Large eddy simulations of turbulent flows and aeroacoustics noise predictions using high-order methods

Large eddy simulation (LES) has received increased attention in industrial applications over the past few decades for challenging vortex-dominated turbulent flows. Direct numerical simulations (DNS) have also been used to study interesting flow physics at low to moderate Reynolds numbers. This is due to the advancements in computational algorithms and computing power of modern computers which paved the way for simulating more practical flow problems. In its 2030 vision, NASA has predicted that scale resolving simulations will be increasingly used for vortex-dominated turbulent flow simulations such as rotorcraft flows and turbomachinery flows in aircraft engines. Multiple international workshops on high-order CFD methods have conclusively demonstrated the advantage of high-order methods over 1st and 2nd order ones in accuracy/efficiency for such scale-resolving simulations due to their lower dispersion and dissipation errors. In this dissertation, we analyze the performance of high-order CFD methods for LES using Fourier analysis techniques. We also propose new ideas and approaches for studying the dispersion/dissipation of high-order multi-degree of freedom methods. In addition, we study aspects of mesh resolution requirements for DNS and LES of turbomachinery flows using the high-order flux reconstruction/correction procedure via reconstruction (FR/CPR) method. Finally, we offer an efficient implementation of the Ffowcs-Williams & Hawkings (FWH) acoustic analogy formulation in a hybrid framework with the FR/CPR method for jet noise predictions of supersonic jets