This study analyzes the influence of nozzle geometry on the vortex and cavitation cloud structures. The differences between the coherent structures of the Helmholtz nozzle, organ pipe nozzle, and venturi nozzle jets are investigated through large eddy simulation. The vorticity transport equation is used to investigate the relationship between the cavitation cloud and diagonal pressure torque terms. The cavitation and vortex structure shedding frequencies of the jets are investigated using the dynamic mode decomposition method. Three distinct stages of the cavitation bubbles are illustrated: priming, expansion, and collapse. The nozzle structure determines the shape of the primary cavitation bubbles. Moreover, turbulent kinetic energy convergence facilitates the maintenance of the coherent structure. Organ pipe nozzle jets have a high peak velocity at the center axis. Their vortex structure only exhibits a stretched state in the downstream and collapses later than the vortex structures of other nozzles. Advantageously, organ pipe nozzles maintain the stability of the coherent structure. The jets generated by the three nozzles have similar static modes. Helmholtz nozzles produce jets with higher energy and periodically shedding small-scale vortex structural modes. These modes are coupled to the static flow field, resulting in quasi-periodic oscillations of the Helmholtz nozzle jets. The periodic oscillation effect of the Helmholtz nozzle jets is superior to that of the other nozzle jets. The high-energy modes of the venturi nozzle jets have anisotropic and small-scale vortex structures. Furthermore, the venturi nozzle jets exhibit good dispersion and cavitation properties. This study provides guidance for the use of jets with different properties in the respective engineering fields.

Lattice-Boltzmann method (LBM) simulations of a gas-fluidised bed have been performed. In contrast to the current state-of-the-art coupled computational fluid dynamics–discrete element method (CFD–DEM) simulations, the LBM does not require a closure relationship for the particle–fluid interaction force. Instead, the particle–fluid interaction can be calculated directly from the detailed flow profile around the particles. Here a comparison is performed between CFD–DEM and LBM simulations of a small fluidised bed. Simulations are performed for two different values of the superficial gas velocity and it is found that the LBM predicts a larger bed expansion for both flowrates. Furthermore the particle–fluid interaction force obtained for LBM simulations is compared to the force which would be predicted by a CFD–DEM model under the same conditions. On average the force predicted by the CFD–DEM closure relationship is found to be significantly smaller than the force obtained from the LBM.

High-speed water jets are widely used in deep mining and the in-depth study of jet characteristics helps to improve drilling efficiency. Three-dimensional Large Eddy Simulation is used to simulate turbulent flows generated by an organ-pipe nozzle. The simulation is validated with existing experimental data and is focused on the evolution and interaction of cavitation bubbles and vortices. Dynamic mode decomposition is performed to extract structural information about the different motion modes and their stability. Results show that the dominant fluid frequency is positively correlated with inlet pressure while unrelated to the divergence angle. Meanwhile, jets’ oscillation is amplified by a large divergence angle, which facilitates the occurrence of cavitation. Results about the flow field outside of an organ-pipe nozzle advance the understanding of the basic mechanism of cavitation jets.

Computing Gaussian curvature is a fundamental task in image and video processing. However, this task becomes more and more time consuming when the image resolution goes higher and higher. In this paper, we tackle this issue from two aspects. First, we develop a novel discrete computing scheme for Gaussian curvature of discrete images. Our method does not require the image to be smooth. Second, we propose to perform the actual calculation by lookup tables, which significantly reduce the computation time. As a result, our method can compute the Gaussian curvature for 4K videos in real time, without requiring the image to be smooth. Moreover, our method can be implemented on mobile devices. Several experiments confirm the efficiency and effectiveness of our method. Our method can be applied on a large range of image and video processing applications that involve Gaussian curvature.