Interfacial instability and spray heat transfer problems of two phase flow
This thesis describes detailed investigations of two different problems in gas-liquid two-phase flow, namely, a study of interfacial stability in a partially filled cylinder subjected to vertical oscillations and a study of heat and mass transfer from hot spray droplets injected into an closed vessel. The interfacial instability study considers experimental data taken from the author's previous work. Cylinders of various diameters, partially filled with water, ethanol or glycerol were subjected to a sinusoidal vertical motion. The critical acceleration, causing the interfacial wave to grow unstable, was found to be approximately constant for a given cylinder diameter, independent on the amplitude of the forcing oscillations. The experiments also indicate that the critical Acceleration always decreases with increasing cylinder diameter. A mathematical analysis of the interfacial instability is based on a stability investigation of a Mathieu equation. It is shown that the experimental data fall into unstable regions for a single, first mode of oscillations. This finding is supported by the experimental analysis given by Cilliberto and Gollub. The analysis shows the effects of the liquid column height on the interfacial instability to be dependent on tanh (k..l.). This multiplier is equal to 1 for the column heights of 250mm, 500 mm and 750 mm, investigated, and a given cylinder diameter, thus having no effect on the results. Computational analysis of the interfacial problem is developed which is based on the simplified MAC method incorporating the Continuum Surface Force (CSF) model for simulating the effects of surface tension. Computational experiments were run for water and glycerol, the two liquids of significantly different properties. The results are presented in the form of time sequenced plots showing the interfacial positions and graphs relating the interfacial wave amplitude and time. Stability of the interface is found to be dependent on the initial surface disturbance. Growth of the interfacial wave is observed in some cases. In the range of situations investigated, surface tension effects are found to have only a small influence both on the stability and frequency of the interfacial oscillations. The period of interfacial oscillations with no forcing vibrations is found to be in good agreement with the period predicted by mathematical analysis. Influence of the initial disturbance profile was also investigated. The results indicate that the interfacial wave adopts oscillatory behaviour similar to the other cases. The oscillation frequency of the interfacial wave undergoing forcing vibrations is found to match the findings of the mathematical analysis. The wave oscillates with an angular velocity equal to the multiples of the half the forcing vibration angular velocity, co/2. In the second investigation a testing rig was constructed to investigate the heat and mass transfer processes in dense hot sprays injected into an enclosed cylindrical vessel. Heat and mass transfer rates were investigated indirectly from the measurements of the gas - vapour mixture pressure rise in the cylinder. The experiments covered different combinations of the parameters influencing the processes. The number and size of spray nozzles, the vessel volume, the type of gas and the initial pressure level in the cylinder were investigated. The experimental results indicate that, for the range of solid cone nozzles tested, the heat and mass transfer characteristics are, to a first approximation independent of the size of the nozzles. The results also show that the rise of spray chamber internal pressure is directly proportional to liquid temperature and flowrate. An analysis, based on energy balances for the whole cylinder, has yielded a new dimensionless group incorporating the important parameters of droplet heat transfer namely the droplet velocity and radius, spray chamber dimensions, gravity, conductivity and convectivity. A good match has been found between the analytical results and experimental findings. An improved analysis, incorporating the effect of evaporation from drops, is also presented. It is based on simultaneous solution of energy and mass balance equations for a single droplet. Again, good agreement with the experimental results is found. Both analyses indicate that, for this particular case of dense, evaporative spray, the Nusselt number tends to have a value equal to I.