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
P 0
P sh
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)
P 0
初期圧力(実数)
[
Pa
]
P sh
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
]
例
#---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)
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
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。
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@
は
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。
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@
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.
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)