Determination of Thermal Conductivity of Wood Exposed to Fire based on Small Scale Laboratory Trials for Finite Element Calculations

Transcription

1 Determination of Thermal Conductivity of Wood Exposed to Fire based on Small Scale Laboratory Trials for Finite Element Calculations Johnny Chung Fire Engineering, masters level 2017 Luleå University of Technology Department of Civil, Environmental and Natural Resources Engineering

2 DETERMINATION OF THERMAL CONDUCTIVITY OF WOOD EXPOSED TO FIRE BASED ON SMALL SCALE LABORATORY TRIALS FOR FINITE ELEMENT CALCULATIONS MAY 2017 LULEÅ UNIVERSITY OF TECHNOLOGY MASTER PROGRAMME IN FIRE ENGINEERING

3 I

4 Preface Johnny Chung II

5 Abstract III

6 Sammanfattning IV

7 Nomenclature α T AST ρ ε T g q abs q emi q con q rad h c q inc l u c e σ T s k q tot V

8 Table of contents VI

9 VII

10 VIII

11 1. Introduction 1.1 Objective of the thesis Questions to be answered 1

12 1.2 Boundaries of the report 2

13 2. Method Experimental trials in the cone calorimeter (cc) Using the finite element program TASEF to: Create the same test stand used in the cc-trials Defining relevant thermal properties for the involved materials Defining same boundary conditions Developing of the conductivity of wood based on back calculations in TASEF Figure 1. The implementation plan of development of the conductivity (first part). 3

14 Figure 2. The implementation scheme of the back calculation process 4

15 Figure 3. The implementation plan of the validation of the conductivity (second part). 5

16 3. Theory 3.1 Wood Charring Figure 4. Charring behaviour of wood. (SVENSKT TRÄ, 2013) 6

17 3.1.2 Thermal conductivity W/m 2 K Figure 5. Different directions in a wood element, Longitudinal (L), Radial (R) and Tangential (T). (Jansson, 2004) 3.2 Heat Transfer Theory 7

18 Figure 6. 1 st kind: Predefined surface temperature, 2 nd kind: Constant heat flux, 3 rd kind: Radiation and Convection Third kind of boundary condition Convection heat q con q con = β (T g T s ) γ T g T s γ β q con = h c (T g T s ) h c Radiation heat 8

19 q rad q abs q emi q rad = q abs q emi q inc q abs = α q inc α ε s T s 4 σ 4 q emi = ε s σ T s α ε s q rad = ε s (q inc σ T 4 s ) q tot q inc σ T s 4 q tot = q rad + q con = ε s (q inc σ T 4 s ) + h c (T g T s ) 3.3 The Adiabatic surface temperature T AST T r T g ε s (q inc σ T 4 AST ) + h c (T g T AST ) = 0 9

20 T s T AST 3.4 The Plate thermometer Figure 7. A plate thermometer (Wickström, 2016) 10

21 3.5 Cone Calorimeter Figure 8. Cone Calorimeter 11

22 Figure 9. Cone heater (Babrauskas, 2016) 3.6 Temperature Analysis of Structures Exposed to Fire (TASEF) δ δt (k δx δx ) + δ δt (k δy δy ) δe δt + Q = 0 x y T k 12

23 3.6.1 Geometry Thermal properties Specific heat capacity c ρ Figure 10. The specific heat of wood at elevated temperatures given in EN

24 Specific volumetric enthalpy e T 2 e = c ρ dt + l i T 1 i i l i Dry substance e = c dry ρ dry T c dry ρ dry T Moist substance 14

25 Figure 11. The dotted line shows the enthalpy curve of a dry substance with constant material properties. The full line shows an enthalpy curve of a moist substance with constant material properties. Notice the increased of enthalpy at T1-T2 which is due to the existence of the latent heat needed to vaporize the moisture content. a w 15

26 Table 1. The calculation procedure of the developement of the specific volumetric enthalpy curve u = ρ moist ρ dry ρ dry 100 e = c dry ρ dry T = 0 T 0 = 0 e 1 = c dry ρ dry T 1 + u 100 c w T 1 ρ dry T 0 T 1 e 2 = e 1 + ρ dry (T 2 T 1 ) ( u 100 c w + c dry ) + u 100 a w ρ dry T 1 T 2 e 3 = e 2 + c dry ρ dry (T 2 T 1 ) T 2 T Boundary conditions Back calculation 16

27 4. Laboratory set-ups 4.1 One-dimensional cone calorimeter trials The Test Stand Pine wood Figure 12. The custom made holder for the cone calorimeter trials. The figure is not drawn to scale. 17

28 Table 2. Dimensions and weights of the tested pine wood sample in the cone calorimeter 1-4 Figure 13 Figure 13. One of the four pine wood sample with dimensions of 100 mm x 100 mm x 10 mm Table 3. The measurements of the fifth pine wood sample for determining the moisture content Metal sheet 18

29 Table 4. The dimensions of the metal sheet for measuring the temperature behind the pine wood sample during the cone calorimeter trials. Figure 14. The bottom side of the metal sheet with a welded thermocouple in the centre of the sheet for measuring the steel temperature Insulation material Table 5 The dimensions of one ceramic wool blanket 19

30 Figure 15. A fully assembled custom made test stand for the cone calorimeter trials 4.2 One-dimensional fire furnace trials First set up for the fire furnace trials 20

31 Figure 16 The cross-section of the test stand for the fire furnace trials. The figure is not drawn to scale Glue laminated timber Table 6. Measured dimensions of the glue laminated timber beam C Figure 17. Placement of the lower layer of gypsum boards Figure 18. Placement of the upper layer of gypsum boards 21

32 Table 7. Dimensions of the lower and upper gypsum boards respectively. Figure 19. Placement of the glue laminated beam together with the supporting wood joints at the ends. Table 8. Dimensions of the supporting wood joints 22

33 Figure 20. Sealing tapes were attached along the sides of the specimen and along the wood joints for preventing air gaps Steel plate Figure 21 A steel plate 225 mm x 225 mm x 4 mm where placed at the middle of the beam for measuring the temperature during the furnace trials Table 9 Dimensions of the steel plate 23

34 Insulation material Figure 22. Small nails were nailed into the timber beam for stabilizing the steel plate Figure 23. Stone wool blanket at the sides of the specimen Figure 24. Stone wool blanket on top of the specimen Table 10 The dimensions of the stone wool blankets 24

35 Figure 25. A fully assembled set-up for the fire furnace trials Figure 26. The bottom side of the test stand. Sealing tapes were put on the air gaps to minimize the air influence Second set up for the fire furnace trials 25

36 Figure 27. A whole gypsum board was used for the second set up for the fire furnace trials Figure 28. The placement of the steel plate on top of the glue laminated timber beams Figure 29. Stone wool insulation blankets Figure 30. The bottom side of the test stand. Sealing tapes were put along the cut-out of the gypsum board for preventing air influences 26

37 Figure 31. A plywood was placed on top of the second test stand for facilitating the transport of the set up to the fire furnace Figure 32. Gypsum boards were placed at the sides of the wood joints for safety reasons. 27

38 5. Set-up in TASEF 5.1 Input data in TASEF regarding the cone calorimeter trials Pine wood Specific heat c dry T w c dry = T w 28

39 Table 11. Calculated specific heat of a dry wooden substance using Equation Moisture content u = % Density u 29

40 Table 12 The calculated density for the pine wood sample at elevated temperatures. u u Specific volumetric enthalpy Sensitive heat of the dry substance at 100 C e dry,100 = c dry ρ dry T 1 = = J/m Sensitive heat of the free water at 100 C 30

41 e w,100 = u 100 c w T 1 ρ dry = (100 0) = J/m 3 e tot,100 = = J/m Sensitive heat of the dry substance and the free water between 100 C C e dry,120 e s,w,120 e dry,120 = 1666 ( ) = J/m 3 e s,w,120 = ( ) = J/m Latent heat of the free water between 100 C 120 C e l,w,120 = a w u 100 a w ρ dry = = J/m3 100 e tot,100 = = J/m Enthalpy curve of the pine wood with a moisture content of 10 % 31

42 Table 13. The developed specific volumetric enthalpy of the pine wood sample with a moisture content of 10 % up to 1200 C C 32

43 Specific volumetric enthalpy [Wh/m 3 ] Temperature [ C] 5.2 Geometry Figure 33. The calculated enthalpy curve of the pine wood sample with a moisture content of 10 %. 33

44 Figure 34. The created finite element model in TASEF based on Figure 12. The custom made holder for the cone calorimeter trials. The figure is not drawn to scale. Table 14. Defined gridlines in x-direction of Figure 32. Table 15. Defined gridlines in y-direction of Figure Boundary conditions 34

45 5.4 Input data in TASEF regarding the fire furnace trials 35

46 TASEF Glue laminated timber Specific heat Moisture content Density 36

47 Table 16. The calculated density for the glue laminated timber beam at certain temperatures. u u Specific volumetric enthalpy Sensitive heat of the dry substance at 100 C e dry,100 = c dry ρ dry T 1 = = J/m Sensitive heat and the latent heat of the free water at 100 C e w,100 = u 100 c w T 1 ρ dry = = J/m

48 e tot,100 = = J/m Sensitive heat of the dry substance and the free water between 100 C 120 C e dry,120 = 1666 ( ) = J m 3 e s,w,120 = 12 J 4180 ( ) = m Latent heat of the free water at 100 C C a w e l,w,120 = u 100 a w ρ dry = 12 J = m 3 e tot,100 = = J/m Enthalpy curve of the glue laminated timber with a moisture content of 12 % 38

49 Specific volumetric enthalpy [Wh/m 3 ] Table 17. The developed enthalpy of the glue laminated timber with a moisture content of 12 % up to 1200 C Temperature [ C] Figure 35. The calculated enthalpy curve of the glue laminated timber beam with a moisture content of 12 % 5.5 Geometry 39

50 Figure 36. The created model in TASEF based on Figure 16 The cross-section of the test stand for the fire furnace trials. The figure is not drawn to scale.. Table 18. Defined gridlines in x-direction of Figure 34. Table 19. Defined gridlines in y-direction of Figure Boundary conditions condition 40

51 41

52 Temperature [ C] 6. Results from the experimental trials 6.1 Cone calorimeter trials Boundary condition Time [min] Gas temperature Adiabatic surface temperature Figure 37. The cone heater was set to give a constant incident radiation of 50 kw/m 2. The measured adiabatic surface temperature was ~ 650 and the gas temperature ~

53 Temperature [ C] Measured steel temperatures from the cone calorimeter trials Time [min] Steel temp 1 Steel temp 2 Steel temp 3 Steel temp. 4 Figure 38. The measured steel tempertures from the cone calorimeter trials. A plataeu can be seen at 100 C due to the vaporization of the moisture contents in the pine wood samples. The pine wood samples consisted of a moisture content of 10 % Review of the cone calorimeter trials 43

54 Figure 39 The pine wood sample before it was expose to heat Figure 40 The pine wood after being exposed for about 8 minutes of heating 6.2 Fire furnace trials Boundary condition 44

55 Temperature [ C] Time [min] Furnace temp. ISO 834 Figure 41. The measured fire temperature i.e. ISO 834, in the fire furnace by using a PT (full line) togheter with the calculated standard fire temperature curve (dotted line) Measured steel temperatures from the fire furnace trials 45

56 Temperature [ C] Temperature [ C] Time [min] TC1 TC2 TC3 TC4 TC5 Figure 42 Measured steel plate temperatures of the first set-up of furnace trials. Five thermocouples ( = 0.25), TC1 TC4 in the four corners and TC5 in the middle. A plateau can be noticed at 100 C due to the evaporation of free water Time [min] TC1 TC2 TC3 TC5 Figure 43. Measured steel plate temperatures of the second set-up of furnace trials. Five thermocouples ( = 0.25), TC1 TC4 in the four corners and TC5 in the middle. A plateau can be noticed at 100 C due to the evaporation of free water. The temperature curve for TC4 has been removed from the graph due to incorrect measured temperature data Review of the fire furnace trials 46

57 Figure 44. The test specimen was fully burned through and fully charred along the beam after the experimental trials were ended. 47

58 7. Analysis in TASEF 7.1 Back calculations in TASEF regarding the cone calorimeter trials 7.2 Developed conductivity values for the pine wood in TASEF k pw,20 k pw,20 = ρ dry ( u) 1000 ρ dry u ( ) = 0.09 W/mK

59 Temperature [ C] Thermal conductivity [W/mK] Temperture [ C] Figure 45. Final combinations of conductivity values of the pine wood at 100 C, 300 C and 500 C. The conductivity higher than 500 C is assumed as constant. At 20 C, the conductivity has been calculated using formulas given in literature Time [min] Measured steel temperature Back calculated temperature in TASEF Figure 46. Results of the best fit calculations performed in TASEF (full line) compared with measured steel temperatures during the cone calorimeter trials (dotted line). 49

60 7.3 Derived conductivity values for the glue laminated timber in TASEF ( u) = W/mK = 1.5 Table 20 Numerical values of the derived conductivity for the glue laminated timber (GLT) based on developed conductivities showed in 50

61 Thermal conductivty [W/mk] Temperature [ C] Figure 47. Derived conductivity for the glue laminated timber with a moisture content of 12 % presented in table 20. The conductivity values between 500 C to 1200 C are assumed as constant. 7.4 Comparison with measured steel temperatures during the fire furnace trials. Figure 48 Comparison between steel temperature curves measured during the fire furnace trial (blue line) and calculated steel temperatures in TASEF with derived conductivity of the glue laminated timber presented in table 20 Table 20 Numerical values of the derived conductivity for the glue laminated timber (GLT) based on developed conductivities showed in Figure

62 Temperature [ C] Time [min] Measured steel temperature from the second furnce trial (TC5) TASEF results based on derived conductivity from table 20 Figure 48 Comparison between steel temperature curves measured during the fire furnace trial (blue line) and calculated steel temperatures in TASEF with derived conductivity of the glue laminated timber presented in table Review of the derived conductivity of wood Wood type 2 Wood type 1 Figure 49. A developing scheme for deriving the conductivity of the glue laminated timber(wood type 2) 52

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64 8. Discussion 54

65 55

66 Results of the best fit calculations performed in TASEF (full line) compared with measured steel temperatures during the cone calorimeter trials (dotted line). 56

67 57

68 9. Conclusion 9.1 Further studies 58

69 10. Bibliography 59

70 60

71 11. Appendices Appendix A Thermal properties of Gypsum board used in TASEF Table A1 Specific volumetric enthalpy of a gypsum substance consisting of 23 % of crystalline water. 61

72 Table A2 Thermal conductivity of gypsum board, Gyproc Protect F 62

73 Appendix B Thermal properties of Stone wool used in TASEF Table B1. The specific heat of the stone wool blanket 63

74 Table B2 The calculated specific volumetric enthalpy of stone wool Table B3 Thermal conductivity of stone wool 64

75 Appendix C Thermal properties of Ceramic wool used in TASEF developement of the specific volumetric enthalpy curve The calculation procedure of the Table C1 The calculated specific volumetric enthalpy of ceramic wool Table C2 Thermal conductivity of the ceramic wool 65

76 Oxygen level [%] Pressure [Pa] Appendix D Additional data regarding the fire furnace trials Figure D2 Measured oxygen level in the furnace during the first trial Pressure Time [min] Figure D1 Measured Pressure level in the furnace during the first trial Oxygen level Time [min] Figure D2 Measured oxygen level in the furnace during the first trial. 66

77 Oxygen level [%] Pressure [Pa] Time [min] Pressure Figure D3 Measured Pressure level in the furnace during the second trial Time [min] Figure D4 Measured oxygen level in the furnace during the second trial 67