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Fractal-generated Turbulent Flows

Christos Vassilicos & Sylvain Laizet,
Imperial College

A fractal square and a fractal I grid with N = 4 fractal iterations, and computer visualisation (obtained on HECToR with code Incompact3d) of the streamwise velocity in one of the planes normal to a turbulence-generating fractal square grid. (From Laizet & Vassilicos 2009.)

New industrial flow solutions based on new flow concepts are urgently needed to meet the unprecedented requirements set by the dramatically evolving energy, environmental and climatic constraints. What is needed is not just improvements to existing solutions, but radical new developments that can dramatically increase energy savings and reduce adverse environmental impacts. The development of new flow concepts on which such solutions will eventually be based requires unprecedented fully resolved simulations because existing turbulence models cannot be applied indiscriminately on radically new flow concepts.

One very recent example of a new flow concept originating from the UK is turbulent flows generated by fractal grids (see figure). Fractal grids are made from a structure, such as a square, repeated at different scales. As attested by recent patent applications by Imperial Innovations, proof-of-concept studies at Imperial and reports in various popular science and engineering periodicals (Food Manufacture, June 2008; The Chemical Engineer, July 2008; Process Engineering, 18 July 2008; Speciality Chemicals, September 2008; Scientific Computing World, August 2008; see this class of new flow concepts offers alternative and efficient solutions for industrial mixers, silent airbrakes and spoilers, natural ventilation, sun-roofs and combustion among others.

For example, fractal grids make very efficient mixers. They create intense turbulence with very little effort or power input, and you only need to make very small changes to the grid to have an enormous effect. The first ever successful simulations of turbulence generated by fractal grids (see figure) have been performed on HECToR in 2008 and 2009. The size of these simulations is so large that they are impossible without High Performance Computing. Industries that need to create or minimize turbulence have an interest in this work. They include the chemical and process industries, which use turbulence for mixing, and the aerospace and automotive industries, which need to reduce noise, fuel consumption and pollutant emissions through the control of turbulent flows.