Tank Experiment

Injected mass curve and injection temperature can be obtained from:
  • the airbag manufacturer
  • a tank test
With a tank test it is possible to measure temperature at injection point or in the middle of the tank. For pressure the two values are equal.
図 1. Tank Experiment Schema


Tin and P are known

図 2.
m ˙ = d P d t V γ ( γ − 1 ) C V T i n MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aaceWGTbGbaiaacqGH9aqpdaWcaaqaamaalaaabaGaamizaiaadcfa aeaacaWGKbGaamiDaaaacaWGwbaabaGaeq4SdC2aaeWaaeaacqaHZo WzcqGHsislcaaIXaaacaGLOaGaayzkaaGaam4qamaaBaaaleaacaWG wbaabeaakiaadsfadaWgaaWcbaGaamyAaiaad6gaaeqaaaaaaaa@4AB1@

T and P are known

図 3.
m ˙ = ( T d P d t − P d T d t ) V γ ( γ − 1 ) C V T 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake Gabaaeoiqad2gagaGaaiabg2da9maalaaabaWaaeWaaeaacaWGubWa aSaaaeaacaWGKbGaamiuaaqaaiaadsgacaWG0baaaiabgkHiTiaadc fadaWcaaqaaiaadsgacaWGubaabaGaamizaiaadshaaaaacaGLOaGa ayzkaaGaamOvaaqaaiabeo7aNnaabmaabaGaeq4SdCMaeyOeI0IaaG ymaaGaayjkaiaawMcaaiaadoeadaWgaaWcbaGaamOvaaqabaGccaWG ubWaaWbaaSqabeaacaaIYaaaaaaaaaa@5186@
Or,
図 4.
m = P V ( γ − 1 ) C V T MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyBaiabg2 da9maalaaabaGaamiuaiaadAfaaeaadaqadaqaaiabeo7aNjabgkHi TiaaigdaaiaawIcacaGLPaaacaWGdbWaaSbaaSqaaiaadAfaaeqaaO Gaamivaaaaaaa@4138@
図 5.
T ​ = i n T 2 d P d t γ ( T d P d t − P d T d t ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake GabaaeoiaadsfacaaMb8+aaSraaSqaaiaadMgacaWGUbaabeaakiab g2da9maalaaabaGaamivamaaCaaaleqabaGaaGOmaaaakmaalaaaba GaamizaiaadcfaaeaacaWGKbGaamiDaaaaaeaacqaHZoWzdaqadaqa aiaadsfadaWcaaqaaiaadsgacaWGqbaabaGaamizaiaadshaaaGaey OeI0IaamiuamaalaaabaGaamizaiaadsfaaeaacaWGKbGaamiDaaaa aiaawIcacaGLPaaaaaaaaa@5134@
Or,
図 6.
T ​ = i n T γ + m d T d t γ m MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake GabaaeoiaadsfacaaMb8+aaSraaSqaaiaadMgacaWGUbaabeaakiab g2da9maalaaabaGaamivaaqaaiabeo7aNbaacqGHRaWkdaWcaaqaai aad2gadaWcaaqaaiaadsgacaWGubaabaGaamizaiaadshaaaaabaGa eq4SdCMaamyBaaaaaaa@493A@

And if T MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamivaaaa@36CF@ is constant: T i n = T / γ .