Environmental Engineering Reference
In-Depth Information
x
s
s
x
s
s
s
x
x
þ
u
0s
0
x
0i
u
0s
0
x
u
0s
0
x
0j
þ
u
0s
0
x
u
0
0i
u
0
0j
¼
u
0
0i
u
0
0j
þ
u
0
0j
0i
u
0
0j
ð
12
Þ
0j
The first term is the ARS, but the other terms are sub-grid scale stresses that are
to be modelled. The second term refers primarily to turbulent
fluctuations, but the
last two terms indicate turbulence-acoustic interaction (TAI) terms.
fl
3 Solution Methodology
Simulations reported in this work are performed using modi
ed versions of open
source codes FASTEST (
http://www.fnb.tu-darmstadt.de/forschung_fnb/software_
fnb/software_fnb.en.jsp
,
2002) and CLAWPACK (
http://depts.washington.edu/
(
5
)) and
acoustic sets of equations (Eqs.
8
and
11
), respectively. Only the momentum and
energy balance equations are solved for acoustic
fl
ow (Eqs. (
1
)
-
field, since its eigenvalues are only
two (+c and
-
c, where c is the speed of sound (Chakravarthy et al.
2007
)).
In FASTEST, the spatial discretisation is second order accurate and the deferred
correction procedure (Ferziger and Peric
2002
) is followed to discretise the con-
vective terms. Flux limiters that blend the
first order upwind and the second order
central differencing schemes depending upon the local distribution of a scalar are
also employed. Temporal discretization is performed with second order accurate
Crank
Nicolson technique. The matrix inversions are performed by the strongly
implicit procedure (SIP) (Ferziger and Peric
2002
).
In all the acoustic computations reported in the present work, the
-
rst order
Godunov-split method is employed. This method in combination with high-reso-
lution methods to compute wave propagation yields results that are very close to
methods that employ the second order accurate Strang splitting (Leveque
2002
).
Turbulence in the
flow is handled by means of LES, and the sub-grid scale
(SGS) terms (including the TAI terms) are simulated by adopting the monotonically
implicit LES (MILES) approach (Chakravarthy et al.
2007
). A single-step global
chemical reaction is adopted with laminar
fl
finite-rate Arrhenius kinetics to compute
the production rate of species.
In-house benchmarks are performed using FASTEST to compute
ow through
backward facing step (Armaly et al.
1983
; Friedrich and Arnal
1990
) and channel
fl
fl
flows (Hussain and Reynolds
1975
). Its capability to compute incompressible
variable density
flow is validated following (Nicoud
2000
). CLAWPACK is tested
to reproduce the duct natural frequencies in the presence of mean temperature
gradient (Sujith et al.
1995
).
The acoustic damping is the only aspect that is modelled in an ad hoc fashion,
and together with this,
fl
the strength of the dilatation source term driving the
acoustics is arti
cially tuned to calibrate for acoustic amplitudes against
the
experimental data.
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