The work of this thesis contributes to cavitation science, water jet fundamentals and cavitating water jet performance.
The cavitating water jet is considered a prospective approach for rock drilling under submerged conditions. Previous researches have shown that cavitating water jets are more effective in erosion of hard materials than non-cavitating jets. However, the mechanism of cavitation and erosion of water jets has not been well understood and the behaviour of a submerged water jet, such as the size of the bubble cloud and the erosion rate could not be predicted. These issues have limited the improvement in the design of nozzles. One major goal of this thesis is to reach a better understanding of the cavitation and erosion phenomena in submerged water jets, and hence to develop methods and tools to improve drilling efficiency. In particular, three major numerical models are established: (1) a computational fluid dynamics (CFD) model for computation of flow properties of nozzle flows, (2) a bubble life cycle (BLC) model for simulation of bubble growth and collapse in the nozzle flow and (3) an erosion model for estimation of erosion rate for a water jet drilling a particular target material. These models explain the occurrences of cavitation and erosion by directly linking the bubble clouds and the erosion produced to the profiles of pressure and velocity, hence allowing quantitative predictions of bubble cloud length and erosion rate of a water jet. The models developed in this thesis promise to be useful tools for optimising geometrical design of a nozzle at given operating conditions.
This investigation begins with the derivation of the dynamic equation of a spherical bubble, which describes the growth and collapse of a bubble in liquid. Literature on bubble collapse and its accompanied erosion phenomena is reviewed. Through comparisons of various nozzles used by previous researchers, the convergent-divergent nozzle is proposed for further study due to its high potential for generating cavitation bubbles. Theoretical analysis indicates that a low pressure even tensile stress field in the throat of a convergent-divergent nozzle may be generated. A hypothesis is proposed in which the bubbles form in the throat and are transported downstream.
By distinguishing cavitating pressure and vapour pressure as well as interpreting the pressure definition for liquids, a better understanding of the phenomenon of cavitation has been reached. It is found that, when a micro bubble is sufficiently small, negative absolute pressure (tensile stress) is required for the bubble to grow. A cavitation bubble in a water jet arises from the growth of an existing micro bubble.
To explore the distributions of the jet parameters such as pressure, velocity and turbulent kinetic energy, a CFD model is developed using the commercial code FLUENT to simulate the turbulent water jet in CMTE's cavitation cell. Several turbulence models built in the commercial code, FLUENT, have been tested in the CFD simulations of nozzle flows. Among them, the RNG k - ε turbulence model not only produces satisfactory flow patterns (reasonable separation and recirculation and potential jet core), but also predicts flow rates matching best with the measurements. This model has been chosen for the simulation of nozzle flows for the purpose of obtaining profiles of pressure, velocity and turbulent kinetic energy. The turbulent kinetic energy profile calculated is used to estimate the amplitude of pressure fluctuation caused by turbulence, explaining one important mechanism of bubble formation in both convergent-divergent and convergent-straight nozzle flows. This mechanism comes into effect when the ambient (cell) pressure is not too high. The most important finding from the CFD simulations is that negative pressures (tensile stresses) appear in the throat of the convergent-divergent nozzle but not in the convergent-straight nozzle. This is another mechanism for generation of bubbles in convergent-divergent nozzles, which becomes significant when the ambient pressure is large. The simulated negative pressure in the throat of convergent-divergent nozzle explains why the convergent-divergent nozzles generate larger bubble clouds and produce more erosion than the convergent-straight nozzles.
To explore the mechanisms of erosion, experiments are undertaken using CMTE's cavitation cell. The cavitation bubble clouds are studied using photographic techniques while the erosion rates of target materials are determined by mass loss under controlled conditions. The experimental results indicate that the erosion on the target is caused by the collapse of cavitation bubbles. Erosion occurs only when the target is placed in the range of bubble cloud length. The bubble cloud length correlates with drilling ability of a submerged water jet.
To predict the bubble cloud length, a bubble life cycle (BLC) model, which is based on the Rayleigh-Plesset bubble dynamics equation, is developed. A variable time step technique is developed to solve the highly non-linear second-order differential equation. This technique successfully solves the Rayleigh-Plesset equation for wide ranges of pressure variation and bubble original size and saves considerable computing time. The model is able to use the data from the CFD calculation to simulate the process of bubble growth and collapse. To accurately simulate the process of bubble growth, collapse and rebounding, a heat transfer model, which includes the effects of conduction and radiation, is developed to describe the thermodynamics of the air inside the bubble. The calculated bubble travel distance from the nozzle exit to the point where the bubble size becomes invisible is used to estimate the bubble cloud length. The predictions are in good agreement with the experimental results for different nozzles operating at different pressure conditions. Various factors are tested using the BLC model to find their effects on the bubble cloud. The computations indicate that, while the ambient pressure, the throat pressure and the exit velocity have significant effects on the bubble cloud length, the bubble original radius has almost no effect on the calculated bubble cloud length.
The erosion model developed is for simulation of the erosion caused by cavitation bubble collapse. It takes into account the pressure distribution produced by the bubble collapse, the path line along which the bubble travels, the population of micro bubbles in water and the mechanical properties of the target material. Equations for computing the pressure distribution are derived from the analysis of bubble dynamics. An extremely large pressure is predicted for the water surrounding a bubble when the bubble collapses to its minimum size and starts to rebound. This large pressure explains why a cavitating water jet with a relatively low pump pressure can drill very hard materials. The path lines for bubbles are obtained from the CFD model simulating the nozzle flow. The computation of the population of micro bubbles is based on measurements reported by previous researchers. The erosion model can reasonably explain the annular erosion pattern on the specimens caused by a cavitation water jet. Using appropriate assumptions for bubble population based on the experimental evidence, the model predicts erosion rates in close agreement with the experimental results for four different materials. The predictions are especially good for brittle materials such as cast iron and granite.