A theoretical model for the dynamics of a bubble in an elastic blood vessel is applied to study numerically the effect of confinement on the free oscillations of a bubble. The vessel wall deformations are described using a lumped-parameter membrane-type model, which is coupled to the Navier-Stokes equations for the fluid motion inside the vessel. It is shown that the bubble oscillations in a finite-length vessel are characterized by a spectrum of frequencies, with distinguishable high-frequency and low-frequency modes. The frequency of the high-frequency mode increases with the vessel elastic modulus and, for a thin-wall vessel, can be higher than the natural frequency of bubble oscillations in an unconfined liquid. In the limiting case of an infinitely stiff vessel wall, the frequency of the low-frequency mode approaches the well-known solution for a bubble confined in a rigid vessel. In order to interpret the results, a simple two-degree-of-freedom model is applied. The results suggest that in order to maximize deposition of acoustic energy, a bubble confined in a long elastic vessel has to be excited at frequencies higher than the natural frequency of the equivalent unconfined bubble.

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In this paper a breakup model for analysing the evolution of transient fuel sprays characterised by a coherent liquid core emerging from the injection nozzle, throughout the injection process, is proposed. The coherent liquid core is modelled as a liquid jet and a breakup model is formulated. The spray breakup is described using a composite model that separately addresses the disintegration of the liquid core into droplets and their further aerodynamic breakup. The jet breakup model uses the results of hydrodynamic stability theory to de ne the breakup length of the jet, and downstream of this point, the spray breakup process is modelled for droplets only. The composite breakup model is incorporated into the KIVA II Computational Fluid Dynamics (CFD) code and its results are compared with existing breakup models, including the classic WAVE model and a previously developed composite WAVE model (modi ed WAVE model) and in{house experimental observations of transient Diesel fuel sprays. The hydrodynamic stability results used in both the jet breakup model and the WAVE droplet breakup model are also investigated. A new velocity pro le is considered for these models which consists of a jet with a linear shear layer in the gas phase surrounding the liquid core to model the e ect of a viscous gas on the breakup process. This velocity pro le changes the driving instability mechanism of the jet from a surface tension driven instability for the currently used plug ow jet with no shear layers, to an instability driven by the thickness of the shear layer. In particular, it is shown that appreciation of the shear layer instability mechanism in the composite model allows larger droplets to be predicted at jet breakup, and gives droplet sizes which are more consistent with the experimental observations. The inclusion of the shear layer into the jet velocity pro le is supported by previous experimental studies, and further extends the inviscid ow theory used in the formulation of the classic WAVE breakup model

As part of the Carbon Capture and Storage (CCS) process, pipeline transportation of dense phase CO2 is the safest and most economic option for delivering captured CO2 to a storage site .However, in the event of pipeline rupture an enormous mass of CO2 may be released very rapidly, presenting several risks to the pipeline and surrounding population including the significantly increased risk of brittle fracture in the pipe wall. The study of pressure variation and phase change in CO 2 during pipeline blowdown can contribute to the understanding of brittle fracture initiation and propagation, as well as downstream CO 2 diffusion behaviour. As part of the CO2QUEST project, a reusable, industrial scale pipeline experimental apparatus with a total length of 258 m and the inner diameter of 233 mm was fabricated to study CO 2 pipeline blowdown. A dual-disc blasting device was used to remotely control the opening of the pipeline, three different orifice diameters were used in experiments (15 mm, 50 mm and Full Bore Rupture). Different initial conditions in the inventory were achieved by heating the charged * Corresponding author.

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a b s t r a c tThe development, testing and validation of a two-fluid transient flow model for simulating outflow following the failure of high pressure CO 2 pipelines is presented. Thermal and mechanical non-equilibrium effects during depressurisation are accounted for by utilising simple constitutive relations describing inter-phase mass, heat and momentum transfer in terms of relaxation to equilibrium. Pipe wall/fluid heat exchange on the other hand is modelled by coupling the fluid model with a finite difference transient heat conduction model. The two-fluid transient flow model's performance is tested by comparison of the predicted transient pressure and temperature profiles along the pipeline against those based on the simplified homogeneous equilibrium model (HEM) as well as real data captured during the full bore rupture of a 260 m long, 233 mm internal diameter pipeline containing CO 2 at 36 bara and 273 • C. The two-fluid model is found to produce a reasonably good degree of agreement with the experimental data throughout the depressurisation process. The HEM based flow model on the other hand performs well only near the rupture plane and during the early stages of the depressurisation process.

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