Etude de la combustion de gaz de synthèse issus d'un processus de ...
Etude de la combustion de gaz de synthèse issus d'un processus de ... Etude de la combustion de gaz de synthèse issus d'un processus de ...
Appendix A – Overdetermined linear equations systems b −AX ≤ b −AY , ∀Y ∈R n (A-15) Rewriting b − AY as ( ) ( ) b − AY = b − AX + A X −Y (A-16) and taking the norm, we obtain 2 2 ( ) ( ) T (( b AX) A( X Y) ) (( b AX) A( X Y) ) T ( b AX) 2( A( X Y) ) ( b AX) A( X Y) b − AY = b − AX + A X −Y = − + − − + − 2 2 = − + − − + − (A-17) tel-00623090, version 1 - 13 Sep 2011 Moreover, by (A-9) we have Therefore, we conclude: T T T ( A( X −Y) ) ( b − AX) = ( X −Y) A ( b − AX) = 0 2 2 2 2 ( ) ( ) ( ) b − AY = b − AX + A X −Y ≥ b −AX The equality in (A-19) only occurs when A( X − Y) = 0 of the matrix A are linearly independent, then A( X − Y) = 0 that ( X − Y) = 0 , i.e., X = Y . (A-18) (A-19) . Furthermore, once the columns which implies 218
Appendix B- Syngas-air mixtures properties Appendix B - SYNGAS-AIR MIXTURE PROPERTIES tel-00623090, version 1 - 13 Sep 2011 P i (bar) 0.5 1.0 2.0 5.0 0.5 1.0 2.0 5.0 0.5 1.0 2.0 5.0 φ P v (bar) C p /C v ρ u ρ b T v (K) (kg/m 3 ) (kg/m 3 ) Updraft syngas-air mixture properties μ (m 2 /s) α (m 2 /s) 0.6 2.980 1.395 1859.5 0.581 0.09621 3.08E-05 4.24E-05 0.8 3.312 1.394 2091.2 0.5773 0.10426 3.08E-05 4.32E-05 1 3.494 1.393 2218.6 0.5743 0.09624 3.09E-05 4.39E-05 1.2 3.373 1.392 2125.2 0.5718 0.10298 3.09E-05 4.44E-05 0.6 5.962 1.395 1860.2 1.162 0.23535 1.54E-05 2.12E-05 0.8 6.637 1.394 2095.8 1.1546 0.20854 1.54E-05 2.16E-05 1 7.026 1.393 2232.7 1.1486 0.19289 1.54E-05 2.19E-05 1.2 6.752 1.392 2127.3 1.1437 0.20415 1.54E-05 2.22E-05 0.6 11.927 1.395 1860.8 2.324 0.38485 7.69E-06 1.06E-05 0.8 13.293 1.394 2099.3 2.3093 0.41702 7.70E-06 1.08E-05 1 14.119 1.393 2245.2 2.2973 0.38508 7.71E-06 1.10E-05 1.2 13.511 1.392 2128.7 2.2874 0.41192 7.72E-06 1.11E-05 0.6 29.825 1.395 1861.3 5.8101 1.17669 3.08E-06 4.24E-06 0.8 33.281 1.394 2102.7 5.7731 1.04223 3.08E-06 4.32E-06 1 35.491 1.393 2259.5 5.7432 0.9608 3.09E-06 4.39E-06 1.2 33.796 1.392 2129.9 5.7184 1.02068 3.09E-06 4.44E-06 Downdraft syngas-air mixture properties 0.6 2.914 1.393 1838.2 0.5743 0.1187 3.10E-05 4.54E-05 0.8 3.218 1.392 2057.5 0.5695 0.10573 3.11E-05 4.67E-05 1 3.383 1.391 2179.4 0.5657 0.09825 3.12E-05 4.77E-05 1.2 3.252 1.390 2080.8 0.5626 0.10387 3.13E-05 4.86E-05 0.6 5.829 1.393 1838.8 1.1486 0.23738 1.55E-05 2.27E-05 0.8 6.447 1.392 2061.4 1.139 0.2114 1.56E-05 2.33E-05 1 6.800 1.391 2192.1 1.1314 0.19613 1.56E-05 2.39E-05 1.2 6.508 1.390 2082.4 1.1252 0.20774 1.56E-05 2.43E-05 0.6 11.662 1.393 1839.8 2.2971 0.47475 7.76E-06 1.13E-05 0.8 12.910 1.392 2064.5 2.2781 0.42271 7.78E-06 1.17E-05 1 13.660 1.391 2203.2 2.2628 0.39163 7.80E-06 1.19E-05 1.2 13.021 1.390 2083.5 2.2504 0.41546 7.82E-06 1.21E-05 0.6 29.162 1.393 1839.9 5.7428 1.18683 3.10E-06 4.54E-06 0.8 32.314 1.392 2067.4 5.6952 1.05657 3.11E-06 4.67E-06 1 34.318 1.391 2215.8 5.6571 0.97742 3.12E-06 4.77E-06 1.2 32.566 1.390 2084.4 5.6259 1.03903 3.13E-06 4.86E-06 Fluidized-bed syngas-air mixture properties 0.6 2.851 1.388 1736.5 0.5944 0.12579 2.97E-05 4.03E-05 0.8 3.186 1.386 1955.5 0.5933 0.11167 2.96E-05 4.07E-05 1 3.395 1.384 2091.4 0.5923 0.10314 2.95E-05 4.11E-05 1.2 3.203 1.382 1946.7 0.5916 0.11111 2.94E-05 4.13E-05 0.6 5.703 1.388 1736.8 1.1888 0.25158 1.49E-05 2.02E-05 0.8 6.378 1.386 1957.4 1.1865 0.22329 1.48E-05 2.04E-05 1 6.816 1.384 2100.4 1.1847 0.20604 1.47E-05 2.05E-05 1.2 6.406 1.382 1947.1 1.1831 0.22221 1.47E-05 2.07E-05 0.6 11.406 1.388 1737 2.3776 0.50315 7.43E-06 1.01E-05 0.8 12.764 1.386 1958.9 2.3731 0.44653 7.40E-06 1.02E-05 1 13.675 1.384 2108.1 2.3694 0.41168 7.37E-06 1.03E-05 1.2 12.814 1.382 1947.4 2.3663 0.44441 7.34E-06 1.03E-05 0.6 28.52 1.388 1737.3 5.9439 1.25785 2.97E-06 4.03E-06 0.8 31.931 1.386 1960.3 5.9327 1.11623 2.96E-06 4.07E-06 1 34.307 1.384 2116.7 5.9234 1.02815 2.95E-06 4.11E-06 1.2 32.04 1.382 1947.7 5.9157 1.11102 2.94E-06 4.13E-06 219
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Appendix B- Syngas-air mixtures properties<br />
Appendix B - SYNGAS-AIR MIXTURE PROPERTIES<br />
tel-00623090, version 1 - 13 Sep 2011<br />
P i (bar)<br />
0.5<br />
1.0<br />
2.0<br />
5.0<br />
0.5<br />
1.0<br />
2.0<br />
5.0<br />
0.5<br />
1.0<br />
2.0<br />
5.0<br />
φ<br />
P v<br />
(bar)<br />
C p /C v<br />
ρ u<br />
ρ b<br />
T v (K)<br />
(kg/m 3 ) (kg/m 3 )<br />
Updraft syngas-air mixture properties<br />
μ<br />
(m 2 /s)<br />
α<br />
(m 2 /s)<br />
0.6 2.980 1.395 1859.5 0.581 0.09621 3.08E-05 4.24E-05<br />
0.8 3.312 1.394 2091.2 0.5773 0.10426 3.08E-05 4.32E-05<br />
1 3.494 1.393 2218.6 0.5743 0.09624 3.09E-05 4.39E-05<br />
1.2 3.373 1.392 2125.2 0.5718 0.10298 3.09E-05 4.44E-05<br />
0.6 5.962 1.395 1860.2 1.162 0.23535 1.54E-05 2.12E-05<br />
0.8 6.637 1.394 2095.8 1.1546 0.20854 1.54E-05 2.16E-05<br />
1 7.026 1.393 2232.7 1.1486 0.19289 1.54E-05 2.19E-05<br />
1.2 6.752 1.392 2127.3 1.1437 0.20415 1.54E-05 2.22E-05<br />
0.6 11.927 1.395 1860.8 2.324 0.38485 7.69E-06 1.06E-05<br />
0.8 13.293 1.394 2099.3 2.3093 0.41702 7.70E-06 1.08E-05<br />
1 14.119 1.393 2245.2 2.2973 0.38508 7.71E-06 1.10E-05<br />
1.2 13.511 1.392 2128.7 2.2874 0.41192 7.72E-06 1.11E-05<br />
0.6 29.825 1.395 1861.3 5.8101 1.17669 3.08E-06 4.24E-06<br />
0.8 33.281 1.394 2102.7 5.7731 1.04223 3.08E-06 4.32E-06<br />
1 35.491 1.393 2259.5 5.7432 0.9608 3.09E-06 4.39E-06<br />
1.2 33.796 1.392 2129.9 5.7184 1.02068 3.09E-06 4.44E-06<br />
Downdraft syngas-air mixture properties<br />
0.6 2.914 1.393 1838.2 0.5743 0.1187 3.10E-05 4.54E-05<br />
0.8 3.218 1.392 2057.5 0.5695 0.10573 3.11E-05 4.67E-05<br />
1 3.383 1.391 2179.4 0.5657 0.09825 3.12E-05 4.77E-05<br />
1.2 3.252 1.390 2080.8 0.5626 0.10387 3.13E-05 4.86E-05<br />
0.6 5.829 1.393 1838.8 1.1486 0.23738 1.55E-05 2.27E-05<br />
0.8 6.447 1.392 2061.4 1.139 0.2114 1.56E-05 2.33E-05<br />
1 6.800 1.391 2192.1 1.1314 0.19613 1.56E-05 2.39E-05<br />
1.2 6.508 1.390 2082.4 1.1252 0.20774 1.56E-05 2.43E-05<br />
0.6 11.662 1.393 1839.8 2.2971 0.47475 7.76E-06 1.13E-05<br />
0.8 12.910 1.392 2064.5 2.2781 0.42271 7.78E-06 1.17E-05<br />
1 13.660 1.391 2203.2 2.2628 0.39163 7.80E-06 1.19E-05<br />
1.2 13.021 1.390 2083.5 2.2504 0.41546 7.82E-06 1.21E-05<br />
0.6 29.162 1.393 1839.9 5.7428 1.18683 3.10E-06 4.54E-06<br />
0.8 32.314 1.392 2067.4 5.6952 1.05657 3.11E-06 4.67E-06<br />
1 34.318 1.391 2215.8 5.6571 0.97742 3.12E-06 4.77E-06<br />
1.2 32.566 1.390 2084.4 5.6259 1.03903 3.13E-06 4.86E-06<br />
Fluidized-bed syngas-air mixture properties<br />
0.6 2.851 1.388 1736.5 0.5944 0.12579 2.97E-05 4.03E-05<br />
0.8 3.186 1.386 1955.5 0.5933 0.11167 2.96E-05 4.07E-05<br />
1 3.395 1.384 2091.4 0.5923 0.10314 2.95E-05 4.11E-05<br />
1.2 3.203 1.382 1946.7 0.5916 0.11111 2.94E-05 4.13E-05<br />
0.6 5.703 1.388 1736.8 1.1888 0.25158 1.49E-05 2.02E-05<br />
0.8 6.378 1.386 1957.4 1.1865 0.22329 1.48E-05 2.04E-05<br />
1 6.816 1.384 2100.4 1.1847 0.20604 1.47E-05 2.05E-05<br />
1.2 6.406 1.382 1947.1 1.1831 0.22221 1.47E-05 2.07E-05<br />
0.6 11.406 1.388 1737 2.3776 0.50315 7.43E-06 1.01E-05<br />
0.8 12.764 1.386 1958.9 2.3731 0.44653 7.40E-06 1.02E-05<br />
1 13.675 1.384 2108.1 2.3694 0.41168 7.37E-06 1.03E-05<br />
1.2 12.814 1.382 1947.4 2.3663 0.44441 7.34E-06 1.03E-05<br />
0.6 28.52 1.388 1737.3 5.9439 1.25785 2.97E-06 4.03E-06<br />
0.8 31.931 1.386 1960.3 5.9327 1.11623 2.96E-06 4.07E-06<br />
1 34.307 1.384 2116.7 5.9234 1.02815 2.95E-06 4.11E-06<br />
1.2 32.04 1.382 1947.7 5.9157 1.11102 2.94E-06 4.13E-06<br />
219
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