phase with the similar
motion of the flame trajec -
tory. Similar oscillatory
pressure behavior has been
observed by researchers for
many years, although there
is still some question as to
whether all such oscillatory
behavior is acoustical in
origin.

The figure also shows the large pressure excursions occurring at the sphere center. This is to be expected since the pressure of collapsing spherical waves increases with decreasing radius.

Figures 6 and 7 show plots of the spatial-average sound speed and spatialaverage static pressure, respectively, for this system. Figure 6 shows that the sound speed of the unburned mixture increases from an initial value of 354 m sec-1 to a final value of about 500 m sec-1. The plot of the burned gas sound speed shows the same exponential growth as that of equation 8. The reason for this is that the density of the unburned gases used to calculate the sound speed was obtained from the expansion ratio (E) given by equation 8. However, tests show that this initial exponential sound-speed growth had no detectable effect on the subsequent

-1

to

system history. Ignoring this initial exponential growth, the plot shows the burned gas sound speed increases from a steady value of about 1,050 m sec

a final value of about 1,500 m sec

We will leave a discussion of the spatial-average pressure plot to a subsequent section and turn our attention to systems with burning velocities less

TIME, msec

FIGURE 6. Spatial-average sound speed histories for both the burned

and unburned gases for (S,/C ̧) = 0.5.

C wave.

lated by the ISS and FSS theories.

extremes are also shown in

figure 8. Careful con

struction of the Mach lines shows that points B, C, and D and all the extremes between D and F (not shown

in figure 8), except E, are not the direct result of any of the Mach lines drawn. Apparently, these extremes result from more complex interactions between C, C., R, and the flame front. Although not apparent from the figures, there is a steepening of the leading edge of the disturbance behind the This the first indication of the creation of a shock front, which is to be expected since the flame is traveling at 70 pct the speed of sound. However, since the flow is assumed to be isentropic, a shock cannot be realistically represented. Figure 9 better illustrates the complex nature of this case where the flame speed undergoes many rapid erratic excursions. shows the spatial-average static pressure history, which is discussed in a

later section.

Figure 10

6

TIME, msec

FIGURE 10. Spatial-average static pressure histories calculated by ISS and FSS

-1

In the third example we choose a burning velocity of 7 m sec all remaining parameters again assuming their same values. Since E = 10, the initial flame speed corresponds to 70 m sec -1 or 20 pct the speed of sound. The histories for the particle velocity and flame speed for this case are shown in figures 11 and 12, respectively. Figure 11 clearly shows the development of an oscillatory disturbance in the burned region. The frequency of this disturbance, as measured from figure 11, corresponds to about 500 Hz in this zone and to about 150 Hz in the unburned zone. Unlike the higher flame speed example, the oscillations are now very regular and almost sinusoidal in This is also apparent from the flame speed history shown in

character.

figure 12.