Numerical Simulation of the Dynamics of Turbulent Swirling Flames

Identification of Flame Transfer Functions using LES/SI
Figure 5.17: Heat release ( ˙Q ′ ) and acoustic velocity (u r ′ ) fluctuations at 70 mm
upstream of the burner exit (Dump plane of combustor at
z=0 mm) normalized by their mean values without filtering for
case with 50 kW.
concept of linear and time-invariant systems. If the same system is excited
using two different simulations (similar to say at two “different times”) and
with the same excitation signal, the response of both simulations will be similar.
Thus various simulations can be used to “continue” a previous one. This is
illustrated in the following example: In Fig. 5.19, two input signals (normalized
velocity fluctuations) are shown with their respective responses (normalized
heat release fluctuations). The system is excited first with signal 1 until 750000
iterations. After this, the same system at the same initial point of the run with
signal 1 is excited with signal 2 also for 750000 iterations. The values of signal 2
in the first 250000 iterations are the same as the last 250000 values of signal 1.
It is shown that after a time interval (approx. 55000 iterations), both cases exhibit
the same response. At this point both signals can be joined into a single
joint time series consisting in information from signal 1 from iterations 0 to
555000 and from signal 2 from iterations 555000 to 1250000. The joint time
series can be extended with additional simulations. In this way, the influence
of the transversal mode is reduced and it is possible to obtain a single long
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