Universal Spray Model for Engineering Applications

An LES-based spray model has been produced that takes into account finite thermal conductivity and recirculation of liquid inside droplets, the effects of sub-grid turbulence on droplet dispersion and evaporation, and droplet collisions followed by coalescence or break-up.

Validation studies have demonstrated the capability of the model and the software tool to predict the heating, evaporation and movement of a single droplet, turbulent subsonic jet air flow, and a turbulent evaporating spray. The model has been applied to investigate the effect of spray refinement on the internal structure of and the evaporation rate in water sprays, replicating those used in fire suppression.

To predict droplet heating and evaporation, the Abramzon and Sirignano model has been implemented. Droplet movement has been modelled using the conventional drag law for spheres. To allow for the temperature gradient and liquid circulation inside vaporizing droplets, the effective conductivity model has been used. Both unsteady and a quasi-steady parabolic temperature profile have also been utilised. Simulations performed for realistic experimental conditions and comparisons made using the previously reported simulation results (these results were obtained using more precise approach based on the analytical solution of transient heat conductivity equation for internal droplet temperature) have shown that the use of a parabolic temperature profile with corrected surface temperature results in close agreement with transient (analytical or numerical) approaches. The clear advantage of the parabolic model is that it does not incur additional computational costs yet allows for the temperature gradient inside droplets.

The important part of this work is the development of a robust, unconditionally stable and computationally efficient numerical algorithm for solving inherently stiff equations of droplet heating and evaporation. Stiffness of the equations stems from the disparity of two governing time scales corresponding to:
(1) rapid droplet heating (or cooling) from the initial temperature to the equilibrium (wet bulb) temperature and
(2) slow droplet evaporation at the equilibrium temperature.
The droplet heating and evaporation submodel has been incorporated into the inhouse CFD code which was then applied to replicate experimental conditions for turbulent evaporating sprays of water, acetone and Diesel sprays (in the latter case, the measurement data were obtained at Brighton). In all of the cases considered, reasonable agreement was obtained for spray structure, droplet size distributions and penetration dynamics.