About RANS (and hybrid RANS-LES) k - νt turbulence models : recent advance based on databases and an analytic theory

The analytical expressions validated for νt , as the product of a function of y+ (wall - normal distance in inner units) and a function of y/δ (wall - normal distance in outer units), were used by Stefan Heinz and I as a starting point to derive an exact transport equation for νt , which should be valid for all ‘turbulent wall flows’ as soon as the inner units Reynolds number Reτ & 500, and in the limit Reτ → ∞. This νt equation has one production and two dissipation terms. Remarkably, the larger dissipation term is universal and peaks near the wall, in good agreement with the wall damping idea. All this yields a test and working bench, based on a priori calculations, of existing RANS models with a similar νt equation. I will thus display problems with the model of Spalart & Allmaras and the base original Menter’s SA model (SAM). I will then propose a more physical SA model (SAP) which behaves much more correctly than the original in the near-wall region in channel flow but also, hopefully, near any wall, as long as the flow remains attached. Moreover, this new model may also function in hybrid RANS-LES mode. I will finally show results of Freefem++ ab initio computations in channel flow, in RANS mode, which display how the flaws evidenced by our νt budgets lead to large discrepancies between SAM and DNS.

I will conclude with prospects regarding model developments on the theoretical and CFD sides.