/EOS/STIFF-GAS

ブロックフォーマットキーワード 強化ガスの理想気体の状態方程式 P ( μ , E ) = ( γ 1 ) ( 1 + μ ) E γ P * MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa WdbiaadcfadaqadaWdaeaapeGaeqiVd0MaaiilaiaadweaaiaawIca caGLPaaacqGH9aqpdaqadaWdaeaapeGaeq4SdCMaeyOeI0IaaGymaa GaayjkaiaawMcaamaabmaapaqaa8qacaaIXaGaey4kaSIaeqiVd0ga caGLOaGaayzkaaGaamyraiabgkHiTiabeo7aNjaadcfadaahaaWcbe qaaiaacQcaaaaaaa@4C31@ を記述します。

この状態方程式は元々、水中爆発の水をモデルにしたものです。

フォーマット

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/EOS/STIFF-GAS/mat_ID/unit_ID
eos_title
γ P0 Psh P * MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa WdbiaadcfadaahaaWcbeqaaiaacQcaaaaaaa@382F@ ρ 0

定義

フィールド 内容 SI 単位の例
mat_ID 材料識別子

(整数、最大10桁)

 
unit_ID 単位識別子

(整数、最大10桁)

 
eos_title 状態方程式のタイトル。

(文字、最大100文字)

 
γ 熱容量の比 γ = C p C v MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaeq4SdCMaeyypa0ZaaSaaa8aabaWdbiaadoeapaWaaSbaaSqaa8qa caWGWbaapaqabaaakeaapeGaam4qa8aadaWgaaWcbaWdbiaadAhaa8 aabeaaaaaaaa@3D36@

(実数)

 
P0 初期圧力

(実数)

[ Pa ]
Psh 圧力シフト

(実数)

[ Pa ]
P * MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa WdbiaadcfadaahaaWcbeqaaiaacQcaaaaaaa@382F@ EOS追加圧力項。

(実数)

[ Pa ]
ρ 0 参照密度

デフォルト = 材料密度(実数)

[ k g m 3 ]

#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
                   g                  mm                  ms
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW06/7/1
water
#              RHO_I        
               0.001          
#                 NU                PMIN
 
/EOS/STIFF-GAS/7/1
STIFF_GAS_WATER
#              GAMMA                  P0                 PSH              P_STAR                RHO0
                 6.1                0.10                   0              368.85  
/ALE/MAT/7
 
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#enddata

コメント

  1. (1)
    P ( μ , E ) = ( γ 1 ) ( 1 + μ ) E γ P * MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa WdbiaadcfadaqadaWdaeaapeGaeqiVd0MaaiilaiaadweaaiaawIca caGLPaaacqGH9aqpdaqadaWdaeaapeGaeq4SdCMaeyOeI0IaaGymaa GaayjkaiaawMcaamaabmaapaqaa8qacaaIXaGaey4kaSIaeqiVd0ga caGLOaGaayzkaaGaamyraiabgkHiTiabeo7aNjaadcfadaahaaWcbe qaaiaacQcaaaaaaa@4C31@
    ここで、
    E = E i n t V 0
    µ = ρ ρ 0 1
  2. 強化ガスEOSは、理想気体の状態方程式を基準にして、追加の圧力項( P * MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuamaaCa aaleqabaGaaiOkaaaaaaa@37A7@ )を導入します。EOSはこのフォームで記されます。なぜならば、水の中での音速は:(2)
    c s = γ ( P + P * ) ρ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4yamaaBa aaleaacaWGZbaabeaakiabg2da9maakaaabaWaaSaaaeaacqaHZoWz caGGOaGaamiuaiabgUcaRiaadcfadaahaaWcbeqaaiaacQcaaaGcca GGPaaabaGaeqyWdihaaaWcbeaaaaa@416E@

    このようにして、 P * P MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuamaaCa aaleqabaGaaiOkaaaakiablUMi=iaadcfaaaa@39E3@ を考慮することで、音速は P MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuaaaa@36CC@ の変動と c s γ P * ρ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4yamaaBa aaleaacaWGZbaabeaakiabgIKi7oaakaaabaWaaSaaaeaacqaHZoWz caWGqbWaaWbaaSqabeaacaGGQaaaaaGcbaGaeqyWdihaaaWcbeaaaa a@3F0A@ の影響を受けません。

  3. P * MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuamaaCa aaleqabaGaaiOkaaaaaaa@37A7@ は次のように計算できます:(3)
    P * = ρ c s 2 γ P MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuamaaCa aaleqabaGaaiOkaaaakiabg2da9maalaaabaGaeqyWdiNaam4yamaa DaaaleaacaWGZbaabaGaaGOmaaaaaOqaaiabeo7aNbaacqGHsislca WGqbaaaa@40C2@

    P * P MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuamaaCa aaleqabaGaaiOkaaaakiablUMi=iaadcfaaaa@39E3@ であるため、 P * ρ c s 2 γ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuamaaCa aaleqabaGaaiOkaaaakiabgIKi7oaalaaabaGaeqyWdiNaam4yamaa DaaaleaacaWGZbaabaGaaGOmaaaaaOqaaiabeo7aNbaaaaa@3FAB@ P * MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuamaaCa aaleqabaGaaiOkaaaaaaa@37A7@ の良好な推定につながります。

  4. 強化ガスOS 1は多項式EOSから導出することができます:(4)
    P = C 0 + C 1 μ + C 2 μ 2 + C 3 μ 3 + ( C 4 + C 5 μ ) E 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuaiabg2 da9iaadoeadaWgaaWcbaGaaGimaaqabaGccqGHRaWkcaWGdbWaaSba aSqaaiaaigdaaeqaaOGaeqiVd0Maey4kaSIaam4qamaaBaaaleaaca aIYaaabeaakiabeY7aTnaaCaaaleqabaGaaGOmaaaakiabgUcaRiaa doeadaWgaaWcbaGaaG4maaqabaGccqaH8oqBdaahaaWcbeqaaiaaio daaaGccqGHRaWkdaqadaqaaiaadoeadaWgaaWcbaGaaGinaaqabaGc cqGHRaWkcaWGdbWaaSbaaSqaaiaaiwdaaeqaaOGaeqiVd0gacaGLOa GaayzkaaGaamyramaaBaaaleaacaaIWaaabeaaaaa@5292@
    ここで、
    C 0 = γ P * MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBa aaleaacaaIWaaabeaakiabg2da9iabgkHiTiabeo7aNjaadcfadaah aaWcbeqaaiaacQcaaaaaaa@3CF9@
    C 1 = C 2 = C 3 = 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBa aaleaacaaIXaaabeaakiabg2da9iaadoeadaWgaaWcbaGaaGOmaaqa baGccqGH9aqpcaWGdbWaaSbaaSqaaiaaiodaaeqaaOGaeyypa0JaaG imaaaa@3EF1@
    C 4 = C 5 = γ 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBa aaleaacaaI0aaabeaakiabg2da9iaadoeadaWgaaWcbaGaaGynaaqa baGccqGH9aqpcqaHZoWzcqGHsislcaaIXaaaaa@3ECB@
    E 0 = P 0 C 0 C 4 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyramaaBa aaleaacaaIWaaabeaakiabg2da9maalaaabaGaamiuamaaBaaaleaa caaIWaaabeaakiabgkHiTiaadoeadaWgaaWcbaGaaGimaaqabaaake aacaWGdbWaaSbaaSqaaiaaisdaaeqaaaaaaaa@3EE3@
  5. たとえば水の場合、 ρ = 0.001 g . m m 3 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyWdiNaey ypa0JaaGimaiaac6cacaaIWaGaaGimaiaaigdacaWGNbGaaiOlaiaa d2gacaWGTbWaaWbaaSqabeaacqGHsislcaaIZaaaaaaa@41B1@ c s = 1500 m m . m s 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4yamaaBa aaleaacaWGZbaabeaakiabg2da9iaaigdacaaI1aGaaGimaiaaicda caWGTbGaamyBaiaac6cacaWGTbGaam4CamaaCaaaleqabaGaeyOeI0 IaaGymaaaaaaa@4255@ および γ = 6.1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4SdCMaey ypa0JaaGOnaiaac6cacaaIXaaaaa@3AD1@ は文献に記載されています。1 これが P * = 368.852 M P a MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuamaaCa aaleqabaGaaiOkaaaakiabg2da9iaaiodacaaI2aGaaGioaiaac6ca caaI4aGaaGynaiaaikdacaWGnbGaamiuaiaadggaaaa@4072@ につながります。したがって、強化ガスEOSは大気圧では次のような挙動を示します:


    図 1.
  6. Radiossにより流体力学的圧力の計算に用いられ、右記の材料則と適合性のある状態方程式:
    • /MAT/LAW3 (HYDPLA)
    • /MAT/LAW4 (HYD_JCOOK)
    • /MAT/LAW6 (HYDROまたはHYD_VISC)
    • /MAT/LAW10 (DPRAG1)
    • /MAT/LAW12 (3D_COMP)
    • /MAT/LAW49 (STEINB)
    • /MAT/LAW102 (DPRAG2)
    • /MAT/LAW103 (HENSEL-SPITTEL)
1 Cole, R. H.; "Underwater Explosions.Princeton University Press" Princeton, New Jersey (1948)