JP4057866B2

JP4057866B2 - Electromagnetic fluid analysis method, apparatus, computer program, and computer-readable storage medium

Info

Publication number: JP4057866B2
Application number: JP2002257961A
Authority: JP
Inventors: 敬介藤崎
Original assignee: Nippon Steel Corp
Current assignee: Nippon Steel Corp
Priority date: 2002-09-03
Filing date: 2002-09-03
Publication date: 2008-03-05
Anticipated expiration: 2022-09-03
Also published as: JP2004093498A

Description

【０００１】
【発明の属する技術分野】
本発明は、電磁力が作用する電気伝導性流体の運動を解析する電磁流体解析方法、装置、コンピュータプログラム、及びコンピュータ読み取り可能な記憶媒体に関する。
【０００２】
【従来の技術】
電磁流体解析（ＭＨＤ（magneto hydro dynamic）解析）とは、電磁場の作用の下における電気伝導性流体の運動を解析するものである。例えば、図６に示すように、容器１０１内に水銀等の流体１０２を入れて、容器１０１の側壁に巻き付けられた電磁コイル１０３に電流を流すことにより流体１０２に電磁力を作用させて、その運動を解析する。
【０００３】
電磁流体解析に際しては、図７に示すように、電磁力をマクスウェルの方程式を用いて求めた後（電磁場解析）、その電磁力による流体１０２の運動をナビエ・ストークス方程式を用いて解析して自由表面形状を求める（流体解析）。流体解析における自由表面のモデル化手法としては、例えばＶＯＦ法（volume of fluid）が知られている。
【０００４】
流体１０２の自由表面形状が変形するとマクスウェルの方程式における境界条件も変化するため、自由表面形状の変形後の電磁力をマクスウェルの方程式を用いて求めた後、その電磁力による流体１０２の運動をナビエ・ストークス方程式を用いて解析してＶＯＦ法により自由表面形状を求める。
【０００５】
これら電磁場解析及び流体解析を繰り返すことによって、流体１０２の運動を動的に解析することができる。
【０００６】
【発明が解決しようとする課題】
しかしながら、上述した電磁場解析及び流体解析を繰り返す手法では、時々刻々における流動、つまり自由表面形状において電磁場解析を行う必要があり、計算負荷が増加して多くの計算時間がかかってしまう。
【０００７】
また、流体１０２の自由表面形状を固定化して解析することも考えられるが、それでは解析精度が劣ってしまう。
【０００８】
本発明は上記のような点に鑑みてなされたものであり、電気伝導性流体の自由表面形状の変形を考慮しつつ簡単な計算により電磁流体解析が可能となるようにすることを目的する。
【０００９】
【課題を解決するための手段】
本発明の電磁流体解析方法は、容器内に電気伝導性流体を入れて、該容器の側壁に巻き付けられた電磁コイルに電流を流すことにより該電気伝導性流体に電磁力を作用させたときの該電気伝導性流体の運動を解析する電磁流体解析方法であって、上記電磁コイルに電流を流すことにより該電気伝導性流体に作用する電磁力を算出して求める電磁場解析手順と、電磁力による該電気伝導性流体の自由表面形状の変形を算出して求める流体解析手順と、変形前電気伝導性流体内の点Ｐ１と電磁コイルの中心軸とを含む平面内において、該点Ｐ１を通り該中心軸に垂直な直線と変形前自由表面との交点を点Ｑ１とし、該点Ｑ１を通り該中心軸に平行な直線と変形後自由表面との交点を点Ｑ２とし、該点Ｑ２を通り該中心軸に垂直な直線と該点Ｐ１を通り該中心軸に平行な直線との交点を変形後電気伝導性流体内の点Ｐ２とし、上記変形前電気伝導性流体内の点Ｐ１における電磁力を上記変形後電気伝導性流体内の点Ｐ２における電磁力として、変形後電気伝導性流体内の任意の位置における電磁力を算出する電磁力算出手順とを有し、上記流体解析手順と上記電磁力算出手順とを繰り返す点に特徴を有する。
本発明の別の電磁流体解析方法は、容器内に電気伝導性流体を入れて、該容器の側壁に巻き付けられた電磁コイルに電流を流すことにより該電気伝導性流体に電磁力を作用させたときの該電気伝導性流体の運動を解析する電磁流体解析方法であって、上記電磁コイルに電流を流すことにより該電気伝導性流体に作用する電磁力を算出して求める電磁場解析手順と、電磁力による該電気伝導性流体の自由表面形状の変形を算出して求める流体解析手順と、上記電気伝導性流体の自由表面より低い位置に、上記電磁コイルの中心軸に垂直な面である基準面を考え、変形前電気伝導性流体内の点Ｐ１を通り該中心軸に平行な直線と該基準面との交点を基準点Ｏ、該直線と上記変形前自由表面との交点を点Ｑ１、該直線と上記変形後自由表面との交点を点Ｑ２とし、該直線上にあり位置が未定の点Ｐ２が、基準点Ｏから各点Ｐ１、Ｑ１、Ｑ２、Ｐ２迄の距離について、比例式
【数８】

を満足する点として位置が決定される点を、上記変形後電気伝導性流体内の点Ｐ２とし、上記変形前電気伝導性流体内の点Ｐ１における電磁力を上記変形後電気伝導性流体内の点Ｐ２における電磁力として、変形後の該電気伝導性流体の任意の位置における電磁力を算出する電磁力算出手順とを有し、上記流体解析手順と上記電磁力算出手順とを繰り返す点に特徴を有する。
【００１０】
本発明の電磁流体解析装置は、容器内に電気伝導性流体を入れて、該容器の側壁に巻き付けられた電磁コイルに電流を流すことにより該電気伝導性流体に電磁力を作用させたときの該電気伝導性流体の運動を解析する電磁流体解析装置であって、上記電磁コイルに電流を流すことにより該電気伝導性流体に作用する電磁力を算出して求める第１の演算手段と、電磁力による該電気伝導性流体の自由表面形状の変形を算出して求める第２の演算手段と、変形前電気伝導性流体内の点Ｐ１と電磁コイルの中心軸とを含む平面内において、該点Ｐ１を通り該中心軸に垂直な直線と変形前自由表面との交点を点Ｑ１とし、該点Ｑ１を通り該中心軸に平行な直線と変形後自由表面との交点を点Ｑ２とし、該点Ｑ２を通り該中心軸に垂直な直線と該点Ｐ１を通り該中心軸に平行な直線との交点を変形後電気伝導性流体内の点Ｐ２とし、上記変形前電気伝導性流体内の点Ｐ１における電磁力を上記変形後電気伝導性流体内の点Ｐ２における電磁力として、変形後電気伝導性流体内の任意の位置における電磁力を算出する第３の演算手段とを有し、上記第２の演算手段による流体解析と上記第３の演算手段による電磁力算出とを繰り返す点に特徴を有する。
本発明の別の電磁流体解析装置は、容器内に電気伝導性流体を入れて、該容器の側壁に巻き付けられた電磁コイルに電流を流すことにより該電気伝導性流体に電磁力を作用させたときの該電気伝導性流体の運動を解析する電磁流体解析装置であって、上記電磁コイルに電流を流すことにより該電気伝導性流体に作用する電磁力を算出して求める第１の演算手段と、電磁力による該電気伝導性流体の自由表面形状の変形を算出して求める第２の演算手段と、上記電気伝導性流体の自由表面より低い位置に、上記電磁コイルの中心軸に垂直な面である基準面を考え、変形前電気伝導性流体内の点Ｐ１を通り該中心軸に平行な直線と該基準面との交点を基準点Ｏ、該直線と上記変形前自由表面との交点を点Ｑ１、該直線と上記変形後自由表面との交点を点Ｑ２とし、該直線上にあり位置が未定の点Ｐ２が、基準点Ｏから各点Ｐ１、Ｑ１、Ｑ２、Ｐ２迄の距離について、比例式
【数９】

を満足する点として位置が決定される点を、上記変形後電気伝導性流体内の点Ｐ２とし、上記変形前電気伝導性流体内の点Ｐ１における電磁力を上記変形後電気伝導性流体内の点Ｐ２における電磁力として、変形後の該電気伝導性流体の任意の位置における電磁力を算出する第３の演算手段とを有し、上記第２の演算手段による流体解析と上記第３の演算手段による電磁力算出とを繰り返す点に特徴を有する。
【００１１】
本発明のコンピュータプログラムは、容器内に電気伝導性流体を入れて、該容器の側壁に巻き付けられた電磁コイルに電流を流すことにより該電気伝導性流体に電磁力を作用させたときの該電気伝導性流体の運動を解析する処理をコンピュータに実行させるコンピュータプログラムであって、上記電磁コイルに電流を流すことにより該電気伝導性流体に作用する電磁力を算出して求める電磁場解析処理と、電磁力による該電気伝導性流体の自由表面形状の変形を算出して求める流体解析処理と、変形前電気伝導性流体内の点Ｐ１と電磁コイルの中心軸とを含む平面内において、該点Ｐ１を通り該中心軸に垂直な直線と変形前自由表面との交点を点Ｑ１とし、該点Ｑ１を通り該中心軸に平行な直線と変形後自由表面との交点を点Ｑ２とし、該点Ｑ２を通り該中心軸に垂直な直線と該点Ｐ１を通り該中心軸に平行な直線との交点を変形後電気伝導性流体内の点Ｐ２とし、上記変形前電気伝導性流体内の点Ｐ１における電磁力を上記変形後電気伝導性流体内の点Ｐ２における電磁力として、変形後電気伝導性流体内の任意の位置における電磁力を算出する電磁力算出処理とをコンピュータに実行させ、上記流体解析処理と上記電磁力算出処理とを繰り返す点に特徴を有する。
本発明の別のコンピュータプログラムは、容器内に電気伝導性流体を入れて、該容器の側壁に巻き付けられた電磁コイルに電流を流すことにより該電気伝導性流体に電磁力を作用させたときの該電気伝導性流体の運動を解析する処理をコンピュータに実行させるコンピュータプログラムであって、上記電磁コイルに電流を流すことにより該電気伝導性流体に作用する電磁力を算出して求める電磁場解析処理と、電磁力による該電気伝導性流体の自由表面形状の変形を算出して求める流体解析処理と、上記電気伝導性流体の自由表面より低い位置に、上記電磁コイルの中心軸に垂直な面である基準面を考え、変形前電気伝導性流体内の点Ｐ１を通り該中心軸に平行な直線と該基準面との交点を基準点Ｏ、該直線と上記変形前自由表面との交点を点Ｑ１、該直線と上記変形後自由表面との交点を点Ｑ２とし、該直線上にあり位置が未定の点Ｐ２が、基準点Ｏから各点Ｐ１、Ｑ１、Ｑ２、Ｐ２迄の距離について、比例式
【数１０】

を満足する点として位置が決定される点を、上記変形後電気伝導性流体内の点Ｐ２とし、上記変形前電気伝導性流体内の点Ｐ１における電磁力を上記変形後電気伝導性流体内の点Ｐ２における電磁力として、変形後の該電気伝導性流体の任意の位置における電磁力を算出する電磁力算出処理とをコンピュータに実行させ、上記流体解析処理と上記電磁力算出処理とを繰り返す点に特徴を有する。
【００１２】
本発明のコンピュータ読み取り可能な記憶媒体は、上記本発明のコンピュータプログラムを格納した点に特徴を有する。
【００１３】
【発明の実施の形態】
以下、図面を参照して、本発明の電磁流体解析方法、装置、コンピュータプログラム、及びコンピュータ読み取り可能な記憶媒体の好適な実施の形態について説明する。
【００１４】
（第１の実施の形態）
本実施の形態における電磁流体解析について説明する。図６に示すように、容器１０１内に水銀等の流体１０２を入れて、容器１０１の側壁に巻き付けられた電磁コイル１０３に電流を流すことにより流体１０２に電磁力を作用させる。
【００１５】
電磁流体解析に際しては、図１に示すように、まず電磁力を求める（ステップＳ１）。電磁力Ｆ_emは、下式（１）〜（４）に示すマクスウェルの方程式（変位電流を無視）を用いて、下式（５）に示すように求められる。
【００１６】
【数２】

【００１７】
次に、その電磁力Ｆ_emによる流体１０２の運動を、下式（６）に示すナビエ・ストークス方程式を用いて解析して、例えばＶＯＦ（volume of fluid）法により自由表面形状の変形を求める（ステップＳ２）。ＶＯＦ法では、複数に分割されたセルを考え、各セルの液体充填率（０から１の間の値をとる）が定義された上で、液体と気体が共存する共存セル内の液体位置を決定し、各セルの液体充填率を計算された流速場に従って移流させる。そして、時間を進めて計算を繰り返すことにより、液面の移動を解析する。この場合に、液体充填率の時間依存性は、下式（７）に支配される。
【００１８】
【数３】

【００１９】
【数４】

【００２０】
次に、流体１０２の変形前流体内の任意の点Ｐ１を射影（写像）した変形後流体内の点Ｐ２を求め、点Ｐ１における電磁力に基づいて点Ｐ２における電磁力を求める（ステップＳ３）。
【００２１】
ここで、図２を参照して、本実施の形態における射影手法について説明する。電磁力により流体１０２の自由表面形状が変形する方向（Ｚ軸）を想定する。つまり、電磁力により流体１０２の自由表面形状はＺ軸方向の凸形状となることを想定する。
【００２２】
いま、電磁力によって、変形前自由表面（図中の点線Ｓ１）が、変形後自由表面（図中の実線Ｓ２）に変形したものとする。この場合に、変形前流体内の任意の点Ｐ１が、変形後流体内の点Ｐ２にどのように射影するかが命題となる。この命題が解決されれば、点Ｐ１における電磁力を点Ｐ２における電磁力とすることで、変形後流体内での電磁力分布を求めることができる。
【００２３】
そこで、本実施の形態では、変形前流体内の任意の点Ｐ１を通るＺ軸に垂直な線（面）Ｌ１を考え、線Ｌ１と変形前自由表面Ｓ１との交点をＱ１とする。次に、点Ｑ１を通るＺ軸に平行な線ＬＱを考え、線ＬＱと変形後自由表面Ｓ２との交点をＱ２とする。そして、点Ｑ２を通るＺ軸に垂直な線（面）Ｌ２を考え、線Ｌ２と点Ｐ１を通るＺ軸に平行な線ＬＰとが交わる点をＰ２とする。これにより、変形前流体内の任意の点Ｐ１は、変形後流体内の点Ｐ２に一対一に射影（写像）したことになる。
【００２４】
すなわち、電磁コイル１０３に垂直な方向において、点Ｐ₁の電磁コイル１０３からの距離と、点Ｐ₂の電磁コイル１０３からの距離とは等しい。そして、変形前自由表面Ｓ₁上の点Ｑ₁の電磁コイル１０３からの距離と変形後自由表面Ｓ₂上の点Ｑ₂の電磁コイル１０３からの距離とは等しく、また、点Ｑ₁と点Ｐ₁との距離Ｐ₁−Ｑ₁と点Ｑ₂と点Ｐ₂との距離Ｐ₂−Ｑ₂とは等しい。したがって、線Ｌ₁及び線Ｌ₂における境界点Ｑ₁、Ｑ₂と、導電体（流体１０２）内における点Ｐ₁、Ｐ₂とは、一次元（二次元）での電磁現象としては同じであり、点Ｐ₁の電磁力を点Ｐ₂の電磁力に射影しても電磁現象は同じであるといえる。
【００２５】
以上述べたように、変形前流体内の任意の点Ｐ１は、変形後流体内の点Ｐ２に一対一に射影（写像）しているので、変形後流体内の任意の点における電磁力を求めることができる。
【００２６】
なお、上記射影手法における条件として、Ｚ軸が電磁コイル１０３と平行である必要がある。また、Ｚ軸は曲線であっても、Ｚ軸、電磁コイル１０３、線ＬＰ、線ＬＱがそれぞれ平行であればよい。
【００２７】
図１に説明を戻して、上述したように変形後流体内の点Ｐ２点における電磁力が求められると、電磁流体解析が終了するか否か判定し（ステップＳ４）、まだ終了でない場合ステップＳ２に戻り、射影により得られた電磁力を基づいて流体解析を行う。これらの流体解析及び射影を繰り返すことによって、流体１０２の運動を動的に解析することができる。
【００２８】
以上述べた実施の形態によれば、電磁場解析及び流体解析を繰り返すのではなく、いったん電磁場解析を行ったならば、その後は流体解析及び射影を繰り返せばよいので、計算負荷を軽減することができる。
【００２９】
また、流体の自由表面形状の変形を捉えて解析するので、自由表面形状を固定化して解析するのに比べれば、解析精度を向上させることができる。
【００３０】
（第２の実施の形態）
第２の実施の形態は、図１のフローチャートにおけるステップＳ３の処理、すなわち射影手法を変更した例である。以下、図３を参照して、本実施の形態における射影手法について説明する。上記第１の実施の形態では、自由表面形状が凸状に変形することを想定したが、凹凸に変形する場合もある。そこで、本実施の形態では、かかる場合のモデル化について考える。
【００３１】
変形前流体内の任意の点Ｐ１を通るＺ軸に平行な線（面）ＬＰを考え、線ＬＰと変形前自由表面Ｓ１との交点をＱ１とし、線ＬＰと変形後自由表面Ｓ２との交点をＱ２とする。
【００３２】
また、Ｚ軸に垂直な線（面）である基準線を考え、線ＬＰとの交点を基準点Ｏとする。
【００３３】
そして、変形後流体内の点に対して、下式を満たす点をＰ２とする。
【００３４】
【数５】

【００３５】
点Ｐ２は変形後流体内に存在し、任意の点を表している。つまり、変形前流体内の任意の点Ｐ１は、変形後流体内の点Ｐ２に一対一に射影（写像）したことになるので、点Ｐ１における電磁力を点Ｐ２における電磁力とする。
【００３６】
本実施の形態では、自由表面形状が凹凸となる場合でも、変形後流体内の任意の点における電磁力を求めることができる。ただし、上記第１の実施の形態では電磁コイル１０３との距離が一定である点を求めており、電磁現象にある制約があったが、本実施の形態ではその制約がないので、一対一の射影によって電磁力・電磁現象が同一であるとの保障、制約はない。
【００３７】
なお、上記の射影手法における条件として、Ｚ軸は曲線であっても、線ＬＰがＺ軸に平行であればよい。また、基準線は、自由表面形状の変形によっても、電磁力の射影がスムースにいくように選択する。
【００３８】
図４には、上記実施の形態の電磁流体解析による結果を示す。同図には、２００[Hz]の交番磁場における測定結果（実線）と上記実施の形態の電磁流体解析による計算結果（点線）とを示し、横軸は時間[sec]、縦軸は自由表面変位[mm]を表す。
【００３９】
条件として、容器１０１の内幅（図６のｘ、ｙ）が１００[mm]、内高さ（図６のｚ）が２１５[mm]、厚さが２４．５[mm]である。また、流体１０２として水銀を用い、導電率が１．０×１０⁶[S/m]、質量密度が１３．５×１０³[kg/m³]、粘性が１．５５×１０^-3[Pa・s]である。また、電磁コイル１０３に流す電流が２１６００[AT]、周波数が２００[Hz]である。
【００４０】
図４からも分かるように、上記実施の形態の電磁流体解析による計算結果（点線）として、実測値（実線）と比べても概ね良好な結果が得られた。
【００４１】
図５には、電磁流体解析装置を構成可能なハードウェア構成の一例を示す。同図に示すように本実施の形態の電磁流体解析装置６５０は、ＣＰＵ６５１と、ＲＯＭ６５２と、ＲＡＭ６５３と、キーボード（ＫＢ）６５９のキーボードコントローラ（ＫＢＣ）６５５と、表示部としてのディスプレイ（ＣＲＴ）６６０のディスプレイコントローラ（ＣＲＴＣ）６５６と、ハードディスク（ＨＤ）６６１及びフレキシブルディスク（ＦＤ）６６２のディスクコントローラ（ＤＫＣ）６５７と、ネットワー６７０との接続のためのネットワークインターフェースコントローラ（ＮＩＣ）６５８とが、システムバス６５４を介して互いに通信可能に接続されて構成されている。
【００４２】
ＣＰＵ６５１は、ＲＯＭ６５２或いはハードディスク６６１に記憶されたソフトウェア、或いはＦＤ６６２より供給されるソフトウェアを実行することで、システムバス６５４に接続された各構成部を総括的に制御する。すなわち、ＣＰＵ６５１は、所定の処理シーケンスに従った処理プログラムを、ＲＯＭ６５２、或いはハードディスク６６１、或いはフレキシブルディスク６６２から読み出して実行することで、本実施の形態での動作を実現するための制御を行う。
【００４３】
ＲＡＭ６５３は、ＣＰＵ６５１の主メモリ或いはワークエリア等として機能する。
【００４４】
キーボードコントローラＫＢＣ６５５は、キーボードＫＢ６５９や図示していないポインティングデバイス等からの指示入力を制御する。
【００４５】
ディスプレイコントローラ６５６は、ディスプレイ６６０の表示を制御する。
【００４６】
ディスクコントローラ６５７は、ブートプログラム、種々のアプリケーション、編集ファイル、ユーザファイル、ネットワーク管理プログラム、及び本実施の形態における所定の処理プログラム等を記憶するハードディスク６６１及びフレキシブルディスク６６２とのアクセスを制御する。
【００４７】
ネットワークインターフェースコントローラ６５８は、ネットワーク６７０上の装置或いはシステムと双方向にデータをやりとりする。
【００４８】
上記のように構成された電磁流体解析装置６５０において、ＣＰＵ６５１、ＲＯＭ６５２、及びＲＡＭ６５３により上記実施の形態で説明した各処理が行われ、本発明でいう演算手段が構成されるものである。
【００４９】
（その他の実施の形態）
上述した実施の形態の機能を実現するべく各種のデバイスを動作させるように、該各種デバイスと接続された装置或いはシステム内のコンピュータに対し、上記実施の形態の機能を実現するためのソフトウェアのプログラムコードを供給し、そのシステム或いは装置のコンピュータ（ＣＰＵ或いはＭＰＵ）に格納されたプログラムに従って上記各種デバイスを動作させることによって実施したものも、本発明の範疇に含まれる。
【００５０】
また、この場合、上記ソフトウェアのプログラムコード自体が上述した実施の形態の機能を実現することになり、そのプログラムコード自体は本発明を構成する。そのプログラムコードの伝送媒体としては、プログラム情報を搬送波として伝搬させて供給するためのコンピュータネットワーク（ＬＡＮ、インターネット等のＷＡＮ、無線通信ネットワーク等）システムにおける通信媒体（光ファイバ等の有線回線や無線回線等）を用いることができる。
【００５１】
さらに、上記プログラムコードをコンピュータに供給するための手段、例えばかかるプログラムコードを格納した記録媒体は本発明を構成する。かかるプログラムコードを記憶する記録媒体としては、例えばフレキシブルディスク、ハードディスク、光ディスク、光磁気ディスク、ＣＤ−ＲＯＭ、磁気テープ、不揮発性のメモリカード、ＲＯＭ等を用いることができる。
【００５２】
なお、上記実施の形態において示した各部の形状及び構造は、何れも本発明を実施するにあたっての具体化のほんの一例を示したものに過ぎず、これらによって本発明の技術的範囲が限定的に解釈されてはならない。すなわち、本発明はその精神、又はその主要な特徴から逸脱することなく、様々な形で実施することができる。
【００５３】
【発明の効果】
以上述べたように本発明によれば、電磁場解析及び流体解析を繰り返すのではなく、いったん電磁場解析を行ったならば、その後は流体解析及び射影を繰り返せばよいので、計算負荷を軽減することができ、電気伝導性流体の自由表面形状の変形を考慮しつつ簡単な計算により電磁流体解析を行うことができる。
【図面の簡単な説明】
【図１】電磁流体解析処理の流れを説明するためのフローチャートである。
【図２】第１の実施の形態における射影手法を説明するための図である。
【図３】第２の実施の形態における射影手法を説明するための図である。
【図４】本実施の形態の手法を用いた電磁流体解析の結果を示す図である。
【図５】本実施の形態の電磁流体解析装置を構成可能なハードウェア構成の一例を示す図である。
【図６】電磁流体解析に用いられるモデルを説明するための図であり、（ａ）が平面図、（ｂ）が側面図である。
【図７】従来の電磁流体解析を説明するための図である。
【符号の説明】
１０１容器
１０２流体
１０３電磁コイル
６５０電磁流体解析装置
６５１ＣＰＵ
６５２ＲＯＭ
６５３ＲＡＭ
６５４システムバス
６５５キーボードコントローラ（ＫＢＣ）
６５６ディスプレイコントローラ（ＣＲＴＣ）
６５７ディスクコントローラ（ＤＫＣ）
６５８ネットワークインターフェースコントローラ（ＮＩＣ）
６５９キーボード
６６０ディスプレイ
６６１ハードディスク
６６２フレキシブルディスク
６７０ネットワーク[0001]
BACKGROUND OF THE INVENTION
The present invention relates to an electromagnetic fluid analysis method, an apparatus, a computer program, and a computer-readable storage medium for analyzing the motion of an electrically conductive fluid on which an electromagnetic force acts.
[0002]
[Prior art]
Electromagnetic fluid analysis (MHD (magneto hydro dynamic) analysis) analyzes the motion of an electrically conductive fluid under the action of an electromagnetic field. For example, as shown in FIG. 6, a fluid 102 such as mercury is put in a container 101, and an electromagnetic force is applied to the fluid 102 by causing a current to flow through an electromagnetic coil 103 wound around the side wall of the container 101. Analyze movement.
[0003]
In the electromagnetic fluid analysis, as shown in FIG. 7, after obtaining the electromagnetic force using Maxwell's equation (electromagnetic field analysis), the motion of the fluid 102 due to the electromagnetic force is analyzed using the Navier-Stokes equation. Determine the surface shape (fluid analysis). As a free surface modeling method in fluid analysis, for example, the VOF method (volume of fluid) is known.
[0004]
When the free surface shape of the fluid 102 is deformed, the boundary conditions in the Maxwell equation also change. Therefore, after obtaining the electromagnetic force after the deformation of the free surface shape using the Maxwell equation, the motion of the fluid 102 due to the electromagnetic force is determined by Navier.・ Analyze using Stokes equation and obtain free surface shape by VOF method.
[0005]
By repeating these electromagnetic field analysis and fluid analysis, the motion of the fluid 102 can be dynamically analyzed.
[0006]
[Problems to be solved by the invention]
However, in the method of repeating the above-described electromagnetic field analysis and fluid analysis, it is necessary to perform an electromagnetic field analysis on an occasional flow, that is, a free surface shape, which increases the calculation load and takes a lot of calculation time.
[0007]
In addition, it is conceivable to analyze the fluid 102 with the free surface shape fixed, but this results in poor analysis accuracy.
[0008]
The present invention has been made in view of the above points, and an object thereof is to enable an electromagnetic fluid analysis by a simple calculation while taking into account the deformation of the free surface shape of an electrically conductive fluid.
[0009]
[Means for Solving the Problems]
The electromagnetic fluid analysis method of the present invention is a method in which an electroconductive fluid is put in a container, and an electromagnetic force is applied to the electroconductive fluid by passing an electric current through an electromagnetic coil wound around the side wall of the container. An electromagnetic fluid analysis method for analyzing the motion of the electrically conductive fluid, comprising: an electromagnetic field analysis procedure for calculating and obtaining an electromagnetic force acting on the electrically conductive fluid by passing a current through the electromagnetic coil; In a plane including a fluid analysis procedure for calculating and determining the deformation of the free surface shape of the electrically conductive fluid and the point P1 in the electrically conductive fluid before deformation and the central axis of the electromagnetic coil, the point P1 passes through the point P1 The intersection point between the straight line perpendicular to the central axis and the free surface before deformation is defined as point Q1, the intersection point between the straight line passing through the point Q1 and parallel to the central axis and the free surface after deformation is defined as point Q2, and the point Q2 passes through the point Q2. A straight line perpendicular to the central axis and the point P1 The intersection point with the straight line parallel to the central axis is defined as a point P2 in the electrically conductive fluid after deformation, and the electromagnetic force at the point P1 in the electrically conductive fluid before deformation is defined as a point P2 in the electrically conductive fluid after deformation. The electromagnetic force calculation procedure for calculating the electromagnetic force at an arbitrary position in the electrically conductive fluid after deformation, and the fluid analysis procedure and the electromagnetic force calculation procedure are repeated.
In another electromagnetic fluid analysis method of the present invention, an electroconductive fluid is placed in a container, and an electromagnetic force is applied to the electroconductive fluid by flowing an electric current through an electromagnetic coil wound around the side wall of the container. An electromagnetic fluid analysis method for analyzing the motion of the electrically conductive fluid at the time, comprising: an electromagnetic field analysis procedure for calculating and obtaining an electromagnetic force acting on the electrically conductive fluid by passing a current through the electromagnetic coil; A fluid analysis procedure for calculating the deformation of the free surface shape of the electrically conductive fluid by force, and a reference surface that is a surface perpendicular to the central axis of the electromagnetic coil at a position lower than the free surface of the electrically conductive fluid , The intersection of the straight line passing through the point P1 in the pre-deformation electrically conductive fluid and parallel to the central axis and the reference plane is a reference point O, and the intersection of the straight line and the free surface before deformation is the point Q1, Intersection of straight line and free surface after deformation And the point Q2, is on a straight line position undetermined point P2, the distance from the reference point O to each point P1, Q1, Q2, P2, proportional Equation 8]

Is determined as a point P2 in the post-deformation electrically conductive fluid, and the electromagnetic force at the point P1 in the pre-deformation electroconductive fluid is defined as a point in the post-deformation electroconductive fluid. An electromagnetic force calculation procedure for calculating an electromagnetic force at an arbitrary position of the deformed electrically conductive fluid as the electromagnetic force at the point P2, and the fluid analysis procedure and the electromagnetic force calculation procedure are repeated. Have
[0010]
The electromagnetic fluid analyzing apparatus according to the present invention is configured such that an electrically conductive fluid is put in a container, and an electromagnetic force is applied to the electrically conductive fluid by causing an electric current to flow through an electromagnetic coil wound around the side wall of the container. A magnetohydrodynamic analysis apparatus for analyzing the motion of the electrically conductive fluid, the first computing means for calculating and obtaining an electromagnetic force acting on the electrically conductive fluid by passing a current through the electromagnetic coil; In a plane including second calculation means for calculating and determining the deformation of the free surface shape of the electrically conductive fluid due to force, the point P1 in the electrically conductive fluid before deformation and the central axis of the electromagnetic coil, the point The point of intersection between the straight line passing through P1 and perpendicular to the central axis and the free surface before deformation is point Q1, the point of intersection between the straight line passing through point Q1 and parallel to the central axis and the free surface after deformation is point Q2, A straight line passing through Q2 and perpendicular to the central axis and the point P1 The intersection point with the straight line parallel to the central axis is a point P2 in the electrically conductive fluid after deformation, and the electromagnetic force at the point P1 in the electrically conductive fluid before deformation is the point P2 in the electrically conductive fluid after deformation. A third calculation means for calculating an electromagnetic force at an arbitrary position in the electrically conductive fluid after deformation as the electromagnetic force in the fluid, and the fluid analysis by the second calculation means and the electromagnetic force by the third calculation means. It is characterized in that force calculation is repeated.
Another electromagnetic fluid analyzing apparatus according to the present invention puts an electrically conductive fluid in a container and causes an electromagnetic force to act on the electrically conductive fluid by flowing an electric current through an electromagnetic coil wound around the side wall of the container. A first fluid calculation device for analyzing the motion of the electrically conductive fluid at the time, wherein the first computing means calculates and obtains an electromagnetic force acting on the electrically conductive fluid by passing a current through the electromagnetic coil; Second calculating means for calculating and calculating deformation of the free surface shape of the electrically conductive fluid by electromagnetic force, and a surface perpendicular to the central axis of the electromagnetic coil at a position lower than the free surface of the electrically conductive fluid And the intersection of the straight line passing through the point P1 in the electrically conductive fluid before deformation and parallel to the central axis and the reference surface is a reference point O, and the intersection of the straight line and the free surface before deformation is Point Q1, intersection of the straight line and the free surface after deformation Was a point Q2, it is on a straight line position undetermined point P2, the distance from the reference point O to each point P1, Q1, Q2, P2, proportional Equation 9]

Is determined as a point P2 in the post-deformation electrically conductive fluid, and the electromagnetic force at the point P1 in the pre-deformation electroconductive fluid is defined as a point in the post-deformation electroconductive fluid. A third calculation means for calculating an electromagnetic force at an arbitrary position of the electrically conductive fluid after deformation as the electromagnetic force at the point P2, and fluid analysis by the second calculation means and the third calculation. It is characterized in that the electromagnetic force calculation by the means is repeated.
[0011]
The computer program of the present invention puts the electric conductive fluid into a container and applies the electric force to the electric conductive fluid by causing an electric current to flow through an electromagnetic coil wound around the side wall of the container. A computer program for causing a computer to execute a process for analyzing a motion of a conductive fluid, wherein an electromagnetic field analysis process for calculating and obtaining an electromagnetic force acting on the electrically conductive fluid by passing a current through the electromagnetic coil; In a plane including a fluid analysis process for calculating and calculating the deformation of the free surface shape of the electrically conductive fluid due to force, and the point P1 in the electrically conductive fluid before deformation and the central axis of the electromagnetic coil, the point P1 is A point of intersection between the straight line perpendicular to the central axis and the free surface before deformation is defined as a point Q1, and a point of intersection between the straight line passing through the point Q1 and parallel to the central axis and the free surface after deformation is defined as a point Q2. 2 is defined as a point P2 in the electrically conductive fluid after deformation, and the point P1 in the electrically conductive fluid before deformation is defined as an intersection of the straight line passing through the line 2 and perpendicular to the central axis and parallel to the central axis. The computer executes an electromagnetic force calculation process for calculating an electromagnetic force at an arbitrary position in the post-deformation electrically conductive fluid as an electromagnetic force at the point P2 in the post-deformation electrically conductive fluid. It is characterized in that the analysis process and the electromagnetic force calculation process are repeated.
According to another computer program of the present invention, when an electrically conductive fluid is placed in a container and an electric current is applied to an electromagnetic coil wound around the side wall of the container, an electromagnetic force is applied to the electrically conductive fluid. A computer program for causing a computer to execute a process for analyzing the motion of the electrically conductive fluid, the electromagnetic field analyzing process for calculating and obtaining an electromagnetic force acting on the electrically conductive fluid by passing a current through the electromagnetic coil; A fluid analysis process for calculating the deformation of the free surface shape of the electrically conductive fluid by electromagnetic force, and a plane perpendicular to the central axis of the electromagnetic coil at a position lower than the free surface of the electrically conductive fluid Considering the reference plane, the intersection of the straight line passing through the point P1 in the pre-deformation electrically conductive fluid and parallel to the central axis and the reference plane is the reference point O, and the intersection of the straight line and the free surface before deformation is the intersection. Q1, the intersection of the straight line and the free surface after deformation is defined as point Q2, and the point P2 on the straight line and whose position is undetermined is proportional to the distance from the reference point O to each of the points P1, Q1, Q2, and P2. Formula [10]

Is determined as a point P2 in the post-deformation electrically conductive fluid, and the electromagnetic force at the point P1 in the pre-deformation electroconductive fluid is defined as a point in the post-deformation electroconductive fluid. As the electromagnetic force at the point P2, the computer is caused to execute an electromagnetic force calculation process for calculating an electromagnetic force at an arbitrary position of the deformed electrically conductive fluid, and the fluid analysis process and the electromagnetic force calculation process are repeated. It has the characteristics.
[0012]
The computer-readable storage medium of the present invention is characterized in that the computer program of the present invention is stored.
[0013]
DETAILED DESCRIPTION OF THE INVENTION
DESCRIPTION OF EXEMPLARY EMBODIMENTS Hereinafter, preferred embodiments of an electromagnetic fluid analysis method, an apparatus, a computer program, and a computer-readable storage medium according to the invention will be described with reference to the drawings.
[0014]
(First embodiment)
The magnetohydrodynamic analysis in the present embodiment will be described. As shown in FIG. 6, a fluid 102 such as mercury is put in a container 101, and an electromagnetic force is applied to the fluid 102 by causing a current to flow through an electromagnetic coil 103 wound around the side wall of the container 101.
[0015]
In the electromagnetic fluid analysis, as shown in FIG. 1, first, an electromagnetic force is obtained (step S1). The electromagnetic force F _em is obtained as shown in the following equation (5) using Maxwell's equation (ignoring displacement current) shown in the following equations (1) to (4).
[0016]
[Expression 2]

[0017]
Next, the motion of the fluid 102 due to the electromagnetic force F _em is analyzed using the Navier-Stokes equation shown in the following formula (6), and the deformation of the free surface shape is obtained by, for example, the VOF (volume of fluid) method ( Step S2). In the VOF method, a cell divided into a plurality of parts is considered, and after the liquid filling rate of each cell (a value between 0 and 1) is defined, the liquid position in the coexistence cell where the liquid and the gas coexist is determined. Determine the liquid filling rate of each cell according to the calculated flow field. Then, the movement of the liquid level is analyzed by repeating the calculation by advancing the time. In this case, the time dependency of the liquid filling rate is governed by the following equation (7).
[0018]
[Equation 3]

[0019]
[Expression 4]

[0020]
Next, a point P2 in the fluid after deformation obtained by projecting (mapping) an arbitrary point P1 in the fluid 102 before deformation of the fluid 102 is obtained, and an electromagnetic force at the point P2 is obtained based on the electromagnetic force at the point P1 (step S3). .
[0021]
Here, with reference to FIG. 2, the projection method in this Embodiment is demonstrated. A direction (Z axis) in which the free surface shape of the fluid 102 is deformed by electromagnetic force is assumed. That is, it is assumed that the free surface shape of the fluid 102 becomes a convex shape in the Z-axis direction due to the electromagnetic force.
[0022]
Now, it is assumed that the pre-deformation free surface (dotted line S1 in the figure) is transformed into the post-deformation free surface (solid line S2 in the figure) by electromagnetic force. In this case, how to project an arbitrary point P1 in the fluid before deformation onto the point P2 in the fluid after deformation is a proposition. If this proposition is solved, the electromagnetic force distribution in the post-deformation fluid can be obtained by using the electromagnetic force at the point P1 as the electromagnetic force at the point P2.
[0023]
Therefore, in the present embodiment, a line (plane) L1 perpendicular to the Z axis passing through an arbitrary point P1 in the fluid before deformation is considered, and an intersection point between the line L1 and the free surface S1 before deformation is defined as Q1. Next, a line LQ parallel to the Z-axis passing through the point Q1 is considered, and an intersection of the line LQ and the free surface after deformation S2 is defined as Q2. A line (surface) L2 perpendicular to the Z axis passing through the point Q2 is considered, and a point where the line L2 and a line LP parallel to the Z axis passing through the point P1 intersect is defined as P2. As a result, an arbitrary point P1 in the fluid before deformation is projected (mapped) one-to-one on the point P2 in the fluid after deformation.
[0024]
That is, in the direction perpendicular to the electromagnetic coil 103, equal to the distance from the electromagnetic coil 103 of the point P _1, the distance from the electromagnetic coil 103 of the point P _2. Then, equal to the distance from the undeformed free surface S ₁ on the point to Q ₁ electromagnetic coil 103 a distance between the deformed free surface S ₂ on the point Q ₂ of the electromagnetic coil 103 from the, also, the point Q _1, point equal to the distance P ₂ -Q ₂ and the distance P ₁ -Q ₁ and point Q ₂ and the point P ₂ and P _1. Accordingly, the boundary point Q _1, Q ₂ along line L ₁ and the line L _2, the point P _1, P ₂ in the conductor (the fluid 102), the same as the electromagnetic phenomena in one dimension (two-dimensional) Yes, it can be said that the electromagnetic phenomenon is the same even if the electromagnetic force at the point P ₁ is projected onto the electromagnetic force at the point P ₂ .
[0025]
As described above, since the arbitrary point P1 in the fluid before deformation is projected (mapped) one-to-one on the point P2 in the fluid after deformation, the electromagnetic force at any point in the fluid after deformation is obtained. be able to.
[0026]
As a condition in the above projection method, the Z axis needs to be parallel to the electromagnetic coil 103. Even if the Z axis is a curve, the Z axis, the electromagnetic coil 103, the line LP, and the line LQ may be parallel to each other.
[0027]
Returning to FIG. 1, when the electromagnetic force at the point P2 in the deformed fluid is obtained as described above, it is determined whether or not the electromagnetic fluid analysis is finished (step S4). Returning to, fluid analysis is performed based on the electromagnetic force obtained by the projection. By repeating these fluid analysis and projection, the motion of the fluid 102 can be dynamically analyzed.
[0028]
According to the embodiment described above, instead of repeating the electromagnetic field analysis and the fluid analysis, once the electromagnetic field analysis is performed, the fluid analysis and the projection may be repeated thereafter, so that the calculation load can be reduced. .
[0029]
Further, since the analysis is performed by capturing the deformation of the free surface shape of the fluid, the analysis accuracy can be improved as compared with the case where the analysis is performed by fixing the free surface shape.
[0030]
(Second Embodiment)
The second embodiment is an example in which the process of step S3 in the flowchart of FIG. 1, that is, the projection method is changed. Hereinafter, the projection method in the present embodiment will be described with reference to FIG. In the first embodiment, it is assumed that the free surface shape is deformed into a convex shape, but it may be deformed into an uneven shape. Therefore, in the present embodiment, modeling in such a case is considered.
[0031]
Considering a line (plane) LP parallel to the Z axis passing through an arbitrary point P1 in the fluid before deformation, the intersection of the line LP and the free surface S1 before deformation is defined as Q1, and the intersection of the line LP and the free surface S2 after deformation. Is Q2.
[0032]
A reference line that is a line (plane) perpendicular to the Z-axis is considered, and an intersection with the line LP is set as a reference point O.
[0033]
And the point which satisfy | fills the following Formula is set to P2 with respect to the point in the fluid after a deformation | transformation.
[0034]
[Equation 5]

[0035]
The point P2 exists in the fluid after deformation and represents an arbitrary point. That is, since an arbitrary point P1 in the fluid before deformation is projected (mapped) one-to-one on the point P2 in the fluid after deformation, the electromagnetic force at the point P1 is set as the electromagnetic force at the point P2.
[0036]
In the present embodiment, even when the free surface shape is uneven, the electromagnetic force at an arbitrary point in the fluid after deformation can be obtained. However, in the first embodiment, a point where the distance to the electromagnetic coil 103 is constant is obtained, and there is a restriction in the electromagnetic phenomenon. However, in this embodiment, there is no restriction, so there is a one-to-one relationship. There is no guarantee or restriction that the electromagnetic force and phenomenon are the same by projection.
[0037]
As a condition in the above projection method, the line LP may be parallel to the Z axis even if the Z axis is a curve. The reference line is selected so that the projection of the electromagnetic force goes smoothly even when the free surface shape is deformed.
[0038]
In FIG. 4, the result by the electromagnetic fluid analysis of the said embodiment is shown. The figure shows the measurement result (solid line) in an alternating magnetic field of 200 [Hz] and the calculation result (dotted line) by the magnetohydrodynamic analysis of the above embodiment, the horizontal axis is time [sec], and the vertical axis is the free surface. Indicates displacement [mm].
[0039]
As conditions, the inner width (x, y in FIG. 6) of the container 101 is 100 [mm], the inner height (z in FIG. 6) is 215 [mm], and the thickness is 24.5 [mm]. Further, mercury is used as the fluid 102, the conductivity is 1.0 × 10 ⁶ [S / m], the mass density is 13.5 × 10 ³ [kg / m ³ ], and the viscosity is 1.55 × 10 ⁻³ [ Pa · s]. The current flowing through the electromagnetic coil 103 is 21600 [AT] and the frequency is 200 [Hz].
[0040]
As can be seen from FIG. 4, as the calculation result (dotted line) by the electromagnetic fluid analysis of the above embodiment, a generally good result was obtained even when compared with the actual measurement value (solid line).
[0041]
FIG. 5 shows an example of a hardware configuration capable of configuring the electromagnetic fluid analyzing apparatus. As shown in the figure, the electromagnetic fluid analyzing apparatus 650 of this embodiment includes a CPU 651, a ROM 652, a RAM 653, a keyboard controller (KBC) 655 of a keyboard (KB) 659, and a display (CRT) 660 as a display unit. Display controller (CRTC) 656, hard disk (HD) 661 and flexible disk (FD) 662 disk controller (DKC) 657, and network interface controller (NIC) 658 for connection to network 670. The buses 654 are communicably connected to each other.
[0042]
The CPU 651 comprehensively controls each component connected to the system bus 654 by executing software stored in the ROM 652 or the hard disk 661 or software supplied from the FD 662. That is, the CPU 651 performs a control for realizing the operation according to the present embodiment by reading a processing program according to a predetermined processing sequence from the ROM 652, the hard disk 661, or the flexible disk 662 and executing it.
[0043]
The RAM 653 functions as a main memory or work area for the CPU 651.
[0044]
The keyboard controller KBC 655 controls an instruction input from a keyboard KB 659 or a pointing device (not shown).
[0045]
The display controller 656 controls display on the display 660.
[0046]
The disk controller 657 controls access to the hard disk 661 and the flexible disk 662 that store a boot program, various applications, edit files, user files, a network management program, a predetermined processing program in the present embodiment, and the like.
[0047]
The network interface controller 658 exchanges data bidirectionally with devices or systems on the network 670.
[0048]
In the electromagnetic fluid analyzing apparatus 650 configured as described above, each processing described in the above embodiment is performed by the CPU 651, the ROM 652, and the RAM 653, and the arithmetic means referred to in the present invention is configured.
[0049]
(Other embodiments)
Software program for realizing the functions of the above-described embodiment for an apparatus or a computer in the system connected to the various devices so as to operate the various devices to realize the functions of the above-described embodiments. What was implemented by supplying the code and operating the various devices in accordance with a program stored in a computer (CPU or MPU) of the system or apparatus is also included in the scope of the present invention.
[0050]
In this case, the program code of the software itself realizes the functions of the above-described embodiments, and the program code itself constitutes the present invention. As a transmission medium for the program code, a communication medium (wired line or wireless line such as an optical fiber) in a computer network (LAN, WAN such as the Internet, wireless communication network, etc.) system for propagating and supplying program information as a carrier wave Etc.) can be used.
[0051]
Further, means for supplying the program code to the computer, for example, a recording medium storing the program code constitutes the present invention. As a recording medium for storing the program code, for example, a flexible disk, a hard disk, an optical disk, a magneto-optical disk, a CD-ROM, a magnetic tape, a nonvolatile memory card, a ROM, or the like can be used.
[0052]
It should be noted that the shapes and structures of the respective parts shown in the above embodiments are merely examples of implementation in carrying out the present invention, and these limit the technical scope of the present invention. Should not be interpreted. That is, the present invention can be implemented in various forms without departing from the spirit or the main features thereof.
[0053]
【The invention's effect】
As described above, according to the present invention, instead of repeating the electromagnetic field analysis and the fluid analysis, once the electromagnetic field analysis is performed, the fluid analysis and the projection may be repeated thereafter, so that the calculation load can be reduced. The electromagnetic fluid analysis can be performed by a simple calculation while taking into account the deformation of the free surface shape of the electrically conductive fluid.
[Brief description of the drawings]
FIG. 1 is a flowchart for explaining a flow of electromagnetic fluid analysis processing;
FIG. 2 is a diagram for explaining a projection method in the first embodiment.
FIG. 3 is a diagram for explaining a projection method according to a second embodiment.
FIG. 4 is a diagram showing the results of magnetohydrodynamic analysis using the method of the present embodiment.
FIG. 5 is a diagram illustrating an example of a hardware configuration capable of configuring the magnetohydrodynamic analysis device of the present embodiment.
6A and 6B are diagrams for explaining a model used for electromagnetic fluid analysis, where FIG. 6A is a plan view and FIG. 6B is a side view.
FIG. 7 is a diagram for explaining conventional electromagnetic fluid analysis;
[Explanation of symbols]
101 Container 102 Fluid 103 Electromagnetic Coil 650 Electromagnetic Fluid Analyzer 651 CPU
652 ROM
653 RAM
654 System bus 655 Keyboard controller (KBC)
656 Display Controller (CRTC)
657 Disk controller (DKC)
658 Network Interface Controller (NIC)
659 Keyboard 660 Display 661 Hard disk 662 Flexible disk 670 Network

Claims

Analysis of the motion of the electrically conductive fluid when an electromagnetic force is applied to the electrically conductive fluid by putting an electrically conductive fluid in the container and passing an electric current through an electromagnetic coil wound around the side wall of the container. An electromagnetic fluid analysis method for
An electromagnetic field analysis procedure for calculating and obtaining an electromagnetic force acting on the electrically conductive fluid by passing a current through the electromagnetic coil;
A fluid analysis procedure for calculating and calculating the deformation of the free surface shape of the electrically conductive fluid by electromagnetic force;
In a plane including the point P1 in the pre-deformation electrically conductive fluid and the central axis of the electromagnetic coil, an intersection of a straight line passing through the point P1 and perpendicular to the central axis and the free surface before deformation is defined as a point Q1, An intersection of a straight line passing through Q1 and parallel to the central axis and the free surface after deformation is defined as a point Q2, a straight line passing through the point Q2 and perpendicular to the central axis, and a straight line passing through the point P1 and parallel to the central axis. The intersection point is defined as a point P2 in the electrically conductive fluid after deformation, and the electromagnetic force at the point P1 in the electrically conductive fluid before deformation is defined as the electromagnetic force at the point P2 in the electrically conductive fluid after deformation. An electromagnetic force calculation procedure for calculating an electromagnetic force at an arbitrary position in the fluid,
An electromagnetic fluid analysis method comprising repeating the fluid analysis procedure and the electromagnetic force calculation procedure.

Analysis of the motion of the electrically conductive fluid when an electromagnetic force is applied to the electrically conductive fluid by putting an electrically conductive fluid in the container and passing an electric current through an electromagnetic coil wound around the side wall of the container. An electromagnetic fluid analysis method for
An electromagnetic field analysis procedure for calculating and obtaining an electromagnetic force acting on the electrically conductive fluid by passing a current through the electromagnetic coil;
A fluid analysis procedure for calculating and calculating the deformation of the free surface shape of the electrically conductive fluid by electromagnetic force;
Considering a reference plane which is a plane perpendicular to the central axis of the electromagnetic coil at a position lower than the free surface of the electrically conductive fluid, a straight line passing through the point P1 in the electrically conductive fluid before deformation and parallel to the central axis The point of intersection with the reference plane is the reference point O, the point of intersection of the straight line and the free surface before deformation is the point Q1, the point of intersection of the straight line and the free surface after deformation is the point Q2, and the position on the straight line is undetermined The point P2 is proportional to the distance from the reference point O to each of the points P1, Q1, Q2, and P2.

Is determined as a point P2 in the post-deformation electrically conductive fluid, and the electromagnetic force at the point P1 in the pre-deformation electroconductive fluid is defined as a point in the post-deformation electroconductive fluid. An electromagnetic force calculation procedure for calculating an electromagnetic force at an arbitrary position of the electrically conductive fluid after deformation as the electromagnetic force at the point P2,
An electromagnetic fluid analysis method comprising repeating the fluid analysis procedure and the electromagnetic force calculation procedure.

Analysis of the motion of the electrically conductive fluid when an electromagnetic force is applied to the electrically conductive fluid by putting an electrically conductive fluid in the container and passing an electric current through an electromagnetic coil wound around the side wall of the container. An electromagnetic fluid analyzing device,
First calculating means for calculating and obtaining an electromagnetic force acting on the electrically conductive fluid by passing a current through the electromagnetic coil;
A second computing means for calculating and determining the deformation of the free surface shape of the electrically conductive fluid by electromagnetic force;
In a plane including the point P1 in the pre-deformation electrically conductive fluid and the central axis of the electromagnetic coil, an intersection of a straight line passing through the point P1 and perpendicular to the central axis and the free surface before deformation is defined as a point Q1, An intersection of a straight line passing through Q1 and parallel to the central axis and the free surface after deformation is defined as a point Q2, a straight line passing through the point Q2 and perpendicular to the central axis, and a straight line passing through the point P1 and parallel to the central axis. The intersection point is defined as a point P2 in the electrically conductive fluid after deformation, and the electromagnetic force at the point P1 in the electrically conductive fluid before deformation is defined as the electromagnetic force at the point P2 in the electrically conductive fluid after deformation. Third calculating means for calculating an electromagnetic force at an arbitrary position in the fluid,
An electromagnetic fluid analyzing apparatus characterized in that the fluid analysis by the second calculation means and the electromagnetic force calculation by the third calculation means are repeated.

Analysis of the motion of the electrically conductive fluid when an electromagnetic force is applied to the electrically conductive fluid by putting an electrically conductive fluid in the container and passing an electric current through an electromagnetic coil wound around the side wall of the container. An electromagnetic fluid analyzing device,
First calculating means for calculating and obtaining an electromagnetic force acting on the electrically conductive fluid by passing a current through the electromagnetic coil;
A second computing means for calculating and determining the deformation of the free surface shape of the electrically conductive fluid by electromagnetic force;
Considering a reference plane which is a plane perpendicular to the central axis of the electromagnetic coil at a position lower than the free surface of the electrically conductive fluid, a straight line passing through the point P1 in the electrically conductive fluid before deformation and parallel to the central axis The point of intersection with the reference plane is the reference point O, the point of intersection of the straight line and the free surface before deformation is the point Q1, the point of intersection of the straight line and the free surface after deformation is the point Q2, and the position on the straight line is undetermined The point P2 is proportional to the distance from the reference point O to each of the points P1, Q1, Q2, and P2.

Is determined as a point P2 in the post-deformation electrically conductive fluid, and the electromagnetic force at the point P1 in the pre-deformation electroconductive fluid is defined as a point in the post-deformation electroconductive fluid. A third calculating means for calculating the electromagnetic force at an arbitrary position of the electrically conductive fluid after deformation as the electromagnetic force at the point P2,
An electromagnetic fluid analyzing apparatus characterized in that the fluid analysis by the second calculation means and the electromagnetic force calculation by the third calculation means are repeated.

Analysis of the motion of the electrically conductive fluid when an electromagnetic force is applied to the electrically conductive fluid by putting an electrically conductive fluid in the container and passing an electric current through an electromagnetic coil wound around the side wall of the container. A computer program for causing a computer to execute processing to be performed,
An electromagnetic field analysis process for calculating and obtaining an electromagnetic force acting on the electrically conductive fluid by passing a current through the electromagnetic coil;
Fluid analysis processing for calculating and calculating the deformation of the free surface shape of the electrically conductive fluid by electromagnetic force;
In a plane including the point P1 in the pre-deformation electrically conductive fluid and the central axis of the electromagnetic coil, an intersection of a straight line passing through the point P1 and perpendicular to the central axis and the free surface before deformation is defined as a point Q1, An intersection of a straight line passing through Q1 and parallel to the central axis and the free surface after deformation is defined as a point Q2, a straight line passing through the point Q2 and perpendicular to the central axis, and a straight line passing through the point P1 and parallel to the central axis. The intersection point is defined as a point P2 in the electrically conductive fluid after deformation, and the electromagnetic force at the point P1 in the electrically conductive fluid before deformation is defined as the electromagnetic force at the point P2 in the electrically conductive fluid after deformation. Causing the computer to execute an electromagnetic force calculation process for calculating an electromagnetic force at an arbitrary position in the fluid,
A computer program characterized by repeating the fluid analysis process and the electromagnetic force calculation process.

Analysis of the motion of the electrically conductive fluid when an electromagnetic force is applied to the electrically conductive fluid by putting an electrically conductive fluid in the container and passing an electric current through an electromagnetic coil wound around the side wall of the container. A computer program for causing a computer to execute processing to be performed,
An electromagnetic field analysis process for calculating and obtaining an electromagnetic force acting on the electrically conductive fluid by passing a current through the electromagnetic coil;
Fluid analysis processing for calculating and calculating the deformation of the free surface shape of the electrically conductive fluid by electromagnetic force;
Considering a reference plane which is a plane perpendicular to the central axis of the electromagnetic coil at a position lower than the free surface of the electrically conductive fluid, a straight line passing through the point P1 in the electrically conductive fluid before deformation and parallel to the central axis The point of intersection with the reference plane is the reference point O, the point of intersection of the straight line and the free surface before deformation is the point Q1, the point of intersection of the straight line and the free surface after deformation is the point Q2, and the position on the straight line is undetermined The point P2 is proportional to the distance from the reference point O to each of the points P1, Q1, Q2, and P2.

Is determined as a point P2 in the post-deformation electrically conductive fluid, and the electromagnetic force at the point P1 in the pre-deformation electroconductive fluid is defined as a point in the post-deformation electroconductive fluid. As an electromagnetic force at the point P2, the computer executes an electromagnetic force calculation process for calculating an electromagnetic force at an arbitrary position of the electrically conductive fluid after deformation,
A computer program characterized by repeating the fluid analysis process and the electromagnetic force calculation process.

A computer-readable storage medium storing the computer program according to claim 5 or 6.