**3.2 Combustion in airflow with medium humidity**

292 Mass Transfer in Chemical Engineering Processes

 *T* <sup>∞</sup> (K) *a* (s-1) △ 320 3300 ◆ 1280 3300 〇 320 820 *Y* A=0.01

0

1000 1500 2000 Surface tempareture *T* s , K

*Y* O=0.23, *Y* P=0.00 ρC=1.25×103

(a) (b)

drawing of the experimental setup is also shown.

2003) that enhances the mass-transfer rate of oxidizer.

*T* s,ig=1830 K

kg/m3

0

1000 1500 2000 Surface tempareture *T* s , K

Fig. 3. Combustion rate in the high-temperature airflow with the velocity gradient *a*=3300 s-1, as a function of the surface temperature *T*s; (a) for the H2O mass-fraction *Y*A=0.003 (Makino, et al., 2003); (b) for *Y*A=0.01 (Makino & Umehara 2007). For comparisons, results in the room-temperature airflows with the same mass flow rate and the same velocity gradient are also shown. Data points are experimental with the test specimen of 1.25103 kg/m3 in graphite density; curves are results of the explicit combustion-rate expressions. Schematical

combustion rate. As for the effect of the high-temperature airflow, we can say that it promotes the combustion rate, because of the elevated transport properties (Makino, et al.,

This promoting effect can also be understood by use of a functional form of the combustion rate *m* ~ (*a*)1/2, derived from Eq. (9), for the diffusion-limited conditions. In this situation, we have *a* = const. when the mass flow rates of air are the same, so that *m* ~ ()1/2. Since the viscosity , which can also be regarded as the mass diffusivity (*D*) when the Schmidt number is unity, is elevated with increasing air temperature, the combustion rate in the high-temperature airflow is necessarily higher than that in the room-temperature airflow. Results in the room-temperature airflow with *a*=3300 s-1 are also shown in Fig. 3(a). The combustion rate increases monotonically, in the same manner as that in the hightemperature airflow. Note that when the velocity gradients are the same, the combustion rate in the high-temperature airflow is lower than that in the room-temperature airflow by about 30%, because of the reduced mass-transfer rate of oxygen, due to thickened boundary layer (Makino, et al., 2003), through overcoming an increase in the mass diffusivity (*D* ~ ). This situation can easily be understood by use of a functional form of the combustion rate *m* ~ (/), from Eq. (9), for the diffusion-limited conditions, where is a measure of the

boundary-layer thickness, expressed as ~ [(/)/*a*]1/2 (Schlichting, 1979).

*Y* O=0.23, *Y* P=0.00 ρC=1.25×10<sup>3</sup>

*T* s,ig=1670 K

*T* s,ig=1820 K

kg/m3

0.01

0.02

Combustion rate , kg/(m2

・s)

0.03

0.04

0.01

0.02

Combustion rate , kg/(m2

・s)

0.03

0.04

 *T* <sup>∞</sup> (K) *a* (s-1) △ 320 3300 ◆ 1280 3300 〇 320 820 *Y* A=0.003

> Figure 3(b) shows similar plots of the combustion rate when the H2O mass-fraction *Y*A = 0.01. Although nearly the same trends are observed, there exist slight differences. Specifically, there exists a slight decrease in the combustion rate, even in the hightemperature airflow, at about 1800 K. This can be attributed to the establishment of COflame, facilitated even in the fast airflow with *a*=3300 s-1, because of the increased H2O massfraction. As for the combustion in the room-temperature airflow with *a*=820 s-1, the ignition surface-temperature is reduced to be about 1650 K, suggesting that the CO-flame can easily be established. Theoretical results are also shown and fair agreement is demonstrated, suggesting that the Frozen and the Flame-detached modes, respectively, represent the combustion behavior before and after the establishment of CO-flame. The ignition surfacetemperature is predicted to be 1820 K for the high-temperature airflow with *a*=3300 s-1 and 1670 K for the room-temperature airflow with *a*=820 s-1, which are also in accordance with experimental observation.
