Fractal-generated wakes

Abstract

This thesis aims at getting a better understanding of the properties, scalings and similarities of turbulent axisymmetric wakes, as well as possible applications that arise from the information learnt. Over the last 60 years, axisymmetric wakes have been generated using axisymmetric bodies, such as disks, spheres and bodies of revolution, and key parameters such as the drag coefficient, shedding frequency and similarity and scaling of the wake width and velocity deficit have been documented and verified by numerous experimental and numerical studies. However, in this thesis the aim is to use asymmetric wake generators to generate the axisymmetric wakes and see if this has any effect on the results. These asymmetric wake generators are made up of a square plate and a number of fractal plates, where the perimeter of the plates can be increased by as much as 16 times that of the square. As well as increasing the perimeter, the irregularity, or fractal dimension, is also increased. It is found that the drag coefficient of the fractal plates is increased to beyond the values observed for regular polygons and a theory is presented that could explain this possible change in the drag coefficient, whereby the drag coefficient is the product of the volume of the wake and the dissipation of the turbulent kinetic energy within the wake. Wake profiles were taken over a moderate downstream distance of up to 50l, where l is the characteristic length of the plates, defined as the square root of the frontal area. Using the measured integral width of the wake directly, it was found that the volume of the wake decreased with increasing fractal dimension and iteration. Using these values, the similarity and scaling of the wake was carried out and a new high local Reynolds number scaling for turbulent axisymmetric wakes was discovered and for which the data from the fractal plates fit very well. The intensity of the vortex shedding is also shown to decrease with increasing perimeter and fractal dimension and it is found that the rate at which these vortices are shed is the same for all plates if the characteristic length is used to normalise the frequency. It is also discussed how the decrease in the energy of the vortex shedding is linked to the volume of the wake. Finally, the use of fractal geometries to manipulate the wake to reduce noise is also investigated, with emphasis placed on various aspects of an aircrafts wing.