The objective of this section is to provide the investigator with a method of procuring, processing, and interpreting the depth of char occurring to wood subjected to fire.
Identification of subject area
3.1 Greatest degree of observable charring.
3.2 A systematic sampling survey of adjoining regions to those specifically targeted.
3.3 Areas related to potentially conflict in patterns of trying.
3.4 Controls specimens protected from thermally induced change as a function of the fire.
Sampling
4.1 Marking for pre-removal photos.
4.2 Mapping specimen location for identification accuracy.
Visual analysis
8.1 Measurements of pyrolysis
200 ° C isotherm (beginning pyrolysis and discoloration)
280 ° C isotherm (active pyrolysis zone)
500 ° C isotherm (completely pyrolyzed)
8.2 The depths of char (280 ° C pyrolysis zone) can be determined by subtracting distance from the unpyrolyzed back side of the sample to the 280 ° C pyrolyzed isotherm from the original, pre-fire specimen. However, the best way to establish this is to use the control specimen.
Application
7.2 Photographic images of wood
One of the main objectives of this dissertation is to provide a scientific method to interpret fire scene evidence. This atlas accomplishes part of this goal for wood. In the following figures, we present a photograph of the wood sample and note the type of wood, orientation, and conditions of exposure. The intent is to facilitate matching specimens from the field to these laboratory specimens, making a scientific method of interpreting wood fire scene evidence easier and more complete. This atlas is found in Figure 75 through Figure 134.
Figure 75 1DFL3 - exposed surface
Figure 76 1DFL3 - cross-section
Figure 77 1DFL2 - exposed surface
Figure 78 1DFL2 - cross-section
Figure 79 1DFL9 - exposed surface
Figure 80 1DFL9 - cross-section
Figure 81 1DFL6 - exposed surface
Figure 82 1DFL6 - cross-section
Figure 83 1DFL4 - exposed surface
Figure 84 1DFL4 - cross-section
Figure 85 1DFX4 - exposed surface
Figure 86 1DFX4 - cross-section
Figure 87 1DFX2 - exposed surface
Figure 88 1DFX2 - cross-section
Figure 89 1DFX7 - exposed surface
Figure 90 1DFX7 - cross-section
Figure 91 1DFX5 - exposed surface
Figure 92 1DFX5 - cross-section
Figure 93 1DFX3 - exposed surface
Figure 94 1DFX3 - cross-section
Figure 95 1RL3 - exposed surface
Figure 96 1RL3 - cross-section
Figure 97 1RL2 - exposed surface
Figure 98 1RL2 - cross-section
Figure 99 1RL9 - exposed surface
Figure 100 1RL9 - cross-section
Figure 101 1RL8 - exposed surface
Figure 102 1RL8 - cross-section
Figure 103 1RL4 - exposed surface
Figure 104 1RL4 - cross-section
Figure 105 1RX3 - exposed surface
Figure 106 1RX3 - cross-section
Figure 107 1RX_6 - exposed surface
Figure 108 1RX_6 - cross-section
Figure 109 1RX10 - exposed surface
Figure 110 1RX10 - cross-section
Figure 111 1RX1 - exposed surface
Figure 112 1RX1 - cross-section
Figure 113 1OL_1 - exposed surface
Figure 114 1OL_1 - cross-section
Figure 115 1OL_2 - exposed surface
Figure 116 1OL_2 - cross-section
Figure 117 1OL_5 - exposed surface
Figure 118 1OL_5 - cross-section
Figure 119 1OX_1 - exposed surface
Figure 120 1OX_1 - cross-section
Figure 121 1OX_2 - exposed surface
Figure 122 1OX_2 - cross-section
Figure 123 1OX_3 - exposed surface
Figure 124 1OX_3 - cross-section
Figure 125 1ML_4 - exposed surface
Figure 126 1ML_4 - cross-section
Figure 127 1ML_5 - exposed surface
Figure 128 1ML_5 - cross-section
Figure 129 1ML_1 - exposed surface
Figure 130 1ML_1 - cross-section
Figure 131 1MX_1 - exposed surface
Figure 132 1MX_1 - cross-section
Figure 133 1MX_2 - exposed surface
Figure 134 1MX_2 - cross-section
7.2.2 Pyrolysis zone width study
In the original conclusions on wood (Section 2.8), we claimed that the pyrolysis zone was extremely narrow. This finding supported the conclusions of Zicherman and Williamson [32] and stood in contrast to the often-referenced Roberts theory [22]. The following figures provide photographic evidence that the pyrolysis zone in the wood specimens examined for this research is indeed very narrow. This evidence is shown in Figure 135 through Figure 142.
Figure 135 Pyrolysis zone: 1DFL2
Figure 136 Pyrolysis zone: 1DFX5
Figure 137 Pyrolysis zone: 1RL3
Figure 138 Pyrolysis zone: 1RX3
Figure 139 Pyrolysis zone: 1OL_1
Figure 140 Pyrolysis zone: 1OX_1
Figure 141 Pyrolysis zone: 1ML4
Figure 142 Pyrolysis zone: 1MX1
7.3 Data, measurements, and analysis
This section contains the raw data, the analysis, and the results which were shown in the main body of the dissertation in the figures. It is intended as a supplement to the final results shown in the body of the thesis.
Table 5 List of wood specimens and selected test data
(specimen listing continued in Table 6)
|
|
Sample ID36 |
Wood Type |
Heat Flux |
Duration |
Char Depth |
Cracks per 25 mm2 |
|
Wood |
10L_1 |
Oak |
25 |
1500 |
13 |
3 |
|
Wood |
10L_2 |
Oak |
25 |
4500 |
38 |
2 |
|
Wood |
10L_3 |
Oak |
75 |
1500 |
22 |
4 |
|
Wood |
10L_4 |
Oak |
75 |
1500 |
22 |
4 |
|
Wood |
10L_5 |
Oak |
75 |
1500 |
22 |
3 |
|
Wood |
10X_1 |
Oak |
25 |
1500 |
12 |
10 |
|
Wood |
10X_2 |
Oak |
25 |
4500 |
18 |
5 |
|
Wood |
10X_3 |
Oak |
75 |
1500 |
18 |
5 |
|
Wood |
10X_4 |
Oak |
75 |
1500 |
18 |
8 |
|
Wood |
10X_5 |
Oak |
75 |
1500 |
18 |
8 |
|
Wood |
1DFL1 |
DougFir |
75 |
1500 |
24 |
2 |
|
Wood |
1DFL2 |
DougFir |
75 |
1500 |
22.5 |
2 |
|
Wood |
1DFL3 |
DougFir |
25 |
1500 |
18 |
5 |
|
Wood |
1DFL4 |
DougFir |
75 |
1500 |
24 |
3 |
|
Wood |
1DFL6 |
DougFir |
50 |
1500 |
22 |
1 |
|
Wood |
1DFL7 |
DougFir |
50 |
1500 |
22 |
2 |
|
Wood |
1DFL8 |
DougFir |
50 |
1500 |
22 |
2 |
|
Wood |
1DFL9 |
DougFir |
35 |
1500 |
21 |
2 |
|
Wood |
1DFX1 |
DougFir |
75 |
1500 |
22 |
5 |
|
Wood |
1DFX2 |
DougFir |
75 |
1500 |
23 |
7 |
|
Wood |
1DFX3 |
DougFir |
75 |
4500 |
50 |
1 |
|
Wood |
1DFX4 |
DougFir |
25 |
1500 |
16 |
10 |
|
Wood |
1DFX5 |
DougFir |
75 |
1500 |
25 |
7 |
|
Wood |
1DFX6 |
DougFir |
50 |
1500 |
23 |
5 |
|
Wood |
1DFX7 |
DougFir |
50 |
1500 |
22 |
6 |
|
Wood |
1ML_1 |
Maple |
75 |
1500 |
28 |
6 |
|
Wood |
1ML_2 |
Maple |
75 |
1500 |
26 |
6 |
|
Wood |
1ML_3 |
Maple |
75 |
1500 |
27 |
6 |
|
Wood |
1ML_4 |
Maple |
25 |
1500 |
18 |
4 |
|
Wood |
1ML_5 |
Maple |
25 |
4500 |
43 |
4 |
|
Wood |
1MX_1 |
Maple |
25 |
1500 |
13 |
34 |
|
Wood |
1MX_2 |
Maple |
25 |
4500 |
50 |
18 |
|
Wood |
1MX_3 |
Maple |
75 |
1500 |
20 |
29 |
|
Wood |
1MX_4 |
Maple |
75 |
1500 |
28 |
48 |
|
Wood |
1MX_5 |
Maple |
75 |
1500 |
20 |
42 |
|
Wood |
1RL1 |
Redwd |
75 |
1500 |
31 |
2 |
|
Wood |
1RL2 |
Redwd |
75 |
1500 |
26 |
2 |
|
Wood |
1RL3 |
Redwd |
25 |
1500 |
18.5 |
2 |
|
Wood |
1RL6 |
Redwd |
50 |
1500 |
27 |
2 |
|
Wood |
1RL7 |
Redwd |
50 |
1500 |
26 |
3 |
|
Wood |
1RL8 |
Redwd |
50 |
1500 |
27 |
2 |
|
Wood |
1RL9 |
Redwd |
35 |
1500 |
23 |
1 |
|
Wood |
1RX_6 |
Redwd |
25 |
4500 |
32 |
1 |
|
Wood |
1RX1 |
Redwd |
75 |
1500 |
30 |
2 |
|
Wood |
1RX10 |
Redwd |
35 |
1500 |
25 |
4 |
|
Wood |
1RX2 |
Redwd |
75 |
1500 |
32 |
8 |
|
Wood |
1RX3 |
Redwd |
25 |
1500 |
22 |
12 |
|
Wood |
1RX4 |
Redwd |
75 |
1500 |
28 |
10 |
|
Wood |
1RX7 |
Redwd |
50 |
1500 |
||
|
Wood |
1RX8 |
Redwd |
50 |
1500 |
||
|
Wood |
1RX9 |
Redwd |
50 |
1500 |
33 |
3 |
Table 6 List of wood specimens and selected test data (continued)
(specimen listing continued from Table 5)
|
|
Sample ID38 |
Pre Density (kg/m3) |
Pretest Mass |
Post-test Mass |
Moisture content, side, pretest |
Moisture content, top, pretest |
|
Wood |
10L_1 |
738.234 |
354.5 |
283.1 |
5.2 |
0 |
|
Wood |
10L_2 |
756.976 |
363.5 |
146.5 |
5.2 |
0 |
|
Wood |
10L_3 |
750.720 |
360.5 |
220.2 |
4.8 |
0 |
|
Wood |
10L_4 |
757.184 |
363.6 |
216.8 |
5.2 |
0 |
|
Wood |
10L_5 |
759.475 |
364.7 |
220.9 |
5.2 |
0 |
|
Wood |
10X_1 |
680.758 |
326.9 |
261.1 |
5.2 |
0 |
|
Wood |
10X_2 |
681.382 |
327.2 |
127 |
5.2 |
0 |
|
Wood |
10X_3 |
670.345 |
321.9 |
187.4 |
5.2 |
0 |
|
Wood |
10X_4 |
679.716 |
326.4 |
189.9 |
5.2 |
0 |
|
Wood |
10X_5 |
680.133 |
326.6 |
196 |
5.2 |
0 |
|
Wood |
1DFL1 |
504.727 |
232.7 |
125.1 |
9.1 |
11 |
|
Wood |
1DFL2 |
519.766 |
244.6 |
149.7 |
9.8 |
9.6 |
|
Wood |
1DFL3 |
480.660 |
226.2 |
167.9 |
9.8 |
10 |
|
Wood |
1DFL4 |
503.656 |
234.6 |
133.4 |
9.4 |
9.8 |
|
Wood |
1DFL6 |
478.134 |
229.6 |
142.9 |
5.3 |
|
|
Wood |
1DFL7 |
490.420 |
235.5 |
147.7 |
5.3 |
|
|
Wood |
1DFL8 |
225.9 |
139.8 |
8.7 |
||
|
Wood |
1DFL9 |
231.9 |
161.4 |
|||
|
Wood |
1DFX1 |
476.691 |
221.9 |
126.4 |
10 |
10 |
|
Wood |
1DFX2 |
442.463 |
208.2 |
114.3 |
9.8 |
10 |
|
Wood |
1DFX3 |
212.6 |
35.3 |
8.6 |
12 |
|
|
Wood |
1DFX4 |
456.630 |
212.7 |
154 |
10 |
12 |
|
Wood |
1DFX5 |
444.402 |
207 |
115.6 |
10 |
11 |
|
Wood |
1DFX6 |
416.076 |
199.8 |
113.8 |
5.3 |
|
|
Wood |
1DFX7 |
418.783 |
201.1 |
125.2 |
8.7 |
|
|
Wood |
1ML_1 |
745.939 |
358.2 |
201.4 |
4.8 |
0 |
|
Wood |
1ML_2 |
741.149 |
355.9 |
199.9 |
4.8 |
0 |
|
Wood |
1ML_3 |
743.231 |
356.9 |
193.2 |
4.8 |
0 |
|
Wood |
1ML_4 |
743.440 |
357 |
267.4 |
0 |
0 |
|
Wood |
1ML_5 |
730.320 |
350.7 |
117.4 |
4.8 |
0 |
|
Wood |
1MX_1 |
744.273 |
357.4 |
281.2 |
4.8 |
0 |
|
Wood |
1MX_2 |
731.153 |
351.1 |
131.3 |
4.8 |
0 |
|
Wood |
1MX_3 |
756.351 |
363.2 |
201.5 |
4.8 |
0 |
|
Wood |
1MX_4 |
740.108 |
355.4 |
189.1 |
4.8 |
0 |
|
Wood |
1MX_5 |
739.483 |
355.1 |
194.1 |
4.8 |
0 |
|
Wood |
1RL1 |
344.080 |
157 |
70.1 |
12 |
14 |
|
Wood |
1RL2 |
362.271 |
165.3 |
84.6 |
10 |
12 |
|
Wood |
1RL3 |
356.810 |
166.2 |
113.1 |
11 |
12 |
|
Wood |
1RL6 |
321.324 |
154.3 |
79.1 |
5.1 |
|
|
Wood |
1RL7 |
332.153 |
159.5 |
89.2 |
5.1 |
|
|
Wood |
1RL8 |
153.3 |
87.2 |
11 |
||
|
Wood |
1RL9 |
156.9 |
98.1 |
8.1 |
||
|
Wood |
1RX_6 |
312.161 |
149.9 |
36.6 |
5.1 |
0 |
|
Wood |
1RX1 |
349.734 |
157.8 |
76.2 |
9.6 |
13 |
|
Wood |
1RX10 |
144.2 |
83.6 |
8.1 |
||
|
Wood |
1RX2 |
336.748 |
150.5 |
63.5 |
8.6 |
11 |
|
Wood |
1RX3 |
339.457 |
150.1 |
96.4 |
9.6 |
13 |
|
Wood |
1RX4 |
348.241 |
160.4 |
79.7 |
9.6 |
11 |
|
Wood |
1RX7 |
302.582 |
145.3 |
66.5 |
5.1 |
|
|
Wood |
1RX8 |
371.928 |
178.6 |
96.8 |
5.1 |
|
|
Wood |
1RX9 |
141.6 |
70.6 |
9.6 |
7.3.2 Graphs of composite wood behavior
One of the central tenets of this thesis is that wood burns in a highly variable manner, which is not reliable enough for scientific application. The next figures illustrate this more clearly. Figure 143 shows the variability in time versus temperature at a known depth, experienced when wood is subjected to a relatively low (25 kW/m2) heat flux. The measurements were made at 12 mm. Notice how the high and low values go further and further away from the average as the time goes on. This indicates a relatively high variability. Figure 144 shows the similar variability for a higher heat flux (75 kW/m2), measured closer to the surface (4 mm). The variability is relatively large especially in the beginning when the wood burns within a particularly wide range. Figure 145 shows the variability achieved when wood is exposed to a 75 kW/m2 heat flux, and measured at a 12 mm depth. The variability was so large, that outliers were located and also graphed. From this graph, it is possible to see the tremendous range of variability for wood, especially at high temperatures, or when it has burned a long time, which makes it extremely difficult to determine heat flux exposure or time of exposure from char characteristics.
7.3.3 Analysis: rate of charring
A large part of the analysis involves the rate of char. The literature often assumes a constant rate of char for wood, often overlooks the wood species and grain orientation, and makes no mention of the zone. 39
In this section, we detail the calculations which were performed to draw our conclusions about rate of charring. The analysis was performed in the following manner. The 280° isotherm was used as the char frontier, which corresponds to distinct blackening of the wood samples. For each thermocouple, the time between insertion into the cone calorimeter and the time when the thermocouple hit 280 ° C was measured. The distance between the exposed surface and the thermocouple was already known. Because we used the 4 mm and the 12 mm depth thermocouples for these measurements, there were three different zones generated. With a known distance, and a measured time, the rate of char (rate of the 280° C isotherm) could be calculated. The detailed calculations for the wood samples are shown in Table 7.
Table 7 Calculation of wood char rates in the different zones
(This table gives raw times until pyrolysis. The rate calculations are in Table 8)
|
Column A |
Column B |
Column C |
||
|
Time until pyrolysis reaches 4 mm |
Time until pyrolysis reaches 12 mm |
Time until pyrolysis reaches 24 mm |
||
|
Heat Flux (kW/m2)41 (* denotes 4500 second duration) |
Sample ID |
4 mm |
12 mm |
24 mm |
|
25 |
10L_1 |
276 |
877 |
|
|
*25 |
10L_2 |
341 |
949 |
2921 |
|
25 |
10X_1 |
279 |
928 |
|
|
*25 |
10X_2 |
363 |
1346 |
2736 |
|
25 |
1DFL3 |
389 |
938 |
|
|
25 |
1DFX4 |
255 |
699 |
|
|
25 |
1ML_4 |
236 |
575 |
|
|
*25 |
1ML_5 |
155 |
612 |
1750 |
|
25 |
1MX_1 |
350 |
952 |
|
|
*25 |
1MX_2 |
801 |
2676 |
|
|
25 |
1RL3 |
286 |
872 |
|
|
25 |
1RX3 |
221 |
641 |
|
|
*25 |
1RX_6 |
196 |
600 |
1468 |
|
50 |
1DFL6 |
199 |
704 |
|
|
50 |
1DFL7 |
289 |
1005 |
|
|
50 |
1DFX6 |
150 |
549 |
1441 |
|
50 |
1DFX7 |
129 |
514 |
1463 |
|
50 |
1RL6 |
86 |
463 |
1094 |
|
50 |
1RL7 |
106 |
417 |
1302 |
|
50 |
1RX7 |
97 |
425 |
1082 |
|
50 |
1RX8 |
111 |
450 |
1183 |
|
75 |
10L_3 |
66 |
||
|
75 |
10L_4 |
140 |
365 |
1509 |
|
75 |
10L_5 |
125 |
598 |
|
|
75 |
10X_3 |
53 |
537 |
1360 |
|
75 |
10X_4 |
52 |
423 |
1115 |
|
75 |
10X_5 |
116 |
528 |
|
|
75 |
1DFL1 |
152 |
519 |
|
|
75 |
1DFL2 |
133 |
631 |
|
|
75 |
1DFL4 |
271 |
815 |
|
|
75 |
1DFX1 |
127 |
537 |
|
|
75 |
1DFX2 |
79 |
416 |
1280 |
|
75 |
1DFX5 |
93 |
454 |
1232 |
|
75 |
1ML_1 |
61 |
289 |
1123 |
|
75 |
1ML_2 |
22 |
203 |
924 |
|
75 |
1ML_3 |
41 |
275 |
1113 |
|
75 |
1MX_3 |
76 |
392 |
1093 |
|
75 |
1MX_4 |
124 |
419 |
1177 |
|
75 |
1MX_5 |
84 |
396 |
1197 |
|
75 |
1RL1 |
99 |
317 |
880 |
|
75 |
1RL2 |
56 |
364 |
1193 |
|
75 |
1RX1 |
64 |
359 |
843 |
|
75 |
1RX2 |
46 |
257 |
|
|
75 |
1RX4 |
53 |
275 |
978 |
Table 8 Calculation of wood char rates in the different zones (continued)
(These rates are calculated from the times shown in Table 7, which contains the data for Columns A, B, and C)
|
Column D |
Column E |
Column F |
||
|
Rate of Active Pyrolysis Zone 042 |
Rate of Active Pyrolysis Zone 143 |
Rate of Active Pyrolysis Zone 244 |
||
|
Heat Flux (* denotes 4500 second duration) |
Sample ID |
= 4 mm / Col. A |
= 8 mm / (Col. B - Col A) |
= 12 mm /(Col. C - Col. B) |
|
25 |
10L_1 |
0.0144928 |
0.0133111 |
|
|
*25 |
10L_2 |
0.0117302 |
0.0131579 |
0.0060852 |
|
25 |
10X_1 |
0.0143369 |
0.0123267 |
|
|
*25 |
10X_2 |
0.0110193 |
0.0081384 |
0.0086331 |
|
25 |
1DFL3 |
0.0102828 |
0.0145719 |
|
|
25 |
1DFX4 |
0.0156863 |
0.0180180 |
|
|
25 |
1ML_4 |
0.0169492 |
0.0235988 |
|
|
*25 |
1ML_5 |
0.0258065 |
0.0175055 |
0.0105448 |
|
25 |
1MX_1 |
0.0114286 |
0.0132890 |
|
|
*25 |
1MX_2 |
0.0064000 |
||
|
25 |
1RL3 |
0.0139860 |
0.0136519 |
|
|
25 |
1RX3 |
0.0180995 |
0.0190476 |
|
|
*25 |
1RX_6 |
0.0204082 |
0.0198020 |
0.0138249 |
|
50 |
1DFL6 |
0.0201005 |
0.0158416 |
|
|
50 |
1DFL7 |
0.0138408 |
0.0111732 |
|
|
50 |
1DFX6 |
0.0266667 |
0.0200501 |
0.0134529 |
|
50 |
1DFX7 |
0.0310078 |
0.0207792 |
0.0126449 |
|
50 |
1RL6 |
0.0465116 |
0.0212202 |
0.0190174 |
|
50 |
1RL7 |
0.0377358 |
0.0257235 |
0.0135593 |
|
50 |
1RX7 |
0.0412371 |
0.0243902 |
0.0182648 |
|
50 |
1RX8 |
0.0360360 |
0.0235988 |
0.0163711 |
|
75 |
10L_3 |
0.0606061 |
||
|
75 |
10L_4 |
0.0285714 |
0.0355556 |
0.0104895 |
|
75 |
10L_5 |
0.0320000 |
0.0169133 |
|
|
75 |
10X_3 |
0.0754717 |
0.0165289 |
0.0145808 |
|
75 |
10X_4 |
0.0769231 |
0.0215633 |
0.0173410 |
|
75 |
10X_5 |
0.0344828 |
0.0194175 |
|
|
75 |
1DFL1 |
0.0263158 |
0.0217984 |
|
|
75 |
1DFL2 |
0.0300752 |
0.0160643 |
|
|
75 |
1DFL4 |
0.0147601 |
0.0147059 |
|
|
75 |
1DFX1 |
0.0314961 |
0.0195122 |
|
|
75 |
1DFX2 |
0.0506329 |
0.0237389 |
0.0138889 |
|
75 |
1DFX5 |
0.0430108 |
0.0221607 |
0.0154242 |
|
75 |
1ML_1 |
0.0655738 |
0.0350877 |
0.0143885 |
|
75 |
1ML_2 |
0.1818182 |
0.0441989 |
0.0166436 |
|
75 |
1ML_3 |
0.0975610 |
0.0341880 |
0.0143198 |
|
75 |
1MX_3 |
0.0526316 |
0.0253165 |
0.0171184 |
|
75 |
1MX_4 |
0.0322581 |
0.0271186 |
0.0158311 |
|
75 |
1MX_5 |
0.0476190 |
0.0256410 |
0.0149813 |
|
75 |
1RL1 |
0.0404040 |
0.0366972 |
0.0213144 |
|
75 |
1RL2 |
0.0714286 |
0.0259740 |
0.0144753 |
|
75 |
1RX1 |
0.0625000 |
0.0271186 |
0.0247934 |
|
75 |
1RX2 |
0.0869565 |
0.0379147 |
|
|
75 |
1RX4 |
0.0754717 |
0.0360360 |
0.0170697 |
Table 9 Rate of char isotherm through wood: variation by zone and heat flux
|
Heat flux |
Average rate of char: Zone 0 |
Max rate of char: Zone 0 |
Min rate of char: Zone 0 |
|
25 |
0.015352176 |
0.025806452 |
0.010282776 |
|
50 |
0.031642047 |
0.046511628 |
0.013840830 |
|
75 |
0.051670461 |
0.097560976 |
0.014760148 |
|
Heat flux |
Average rate of char: Zone 1 |
Max rate of char: Zone 1 |
Min rate of char: Zone 1 |
|
25 |
0.015534902 |
0.023598820 |
0.008138352 |
|
50 |
0.020347101 |
0.025723473 |
0.011173184 |
|
75 |
0.025669113 |
0.037914692 |
0.014705882 |
|
Heat flux (kW/m2) |
Average rate of char: Zone 2 |
Max rate of char: Zone 2 |
Min rate of char: Zone 2 |
|
25 |
0.009097597 |
0.013824885 |
0.006085193 |
|
50 |
0.015551746 |
0.019017433 |
0.012644889 |
|
75 |
0.016144019 |
0.024793388 |
0.010489510 |
7.3.4 Determination of exposure time and heat flux
Because wood burns so variably, it is difficult to determine exposure time or heat flux. However, the following methodology was employed to create a map. Define the following variables:
|
Let |
||
|
x |
= |
The distance from the exposed face to this thermocouple (in millimeters). This will be our variable of integration. |
|
q |
= |
The heat flux (in kW/m2) |
|
z |
= |
The zone of the wood, z = 0, 1, 2 (corresponding to thermocouple depths of 4, 12, and 24 mm) |
|
r(z, q) |
= |
Rate at which wood chars in zone Z when the exposed surface experiences heat flux q |
|
t(d, q) |
= |
Time required for a heat flux q to char wood to depth d. This is the variable we wish to determine. |
We can write the calculations for t(d, q) as follows:


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Experimental data was gathered, averaged, and calculated, shown in Table 9. This data was then used to calculate the map, and the results are presented below. The numbers in Table 10 make up Figure 26.
Table 10 Calculation of map for wood char using rate of isotherm movement
|
Heat flux |
Depth of thermocouple |
Average time for char isotherm to reach the depth |
Max time for char isotherm to reach the depth |
Min time for char isotherm to reach the depth |
|
25 |
0 |
0 |
0 |
0 |
|
25 |
4 |
260 |
389 |
155 |
|
25 |
12 |
775 |
1372 |
494 |
|
25 |
24 |
2094 |
3344 |
1362 |
|
50 |
0 |
0 |
0 |
0 |
|
50 |
4 |
126 |
289 |
86 |
|
50 |
12 |
519 |
1005 |
397 |
|
50 |
24 |
1291 |
1954 |
1028 |
|
75 |
0 |
0 |
0 |
0 |
|
75 |
4 |
77 |
271 |
41 |
|
75 |
12 |
389 |
815 |
252 |
|
75 |
24 |
1132 |
1959 |
736 |