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

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

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

I

II

Preface

Johnny Chung

III

Abstract

IV

Sammanfattning

V

Nomenclature

𝛼 𝑇

𝜌 𝜀 𝑇

𝑞̇

𝑞̇

𝑞̇

𝑞̇

ℎ

𝑞̇

𝑙

𝑢

𝑐

𝑒

𝜎

𝑇

𝑘

𝑞̇

VI

Table of contents

VII

VIII

1

1. Introduction

1.1 Objective of the thesis

1.1.1 Questions to be answered

2







1.2 Boundaries of the report

3

2. Method

Figure 1. The implementation plan of development of the conductivity (first part).

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

Developing of the conductivity of wood based on back

calculations in TASEF

Defining same boundary conditions

4

Figure 2. The implementation scheme of the back calculation process

5

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

6

3. Theory

3.1 Wood

3.1.1 Charring

Figure 4. Charring behaviour of wood. (SVENSKT TRÄ, 2013)

7 3.1.2 Thermal conductivity

𝑊/𝑚

𝐾

Figure 5. Different directions in a wood element, Longitudinal (L), Radial (R) and Tangential (T). (Jansson, 2004)

3.2 Heat Transfer Theory

8

Figure 6. 1^st kind: Predefined surface temperature, 2^nd kind: Constant heat flux, 3^rd kind: Radiation and Convection

3.2.1 Third kind of boundary condition

3.2.2 Convection heat

𝑞̇

𝑞̇

= 𝛽 (𝑇

− 𝑇

)

𝑇

𝑇

𝛾 𝛽

𝑞̇

= ℎ

(𝑇

− 𝑇

) ℎ

3.2.3 Radiation heat

9

𝑞̇

𝑞̇

𝑞

𝑞̇

= 𝑞̇

− 𝑞̇

𝑞̇

𝑞̇

= 𝛼 𝑞̇

𝛼

𝜀

𝑇

𝜎

𝑞̇

= 𝜀

𝜎 𝑇

𝛼 𝜀

𝑞̇

= 𝜀

(𝑞̇

− 𝜎 𝑇

)

𝑞̇

≡ 𝜎 𝑇

𝑞̇

𝑞̇

= 𝑞̇

+ 𝑞̇

= 𝜀

(𝑞̇

− 𝜎 𝑇

) + ℎ

(𝑇

− 𝑇

)

3.3 The Adiabatic surface temperature

𝑇

𝑇

𝑇

𝜀

(𝑞̇

− 𝜎 𝑇

) + ℎ

(𝑇

− 𝑇

) = 0

10

𝑇

𝑇

3.4 The Plate thermometer

Figure 7. A plate thermometer (Wickström, 2016)

11

3.5 Cone Calorimeter

Figure 8. Cone Calorimeter

12

Figure 9. Cone heater (Babrauskas, 2016)

3.6 Temperature Analysis of Structures Exposed to Fire (TASEF)

𝛿

𝛿𝑥 × (𝑘 𝛿𝑇 𝛿𝑥 ) + 𝛿

𝛿𝑦 × (𝑘 𝛿𝑇 𝛿𝑦 ) − 𝛿𝑒

𝛿𝑡 + 𝑄 = 0

𝑥 𝑦 𝑇 𝑘

13 3.6.1 Geometry

3.6.2 Thermal properties

3.6.2.1 Specific heat capacity

𝑐 𝜌

Figure 10. The specific heat of wood at elevated temperatures given in EN 1995-1-2

14 3.6.2.2 Specific volumetric enthalpy

𝑒

𝑒 = ∫ 𝑐 ∗ 𝜌 𝑑𝑇 + ∑ 𝑙

𝑖 𝑇₂

𝑇₁

∑ 𝑙

℃

3.6.2.2.1 Dry substance

𝑒 = 𝑐

∗ 𝜌

∗ 𝑇

𝑐

𝜌

𝑇

3.6.2.2.2 Moist substance

℃

15

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

℃

16

Table 1. The calculation procedure of the developement of the specific volumetric enthalpy curve

𝑢 = 𝜌

− 𝜌

𝜌

∗ 100

𝑒 = 𝑐

∗ 𝜌

∗ 𝑇 = 0 𝑇

= 0

𝑒

= 𝑐

∗ 𝜌

∗ 𝑇

+ 𝑢

100 ∗ 𝑐

∗ 𝑇

∗ 𝜌

𝑇

→ 𝑇

𝑒

= 𝑒

+ 𝜌

∗ (𝑇

− 𝑇

) ( 𝑢

100 ∗ 𝑐

+ 𝑐

) + 𝑢

100 ∗ 𝑎

∗ 𝜌

𝑇

→ 𝑇

𝑒

= 𝑒

+ 𝑐

∗ 𝜌

∗ (𝑇

− 𝑇

) 𝑇

→ 𝑇

3.6.3 Boundary conditions

3.6.4 Back calculation

17

4. Laboratory set-ups

4.1 One-dimensional cone calorimeter trials

4.1.1 The Test Stand

Figure 12. The custom made holder for the cone calorimeter trials. The figure is not drawn to scale.

4.1.2 Pine wood

18

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

4.1.3 Metal sheet

19

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

4.1.4 Insulation material

Table 5 The dimensions of one ceramic wool blanket

20

Figure 15. A fully assembled custom made test stand for the cone calorimeter trials

4.2 One-dimensional fire furnace trials

4.2.1 First set up for the fire furnace trials

21

Figure 16 The cross-section of the test stand for the fire furnace trials. The figure is not drawn to scale.

4.2.1.1 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

22

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

23

Figure 20. Sealing tapes were attached along the sides of the specimen and along the wood joints for preventing air gaps.

4.2.1.2 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

24

Figure 22. Small nails were nailed into the timber beam for stabilizing the steel plate

4.2.1.3 Insulation material

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

25

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.

4.2.2 Second set up for the fire furnace trials

26

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 Figure 29. Stone wool insulation blankets the glue laminated timber beams

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

27

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.

28

5. Set-up in TASEF

5.1 Input data in TASEF regarding the cone calorimeter trials

5.1.1 Pine wood

5.1.1.1 Specific heat

𝑐

𝑇

𝑐

= 1.114 + 0.0046 ∗ 𝑇

29

Table 11. Calculated specific heat of a dry wooden substance using Equation 13

5.1.1.2 Moisture content

𝑢 = 340 − 309

309 ∗ 100 ≈ 10 %

5.1.1.3 Density

u

30

Table 12 The calculated density for the pine wood sample at elevated temperatures.

u u

5.1.2 Specific volumetric enthalpy

5.1.2.1 Sensitive heat of the dry substance at 100 °C

𝑒

= 𝑐

∗ 𝜌

∗ 𝑇

= 1574 ∗ 309.29 ∗ 100 = 48682875 𝐽/𝑚

5.1.2.2 Sensitive heat of the free water at 100 °C

31 𝑒

= 𝑢

100 ∗ 𝑐

∗ 𝑇

∗ 𝜌

= 10

100 ∗ 4180 ∗ (100 − 0) ∗ 309.29

= 12996444 𝐽/ 𝑚

𝑒

= 48682875 + 1299644 = 61679319 ≈ 61680000 𝐽/ 𝑚

5.1.2.3 Sensitive heat of the dry substance and the free water between 100 °C - 120 °C

𝑒

𝑒

𝑒

= 1666 ∗ (120 − 100) ∗ 309.29 = 10305675 𝐽/ 𝑚

𝑒

= 10

100 ∗ 4180 ∗ (120 − 100) ∗ 309.29 = 2599288 𝐽/ 𝑚

5.1.2.4 Latent heat of the free water between 100 °C – 120 °C

𝑎

𝑒

= 𝑢

100 ∗ 𝑎

∗ 𝜌

= 10

100 ∗ 2260000 ∗ 309.29 = 70267856 𝐽/ 𝑚

𝑒

= 10305675 + 25992288 + 70267856 = 144852140

≈ 144900000𝐽/ 𝑚

5.1.3 Enthalpy curve of the pine wood with a moisture content of 10 %

32

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

°C

33

Figure 33. The calculated enthalpy curve of the pine wood sample with a moisture content of 10 %.

5.2 Geometry

0 20000 40000 60000 80000 100000 120000

0 100 200 300 400 500 600 700 800 900 1000 1100 1200

Specific volumetric enthalpy [Wh/m3]

Temperature [°C]

34

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 32

5.3 Boundary conditions

35

5.4 Input data in TASEF regarding the fire furnace trials

36

TASEF 5.4.1 Glue laminated timber

5.4.1.1 Specific heat

5.4.1.2 Moisture content

5.4.1.3 Density

37

Table 16. The calculated density for the glue laminated timber beam at certain temperatures.

u u

5.4.2 Specific volumetric enthalpy.

5.4.2.1 Sensitive heat of the dry substance at 100 °C

𝑒

= 𝑐

∗ 𝜌

∗ 𝑇

= 1574 ∗ 440.43 ∗ 100 = 69324400 𝐽/𝑚

5.4.2.2 Sensitive heat and the latent heat of the free water at 100 °C

𝑒w,100= 𝑢

100∗ 𝑐𝑤∗ 𝑇1∗ 𝜌𝑑𝑟𝑦=

12

100∗ 4180 ∗ 100 ∗ 440.43 = 22092197 𝐽/

𝑚

38

𝑒

= 69324400 + 22092197 = 91416598 ≈ 91420000𝐽/ 𝑚

5.4.2.3 Sensitive heat of the dry substance and the free water between 100 °C – 120 °C

𝑒

= 1666 ∗ (120 − 100) ∗ 440.43 = 14675279 𝐽 𝑚

𝑒

= 12

100 ∗ 4180 ∗ (120 − 100) ∗ 440.43 = 4418439 𝐽 𝑚

5.4.2.4 Latent heat of the free water at 100 °C - 120 °C

𝑎

𝑒

= 𝑢

100 ∗ 𝑎

∗ 𝜌

= 12

100 ∗ 2260000 ∗ 440.43 = 119445854 𝐽 𝑚

𝑒

= 14675279 + 4418439 + 119445854 = 144852140

≈ 144900000𝐽/ 𝑚

5.4.3 Enthalpy curve of the glue laminated timber with a moisture content of 12 %

39

Table 17. The developed enthalpy of the glue laminated timber with a moisture content of 12 % up to 1200 °C

Figure 35. The calculated enthalpy curve of the glue laminated timber beam with a moisture content of 12 %

5.5 Geometry

0 20000 40000 60000 80000 100000 120000 140000 160000 180000

0 100 200 300 400 500 600 700 800 900 1000 1100 1200

Sp ecific vo lu m et ric entha lp y [Wh /m

]

Temperature [°C]

40

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 34

5.6 Boundary conditions

condition

41

42

6. Results from the experimental trials

6.1 Cone calorimeter trials

6.1.1 Boundary condition

Figure 37. The cone heater was set to give a constant incident radiation of 50 kW/m². The measured adiabatic surface temperature was ~ 650 ℃ and the gas temperature ~ 130 ℃ .

0 100 200 300 400 500 600 700

0 2 4 6 8 10 12

Temperature [°C]

Time [min]

Gas temperature Adiabatic surface temperature

43

6.1.2 Measured steel temperatures from the cone calorimeter trials

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 %.

6.1.3 Review of the cone calorimeter trials

0 100 200 300 400 500 600

0 2 4 6 8 10 12

Temperature [°C]

Time [min]

Steel temp 1 Steel temp 2 Steel temp 3 Steel temp. 4

44

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

6.2.1 Boundary condition

45

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)

6.2.2 Measured steel temperatures from the fire furnace trials

0 200 400 600 800 1000 1200

0 10 20 30 40 50 60 70

Temperature [°C]

Time [min]

Furnace temp. ISO 834

46

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.

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

6.2.3 Review of the fire furnace trials

0 100 200 300 400 500 600 700 800 900

0 10 20 30 40 50 60

Temperature [°C]

Time [min]

TC1 TC2 TC3 TC4 TC5

0 100 200 300 400 500 600 700 800

0 10 20 30 40 50 60

Temperature [°C]

Time [min]

TC1 TC2 TC3 TC5

47

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

48

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

k

= 0.01864 + 𝜌

1000 (0.1941 + 0.004064 ∗ 𝑢)

𝜌

𝑢

0.01864 +

1000

(0.1941 + 0.004064 ∗ 10) = 0.09 𝑊/𝑚𝐾

49

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.

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).

0.09 0.07

0.05

0.35

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

0 200 400 600 800 1000 1200 1400

Thermal conductivity [W/mK]

Temperture [°C]

0 50 100 150 200 250 300 350 400 450

0 1 2 3 4 5 6 7 8 9

Temperature [°C]

Time [min]

Measured steel temperature Back calculated temperature in TASEF

50

7.3 Derived conductivity values for the glue laminated timber in TASEF

0.01864 + 440

1000 (0.1941 + 0.006 ∗ 𝑢) = 0.135 𝑊/𝑚𝐾

0.135 0.09 = 1.5

Table 20 Numerical

values of the derived conductivity for the glue laminated timber (GLT) based on developed

conductivities showed in

51

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 45.

0.135 0.105

0.075

0.35

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

0 200 400 600 800 1000 1200 1400

Thermal conductivty [W/mk]

Temperature [°C]

52

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.

7.5 Review of the derived conductivity of wood

Figure 49. A developing scheme for deriving the conductivity of the glue laminated timber(wood type 2) 0

50 100 150 200 250 300 350 400 450

0 10 20 30 40 50 60

Temperature [°C]

Time [min]

Measured steel temperature from the second furnce trial (TC5) TASEF results based on derived conductivity from table 20

𝑊𝑜𝑜𝑑 𝑡𝑦𝑝𝑒 2 𝑊𝑜𝑜𝑑 𝑡𝑦𝑝𝑒 1

°

53

54

8. Discussion

55

56

Results of the best fit calculations performed in TASEF (full line) compared with

measured steel temperatures during the cone calorimeter trials (dotted line).

57

58

9. Conclusion

9.1 Further studies







59

10. Bibliography

60

61

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.

℃

62

Table A2 Thermal conductivity of gypsum board, Gyproc Protect F

℃

63

Appendix B – Thermal properties of Stone wool used in TASEF

Table B1. The specific heat of the stone wool blanket

64

Table B2 The calculated specific volumetric enthalpy of stone wool

Table B3 Thermal conductivity of stone wool

65

Appendix C – Thermal properties of Ceramic wool used in TASEF

The calculation procedure of the developement of the specific volumetric enthalpy curve

Table C1 The calculated specific volumetric enthalpy of ceramic wool

Table C2 Thermal conductivity of the ceramic wool

66

Appendix D – Additional data regarding the fire furnace trials

Figure D2 Measured oxygen level in the furnace during the first trial.

Figure D1 Measured Pressure level in the furnace during the first trial.

Figure D2 Measured oxygen level in the furnace during the first trial.

0 5 10 15 20 25 30 35 40 45 50

0 5 10 15 20 25 30 35 40 45 50

Pressure [Pa]

Time [min]

Pressure

0 1 2 3 4 5 6 7 8

0 10 20 30 40 50 60

Oxygen level [%]

Time [min]

Oxygen level

67

Figure D3 Measured Pressure level in the furnace during the second trial.

Figure D4 Measured oxygen level in the furnace during the second trial 0

10 20 30 40 50 60 70 80 90 100

0 10 20 30 40 50 60

Pressure [Pa]

Time [min]

Pressure

0 2 4 6 8 10 12

0 10 20 30 40 50 60

Oxygen level [%]

Time [min]