The computation of complex turbulent flows design optimization processes is currently limited by the lack of accuracy of Reynolds-Averaged Navier-Stokes (RANS) in massively separated flows and the infeasible cost of multiple Large-Eddy Simulation (LES) evaluations. A novel method is presented, injecting data from LES or other high-fidelity source such as DNS into the RANS equations, forming a Hybrid Injected RANS (HIRANS) model. The aim is to construct a multi-fidelity design optimization framework that outperforms single-fidelity RANS and LES variants. Two different formulations, injecting a scaled version of the non-dimensional anisotropic part of the Reynolds stress tensor and both isotropic and anisotropic components, are tested in the periodic hill case. A cost-effective LES configuration is assessed, and the agreement of the RANS and HIRANS results with respect to the LES reference is investigated. The original geometry is parametrized using a hill width multiplier, computing several LES evaluations. The injection of LES information from the same geometry into HIRANS and the prediction capabilities when using interpolated data from different geometries are tested. A global design optimization process is computed, using single-fidelity RANS, HIRANS and LES Kriging and multi-fidelity RANS-LES and HIRANS-LES Co-Kriging surrogates. The objective function is based on a combination of turbulent mixing and total pressure losses.

The correction of the mean velocity components required of the injection of both isotropic and anisotropic components for the test case. The LES setup analysis yielded similar results to the reference data with one tenth of grid points and forty percent of its averaging period. The locally corrected HIRANS model successfully reduced the L2 norms of the Reynolds stresses with respect to LES to a third part of the original RANS values in the fifty-nine LES samples tested, with a modest improvement in the mean velocity components. The non-local corrections yielded irregular results for the mean velocity components, with successful corrections of the Reynolds stresses despite the long distances in the parameter space and different flow features of neighbouring LES cases to interpolate from. In the optimization process, the Co-Kriging LES-HIRANS was not able to outperform the Co-Kriging LES-HIRANS and Kriging LES methods. It improved the initial prediction of the underlying function, but the surrogate yielded artificially low predicted errors far away from the LES samples, leading to an overly exploitative method. An error correction formulation combining two HIRANS fidelity levels was simulated using a modified Kriging believer criterion, outperforming the original formulation and achieving similar results as Kriging LES. The computational efficiency improvements for future research of the Co-Kriging HIRANS are suggested to be linked to an adequate error estimation integration into the surrogate model.