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In the framework of two-dimensional ideal hydrodynamics, we define a vortex system as a smooth vorticity function with a few local positive maximums and negative minimums separated by curves of zero vorticity. We discuss the invariants of such structures that follow from the vorticity conservation law and the invertibility of Lagrangian motion. Introducing new functional variables diagonalizing the original noncanonical Poisson bracket, we develop a Hamiltonian formalism for vortex systems. [ABSTRACT FROM AUTHOR]

We construct a class of self-similar 2d incompressible Euler solutions that have initial vorticity of mixed sign. The regions of positive and negative vorticity form algebraic spirals. [ABSTRACT FROM AUTHOR]

Wall deposition is one of the most conventional problems in the spray drying process. The operation of a spray dryer is affected by the wall deposition fluxes inside the equipment. In this study, computational fluid dynamic (CFD) simulation was used to investigate the effect of spray dryer geometry on wall deposition. A CFD model was developed for different geometries of spray dryer with a conical (case A) or a parabolic (cases B and C) bottom. The results implied that the parabolic geometry resulted in a lower deposition rate on the spray dryer walls. A comparison of results using the P-values (F-test) of the air velocity, in the conical and parabolic geometries, showed that there was a significant difference in air stability between them. The flow field in conical geometry case A was significantly more unstable, and parabolic geometry case C produced the most uniform airflow patterns. Moreover, the higher wall shear stress in case C, with lower values of the vorticity, would result in less wall deposition. [ABSTRACT FROM PUBLISHER]

The properties of spray-induced vortex-like structures for asymmetric pressure swirl atomizer were studied experimentally with different injection pressures. The high-speed Particle Imaging Velocimetry (PIV) was used to study the spray characteristics such as velocity and vorticity. The vortex centers were identified by velocity weighted vorticity. The translational velocity components of vortex centers were computed from its displacement divided by the time interval. For five different pressure conditions, the motion trajectories of vortex center were the same in an earlier period of spray, but were different in a later period of spray. The normalized translational velocity of vortex center and normalized time were introduced to compare with vortex ring model. The results indicated that the normalized axial translational velocity decreased with increasing normalized time, which converged to the predictions of the model in long time limit where α = -0.75 in the turbulent case. However, the results for the normalized radial translational velocity were different from the predictions of the model. The normalized radial translational velocity decreased with the increase of the normalized time when the injection pressure was lower than a critical value, but it obviously increased with the increase of the normalized time in case of the injection pressure higher than the critical value. Furthermore, the average vorticities at the vortex center were obtained and increased with the increase of the injection pressure. This study provides references for developing spray theory and improving injection technology. [ABSTRACT FROM AUTHOR]