these simulation numerique et modelisation de l'ecoulement autour ...

2 S. Mendez and F. Nicoud
COMBUSTION CHAMBER: injection side
Hot products
Cooling film
Effusion jets
Cooling air
CASING: suction side
Figure 1. Principle of full-coverage film cooling: fresh air flowing in the casing is injected into
the combustion chamber through the liner perforations and forms an isolating film protecting
the internal face of the liner from the combustion gases.
When wall cooling is ensured by FCFC, the number of submillimetric holes is large
and does not allow a complete description of the generation and coalescence of the jets
when computing the 3-D turbulent reacting flow within the burner. Effusion is however
known to have drastic effects on the whole flow structure, notably by changing the flame
position and subsequently modifying the temperature field. An appropriate model is thus
needed to reproduce the effect of effusion cooling on the main flow. Such a modelling
has already been done for transpired boundary layers and extended law-of-the-wall for
moderate uniform blowing or suction is available (Piomelli et al. 1989; Simpson 1970).
However, existing models accounting for moderate transpiration can hardly been adapted
to FCFC. It is quite obvious that for a given mass flow rate per unit area ṁ, the injected
momentum flux per unit area is different depending on the type of injection: it will be
ṁ 2 /ρ (with ρ the mass density of the injected fluid) in the case of a uniform injection
whereas of order ṁ 2 /ρσ if the injection is through a multi-perforated plate of porosity σ
(hole-to-total surface ratio). As a consequence, new wall models for turbulent flows with
effusion are required to perform predictive full-scale computations. Note also that for
practical reasons, existing models are essentially local in space: they allow the assessment
of the fluxes through a (solid) boundary at a given position based on the knowledge of
the outer flow conditions right above that same position. For example, when computing a
spatially evolving boundary layer at high-Reynolds number, a Reynolds-Averaged Navier-
Stokes (RANS) approach will use the classical logarithmic law-of-the-wall to evaluate the
local wall shear stress based on the tangential velocity at the first off-wall grid point or
cell centre. This law-of-the-wall is local in the sense that the knowledge of the distance
from the leading edge is not required for assessing the wall shear stress. To be useful
in practical RANS computations, any FCFC model should meet the same property and
relate the fluxes through the effusion plate at a given position to the outer flow quantities
at the same position, on both the suction and the injection sides. Note that despite the
numerous studies dealing with FCFC and FC, data relating wall fluxes to suction and
injection quantities are unusual.
Tables 1 and 2 give an overview of the main experimental (table 1) and numerical
(table 2) studies related to injection/suction through perforated plates: Jet in Cross
Flow (JCF); one row of holes (FC) or several rows of holes (FCFC). JCF references are
included because in the combustion chamber side of the liner, the cooling film arising
from FCFC is generated by hundreds of tiny JCF. Note however that the FCFC jets differ