8 Some Aspects on Pulsating Detonation Wave Numerical Simulation …
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Fig. 8.3 Temperature (above) and density (below) distributions in shock reference frame at the
successive time moments within the acoustic wave cycle. The time interval is 620–660 µs. The
arrows show the order of profiles in time. T scale = 2000 K
cycle. Figure 8.4 shows the time evolution of temperature and density profiles every
10 µs during the time interval 660–700 µs. At this stage the disturbance propagates
back into the induction zone and the attenuation of LSW occurs as shown in Fig. 8.4.
The cycle is also characterized by an increase in the size of the induction zone and
the formation of conditions for a next acoustic cycle. Note that the obtained density
and temperature profiles qualitatively well correlate with the results from [9].
One can also see that the HA mode includes the period-doubling effect, i.e., the
dual oscillations in the peak pressure history are observed. For example, the time
interval 700–800 µs contains two local maximum values of pressure. The first one
is associated with the time moment of about 750 µs and the pressure value 3.3 atm,
and corresponds to the mechanism discussed above. Consider the time interval 760–
767 µs that is associated with the second maximum. Figure 8.5 demonstrates the
distributions of pressure and mass fraction of the H 2 component every 1 µs in this
time interval. After the collision of the combustion wave with LSW the reaction
of combustion of the mixture occurs directly behind LSW with the formation of a
pocket of partly burnt gas. The burning of the mixture in the pocket at some distance
behind LSW leads to a new combustion wave and an increase in temperature and
pressure of the gas. As a result, the second local maximum of pressure corresponds
to the time moment of about 766 µs in Fig. 8.2 and has the value of about 4.6 atm.
The dual oscillations of the HA mode in other time intervals in Fig. 8.2 takes place
in accordance with the mechanism noted above.
111
Fig. 8.3 Temperature (above) and density (below) distributions in shock reference frame at the
successive time moments within the acoustic wave cycle. The time interval is 620–660 µs. The
arrows show the order of profiles in time. T scale = 2000 K
cycle. Figure 8.4 shows the time evolution of temperature and density profiles every
10 µs during the time interval 660–700 µs. At this stage the disturbance propagates
back into the induction zone and the attenuation of LSW occurs as shown in Fig. 8.4.
The cycle is also characterized by an increase in the size of the induction zone and
the formation of conditions for a next acoustic cycle. Note that the obtained density
and temperature profiles qualitatively well correlate with the results from [9].
One can also see that the HA mode includes the period-doubling effect, i.e., the
dual oscillations in the peak pressure history are observed. For example, the time
interval 700–800 µs contains two local maximum values of pressure. The first one
is associated with the time moment of about 750 µs and the pressure value 3.3 atm,
and corresponds to the mechanism discussed above. Consider the time interval 760–
767 µs that is associated with the second maximum. Figure 8.5 demonstrates the
distributions of pressure and mass fraction of the H 2 component every 1 µs in this
time interval. After the collision of the combustion wave with LSW the reaction
of combustion of the mixture occurs directly behind LSW with the formation of a
pocket of partly burnt gas. The burning of the mixture in the pocket at some distance
behind LSW leads to a new combustion wave and an increase in temperature and
pressure of the gas. As a result, the second local maximum of pressure corresponds
to the time moment of about 766 µs in Fig. 8.2 and has the value of about 4.6 atm.
The dual oscillations of the HA mode in other time intervals in Fig. 8.2 takes place
in accordance with the mechanism noted above.