“…the smallest eddies are almost numberless, and large things are rotated only by large eddies and not by small ones, and small things are turned by small eddies and large” – Leonardo di ser Piero da Vinci
The remarkably modern quote dated a few hundreds of years ago, generally envision the apparent frustration from the “order in chaos” found in turbulence and emanating from the Navier-Stokes equations. A full description of the phenomena is entangled in a seemingly simple set equation, the Navier-Stokes equations, their nature is such that analytic solutions to even the most simple turbulent flows can not be obtained and resorting to numerical solutions seems like the only hope.
But the resourcefulness of the plea to a direct numerical description of the equations is a mixed blessing as it seems the availability of such a description is directly matched to the power of a dimensionless number reflecting on how well momentum is diffused relative to the flow velocity (in the cross-stream direction) and on the thickness of a boundary layer relative to the body – The Reynolds Number.
It is found that the computational effort in Direct Numerical Simulation (DNS) of the Navier-Stokes equations rises as Reynolds number in the power of 9/4 which renders such calculations as prohibitive for most engineering applications of practical interest and it shall remain so for the foreseeable future, its use confined to simple geometries and a limited range of Reynolds numbers in the aim of supplying significant insight into turbulence physics that can not be attained in the laboratory.
Having said all that, engineering applications could not have been left out and simplified methodologies to capture flow features of interest were developed, their complexity and range of applicability dictated by the simplifying assumption, a direct consequence of computational effort limitations and generally predicted by “Moore’s Law”.
One huge leap forward was achieved through the ability to simulate Navier-Stokes Methods Such as Reynolds-Averged Navier-Stokes (RANS), Large Eddy Simulation (LES) and hybrid RANS-LES Methods.
RANS methods have become an industrial CFD working horse, whose strength has proven itself for wall bounded attached flows due to calibration according to the law-of-the-wall. However, for free shear flows, especially those featuring a high level of unsteadiness and massive separation RANS has shown poor performance following its inherent limitations emanating directly from the decomposition.
In LES the large energetic scales are resolved while the effect of the small unresolved scales is modeled using a subgrid-scale (SGS) model and tuned for the generally universal character of these scales. LES has severe limitations in the near wall regions, as the computational effort required to reliably model the innermost portion of the boundary layer (sometimes constituting more than 90% of the mesh) where turbulence length scale becomes very small is far from the resources available to the industry. Anecdotally, best estimates speculate that a full LES simulation for a complete airborne vehicle at a reasonably high Reynolds number will not be possible until approximately 2050. Nonetheless, for highly unsteady, vortex dominating flows of which the physical phenomena is mainly derived by the large eddies, LES might be affordable and prevails.
The intention of the post is to slide through the subtleties of employing proper LES, briefly summarising issues such as subgrid-scale modelling, inflow conditions, outflow and other numerical boundary conditions, spatial and temporal resolution considerations and correct methods to validate LES simulation.
This is just me blogging and this is just a blog (i.e. me having fun… 😉 ), hence no full coverage of such a deep topic should be expected. Some pointers are left out and some might even be crucial. LES is one of the subtle technologies in CFD and scrutiny is always recommended.
Now go to LET’s LES II and watch the the subtleties confronted heads on…