A Blended Model Based on Fuzzy Logic for the Calculation of Reynolds Stresses in Turbulent Flows

A novel blended model for turbulent stresses is hereby introduced, combining two well-established turbulence models: the k-ε model and the explicit algebraic stress model of Wallin and Johansson (WJ). The blending of these models can be implemented in two ways: a binary approach, where the k-ε model is used for shear stresses and the explicit algebraic stress model for normal stresses; or a fuzzy approach, which integrates both models in a more flexible manner. The model is implemented by formulating the momentum equations based on the k-ε model and incorporating additional momentum source terms from the blended formulation. This approach leverages the strengths of both k-ε and algebraic stress models, enhancing accuracy while maintaining computational efficiency. CFD simulations of a benchmark case, a backward-facing step, demonstrate that both the binary and fuzzy implementations effectively predict turbulent normal and shear stresses. The findings indicate that the blended model exhibits superior performance in terms of accuracy when compared with both the k-ε model and the explicit algebraic model. Furthermore, the fuzzy approach yielded the most precise results, surpassing those of the k-ε model, WJ model, and binary model. In terms of computational cost, the fuzzy and binary blended models require 1.58 and 1.56 times the CPU time of the k-ε model, respectively, while the WJ model is the most computationally expensive, requiring 1.76 times the CPU time of the k-ε model.