Near-wall LES closure based on one-dimensional turbulence modeling

Abstract

A novel near-wall LES closure model is developed based on a revised form of the one-dimensional turbulence (ODT) model of Kerstein and is tested by performing LES calculations of turbulent channel flow at Reynolds numbers based on friction velocity ranging from 395 to 10,000. In contrast to previous models, which invoke Reynolds averaging, near-wall velocity fluctuations and turbulent transport are simulated down to the smallest scales, and can be compared directly to DNS data. Thus, the approach provides more than just a boundary condition. Rather, it is itself a complete (although simplified) model for the wall-normal profiles of velocity within the near-wall region. LES/ODT coupling is bi-directional and occurs both through the direct calculation of the subgrid turbulent stress by temporally and spatially filtering the ODT-resolved momentum fluxes (up-scale coupling), and through the LES-resolved pressure and velocities impacting the ODT behavior (down-scale coupling). The formulation involves finely resolved ODT lines that are embedded within each wall-adjacent LES cell – denoted the inner region. LES cells that are within approximately one LES filter width of the inner region belong to an overlap region where both ODT and LES modeling is active. All other cells are treated using a standard LES approach. Although more expensive than simpler models, the cost of the model relative to the LES portion of the simulation scales favorably with problem size, leading to computationally affordable simulations even at relatively high Reynolds numbers.