Baldwin Barth One-Equation Model Reviewed

During the present semester, I reexamined the Baldwin-Barth one-equation turbulence model. This model constitutes a reformulation of the $k$ and $\epsilon$ equations, culminating in a single partial differential equation for the turbulent eddy viscosity, denoted as $\nu_t$, multiplied by the turbulent Reynolds number, $Re_t$. The model’s closure for the Reynolds-averaged Navier-Stokes (RANS) equations was a major advancement in turbulence modeling, laying the groundwork for the renowned Spalart-Allmaras model. Though, the SA model was also influenced by Soviet research.

A notable aspect of this model is the intuitive appeal of the turbulent Reynolds number for engineers, coupled with its measurability, which simplifies the specification of boundary conditions at inlet boundary conditions. Despite its innovative closure approach, the model’s widespread adoption was hindered by several limiting factors. Nevertheless, it served as a foundational framework for subsequent research efforts, many of which remain highly relevant in contemporary applications.