**3. High-temperature air combustion**

290 Mass Transfer in Chemical Engineering Processes

within 3% error when the O2 mass-fraction *Y*O, is 0.233 (cf. Fig. 2(b); Makino, et al., 1998b); for *Y*O,=0.533, error is within 5%; for *Y*O,=1, error is within 8%. Examinations have been made in the range of the surface Damköhler numbers *Da*s,O and *Da*s,P from 106 to 1010, that of the surface temperature *T*s from 1077 K to 2424 K, and that of the freestream temperature *T* from 323 K to 1239 K. The Frozen and Flame-attached modes can fairly be correlated by the single Eq. (16) because the gas-phase temperature profiles are the same. Note that the combustion rate in high O2 concentrations violates the assumption that (-*fs*)<<1. Nonetheless, the expressions appear to provide a fair representation because these

For axisymmetric stagnation flow, it turns out that the combustion rate in the Frozen and/or

1 ~ ~

 

3 2

 

2

2

s s

~

s s

1 ~ ~

for the transition state, while it increases up to 15% around the state.

1 ~ ~

 

3 2

**2.5 Experimental comparisons at high velocity gradients** 

 

The error is nearly the same as that for the two-dimension case.

*T*

 

*T*

 

~

 

 *<sup>Y</sup> T T*

can fairly represent the combustion rate in two-dimensional stagnation flow, within 4% error when the O2 mass-fraction *Y*<sup>O</sup> is 0.233 and 0.533, although the error becomes 6% near the transition state for the flame attaches. In an oxygen flow, the error is within 6% except

For axisymmetric stagnation flow, the combustion rate in the Flame-detached mode can be

 

In order to verify the validity of the explicit combustion-rate expressions, comparisons have been made with their values and the experimental results (Makino, et al., 1998b). Kinetic parameters are those evaluated in Section 5 in Part 1. The values of thermophysical properties are those at *T*=320 K, which yields =2.1210-5 kg2/(m4・s) and /=1.7810-5 m2/s. Results for the explicit combustion-rate expressions are shown in Figs. 1(a) and 1(b) by solid curves. As shown in Fig. 1(a), up to the ignition surfacetemperature, a reasonable prediction can be made by Eq. (2), with the transfer number for the Frozen mode in Eq. (5) and the correction factor *K* in Eq. (16), for two-dimensional case.

 *<sup>Y</sup> T T*

<sup>~</sup> 0.05 <sup>1</sup> <sup>2</sup> <sup>~</sup>

*T*

,

<sup>2</sup>

*<sup>T</sup> <sup>K</sup>* (18)

.

O,

*<sup>T</sup> <sup>K</sup>* (19)

2

O,

*<sup>T</sup> <sup>K</sup>* (17)

<sup>2</sup> <sup>~</sup>

 

2

*T T*

s s

within 3% error for *Y*O,=0.233 (Makino, et al., 1998b); within 5% error for *Y*O,=0.7. Difference in the forms between Eq. (16) and Eq. (17) can be attributed to the difference in

For the combustion rate in the Flame-detached mode, not only the surface and freestream temperatures but also the oxidizer concentration must be taken into account. It has turned

<sup>~</sup> 0.05 <sup>1</sup> <sup>2</sup> <sup>~</sup>

~

expressions vary as the natural logarithm of the transfer number.

Flame-attached modes can fairly be represented with

the flow configuration.

represented with

out that

Here, carbon combustion has been examined, relevant to the High-Temperature Air Combustion, characterized by use of hot air (~1280 K) and attracted as one of the new technology concepts for pursuing energy saving and/or utilization of low-calorific fuels. Although it has been confirmed to reduce NO*x* emission through reduction of O2 concentration in furnaces, without reducing combustion rate of gaseous and/or liquid fuels (Katsuki & Hasegawa, 1998; Tsuji, et al., 2003), its appropriateness for solid-fuel combustion has not been examined fully. Since solid fuels are commonly used as one of the important energy sources in industries, it is strongly required to examine its appropriateness from the fundamental viewpoint. Here, focus is put on examinations for the promoting and suppressing effects that the temperature and water vapor in the airflow have. From the practical point of view, the carbon combustion in airflow at high temperatures, especially, in high velocity gradients, is related to evaluation of ablative carbon heat-shield for atmospheric re-entry. As for that in airflow at high H2O concentrations, it is related to evaluation of protection properties of rocket nozzles, made of carbonaceous materials, from erosive attacks of water vapor, contained in working fluid for propulsion, as well as the coal/char combustion in such environments with an appreciable amount of water vapor.
