| Abstract |
Pumping fluids through pipes is an important part of many industrial processes. On the surface, this seems a simple enough problem where the hard you force the fluid, the quicker it flows. In practice this turns out only to be true up to moderate forcing rates. After this turbulence - chaotic mixing flow - begins to be observed, and this greatly reduces the efficiency. In theory it is possible to avoid triggering turbulence as it is only initiated by disturbances above a certain amplitude. Knowledge of this critical amplitude tells us how smooth the pipe needs to be to avoid turbulence. For classical fluids, such as water and oil, this critical amplitude has recently been calculated and is very low indeed - so low that in practice it may be entirely impossible to avoid turbulence for anything above moderate flow rates. This presents a major obstacle for the engineering community. Instead of seeking to avoid turbulence altogether, one possible solution is to change the characteristics of the observed turbulence hence mitigating the problem. Adding small quantities of polymers to a fluid can change its fundamental properties. In this way it is possible to create a shear thinning fluid - one which becomes less viscous as it is forced through a pipe. Counter-intuitively, reducing the viscosity of classical fluids can actually exacerbate the problem of turbulence by reducing further the size of disturbance required to initiate turbulence. However, shear-thinning fluids actually exhibit two types of turbulence. As well as the usual turbulence observed for oil or water, there is also an intermediate `weak turbulence' that has a much smaller impact on pumping efficiency. One practical means of maintaining a good throughput in a pipe would be to constrain the flow to this little understood weakly turbulent state, as a compromise between the highly efficient smooth flow and the uneconomic strong turbulence. This proposal seeks to explore and understand the weak state and to find conditions for holding off turbulence. The weakly turbulent state has a simple form of two streaks, one fast one slow, each occupying half the pipe's cross-section and with no variation along the pipe. Superimposed on this are slow, weak fluctuations. This gentle form and variation is attractive for a theoretical approach. Where previous attempts have looked - and struggled - to make progress by making the linear simplification, this project will tackle the full nonlinear problem. |
