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.


Figure 1. Tank Experiment Schema

Tin and P are known

(1)
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

(2)
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,(3)
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@
(4)
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,(5)
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 .