We experimentally investigate the deformation and breakup of droplets interacting with an oblique continuous air stream. A high-speed imaging system is employed to record the trajectories and topological changes of the droplets of different liquids. The droplet size, the orientation of the air nozzle to the horizontal and fluid properties (surface tension and viscosity) are varied to study different breakup modes. We found that droplet possessing initial momentum prior to entering the continuous air stream exhibits a variation in the required Weber number for the vibrational to the bag breakup transition with a change in the angle of the air stream. The critical Weber numbers (W ecr) for the bag-type breakup are obtained as a function of the Eötvös number (Eo), angle of inclination of the air stream (α) and the Ohnesorge number (Oh). It is found that although the droplet follows a rectilinear motion initially that transforms to a curvilinear motion at later times when the droplet undergoes topological changes. The apparent acceleration of the droplet and its size influence the critical Weber number for the bag breakup mode. The departure from the crossflow arrangement shows a sharp decrease in the critical Weber number for the bag breakup which asymptotically reaches to a value associated with the in-line (opposed) flow configuration for the droplet breakup.

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The interaction of a droplet with a swirling airstream is investigated experimentally using shadowgraphy and particle image velocimetry techniques. In swirl flow, the droplet experiences oppose-flow, cross-flow and co-flow conditions depending on its ejection location, the velocity of the airstream and the swirl strength, which results in distinct droplet morphologies as compared with the straight airflow situation. We observe a new breakup phenomenon, termed as ‘retracting bag breakup’, as the droplet encounters a differential flow field created by the wake of the swirler's vanes and the central recirculation zone in swirl airflow. A regime map demarcating the various modes, such as no breakup, vibrational breakup, retracting bag breakup and bag breakup modes, is presented for different sets of dimensionless parameters influencing the droplet morphology and its trajectory. In contrast to the straight flow, the swirl flow promotes the development of the Rayleigh–Taylor instability, enhancing the stretching factor in the droplet deformation process, resulting in a larger number of fingers on the droplet's surface. In order to gain physical insight, a modified theoretical analysis based on the Rayleigh–Taylor instability is proposed for the swirl flow. The experimental behaviour of droplet deformation phenomena in swirl flow conditions can be determined by modifying the stretching factor in the theoretical model.

Abel inverse integral to obtain local field distributions from path-integrated measurements in an axisymmetric medium is an ill-posed problem with the integrant diverging at the lower integration limit. Existing methods to evaluate this integral can be broadly categorized as numerical integration techniques, semianalytical techniques, and least-squares whole-curve-fit techniques. In this study, Simpson's 1/3rd rule (a numerical integration technique), one-point and two-point formulas (semianalytical techniques), and the Guass-Hermite product polynomial method (a least-squares whole-curve-fit technique) are compared for accuracy and error propagation in Abel inversion of deflectometric data. For data acquired at equally spaced radial intervals, the deconvolved field can be expressed as a linear combination (weighted sum) of measured data. This approach permits use of the uncertainty analysis principle to compute error propagation by the integration algorithm. Least-squares curve-fit techniques should be avoided because of poor inversion accuracy with large propagation of measurement error. The two-point formula is recommended to achieve high inversion accuracy with minimum error propagation.

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