Deeper understanding of turbulence modeling works to improve simulation based design

Richard Feynman once described turbulence as “the most important unsolved problem in classical physics.” Now, more than 50 years later, scientists still lack a reliable way for predicting turbulent flows besides a few analytical solutions and simplified turbulence models. Moreover, these turbulence models have errors and uncertainties associated with them, which can lead to unreliable and even unsafe engineering designs. Current approaches for estimating such uncertainties in turbulence model, albeit somewhat successful, are not well understood.

Mishra et al. analyzed the primary methodology currently used, which applies tensor perturbations to the modeled Reynolds stress tensor. They outlined the modeling structure represented by this procedure to estimate model form uncertainties for closures, in Reynolds-averaged Navier Stokes models and in subgrid scale closures for large-eddy simulations, and quantified the limitations and derived realizability constraints of such methodologies.

“Until now, these uncertainty quantification approaches have been a black box. Researchers know that they work, but don’t know how they work, or even why they work,” said author Aashwin Mishra. “When you gain deeper insight into what everyone is doing, you might gain insight into what everyone is doing wrong.”

Such uncertainty quantification approaches have been applied in the design and analysis of aircraft, scramjets, turbomachinery, urban canopies, wind turbines, etc. In light of these new realizability conditions, many such studies may need to be re-visited for their physical imprimatur.

Source: “Theoretical analysis of tensor perturbations for uncertainty quantification of Reynolds averaged and subgrid scale closures,” by A. A. Mishra and G. Iaccarino, Physics of Fluids (2019). The article can be accessed at https://doi.org/10.1063/1.5099176 .