舶用ディーゼル機関における水エマルジョン燃料油滴の

本論文
Journal of National Fisheries University　64　（2）
86 － 102（2016）
舶用ディーゼル機関における水混合エマルジョン燃料
油滴の燃焼過程の基礎モデル
石田武志1†
Cellular Automata Model to Calculate Combustion Process of
Water Emulsified Fuel Used with Marine Diesel Engine
Takeshi Ishida1
Abstract：Previous models concerning diesel spray are impossible to calculate micro-explosion
process and combustion process of water emulsified fuel. My study constructed mesoscale discrete
particle models to simulate complex motion of emulsified fuel particles. Two models were constructed;
micro-explosion process model and combustion process model of fuel droplet. These models based on
cellular automata model which has a feature of both time and space discretization. Micro-explosion
model simulates the microparticulated motion of vapor explosion. Furthermore combustion model can
trace the combustion process of each microparticulated fuel droplet. My results show that emulsified
fuel droplets burned rapidly rather than normal fuel droplets. Although these are simple models,
it is thought that my models will be the base model to consider water emulsified fuel combustion
theoretically.
Key words：Diesel engines, Diesel spray model, Water emulsified fuel, Cellular automata model,
Micro-explosion
緒　言
式脱硝装置（SCR ：Selective Catalytic Reduction）
，排気再
循環（EGR：Exhaust Gas Recirculation）システム，水エマ
船舶からの排気ガス規制は，IMO（国際海事機関）にお
ルジョン燃料（Water emulsified fuel）などが検討されてい
いて 1990 年代から議論が進められ，船舶からの海洋汚染
る。この中でも，水エマルジョン燃料は，NOx の低減に
な ど を 防 止 す る 国 際 条 約 で あ る「 海 洋 汚 染 防 止 条 約
加えて，粒子状物質（PM）の低減，燃費改善効果も得られ，
（MARPOL 条約）」に附属書Ⅵ〔大気汚染防止〕を追加す
対策コストの面からも既存船において有望な対策と考えら
る形で１次規制が設定された。窒素酸化物（NOx）排出量
れている。
の１次規制は 2005 年 5 月 19 日に発効され，その後 2008
水エマルジョン燃料は，燃料油に水と界面活性剤（界面
年 10 月に採択された改正 MARPOL 条約附属書Ⅵに２次
活性剤を使用しない場合もある）を添加し，機械的に攪拌
規制が盛り込まれた。さらに NOx 規制は 2016 年から 3 次
して燃料中に微細粒子化した水を分散させたものである。
規制が適用される予定であり，舶用ディーゼル機関からの
水エマルジョン燃料には，油中に微小な水粒子が分布して
さらなる NOx 低減が求められている状況である。　いる「微小水粒型（water in oil; W/O 型）」と，水中に微小
これらの規制に対応する技術としては，選択触媒還元方
な油粒子が分布している「微小油粒型（oil in water; O/W
1
水産大学校海洋機械工学科（Department of Ocean Mechanical Engineering, National Fisheries University）
別刷り請求先（corresponding author）
：ishida@fish-u.ac.jp
†
87
石田武志
型）
」がある。実用のエマルジョン燃料では，水の添加割
油滴モデル（Discrete Droplet Model）によりモデル化して
合が 20 ～ 30％のものが多く，この場合，油分が多いため
いる。噴霧内に存在する油滴数は 1014 ～ 1016 個のオーダー
微小水粒（W/O）型となる。
といわれているが，この全ての粒子の運動を解くことは計
水エマルジョン燃料を舶用エンジンに適用した事例は数
算機の性能上困難であり，一般に 1,000 ～ 10,000 個程度の
多く報告
1）など
されている。これらの既往研究において，
パーセルに分割し，個々のパーセルの動きを解いていく。
水エマルジョン燃料の舶用ディーゼル機関への適用効果と
また，油滴は拡散する過程で分裂し微細化していく。この
して，水の添加割合を増加させると直線的に NOx や PM
過程のモデル化は，TAB モデル 7) や，WAVE モデル 9),10)
が低減することが多く報告されている。例えば文献 1) では，
が標準的に用いられている。TAB モデルは，噴孔径と同
50％の水添加で 30％の NOx 低減が示されている。また燃
じサイズの液滴を噴霧し，空気抵抗による液滴のねじれと
料消費率に関しても，水の混合により燃費の改善が報告さ
振動をばね系として計算し，表面張力との関係により液滴
1）
れており，改善効果は，0 ～ 1％程度である 。また，文
2)
を分裂させるものである。WAVE モデルは，噴孔からシリ
献 では 1 ～ 4％程度の燃費改善が報告されている。
ンダ内に入った燃料油の液柱表面に発生する波動によっ
このようなエマルジョン燃料によって NOx，PM，燃料
て，表面の不安定性を求め，液柱の分裂時間と分裂後の粒
消費率が改善される機構は，一般に以下のように考えられ
子径を求めるものである。さらに燃焼反応においては，
ている。微小水粒（W/O）型の水エマルジョン燃料中にお
Schreiber らの５段階準総括反応モデル 11) などの燃焼モデ
いては，燃料の油滴中に数～数十 µ ｍ程度の粒子化された
ルを用いて，計算格子ごとに各種成分の濃度変化を反応速
水が存在するという形態となっている
3）など
。これをディー
度モデルから計算し，生成物などの見積もりが行われる。
ゼル機関において噴霧燃焼させた場合，シリンダ内に噴霧
ススの形成には，スス形成モデルがいくつか提案されてい
された燃料油滴中に水粒子が含まれた状態になる。シリン
る。以上のようなディーゼル噴霧・燃焼過程のモデル式に
ダ内の高温・高圧環境下において，まず水粒子が爆発的に
は，多くの未知の係数が含まれ，様々な実験によりパラメー
蒸発・膨張し（ミクロ爆発過程），その周囲の燃料油を飛
タが調整され，実験データとの整合性が高くなってきてお
散せて，燃料を微粒化させることにより，油粒子がすばや
り，エンジン開発の現場でも用いられるようになってきて
く蒸発し，可燃性の混合空気が形成され，燃焼効率が高く
いる。　なり，燃料消費率が改善される。同時にエマルジョン燃料
一方で，エマルジョン燃料を用いた場合の噴霧・燃焼過
中の水分が蒸発するため燃焼温度が低く保たれるため，
程に対しては以上で述べたモデルをそのまま用いることが
NOx の生成が抑制される。また燃焼効率が高くなること
できず，これらの計算を行った報告もみられない。エマル
により，未燃分の燃料が減り，PM が減少すると考えられ
ジョン燃料のミクロ爆発過程をモデル化するためには，モ
ている。
デル式の構築と，パラメータ調整のための多くの実験デー
一方でシリンダ内における水エマルジョン燃料の挙動お
タが必要であるが，ミクロ爆発過程を詳細にデータ化する
よび燃料過程は複雑であり，水の添加割合と環境負荷低減
ことは一般に困難である。
効果，および燃費向上効果のメカニズムを定量的に予測す
ミクロ爆発・燃焼過程は，気液２相の物質が化学変化を
るモデルが構築されていない状況である。本研究は，微粒
伴い急速に変化する複雑な現象であり，一般的な熱や流体
化された水エマルジョン燃料油滴をモデル化し，その粒径
の数値シミュレーション（ナビエストークス方程式などの
分布や油の蒸発過程などをセルオートマトンモデルにより
流体支配方程式を数値的に解く方法）を単純に適用するこ
モデル化することで，燃費改善効果の定量的な考察の可能
とが困難である。ミクロ爆発過程を流体力学的な手法によ
性を示すことを目的としたものである。
り解いた事例 12) などがあるが、計算が複雑なため油滴内
ディーゼル機関の噴霧燃焼過程のシミュレーションモデ
部の水粒子の数に限界があると考えらえる。このような複
ルは数多く報告されている
4) ～ 7) など
。これらのモデルは，
雑な化学変化を伴う現象をシミュレーションする方法とし
シリンダ内の流れについては，ナビエストークス方程式を
て，粒子法，格子ボルツマン法などがある。そのきわめて
数値的に解く方法が用いられ，乱流成分については様々な
単純なモデルとしてセルオートマトン法がある。セルオー
乱流モデル（LES 等）が用いられている。シリンダ内に噴
トマトンモデルは，空間と時間の両方を離散化したモデル
霧された燃料油の挙動については，燃料ノズル出口から微
であり，空間をセルという区分に分割し，隣接するセル間
粒化された油滴群が流れにのって拡散していく過程を離散
の状態の遷移でマクロな現象を再現するものである。セル
水混合エマルジョン燃料油滴の燃焼モデル
88
間の状態の変化は予め定められた遷移ルールに従う。この
計算機性能の制約により mm オーダーであるが，油滴１
セルオートマトンモデルにおいて，様々な物理現象や，生
つ１つの現象や PM の大きさは，μm のオーダーであり既
物の形態モデルなどが研究されている。
往モデルで油滴の挙動や PM の生成過程を直接モデル化す
本研究は，２次元セルオートマトンを用いて油滴粒子の
ることは困難である。一方で近年，量子化学に基づき燃焼
蒸発・燃焼過程をあらわす基礎的なモデルを構築したもの
反応を理論的に導出する研究もおこなわれているが，これ
である。燃焼過程は３次元空間での現象であり，２次元の
らの燃焼素過程の現象は nm オーダーの現象をとらえるも
セルオートマトンモデルでの検討では，３次元モデルと数
のである。本研究のセルオートマトンモデルは，μm オー
値が変わってくると考えられるが，本法では，検討手順の
ダーの現象をモデル化するもので，このモデルにより，既
有効性を考えるため，２次元で検討することとし，３次元
往の噴霧燃焼モデルと，量子化学による燃焼モデルの橋渡
モデルは今後の課題とした。２次元モデルにおいても，３
しをし，統合することが可能であると考えられる。このよ
次元と同様な定性的な傾向は見えてくると考えられる。
うな統合モデルを進めることにより，将来は，PM の粒子
図 1 に示すように，既存のディーゼル噴霧モデルの流動
数や粒径分布なども正確に算出できる可能性が高くなると
過程の空間メッシュの細かさや，油滴パーセルの大きさは，
考えられる。
Fig. 1.　Relations of my models of this study and other models.
Fig. 1 Relations of my models of this study and other models.
89
石田武志
モデル構築
一定の時間ステップで時間を離散化しているセルオートマ
トンモデルにおいては，同一に取り扱わないほうがよいと
考えたからである。
ディーゼルエンジンはピストンを用い圧縮加熱したシリ
ンダ内の空気に，液体燃料を噴射することで着火させる圧
縮着火機関である。噴霧された燃料は油滴となりシリンダ
エマルジョン燃料の油滴のミクロ爆発過程のモデル化
内に拡散・蒸発し，空気と混合され，発火点を超えた時点
ａ．セルオートマトン空間
で自己発火する。通常燃料と水エマルジョン燃料（Ｗ / Ｏ
図 2 に示すような２次元の正方格子（セル）による空間
型）では，噴霧燃焼過程には以下のような相違が生まれる
を考えて，エマルジョン油粒 1 つのミクロ爆発過程をシ
と考えられる。
ミュレーションするモデルを作成した。セル数は 40 × 40
①油滴の拡散過程において，油滴のみの場合と油滴中
である。各セルは状態値として 1 つの数値を保持している。
に水が含まれている場合とでは，分裂，微粒化過程
状態は，以下のように規定した。この状態量は膨張，移動
が変化する可能性がある。
過程で隣接セルにその一部が渡されるが，計算空間全体で
は，総量が保持されるとした。
②エマルジョン燃料の油滴のミクロ爆発過程により，
0　：　空気
油滴がさらに微小化される。
0 より大きく 5000 未満　：　燃料油
③油滴粒子の大きさの相違と空間分布の相違により，
油粒子の蒸発，空気の混合，着火，火炎の伝搬過程
5000 以上　：　水蒸気
の状況が変化する。
本研究では，この②と③について，それぞれセルオート
初期の状態としては，図 2 に示すように，油滴中に水滴
マトンによるモデルを構築した。②と③は別々のモデルと
が存在し，その水滴が高温下で蒸発した瞬間を想定した。
した。これは，ミクロ爆発過程の時間スケールと，油滴の
油滴中の蒸気は膨張し，周囲の油を押し押しのけながら広
拡散燃焼過程の時間スケールが必ずしも同じでないため，
がっていく過程を考察した。
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##
##
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##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
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##
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##
0
0
0
0
0
0
0
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0
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0
##
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0
0
0
0
0
0
0
0
0
0
0
0
0
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0
0
0
0
0
0
0
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0
0
0
0
0
##
##
##
##
##
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##
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##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
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##
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##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
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0
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0
0
0
0
0
0
0
0
0
0
0
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0
0
0
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0
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0
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0
0
0
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0
0
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0
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0
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0
0
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0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
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0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
100
0
0
6000
100
0
6000
100
100
：
Air（0）
：
Oil（0～5000）
：
Water vapor
（5000～）
Fig. 2.　Modeling of the micro-explosion process by the two dimensional grid and setting method of
numerical
gridmicro-explosion
state.
of the
process by the two dimensional grid and setting
Fig. 2 Modeling
method of numerical grid state.
90
水混合エマルジョン燃料油滴の燃焼モデル
0
0
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0
ｂ．遷移則の設定
0
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0
0
0
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0
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0
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0
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0
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0
0
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0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
0
0
0
0
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0
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0
0
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0
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0
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0
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##
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##
0
0
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0
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0
##
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##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
0
0
0
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0
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
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0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
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##
0
0
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0
0
0
0
0
0
0
0
0
0
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0
0
0
0
0
0
0
0
##
##
##
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##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
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##
##
##
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##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
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##
##
##
##
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
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##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
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##
##
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##
##
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##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
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##
0
0
0
0
0
0
0
0
0
0
0
0
0
与えられた初期状態において，セルごとに以下の遷移則
を適用し，空間内の状態を変化させた。各セルの状態は，
一つ前のタイムステップにおける自身のセルの状態量と隣
接する 8 つのセルの状態から計算される。遷移ルール中で
示す蒸発や油の流動域の概要を図３に示す。
（遷移ルール）
1）水蒸気膨張域の特定；状態が油のセルで，隣接に水
蒸気のセルがある部分を抽出，隣接の水蒸気セルの
数をカウント（ただし空気相に隣接する場合は除
外）
。
2）水蒸気膨張域への水蒸気状態量の受け渡し；状態が
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3）油の流動域の特定と油状態量の受け渡し；油が水蒸
気に押されて流動するセルを特定し，油セルの状態
量を受け渡す。具体的にはまず空気相か油相のセル
100
0
0
で，周囲に蒸発領域があるセルを特定する。そして，
6000
0
100
水蒸気膨張領域に元々ある油を，油流動領域で分割
する分割数をもとめ，分割量を算出する。さらに油
6000
100
100
流動領域への状態量（油量）の受け渡しを行う。
4）水蒸気が空気相に触れた場合（水蒸気相の隣接に空
気相がある場合）は空気相内に水蒸気が拡散し圧力
：
Air（0）
が低下するため，油を押しのける手順を除外する。
： Oil（0～5000）
水蒸気セルにおいて，隣接する空気セルの数から分
割数を算定し，自身の水蒸気量を隣接空気相に分割
： Water vapor
していく。
（5000～）
水蒸気のセルにおいて，水蒸気を周囲の水蒸気膨張
5）油相が空気相を押し広げる過程；空気相に接してい
領域に分割する分割数を求める（水蒸気セルの数も
る油相で，油量が 100 以上の場合は，100 を超える
Fig. 2 Modeling of the micro-explosion process分を，空気セルに分配していく。
by the two dimensional grid and setting
含める）。この分割数と水蒸気セルの状態量から隣
接する水蒸気膨張域への水蒸気の受け渡し量を算定
method of numerical grid state.
し，水蒸気膨張域に数値を受け渡す。
Fig. 3.　Domain division of the micro-explosion model in the transition rules
Fig. 3 Domain division of the micro-explosion
model in the
transition rules
の含有率として
15％，30％，5％の場合と考え，さらに水
以上のように遷移ルールは，基本的に物質の流動を状態
量の受け渡しのみで表現している。実際は，油滴の表面張
粒子を一つのセルとした場合と 2 × 2 のセルであらわした
力，水蒸気の爆発力，油滴内のせん断力などを検討する必
17
場合を検討した。図 4 に初期値の状態を示す。本モデルは，
要があるが，初期モデルとして位置づけ，単純な流動モデ
遷移ルールと初期状態でのみ状態が規定されるため，その
ルとした。
他のパラメータは存在しない。
ｃ．初期状態
空間セル中の中央の 240 セル分を油滴領域として，油セ
ルと水蒸気セルを設定した。油セルの初期値を 100，水蒸
気セルの状態量の初期値を 6,000 とした。油滴中の水粒子
91
石田武志
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0
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0
Case A (Water content 30 %)
0
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0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Case F (Water content 5 %)
Case E (Water content 15 %)
Air
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Case C (Water content 5 %)
Case B (Water content 15 %)
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Case D (Water content 30 %)
：
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
：
Water Vapor
Fig. 4.　Initial states of micro micro-explosion model
Fig. 4 Initial states of micro micro-explosion model
燃料油滴の燃焼過程のモデル化
して，空間内に油粒子を設定した。空気と接する油粒子は
ａ．セルオートマトン空間
油蒸気になり，油蒸気は，隣接するセル間で平均操作によ
図 5 に示すように，ミクロ爆発過程と同様に 40 × 40 の
り拡散していく。油粒子がある濃度以下になったら（空気
２次元の正方格子空間を考えて，油粒の蒸発，燃焼過程を
と混合され）着火して火炎になる。火炎は，隣接する火炎・
シミュレーションする簡単なモデルを作成した。初期値と
空気セル間で平均操作により拡散していく。
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Liquefied Oil
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
-5
-12
-18
-18
-12
-5
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
-5
-18
-20
-23
-18
-18
-23
-20
-18
-5
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
-10
-14
-24
-20
-23
-18
-18
-23
-20
-24
-14
-10
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
-10
-18
-20
-23
-15
-11
54
54
-11
-15
-23
-20
-18
-10
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
-10
-18
-23
-15
-7
56
72
81
81
72
56
-7
-15
-23
-18
-10
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-5
-14
-20
-15
-7
63
81
92
100
100
92
81
63
-7
-15
-20
-14
-5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-14
-20
-20
-7
63
85
100
100
100
100
100
100
85
63
-7
-20
-20
-14
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-23
-23
-23
54
80
100
100
100
100
100
100
100
100
80
54
-23
-23
-23
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-30
-30
-30
64
87
100
100
100
100
100
100
100
100
87
64
-30
-30
-30
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-30
-30
-30
64
87
100
100
100
100
100
100
100
100
87
64
-30
-30
-30
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-23
-23
-23
54
80
100
100
100
100
100
100
100
100
80
54
-23
-23
-23
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-14
-20
-20
-7
63
85
100
100
100
100
100
100
85
63
-7
-20
-20
-14
0
0
0
0
0
0
0
0
0
0
0
0
Oil Vapor
0
0
0
0
0
0
0
0
0
0
-5
-14
-20
-15
-7
63
81
92
100
100
92
81
63
-7
-15
-20
-14
-5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
-10
-18
-23
-15
-7
56
72
81
81
72
56
-7
-15
-23
-18
-10
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
-10
-18
-20
-23
-15
-11
54
54
-11
-15
-23
-20
-18
-10
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
-10
-14
-24
-20
-23
-18
-18
-23
-20
-24
-14
-10
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
-1
-5
-18
-20
-23
-18
-18
-23
-20
-18
-5
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
0
0
0
0
-1
-5
-12
-18
-18
-12
-5
-1
0
0
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0
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0
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0
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0
0
0
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18
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0
：
Air（0）
：
Oil（100～）
： Vapor oil（1～99）
：
Flame（-1～-99）
Flame
Fig. 5.　Modeling of the combustion process model by the two dimensional grid and setting method of
numerical grid state.
Fig. 5 Modeling of the combustion process model by the two dimensional grid and setting
method of numerical grid state.
92
水混合エマルジョン燃料油滴の燃焼モデル
4）火炎相も油蒸気相と同様に空気層に、隣接セルとの
ｂ．遷移則の設定
平均操作により拡散していく。
与えられた初期状態において，セルごとに以下の遷移則
5）火炎相の状態量が－ 1 より大きくなる（－ 1 と 0 の間）
を適用し，空間内の状態を変化させた。各セルの状態は，
になった場合，燃え尽きたとする。
一つ前のタイムステップにおける自身のセルの状態量と隣
接する 8 つのセルの状態から計算される。
以上のように遷移ルールは，油滴の燃焼を直線的な蒸発，
拡散燃焼過程のみで表現している。実際は，燃料噴霧の流
（ルールの記述）
1）燃料油滴が空気に接する部分が気化されていく。油
動の中で，各油滴同士の間隔も広がっていくと考えらえる
セルで状態量が 100（液体相）のものは，99 に置換
が，噴霧の中のごく一部をモデル化し，噴霧全体が燃焼す
され，油蒸発相になる。ただし油相のうち周りに油
る時間スケールよりも小さい個々の油滴の燃焼をみている
相が７つ以上ある場合は，蒸発しない，それ以外は
ため，油滴同士の位置が相対的に大きくなっていく効果は
蒸発して油蒸気（99）になる。これは油の蒸発速度
検討していない。
は粒子の表面積に比例して，蒸発量が決まるとの仮
定に基づく。粒径が大きいほど全てが蒸発するのに
ｃ．初期状態
時間がかかり，同じ量の燃料であれば，粒径が細か
空間セル中の中央の 100 セル分を油滴領域として，油セ
くなっているほど，蒸発が速い。
ルを設定した。油セルのセル数と同等として，2，4，8 分
2）油蒸気相は周囲の空気層との間で，状態量の平均操
割した初期値を考えた（図 6）。さらに，ミクロ爆発過程
作で，拡散されていく。
の結果から，油滴の飛散状態を初期値とした場合を計算し
3）油の蒸気が空気と混合し，一定の濃度以下になると
た。ミクロ爆発過程の結果においては，計算結果をそのま
着火すると仮定した。具体的には，油蒸気の状態量
ま用いるため，油滴のセル数を正確に 100 にすることが困
が 10 以下になったら着火して火炎相（状態量×－
難であるが，次項の計算ケースの設定で示すようにおよそ
10）になる。本モデルでは火炎相は負の数字であら
100 前後となっている。
わしている。既に火炎相の部分は数字が引き継がれ
る。
0
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0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Case 2（two-fraction model）
Case 1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Case 3（four-fraction model）
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Case 4（eight-fraction model）
Fig. 6.　Initial states of combustion process.
Fig. 6 Initial states of combustion process.
Table 1 Calculation cases of micro-explosion model.
Case
Water content
The ratio of number of
93
石田武志
計算ケースの設定と評価方法
ｂ．評価方法
ａ．計算ケースの設定
ミクロ爆発過程の結果は，爆発後の油滴の分布状態など
遷移ルール中に数値を変更するパラメータ等がないた
から定性的な評価，考察を行った。また蒸発・燃焼モデル
め，計算ケースは，初期状態の設定ケースと一致する。本
においては，あるタイムステップ間（1 ～ 5 ステップ及び
研究で計算をしたミクロ爆発過程の計算ケース（Case A
1 ～ 10 ステップ）での火炎のセル数で評価した。これは，
～ F）は表１のようになる。さらに燃焼過程の計算ケース
より短時間で，広い空間に燃焼した火炎が広がるほど，燃
（Case 1 ～ 10）をまとめると表２のようになる。
焼効率が良く，未燃成分やススが発生しにくいと考えたた
めである。
Table 1 Calculation cases of micro-explosion model.
Case
Water content
The ratio of number of cells; oil cell
number : water vapor cell number
Case A
30% (water particle: 2 × 2 cells)
164：76
Case B
15% (water particle: 2 × 2 cells)
204：36
Case C
5% (water particle: 2 × 2 cells)
228：12
Case D
30% (water particle: 1 × 1 cell)
168：72
Case E
15% (water particle: 1 × 1 cell)
204：36
Case F
5% (water particle: 1 × 1 cell)
228：12
Table 2 Calculation cases of combustion process model
Case
Water content
Number of oil cell
Friction of oil
droplet
Case 1
0％
100
1
Case 2
0％
100
2
Case 3
0％
100
4
Case 4
0％
100
8
Case 5
30% (water particle: 2 × 2 cells)
110 (Result of micro-explosion
model: Case A)
－
Case 6
model:
15% (water particle: 2 × 2 cells) 87 (Result of micro-explosion
Case B)
－
Case 7
5% (water particle: 2 × 2 cells)
65 (Result of micro-explosion model:
Case C)
－
Case 8
30% (water particle: 1 × 1 cell)
164 (Result of micro-explosion
model: Case D)
－
Case 9
15% (water particle: 1 × 1 cell)
161 (Result of micro-explosion
model: Case E)
－
Case 10
5% (water particle: 1 × 1 cell)
106 (Result of micro-explosion
model: Case F)
－
In case 5-10, the initial number of the oil cells differs each case because these cases used the result of the micro-explosion model.
94
水混合エマルジョン燃料油滴の燃焼モデル
る。特に水含有率が高い場合は，油滴の中心部の水滴の蒸
シミュレーション結果及び考察
発爆発が，同時におきるため，相互に力が相殺され，油滴
ミクロ爆発過程モデル
中央部の油が外側に飛散しない現象がみられる。また初期
ミクロ爆発過程モデルの結果を図 7 ～ 9 に示す。図 7 は，
の水粒子の分布によって，油の飛散方向に若干のゆがみが
ケース A の場合のタイムステップごとの結果である。油
でる。
滴内の蒸気が膨張し，周囲の油滴を外側に押し出して飛散
図 9 に示すように，さらに水粒子を細かくした場合にお
してく様子が計算できている。油滴内部の蒸気が外部の空
いては，細かくすることで必ずしも飛散状態が良くなるわ
気に接すると，膨張が止まるというルールにしているため，
けではないことが分かる。これは，ケース A と同様に，
3 ステップ以後で飛散がとまった状態になる。実際のシリ
油滴の細かい水滴同士の蒸発爆発の力が相殺され，油滴中
ンダ内の流れでは，噴霧の大きな流れや循環流により，こ
央部が外側に飛散しないためである。実際のシリンダ内の
の後も油粒子は広がっていくと考えられる。
流れでは，噴霧の大きな流れや循環流により，中央部の油
図 8 は，初期状態を変えた場合の結果となる。計算ケー
粒子の集合体も周囲に広がっていくと考えられるが，これ
ス A，B，C の比較では，水含有率が高いほど必ずしも油
らの検討には更なるモデルの改良が必要である。
の微粒子がよく飛散するわけではないことを示唆してい
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
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33
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33
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1
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67
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40
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70
20
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70
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33
67
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67
33
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33
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58
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58
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78
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78
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65
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65
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65
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78
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(Step 1)
0
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33
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33
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33
67
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67
33
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(Step 4)
：
0
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70
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97
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0
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33
58
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33
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(Step 5)
Water vapor
Fig. 7.　Simulation results of micro-explosion model (Case E).
Fig. 7 Simulation results of micro-explosion model (Case E).
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89
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95
石田武志
Case A (water content 30%)
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##
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0
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0
0
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0
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0
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0
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0
0
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0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
0
0
0
0
0
0
0
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
0
0
0
0
0
0
0
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
0
0
0
0
0
0
0
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
0
0
0
0
0
0
0
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
0
0
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
1
#
#
#
#
#
#
#
#
#
0
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
#
#
#
#
#
#
#
#
#
1
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
0
0
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
0
0
0
0
0
0
0
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
0
0
0
0
0
0
0
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
0
0
0
0
0
0
0
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
0
0
0
0
0
0
0
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Case B (water content 15%)
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
9
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
Case C (water content 5%)
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
： Air
：
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
Oil
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
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#
#
#
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#
#
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#
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#
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#
#
#
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#
#
#
#
#
#
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#
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#
#
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#
#
#
0
0
#
#
#
#
#
#
#
#
#
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#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
： Water vapor
Fig. 8.　Simulation results of micro-explosion model (Case D, E, F).
Fig. 8 Simulation results of micro-explosion model (Case A, B, C).
Case D (water content 30%)
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
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0
0
0
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0
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0
0
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0
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0
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0
0
0
0
0
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0
0
0
0
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0
0
0
0
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0
0
0
0
0
0
0
0
0
0
0
0
0
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0
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0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
#
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0
0
0
0
0
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0
0
0
0
0
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0
0
0
0
0
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0
0
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0
0
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0
0
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0
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0
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0
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0
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0
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0
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1
#
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0
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0
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0
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0
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0
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0
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0
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1
#
#
#
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0
#
#
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#
#
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#
#
#
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#
#
#
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0
#
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#
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#
#
#
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0
#
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#
#
#
#
#
#
#
#
#
#
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#
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#
0
#
#
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#
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#
#
#
#
#
#
#
#
#
#
#
#
#
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#
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#
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#
0
#
#
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#
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#
#
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#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
#
#
#
#
#
#
#
#
#
#
#
5
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
0
0
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
0
0
0
0
0
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
#
0
0
0
0
0
0
0
0
0
Case E (water content 15%)
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
##
##
##
##
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##
##
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0
0
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0
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0
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##
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##
##
##
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##
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##
##
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0
0
0
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0
0
0
0
0
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##
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0
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0
0
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0
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0
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0
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0
0
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0
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0
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0
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0
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0
0
0
0
0
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0
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0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
0
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0
0
0
0
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0
0
0
0
0
0
0
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0
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0
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0
0
0
0
0
0
0
0
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0
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0
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0
0
0
0
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0
0
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0
0
0
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0
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0
0
0
0
0
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0
0
0
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0
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0
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0
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0
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0
0
0
0
0
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0
0
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0
0
0
0
0
0
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0
0
0
0
0
0
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0
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0
0
0
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0
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0
0
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0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
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0
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0
0
0
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0
0
0
0
0
0
0
0
0
0
0
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0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
0
0
0
0
0
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0
0
0
0
0
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0
0
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0
0
0
0
0
0
0
0
0
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0
0
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0
Case F (water content 5%)
0
0
0
0
0
0
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0
0
0
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0
0
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0
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0
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0
0
0
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0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
0
0
0
0
0
0
0
0
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0
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0
0
0
0
0
0
0
0
0
0
0
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0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
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Water vapor
Fig. 9 Simulation
results
of micro-explosion
model(Case
(CaseA,
D, B,
E, F).
Fig. 9.　Simulation
results
of micro-explosion
model
C).
24
96
水混合エマルジョン燃料油滴の燃焼モデル
蒸発・燃焼過程モデル
さらに図 11 にミクロ爆発過程による油粒子分布を初期値
油の油滴径が大きい場合（ケース 1）と，同じ油量で，
として計算した場合を示す。水蒸気は、ミクロ爆発により
粒径を半分以下にした場合（ケース 2，3，4）の蒸発・燃
空間に比較的一様に分布しているとみなして、燃焼過程で
焼過程を比較すると図 10 のようになる。油粒子の径が小
は水蒸気の存在の影響は考慮せず、油粒の分布のみミクロ
さいほど，拡散が速く，燃焼がすばやく進むことがわかる。
爆発過程のモデルの結果を利用している。
Case 1 (one oil droplet)
0
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0 0 100
0 0 100
0 100 100
0 100 100
0 0 100
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0 0 0
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0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 -7
0 0 0 0 -8 -14
0 0 0 -8 -15 -22
0 0 -7 -15 -22 -15
0 0 -7 -15 -15 -8
0 -7 -14 -14 -7 72
0 -7 -7 -7 60 87
0 -7 -7 -7 70 92
0 -7 -7 -7 70 92
0 -7 -7 -7 60 87
0 -7 -14 -14 -7 72
0 0 -7 -15 -15 -8
0 0 -7 -15 -22 -15
0 0 0 -8 -15 -22
0 0 0 0 -8 -14
0 0 0 0 0 -7
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0
0
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0
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Air
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Oil
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Oil vapor
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Fig.Fig.
1010.　Simulation
results
of combustion
process
(Case 1-4,
of the
Simulation results
of combustion
process model
(Casemodel
1-4, Comparison
of theComparison
combustion process
by the difference in oil droplet size)(1).
combustion process by the difference in oil droplet size)(1).
25
97
石田武志
Case 3 (four-friction oil droplet)
0
0
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-6
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0 100 100 100 100 100 100
0 100 100 100 100 100 100
0 0 100 100 100 100 0
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0 100 100 100 100 100 100
0 100 100 100 100 100 100
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-8
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-6
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-6
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-20
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-8
66
67
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67
68
54
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66
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43
18
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68
-7
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0 0 0 0
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0 0 -5 -10
0 0 -10 -21
0 0 -16 -31
0 0 -10 -21
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0 -5 -10 -16
0 -10 -21 -31
0 -16 -31 -47
0 -10 -21 -31
0 -5 -10 -16
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0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Case 4 (eight-friction oil droplet)
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 100 100 0 0 0 0 0
0 100 100 100 100 0 0 0 0
0 100 100 100 100 0 0 0 0
0 0 100 100 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 100 100 100
0 0 0 0 0 100 100 100 100
0 0 0 0 0 100 100 100 100
0 0 0 0 0 0 100 100 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 100 100 0 0 0 0 0
0 100 100 100 100 0 0 0 0
0 100 100 100 100 0 0 0 0
0 0 100 100 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-6
-6
-6
-6
-6
-6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-6
-6
-6
-6
-6
-6
0
0
0
0
0
0
0
0
0
0
0
-6
-12
-12
-6
-6
-12
-12
-6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-6
-12
-12
-6
-6
-12
-12
-6
0
0
0
0
0
0
0
0
0
0
-6
-12
-12
-6
-6
-12
-12
-6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-6
-12
-12
-6
-6
-12
-12
-6
0
0
0
0
0
0
0
0
0
0
-6
-6
-6
54
54
-6
-6
-6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-6
-6
-6
54
54
-6
-6
-6
0
0
0
0
0
0
0
0
0
0
-6
-6
-6
54
54
-6
-6
-6
0
0
0
0
-6
-6
-6
-6
-6
-6
0
0
0
0
-6
-6
-6
54
54
-6
-6
-6
0
0
0
0
0
0
0
0
0
0
-6
-12
-12
-6
-6
-12
-12
-6
0
0
0
-6
-13
-13
-6
-6
-12
-12
-6
0
0
0
-6
-12
-12
-6
-6
-12
-12
-6
0
0
0
0
0
0
0
0
0
0
-6
-12
-12
-6
-6
-12
-12
-6
0
0
0
-6
-13
-13
-6
-6
-12
-12
-6
0
0
0
-6
-12
-12
-6
-6
-12
-12
-6
0
0
0
0
0
0
0
0
0
0
0
-6
-6
-6
-6
-6
-6
0
0
0
0
-6
-6
-6
56
55
-6
-6
-6
0
0
0
0
-6
-6
-6
-6
-6
-6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
17
40
62
56
-6
-6
-6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
0
0
0
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0
0
0
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0
0
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0
0
0
0
0
0
0
0
0
0
0
0
0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 100 100 100 0
0 100 100 100 100
0 100 100 100 100
0 0 100 100 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 100 100 0
0 100 100 100 100
0 100 100 100 100
0 0 100 100 100
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-5
-5
-5
40
-6
-13
-13
-6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
0
-5
-5
-5
17
-6
-13
-13
-6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-5
-5
-5
0
-6
-6
-6
0
0
0
0
-5
-5
-5
0
-6
-6
-6
0
0
0
0
0
-6
-6
-6
-6
-6
-6
0
0
0
0
0
0
0
0
0
0
0
-5
-5
-5
17
-6
-13
-13
-6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-6
-12
-12
-6
-6
-13
-13
-6
0
0
0
0
0
0
0
0
0
0
-5
-5
-5
40
-6
-13
-13
-6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-6
-12
-12
-6
-6
-13
-13
-6
0
0
0
0
0
0
0
0
0
0
0
17
40
62
56
-6
-6
-6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-6
-6
-6
55
56
-6
-6
-6
0
0
0
0
0
0
0
0
0
0
-6
-6
-6
56
55
-6
-6
-6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-6
-6
-6
56
62
40
17
0
0
0
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0 0 0 0 0 0 0 0 0 0
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0 0 0 0 0 0 0 0 0 0
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0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 100 100 0 0
0 0 0 0 0 100 100 100 100 0
0 0 0 0 0 100 100 100 100 0
0 0 0 0 0 0 100 100 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
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0 0 0 0 0 0 0 0 0 0
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0 0 0 0 0 0 0 100 100 0
0 0 0 0 0 0 100 100 100 100
0 0 0 0 0 0 100 100 100 100
0 0 0 0 0 0 0 100 100 0
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0
0
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-6
-13
-13
-6
-6
-12
-12
-6
0
0
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0
0
0
0
0
0
0
0
0
0
0
-6
-13
-13
-6
40
-5
-5
-5
0
0
0
0
0
0
0
0
0
0
-6
-13
-13
-6
-6
-12
-12
-6
0
0
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0
0
0
0
0
0
0
0
0
0
0
-6
-13
-13
-6
17
-5
-5
-5
0
0
0
0
0
0
0
0
0
0
0
-6
-6
-6
-6
-6
-6
0
0
0
0
-6
-6
-6
-6
-6
-6
0
0
0
0
0
0
-6
-6
-6
0
-5
-5
-5
0
0
0
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0
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0
0
-6
-12
-12
-6
-6
-13
-13
-6
0
0
0
0
0
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0
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-19
-18
-18
-19
-18
-14
-5
0
-1
-5
-12
-18
-18
-12
-5
-1
0
0
0
-5
-14
-18
-20
-22
-26
-22
-26
-18
-14
0
0
0
0
0
0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 -4 -8 -13 -8 -4 0
0 -8 -17 -25 -17 -8 0
0 -13 -25 -38 -25 -13 0
0 -8 -17 -25 -17 -8 0
0 -4 -8 -13 -8 -4 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
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0 0 0 0 0 0 0
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0 0 0 0 0 0 0
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0 0 0 0 0 0 0
0 0 -4 -8 -13 -8 -4
0 0 -8 -17 -25 -17 -8
0 0 -13 -25 -38 -25 -13
0 0 -8 -17 -25 -17 -8
0 0 -4 -8 -13 -8 -4
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0
0
-1
-10
-14
-19
-18
-18
-19
-14
-10
-1
-1
-10
-14
-19
-18
-18
-19
-14
-10
-1
0
0
-1
-10
-14
-20
-22
-26
-22
-18
-10
-5
0
0
0
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-1
-5
-12
-18
-18
-12
-5
-1
0
-5
-14
-18
-19
-18
-18
-19
-18
-14
-5
0
0
0
-1
-5
-14
-22
-26
-22
-14
-5
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
-12
-19
-19
-7
50
50
-7
-20
-20
-14
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
-5
-12
-18
-18
-12
-5
-1
0
-18
-18
-18
50
72
73
53
-22
-22
-22
0
0
0
0
0
0
0
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0
0
0
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0
0
0
0
-1
-10
-14
-19
-18
-18
-19
-14
-10
-1
-18
-18
-18
50
73
76
56
-26
-26
-26
0
0
0
-1
-5
-12
-18
-18
-12
-5
-1
0
0
0
0
0
0
0
0
0
-5
-14
-18
-19
-18
-18
-19
-18
-14
-5
-12
-19
-19
-7
53
56
44
-22
-22
-22
0
0
-1
-10
-14
-19
-18
-18
-19
-14
-10
-1
0
0
0
0
0
0
0
0
-12
-19
-19
-7
50
50
-7
-19
-19
-12
-5
-14
-18
-20
-22
-26
-22
-26
-18
-14
0
0
-5
-14
-18
-19
-18
-18
-19
-18
-14
-5
0
0
0
0
0
0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 -4 -8 -13 -8 -4
0 -8 -17 -25 -17 -8
0 -13 -25 -38 -25 -13
0 -8 -17 -25 -17 -8
0 -4 -8 -13 -8 -4
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
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0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
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0 0 0 0 0 0
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0
0
-18
-18
-18
50
72
72
50
-18
-18
-18
-1
-10
-14
-20
-22
-26
-22
-18
-10
-5
0
0
-12
-19
-19
-7
50
50
-7
-19
-19
-12
0
0
0
0
0
0
0
0
-18
-18
-18
50
72
72
50
-18
-18
-18
0
-1
-5
-14
-22
-26
-22
-14
-5
-1
0
0
-18
-18
-18
50
72
72
50
-18
-18
-18
0
0
0
0
0
0
0
0
-12
-19
-19
-7
50
50
-7
-19
-19
-12
0
0
0
0
0
0
0
0
0
0
0
0
-18
-18
-18
50
72
72
50
-18
-18
-18
0
0
0
0
0
0
0
0
-5
-14
-18
-19
-18
-18
-19
-18
-14
-5
0
0
0
0
0
0
0
0
0
0
0
0
-12
-19
-19
-7
50
50
-7
-19
-19
-12
0
0
0
0
0
0
0
0
-1
-10
-14
-19
-18
-18
-19
-14
-10
-1
0
0
0
0
0
0
0
0
0
0
0
0
-5
-14
-18
-19
-18
-18
-19
-18
-14
-5
0
0
0
0
0
0
0
0
0
-1
-5
-12
-18
-18
-12
-5
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
-10
-14
-19
-18
-18
-19
-14
-10
-1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
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0
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0
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0
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0
0
0
0
0
0
-1
-5
-12
-18
-18
-12
-5
-1
0
0
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0
Fig. 10.　Simulation results of combustion process model (Case 1-4, Comparison of the combustion process
by the difference
in oilof
droplet
size) (2).
results
combustion
process model (Case 1-4, Comparison of the
Fig. 10 Simulation
combustion process by the difference in oil droplet size) (2).
26
98
水混合エマルジョン燃料油滴の燃焼モデル
Case 5
0
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-2
-6
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-6
-2
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-6
-17
-29
-29
-17
-6
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-12
-23
-35
-35
-23
-12
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-19
-26
-34
-34
-27
-19
0
-3
-10
-17
-17
-10
-3
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-5
-15
-25
-25
-15
-5
-15
-15
-15
-15
-21
-21
-8
-15
-21
-26
-24
-17
-10
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0
：
0
0
0
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0
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0
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0
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0
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0
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0
0
0
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0
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0
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0
0
0
0
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0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
0
0
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0
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0
0
Flame
11.　Simulation
results ofof
combustion
process model
(Case 5,model
7, Comparison
process
Simulation
results
combustion
process
(Caseof the
5, combustion
7, Comparison
of the
Fig. 11Fig.
using the results of micro-explosion model).
combustion process using the results of micro-explosion model).
27
99
石田武志
蒸発・燃焼過程モデルにおける火炎のセル数の推移
各ケースにおけるタイムステップごとの火炎数（火炎状
態のセル数）をまとめると表 3 及び表 4 のようになり，こ
れらの数値をグラフにまとめると図 12 ～ 14 のようになる。
Table 3 Number
of the
cells
offlame
flame
state
(Case 1-4).
Table 3 Number
of the
cells of
state (Case
1-4).
Case 1
Case 2
Case 3
Case 4
Oil droplet( Oil droplet( Oil droplet( Oil droplet(
one particle) two friction four friction eight friction
particles)
particles)
particles)
0
0
0
0
0
0
0
0
180
284
432
672
124
220
292
428
128
180
252
364
128
140
200
100
96
100
100
0
76
60
0
0
56
0
0
0
36
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
824
984
1276
1564
Step 0
Step 1
Step 2
Step 3
Step 4
Step 5
Step 6
Step 7
Step 8
Step 9
Step 10
Step 11
Step 12
Step 13
Step 14
Step 15
Step 16
Total
(The ratio for case 1)
Total from 0 to
5 steps.
560
(The ratio for case 1)
Total from 0 to
10 steps.
824
(The ratio for case 1)
1.19
1.55
1.90
824
1176
1564
1.47
2.10
2.79
984
1276
1564
1.19
1.55
1.90
Table 4 Number
of theof cells
flame
(Case 5-10).
Table 3 Number
the cellsof
of flame
statestate
(Case 1-4).
Case 1
Oil droplet(
one particle)
Step 0
Step 1
Step 2
Step 3
Step 4
Step 5
Step 6
Step 7
Step 8
Step 9
Step 10
Step 11
Step 12
Step 13
Step 14
Step 15
Step 16
Total
0
0
180
124
128
128
96
76
56
36
0
0
0
0
0
0
0
824
(The ratio for case 1)
Total from 0 to
5 steps.
560
1112
1.99
1346
2.40
1110
1.98
922
1.65
1089
1.94
1592
2.84
824
1488
1.81
1346
1.63
1110
1.35
1634
1.98
1742
2.11
1683
2.04
(The ratio for case 1)
Total from 0 to
10 steps.
(The ratio for case 1)
Case 5
Case 6
Case 7
Case 8
Case 9
Case 10
micromicromicromicromicromicroexplosion
explosion
explosion
explosion
explosion
explosion
（Water
（Water
（Water
（Water
（Water
（Water
content 30%) content 15%) content 5%) content 30%) content 15%) content 5%)
0
0
0
0
0
0
0
0
0
0
0
0
470
742
695
316
425
753
320
434
358
222
303
519
182
170
57
183
201
235
140
0
0
201
160
85
118
0
0
161
160
61
96
0
0
160
119
30
74
0
0
129
146
0
54
0
0
148
103
0
34
0
0
114
125
0
0
0
0
103
94
0
0
0
0
90
75
0
0
0
0
65
55
0
0
0
0
45
35
0
0
0
0
25
0
0
0
0
0
0
0
0
1488
1346
1110
1962
2001
1683
1.81
1.63
1.35
2.38
2.43
2.04
28
100
水混合エマルジョン燃料油滴の燃焼モデル
800
Number of flame
700
600
500
400
300
200
100
0
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16
Step
Case 1; Oil droplet( one particle)
Case 2; Oil droplet( two friction particles)
Case 3;Oil droplet( four friction particles)
Case 4; Oil droplet( eight friction particles)
Fig. 12.　Number of the cells of flame state (Case 1-4).
Fig. 12 Number of the cells of flame state (Case 1-4).
800
Number of flame
700
600
500
400
300
200
100
0
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16
Case 5; micro-explosion （Water content 30%)
Step
Case 6; micro-explosion （Water content 15%)
Case 7; micro-explosion （Water content 5%)
Case 1; Oil droplet( one particle)
Fig. 13.　Number of the cells of flame state (Case 1 and 5-7).
Fig. 13 Number of the cells of flame state (Case 1 and 5-7).
800
number of flame
700
600
500
400
29
300
200
100
0
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16
Case 8; micro‐explosion （Water content 30%)
Step
Case 9; micro‐explosion （Water content 15%)
Case 10; micro‐explosion （Water content 5%)
Case 1; Oil droplet( one particle)
Fig. 14.　Number of the cells of flame state (Case 1 and 8-10).
Fig. 14 Number of the cells of flame state (Case 1 and 8-10).
101
石田武志
図 12 において，ケース１に対して，粒径を細かくした
時間に燃焼し，多くの火炎を短時間に集中させることがで
場合（ケース 2 ～ 4）は，蒸発・燃焼が速く進み，火炎も
きることが計算できた。これは，水エマルジョン燃焼によ
短時間で空間内に広がるため，火炎セル数の総数は，19％
る燃費改善効果を理論的に検討する基礎になると考えられ
から 90％増加（表 3）する（≒燃焼効率がよい）ことがわ
る。非常に簡易なモデルであるが，今後は油の分布密度，
かる。特に粒径を細かくした場合は，1 ～ 5 ステップに火
粒径，蒸発・拡散スピードなどを評価することで，より詳
炎が集中しており，短時間で燃焼が進んでいることがわか
細な検討が可能になると考えらえる。
る。図 13 において，水を３割添加しミクロ爆発させたケー
今後の課題としては，以下の点があげられる。
ス 5 ～ 7 とケース１を比較した場合，燃料油量自体は 5 ～
・３次元での計算モデルを考える必要がある。
30％少なくなるものの火炎数は多くなることがわかる。ま
・水の蒸発・拡散も合わせたシミュレーションを行い，
た油滴が蒸発する時点では，水粒子が完全に蒸気となって
NOx 低減効果の評価ができるようにする（燃焼温度の分
空間に広がっており（図 7 ～ 9 に示すように水蒸気が空間
布も評価できるようにする）
全体に広がっている），NOx を生成する高温領域を少なく
・物理的な数値を実態と整合させていく（油滴粒子径，水
するプロセスも定性的ながら確認することができる。この
粒子系，蒸発拡散速度，燃焼速度など）
ように単純なモデルであるが，水エマルジョン燃料におけ
・シリンダ内の大きな流動の中で相対的に粒子間の広がっ
る大気汚染物質の低減と燃費向上の定量的な検討の可能性
ていく効果をモデルに含める。
を示すことができたと考えられる。図 14 においてケース 8，
引用文献
９の場合は，10 ステップ以降も火炎が残った状態になる。
これは，ミクロ爆発過程で，微粒化した油滴が中央部に集
中しており，この部分の拡散燃焼に時間がかかったためで
1）東田正憲，中村卓朗，大西郁美，吉澤克浩，細野隆道：
ある。　EGR と水エマルジョン燃料の組み合わせによる NOx 低
以上のように水エマルジョン燃料によりミクロ爆発過程
減技術，マリンエンジニアリング , 48(6)，747-752 (2013)
を経ることで，油が微細粒子化し，燃焼効率が高くなると
2）広瀬弓夫，豊田済，松原勇二：エマルジョン燃料によ
考えられる。本研究のモデルは，2 次元モデルであり，シ
る燃費節減と波及効果について -- 舶用大形ディーゼル
リンダ内の３次元空間では，水粒子や油粒子の蒸発面積な
機関の場合，日本舶用機関学会誌 , 19(1)，47-52 (1984)
どが異なるため，数値に言及した結論をこれ以上導くこと
3）森本稚仁 , 岩本匡弘 , 廣川翼 , 渕端学：エマルジョン燃
は困難であるが，２次元と３次元という相違があるものの，
料の分散水滴径分布がディーゼル燃焼排出ガスに及ぼ
実験で報告されている燃費向上の機序を考察することが可
す影響 , 日本機械学会関西支部講演会講演論文集 , 85,
能となった。今後，より詳細な３次元モデルを構築するこ
12-11 (2010）
とにより，ミクロ爆発過程，蒸発・燃焼過程の挙動の可能
性を明らかにすることが可能であると考えらえる。
4）Ithnin, A. M., et al., : Combustion performance and emission
analysis of diesel engine fuelled with water-in-diesel
emulsion fuel made from low-grade diesel fuel, Energy
結　論
Conversion and Management 90: 375-382 (2015)
5）小島宏一，川那辺洋，石山拓二，小島宏一： ディーゼ
従来のディーゼル噴霧モデルでは，水エマルジョン燃料
ル噴霧における混合気形成および着火の LES 解析，日
のミクロ爆発過程，燃焼過程を表すことができない。これ
本機械学会論文集 B 編 , 78(787)，652-662 (2012).
に対して本研究は，水エマルジョン燃料の油滴の挙動を表
6）町田和也，羽鳥 , 総一，堀司，千田二郎：LES 解析を用
すため，メソスケールの離散粒子モデルを考案した。具体
いたディーゼル噴霧における分裂モデルの最適化，微
的には２次元セルオートマトンを用いて油滴粒子の蒸発・
粒化 , 20(70), 87-95 (2011)
燃焼過程をあらわす基礎的なモデルを構築した。水粒子を
7）入江恭亮，町田和也，堀司，森吉泰生，千田二郎，藤
含む油滴が，水の蒸発により飛散する過程をトレースする
本元：燃焼形態を考慮した燃焼モデルによるディーゼ
モデルを作り，油滴の微粒子化を観察した，さらに，油滴
ル 噴 霧 火 炎 の LES 解 析， マ リ ン エ ン ジ ニ ア リ ン グ ,
の燃焼モデルを考案し，燃焼火炎の分布を計算した。水エ
45(3)，408-414 (2010)
マルジョン燃焼による燃焼は，従来の噴霧油滴よりも，短
8）O'Rouke, P.J and Amsden, A.A. : The TAB Method for
水混合エマルジョン燃料油滴の燃焼モデル
Numerical Calculation of Spray Droplet Breakup, SAE Paper
872089 (1987)
9）Reitz, R.D. and Bracco, F.V., Encyclopedia of Fluid
Mechanics, ch.10, Gulf Publishing Company, Houston,
(1986)
10）Reitz, R.D., : Modeling atomization processes in highpressure vaporizing sprays, Atomization and Spray
Technology, 3, 309-337, (1987)
11）Schreiber, M., Sakak, A. S. and Lingens, A., : A Reduced
Thermokinetic Model for the Autoignition of Fuels with
Variable Octane Ratings, Proceedings of 25th International
Symposium on Combustion, 933-940 (1994)
12）Shinjo, J., Xia, J., Ganippa, L. C., Megaritis, A., : Physics of
puffing and microexplosion of emulsion fuel droplets,
Physics of Fliuds, 26, 103302 (2014)
102