We use a theoretical framework based on the integral form of the conservation equations, along with a heuristic model of the viscous dissipation, to find a closed-form solution to the liquid atomization problem. The energy balance for the spray renders to a quadratic formula for the drop size as a function, primarily of the liquid velocity. The Sauter mean diameter found using the quadratic formula shows good agreements and physical trends, when compared with experimental observations. This approach is shown to be applicable toward specifying initial drop size in computational fluid dynamics of spray flows.

An incident wave source condition that specifies the field at a single grid point is problematic for the pseudospectral time-domain (PSTD) method because of the spatial Fourier transforms inherent in the algorithm. Previously, it had been suggested in the literature that a spatially smoothed source spanning several grid cells in each direction was required to avoid aliasing errors, referred to as Gibbs phenomena. Here, we show that a spatially compact wave source condition, spanning only two spatial grid cells in each direction, eliminates the numerical artifacts induced by this aliasing/Gibbs effect. We demonstrate the successful implementation of this source condition in two practical PSTD modeling examples: fundamental mode excitation in a dielectric slab waveguide and cylindrical wave excitation via an infinite electric line source in a two-dimensional grid.

A new formulation based on integral form of the conservation equations is developed for analyzing spray droplet and velocity statistics. Both averaged or distributions of the droplet size and velocities can be calculated using this approach, although in this work the authors focus on the droplet size statistics and only compute the averaged droplet velocities. The formulation is based on the conservation equations, and intrinsically involves few assumptions and required inputs. The key is to use the integral form so that the input and output variables are related without having to resolve the complex details of the atomization process. This new approach naturally leads to predictions of SMDs, as well as the drop size distributions and phase velocities, with SMD and drop size distributions achieving good agreement with experimental data if a liquid-phase viscous dissipation term is included. The latter point suggests that the effect of liquid-phase viscosity seems quite important, as the present method overpredicts the effect of injection pressure unless some form of the viscous dissipation is included in the energy balance equation. The use of moment-generating function for the log-normal distribution within the present formulation permits an efficient algorithm that reproduces the experimentally observed droplet size distributions. Further work remains to ascertain some aspects of the present solution approach, in particular the exact form of the viscous dissipation on the spray energy balance. The present integral formulation and the solution approach provide a fundamentally sound basis for analyzing droplet size and velocity statistics with several key parameters that may be adapted for different injector geometries, such as swirl and air-blast sprays, and injection conditions.

Spray cooling of hot steel surfaces is an inherent part of continuous casting and heat treatment. When we consider the temperature interval between room temperature and for instance 1000 °C, different boiling regimes can be observed. Spray cooling intensity rapidly changes with the surface temperature. Secondary cooling in continuous casting starts when the surface temperature is well above a thousand degrees Celsius and a film boiling regime can be observed. The cooled surface is protected from the direct impact of droplets by the vapour layer. As the surface temperature decreases, the vapour layer is less stable and for certain temperatures the vapour layer collapses, droplets reach the hot surface and heat flux suddenly jumps enormously. It is obvious that the described effect has a great effect on control of cooling. The surface temperature which indicates the sudden change in the cooling intensity is the Leidenfrost temperature. The Leidenfrost temperature in spray cooling can occur anywhere between 150 °C and over 1000 °C and depends on the character of the spray. This paper presents an experimental study and shows function for prediction of the Leidenfrost temperature based on spray parameters. Water impingement density was found to be the most important parameter. This parameter must be combined with information about droplet size and velocity to produce a good prediction of the Leidenfrost temperature.