Development, Characterization, and Validation of a Local Wavenumber Adaptive Hybrid Turbulence Model
Creators: name: Padilla, Jose Mario
Publisher: name: University of Notre Dame
Year: 2025
Subjects: classificationCode: 4001
subject: Aerospace engineering

description: Turbulence is a multi-scale phenomenon, where the range of length and time scales are Reynolds number dependent. For high Reynolds number flows, statistical approaches are necessary to reduce the number of resolved scales. Unsteady Reynolds-Averaged Navier-Stokes (RANS) models are computationally inexpensive but lack the ability to resolve scales of turbulence. At the same time, Large-Eddy Simulation (LES) provides high-fidelity solutions at a prohibitive computational cost. Therefore, turbulence models that bridge between unsteady RANS and LES performance are necessary. This research focuses on developing, characterizing, and validating a local wavenumber adaptive hybrid turbulence model.

This dissertation proposes the Wavenumber Adaptive Simulation turbulence model, a novel hybrid approach to address current turbulence model limitations. Based on partial-averaging closure, the model scales turbulent viscosity by the unresolved-to-total turbulent kinetic energy ratio for a given computational grid. Scaling is performed locally by partially integrating a modeled von Kármán spectrum. The research focuses on three key objectives aimed at the validation and characterization of Wavenumber Adaptive Simulation: determining the validity of the scaling function for different flows and assessing the effect of grid anisotropy on its calculation; evaluating the cost-to-fidelity trade-off of Wavenumber Adaptive Simulation in comparison to standard RANS models; and analyzing the model’s performance on both canonical and engineering-relevant flows, with additional emphasis on how grid anisotropy influences solution accuracy.

DNS data from the Johns Hopkins Turbulence Database was queried for forced homogeneous isotropic turbulence and channel flow to assess the validity of the scaling function. Box-filtering was applied to compute the unresolved-to-total turbulent kinetic energy ratio. The ratio was then compared to the modeled scaling function. The results confirmed that the partially-integrated von Kármán spectrum is valid for isotropic turbulence. However, highly anisotropic filters, particularly one-dimensional pencil-like filters, showed poor agreement, while two-dimensional sheet-like filters performed better with the modified cubic root filter width. In channel flow, the scaling function was valid away from the wall but showed poor agreement near the wall, necessitating shielding to prevent improper turbulent viscosity scaling.

The cost-to-fidelity trade-off was evaluated using Taylor-Green vortex simulations on successively refined isotropic grids. Results from k–? SST and Wavenumber Adaptive Simulation were compared against Direct Numerical Simulations. The L2 error norm versus computational run-time showed that Wavenumber Adaptive Simulation outperformed k–? SST, improving accuracy with only a marginal increase in computational cost. Additionally, the results demonstrated that the scaling function is spatially and temporally dependent, emphasizing the necessity for dynamic computation of the scaling function, an aspect not accounted for in standard PANS implementations.

Finally, simulations were performed for a spatially developing mixing layer, D-shaped cylinder, and Rotor 67 using Wavenumber Adaptive Simulation. The cubic root of the cell volume was used as the filter width specification for initial Wavenumber Adaptive simulations. Results showed improved predictions for the D-shaped cylinder and Rotor 67 compared to standard RANS models, while the mixing layer simulation underpredicted turbulent mixing. Exploring the effects of filter width specification revealed that using the maximum filter width improved the mixing layer simulation, although its accuracy remained lower than that of standard RANS models. Rotor 67 results also improved with the maximum filter width, suggesting that high-aspect-ratio grids benefit from this definition. In contrast, the relatively isotropic, polyhedral grid used for the D-shaped cylinder was well-suited to the cubic root filter width. These findings underscore the significant impact of filter width specification and grid anisotropy on the performance of Wavenumber Adaptive Simulation.