Before writing Chapter 4, I would like to talk a little about my background regarding the DSMC method.
About 50 years ago, my former teacher (late) T. Fujimoto was elected as the dean of the university’s engineering department, and as a result, he was no longer able to give me one-on-one guidance (reading specialized books, etc.), and instead, what I was handed was a book on the DSMC method that Bird had just published (Reference 1). I was at a loss as to how to read a book written in English, which I am not good at, by myself, but that’s just me being a sly person, and as I flipped through the book, in the appendix section at the end, I found a FORTRAN program that shows an example of calculating the method. Apparently, it was a complete program, so I’m sure there must be a section somewhere in the book that explains this program. Even after reading the first chapter, I was having trouble because there was no description of the specific calculation method, so I searched for a section that explained the program. It was in Chapter 7. Well, if I can understand Chapter 7, it seems like I can do calculations. I thought so, and although there were many parts that I did not fully understand, I was able to acquire the basic programming techniques necessary for calculations. However, the computer environment at that time was only a slightly better version of today’s program calculators. Although the program example in Bird’s book used only 1,000 molecules (the actual array was prepared for 2,000 molecules), I had a lot of trouble executing the calculations. My commentary on the DSMC method written later (Reference 3) follows Bird’s Chapter 7 and provides an explanation using a complete program for a specific example of a supersonic jet.
Nowadays, only those with a doctoral degree are hired as university instructors (excluding people who are popular in the media, etc.), but at the time, at local universities, people were encouraged to earn a doctoral degree while still working as assistants. This is common, and for that purpose it was necessary for me to improve research results. Looking back, I am grateful that I was able to receive my doctoral degree because of Bird’s book and also because of the precision vacuum gauge (Baratron diaphragm gauge) that I was able to use in my vacuum flow experiments, which created an ideal research environment for comparing the results obtained from experiments on rarefied gas (vacuum) flow with the calculation results of the DSMC method. Even more fortunately, my mentor subsequently returned to his alma mater, a core national university, and became to be in a position to confer a doctoral degree.
After getting my degree, I applied the DSMC method to various problems. At that time, the two people leading DSMC research in Japan were Professor K. Nanbu of Tohoku University and Dr. K. Koura of the National Aerospace Laboratory of Japan, and I received a lot of advice from Prof. K. Nanbu in particular. There were not many people who could perform the DSMC method, so I was able to write several papers, partly because it was a novelty. After that, a turning point came when I met Professor K. Teshima, who was conducting experiments on supersonic jets. I think I had met him at international conferences up until then, but his university was in Kyoto and I had no contact with him. Suddenly, I received a phone call from the professor and asked if I would be interested in using the DSMC method to calculate the jet structure. Until then, the resistance value of a rarefied gas flow ejected through a small aperture had been calculated using the DSMC method, but when it comes to reproducing the jet structure, I don’t know how to display the results. Then I came across the free software ‘gnuplot’. First, I performed DSMC calculations to reproduce the jet structure with a pressure ratio of 50 and an upstream pressure of 50 mmHg, but I wonder if the results are really good. When I timidly displayed the calculation results using ‘gnuplot’, the unique structure of a supersonic jet jumped out at me: at the position where the normal shock wave is formed, the density increases like one step of a staircase, the flow velocity suddenly decreases, and the temperature rapidly increases. At that moment, I was moved and thought, “I did it.” And that is the analysis handled in “2. Test calculations” of this blog (however, the calculations at that time were performed using the Bird method).
Afterwards, while focusing on this jet flow calculation, I also conducted DSMC analysis of Taylor vortices and Karman vortices in parallel, and a few years before I retired, I arrived at the analysis of turbulence that occurs at the rear and boundary of the jet (Reference 10). Until then, we had mainly treated jets with pressure ratios of about 50 or higher, but if we used smaller pressure ratios, we could reproduce the neatly arranged jet cells of underexpanded jets from nozzles that often appear in textbooks on compressible fluids. I thought it might be possible, so I performed a DSMC calculation with a pressure ratio of 4 and an upstream pressure 1atm (760mmHg). However, no matter how long I waited, only a distorted jet structure appeared, and I was at a loss for a while. If you are not getting the expected results, you must consider that there may be an error somewhere in the program. However, no matter how hard I searched, I couldn’t find any defects. In conclusion, the distorted jet shape was correct. Because the rear and boundary of the jet are constantly turbulent, the instantaneous view of the jet structure appears distorted. Therefore, it was discovered that the jet structure that we can actually see can only be obtained by averaging the instantaneous results over a long period of time. Furthermore, by observing the results from moment to moment, it is possible to reproduce the turbulence at the rear and boundary of the jet in a video.
In Section 4.2, we will provide software for “turbulence analysis of supersonic jet,” which is also posted as an example in “1. Greetings” of this blog. Please read the overview of the example provided in Chapter 1.