Numeerisen analyysin ja laskennallisen
tieteen seminaari
13.2.2006 klo
14.15
U356
Antti
Hellsten, TKK, Aerodynamiikan Laboratorio
How to simulate
turbulent flows of high Reynolds number?
Turbulence in fluid flow remains a grand challenge. It is of
great
practical importance in engineering and in many other disciplines. Low
Reynolds number (Re) flows in simple geometries can be simulated
accurately by numerically solving the Navier-Stokes equations
(DNS). However, high Reynolds number wall-bounded flows (to which
class most of the practical problems belong) can only be predicted
approximately based on the Reynolds averaged Navier-Stokes (RANS)
equations and statistical turbulence modelling. This is because the
computational resolution requirement N of DNS is estimated to increase
as Re2.25. For many flow problems,
however, RANS-modelling is not
sufficiently reliable. Large eddy simulation (LES) is a promising
approach if walls have little signifigance to the flow or if Re is
low. Then N~Re0.4, but for wall bounded
flows N~Re1.8 -- almost the
same as for the DNS.
We are interested in questions related to combining the RANS and LES
approaches to be able to apply LES for high-Reynolds number
wall-bounded flows. The RANS and LES equations are formally similar,
but modelling of unclosed terms (turbulent stresses) differ from each
other. The question is: could we apply RANS modelling near walls and
LES modelling for the rest (most) of the domain of the same problem?
The fundamental issue here is that the interpretation of the turbulent
stress terms are different in these two approaches. It is likely that
there is no general way around this obstacle. The boundary conditions
between the RANS- and LES-regions simply do not match as a consequence
of the different physical interpretation of the turbulent stress
terms.
Since there is no general strategy, approximations must be done. This
does not necessarily ruin the idea of combining the RANS and LES
approaches, since both approaches rely on approximations (modelling)
themselves. We can pursue methods in which the error resulting from
the interface matching is not much larger than the modelling errors
inside the RANS and LES regions. This probably means that different
flow problems might need different combination strategies. The
strategies and methods proposed so far will be discussed.