Mechanical Engineering - Theses
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ItemConvective methods of pumping and drag reduction( 2013)It is the convection of the velocity field by itself that renders many fluid mechanics problems mathematically challenging, and produces complicated, and often non-intuitive flow phenomena. Pumping and drag reduction are effectively related concepts, in that they both involve increasing the volume flux of the fluid. In this work, we consider three different methods of pumping and drag reduction, all of which result, partially or entirely, from the effect of convection. The first of these methods is the drag reduction obtained by the addition of elastic polymers to a turbulently flowing liquid. This effect is not well understood, and a complete physical explanation of the phenomenon remains to be made. However, it is clear that the polymer has the capacity to transport energy and momentum within the fluid, and energy may also dissipate within the polymer itself. In this work, it is proved that the addition of elastic polymers to a turbulent flow cannot reduce the drag to a level below that of the equivalent laminar flow. This proof can also be applied to similar methods of drag reduction, such as the presence of surfactant micelles within a turbulently flowing liquid and the presence of sand particles within high winds and water droplets within cyclones. The second method is known as "transpiration", and consists of a dynamic regime of blowing and suction at the wall of the pipe or channel which imparts no net volume flux upon the flow. Using a perturbation analysis, the pumping effect of transpiration has been quantified in this work. It is shown that this pumping results from convection, and relies on the presence of large velocity gradients within the flow. The third method consists of oscillating waves in the wall of the pipe or channel. This has particular relevance to the valveless impedance pump, which consists of a thin tube, one section of which is elastic and is subjected to rhythmic pinching at some point offset from its centre. This pinching induces oscillating waves within the wall of the tube, which in turn induce a flow. The flow induced by small-amplitude oscillations, in the wall, has been derived through a perturbation analysis. In this way, we are able to separate the effect of convection from the more readily intuitive dragging effect that the wave has upon the fluid, and thereby quantify the importance of convection in such systems. It is found that even within small tubes, the effect of convection remains generally of the same order of magnitude as the dragging effect, and that no effective model of the valveless impedance pump could safely neglect the effect of convection.