Environmental Engineering Reference
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These computations based on compressible NS equations can provide a rea-
sonably accurate description of the underlying
flow physics. However, the com-
putational resource and time required to compute practical turbulent
fl
fields are
enormous. This motivates the development of reduced order modelling approaches
to compute these
fl
ow
flows. In a majority of the reduced order models, the linear
evolution equations for the acoustic
fl
field are considered, and the unsteady heat
release rate from the
field, in a
somewhat ad hoc manner. In these approaches, the acoustic variable, usually the
acoustic velocity, is related to the heat release rate to close the acoustic equation.
The acoustic equations are generally solved in the frequency domain and the
unsteadiness of the
fl
flame is modelled to act as a source of the acoustic
flame (or its heat release rate) in response to the acoustic
velocity at the inlet in the frequency range of interest is computed or measured
fl
rst
and used in the acoustic evolution equation subsequently. This is known as the
fl
ame-
describing function (FDF) obtained at different amplitudes. Non-linear effects such
as transient frequency shifts are triggered when the FDF is used. Vortex-based
fl
flame transfer function (FTF). Recently, Boudy et al. ( 2011 ) adopted the
fl
uc-
tuations that drives duct acoustics are due to large-scale vortical structures that are
formed in the
flame models are used when the dominant mechanism for heat-release rate
fl
fl
flame stabilising regions (Culick 1988 ; Sterling 1993 ; Matveev and
Culick 2003 ).
Most of these models presume the characteristic time scale of the flame as the
same as that of the duct acoustic modes. During the operation of combustors,
however, it is observed that the
fl
flame dynamically evolves as it interacts with the
acoustic
field (Searby 1992 ; Balachandran et al. 2008 ; Chakravarthy et al. 2007 ).
The time scales of the
flow and acoustics are observed to approach each other
(Chakravarthy et al. 2007 ) as the system enters into instability mode.
Wu et al. ( 2003 ) considered the dynamic evolution of the
fl
fl
flame as it got coupled
with the duct acoustics. The
flame was shown to drive the acoustics by inducing a
jump in the longitudinal velocity and the acoustics affected the
fl
ame through the
global acceleration term. Tyagi et al. ( 2007 ) also considered the simultaneous
evolution of a non-premixed
fl
fl
flame in the Burke
Schumann geometry along with
-
the duct acoustics.
The present work adopts a framework of simultaneous multiple length and time
scales, wherein the
ame evolves at long time and short length scales, whereas
the acoustics evolves at short time and long length scales. This approach results in
work done due to the
fl
ow/
fl
field and the
stress due to acoustic velocity (acoustic Reynolds stress, ARS) as the contribution
from the acoustic
fl
fluid expansion as the source to the acoustic
ow.
Acoustics interacts with the base
field to the
fl
flow in the interior region through the ARS
(Nyborg 1965 ; Lighthill 1978 ). The mixing or
fl
'
'
characteristics of the ARS
is highlighted by (1965), who also points out the wide application of the ARS in
areas of heat transfer, surface reaction, biological cell changes etc., in enhancing the
rate at which these processes occur. Tanabe et al. ( 2000 ) investigated the impor-
tance of the ARS in enhancing the evaporation rate of droplets that are present in an
acoustic standing wave
stirring
field. In this paper, evidence of the ARS promoting mixing
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