The outflow of the effervescent atomization spray is simulated by a comprehensive numerical model based on the Navier-Stokes equation and the particle tracking method. The droplet mean diameter under different operating conditions and liquid properties were calculated. Based on the extensive computations, a formula relating droplet Sauter mean diameter to the operating conditions and liquid physical parameters were obtained with curve fitting technique. The results calculated from the formulae were compared with the experimental data and a good agreement was obtained. The formulae can be used to predict the droplet mean diameter for various Newtonian liquid in axisymmetric effervescent atomization spray conveniently and effectively.

The study and modeling process of effervescent atomization are reviewed. The mechanism of droplet events and the treatment of liquid fragmentation process and dispersed particles are systematically presented, which includes the primary atomization of Newtonian and non-Newtonian fluid, instability analysis, turbulence treatment, particle tracking, secondary atomization and droplets collision. The review on the sub-models involved in the simulation of effervescence is followed by a summary of the achievements of modeling. First is the validation of models; then the parametric study is summarized; the third part introduces the fitting formula of droplet mean size and impinging factors, and finally the scope of future study is indicated. effervescent atomization spray, modeling, review PACS: 47.55.Ca, 47.55.df, 47.60.Kz ALR air-to-liquid ratio, by mass C D drag coefficient D noz nozzle diameter, m d d the droplet diameter, m e internal energy, J F force, N g gravity force, N k turbulent kinetic energy per unit mass k bu breakup frequency, s 1 k  wave number m  mass flow rate, kg/s m mass, kg p pressure kg s 2 /m Q heat source, J q heat flux vector r droplet radius, m Re Reynolds number Sr nterface velocity slip ratio SMD Sauter mean diameter, m U rel relative velocity vector, m/s u, v, w velocity, m/s x radial coordinate, m y axial coordinate, m Greek symbols  volume fraction of gas  deformation parameter  dynamic viscosity, kg/ms  density, kg/m 3  surface tension, kg/m 2  thickness sheet, m  growth rate  viscous dissipation rate, J/ms  distance between the center of one drop and U rel , m  drop oscillation frequency, /s  viscous shear stress tensor Subscript cr criteria g gas l liquid

Background. A comprehensive model in the Eulerian-Lagrangian scheme is used to investigate the performance of the gas-droplet two-phase flow for a typical effervescent atomization spray with different atomized liquids. Method of Approach. Based on the particle tracking method, the droplet primary and secondary breakup, droplets collision and coalescence are taken into consideration. Results. The predicted droplet mean size is compared well with the published experimental data. The influences of liquid physical properties are discussed not only on droplet mean size, but also on droplet velocity, distribution, events of breakup and collision, Weber number, Ohnesorge number and their evolutions. Conclusions. Results show liquid viscosity has a slight effect on the droplet size and its distribution. While a decrease in liquid surface tension serves to get finer droplets and wider droplet spatial distribution. Small liquid density, surface tension and viscosity are benefit for getting higher atomized droplet velocity.

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In pneumatic atomizers, the shaping air holes play an important role in the spraying system. The pressure and intersection of shaping air holes are the two most important parameters in engineering. In this paper, the Euler–Lagrangian method is used to describe the two-phase spray flow. The spraying process of the pneumatic nozzle is simulated numerically, and the experiment is designed to verify this simulation. By setting different air pressures and distances between the intersection and the paint hole, target surface pressure and droplet size distribution are investigated in detail, in order to explore the relationship between shaping air holes in pneumatic nozzles and overspray. From the results of the numerical simulation, it is found that an increase in the distance between the intersection and the paint hole increases the gas velocity at the central axis of the nozzle and the central pressure of the target surface, the droplet size becomes larger, and the distribution of droplets is more concentrated on the target surface, which easily leads to overspray. With the increase in the pressure of the shaping air holes, the central pressure of the target surface decreases, and the ovality of the spraying pattern on the target surface increases.

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