In Week 2, we'll explore flows in diffusors and nozzles are studied. They are generic representations of diverging or converging cross-sections of flow paths found in many engineering applications. In both diffusors and nozzles flow separation and recirculations occurs if diverging/converging angles are high enough. In symmetric diffusor geometries the flow is often asymmetric, and in nozzles vena contracta may occur. These phenomena and the evaluation of efficiency of energy conversion as well as the energy losses are explained. The effects of geometrical details (variation of expansion/contraction angle, rounding of corners by different radii) and suction through diffusor walls are also analyzed. Detailed studies of grid-dependence of solutions are performed and the effect of the order of discretization for convection fluxes is analyzed.

In Week 3, we'll explore pressure or turbulence induced flow in directions other than the primary flow path are studied. First three-dimensional pressure-driven secondary flows in duct or pipe bends are analyzed in detail, followed by the analysis of turbulence-driven secondary flow in ducts with non-circular cross-sections. The physics behind these phenomena is described and the ways of simulating them are explained. Next, horseshoe vortex and tip vortex flows are analyzed; they too are generic representations of flows resulting in many practical applications with body junctions and free tips. The flow physics, computational details (design of an optimal grid and its local refinement, the choice of physics models and the simulation approach) are explained.

In Week 4, we'll explore flows around a circular cylinder at Reynolds numbers between 5 and 5 million are studied. Circular cylinder is a generic representation of a slender body exposed to a cross-flow; such situations are found in many practical applications. Depending on the Reynolds number, the flow may be creeping, steady or unsteady laminar, or turbulent. The flow separation and recirculation can have many different forms, leading to vortex shedding (the von Karman vortex street), transition to turbulence in the wake, in shear layers, or in boundary layers on cylinder surface. Both the drag crises on a cylinder at the critical Reynolds number and the Magnus effect on a rotating cylinder are described. Different techniques of simulating turbulent flows - direct numerical simulation, large-eddy simulation or solution of the Reynolds-averaged Navier-Stokes equations using different turbulence models are presented and it is explained which technique is appropriate for which type of flow.

In Week 5, we'll explore heat transfer, including conduction in solids, natural and forced convection in fluids, and conjugate heat transfer. I’ll explain how the heat is transferred between continua at the solid-fluid interface, what is different in laminar and turbulent flows, which properties of a computational grid are desirable at the fluid-solid interface, and why are prism layers at walls important. The difference between stable and unstable stratification in natural convection flows and the importance of accounting for the correct dependence of fluid properties on temperature are emphasized. Finally, it is explained how to optimally simulate simultaneous heat transfer across multiple flow streams separated by solid bodies.