One-Equation Near-Wall Turbulence Modeling With the Aid of Direct Simulation Data

The length scales appearing in the relations for the eddy viscosity and dissipation rate in one-equation models were evaluated from direct numerical (DNS) simulation data for developed channel and boundary-layer flow at two Reynolds numbers each. To prepare the ground for the evaluation, the distribution of the most relevant mean-flow and turbulence quantities is presented and discussed, also with respect to Reynolds-number influence and to differences between channel and boundary-layer flow. An alternative model is examined in which (v′²)^1/2 is used as velocity scale instead of k^1/2. With this velocity scale, the length scales now appearing in the model follow closely a linear relationship near the wall. The resulting length-scale relations together with a DNS based relation between v′²/k and y* = k^1/2y/v form a new one-equation model for use in near-wall regions. The new model was tested as near wall component of a two-layer model by application to developed-channel, boundary-layer and backward-facing-step flows.