**3.1 Combustion in relatively dry airflow**

Figure 3(a) shows the combustion rate as a function of the surface temperature *T*s, with the airflow temperature *T* taken as a parameter. The H2O mass-fraction *Y*A=0.003 in the airflow, considered to be dry, practically. The combustion rate in the high-temperature airflow (*T*=1280 K), shown by a solid diamond, increases monotonically and reaches the diffusion-limited value with increasing *T*s. Monotonic change in the combustion rate is attributed to the high velocity gradient (*a*=3300 s-1), which is too high for the CO-flame to be established (Makino, et al., 2003), so that the combustion here is considered to proceed solely with the surface C-O2 reaction. Note that this velocity gradient has been chosen, so as to suppress the abrupt changes in the combustion rates, in order to clarify effects of the High-Temperature Air Combustion.

Results in the room-temperature airflow (*T*=320 K) with the same mass flow rate (*a*=820 s-1) are also shown. The combustion rate first increases, then decreases abruptly, and again increases, with increasing *T*s, as explained in the previous Section. The ignition surfacetemperature observed is about 1800 K, in accordance with the abrupt decrease in the

Mass Transfer Related to Heterogeneous Combustion of Solid Carbon

effects of the H2O concentration are to be examined.

**3.2 Combustion in airflow with medium humidity** 

experimental observation.

3(b).

**3.3 Combustion in humid airflow** 

in the Forward Stagnation Region - Part 2 - Combustion Rate in Special Environments 293

Solid curves are theoretical (Makino, et al., 1998b; 2003). For the airflow with *a*=3300 s-1, the Frozen mode is used. For the airflow with *a*=820 s-1, up to the ignition surface-temperature predicted to be 1830 K, the Frozen mode is used, whereas the Flame-detached mode is used above the ignition surface-temperature. It is seen that a fair degree of agreement is demonstrated between experimental and theoretical results, reconfirming the appropriateness to use the Frozen and Flame-detached modes for representing the

As shown in Fig. 3(a), when the mass flow rates of airflows are the same, the combustion rate in the high-temperature airflow is enhanced, so that the advantage of this technique looks trivial. However, its quantitative evaluation is not so straightforward, because there can appear abrupt changes in the combustion rate, related to the establishment of CO-flame that depends on the H2O mass-fraction in airflow. Furthermore, water vapor can even be an oxidizer for carbon. So, in evaluating the High-Temperature Air Combustion technique,

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

A further increase in the H2O mass-fraction can considerably change the combustion behavior (Makino & Umehara, 2007). The H2O mass-fraction *Y*<sup>A</sup> is now increased to be 0.10, the dew point of which is as high as 328 K (55°C). Note that this H2O mass-fraction is even higher than that ever used in the previous studies with humid airflow (Matsui, et al., 1983; 1986), by virtue of a small-sized boiler installed in the experimental apparatus. Figure 4(a) shows the combustion rate in the high-temperature airflow with *a*=3300 s-1, as a function of the surface temperature *T*s. The O2 mass-fraction is reduced, because of the increased H2O concentration. It is seen that the combustion rate increases first gradually and then rapidly with increasing surface temperature. This trend is quite different from that in Figs. 3(a) or

In order to elucidate causes for this trend, theoretical results are obtained, with additional surface C-H2O and global gas-phase H2-O2 reactions taken into the formulation (Makino & Umehara, 2007), which will be explained later. Not only results in the Frozen and Flamedetached modes, but also that in the Flame-attached mode is shown. In the Flame-attached mode, it is assumed that combustion products of the surface reactions can immediately be

combustion behavior before and after the establishment of CO-flame, respectively.

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 drawing of the experimental setup is also shown.

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

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).

Solid curves are theoretical (Makino, et al., 1998b; 2003). For the airflow with *a*=3300 s-1, the Frozen mode is used. For the airflow with *a*=820 s-1, up to the ignition surface-temperature predicted to be 1830 K, the Frozen mode is used, whereas the Flame-detached mode is used above the ignition surface-temperature. It is seen that a fair degree of agreement is demonstrated between experimental and theoretical results, reconfirming the appropriateness to use the Frozen and Flame-detached modes for representing the combustion behavior before and after the establishment of CO-flame, respectively.

As shown in Fig. 3(a), when the mass flow rates of airflows are the same, the combustion rate in the high-temperature airflow is enhanced, so that the advantage of this technique looks trivial. However, its quantitative evaluation is not so straightforward, because there can appear abrupt changes in the combustion rate, related to the establishment of CO-flame that depends on the H2O mass-fraction in airflow. Furthermore, water vapor can even be an oxidizer for carbon. So, in evaluating the High-Temperature Air Combustion technique, effects of the H2O concentration are to be examined.
