9781441979421-c1

# What is the main reason for such a big discrepancy

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Unformatted text preview: perature is 2,425.1 K. The equilibrium mole fractions are listed below Mole fractions Species H2 O2 N2 H2O xreactant 0.2958 0.1479 0.5563 0 xproduct 0.0153 0.0079 0.6478 0.3286 Note that there is a small amount (~1.5%) of H2 existing in the products due to the dissociation of H2O at high temperature. Results of the above three methods agree with each other within 100–200 K which is less than 12% of the ﬂame temperature. If radicals, such as H, OH, and O, are also included in the products, the equilibrium temperature drops to 2,384 K because additional dissociation occurs. This 41 K difference is about 1.7% of the ﬂame temperature. Example 2.7 The space shuttle burns liquid hydrogen and oxygen in the main engine. To estimate the maximum ﬂame temperature, consider combustion of 1 mol of gaseous hydrogen with 0.5 mol of gaseous O2 at 101.3 kPa. Determine the adiabatic ﬂame temperatures using the average cp method. Solution: The combustion stoichiometry is H2ðgÞ þ 0:5O2 ðgÞ ! H2 OðgÞ À Q0 ;p ¼ LHV of H2 at constant pressure rxn ÀQ0 ;p ¼ rxn X i ^ Ni;R Dho;R À i X ^ ^ ^ ^ Ni;P Dho;P ¼ Dho 2 þ 0:5Dho 2 À 1Dho 2O i H O H i ¼ 0 þ 0 À 1 molðÀ241:88 kJ/molÞ ¼ 241:88 kJ Guessing a ﬁnal temperature of about 3,000 K, we use average speciﬁc heats evaluated at 1,500 K 2.4 Adiabatic Flame Temperature 39 P ^ ÀQ0 ;p þ Ni;R hsi;R ðTR Þ rxn i P TP ¼ T0 þ ^ Ni;P cpi i 241:88 kJ=mol ¼ 300 K þ 0:047 kJ/mol À K \$ 5; 822 K Discussion: This temperature is evidently much higher than the NASA reported value of ~3,600 K. What is the main reason for such a BIG discrepancy? The estimated temperature is well above 2,000 K and one expects a substantial dissociation of H2O back to H2 and O2. That is, H2(g) þ 0.5 O2 (g) ↔ H2O (g). Now we use Cantera or a commercial software program, such as Chemkin, to compute the equilibrium temperature with only three species H2, O2, and H2O. The predicted adiabatic ﬂame temperature drops to 3508.7 K. The mole fractions of the...
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## This document was uploaded on 01/20/2014.

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