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.