## Section: Scientific Foundations

### Computational fluid mechanics: resolving versus modelling small scales of turbulence

A typical continuous solution of the Navier Stokes equations is governed
by a spectrum of time and space scales.
The broadness of that spectrum is directly controlled by the
Reynolds number defined as the ratio
between the inertial forces and the viscous forces. This number
is quite helpful to determine if the flow is turbulent or not.
In the former case, it indicates the range of scales of fluctuations
that are present in the flow under study. Typically, for instance for the
velocity field, the ratio between the largest scale
(the integral length scale) to the smallest one
(Kolmogorov scale) scales as $R{e}^{3/4}$. The smallest scales may have a certain
effect on the largest ones which implies that an accurate framework for the
computation of flows
must take into account all these scales. This can be achieved either by
solving directly the Navier-Stokes equations (Direct numerical simulations
or DNS) or by first applying a time filtering
(Reynolds Average Navier-Stokes or RANS) or a spatial filtering operator
to the Navier-Stokes equations (large-eddy simulations or LES).
The new terms brought about by the filtering operator have to be modelled.
From a computational point of view, the RANS
approach is the less demanding, which explains why historically it has been
the workhorse in both the academic and the industrial sectors. Although it
has permitted quite a substantive progress in the understanding of various
phenomena such as turbulent combustion or heat transfer, its inability to
provide a time-dependent information has led to promote in the last decade
the recourse to either LES or DNS. By simulating the large scale structures
while modelling the smallest ones supposed to be more isotropic,
LES proved to be
quite a step through that permits to fully take advantage of the increasing
power of computers to study complex flow configurations. In the same time, DNS
was progressively applied to geometries of increasing complexity
(channel flows, jets, turbulent premixed flames), and proved to be a
formidable tool that permits **(i)** to improve our knowledge of turbulent
flows and **(ii)** to test (i.e. validate or invalidate)
and improve the numerous
modelling hypotheses inherently associated to the RANS and LES approaches.
From a numerical point of view, if the steady nature of the RANS equations
allows to perform iterative
convergence on finer and finer meshes, this is no longer possible for LES or
DNS which are time-dependent. It is therefore necessary to develop
high accuracy schemes in such frameworks. Considering that the Reynolds number
in an engine combustion chamber is significantly larger than 10000, a direct
numerical simulation of the whole flow domain is not conceivable on a routine
basis but the simulation of generic flows which feature some of the phenomena
present in a combustion chamber is accessible considering the recent
progresses in High Performance Computing (HPC).
Along these lines, our objective is to develop a DNS
tool to simulate a jet in crossflow configuration which is the generic flow
of an aeronautical combustion chamber as far as its effusion cooling is
concerned.