Calculation of ODH classification for Nevis LHe e-bubble Chamber Cryostat

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Ἀσκληπιάδης Αργυριάδης
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1 Calculaton of ODH classfcaton for Nevs LHe e-bubble Chamber Cryostat. Physcal parameters Thermal propertes of Helum and Ntrogen Yongln Ju Nevs Laboratores, Columba Unversty, NY 533 T 3 [K] Pa 76 [mmhg] ρhe.625 [kg/m 3 ] ρn2.56 [kg/m 3 ] T_he.2 [K] Pv.3. 5 [Pa] ρfv 2.8 [kg/m 3 ] ρgv 6.9 [kg/m 3 ] hfv [J/kg] hgv [J/kg] hfgv hgv hfv hfgv = [J/kg] T_n ρfn 86.8 [kg/m 3 ] ρgn.623 [kg/m 3 ] hfn [J/kg] hgn [J/kg] hfgn hgn hfn hfgn = [J/kg] R [J/kg.K] A. LHe Dewar he 25 [L] tt.. he tt. [L/h] [LHe dewar normal bol-off rate, %] B. LN2 Dewar n2 25 [L] tt2.5. n2 tt2.56 [L/h] [LN2 dewar normal bol-off rate,.5%] C. LHe essel Dr Dr.35 [m] Hr Hr.56 [m] Dz.2 [m] Dn Dn.27 [m] Hn Hn.58 [m] A A2 Dr2 Dn 2 A.6 [m 2 ] A3 Dn. Hn A3 3 [m 2 ] Dr2 Dz 2 A2.73 [m 2 ] A Dr. Hr A.523 [m 2 ] Ar_he A A3 A Ar_he.786 [m 2 ] [Cold surface of the LHe reservor] r r2 Dr2 Dz 2. Hr r. [m 3 ] r. = [L] [olume of LHe n LHe reservor] Dn2 Dz 2. Hn r2 = [m 3 ] r2. = [L] [olume of LHe n neck space] r_he ( r r2). r_he = 5.95 [L] [Total volume of LHe n LHe reservor] D. LN2 essel Dno Dno.356 [m] Dn Dn.52 [m] Hnz Hnz.58 [m] Hfn Hfn = 5 [m] Dn Dn.33 [m] Dn Dn2 = 79 [m] Ar_n2 2. Dno 2 Dn 2 Dno. Hnz Dn. Hfn Ar_n2 = 5 [m 2 ] [Cold surface of LN2 reservor] π r_n2. Dno2 Dn 2. Hnz. r_n2 =.85 [L] [olume of lqud n the LN2 reservor]

2 E. LHe e-bubble Chamber Dv.8 [m] Hv.7 [m] Hfv.5 [m] [Hght of LHe n e-bubble chamber] π Av. Dv2 Av = [m 2 ] Av2 Dv. Hv Av2.58 [m 2 ] Ae_he 2. Av Av2 Ae_he.76 [m 2 ] [Cold surface area of e-bubble chamber] π fv. Dv2. Hfv fv = [m 3 ] e_he fv. e_he.962 [L] [olume of LHe n e-bubble chamber] 2. Mass 2. Thermal Load f vacuum s lost: We assume qt [W/m 2 ] Et_he Et_n2 Ee_he qt. Ar_he Et_he = [W] qt. Ar_n2 Et_n2 = [W] qt. Ae_he Ee_he = 76. [W] 2.2 Mass n LHe vessel: LHe vessel: p.3. 5 [Pa] T.2 K ρfv = 2.8 [kg/m 3 ] hfgv = [J/kg] ρgv = 6.9 [kg/m 3 ] LHe mass at.2k n LHe vessel: Mhe ρfv. r_he Mhe = [kg] Saturated gas helum mass at.2k n LHe vessel: Mghe ρgv. r_he Mghe.758 [kg] The total enthalpy ncrease of load LHe of 5 lters n phase change: Elg Mhe. hfgv Elg = [J] 2.3 Mass n e-bubble Chamber: LHe vessel: p.3. 6 [Pa] T.2 K ρfve 5.55 [kg/m 3 ] hfgv = [J/kg] ρgve 5 [kg/m 3 ] LHe mass at.2k n LHe vessel: Mhee ρfve. e_he Mhee.6 [kg] Saturated gas helum mass at.2k n LHe vessel: Mghee ρgve. e_he Mghee.39 [kg] The total enthalpy ncrease of load LHe of 5 lters n phase change: Elge Mhee. hfgv Elge = [J] 2

3 2. Mass n LN2 vessel: LN2 vessel: p.3. 5 [Pa] T 77.3 K ρfn = 86.8 [kg/m 3 ] hfgn = [J/kg] ρgn =.623 [kg/m 3 ] LHe mass at.2k n LHe vessel: Mn2 ρfn. r_n2 Mn2 = [kg] Saturated gas ntrogen mass at 77.3K n LN2 vessel: Mgn2 ρgn. r_n2 Mgn2.9 [kg] The total enthalpy ncrease of load LHe of lters n phase change: Elg Mn2. hfgn Elg = [J] 3. Mass flow rate and release tme 3. Tme and mass flow rate estmaton for LHe: Et_he = [W] m_he Et_he hfgv m_he.379 [kg/s] t_he Mhe m_he t_he = 5.2 [s] If: Pb.3. 5 [Pa] T [K] Γ.9 τ.659 Po 3. 5 [Pa] Mass flow rate estmaton for relef valve: d. [m] n 2 Ar moutr Γ. Ar. Po τ. R. T 3.2 Tme and mass flow rate estmaton for LHe: Ee_he = 76. [W] d2. n Ar =.57. [m 2 ] moutr [kg/s] > m_he.379 [kg/s] me_he Ee_he hfgv me_he.37 [kg/s] te_he Mhee me_he te_he = [s] If: Pb.3. 5 [Pa] T [K] Γ.9 τ.659 Po. 5 [Pa] Mass flow rate estmaton for relef valve: d. [m] n Ar moutr Γ. Ar. Po τ. R. T 3.3 Tme and mass flow rate estmaton for LN2: Et_n2 = [W] m_n2 Et_n2 hfgn m_n2.3 [kg/s] t_n2 d2. n Ar = [m 2 ] moutr =.7 [kg/s] > me_he.37 [kg/s] Mn2 m_n2 t_n2 = [s] If: Pb.3. 5 [Pa] T [K] Γ.9 τ.659 R [J/kg.K] P 3. 5 [Pa] 3

4 Mass flow rate estmaton for open tube: d d2.9 [m] n2 3 Ar moutr Γ. Ar. P τ. R. T. ODH calculaton wth fan avalable Data of the confned volumn and fan vent rate: d22. n2 Ar = [m 2 ] moutr.338 [kg/s] > m_n2.3 [kg/s] 25.. = 3. 3 [m 3 ] [The confned volumn] C.283 [m 3 /CF] CC CC =.77. [m 3 /s] [Fan rate] 3 [SCFM]. CC [m 3 /s]. [m 3 /s] [The ventlaton rate of the fan] Case I. The normal operaton of 25L LHe and 25L LN2 Dewars The normal vaporzaton rate: % LHe /day and.5% LN2/day Rn tt. 36 [m 3 /s] Rn = [m 3 /s] Rn2 tt2. 36 [m 3 /s] Rn2 =.3. 8 [m 3 /s] R Rn. ρfv ρhe R = R2 Rn2. ρfn ρn2 R2 = R R R2 R = [m 3 /s] <. [m 3 /s] [The spll rate] t tt tt2 t = [hr] t. 36 = [s] R CC R R < C. R. t. 36. e C 92 = After the spll perod (R=) Ce C. 92 e. t C C k.. 8 C k 92 Ce k Oxygen concentraton C Tme [hr]

5 The partal pressure: PO2 C. Pa The fatalty factor: 6.5 G PO2 F f G,, f G <. 7,, G F 92 ODH fatalty rate: φ F φ 92 ODH Classfcaton: ODH <. 7,, <. 5,, <. 3, 2, <., 3, tme Fatalty rate va tme ODH class va tme Fatalty rate [/hr] φ ODH class ODH Tme [hr] Tme [hr] Case 2. The normal operaton of 5L LHe and L LN2 vessel The normal vaporzaton rate: 3 days Rn Rn [m 3 /s] Rn = [m 3 /s] [m 3 /s] Rn2 = [m 3 /s] R Rn. ρfv ρhe R =.333. R2 Rn2. ρfn ρn2 R2 =.77. R2 R R2 R2 = 2.. [m 3 /s] <. [m 3 /s] t 3. 2 t = 72 [hr] t. 36 = [s] R2 CC.5... R2 R2 < C2. R2. t. 36. e C2 72 = After the spll perod (R=). t Ce C2. 72 e C C2 k.. 28 C k 72 Ce k 72 5

6 Oxygen concentraton C Tme [hr] The partal pressure: PO2 C. Pa The fatalty factor: 6.5 G PO2 F f G,, f G <. 7,, G F 72 ODH fatalty rate: φ F φ 72 ODH Classfcaton: ODH <. 7,, <. 5,, <. 3, 2, <., 3, tme Fatalty rate va tme ODH class va tme Fatalty rate [/hr] φ ODH class ODH Tme [hr] Tme [hr] Case 3. LHe vessel n EBC Cryostat broken, and the vacuum s lost m_he.379 [kg/s] t Mhe m_he t = 5.2 [s] R3 m_he ρhe [m 3 /s] R3 = 2.33 [m 3 /s] >. [m 3 /s] R3 = CC

7 .. 6 R3 > C3 R3.. e C3 5 8 After the spll perod (R=). t Ce C3. 5 e C C3 k.. 5 C k 5 Ce k Oxygen concentraton C Tme [sec-hr] The partal pressure: PO2 C. Pa The fatalty factor: G 6.5 PO2 F f G,, f G <. 7,, G F 5 ODH fatalty rate: φ F φ 5 ODH Classfcaton: ODH <. 7,, <. 5,, <. 3, 2, <., 3, tme 7

8 Fatalty rate va tme ODH class va tme Fatalty rate [/hr] φ ODH class ODH Tme [s] Tme [s] Case. LN2 vessel n EBC Cryostat broken, and the vacuum s lost m_n2.3 [kg/s] t Mn2 m_n2 t = [sec] R m_n2 ρn2 [m 3 /s] R.37 [m 3 /s] <. [m 3 /s] R CC = R < C. R. R. e C The oxygen concentraton after the spll perod (R=, =const). t Ce C. 776 e C C k.. 22 C k 776 Ce k Oxygen concentraton C Tme [sec-hr] 8

9 The partal pressure: PO2 C. Pa The fatalty factor: G 6.5 PO2 F f G,, f G <. 7,, G F 776 ODH fatalty rate: φ F φ 776 ODH Classfcaton: ODH <. 7,, <. 5,, <. 3, 2, <., 3, tme Fatalty rate va tme ODH class va tme Fatalty rate [/hr] φ ODH class ODH Tme [s] Tme [s] Case 5. LHe e_bubble Chamber broken, and the vacuum s lost me_he.37 [kg/s] t Mhee me_he t = [s] R5 me_he ρhe [m 3 /s] R5 = 26 [m 3 /s] >. [m 3 /s] R5 CC = R5 > C5 R5.. e C5 = After the spll perod (R=). t. 36 Ce C5. e C C5 k.. 26 C k Ce k 9

10 Oxygen concentraton C Tme [sec-hr] The partal pressure: PO2 C. Pa The fatalty factor: 6.5 G PO2 F f G,, f G <. 7,, G F 5 ODH fatalty rate: φ F φ 5 ODH Classfcaton: ODH <. 7,, <. 5,, <. 3, 2, <., 3, tme Fatalty rate va tme ODH class va tme Fatalty rate [/hr] φ ODH class ODH Tme [s] Tme [s]

11 Concluson Fatalty factor = 3*-6 Fatalty rate < -9 ODH class Under the worst case condton, fatalty rate s lower than -9 for Nevs e-bubble Chamber Cryostat at Atlas Buldng. Therefore, ODH s unclassfed accordng to "BNL ODH Rsk Assessment".

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