Mesh Adaptation for Large Eddy Simulation with the FR/CPR Method

The computational mesh for a Computational Fluid Dynamics (CFD) simulation must provide sufficient cell density at proper locations in the domain in order to resolve the flow physics impactful to the targeted engineering parameters. The key locations for resolution are often imprecisely known and so must be found by trial and error. This dissertation discusses CFD mesh adaptation—the computer guided adjustment of the mesh in response to the simulation. Specifically, this document addresses mesh adaptation for Large Eddy Simulation (LES) with the Flux Reconstruction / Correction Procedure via Reconstruction (FR/CPR) method. It presents a computer program to adaptively refine 3D unstructured hexahedral meshes, guided by the distribution of error within the flow field, estimated by an error indicator algorithm integrated into the flow solver. Furthermore, it introduces four error indicator algorithms for tracking the location and the amount of under-resolution in turbulent flow fields. The error estimators are derived, mathematically analyzed, and numerically tested upon two well-known benchmark LES simulations. The analysis leads to a performance evaluation of the error indicators, judged on their ability to drive the CFD simulation toward truth. The four error indicators are: 1) The Unsteady Residual Indicator (unStdE), based on the unsteady residual from the FR/CPR calculation, 2) The Smoothness Indicator (smthE), based on a local smoothness indicator, 3) The adapted Toosi-Larson Indicator (T.L.errE), based on the estimated small scale turbulent kinetic energy, and 4) The Average Toosi-Larson Indicator (avgT.L.errE), conceptually the same as T.L.errE but formulated to be less costly to compute. Upon LES simulations that model transitional flow past the T106 low pressure turbine blade, all of the error indicators demonstrate ability to boost resolution of the flow field, improving simulation accuracy of force coefficients, vortex structure, Reynolds stresses, and the energy spectra. unStdE and T.L.errE are found to be the fastest to bring improvement to coarse-meshed simulations. Of the two, unStdE is mathematically simpler and easier to compute

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