Optimization of Reynolds stress model coefficients at multiple discrete flow regions for three-dimensional realizations of fractal-generated turbulence

The quantification of global turbulence statistical moments generated by grid turbulators is crucial for the enhancement of conjugate heat transfer in industrial thermo-fluid systems. As such, there is a need for precise, low-cost alternatives to numerically model three-dimensional flow dynamics of fractal-generated turbulence (FGT) behind multilength-scale square fractal grids (SFGs), in contrast to previously-reported direct numerical simulations. In this study, a numerical framework consisting of multiple applications of the Reynolds stress model (RSM), each employing its own distinct set of optimized coefficient values, is developed by segregating an FGT flow domain into its production and decay regions with Nelder-Mead optimization on key coefficients then performed independently for each region. The flow fields predicted by such RSM framework achieved overall disparities below 3% and 13% w.r.t. reported experimental measurements of mean velocity and turbulence intensity, respectively, considering the evolution in the flow domain along the streamwise, vertical, and spanwise directions. This is therefore the first documentation of any RANS-turbulence model being validated for mean velocity and turbulence intensity predictions of FGT in all three-dimensions. Thereafter, this proposed RSM framework is generalized to predict industry-relevant turbulence statistical moments of four additional FGT flows. The predicted centerline-statistics are verified against reported experiments, and the findings potentially enable realizations of FGT induced by arbitrary SFGs without relying on a posteriori validation while eliminating further reliance on the Nelder-Mead optimization algorithm on a case-by-case basis. The findings indicate a potential to apply the model coefficients as continuous functions of space to simulate the entire FGT domain. Overall, the accurate and numerically sustainable realizations of FGT in 3D provide valuable insights to engineer potent fluid-solid heat transfer via passive turbulence management within HVAC systems.