The behaviour of fluid flow is described by well-established partial differential equations – the Navier-Stokes equations – which are, essentially, generalised (fluid-flow-specific) forms of Newton’s laws of motion, supplemented by an equation describing the conservation of mass. Except for very simple conditions, these equations need to be solved numerically with the aid of computers (often supercomputers). To this end, the predefined flow domain is covered by a numerical mesh. This defines nodes at mesh cross-sections and finite volumes or finite elements, which are patches (or cells) of area or volume around nodes or between consecutive mesh lines.
The differential flow-governing equations are then approximated, using numerical discretisation techniques, as sets of algebraic equations, each pertaining to a node or a finite volume or a finite element. The set of coupled algebraic equations – often numbering millions – are then solved, by means of linear-algebra methods, on a computer to yield discrete values of velocity and pressure at mesh nodes. If relevant, additional transport equations for the energy, chemical species and different phases (e.g., particles, bubbles, droplets) may be solved, alongside the equations of motion and mass conservation, to calculate the temperature, species concentrations, chemical reactions and multi-phase interactions.
The collection of theoretical, numerical and computational techniques that facilitate this process is called Computational Fluid Dynamics.
Within the area of Computational Fluid Dynamics, some of the most challenging flows are those in which turbulence plays an important role – or, indeed, in which turbulence is the phenomenon to be resolved and studied. Particular interest in turbulence derives from the fact that it is largely responsible for mixing, dispersion, frictional losses, vibrations and noise.
As turbulence is a highly effective mechanism for redistributing (mixing) momentum, it has a major impact on gross aero- or hydrodynamic characteristics in most practically relevant flows. It dictates, in particular, whether a flow along a wall remains attached or separated (locally reversing its direction) when subjected to adverse pressure gradient. For example, the turbulence characteristics in a flow over the suction side of a wing will strongly influence the ability of the flow to remain attached rather than becoming detached (separating) from the wing – as is illustrated in the figure below.
Any turbulent flow may be likened to a contorted and convoluted stream of fluid containing numerous mutually interacting, continuously changing eddies and vortices that move with the stream. This is illustrated by the snapshots below of a jet and a mixing layer undergoing transition and evolution towards a fully turbulent state. The vortices cover a wide range of size and time scales, and they change continuously in time and space as they evolve, stretch, deform and break up. These eddies are responsible for the high levels of mixing, diffusion and dissipation observed in turbulence.
Current approaches to computing turbulent flows fall under the headings of either simulation or modelling - a distinction pursued in the sub-section Simulation vs. Modelling.
