Acoustic Reynolds Stress: The Source of Coherent Structures During Combustion Instability - Novel Combustion Concepts for Sustainable Energy Development - page 364

respectively. The inlet temperature at both the air and fuel ducts is speci ed as 298 K

corresponding to experiments. The thermodynamic pressure is taken as 101,325 Pa.
A simpli

4P + 12N is considered. The
molecular weight of all the species is taken equal as 28 kg/kmol. The reaction rate is
taken to be of Arrhenius type and the pre-exponential factor and activation tem-
perature are taken as 3

ed reaction of the form F + 3O + 12N

→

Þ ð 1 t 1 t 2 Þ =

10 12 gmol

υ 2 are the
exponents in the rate equation for the fuel and oxidizer (air) species, respectively,
and are taken as 0.15 and 1.15, respectively. The calori

: 3 ð = cm s and 2,300 K; υ 1 and

c value of the fuel is taken as
50 MJ/kg. Most of the parameters are chosen such that the process closely resembles
methane-air combustion overall.
For the acoustic computations, the entire length of the duct as in the experiment
is considered as the domain, and an uniform grid with a spatial resolution of
*

8 mm is employed. An open-open boundary condition is prescribed at the inlet
and exit planes of the duct; other surfaces are treated as walls. The flow properties

and the acoustic source are spatially averaged in 3D over half the step height as the
reference

fl

flow length scale and communicated to the acoustic solver. Upstream of
the embedded domain, they are taken as constant corresponding to the experimental
conditions at 298 K.
In the embedded region, they are communicated at the start of every

fl

fl flow time

step. For the downstream part, the s exit plane average properties are

computed and communicated to the acoustic solver at the start of every

fl flow domain '

fl flow time

step.
All the computations reported in this work are calibrated against experimental
data (Chakravarthy et al. 2007 ) by introducing factors that modify the acoustic
source and damping (rhs of Eqs. ( 8 ) and ( 11 ), respectively). These are kept as 0.3
and 15, respectively.
Figure 2 a shows the evolution of pressure monitored at the top wall just
downstream of the step plane for Re = 18,000 and 33,000. The pressure amplitude
is observed to vary with time for Re = 18,000 at a time scale larger than the acoustic
time scale, whereas for Re = 33,000, the time scale over which the pressure
amplitude varies becomes close to the acoustic time scale, and therefore, no distinct
long time scale variation in its amplitude is seen. Figure 2 b shows the spectra of
these time series. A shift in the dominant frequency of the coupled system is seen
for Re = 33,000. This corresponds to lock-on of the duct acoustics to the ow, and

is observed to occur in experiments (Chakravarthy et al. 2007 ) at the same Re.
Figure 3 shows the computational and experimental comparisons of Helmholtz
number He, Strouhal number St, and pressure amplitude, corresponding to the
dominant frequency, along the top wall downstream of the step. The shift from the
constant He to a linearly increasing trend in the 33,000 < Re < 45,000 range
(Fig. 3 a) correspond to the lock-on of the duct acoustic frequency to the vortex
shedding mode (St = 0.2 (Chakravarthy et al. 2007 )). The coupled computation
using the multiple time and length scales approach is able to reproduce this
behaviour. Good comparison is obtained for variation of St with Re as well
(Fig. 3 b). The combustion-acoustic lock-on is characterised by non-linear variation

fl