(The description in English is shown after the Japanese sentence.)
第４章を書くにあたって，私のDSMC法に関する経歴について，少しお話します．
今から約50年前，恩師の故・藤本哲夫先生が大学の工学部長に選出され，そのため，それまで一対一で行っていた私に対する指導（専門書読み等）ができなくなって，その代わりに手渡されたのが，Birdが出版したばかりのDSMC法に関する著書（参考文献１）でした．不得意な英語の図書を一人でどうやって読んでいったらいいのか途方にくれましたが，そこは，ずる賢い私のこと，その本をペラペラめくっていくと，最後の方の付録欄に，DSMC法の計算例のFORTRANプログラムが目に入りました．どうやら，完全なプログラムらしかったので，きっと，このプログラムを解説している箇所が，本のどこかにあるに違いない．最初の章を読んでも具体的な計算法の記述がなくて困っていた私は，ともかく，そのプログラムの説明が書かれてある箇所を探しました．それは，第７章にありました．なんだ，第７章さえ理解できれば，とりあえずは計算ができそうだ．そう思った私は，十分理解できない箇所は多くあったものの，ともかく計算に必要な基礎的なプログラム技法については手に入れることができました．ただ，当時の計算機環境は，現在のプログラム電卓を少し良くした程度のもので，Birdの著書のプログラム例で使われていたたった1000個の分子（実際の配列は2000個分用意されていた）を使った計算でも，実行するには大変な思いをしました．のちに私が書いたDSMC法に関する解説（参考文献３）は，このBirdの第７章に倣って，具体例（超音速ジェット）の完全プログラムを示しながら説明を行っている．
大学の教員には，今では，博士の学位を持っている者しか採用されませんが（マスコミ等で人気のある人物は別），当時の地方大学では，助手でいる間に博士を取るというのは一般的で，そのために研究業績を上げる必要がありました．今から思うと，私が博士の学位を取れたのは，このBirdの図書と，あと，真空流れの実験で使うことができた精密真空計（バラトロン隔膜真空計）のおかげであると感謝しています．希薄気体（真空）流れの実験で得られた結果を，DSMC法の計算結果と比較するという，理想的な研究環境が整ったわけです．さらに幸運だったのは，その後，恩師が母校である中核の国立大学へ戻って，学位を授けられる立場になったということです．
学位を取った後は，いろいろな問題にDSMC法を適用しました．そのころ日本でDSMC研究を牽引していたのは，東北大学の南部健一先生と航空宇宙技術研究所の古浦勝久先生のお二人で，特に，南部健一先生からは多くの助言を頂きました．当時はまだDSMC法を行える人がそれほど多くなかったので，珍しさもあって，いくつか論文を書くことはできました．その後，転機が訪れたのは，超音速噴流の実験を行っていた手島光司先生との出会いです．それまで国際会議では会っていたと思いますが，大学は京都にあって交流がない先生でした．その先生から突然電話がかかってきて，噴流構造の計算をDSMC法でやってくれないかと言われました．それまで，小さな孔を通って噴出する希薄気体流の抵抗値などはDSMC法で計算していましたが，噴流構造の再現となると，その結果を表示する方法が分かりません．そしてたどり着いたのが，フリーソフトのgnuplotでした．最初，圧力比50，上流圧力50mmHg で噴流構造再現のDSMC計算をしましたが，はたして結果がうまく出ているか．恐る恐る計算結果をgnuplotで表示してみると，垂直衝撃波のできる位置で密度は階段１段のように増加，流速は急減，温度は急増といった，超音速噴流特有の構造が目の中に飛び込んできて，このときばかりは，我ながら「やった」と感動しました．そして，それがこのブログの「2. 試し計算」で取り扱った解析なのです（ただし，このときの計算はBird法で行っている）．
その後，この噴流計算を主軸にしながら，さらにはテイラー渦やカルマン渦のDSMC解析も並行して行って，退職の数年前に，噴流の後方や境界で生じる乱れの解析にたどり着いたのです（参考文献10）．それまでは，圧力比が50程度以上の噴流を主として取り扱っていましたが，もっと小さな圧力比で行ったら，圧縮性流体の教科書によく現れるノズルからの不足膨張噴流の整然と並んだ噴流セルが再現できるのではないかと思い，上流圧力1atm(760mmHg)，圧力比4 でDSMC計算を行ってみました．ところが結果は，待てど暮らせど，ゆがんだ噴流形状しか現れて来ず，一時は途方に暮れてしまいました．予想している結果が出て来ない場合に考えるのは，プログラムのどこかに誤りがあるのではないかということです．ところがどんなに調べても欠陥は見つかりません．結論を言えば，そのゆがんだ噴流形状こそが正しかったのです．噴流の後方や境界は絶えず乱れているため，瞬間的に眺めた噴流形状はひずんで見えてしまう．そのため，瞬間瞬間の結果を長時間平均することによってのみ，本来，我々が目にすることのできる噴流形状が得られることが分かったのでした．さらに，瞬間瞬間の結果をつなげて観察すれば，噴流の乱れの様子が動画で再現できるわけです．
第４章では，このブログの「1. ご挨拶」の中にも例として掲載している「超音速噴流の乱れ解析」のソフトウェアを 4.2 節で提供します．概要は，第1章にも書かれていますのでお読みください．
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.