Standard k-Epsilon Model

In the last few years a number of models of turbulent heat and momentum transport have been developed in which the effective transport coefficients are related to local values of certain turbulent correlations; these correlations are computed simultaneously with the mean field variables. Models of this kind achieve significantly greater breadth of applicability than do simpler approaches based on mean-flow quantities alone. One of the more successful of these newer approaches is the energy-dissipation model developed by Jones and Launder. Its originators applied it to the calculation of numerous boundary layer flows with severe streamwise pressure gradient or surface mass transfer. No applications have been reported, however, of its use to predict swirling flows, an omission that the present note remedies. The flow considered (that generated by a rotating disc in a quiescent atmosphere) produces very high gradients of swirl velocity in the vicinity of the disc which in turn brings to prominence terms in the kinetic energy and dissipation equations that have formerly been absent or of only small importance. This application thus provides a test of the generality of the model for an important class of fluid flows.

The Standard k-epsilon model, Launder and Sharma, 1974.

Experiments in a Large-Boundary Layer Wind Tunnel: Propagation of Noise through the Turbulent Boundary Layer

My Group recently published a paper on a multiyear experiment campaign. We used the National Science Foundation Boundary Layer Wind Tunnel and sent acoustic waves through the boundary layer. We examined how turbulent structures altered the waveforms. The purpose is to create a high quality database available to the community to understand acoustic-turbulent interactions.

Zhang, T., Ojeda-Tuz, M. A., Gurley, K. R., and Miller, S. A. E., “Experiments in a Large-Boundary Layer Wind Tunnel: Propagation of Noise through the Turbulent Boundary Layer,” ASCE Journal of Structural Engineering, Vol. 148, No. 5, 2022. pp. 1-14. DOI: 10.1061/(ASCE)ST.1943-541X.0003275 [Link via DOI][PDF]

Paul Richard Heinrich Blasius

At Easter 1902 I had sat my final college examination, and was now studying mathematics. This was not simple for me: Although one can see what follows from certain algebraic manipulations, why would this be done? “By mathematics, you are convicted, instead of convinced”, according to the philosopher Schopenhauer. After some time, I realized that, for me, mathematics was a collection of tricks. While my friends were busy with ions, with electrons, the Zeeman-effect and more, I stayed with the basics, with questions relating to philosophy and psychology, and remained unsatisfied. Accordingly, I changed to astronomy, but this was too subtle, and I continued with physics finally. I was asked to work on inhomogeneous waves generated due to total reflection in a second medium, as a Ph.D. topic. This was of interest to Prof. Voight but not to me! I continued with Prof. Prandtl and submitted a Ph.D. thesis on boundary layer flow in July 1907. I also added two or three cases for his theory. He told me after the exam that I hadn’t known all that he wanted. But he said that what I knew I had understood, and I was satisfied.

I stayed for a short period with Prandtl as an auxiliary assistant, and then moved to (Preussische) Versuchsanstalt für Wasserbau und Schiffbau at Berlin, where I worked on fluid friction in pipe flow, among other topics. In addition, I also submitted scientific works, such as on flow around wings and turbine blades using complex variables. All this was unprofitable, without success. I tried to continue working in turbulence, again without success, and finally told myself: “You are not a scientific.” Also, I admit that I did not have enough interest in the subject, but more for the approach. Prandtl was slightly disappointed because I was not interested in his wind tunnel, nor did I drive to the Rhön valley to glide model airplanes. I was asked why I did not look for a position as a professor. Evidently, you dream of this position as a student, and maybe I would have made it. At Aachen, I once achieved second ranking. My friend Barkhausen wanted to propose me for Dresden university, but I answered: “Let it be, I would disappoint you anyway!” Also, I was no more interested in science than before, and I do not regret it to this day. I feel my place is here at the engineering college. In any case, when you decide not to strive for the top position where you could have problems, choose the second position, where you can really add to progress. Therefore: “Blasius, who once worked in science, has been dead for a long time.” It was good having once been a physicist, but now I am a teacher, not corresponding to a scale model of practice but to its foundation.

At Easter 1912, I started at Hamburg engineering college. After the war, which I survived without harm, I started with my books. I wanted to present a heuristic approach by accounting for the three impressions of the human mind: perception of ideas, elaboration of methods, and description of phenomena. Learning, working and order are thus the three essences of the mind. From 1920 to 1930, I mainly collected examples to present the basics of a problem. Finally, the heat transfer book appeared in 1931 (Blasius 1931), and then three booklets on mechanics by 1935 . At the age of almost 78 years, Blasius (1961) published a work on lubrication.

I distinguish between exact knowledge and learning. As a good teacher, you should allow students to use their notes during exams, and ask questions on their integral knowledge. My concern is specialization, and – forgive me – the present trend in increasing lectures in other branches enhances this. Finally, consider our students: Precious people often interested in knowledge. Certainly, they would also like to earn money, but by working. They are willing to learn; care for them, for they trust you and are devoted to advance! Why at the end I am still here? Certainly not because of interest in the subject or because of money. The only reason I stayed for so long is because of my affection for youth, whom I should like to help in solving problems, and to assist into a profession. Here I am, and here I stay, until I am thrown out!

Blasius written in a letter in 1962 through correspondence of his wife Mrs. Elfriede Blasius.

Some pictures of Blasius

  • Blasius portrait.
  • Blasius playing chess.
  • In the lecture hall
  • Lecturing

Sankar’s Helicopter Aerodynamics

I’m really impressed with Professor Sankar’s website on fundamentals of aerodynamics of helicopters. It is often said in the aerospace community that if you understand the aerodynamics of helicopters then you can understand anything. It is really challenging! He has also posted a number of interesting items on aeroacoustics of rotorcraft. I have learned a lot from browsing his site. See https://sankar.gatech.edu/?q=rotoraero