A Data-Based One-Layer Formulation of the Two-Equation RANS Models

Abstract The conventional k-ε model accurately predicts the slope of the logarithmic law but falls short in estimating its intercept as well as the buffer layer. This limitation can be addressed either through a two-layer formulation or by introducing additional terms. However, both strategies necessitate extra adjustable constants and ad-hoc functions. In contrast, this paper introduces a novel one-layer k-ε model, which seamlessly integrates the law of the wall while preserving the essential structure of the k-ε framework. Our approach modifies the unclosed dissipation terms in the k and ε equations specifically within the wall layer. We invoke no other assumption than the general law of the wall and the assumptions that led to the k-ε model. Neither do we resort to ad hoc source terms. The revised model yields the following physical scalings in the viscous sublayer: k ∼ y2, ε ∼ y0. In addition, we demonstrate analytically the in-feasibility of sustaining the vt ∼ y3 scaling. Beyond the sublayer scalings, our model effectively captures the mean flow characteristics in both the buffer layer and the logarithmic layer, resulting in robust predictions of skin friction for zero-pressure-gradient flat-plate boundary layers and plane channels. To further validate our one-layer formulation, we apply our model to boundary layers under varying pressure gradients and channels experiencing sudden deceleration. Our model’s results closely align with the reference direct numerical simulation and experimental datasets.