Mathematical Modeling of Turbulent Flows Using Advanced Computational Fluid Dynamics Techniques

This research investigates the application of advanced Computational Fluid Dynamics (CFD) techniques in the mathematical modeling of turbulent flows. The accuracy is improved in different engineering systems by using different turbulence models: the k-ε, k-ω, LES and DNS. The main purpose was to investigate fluid flow behavior in industrial, aerospace, biomedical applications. Results of the experimental data are compared with the k-ε model and show that the average deviation is 5.2% when compared to the experimental data of turbulent boundary layers. Dynamic vortex simulations using the LES model resulted in a 12% decrease in error compared to original results. In addition, the DNS model was close to obtaining near exact solutions at the price of greatly increased CPU costs, with a deviation of 1.4% in highly turbulent cases. It was found next that the integration of machine learning algorithmss further improved model predictions, reducing the required simulation times by about 18 percent. It is concluded that for different applications it is important to select the correct turbulence model so as to balance accuracy and computational efficiency. The contribution of this research to refine CFD methodologies and to provide some initial insight in optimizing fluid dynamics simulations for real world engineering problems is provided.