Trunins, Jevgenijs (2018) Experimental and mathematical investigation of the chaotic dripping mode. (PhD thesis), Kingston University, .
Abstract
The dynamics of fluid flow unveils complicated dynamical behaviour. Systems such as a dripping tap are no exception. Flow through a nozzle produces three different modes: periodic dripping, chaotic dripping and jetting streams. This research concentrates on a study of the chaotic behaviour of a dripping tap. This involves both mathematical model studies and experimental studies. In addition, the work involves the development of an experimental facility to allow future study of the system in microgravity conditions. The facility to achieve microgravity conditions is a Drop Tower type, which uses a novel approach to achieve these conditions. The novelty is in the use of linear electromagnetic motors. The facility was built and is in the final stage of the commissioning process, and when it is ready it will allow up to 2.12 s of test time. The mathematical model uses an existing Mass-Spring-Damper model, with Reynolds numbers between 4 to 175, and a step size of 0.4. The results showed multiple bifurcation regions appearing before chaotic regions. Similarly, experimental results showed that some instabilities exist in this region. The model also explained and showed multiple bifurcations and an increase in dripping time due to instabilities, and has identified that those processes are due either to perturbations of the system or due to initial instabilities of the system. These results were confirmed by experiment. To achieve the required experimental goals a test module was developed whose requirements were set to fulfil the microgravity experiment conditions, in case future research is required. The experimental results showed some similarities with the mathematical model. At the same time, there was found to be quite a lot of disagreement. Results identified two different limit cycle attractors in periodic dripping mode: strong single-point attractors and regional attractors. Also, limit cycle attractors and strange attractors in chaotic mode were identified. More importantly, it has been identified that the chaotic region consists of areas where the system is stable (and produces a single region attractor), and others where the system is not (and this produces strange attractors), and there are points where, depending on the disturbances to the system, both types can be observed. The work done has led to several discoveries and achievements. Although the Drop Tower project could not be completed it may nonetheless be considered as a success. The facility has been fully assembled and calibrated to meet the set of design requirements, and to some extent was commissioned allowing future progress to discover modification requirements. The study of the Mass-Spring-Damper model led to the conclusion that the model is oversimplified and in its current state should be used only for descriptive purposes, when illustrating chaotic behaviour. Additionally, it was found that the model predicts bifurcations outside the experimentally determined chaotic region. Nevertheless, the work identified some possible improvements to the model. Experimentally it was found that the region of chaotic behaviour is located around a Reynolds number of 43 in contrast to what was previously reported. The study of the periodic dripping region showed that the system, if disturbed, can develop history dependent phenomena (where the subsequent drop periods follow a well identified sequence). Satellite drops were discovered to exist beyond the previously predicted value of flow rate. It was discovered that the fluid supply system can have a major effect on the drop dynamics (different types of post-detachment developments were found - termed here regular residual mass and wetted mass - along with the discovery of different types of drop detachment (regular mass, mid-size drops and jets) coexisting within the chaotic region. The drop horizontal disturbance study led to the unconfirmed discovery of two modes of vibrations, where the system response follows a standard damped response and an amplitude modulated damped response.
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