Calibration and optimization of rans turbulence models for various cases

Abstract

Reynolds-Averaged Navier-Stokes turbulence models dominate both engineering applications and academic research due to their low computational cost and ability to deliver accurate predictions across a wide range of turbulent flows. Although high-fidelity approaches such as large-eddy simulations and direct numerical simulations can resolve a wide range of turbulent scales, their computational cost makes them impractical for most real-world problem investigations. Even though they offer intriguing alternatives, hybrid approaches like wall-modeled large-eddy simulations and Reynolds-Averaged Navier-Stokes/Large Eddy Simulation coupling still depend on turbulence modeling. Improving engineering design procedures' prediction performance in turbulent flows remains pivotal aspect today because they naturally advance from low-fidelity to high-fidelity methodologies within allowable computational resources. From this perspective, the modeling capabilities of widely-used Reynolds-Averaged Navier-Stokes turbulence models were enhanced for canonical problems in engineering applications and academic research. These improvements were achieved through optimization of their closure coefficients, replacement with defined functions, or coupling different turbulence models. The studies conducted within the scope of thesis have been disseminated to the international literature through one conference paper and three articles. In the first part of the study, round free jet was modeled with standard k − ε turbulence model and the results were compared with experimental measurements. The aim of the first study was to improve the prediction capability of standard k − ε turbulence model, which was known as unsuccessful in modeling flows involving anisotropic Reynolds stresses such as turbulent jets. It was aimed to investigate the effect of model constants such as Cε1, the coefficient of turbulent production; Cε2, the coefficient of turbulent kinetic energy dissipation and Cµ, used to calculate turbulence viscosity. Steady-state and three-dimensional computational fluid dynamics analyses were performed by systematically changing these constants and the results were evaluated based on dimensionless velocity and turbulence profiles, jet half-width, centerline velocity and turbulence intensity along the jet centerline. It was observed that the adjusted new constants achieve more successful results than the default coefficients. By calibrating the model coefficients that alters from the default model coefficients by 16% for Cε1, 17% for Cε2, and 1.2% for Cµ, it is revealed that jet centerline velocity distribution and jet half-width distribution along the jet center axis can be estimated better. The new closure coefficients of the standard k − ε were also validated for different Reynolds numbers. The numerical simulations revealed that the velocity profile change with the calibrated model coefficients and the numerical results aligned well with the experimental observations. By this way, the computation errors due to uncertainty of turbulence modeling encountered in numerical investigations were reduced. In the second part, the investigation of turbulent jet flows was extended. Since Reynolds Stress Models directly solve the Reynolds stress equations rather than relying on modeling approximations, they were anticipated to provide more accurate numerical results for flows characterized by strong anisotropy. Nevertheless, it was observed that the calculated jet half-width, velocity decay, and spreading rate differed from experimental results due to uncertainties inherent in the turbulence model. Consequently, closure coefficients of the Reynolds Stress Model were calibrated using a variant of the Multi-Objective Genetic Algorithm based on jet half-width data obtained experimentally in the near-field region of the jet. With the use of appropriate discretization scheme and computational grid, adjusted coefficient combination for the turbulence model showed improved accuracy in predicting jet half-width at Reynolds numbers of 10000 and 20000, reducing the errors of calculated decay constant and spreading rate approximately from 2% to 1% and from 16% to 5%, respectively. A detailed examination of the turbulence budget along the longitudinal axis in the self-similar region revealed that the new model coefficients enhanced the modeling of diffusion term but compromised the advection term. As a result of the altered advection term, increased error margins were observed in turbulence intensity and velocity distribution along the jet centerline, although dissipation along the axis was improved. Hence, the modeling error in jet half-width calculations using the numerical method was decreased, enhancing performance of the Reynolds Stress Model compared to default coefficients. For the third part of the study, a modified Renormalization Group k − ε turbulence model for axial compressor cascade flows was introduced, developed to improve the prediction of total pressure loss coefficient and wake profiles at various operating conditions. Built on the theoretical foundation of Renormalization Group theory of turbulence, the model incorporates a locally adaptive η0 coefficient, enabling it to better capture flow physics across varying near-wall resolutions and wall treatment approaches. The model was named as RNG Fc and validated using experimental data of The Advisory Group for Aerospace Research and Development Working Group 18, focusing on the V2 and V103 compressor cascades under on design and off-design conditions. Comparative analyses versus original renormalization group k − ε and Shear Stress Transport k − ω models demonstrate that the presented model achieves superior accuracy in total pressure loss calculations and wake region predictions at various inlet Mach numbers. The model's performance remains consistent across different computational grids, including low y+ and high y+ structures, and is compatible with both scalable wall functions and enhanced wall treatments. Notably, the modified model exhibits computational cost efficiency and numerical stability, making it a promising tool for engineering applications. This work highlighted the potential of the RNG Fc model as a robust and cost-effective alternative for turbulence modeling in axial compressor cascade investigations, offering significant improvements over traditional Reynolds Averaged Navier-Stokes models. To overcome another recognized limitation of the Reynolds-Averaged Navier-Stokes framework, particularly in prediction of reattachment mechanisms for flows separating from continuous surfaces, the final part of this study aimed to overcome this deficiency with the widely-used Shear Stress Transport k − ω turbulence model. Although the Shear Stress Transport model performs well for a wide range of flows, its predictive capability deteriorates in wake regions dominated by complex turbulent structures. To enhance its accuracy, a modified model incorporating the Renormalization Group theory of turbulence is proposed. The model correction is introduced as an additional source term into the dissipation equation and limited to the reattachment region through a blending function to ensure computational efficiency and numerical stability. The model is validated using several canonical problems, including the curved backward-facing step, vertical and inclined backward-facing steps, and periodic hills case at various Reynolds numbers. Effects of the inflow boundary condition are carefully examined to isolate the intrinsic performance of the modified model. Comparisons with benchmark Large Eddy Simulation studies and experimental data showed that the RNG-SST model substantially improves the prediction of mean velocity, turbulence kinetic energy, and wall quantities such as pressure coefficient, wall shear stress, and boundary layer parameters. In particular, prediction of the reattachment position is improved, yielding reduced relative errors by nearly half of the default Shear Stress Transport model. These findings demonstrate that integrating Renormalization Group theory provides a computationally cost-effective, numerically robust, and physically consistent improvement to the default Shear Stress Transport turbulence model for separated flows from a continuous surface. Collectively, the thesis demonstrates that targeted calibration, physics-informed coefficient adjustment, and selective coupling can meaningfully reduce turbulence model induced uncertainty in Reynolds Averaged Navier-Stokes closures across jets, compressor cascades, and separated flows. The proposed models retain the low computational cost and robustness required in engineering while delivering accuracy gains typically associated with more complex approaches, thereby advancing the reliability of turbulence modeling within practical numerical investigations.