THESE de DOCTORAT - cerfacs

66 Chapter 4: Validation of the acoustic code AVSP-f
4.2.1 CFD computation
An unsteady CFD computation is needed in order to have the quantities required for the posterior
determination of the source terms. AVBP [3] is the numerical solver used for the unsteady
computation of the laminar premixed flame. In this tool, the full compressible Navier Stokes
equations are solved on hybrid (structured and unstructured) grids with second order spatial
and temporal accuracy. The inlet mean velocity is equal to 4 m/s which is approximately equivalent
to ten times the laminar flame speed of propane at stochiometric equivalent ratio. Two
types of boundary conditions are used for treating the walls. The first one, which is applied
to the intake, imposes a non-slip boundary condition for the flow while the second one allows
the gas to flow tangentially to the chamber walls. Fig. 4.11 shows the boundary conditions
applied. The outlet boundary condition, which imposes a mean pressure at the outlet, needs a
little more of attention. Let us recall that one of the main assumptions of acoustic analogies is
to consider the sources of noise to be totally independent of the acoustic field. In order to make
this assumption valid, it is of extreme importance to reduce the incoming acoustic waves as
much as possible by imposing a non-reflecting boundary condition at the outlet. Note that for
this case, the chamber walls are not considered important as reflecting bodies since transversal
acoustic waves (normal to chamber walls) are not relevant for the band of frequencies under
study.
Boundary conditions in AVBP are based on a method derived by Poinsot and Lele [72] known
as NSCBC (Navier-Stokes Characteristic Boundary Conditions). In all characteristic approaches,
the main issue is the determination of the amplitudes of waves entering the computational domain.
It has been shown that substracting totally the incoming waves (no-reflecting conditions)
may induce a drift in the mean flow values. Some reflection must therefore be tolerated in order
to stabilize the mean pressure at the outlet [91]. In order to characterize the reflection of a
given boundary, it is useful to introduce the reflection coefficient ˆR. The reflection coefficient ˆR
is defined as the ratio between the incoming wave L 2 to the outgoing wave L 1 . It reads
ˆR = L 2 /L 1 (4.9)
A totally non reflecting condition would mean | ˆR| = 0 whereas a totally reflecting condition
would read | ˆR| = 1. The linear relaxation method (LRM) [74, 91] imposes a proportional relation
between the incoming acoustic waves and the difference between the pressure at infinity
p ∞ (the target) and the pressure at the outlet of the computational domain p.
L 2 = K(p − p ∞ ) (4.10)
where the coefficient K stands for the relaxation coefficient. A zero value of K makes L 2 vanish,
while a big value creates a strong reflection, i.e., a big value of L 2 . An expression that relates
the reflection coefficient ˆR to the relaxation coefficient K has been established by Selle et al.[91].