For turbulent channel flow, pipe flow, and zero-pressure gradient boundary layer, Heinz yielded recently analytical formulas for the eddy viscosity v t as a product of a function of y + (the wall-normal distance scaled in inner units) and a function of y / δ (the same scaled in outer units). By calculating the eddy-viscosity turbulent diffusion term, an exact high-Reynolds-number ν t equation with one production and two dissipation terms is constructed for those flows. One dissipation term is universal, peaks near the wall, and scales mainly with y + . The second, smaller one, is flow dependent, peaks in the wake, and scales mainly with y / δ . The production term is flow dependent, peaks in between, and scales similarly. The universal dissipation term implies a length scale analogous to the von Karman length scale used in the scale-adaptive simulation models of Menter. This length scale also appears in the production term. This confirms the relevance of these length scales. An asymptotic analysis of all terms in the ν t budget in the limit of infinite Reynolds numbers is provided. This yields a test bench of existing Reynolds-averaged Navier–Stokes models with a similar ν t equation. It is shown that some models, e.g., the one of Spalart and Allmaras, do not respect the flow physics: they display a production peak in the near-wall region. The most promising model, a scale-adaptive simulation model, is modified. As a step forward toward a solution to the wall damping problem, the ν t equation of our model behaves much more correctly in the near-wall region.


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    Title :

    Exact Eddy-Viscosity Equation for Turbulent Wall Flows—Implications for Computational Fluid Dynamics Models


    Contributors:

    Published in:

    AIAA Journal ; 60 , 3 ; 1347-1364


    Publication date :

    2022-03-01




    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English