Direct and large-eddy simulation of compressible flows with spectral/hp element methods

Hi-fidelity simulation of compressible turbulent flows serve as powerful research tools for understanding the complex flow physics that help engineers to improve the design and performance of various fluid flow systems. Rapid growth of supercomputers has made simulation studies very attractive to the turbulence research community. Two popular approaches are direct numerical simulation (DNS) and large-eddy simulation (LES). While DNS is the more accurate approach, computational cost often limits its applicability to only simple flow geometries. LES on the other hand is computationally more efficient than DNS and as such has received considerable attention lately. There have been limited attempts to perform LES of engineering flows using high-order numerical schemes.;In this dissertation two spectral element based high-order LES methodologies for simulating flows in complex geometries are developed. The first method combines a two-dimensional unstructured nodal discontinuous Galerkin spectral element scheme with a triangle based filtering approach. The success of the method is demonstrated through simulation of two-dimensional plane channel flow at high Reynolds number. The second methodology is developed for three-dimensional flows using a Chebyshev multidomain, spectral collocation scheme. A novel interpolant-projection filtering on hexahedral elements facilitates simulation of flows at high Reynolds numbers. Low numerical errors, flexible meshing and high parallelization efficiency makes this method advantageous over other high-order schemes that are in practice. The numerical tool is used for detailed investigation of three-dimensional flow in dump-combustors. Dump-combustors are used as combustion devices in ramjet and turbojet engines. Fundamental understanding of the flow is essential for successful implementation of various control strategies that could improve engine performance. Compressibility effects on the flow, under different inflow conditions and Reynolds numbers, are analyzed. One of the principal findings is the different response of the transitional and turbulent shear layers with increase in compressibility. Increase in compressibility for the transitional flow leads to an increase in the growth rate of the shear layer due to larger production of turbulent kinetic energy. While for the turbulent shear layer, the growth rate was inhibited with increase in compressibility as a result of higher pressure-dilatation.