A Curvature-Corrected Wall Model for Axisymmetric Turbulent Boundary Layers

In wall-modeled large-eddy simulation (WMLES), the velocity is sampled at a distance from the wall in the turbulence resolving region. Then, using this velocity as a boundary condition, Reynolds-averaged Navier-Stokes equations in thin boundary-layer form are solved down to the wall to obtain the near-wall solution. The Prandtl mixing-length model is often used to determine the eddy viscosity in the wall-model region. In the present work, we derive a new curvature-corrected mixing-length model based on the axisymmetric law of the wall. This new formulation improves agreement with experimental measurements at the radius-based Reynolds number Rea = 4.330 × 103, particularly in the log-law region just below the wall-model sample location. At higher Reynolds numbers, i.e., Rea = 1.060 × 105, 2.185 × 105, the curvature-corrected wall model converges to the baseline model. Importantly, we also introduce a method to estimate, a priori, the increment in wall shear stress due to the use of the curvature-corrected mixing-length model over the planar model. The estimation method predicts increments of less than 1% for Reynolds numbers greater than Rea ≈ O(105) and an increment greater than 10% for Reynolds numbers of order O(103). This is confirmed through WMLES.