Numerical simulation of two-phase turbulent compressible flows with a multidomain spectral method

This thesis develops, validates and implements a multidomain spectral method for direct numerical simulation (DNS) of turbulent compressible (carrier) flows laden with a dispersed phase of solid particles or liquid droplets. The term DNS here refers to the solution of the Navier-Stokes equations without turbulence models. Particles are tracked in a Lagrangian coordinate by implementing well-established expressions for inter-phase interactions.; The DNS of two-phase, compressible flow has received attention only in simple geometries due to computational restrictions. Recent enhancements in computational power and parallel programming allow for simulations in more complex geometries. However, the numerical schemes that are suitable for such simulations are recent.; Here, the method of choice for the numerical simulation is the staggered-grid, multidomain, spectral element method because of its high accuracy, its flexibility and its local character which is favorable for parallel implementation. Specific numerical issues that are investigated are the development of the method for simulation of three-dimensional flows, validation of boundary conditions, development of a particle tracking algorithm suitable for spectral element methods, and implementation of parallel directives.; The characteristics of the method for simulation of two-phase, compressible flows with a large range of scales are assessed through various simulations. In one dimension, resolution requirements and the accuracy of interpolation schemes are acquired through simulations of the running wave problem. The influence of outflow boundary condition treatments are obtained through two-dimensional simulations of the transitional flow over a square cylinder. In three dimensions, simulations of the isotropic decaying turbulence and the turbulent flow in a channel verified the code and assessed resolution requirements for simulation of turbulent flows.; A final simulation of the two-phase compressible flow over a backward-facing step is performed as a first step towards a fundamental physical understanding of the control of combustion in sudden expansion or dump combustor geometries. The focus of the investigation is on the temporal development of flow structures, the flow mechanisms involved in the manipulation through countercurrent shear, and the behavior of the dispersed phase.