Jacqueline “Jackie” Cochran, who set eight world records for speed, altitude, and distance flying in 1961 with this T-38.
  3. Walking On Other Worlds: An interactive experience that provides a seven-minute “tour” of seven different celestial bodies, offering an immersive media exhibit with a nearly 360-degree screen.
  4. Nation of Speed: A collection of vehicles built for speed.
  5. Diverse Stories: A broader story of aviation and space, like Neal Loving’s red Loving WR-3 air racer, a parachute used by Georgia “Tiny” Broadwick, and airline uniforms worn by pioneering women pilots like Emily Howell Warner, Cynthia Berkeley, and Bonnie Tiburzi.

I encourage everyone to plan a D.C. visit to see the grand opening of the entire renovated museum in 2025. It is important to make advance entry reservations before you go. A limited number of same day entry reservations can be made on their website. It is entirely free.

Armstrong’s Lunar Suit (Photo – Miller).
View of the new west gallery from the second floor (Photo – Miller).

Split-Step Simulations to Assess the Effects of Atmospheric Boundary Layer Turbulence on the Dose Variability of N-Waves and Shaped Booms

My former student, Dr. Alex Carr, along with Dr. J. Lonzaga, who are both of NASA Langley Research Center, and myself published an article on the propagation of sonic boom through the turbulent atmosphere.

Abstract: The effects of atmospheric boundary layer turbulence on the loudness variability of a sonic boom N-wave and shaped boom are examined with split-step simulations. The shaped boom is representative of a design iteration of the NASA X-59 aircraft. Inhomogeneous atmospheric boundary layer turbulence is generated in the computational domain by a Fourier synthesis method. The N-wave and shaped boom are propagated through turbulent fields representing eight different convection levels measured at the NASA Kennedy Space Center and the NASA Armstrong Flight Research Center. Probability density functions of the formation of caustic regions along the propagation direction are computed from the N-wave results, and a parameter to collapse the caustic PDFs that accounts for both fluctuation intensities and length scales is proposed. Statistical results concerning loudness metric variability are presented, and the standard deviations of several metrics are shown to collapse across different convection levels of turbulence for small nondimensional propagation distances. The loudness metric distributions are observed to be well approximated by a normal distribution for a given range of propagation distances, and become increasingly skewed as distance increases. A model function for the dose variability is proposed, and the function parameters are found to be related to the convection level of the turbulence. The model for the dose variability distribution is compared to simulation data that were not used to find the regression parameters of the model. At several nondimensional propagation distances, agreement is observed between the model and the simulation data. These results indicate that the model may be suitable for providing quick estimates of noise dose variability in the primary carpet region across a wide range of atmospheric boundary layer conditions.

Carr, A. N., Lonzaga, J. B., Miller, S. A. E., “Split-Step Simulations to Assess the Effects of Atmospheric Boundary Layer Turbulence on the Dose Variability of N-Waves and Shaped Booms,” The Journal of the Acoustical Society of America, No. 571, 2024. pp. 1-28. DOI: 10.1016/j.jsv.2023.118118 [Link via DOI]

Academic Freedom at Florida CLAS

One of my colleagues informed me about a website at the University of Florida, hosted by the College of Liberal Arts and Sciences. The website provides information about academic freedom, and I’m impressed by the college’s effort to create the website. It addresses fundamental questions that people often have about academic freedom, tenure, and other significant university-related topics. The content is presented in a manner that is accessible to everyone, and it includes citations and links for further reading and research. I’ve included the link to the main content below.

  • Academic freedom is a set of norms and practices that guides faculty in the pursuit of research and teaching, as well as matters of shared governance, and as citizens to serve a democratic society for the common good.
  • Academic freedom includes the freedom to teach, discuss, question, and explore freely according to the standards of our disciplines.
  • Shared governance and tenure are important components to support academic freedom.
  • Students have a right to freedom in learning, including freedom to question and discuss material introduced in a course.

“The essentiality of freedom in the community of American universities is almost self evident. No one should underestimate the vital role in a democracy that is played by those who guide and train our youth. To impose any straitjacket upon the intellectual leaders in our colleges and universities would imperil the future of our Nation…. Scholarship cannot flourish in an atmosphere of suspicion and distrust. Teachers and students must always remain free to inquire, to study and to evaluate, to gain new maturity and understanding; other wise our civilization will stagnate and die.”

U.S. Supreme Court, Sweezy v. New Hampshire(opens in new tab), 1957

was designed and implemented over 80 years ago to act as a fundamental pillar supporting academic freedom. It allows faculty to pursue the search for knowledge and to educate students in a manner that is independent of and not beholden to any special interests. Tenured professors report their teaching, research and service activities annually and are evaluated at the department level along with all other faculty.

Source: Academic Freedom at Florida CLAS [Link – https://clas.ufl.edu/academic-freedom-and-responsibility]

Fall 2023

Who would have thought that 7 years go by so quickly at the University of Florida. This year I am teaching introduction to computational fluid dynamics. The last time I taught it was before COVID in the fall of 2020. I am working on a new design program for nozzles. I am basing it on the original method of characteristics, but integrating boundary layer theory, source plane theory for transonics, and trying to build upon some of the previous programs published by NASA.