1. ATLAS muon chambers heat transfer efficient description RFNC – VNIITF SUE «Strela» Snezhinsk, 2003 t.v.lebedeva@vniitf.ru

2. Contents Basic problems Approaches to designing simplified thermal models for muon chambers Simplified thermal models 1 and 2 Chambers as homogeneous objects to simulate heat transfer across them Multilayers and End plugs as homogeneous components to simulate heat transfer along chambers MDT tubes heating of BIS chambers

3. Basic problems to be solved Simplified thermal models for typical muon chambers Heat transfer across chambers Heat transfer along chambers Free-convection heat exchange inside the fragments of ATLAS facility for the most heat loaded chambers Air flow blocking between the MDT chambers

4. The chambers under consideration BIS, BIL without RPC; BMS, BML with RPC on both sides of the chamber; BOL, BOS with RPC on one side of the chamber General scheme of chamber

5. Studied problems Heat transfer across chambers to evaluate temperature gradients between outer surfaces of the multilayers Heat transfer along the BIS chambers with the source in Faraday Cage (FC)

6. Approaches to design simplified thermal models From simple to complex Actual structure is divided into fragments to enable direct simulation of heat transfer Fragment is replaced with homogeneous material having parameters equivalent to those of the initial fragment Set of fragments is replaced with homogeneous material

7. Simplified thermal model (Model 1) for BМS, BМL chambers

8. Simplified thermal model (Model 1) for BOS, BOL chambers

9. Simplified thermal model (Model 1) for BIS chamber

10. Simplified thermal model (Model 1) for BIL chamber

11. Materials of simplified thermal models 1, 3-have specific thermal characteristics and replace the layers of aluminum tubes, RPC, gas-filled gaps, and heat-isolation 2-corresponds to "air" and cross plates. Heat transfer in the material 2 is caused by heat conduction, convection and radiation

12. Simplified thermal models for 2D calculations based on Model 1 The highlighted areas are the heat sources

13. Heat sources RPC releases heat along the perimeter of structure equal to 0.07W/4cm (1.75W/m) Power/mezz board for all types of chambers 1.62 W

14. Thermal model 2 Structure elements treated separately RPC Air gaps and heat-shielding (space between RPC and multilayer) Multilayer, Faraday cage, End plug Space between multilayers (Air + Cross plates)

15. Model 2. BML, BMS chambers

16. Model 2. BOL, BOS chambers

17. Model 2. BIL chamber

18. Model 2. BIS chamber

19. CHAMBERS AS EFFICIENT HOMOGENEOUS OBJECTS TO SIMULATE HEAT TRANSFER ACROSS THE CHAMBERS

20. Multilayer of tubes presented as homogeneous object

21. 2D problems in YZ plane Left and right sides are adiabatic walls Temperature values are given (T2>T1)on the bottom and upper surfaces Heat transfer in gas and in air is caused by heat conduction and convection Radiative heat transfer is not taken into account Direction of gravity force is varied

22. Presentation of multilayers as homogeneous objects Convection inside the tubes has almost no effect on transverse heat transfer for temperature gradients studied Estimated efficient thermal conductivity across multilayers For 3-layers set: æeff =2.00W/(mK) For 4-layers set: æeff =1.76W/(mK)

23. The effecient heat conductivity for the air gap between multilayers depends on the chamber orientation Each muon chamber has its own component of vector g g

24. Components of gravity g

25. The effective heat conductivity for air gap between multilayers Heat transfer between multilayers is caused by heat conductivity convection radiation

26. Heat transfer due to heat conduction and convection T2=290.1, 290.2, 290.5, 291, 292 T1=290 0.2    1/3

27. Simulated values (markers) of efficient heat conductivity and analytical curves for BIL and BML chambers

28. Simulated values (markers) of efficient heat conductivity and analytical curves for BMS and BOL chambers

29. Simulated values (markers) of efficient heat conductivity and analytical curves for BOS chambers

30. Velocity field for chamber BIL01

31. Velocity field for chamber BIL05

32. Velocity field for chamber BMS04

33. Velocity field for chamber BOS04

34. Velocity field for chamber BOL05

35. Velocity field for chamber BML05

36. Cross-plates influence on heat transfer between the mulilayers BIL: BMS: BML: BOS: BOL : æ eff (cond.+conv.+cross_plate) =  +  æ eff (cond.+conv.)

37. Heat transfer by radiation Radiative heat transfer between the multilayers treated as heat exchange between two parallel planes and described by

38. This technology is applied to calculate the value of efficient heat conductivity for specific chamber by means of  Selection of parameters ,   Estimation of average temperatures at the internal surfaces of the multilayers (values of T1, T2)  Selection of ,  corresponded to chosen chamber  And on a final stage estimation of the value of heat conductivity with the help of above expression Calculations of the effective coefficient of heat conductivity for air gap between multilayers

39. Presenting RPC as homogeneous objects For BOS, BMS,BML æ eff =0.0291W/(mK) For BOL æ eff =0.0288W/(mK)

40. Simplified heat models of the BIS chambers MaterialρCæ 19411950.0265 21299381.76 32429509500.054 41339830.1135 51269830.11

41. Simplified thermal models of the BIL chamber s MaterialΡCæ 115011100.027 21299381.76 313990 0.083+0.9953  |  T| δ + 0.17٠4εσ T 3 /(2- ε) 41319620.2

42. Simplified thermal models of the BMS and BML chambers Materialæ for BMSæ for BML 10.028 20.027 32.00 4 0.072+0.996  |  T| δ +0.17٠4εσT 3 /(2- ε) 0.103+0.9965  |  T| δ +0.317٠4εσT 3 /(2- ε) 50.0279 60.0430.044

43. Simplified thermal models of the BOS and BOL chambers Materialæ for BOSæ for BOL 10.028 20.027 32.00 4 0.097+0.9967  |  T| δ +0.317٠4εσT 3 /(2- ε) 0.073+0.9975  |  T| δ +0.317٠4εσT 3 /(2- ε) 50.163 60.044

44. Temperature gradients across chambers for BIS, BIL

45. Temperature gradients across the chambers BMS, BML

46. Temperature gradients across chambers BOS and BOL

47. MULTILAYER AND END PLUGS AS HOMOGENEOUS OBJECTS TO SIMULATE HEAT CONDUCTION ALONG CHAMBERS

48. Single MDT-tube presented as a homogeneous cylinder

49. Dependence of æ eff on tube length, chamber position and temperature gradients æ eff =6.32W/(mK)

50. Presenting a set of MDT-tubes as homogeneous object Fragment of multilayer consisted of 4 monolayers æ=5.44W/(mK) Tube block Fragment of multilayer consisted of 3 monolayers æ=5.51W/(mK)

51. End Plug

52. Simplified model of End Plug for simulations

53. Simplified model of End Plug with indicated materials for calculations

54. Simplified model for End Plug

55. HEATING OF MDT TUBES FOR THE BIS CHAMBER

56. 2D model of a BIS chamber

57. Ventilation of ATLAS cavern Air velocity around the muon chambers

58. Airflow around chambers BIS16 (left), BIS10 (right)

59. Temperature fields in the Faraday Cage of BIS chamber, located in the air cavern Problem statement Inlet KB – 0.03 m/c Inlet AB– 0.06 m/c Outlet DE (0.13m length) 100% of flow Boundaries – adiabatic walls Energy source 5.0676E4 [W/m3]

60. Velocity field for Faraday Cage RO (BIS10)

61. Velocity fields for two regions of Faraday Cage RO (BIS10)

62. Temperature fields for two regions of Faraday Cage RO (BIS10)

63. Temperature field for fragment of BIS10

64. Fragments of BIS10 chamber Temperature in the lower multilayer of tubes Temperature in the upper multilayer of tubes

65. Fragment of velocity field around of BIS16 chamber

66. Temperature field for BIS16 chamber

67. Fragment of velocity field for chamber BIS16

68. Temperature distribution for chamber BIS16

69. Faraday Cage, BIS16 chamber Velocity in the left sub-domain of Faraday Cage Velocity in the right sub-domain of Faraday Cage

70. Conclusion Two type of simplified thermal models were created to be used in the global simulations Simplified thermal models were developed to describe heat transfer across the chambers Heat release in Faraday Cage was simulated and results were applied to describe heat transfer along the BIS chambers.